Large Eddy Simulation of Hydraulic Characteristics after New Lateral Aerator

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液压专业毕业设计科技文献外文翻译--阻尼式溢流阀的建模与动态响应(英语)

Abstract. This paper outlines several possible methods of modelling a passive hydraulic damper with a bypass tube that is opened by a precompressed relief valve. Initially a simple algebraic model is derived which is developed into a more computationally complex model incorporating the dynamics of the internal spring valve and ﬂuid compressibility. Numerical simulations indicate realistic dynamical phenomena and suggest key design parameters. Key words: compressibility, hydraulic damper, nonlinear, relief valve
Figure 4. The required normalised force output against normalised time and velocity for one cycle.
[8–11], to our knowledge the effects of the passive blow-off valve have not been treated in the literature (although relief valves treated on their own have been shown to lead to nonlinear [12, 13] and chaotic dynamics [14].) The resulting model can be used to predict the effect of changing the properties of the damper on the dynamic response. The key features investigated are the sizes of the oriﬁce and bypass tube along with the stiffness and discharge characteristics of the spring and valve respectively. In this paper a simple lumped mass parametric model is derived that incorporates all these effects. The rest of this paper is outlined as follows. Section 2 describes the modelling process used by previous researchers to model Figure 1 as a simpliﬁcation of an automobile shock absorber. Sections 3 and 4 investigate several possible extensions to the model in Section 2 to take into account the blow-off. First an explicit model is derived to give the force for a given displacement input. The relief valve and compressibility of the ﬂuid are then considered separately. A model for the whole system is then derived. Section 5 gives some results using the different models. There is also a discussion in Section

Large Eddy Simulation of Turbulent Channel Flows by the Rational LES Model

arX iv:ma t h /0205264v1[m at h .NA ]24M a y2002Large Eddy Simulation of Turbulent Channel Flows bythe Rational LES ModelT.Iliescu and P.FischerFebruary 1,2008AbstractThe rational large eddy simulation (RLES)model is applied to turbulent channelﬂows.This approximate deconvolution model is based on a rational (subdiagonal Pad´e )approximation of the Fourier transform of the Gaussian ﬁlter and is proposed as an alternative to the gradient (also known as the nonlinear or tensor-diﬀusivity)model.We used a spectral element code to perform large eddy simulations of incompressible channel ﬂows at Reynolds numbers based on the friction velocity and the channel half-width Re τ=180and Re τ=395.We compared the RLES model with the gradient model.The RLES results showed a clear improvement over those corresponding to the gradient model,comparing well with the ﬁne direct numerical simulation.For comparison,we also present results corresponding to a classical subgrid-scale eddy-viscosity model such as the standard Smagorinsky model.1IntroductionLarge eddy simulation(LES)is one of the most successful techniques in the numerical sim-ulation of turbulentﬂows.Contrary to the direct numerical simulation(DNS),which tries to capture all the scales in theﬂow,LES aims at resolving only the large-scaleﬂow fea-tures.The large scales are deﬁned by means of aﬁltering operation:the Navier-Stokes equations are convolved with a spatialﬁlter,and the resultingﬁltered variables become the variables of interest in LES.Thus,a good LES model should be able to compute an accurate approximation of theﬁltered variables.An essential challenge in LES is the modeling of the subgrid-scale(SGS)stresses,rep-resenting the interactions between the large(above theﬁlter width)and small(below the ﬁlter width)scales in theﬁltered Navier-Stokes equations.A remarkable research eﬀort has led to a wide variety of SGS models,surveyed,for example,in[1],[2],and[3].Arguably the most popular class of LES models is the eddy-viscosity type,based on (variants of)the Smagorinsky model[4].The main feature of the eddy-viscosity models is that they properly transfer kinetic energy(by inviscid processes)from large scales to smaller and smaller scales,until this energy is dissipated through viscous eﬀects.These models have several limitations,however,including poor correlation coeﬃcients in a priori tests[5],[6] and inability to provide backscatter.Some of these limitations are circumvented by using a dynamic procedure in calculating the Smagorinsky constant,yielding the dynamic subgrid-scale eddy-viscosity model introduced by Germano et al.[7],and used in many studies[8], [9].Another class of SGS models is the scale-similarity one.The scale-similarity model, introduced by Bardina et al.[6],postulates that the full structure of the velocityﬁeld at scales below theﬁlter width is similar to that at scales above theﬁlter width.A priori tests [6]show high correlations between real and modeled stresses.Another realistic feature of the scale-similarity model is that it produces backscatter.In a posteriori tests,however, the scale-similarity model does not dissipate enough energy and typically leads to inaccurate results.As a remedy,Bardina et al.[6]added a dissipative Smagorinsky term.The resulting model,known as the mixed model,combines the strengths of both the scale-similarity and the Smagorinsky model.The dynamic procedure has been successfully applied to both the pure and the mixed scale-similarity model,yielding improved results[10].A diﬀerent class of SGS models consists of those models aimed at computing an improved SGS stress approximation by replacing the unknown unﬁltered variables with approximately deconvolvedﬁltered variables.An inverseﬁltered model wasﬁrst proposed by Shah and Ferziger[11].This idea was formalized by Geurts[12]for the top hatﬁlter.Kuerten et al.[13]used the approximate inverse to improve the computable estimates in the dynamic Smagorinsky model.Another model in this class is the velocity estimation model of Do-maradzki and Saiki[14],[15],[16].Stolz and Adams[17]developed the approximate decon-volution model,based on repeated application of theﬁlter to approximately deconvolve thedependent variables[18],[19].One popular model in this class is the gradient model(also known as the nonlinear or tensor-diﬀusivity model),which uses explicitﬁltering.In addition to the implicitﬁltering due to the eﬀective truncations(grid and numerical method),this LES model also assumes a regular explicitﬁlter of prescribed shape and eﬀective width larger than the grid spacing.The gradient model is based on a Taylor series approximation of the Fourier transform of theﬁlter and aims at reconstructing theﬁltered-scale stress due to explicitﬁltering.The gradient model was developed in several steps.First,in1974Leonard[20]proposed a model for the“resolved scales”uu′imation.This rational approximation is consistent with the original approximated function (which is a negative exponential):it attenuates the high wave number components.In this paper,the resulting LES model,called in the sequel the rational LES(RLES) model,is applied to the numerical simulations of incompressible channelﬂows at Reτ=180 and Reτ=395.2The Rational LES ModelThe usual LES starts by convolving the Navier-Stokes equations(NSEs)with a spatialﬁlter gδ.Assuming that diﬀerentiation and convolution commute(which is true for homogeneous ﬁlters),theﬁltered NSEs read as follows:uu)−Re−1∆p=u=gδ∗u is the variable of interest.Theﬁltered NSEs(1) do not form a closed system,and a considerable research eﬀort in LES research has been directed at modeling the stressτ=uδ2|k|24γ≈1−gδ(k)=eδ2|k|24γ+O(δ4).(4) Decomposing u into its average and its turbulentﬂuctuationsu=and takingﬁrst the average and then the Fourier transform of the above relation,we getu′= 1u,(6) and thus,u=1u,(7) where u denotes the Fourier transform of u.By taking the inverse Fourier transform and using(4),wegetu≈4γ∆uu−u≈δ2u∇u∇u i u j4γ≈14γ+O(δ4).(11) The resulting LES model,called the rational LES(RLES)model,reads as follows:τ= −δ22γ∇u .(12)The inverse operator in(12)acts as a smoothing operator and represents the approxima-tion of the convolution by the Gaussianﬁlter in the stress tensorτin(2).We note that diﬀerentialﬁlters have been proposed by Germano in[33]:Actually,one can think of(12)as the stress tensor obtained by applying such a diﬀerentialﬁlter.Mullen and Fischer used similarﬁlters in[34].Also,Domaradzki and Holm considered the Navier-Stokes-alpha model(which contains an inverse operator similar to the one in(12)),in an LES framework[35].The mathematical analysis associated with the RLES model(12)was presented in[36]; the smoothing property of the inverse operator in(12)eliminated the necessity for using additional regularization operators(of eddy-viscosity type),as for the gradient model[37]. Theﬁrst steps in the numerical analysis and validation of the RLES model(12)were made in[38]and[39],respectively.This paper presents numerical results for the RLES model(12)applied to the3D channel ﬂow test problem at Reynolds numbers based on the wall shear velocity Reτ=180and Reτ=395.Some preliminary work started in[40];it was signiﬁcantly updated and improved in the present paper.3Numerical SettingThe3D channelﬂow(Figure2)is one of the most popular test problems for the investigation of wall bounded turbulentﬂows[41],[42].We used theﬁne DNS of Moser,Kim,and Mansour [43]as benchmark for our LES simulations.We compared the RLES model(12)with(I)the gradient model(9)τ=δ2u∇S|S:=1u+∇∆x∆z∆y(y),where∆x and∆z are the largest spaces between the Gauss-Lobatto-Legendre(GLL)points in the x and z directions,respectively,and∆y(y) is inhomogeneous and is computed as an interpolation function that is zero at the wall and is twice the normal mesh size for the elements in the center of the channel.The numerical simulations were performed by using a spectral element code based on the l P N−l P N−2velocity and pressure spaces introduced by Maday and Patera[44].The domain is decomposed into spectral elements,as shown in Figure3.Mesh spacing in the wall-normal direction(y)was chosen to be roughly equivalent to a Chebychev distribution having the same number of points.The velocity is continuous across element interfaces andis represented by N th-order tensor-product Lagrange polynomials based on the GLL points. The pressure is discontinuous and is represented by tensor-product polynomials of degree N−2.Time stepping is based on an operator-splitting of the discrete system,which leads to separate convective,viscous,and pressure subproblems without the need for ad hoc pressure boundary conditions.Aﬁlter,which removes2%–5%of the highest velocity mode,is used to stabilize the Galerkin formulation[45];theﬁlter does not compromise the spectral accuracy. Details of the discretization and solution algorithm are given in[46],[47].The initial conditions for the Reτ=180simulations were obtained by superimposing a2D Tollmien-Schlichting(TS)mode of2%amplitude and a3D TS mode of1%amplitude on a parabolic meanﬂow(Poiseuilleﬂow)and integrating theﬂow for a long time(approximately 200H/uτ,where H is the channel’s halfwidth and uτis the wall shear velocity)on aﬁner mesh(72×73×72mesh points).Theﬁnalﬁeldﬁle was further integrated on the actual coarse LES mesh(36×37×36mesh points)for approximately50H/uτto obtain the initial condition for all four Reτ=180simulations.The initial condition for the Reτ=395case was obtained in a similar manner:We started with aﬁeldﬁle corresponding to a Reτ=180simulation,and we integrated it on a ﬁner mesh(96×73×72mesh points)for a long time(approximately50H/uτ).Then,we integrated the resultingﬂow on the actual coarser LES mesh(72×55×54mesh points)for another40H/uτ,and theﬁnalﬁeldﬁle was used as initial condition for all four simulations.For each of the four simulations and for both Reτ=180and Reτ=395,theﬂow was integrated further in time until the statistically steady state was reached(for approximately 15H/uτ).The statistically steady state was identiﬁed by a linear total shear stress proﬁle (see Figure4and Figure5).The statistics were then collected over another5H/uτand contained samples taken after each time step(∆t=0.0002for Reτ=180and∆t=0.00025for Reτ=395).We also averaged over the two halves of the channel.In our numerical experiments,we considered,as aﬁrst step,homogeneous boundary conditions for all LES models tested.The numerical results include plots of the following time-and plane-averaged quanti-ties normalized by the computed uτ:the mean streamwise velocity≪4A Posteriori Tests for Reτ=180We ran a posteriori tests for the RLES model(12),the gradient model(9),the Smagorinsky model,and a coarse DNS(no model).We compared the corresponding results with theﬁne DNS simulation of Moser,Kim,and Mansour[43].Figure6shows the normalized mean streamwise velocity;note the almost perfect over-lapping of the results corresponding to the models tested.We interpret this behavior as a measure of our success in enforcing a constant massﬂux through the channel.Figure7presents the normalized x,y-component of the Reynolds stress.The RLES model(12)is a clear improvement over the rest(i.e.,closest to theﬁne DNS).Similarly,the normalized rms values of the streamwise velocityﬂuctuations in Figure 8show a better(closer to theﬁne DNS benchmark results in[43])behavior for the RLES model(12).Figures9and10,containing the normalized rms values for the wall-normal and spanwise velocityﬂuctuations,merit a more detailed discussion.Figure9shows the normalized rms values of the wall-normal velocityﬂuctuations.Here,the RLES model(12)performs worse than the gradient model(9)near the wall.Away from the wall,the gradient and the RLES model perform similarly.The best results are obtained with the Smagorinsky model.The normalized rms values of the spanwise velocityﬂuctuations in Figure10are better for the RLES model(12)than for the gradient model,except for a portion of1−|y|roughly between0.3and0.5.The Smagorinsky model gives the best results near the wall,but it overpredicts the correct value near the center of the channel.In conclusion,the RLES model(12)performs better than the gradient model,with the exception of the normalized rms values of the wall-normal velocityﬂuctuations.The RLES model(12)is also more stable numerically than the gradient model.5A Posteriori Tests for Reτ=395We ran simulations with all four models for Reτ=395,and we compared our results with theﬁne DNS in[43].Again,as in the Reτ=180case,the normalized mean streamwise velocityﬂuctuations in Figure11are practically identical;this time,however,they do not overlap onto that corresponding to theﬁne DNS.Nevertheless,the meanﬂows are the same, and this is supported by the fact that the models underpredict the correct value near the wall but overpredict it away from the wall.The normalized x,y-component of the Reynolds stress in Figure12is almost identical for all four models.This behavior was also noticed by Winckelmans et al.[23].The same behavior can be noticed for the normalized rms values of the streamwise velocity ﬂuctuations in Figure13:the proﬁles for the four models are almost identical.The RLES model(12)performs slightly better near the wall,and the gradient model performs slightlybetter away from the wall.They both perform better than the Smagorinsky model near the center of the channel.Figure14presents the normalized rms values of the wall-normal velocityﬂuctuations. As for the Reτ=180case,the gradient model performs better near the wall,and the RLES model(12)performs better away from the wall.The Smagorinsky model performs best,but it overpredicts the correct value near the center of the channel.The same behavior is observed for the normalized rms values of the spanwise velocity ﬂuctuations in Figure15,and again the Smagorinsky model performs best.In conclusion,for the Reτ=395case,the gradient and the RLES model(12)yield comparable results.The best results,however,are obtained by using the Smagorinsky model.Again,as in the Reτ=180case,the RLES model(12)is much more stable numerically than the gradient model.6ConclusionsWe have used a spectral element code to test the RLES model(12)in the numerical sim-ulation of incompressible channelﬂows at Reτ=180and Reτ=395.This approximate deconvolution model is based on a rational(Pad´e)approximation to the Fourier transform of the Gaussianﬁlter and is proposed as an alternative to the gradient model(9).We com-pared the RLES model(12)with the gradient model,the Smagorinsky model,and a coarse DNS(no LES model).The corresponding results were benchmarked against theﬁne DNS calculation of Moser,Kim,and Mansour[43].The RLES model(12)yielded the best results for the Reτ=180case.These improved results were accompanied by a much increased numerical stability compared with the gradient model.The situation was diﬀerent for the Reτ=395case.Here the RLES model(12)and the gradient model yielded comparable results,and the Smagorinsky model performed the best. Again,the RLES model(12)was much more stable numerically than the gradient model.We believe that these results for the RLES model are encouraging.They also support our initial thoughts:The RLES model is an improvement over the gradient model as a subﬁlter-scale model,and this is illustrated by the improved results for the Reτ=180case.The RLES model is also more stable numerically because of the additional smoothing operator, and this feature is manifest for both low(Reτ=180)and moderate(Reτ=395)Reynolds numberﬂows.However,the RLES model accounts just for the subﬁlter-scale part of the stress recon-struction.The information lost at the subgrid-scale level must be accounted for in a diﬀerent way,as advocated by Carati et al.[24].This was illustrated by the fact that,even for a mod-erate Reynolds number(Reτ=395)ﬂow,the Smagorinsky model,a classical eddy-viscositymodel,performed best.Along these lines,our next step will be to develop a mixed model,consisting of the RLES model supplemented by a Smagorinsky model.We also plan to study improved boundary conditions,the commutation error[48],[49],and the relationship between theﬁlter radius and the mesh-size in a spectral element discretization.Acknowledgments.This work was supported in part by the Mathematical,Infor-mation,and Computational Sciences Division subprogram of the Oﬃce of Advanced Scientiﬁc Computing Research,U.S.Dept.of Energy,under Contract W-31-109-Eng-38.We thank Professor R.Moser and Mr.A.Das for helpful communications that improved this paper.References[1]C.Meneveau and J.Katz,“Scale invariance and turbulence models for large-eddy sim-ulation,”Annu.Rev.Fluid Mech.32,1(2000).[2]M.Lesieur and O.M´e tais,“New trends in large-eddy simulations of turbulence,”Annu.Rev.Fluid Mech.28,45(1996).[3]P.Sagaut,Large Eddy Simulation for Incompressible Flows(Springer Verlag,Berlin,2001).[4]J.Smagorinsky,“General circulation experiments with the primitive equation:I thebasic experiment,”Mon.Wea.Rev.91,99(1963).[5]R.A.Clark,J.H.Ferziger,and W.C.Reynolds,“Evaluation of subgrid scale modelsusing an accurately simulated turbulentﬂow,”J.Fluid Mech.91,1(1979).[6]J.Bardina,J.H.Ferziger,and W.C.Reynolds,“Improved turbulence models based onlarge eddy simulation of homogeneous,incompressible,turbulentﬂows,”Technical Re-port No.TF-19,Department of Mechanical Engineering,Stanford University,Stanford, CA,1983.[7]M.Germano,U.Piomelli,P.Moin,and W.Cabot,“A dynamic subgrid-scale eddyviscosity model,”Phys.Fluids A3,1760(1991).[8]U.Piomelli,“High Reynolds number calculations using the dynamic subgrid-scale stressmodel,”Phys.Fluids A5,1484(1993).[9]K.Horiuti,“A new dynamic two-paramater mixed model for large-eddy simulation,”Phys.Fluids9,3443(1997).[10]F.Sarghini,U.Piomelli,and E.Balaras,“Scale-similar models for large-eddy simula-tions,”Phys.Fluids11,1596(1999).[11]K.B.Shah and J.Ferziger,“A new non-eddy viscosity subgrid-scale model and itsapplication to turbulentﬂow,”in CTR Annual Research Briefs1995,Center for Turbu-lence Research,Stanford University and NASA Ames Research Center,Stanford,CA, 1995.[12]B.J.Geurts,“Inverse modeling for large-eddy simulation,”Phys.Fluids9,3585(1997).[13]G.J.M.Kuerten,B.J.Geurts,A.W.Vreman,and M.Germano,“Dynamic inverse-modeling and its testing in large-eddy simulation of the mixing layer”,Phys.Fluids11, 3778(1999).[14]J.A.Domaradzki and E.M.Saiki,”A subgrid-scale model based on the estimation ofunresolved scales of turbulence,”Phys.Fluids9,2148(1997).[15]J.A.Domaradzki and K.-C.Loh,”The subgrid-scale estimation model in physical spaceestimation,”Phys.Fluids11,2330(1999).[16]K.-C.Loh and J.A.Domaradzki,“The subgrid-scale estimation model on nonuniformgrids,”Phys.Fluids11,3786(1999).[17]S.Stolz and N.A.Adams,“An approximate deconvolution procedure for large-eddysimulation,”Phys.Fluids11,1699(1999).[18]S.Stolz,N.A.Adams,and L.Kleiser,“An approximate deconvolution model for large-eddy simulation with application to incompressible wall-boundedﬂows,”Phys.Fluids 13,997(2001).[19]S.Stolz,N.A.Adams,and L.Kleiser,“The approximate deconvolution model for large-eddy simulations of compressibleﬂows and its application to shock-turbulent-boundary-layer interaction,”Phys.Fluids13,2985(2001).[20]A.Leonard,“Energy cascade in large eddy simulations of turbulentﬂuidﬂows,”Adv.in Geophysics18A,237(1974).[21]S.Liu,C.Meneveau,and J.Katz,“On the properties of similarity subgrid-scale modelsas deduced from measurements in a turbulent jet,”J.Fluid Mech.275,83(1994). [22]V.Borue and S.A.Orszag,“Local energyﬂux and subgrid-scale statistics in three-dimensional turbulence,”J.Fluid Mech.366,1(1998).[23]G.S.Winckelmans,A.A.Wray,O.V.Vasilyev,and H.Jeanmart,“Explicit-ﬁlteringlarge-eddy simulations using the tensor-diﬀusivity model supplemented by a dynamic Smagorinsky term,”Phys.Fluids13,1385(2001).[24]D.Carati,G.S.Winckelmans,and H.Jeanmart,”On the modeling of the subgrid-scale andﬁltered-scale stress tensors in large-eddy simulation,”J.Fluid Mech.441,119 (2001).[25]B.Vreman,“Direct and large-eddy simulation of the compressible turbulent mixinglayer”,Ph.D.thesis,University of Twente,1995.[26]G.-H.Cottet and A.A.Wray,“Anisotropic grid-based formulas for subgrid-scale mod-els,”in Annual Research Briefs,Center for Turbulence Research,Stanford University and NASA Ames,1997,pp.113–122.[27]G.-H.Cottet and O.V.Vasilyev,“Comparison of dynamic Smagorinsky and anisotropicsubgrid-scale models,”Proceedings of the Summer Program,Center for Turbulence Research,Stanford University and NASA Ames,1998,pp.367–388.[28]B.Vreman,B.Geurts,and H.Kuerten,“Large-eddy simulation of the temporal mixinglayer,”J.Fluid Mech.339,357(1997).[29]G.P.Galdi and yton,“Approximating the larger eddies inﬂuid motion II:amodel for spaceﬁlteredﬂow,”Math.Models and Methods in App.Sci.10,343(2000).[30]B.Vreman,B.Geurts,and H.Kuerten,“Large-eddy simulation of the temporal mixinglayer using the mixed Clark model,”put.Fluid Dyn.8,309(1996). [31]A.A.Aldama,Filtering Techniques for Turbulent Flow Simulation,edited by C.A.Brebbia and S.A.Orszag(Lecture Notes in Engineering56,Springer-Verlag,1990).[32]F.V.Katopodes,R.L.Street,and J.H.Ferziger,“Subﬁlter-scale scalar transport forlarge-eddy simulation,”in14th Symposium on Boundary Layer and Turbulence,(Amer-ican Meteorological Society,2000),pp.472–475.[33]M.Germano,“Diﬀerentialﬁlters for the large eddy numerical simulation of turbulentﬂows,”Phys.Fluids29,1755(1986).[34]J.S.Mullen and P.F.Fischer,“Filtering techniques for complex geometryﬂuidﬂows,”Commun.Numer.Meth.Engng.15,9(1999).[35]J.A.Domaradzki and D.D.Holm,“Navier-Stokes-alpha model:LES equations withnonlinear dispersion,”in Modern Simulation Strategies for Turbulent Flow,edited byB.J.Geurts,(ERCOFTAC Bulletin48,2001).[36]L.C.Berselli,G.P.Galdi,T.Iliescu,and yton,“Mathematical analysis forthe rational large eddy simulation model,”Math.Models and Methods in App.Sci., accepted(2002).[37]P.Coletti,“A global existence theorem for large eddy simulation turbulence model,”Math.Models and Methods in App.Sci.7,579(1997).[38]T.Iliescu,V.John,and yton,“Convergence ofﬁnite element approximation oflarge eddy motion,”Num.Meth.Part.Diﬀ.Eq.,accepted pending revisions(2002).[39]T.Iliescu,V.John,yton,G.Matthies,and L.Tobiska,“A numerical study ofa class of LES models,”submitted(2002).[40]P.Fischer and T.Iliescu,“A3D channelﬂow simulation at Reτ=180using a rationalLES model,”in Proceedings of Third AFOSR International Conference on DNS/LES, edited by C.Liu,L.Sakell,and T.Beutner,(Greyden Press,Columbus,2001)pp.283–290.[41]P.Moin and J.Kim,“Numerical investigation of turbulent channelﬂow,”J.Fluid Mech.118,341(1982).[42]J.Kim,P.Moin,and R.Moser,“Turbulence statistics in fully developed channelﬂowat low Reynolds number,”J.Fluid Mech.177,133(1987).[43]D.R.Moser,J.Kim,and N.N.Mansour,“Direct numerical simulation of turbulentchannelﬂow up to Reτ=590,”Phys.Fluids11,943(1999).[44]Y.Maday and A.T.Patera,“Spectral element methods for the Navier-Stokes equa-tions,”in State of the Art Surveys in Computational Mechanics,edited by A.K.Noor (ASME,New York,1989)pp.71–143.[45]P.F.Fischer and J.S.Mullen,“Filter-based stabilization of spectral element methods,”Comptes rendus de l’Acad´e mie des sciences Paris,t.332,-S´e rie I-Analyse num´e rique, 265(2001).[46]P.F.Fischer,“An overlapping Schwarz method for spectral element solution of theincompressible Navier-Stokes equations,”p.Phys.133,84(1997).[47]P.F.Fischer,ler,and H.M.Tufo,“An overlapping Schwarz method for spectralelement simulation of three-dimensional incompressibleﬂows,’in Parallel Solution of Partial Diﬀerential Equations,edited by P.Bj¨o rstad and M.Luskin(Springer-Verlag, 2000),pp.159-181.[48]S.Ghosal and P.Moin,“The basic equations for the large-eddy simulation of turbulentﬂows in complex geometry,”put.Phys.118,24(1995).[49]S.Ghosal,“An analysis of numerical errors in large-eddy simulations of turbulence,”J.Comput.Phys.125,187(1996).Figure1:(Pad´e) vs.Taylor.Table1:Parameters for the numerical simulations.Nominal ReτL x×L y×L z N x×N y×N z3π36×37×363952π×2×π72×55×54Flow y,vx,uz,wFigure2:Problem setup for the channelﬂow.YXZYXZFigure3:Spectral element meshes:Reτ=180(top),and Reτ=395(bottom).τsteady state was reached.τsteady state was reached.Table2:Computed uτand Reτ.Fixed U m Nominal ReτCase Computed uτComputed Reτ17.54395RLES 1.001025319395.4071960gradient 1.005021334396.9859924Smagorinsky0.9974176884393.9718933coarse DNS0.9901855588391.1294861Figure6:Mean streamwise velocity,Reτ=180.We compared the RLES model(12),the gradient model(9),the Smagorinsky model,and a coarse DNS,with theﬁne DNS of Moser, Kim,and Mansour[43].τmodel(12),the gradient model(9),the Smagorinsky model,and a coarse DNS,with the ﬁne DNS of Moser,Kim,and Mansour[43].τRLES model(12),the gradient model(9),the Smagorinsky model,and a coarse DNS,with theﬁne DNS of Moser,Kim,and Mansour[43].τRLES model(12),the gradient model(9),the Smagorinsky model,and a coarse DNS,with theﬁne DNS of Moser,Kim,and Mansour[43].τRLES model(12),the gradient model(9),the Smagorinsky model,and a coarse DNS,with theﬁne DNS of Moser,Kim,and Mansour[43].Figure11:Mean streamwise velocity,Reτ=395.We compared the RLES model(12),the gradient model(9),the Smagorinsky model,and a coarse DNS,with theﬁne DNS of Moser, Kim,and Mansour[43].τmodel(12),the gradient model(9),the Smagorinsky model,and a coarse DNS,with the ﬁne DNS of Moser,Kim,and Mansour[43].τRLES model(12),the gradient model(9),the Smagorinsky model,and a coarse DNS,with theﬁne DNS of Moser,Kim,and Mansour[43].τRLES model(12),the gradient model(9),the Smagorinsky model,and a coarse DNS,with theﬁne DNS of Moser,Kim,and Mansour[43].τRLES model(12),the gradient model(9),the Smagorinsky model,and a coarse DNS,with theﬁne DNS of Moser,Kim,and Mansour[43].31。

LARGE EDDY SIMULATION

~ f ( x) f ( x)G ( x, x)dx
• Find the unresolved-scale (SGS or SFS):
~ f ( x) f ( x) f ( x)
Examples of filter functions
Top-hat
Gaussian
Example: An 1-D flow field
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~u ~) 2~ ~ ~ ~ ( u u u u i ~ u i g i ~ 1 p ui i j i j uj 2 t x j T0 xi x j x j
SFS
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Different Reynolds number turbulent flows
Numerical methods of studying turbulence
• Reynolds-averaged modeling (RAN) model just ensemble statistics • Direct numerical simulation (DNS) resolve for all eddies • Large eddy simulation (LES) intermediate approach
FUTURE GOAL
Understand PBL in complex environment and improve its parameterization for regional and climate models
– – – – turbulent fluxes air quality cloud chemical transport/reaction
• Small Re flows: laboratory (tea cup) turbulence; largest eddies ~ O(m); RAN or DNS • Medium Re flows: engineering flows; largest eddies ~ O(10 m); RAN or DNS or LES • Large Re flows: geophysical turbulence; largest eddies > km; RAN or LES

large eddy simulation of turbulent flow around tube bundles composed of wavy and circular cylinders

Experimental study and large eddy simulation of turbulent ﬂow around tube bundles composed of wavy and circular cylindersm a,*,Y.F.Lin a ,L.Zou b ,Y.Liu aa Department of Mechanical Engineering,The Hong Kong Polytechnic University,Hung Hom,Kowloon,Hong Kong bSchool of Mechanical and Electronic Engineering,Wuhan University of Technology,Wuhan 430070,PR Chinaa r t i c l e i n f o Article history:Received 4November 2008Received in revised form 19October 2009Accepted 21October 2009Available online 18November 2009Keywords:Tube bundles Wavy cylinders Turbulent ﬂowLarge eddy simulation LDAa b s t r a c tThis paper presents the results of an investigation on the effects of wavy cylindrical tubes in a staggered heat exchanger tube bundle.Experimental measurements and large eddy simulation (LES)technique were used to study the turbulent ﬂow characteristics in a staggered tube bundle arrangement at a sub-critical Reynolds number of Re =7500.The aim of this investigation is to compare the ﬂow charac-teristics of a new conﬁguration of cylindrical tubes with that of a similar arrangement which comprises purely circular cylinders.The ﬁrst row of circular tubes is replaced by a row of wavy cylindrical tubes.The result of the experiment shows that the mean velocity distributions and turbulence intensity,obtained by the present LES method,are in good agreement with the Laser Doppler Anemometer (LDA)measure-ments.The wake patterns around the second row of cylinders become more well organized upon the introduction of wavy cylinders of optimal wavelength (k /D m =6).The turbulent kinetic energy behind the ﬁrst row of tubes is also reduced.The power density spectra of the vortex shedding in the tube bundle are evidently suppressed.As a result,the ﬂuctuating forces of the tube bundles are weakened.However,the drag is not noticeably reduced by such modiﬁcation.Ó2009Elsevier Inc.All rights reserved.1.IntroductionTube bundles are widely employed in cross-ﬂow heat exchang-ers.The complex vortex shedding characteristics behind the cylin-drical tubing can cause severe vibration of the tubes,generally known as ﬂow-induced vibration (FIV).FIV of heat exchanger tube bundles may cause serious structural failure.Over the past years,numerous experimental investigations have been carried out to study the mechanism of FIV in different conﬁgurations of tube bundles.Austermann and Popp (1995)investigated the ﬂuid elastic instability in different tube arrays.They found that stability de-pends on the pattern of tube arrays and on the space ratio of tube.Price et al.(1995)reported the vortex shedding characteristics of tube arrays that were obtained by ﬂow visualization methods.Romberg and Popp (1998a,b)conducted experimental investiga-tions on the stability factors of normal and rotated triangular tube arrays with different pitch-to-diameter ratios.Chen and Srikantiah (2001)presented series of experiments to measure motion-depen-dent ﬂuid forces for various tube arrays.Rottmann and Popp (2003)further investigated the inﬂuence of approach ﬂow on the ﬁrst row of tube bundles.Paul et al.(2007)preformed measure-ments in a staggered tube bundle with ﬁxed pitch-to-diameterratios at sub-critical Reynolds number using the particle image velocimetry technique.Their results showed that the ﬂow exhibits strong Reynolds number dependence in the developing region,however no signiﬁcant Reynolds number effect could be observed in the spatially periodic region.Because of the complicated ﬂow characteristics in the heat ex-changer tube bundles,the vortex structures cannot be clearly ob-served and a lot of valuable information cannot be obtained by experimental techniques alone.It is then suggested that numerical simulations should be able to capture the instantaneous three-dimensional vortex structures and other instantaneous ﬂuid dy-namic parameters,such as drag,lift,pressure,velocity and Rey-nolds stress.Successful numerical investigations of ﬂow around tube bundles had been carried out by Bouris and Bergeles (1999),Watterson et al.(1999),Beale and Spalding (1999),Sweeney and Meskell (2003),Schneider and Farge (2005),Lam et al.(2006)and Paul et al.(2008)using different numerical methods.For tur-bulent ﬂow,large eddy simulation (LES)has become a very popular and reliable numerical method,with which the complex turbulent ﬂow characteristics can be captured accurately.For example,Barsamian and Hassan (1997)examined the non-staggered and staggered tube bundles using the two-dimensional LES method.Rollet-Miet et al.(1999)developed a ﬁnite element LES code com-pared with the Reynolds Averaged Navier–Stokes (RANS)equation.*Corresponding author.Tel.:+852********;fax:+852********.International Journal of Heat and Fluid Flow 31(2010)32–44Contents lists available at ScienceDirectInternational Journal of Heat and Fluid Flowj ou r na l h om e pa ge :w w w.e lse vi e r.c om /lo c at e /ij hffresults by LES method are in very good agreement with the LDA measurements on the investigation of turbulentﬂow around stag-gered tube bundles.Important information such as instantaneous velocityﬁeld,force characteristics,etc.were obtained.All of the above showed that both the experimental measurement and numerical simulation are useful complementary tools for the study of FIV.Although some interesting studies which are based on the pre-mise of modiﬁed tube shapes have been carried out,most of the investigations have focused on the characteristics ofﬂuidelastic instability of tube bundles with the circular cylinders.In our previ-ous investigation,it was found that a cylinder with wavy surface can weaken,to the extent that it may even suppress the FIV com-paring with a circular cylinder at the same Reynolds numbers(Lam et al.,2004a,b).An optimal spanwise wavelength ratio k/D m%6for drag reduction andﬂuctuating lift suppression was found at low Reynolds number of100over a wide wavelength range by Lam and Lin(2007,2009).For turbulentﬂow,Lam and Lin(2008)found an optimal wavelength k/D m%2using the large eddy simulations over a narrow wavelength range.Signiﬁcant drag force reduction and weakening of vibration were found at Re=3000.An extension of investigation onﬂow past a row of wavy cylinders conducted by Lam et al.(2007)showed that the wavy cylinders give rise to a more stableﬂow pattern with lessﬂuctuation and longer wake vortex closure length compared with a row of circular cylinder.Based on the results of the aforementioned experiments,the present investigation aims at controlling FIV of the tube bundles using different combinations of wavy and circular cylinders.It is hoped that by replacing certain circular cylinders with wavy cylin-ders in tube bundle,ﬂow-induced vibration could be minimized or suppressed.Theﬁnite-volume method(FVM)is employed to sim-ulate theﬂow past the wavy and circular tube bundles.For the study of turbulentﬂow,the large eddy simulation(LES)is adopted. Also,experimental measurements using the Laser Doppler Ane-mometer(LDA)technique were performed to supplement the study.The time-average velocity distributions of theﬂowﬁeld are obtained.The forces on the cylinders were measured using a three-component quartz piezoelectric load cell so that the numer-ical results can be conﬁrmed.width,height)with correspondence to the direction of x,y and z, respectively.Two pumps with one electric control system were used to produce a desired mainﬂow velocity in the test section, while the free stream velocity in the testing area could be contin-uously adjusted from0to4m/s.Numbers are assigned to the stag-gered set of tubes.Numbers1–5denote theﬁrst row in the upstream position while,numbers6–9and10–14denote second row and the third rowing tubing,respectively.The tubes height for the present experiment is15D m.Fig.1shows the schematic experimental setup of the tube bundle.Theﬂow characteristic is studied with theﬁrst row of tubes replaced byﬁve wavy cylinders (a cylinder with a varying circular cross section along the spanwise direction)as opposed to a conﬁguration of purely circular cylinders (a cylinder with a constant circular cross section along the span-wise direction).Lam et al.(2007)experimentally investigated tur-bulentﬂow around a row of side by side wavy cylinders with a ﬁxed spacing ratio of1.5D m.Both the in-phase and out-of-phase arrangement of the wavy cylinders were studied.The results show that the out-of-phase arrangement of the wavy cylinders gives rise to a more stableﬂow pattern with lessﬂuctuation.As shown in Fig.1b,theﬁrst row of wavy cylinders is arranged to be out-of-phase according to our previous study.Following the same study, the spacing ratio between the tubes rows isﬁxed at1.5D m(cross-wise direction,y-direction).As the vortex shedding of the wavy cylinder occurs at further downstream compared with a circular cylinder(Lam and Lin,2008,2009),we extend the streamwise (x-direction)spacing ratio of the tubes in each tube rows to aﬁxed value of2.5D m(see Fig.2a).The geometry of the wavy cylinders can be described by the following equation,D z¼D mþ2a cosð2p z=kÞð1ÞHere,D z denotes the local diameter of the wavy cylinder and the mean diameter can be calculated with the equation D m=(D min+D max)/2.D min represents the minimum diameter of cylinder along the span-wise direction,while D max represents the maximum diameter of the wavy cylinder.The amplitude of the curve surface is denoted by‘a’, and‘k’is the wavelength along the spanwise direction.The axial loca-tions with maximum local diameter are termed‘nodes’,while the ax-ial locations of the minimum diameter are called‘saddles’.In theNomenclaturea wave amplitude of a wavy cylinder(m)C s Smagorinsky constant,dimensionlessD m mean diameter of a wavy cylinder(m)D max maximum diameter of a wavy cylinder(m) D min minimum diameter of a wavy cylinder(m) D z local diameter of a wavy cylinder(m)FFT Fast Fourier TransformF D,F L total drag force,total lift force(N)f s vortex shedding frequency(Hz)LDA Laser Doppler AnemometerLES large eddy simulationL x,L y,L z computational domain(m)p pressure(Pa)Re Reynolds number,dimensionlessSGS subgrid-scaleSt Strouhal number,dimensionlesst time(s)D t time step,dimensionlessTKE turbulent kinetic energy(m2/s2)uiﬁltered velocity component(m/s)U,V,W velocity components(m/s)u0,v0,w0root-mean-square velocity(m/s)U c convection velocity(m/s)U1incomingﬂow velocity(m/s)x,y,z cartesian coordinate systemy+non-dimensional cell distance from wallGreek symbolsk spanwise wavelength of a wavy cylinder(m)k z spanwise wavelength of the streamwise vortices(m) m kinematic viscosity(m2/s)qﬂuid density(kg/m3)s ij subgrid-scale stress(m2/s2)m et al./International Journal of Heat and Fluid Flow31(2010)32–4433The position of the ﬁrst row cylinders is 0.2m from the upper wall of the water tunnel test section.The cylinders of the mean diameter D m =0.02m with the height of 0.297m (resulting in as-pect ratios of 14.85)were set in the test section.The incoming In order to obtain the quantitative mean and ﬂuctuating veloc-ity distributions for turbulent ﬂow around the tube bundles,a two-colour ﬁbre-optic LDA (Dantec Model 58N40LDA with enhanced FVA signal processor)was employed in the present investigations.The LDA system is equipped with software for data processing and analysis.The LDA measuring volume has a minor axis 1.18mm and a major axis of 2.48mm.The uncertainties in mean velocity (both of the streamwise and transverse velocities components)and tur-bulence intensity are estimated to be ±3%and ±7%,respectively,for detail uncertainty analysis,refer Wang et al.(2005).The higher errors generally occur in the regions with steep velocity gradients.For each data-point,50,000validated samples were acquired with a data rate of 0.8–4kHz.For similar LDA measurements on tube bundles by Balabani and Yianneskis (1996),as reported by Liang and Papadakis (2007),the uncertainty in mean velocity and turbu-lence quantities are,respectively,1–5%and 5–10%.Furthermore,forces on the cylinders were measured using a three-component quartz piezoelectric load cell characterized by high response,resolution and stiffness.The load cell mounted on the top end of the wavy cylinder is bolted tightly between two stainless machine-polished steel blocks.Static calibrations of the load cell in the lift and drag directions were carried out using dead weights.It could be seen that the load cell had a high linearity in the load/output relation.Moreover,for the force measurements,the test cylinder was cantilever-mounted.The distance between the cylinder lower end and the bottom wall is about 0.003m.For the present study the uncertainty in drag is about ±5%,while that of ﬂuctuating lift is approximately ±12%putational models1234567891011121314Sketch of tube bundle arrangement:(a)tube bundles arrangement and computational gird of the tube bundle with wavy cylinders in the ﬁrst row.Fig.1.(a)Experimental setup of the tube bundle.(b)Schematic of the out-of-phase arrangement of wavy cylinders in the ﬁrst row of the tube bundle.Table 1Tube bundles models:CY =circular cylinder;WY =wavy cylinder.Tube bundles Row-1Row-2Row-3Model-I CY (1–5)k /D m =1CY (6–9)CY (10–14)a/D m =0Model-II WY (1–5)k /D m =6.0CY (6–9)CY (10–14)a/D m =0.15Model-IIIWY (1–5)k /D m =1.5CY (6–9)CY (10–14)a/D m =0.15m et al./International Journal of Heat and Fluid Flow 31(2010)32–44equations,and the small eddies are modeled using a subgrid-scale (SGS)model.The large-scale turbulence motions are strongly dependent on theﬂow geometry and boundary conditions,and they can be predicted by the resolvedﬂow in the LES method. On the other hand,the subgrid-scale model represents the small-scale eddy motion which is more universal in character than the large-scale eddy.By applying theﬁltering operation,the incompressible Navier–Stokes equations for the evolution of the large-scale motions can be obtained.The governing equations employed for LES are@ u i@x i¼0;ð2Þ@ u i @t þ@ u i u j@x j¼À1q@ p@x iþm@2 u i@x j@x jÀ@s ij@x j;ði¼1;2;3Þð3Þwhere u i is theﬁltered velocity component along the Cartesian coordinates x i, p the pressure,q theﬂuid density and m is the kine-matic viscosity of theﬂuid.The inﬂuence of the small scales on the large(resolved)scales is exerted through the subgrid-scale stress which could be deﬁned bysij¼u i u jÀ u i u j;ð4Þwhich are unknowns and must be modeled with a subgrid model. The Smagorinsky constant,C s=0.12,was adopted by Barsamian and Hassan(1997)in turbulentﬂow around tube bundle.Moreover, Liang and Papadakis(2007)used C s=0.1to investigate turbulent ﬂow around a staggered tube bundle at Re=8600.As a result,all computations in the present work were carried out with a Smago-rinsky constant,C s=0.1,which is found to be a suitable value for the applications of the Smagorinsky model to turbulent wake simulation.Detailed descriptions of the present LES method can be found in Lam and Lin(2008).Theﬁnite-volume method(FVM)applied on unstructured grids has been employed to solve the unsteady incompressible Navier–Stokes equations.A second-order central differencing scheme is used for momentum discretization while a second-order implicit scheme is employed to advance the equa-tions in time.The pressure implicit method with splitting of oper-ators(PISO)algorithm is used to deal with the pressure–velocity coupling between the momentum and the continuity equations.putational domain and boundary conditionsThe computational domain is set at L xÂL yÂL z in the x-,y-,z-directions of aﬁxed Cartesian coordinate system.A tube bundle model is built inside it.The origin of the coordinate system is lo-cated at the central position of the wavy tubes(see Fig.1b).The x-axis is aligned with the inletﬂow direction(streamwise direc-tion),the z-axis is parallel to the cylinder axis(spanwise direction) and the y-axis lies perpendicular to both the x-and z-axes(cross-wise direction).In the present simulations,the computational boundaries L x and L y are set at40D m and7.5D m,respectively(refer to the experimen-tal setup).The upstream boundary is set at10D m(determined from the experiment)before the centerline of theﬁrst row of tubes.The downstream boundary is25D m away from the third row of tubes. The experimental studies of Williamson et al.(1995)and William-son(1996)showed that the wavelength scales of the streamwise vortex structures in the near wake of a circular cylinder is given by k z=D m%25ReÀ1=2.Here,k z is the spanwise wavelength of the vortices and the estimated near wake wavelength of streamwise the large-scale eddies,we use L z=3D m for the Model-I tube bun-dles in the spanwise direction is considered to be sufﬁcient for the present simulations of the circular cylinder(see Table2).As mentioned by Lam et al.(2004b)and Zhang et al.(2005),for single wavy cylinder,the periodic vortex structures were experimentally observed to be consistent with the periodic repetition of wavy cyl-inder of spanwise wavelength,k.Recently,Lam and Lin(2007, 2008,2009)captured this kind of phenomenon using the numeri-cal method for both laminarﬂow and turbulentﬂm et al. (2007)discovered this kind of periodic repetition of vortex struc-ture along the spanwise direction of a row of out-of-phase arrange-ment wavy cylinders.In the present simulation,the spanwise domain L z of the Model-II tube bundles is6D m,or is equal to one wavelength k of the wavy cylinder(k/D m=6).While,L z of the Model-III tube bundles is3D m,or equal to two wavelengths2k (k/D m=1.5).The computational domain is divided into a number of unstruc-tured hexahedral grids.The grid is non-uniform in the x–y plane (see Fig.2b),but uniform along the z-direction.The grids are clus-tered near the cylinder surface and the spacing is properly in-creased in a ratio of1.1away from the cylinder.The distance from the cylinder surface to the nearest grid points isﬁxed at y+ close to1.At the inlet boundary,a uniform velocity proﬁle(u=1, v=w=0)is imposed.Moreover,base on the experimental data, at the inlet the relative turbulence intensity is set equal to2%.A convective boundary conditionð@u i=@tþU cð@u i=@xÞ¼0Þis used at the outlet boundary(Breuer(1998),Sohankar et al.(2000), Lam and Lin(2008)),where U c is the convection velocity equal to the mean velocity at the inlet.The no-slip boundary condition (u=v=w=0)is prescribed at the surface of the cylinders and the lateral sides of the domain.The periodic boundary condition is em-ployed at the boundaries in the spanwise direction to reduce the computational time.A validation test is also performed prior to the present simulations.A non-dimensional time step D tU1/D m=0.02was chosen for the simulation,yielding the maximum CFL number close to two and ensuring sufﬁciently small CFL numbers of less than1for most part of the computational domain.It was dictated by the numerical stability of the computations.For all of the present simulations,at least150dimensionless time units(tU1/D m),in correspondence with around30vortex-shedding cycles,were taken in order to ob-tain more reliable statistical average information.4.Results and discussion4.1.Single wavy cylinder testOn the study of turbulentﬂow characteristics,the previous investigation by Lam et al.(2004a)focused mainly on the effects of wavy cylinders with relatively short wavelengths(k/D m63.3). Table2Details of grid model for different tube bundles(Nc:cylinder circumference mesh numbers;Nz:spanwise mesh layers).Model Case Grid Nc Nz L xÂL yÂL z(D m) Model-I Grid-I10,20,096802840Â7.5Â3Grid-II14,26,944963240Â7.5Â3 Model-II Grid-I20,40,192805640Â7.5Â6Grid-II28,53,888966440Â7.5Â6 Model-III Grid-II14,26,944963240Â7.5Â3m et al./International Journal of Heat and Fluid Flow31(2010)32–4435(2008)found that a wavy cylinder with k/D m of around1.9can lead to signiﬁcant drag force reduction and vibration suppression at Re=3000.For laminarﬂow,however,Lam and Lin(2007,2009) numerically investigated theﬂow around wavy cylinders at Re=100over a wide range of spanwise wavelength.Two optimal wavelengths for drag reduction were found at k/D m%2and k/ D m%6.With a larger value of spanwise wavelength k/D m=6,the vortex shedding behind the wavy cylinder was greatly suppressed and the drag force was evidently reduced.This observation is con-sistent with theﬁndings of Darekar and Sherwin(2001).They investigated a wavy square cylinder at low Reynolds numbers. The optimal wavelength obtained was around5.7D m.Similarly, Bearman and Owen(1998)also measured the wavy square cylin-der at high Reynolds number.Their report showed that there was also evidence of drag reduction.Henceforth,it was determined that k/D m=6was the correct optimal wavelength for the suppres-sion of FIV.Considering the results above,it is anticipated that the intro-duction of wavy cylinders with k/D m=6would give better effects in FIV suppression.To conﬁrm that k/D m=6is the optimal wave-length required at sub-critical Reynolds numbers,weﬁrst per-formed force measurements of a wavy cylinder with wavelength ratio(k/D m=6)at Re from6800to13,400.At the same time,the large eddy simulation ofﬂow around a single wavy cylinder(k/ D m=6,a/D m=0.15)at Re=7500was also performed for comparison.Fig.3shows the force coefﬁcients of wavy cylinder(k/D m=6,a/ D m=0.15)obtained by the present load cell measurements and large eddy simulation compared with that of a circular cylinder within the same range of Reynolds numbers.The overall drag coef-ﬁcient is deﬁned with the equation,C D¼2F D=q U21D m L z;while the value of the overall lift coefﬁcient can be determined by C L¼2F L=q U21D m L z.The total drag and total lift are designated as F D and F L,respectively.The mean drag coefﬁcients of a circular cyl-inder( C D)obtained by load cell measurements are in good agree-ment with the experimental results by Zdravkovich(1997).All the values of C D for circular cylinders measured at the Reynolds numbers from6800to13,400are approximately1.1(see Fig.3a). The values of C D for the wavy cylinder(k/D m=6,a/D m=0.15),how-ever,are evidently smaller than those of a circular cylinder within the same Reynolds number range.A result of drag reduction up to 18%could be observed.The values of C D obtained from the LES method for both wavy and circular cylinders are slightly large than those of the measured results.However,the drag reduction of the wavy cylinder of about17.3%is obtained.This value is close to the experimental result(see Fig.3a).Theﬂuctuating lift coefﬁcients captured by load cell technique(C0L,root-mean-square value)are also in good agreement with the empirical results obtained by Nor-berg(2003).The values of C0Lfor the wavy cylinders are also smal-ler than that of a circular cylinder at the same Reynolds number. About75%reduction ofﬂuctuating lift coefﬁcients is obtained.Bythe LES method,however,the values of C0Lfor both wavy and circu-lar cylinders are smaller than that of the experimental results.Thereduction of C0Lfor the wavy cylinder is up to85%,which is slightly lower than the load cell measurements(see Fig.3b).The difference may due to the effect on the periodic boundary condition used by LES method(two wavelengths for the wavy cylinder,resulting in the aspect ratio of12)and theﬁnite length of the cylinder models by load cell measurements(an aspect ratio of14.85for the exper-imental set up).In general,it is concluded that the present LESm et al./International Journal of Heat and Fluid Flow31(2010)32–44method can well predict the characteristic ofﬂow past a wavy cyl-inder.Both the experimental and numerical results conﬁrmed that the wavy cylinder of k/D m=6is a suitable choice for the control of ﬂow-induced vibration.Fig.4shows the Strouhal numbers(St=f s D m/U1)of a circular cylinder and wavy cylinder obtained from the load cell measure-ments and LES calculations.The characteristics of the circular cyl-inder also agree with the results of the empirical relation summarized by Norberg(2003).Here,f s is the vortex shedding fre-quency.Within this sub-critical Reynolds number range,both the Strouhal numbers of the wavy cylinders and circular cylinder are approximately equal to0.21.The results are the same as that ob-tained by Lam et al.(2004a)and Lam and Lin(2008).They found that the wavy shapes have little effect on the frequency character-istics of vortex shedding for wavy cylinders at sub-critical Rey-nolds numbers.Lam et al.(2007)showed that the periodic wake distribution oc-curs on a row of side by side wavy cylinders along the spanwise direction.To validate the accuracy of the present computational domain height and the periodic boundary conditions on wavy tube bundles,a row of side by side wavy cylinders(k/D m=6,a/ D m=0.15)with aﬁxed spacing ratio of 1.5D m was computed.Two wavy cylinder row cases with different computational domain heights were compared.As shown in Fig.5a,the normalized time averaged streamwise velocity distributions of the wavy cylinder row in y–z plane at the positions of x/D m=1.5,4,6,and8show periodic velocity distribution repeatedly in z-direction with the computational domain height of2k.Moreover,the velocity distri-butions of the cylinder row with the computational domain height of1k show similar characteristics as that of the case with2k heights.It conﬁrmed that the periodic boundary condition with only one spanwise wavelength in the computational domain is suf-ﬁciently accurate to simulateﬂow pass tube bundles with wavy cylinders arranged at theﬁrst row.4.2.Velocity and turbulence intensity distributionsThe accuracy of the computational results using LES is highly dependent on the mesh size and cell numbers.The grid indepen-dence test must be carried out prior to extensive numerical simu-lations.With reference to Table2,for each cylinder,the cell numbers were set at80and96around the cylinder circumference, which correspond to the cell numbers in x–y plane of36,432and 44,592,respectively.Uniform layers of28and32wereadopted m et al./International Journal of Heat and Fluid Flow31(2010)32–4437m et al./International Journal of Heat and Fluid Flow31(2010)32–44for Model-I,Grid-I,and Grid-II,respectively.Uniform layers of56 Array and64were used for Model-II,Grid-I,and Grid-II,respectively,be-cause the computational domain along the spanwise direction forModel-II is double that of Model-I.Moreover,the validation testsof the present LES method were also performed by the comparisonof the LES results with the LDA measurements on the tube bundlesat the same Reynolds number of7500.By using the LES methodand LDA technique,the detailed velocity distributions at differentpositions(see Fig.6)in the x–y planes were obtained.Fig.7shows the mean streamwise velocity distributions at x/D m=1.5,4,6,and8for circular and wavy tube bundles(Model-Iand Model-II),respectively.Both the present LES results by Grid-Iand Grid-II show good agreement with the LDA measurements.The gap velocities behind the second row(position of x/D m=4)of tubes are evidently smaller than those behind theﬁrst row(po-sition of x/D m=1.5)and the third row(position of x/D m=6)oftubes.However,no prominent difference in mean streamwisevelocity distributions can be observed between those of tube bun-dles Model-I(ﬁrst row with circular cylinders,CY)and Model-II(ﬁrst row with wavy cylinders,WY:k/D m=6,a/D m=0.15).This im-plies that the drag may not be signiﬁcantly reduced by using eithercircular cylinders or wavy cylinders in theﬁrst row of tube bun-dles.At x/D m=1.5,the velocity distribution in Section1(seeFig.7e)is slightly different from that in Section2(see Fig.7i)forthe tube bundles Model-II.Similarﬂow characteristics are also ob-served for the time averaged transverse velocity distributions asshown in Fig.8.This may be due to the periodic wake structurealong the spanwise direction of the wavy cylinder.At the furtherdownstream positions(x/D m=8),no evident gap velocity is gener-ated as the turbulent vortices amalgamate with each other.Allthese can be easily observed by the vortex structures to be dis-cussed later.。

LARGE EDDY SIMULATION

Example: An 1-D flow field
f
~ f ( x ) ⇒ f ( x ) + f ′′( x )
large eddies
Reynolds averaged model (RAN)
f
f ( x) ⇒ f ( x) + f ' ( x)
non-turbulent
LES EQUATIONS
Different PBL Flow Regimes
• numerical setup • large-scale forcing • flow characteristics
Clear-air convective PBL
Convective updrafts
Ug
z
Θ
Q∗
~ 5 km
Horizontal homogeneous CBL
Future Direction of LES for PBL Research • Realistic surface
–complex terrain, land use, waves • PBL under severe weather
mesoscale model domain 500 km
Coupled with heterogeneous soil
Wet soil
LES model
z
Surface model
Dry soil
the ground
Land model
30 km
Coupled with heterogeneous soil
wet soil
dry soil
(Patton et al 2003)

Large-Eddy Simulation of Unsteady Flow in a Mixed-Flow Pump

The predicted pump heads reproduce the instability and agree fairly well with their measured equivalents, although the predicted stall takes place at a ﬂow-rate ratio that is a few percentage points lower than the measurements. The phaseaveraged distributions of the meridional- and tangentialvelocity components at the impeller’s inlet and exit cross sections were also compared with those measured by laserDoppler velocimetry. Reasonably good agreements have been obtained between the computed and measured proﬁles. The developed LES program thus seems to be a promising design tool for a high–speciﬁc-speed, mixed-ﬂow pump, particularly for off-design evaluations.
Keywords Finite element methods, Large eddy simulation, Mixedﬂow pump, Stall phenomena, Unsteady ﬂow
At present, the Reynolds-averaged Navier-Stokes (RANS) equations are used as the governing equations in most compu-

气浮轴承的fluent 三维仿真

Large eddy simulation of vortex shedding and pressurefluctuation in aerostatic bearingsJincheng Zhu a,Han Chen a,b,Xuedong Chen a,na State Key Laboratory of Digital Manufacturing Equipment and Technology,Huazhong University of Science and Technology,Wuhan430074,Chinab Department of Mechanics,Huazhong University of Science and Technology,Wuhan430074,Chinaa r t i c l e i n f oArticle history:Received21May2012Accepted5March2013Available online28April2013Keywords:Aerostatic bearingLarge eddy simulationVortex sheddingPressure fluctuationVibrationa b s t r a c tIn aerostatic bearings,high speed air flow may induce small vibration,which has beenharmful to the improvement of moving and positioning accuracy of aerostaticallysupported devices in ultra-precision applications.In this paper,the transient flow fieldin the aerostatic bearing is numerically investigated using the large eddy simulationmethod.Turbulent structures are studied and vortex shedding phenomenon is discoveredin the bearing recess.Our computational results demonstrate that vortex shedding causespressure fluctuation in the bearing clearance.Relationship between pressure fluctuationand bearing vibration is established based on our simulation results and experimentallymeasured vibration strength.&2013Elsevier Ltd.All rights reserved.1.IntroductionAerostatic bearings have been widely used in ultra-precision moving and positioning equipments.Due to the merit of near-zero friction and low heat generation,applications of aerostatic bearings make it possible for supported devices to realize nanometer positioning accuracy.However,with the increasing demand of positioning accuracy,the inherent small vibration on the order of nanometers(Kawai et al.,2005)severely damages stability and precision of the bearing,especially in sub-nanometer positioning equipments.To understand and eventually suppress this harmful vibration,traditional design and analysis methods for mass flow rate and load carrying capacity do not suffice anymore,and lots of research efforts have been made on the air flow field in aerostatic bearings.Recently,the relationship between the high speed air flow and the small vibration in aerostatic bearings has been realized by many researchers.Kawai et al.(2005)studied the nano-vibration in ultra-precision machine tools and attributed it to air turbulence due to bearing surface roughness.Chen and He(2006)found vortex flow structures in the bearing recess by computational fluid dynamics(CFD)simulation of the steady air flow field,and suggested that these air vortices are responsible for the instability of the aerostatic bearing.Aoyama et al.(2006)also observed this air vortex flow by CFD simulation and reached a similar conclusion,and accordingly proposed a new restrictor design to weaken the vibration. Zhang et al.(2007)analyzed the high Reynolds number(Re)flow in the bearing clearance,and reduced the vibration of aerostatic bearings by flow laminarization.In a recent work,Yoshimura et al.(2012)attributed nano-vibration of aerostatic bearings with surface restriction to pressure fluctuation at the bearing outlet due to atmospheric turbulence.Although the flow-induced nature of bearing vibration has generally been recognized,the previous works only assumed a steady flowContents lists available at SciVerse ScienceDirectjournal homepage:/locate/jfsJournal of Fluids and Structures0889-9746/$-see front matter&2013Elsevier Ltd.All rights reserved./10.1016/j.jfluidstructs.2013.03.012n Corresponding author.Tel./fax:+862787557325.E-mail address:chenxd@(X.Chen).Journal of Fluids and Structures40(2013)42–51field or averaged the flow field in a Reynolds Averaged Navier –Stokes (RANS)sense.Since this flow-induced vibration is apparently a time dependent process,time dependent is necessary to investigate the transient air flow field in the bearing clearance in order to further understand this harmful small vibration.To numerically analyze the detailed flow characteristics in aerostatic bearings,the full Navier –Stokes equations for compressible fluids have to be solved.Since the high speed air flow in the bearing gap near the orifice outlet is turbulent,RANS simulation is usually employed,and numerical results demonstrate adequate accuracy in predicting mean flow characteristics (Chen and He,2006;Li and Ding,2007).Pressure depressions (Eleshaky,2009;Yoshimoto et al.,2007)and vortex flow structures (Chen et al.,2011)near the orifice outlet have also been reported using RANS simulation.However,RANS simulation adopts a statistical turbulent model and details of turbulent structures remain unresolved.Ideally,direct numerical simulation (DNS)can resolve the whole spectrum of turbulent scales as no turbulent model is assumed,but its computational cost is prohibitively huge.In large eddy simulation (LES),large scale turbulent eddies are solved directly and small scale turbulence is modeled by sub-grid scale models.Thus,coherent turbulent structures can be obtained with acceptable computational cost in LES,which has been validated in various applications (Cheng et al.,2012;Lam et al.,2010;Tucker,2011).In a previous study (Chen et al.,2011),steady RANS simulation method was used to study air flow fields in various aerostatic bearings with different parameters and recess shapes,and the relationship between vortex strength and vibration energy of the bearing was established.However,no transient flow characteristics in the aerostatic bearing could be resolved.In this paper,the transient air flow field is investigated numerically using the LES method.Our simulation results reveal vortex shedding and pressure fluctuation in the bearing recess.Vibration of the bearing is also measured experimentally,and it is demonstrated that vibration strength of the bearing increases with increasing pressure fluctuation induced by vortex shedding in the bearing recess.2.Numerical modeling 2.1.LESIn LES,large eddies of turbulence are directly resolved and eddies with scales smaller than grid spacing are modeled.The governing equations employed in LES are the time-dependent Favre Filtered Navier –Stokes equations,including continuity and momentum equations:∂ρ∂t þ∂∂x iðρ~ui Þ¼0;ð1Þ∂ðρ~u i Þþ∂j ðρ~u i ~u j Þ¼−∂p i þ∂~s ij j −∂jð~τij Þ;ð2Þthe Favre filter is the density-weighted filter,where density and pressure are spatial filtered (denoted by “–”)while velocityis density-weighted (e Ã¼ρÃ=ρ,n denotes a general variable).In Eq.(2),s ij is the viscous stress tensor and τij is the subgrid-scale (SGS)stress,which are defined as~s ij ¼μ∂~u i ∂x j þ∂~u j ∂x i −23δij ∂~u k ∂x k;ð3Þ~τij ¼ρðu i u j $−~ui ~u j Þ;ð4ÞJ.Zhu et al./Journal of Fluids and Structures 40(2013)42–5143where τij needs to be modeled using a SGS rge turbulent eddies can be resolved directly by Eqs.(1)and (2),and turbulent eddies with scales smaller than grid size are modeled.As a SGS model,the Wall-Adapting Local Eddy-Viscosity (WALE)model (Nicoud and Ducros,1999)is adopted in this paper.In this work,LES simulations were performed in the CFD software ANSYS Fluent using the finite volume method.In Fluent,the Pressure-Implicit with Splitting of Operators (PISO)algorithm (Issa,1986)is adopted as the pressure –velocity coupling scheme.In order to minimize numerical dissipation,the second order upwind interpolation is chosen for the density,turbulent kinetic energy and turbulent dissipation rate,while the bounded central differencing is chosen for momentum interpolation in LES.As the transient formulation,the second order implicit scheme is adopted.The Non-Iterative Time-Advancement (NITA)scheme (Issa,1986)is used to improve the computational efficiency,and the time step size Δt ¼1Â10−8s is chosen according to the CFL condition u Δt =Δx o 1,where Δx is the size of control putational domainFor generality and simplicity,a circular pad aerostatic bearing with a single central orifice restrictor is considered as shown in Fig.1.The outer diameter of the bearing is d 2¼20mm and the orifice diameter is d 0¼0.15mm.The cylindrical recess has a diameter d 1¼3mm and depth H ¼0.1mm.The air film thickness is h ¼10μm.In our LES calculations,the air flow domain is divided into 12sections along the circumferential direction,and only one section (Fig.2)is used as the computational domain to reduce the computational cost.This simplification is reasonable for qualitative study on turbulent structures in the aerostatic bearing.In order to allow for a fine resolution of turbulent structures in the bearing recess,the Embedded LES (ELES)modeling technique in Fluent is adopted.Specifically,the computational domain is divided into three regions:orifice,recess and gas film (Fig.2).The realizable k −εmodel is used in the orifice region (RANS region);the flow in the air film is supposed to be laminar and LES is adopted in the recess region.An RANS –LES interface is used to connect the orifice region and the recess putational meshFig.3shows the computational mesh used in the LES,where non-conformal mesh is used.It is known that the accuracy of LES is sensitive to mesh resolution,so more refined mesh is generated in the recess region.Mesh independence tests (see Table 1)are performed until further refinement of the mesh results in insignificant changes in thecomputationalFig.1.Schematic of the aerostatic bearing.putational domain and ELES model.J.Zhu et al./Journal of Fluids and Structures 40(2013)42–5144results.The parameters in Table 1are described as follows.The total number and the volume of the mesh in various regionsare listed.The non-dimensional distance y +can reflect wall-adjacent mesh resolution,which is defined as y þ¼ﬃﬃﬃﬃﬃﬃﬃﬃρτw p y =μ,where y is the distance from the wall to the center of the first neighboring mesh,and τw is the wall shear stress.To resolve accurately turbulent eddies in the near-wall regions,y +is always guaranteed to be less than 1with local mesh refinement.As the calculation results,the mean values and the standard deviations of p A are compared between the coarse mesh case and the fine mesh case,where p A is the time variation (as described in Section 3.2)of area-weighted averaged pressure on the wall 2.2.4.Boundary and initial conditionsAs shown in Fig.2,pressure inlet boundary condition is specified at the orifice inlet,in which turbulent intensities of 1%,5%and 10%are considered;atmospheric pressure is specified at the bearing outlet;two symmetric boundaries are adopted on the two surfaces in the circumferential direction.On the solid walls,no-slip and no heat transfer conditions are specified.In addition,all the walls are assumed to be perfectly smooth.The air used in the simulations is assumed to obey the ideal gas law,hence the density varies according to the state equation.Other physical constants such as viscosity,molecular weight,specific heat and thermal conductivity are 1.7894Â10−5kg/(m s),28.966Â10−3kg/mol,1006.43J/(kg K)and 0.0242W/(m K),respectively.A steady RANS simulation result is used as the initial field of LES,which can help LES to converge quickly.2.5.Validation of numerical modelIn order to justify our numerical model,the existing experiment data (Yoshimoto et al.,2007)of pressure distribution of the aerostatic bearing are utilized as a comparison.Fig.4shows the comparison with our numerical result,where both the realizable k −εRANS result and the LES result are plotted.The LES result is the statistical mean pressure distribution in the bearing clearance.As can be seen in the figure,there is almost no discrepancy between our CFD results and the experimental data except for the region where r /r 2is between 0.034and 0.2.In this region near the orifice outlet,the LES result shows better agreement with experimental data than the RANS one.Therefore,the LES method can be employed in the calculation of the flow field of aerostaticbearings.XZputational mesh.Table 1Mesh refinement study,where Δdenotes mesh volume (μm 3),p A is the time variation of area-weighted averaged pressure (Pa)on the wall 2,E and s denote the mean value and standard deviation,respectively.MeshRecess Orifice Gas film Max y +Total numberMean E ðp A ÞFluctuation s ðp A ÞΔminΔmax Δmin Δmax Δmin Δmax Coarse 1.11129020.6076.271755716101.526807535062862Fine0.434370.651964435046367J.Zhu et al./Journal of Fluids and Structures 40(2013)42–51453.Transient ﬂow characteristics 3.1.Flow structures and vortex sheddingFig.5displays the streamlines and the pressure contours computed from steady RANS simulation when P s ¼4atm,in which flow separation and vortex formation can been seen in the recess near the orifice outlet.It is noted that steady RANS simulation results in axisymmetric flow structures.Fig.6displays the corresponding instantaneous flow field obtained by LES at different times.In Fig.6(a),the iso-surfaces of instantaneous vorticity are depicted.In contrast to the single axisymmetric vortex in Fig.5,the coherent turbulent structure in the recess contains a series of vortices with varying sizes and shapes.The vortex shedding phenomenon can be observed.Specifically,the toroidal spanwise vortices develop after impinging of the orifice outflow on the bottom wall of the bearing,and then stretch in the radial direction along the wall surface with growing size through rolling-up process,and the convected wall vortices quickly break into more sophisticated small eddies downstream and finally are dissipated due to air viscosity.This vortex shedding phenomenon can also be explained as a typical flow pattern of the impinging jet (Lee and Lee,2000),since the high speed orifice outflow impinges perpendicularly on the solid wall.3.2.Pressure depression and fluctuationAs shown in Fig.5,pressure depression (sudden descent and ascent)can be observed near the orifice outlet where the minimum pressure occurs in the vortex core.However,with the vortex shedding displayed in the LES result,more local pressure minima corresponding to vortex centers are induced,as shown in Fig.6(b).Similarly,the positions and the magnitudes of these pressure minima are transiently changing.Fig.7shows an instantaneous pressure distribution on the0246p / P 0r / r 2Fig.4.Pressure distribution along radial direction in the aerostatic bearing:comparison of results among LES,RANS and the existing experiment.Fig.5.Streamlines and pressure contours obtained from steady RANS simulation.J.Zhu et al./Journal of Fluids and Structures 40(2013)42–5146bottom wall (the recess region)of the bearing.It can be seen that the repeated pressure up-and-downs are present not only in the radial direction,but also in the circumferential direction.Fig.8plots pressure variations with time at three different locations (y ¼0.055mm,r ¼0.2,0.5,1.0mm),which are distributed along the radial direction in the bearing recess.Pressure fluctuation can be clearly seen in this figure,which also weakens along the radial direction.Table 1lists some statistical results of the area-weighted averaged pressure variation with time,where s ðp A Þcan represent the intensity of pressure fluctuation.In our simulations,when the intensities of inflow turbulence are respectively set as 1%,5%and 10%,the corresponding s ðp A Þare 62,65and 73,hence the influence of inflow turbulent level on pressure fluctuation is very small.In summary,associated with repeated shedding and downstream advection of vortices is repeated pressure depression (in space)and fluctuation (in time).It should be noted that this repeated pressure depression and fluctuation is not resolvable in RANS due to its essence of statistical averaging.It is manifest that LES results indicate unsteady flow characteristic in the aerostatic bearing even if initial and boundary conditions are all constant.4.DiscussionsAs is known,air supply pressure has a significant influence on the flow field in the aerostatic bearing.Therefore,air supply pressure values are varied in our numerical simulations.Fig.9shows the contours of instantaneous vorticity in the bearing recess when P s ¼2,3and 4atm.From this figure,the air flow is steady and remains in the laminar regime when the supply pressure is 2atm,while becomes unsteady and so vortex shedding is observed in the other two cases.Furthermore,associated with increasing air supply pressure,vorticity magnitude of the flow increases correspondingly.It suggests that the flow in the bearing recess has a transition from lamina to turbulence with increasing supply pressure.The correspondinglocal Reynolds number Re ¼_m=πr μat the recess entrance (r ¼r 0)in each case is calculated,as shown in Table 2.It can be inferred that the flow transition will appear when the local Reynolds number is beyond a certain critical valuebetweenFig.6.Iso-surfaces of instantaneous vorticity (a)and pressure (b).J.Zhu et al./Journal of Fluids and Structures 40(2013)42–51471000and 1500.Once beyond this critical Reynolds number,the air flow is turbulent and so results in pressure fluctuation.It can be observed from Fig.10that this pressure fluctuation becomes more severe as supply pressure increases.For comparison,the transient flow field of the non-recessed bearing (other dimensions being the same)is also calculated.Fig.11displays the instantaneous flow field obtained from LES,where the streamlines show that only one tiny vortex is present near the orifice outlet,and the flow is steady and no air vortex shedding appears.The absence of vortex shedding in the non-recessed bearing can also be explained by the smaller Reynolds number which confines the local flow in a laminarregime.Fig.7.Instantaneous pressure distribution on the bottom wall (the recess region)of the bearing.3.403.443.483.523.56p (P a )5Fig.8.Time 1.0mm).Fig.9.Contours of instantaneous vorticity under different supply pressure values.J.Zhu et al./Journal of Fluids and Structures 40(2013)42–5148-300-1500150300t (ms)f o n o i t a u t c u l F P A (P a )Fig.10.Pressure fluctuations with different supply pressurevalues.Fig.11.Instantaneous flow field of non-recessed bearing.Fig.12.Photo of experimental set-up.Table 2Local Reynolds number computed in different cases.Case Recess P s (atm)_m(kg/s)Re 1Yes 2 2.66Â10−66312Yes 3 6.39Â10−615163Yes 4 1.06Â10−525154No44.52Â10−61070J.Zhu et al./Journal of Fluids and Structures 40(2013)42–5149Vibration of the recessed bearing and the non-recessed bearing is also experimentally measured.Fig.12shows our experimental set-up.The two bearing pads have the same surface roughness.The tested bearing is placed on a marble base (with roughness less than 1μm),and air supply pressure can be regulated with a proportional throttle valve.External loads are applied on top of the aerostatic bearing.The parallelization of the bearing is assured by the displacement sensor (LVDT)which measures the bearing clearance height at three locations.Signals of the vibration acceleration of the aerostatic bearing are obtained by an accelerometer (PCB CA-YD-106),a data acquisition device (LMS SCADAS III),and a data analysis software platform (LMS Test Lab).The spectrum characteristics of bearing vibration acceleration are plotted in Fig.13.It can be seen that the amplitude of vibration acceleration increases with increasing air supply pressure,and the vibration of the non-recessed bearing (Fig.13(b))is much weaker than that of the recessed bearing (Fig.13(a)).Comparing our LES and experimental results,the qualitative behavior of pressure fluctuation is consistent with that of the bearing vibration when subjected to the different air supply pressure values.Although the vibration is also measured in the recessed bearing when P s ¼2atm,it may attribute to bearing surface roughness effect.Specially,compared with the results of the recessed bearing,the non-recessed bearing study clearly indicates that the vibration is relatively small when no pressure fluctuation is induced.Therefore,it can be concluded that vortex shedding results in remarkable pressure fluctuation and can induce small vibration of aerostatic bearings.5.ConclusionsThis paper is focused on the transient flow characteristics in ultra-precision aerostatic bearings.In order to capture turbulent structures and fluctuations,LES method is employed to numerically calculate the transient flow field in the bearing clearance.Vortex structures and pressure fluctuation in the bearing clearance are analyzed.Qualitative behavior of pressure fluctuation,as well as vibration of aerostatic bearing,is also discussed.If ever possible,however,the quantity analysis of the relationship between pressure fluctuation and small vibration of aerostatic bearings is needed in the future work.From the results in this paper,the following conclusions can be drawn:1.Vortex shedding is present in the aerostatic bearing recess for sufficiently large air supply pressure,i.e.,air vortices are repeatedly generated,shed,advected downstream and dissipated.2.Repeated pressure depression (in space)and fluctuation (in time)can be observed in the bearing clearance when vortex shedding occurs.3.Once the flow Reynolds number is beyond a certain value at the recess inlet,vortex shedding in the bearing clearance results in remarkable increase of pressure fluctuation and vibration of the aerostatic bearing.AcknowledgmentsThis study was supported by the National Basic Research and Development Program of China (No.2009CB724205)and the National Natural Science Foundation of China (Nos.51121002and51175196).Fig.13.Influence of air supply pressure on vibration acceleration of the aerostatic bearings in frequency domain.(a)Recessed bearing and (b)non-recessed bearing.J.Zhu et al./Journal of Fluids and Structures 40(2013)42–5150J.Zhu et al./Journal of Fluids and Structures40(2013)42–5151 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Aabort 异常中断, 中途失败, 夭折, 流产, 发育不全，中止计划[任务] accidentally 偶然地, 意外地accretion 增长activation energy 活化能active center 活性中心addition 增加adjacent 相邻的aerosol浮质(气体中的悬浮微粒,如烟,雾等), [化]气溶胶, 气雾剂, 烟雾剂Air flow circuits 气流循环ambient 周围的, 周围环境amines 胺amplitude 广阔, 丰富, 振幅, 物理学名词annular 环流的algebraic stress model(ASM) 代数应力模型algorithm 算法align 排列，使结盟, 使成一行alternately 轮流地analogy 模拟，效仿analytical solution 解析解anisotropic 各向异性的anthracite 无烟煤apparent 显然的, 外观上的，近似的approximation 近似arsenic 砷酸盐assembly 装配associate 联合，联系assume 假设assumption 假设atomization 雾化axial 轴向的Axisymmetry 轴对称的Adiabatic：绝热BBaffle 挡流板battlement 城垛式biography 经历bituminous coal 烟煤blow-off water 排污水blowing devices 鼓风(吹风)装置body force 体积力boiler plant 锅炉装置（车间）Boiling 沸腾Boltzmann 玻耳兹曼Bounded central differencing：有界中心差分格式Brownian rotation 布朗转动bulk 庞大的bulk density 堆积密度burner assembly 燃烧器组件burnout 燃尽Ccapability 性能，（实际）能力，容量，接受力carbon monoxide COCoflow：同向流动carbonate 碳酸盐carry-over loss 飞灰损失Cartesian 迪卡尔坐标的casing 箱，壳，套catalisis 催化channeled 有沟的，有缝的char 焦炭、炭circulation circuit 循环回路circumferential velocity 圆周速度clinkering 熔渣clipped 截尾的clipped Gaussian distribution 截尾高斯分布closure (模型的)封闭cloud of particles 颗粒云close proximity 距离很近cluster 颗粒团coal off-gas 煤的挥发气体coarse 粗糙的coarse grid 疏网格，粗网格Coatingcoaxial 同轴的coefficient of restitution 回弹系数；恢复系数coke 碳collision 碰撞competence 能力competing process 同时发生影响的competing-reactions submodel 平行反应子模型component 部分分量composition 成分computational expense 计算成本cone shape 圆锥体形状configuration 布置，构造confined flames 有界燃烧confirmation 证实, 确认, 批准Configuration 构造，外形conservation 守恒不灭conservation equation 守恒方程conserved scalars 守恒标量considerably 相当地consume 消耗contact angle 接触角contamination 污染contingency 偶然, 可能性, 意外事故, 可能发生的附带事件continuum 连续体Convection 对流converged 收敛的conveyer 输运机convolve 卷cooling duct 冷却管cooling wall 水冷壁coordinate transformation 坐标转换correlation 关联(式)correlation function 相关函数corrosion 腐蚀，锈coupling 联结, 接合, 耦合Cp：等压比热crack 裂缝，裂纹creep up （水）渗上来，蠕升critical 临界critically 精密地cross-correlation 互关联cumulative 累积的curtain wall 护墙，幕墙curve 曲线custom 习惯, 风俗, <动词单用>海关, (封建制度下)定期服劳役, 缴纳租税, 自定义, <偶用作>关税v.定制, 承接定做活的Cyan青色cyano 氰（基），深蓝，青色cyclone 旋风子，旋风，旋风筒cyclone separator 旋风分离器[除尘器]cylindrical 柱坐标的cylindrical coordinate 柱坐标Ddead zones 死区decompose 分解decouple 解藕的defy 使成为不可能Deforming：变形demography 统计Density：密度deposition 沉积derivative with respect to 对…的导数derivation 引出, 来历, 出处, (语言)语源, 词源design cycle 设计流程desposit 积灰，结垢deterministic approach 确定轨道模型deterministic 宿命的deviation 偏差devoid 缺乏Density：密度devolatilization 析出挥发分，液化作用diffusion 扩散diffusivity 扩散系数digonal 二角(的), 对角的，二维的dilute 稀的diminish 减少direct numerical simulation 直接数值模拟discharge 释放discrete 离散的discrete phase 分散相, 不连续相discretization [数]离散化deselect 取消选定dispersion 弥散dissector 扩流锥dissociate thermally 热分解dissociation 分裂dissipation 消散, 分散, 挥霍, 浪费, 消遣, 放荡, 狂饮distribution of air 布风divide 除以dot line 虚线drag coefficient 牵引系数，阻力系数drag and drop 拖放drag force 曳力drift velocity 漂移速度driving force 驱[传, 主]动力droplet 液滴drum 锅筒dry-bottom-furnace 固态排渣炉dry-bottom 冷灰斗，固态排渣duct 管dump 渣坑dust-air mixture 一次风EEBU---Eddy break up 漩涡破碎模型eddy 涡旋effluent 废气，流出物elastic 弹性的electro-staic precipitators 静电除尘器emanate 散发, 发出, 发源，[罕]发散, 放射embrasure 喷口，枪眼emissivity [物]发射率empirical 经验的endothermic reaction 吸热反应enhance 增，涨enlarge 扩大ensemble 组，群，全体enthalpy 焓entity 实体entrain 携带，夹带entrained-bed 携带床Equation 方程equilibrate 保持平衡equilibrium 化学平衡ESCIMO-----Engulfment（卷吞）Stretching（拉伸）Coherence（粘附）Interdiffusion-interaction（相互扩散和化学反应）Moving-observer（运动观察者）exhaust 用尽, 耗尽, 抽完, 使精疲力尽排气排气装置用不完的, 不会枯竭的exit 出口，排气管exothermic reaction 放热反应expenditure 支出，经费expertise 经验explicitly 明白地, 明确地extinction 熄灭的extract 抽出，提取evaluation 评价，估计，赋值evaporation 蒸发(作用)Eulerian approach 欧拉法Ffacilitate 推动，促进factor 把…分解fast chemistry 快速化学反应fate 天数, 命运, 运气，注定, 送命，最终结果feasible 可行的，可能的feed pump 给水泵feedstock 填料Filling 倒水fine grid 密网格，细网格finite difference approximation 有限差分法flamelet 小火焰单元flame stability 火焰稳定性flow pattern 流型fluctuating velocity 脉动速度fluctuation 脉动，波动flue 烟道（气）flue duck 烟道fluoride 氟化物fold 夹层块forced-and-induced draft fan 鼓引风机forestall 防止Formulation:公式，函数fouling 沾污fraction 碎片部分，百分比fragmentation 破碎fuel-lean flamefuel-rich regions 富燃料区，浓燃料区fuse 熔化，熔融Ggas duct 烟道gas-tight 烟气密封gasification 气化(作用)gasifier 气化器Gauge 厚度，直径，测量仪表，估测。

流体力学相关中英文词汇对照表

流体力学相关中英文词汇对照表流体动力学名词英语叫法流体动力学fluiddynamics连续介质力学mechanicsofcontinuousmedia介质medium流体质点fluidparticle无粘性流体nonviscousfluid,inviscidfluid连续介质假设continuousmediumhypothesis流体运动学fluidkinematics水静力学hydrostatics液体静力学hydrostatics支配方程governingequation伯努利方程Bernoulliequation伯努利定理Bernonllitheorem毕奥-萨伐尔定律Biot-Savartlaw欧拉方程Eulerequation亥姆霍兹定理Helmholtztheorem开尔文定理Kelvintheorem涡片vortexsheet库塔-茹可夫斯基条件Kutta-Zhoukowskicondition 布拉休斯解Blasiussolution达朗贝尔佯廖d'Alembertparadox雷诺数Reynoldsnumber施特鲁哈尔数Strouhalnumber随体导数materialderivative不可压缩流体incompressiblefluid质量守恒conservationofmass动量守恒conservationofmomentum能量守恒conservationofenergy动量方程momentumequation能量方程energyequation控制体积controlvolume液体静压hydrostaticpressure涡量拟能enstrophy压差differentialpressure流[动]flow流线streamline流面streamsurface流管streamtube迹线path,pathline流场flowfield流态flowregime流动参量flowparameter流量flowrate,flowdischarge 涡旋vortex涡量vorticity涡丝vortexfilament涡线vortexline涡面vortexsurface涡层vortexlayer涡环vortexring涡对vortexpair涡管vortextube涡街vortexstreet卡门涡街Karmanvortexstreet 马蹄涡horseshoevortex对流涡胞convectivecell卷筒涡胞rollcell涡eddy涡粘性eddyviscosity环流circulation环量circulation速度环量velocitycirculation 偶极子doublet,dipole驻点stagnationpoint总压[力]totalpressure总压头totalhead静压头statichead总焓totalenthalpy能量输运energytransport速度剖面velocityprofile库埃特流Couetteflow单相流singlephaseflow单组份流single-componentflow 均匀流uniformflow非均匀流nonuniformflow二维流two-dimensionalflow三维流three-dimensionalflow准定常流quasi-steadyflow非定常流unsteadyflow,non-steadyflow 暂态流transientflow周期流periodicflow振荡流oscillatoryflow分层流stratifiedflow无旋流irrotationalflow有旋流rotationalflow轴对称流axisymmetricflow不可压缩性incompressibility不可压缩流[动]incompressibleflow浮体floatingbody定倾中心metacenter阻力drag,resistance减阻dragreduction表面力surfaceforce表面张力surfacetension毛细[管]作用capillarity来流incomingflow自由流freestream自由流线freestreamline外流externalflow进口entrance,inlet出口exit,outlet扰动disturbance,perturbation分布distribution传播propagation色散dispersion弥散dispersion附加质量addedmass,associatedmass 收缩contraction镜象法imagemethod无量纲参数dimensionlessparameter 几何相似geometricsimilarity运动相似kinematicsimilarity动力相似[性]dynamicsimilarity平面流planeflow势potential势流potentialflow速度势velocitypotential复势complexpotential复速度complexvelocity流函数streamfunction源source汇sink速度[水]头velocityhead拐角流cornerflow空泡流cavityflow超空泡supercavity超空泡流supercavityflow空气动力学aerodynamics低速空气动力学low-speedaerodynamics 高速空气动力学high-speedaerodynamics 气动热力学aerothermodynamics亚声速流[动]subsonicflow跨声速流[动]transonicflow超声速流[动]supersonicflow锥形流conicalflow楔流wedgeflow叶栅流cascadeflow非平衡流[动]non-equilibriumflow 细长体slenderbody细长度slenderness钝头体bluffbody钝体bluntbody翼型airfoil翼弦chord薄翼理论thin-airfoiltheory构型configuration后缘trailingedge迎角angleofattack失速stall脱体激波detachedshockwave波阻wavedrag诱导阻力induceddrag诱导速度inducedvelocity临界雷诺数criticalReynoldsnumber 前缘涡leadingedgevortex附着涡boundvortex约束涡confinedvortex气动中心aerodynamiccenter气动力aerodynamicforce气动噪声aerodynamicnoise气动加热aerodynamicheating离解dissociation地面效应groundeffect气体动力学gasdynamics稀疏波rarefactionwave热状态方程thermalequationofstate 喷管Nozzle普朗特-迈耶流Prandtl-Meyerflow 瑞利流Rayleighflow可压缩流[动]compressibleflow可压缩流体compressiblefluid绝热流adiabaticflow非绝热流diabaticflow未扰动流undisturbedflow等熵流isentropicflow匀熵流homoentropicflow兰金-于戈尼奥条件Rankine-Hugoniotcondition 状态方程equationofstate量热状态方程caloricequationofstate完全气体perfectgas拉瓦尔喷管Lavalnozzle马赫角Machangle马赫锥Machcone马赫线Machline马赫数Machnumber马赫波Machwave当地马赫数localMachnumber冲击波shockwave激波shockwave正激波normalshockwave斜激波obliqueshockwave头波bowwave附体激波attachedshockwave 激波阵面shockfront激波层shocklayer压缩波compressionwave反射reflection折射refraction散射scattering衍射diffraction绕射diffraction出口压力exitpressure超压[强]overpressure反压backpressure爆炸explosion爆轰detonation缓燃deflagration水动力学hydrodynamics液体动力学hydrodynamics泰勒不稳定性Taylorinstability 盖斯特纳波Gerstnerwave斯托克斯波Stokeswave瑞利数Rayleighnumber自由面freesurface波速wavespeed,wavevelocity波高waveheight波列wavetrain波群wavegroup波能waveenergy表面波surfacewave表面张力波capillarywave规则波regularwave不规则波irregularwave浅水波shallowwaterwave深水波deepwaterwave重力波gravitywave椭圆余弦波cnoidalwave潮波tidalwave涌波surgewave破碎波breakingwave船波shipwave非线性波nonlinearwave孤立子soliton水动[力]噪声hydrodynamicnoise 水击waterhammer空化cavitation空化数cavitationnumber空蚀cavitationdamage超空化流supercavitatingflow水翼hydrofoil水力学hydraulics洪水波floodwave涟漪ripple消能energydissipation海洋水动力学marinehydrodynamics 谢齐公式Chezyformula欧拉数Eulernumber弗劳德数Froudenumber水力半径hydraulicradius 水力坡度hvdraulicslope高度水头elevatinghead水头损失headloss水位waterlevel水跃hydraulicjump含水层aquifer排水drainage排放量discharge壅水曲线backwatercurve压[强水]头pressurehead过水断面flowcross-section 明槽流openchannelflow孔流orificeflow无压流freesurfaceflow有压流pressureflow缓流subcriticalflow急流supercriticalflow渐变流graduallyvariedflow急变流rapidlyvariedflow临界流criticalflow异重流densitycurrent,gravityflow堰流weirflow掺气流aeratedflow含沙流sediment-ladenstream降水曲线dropdowncurve沉积物sediment,deposit沉[降堆]积sedimentation,deposition沉降速度settlingvelocity流动稳定性flowstability不稳定性instability奥尔-索末菲方程Orr-Sommerfeldequation 涡量方程vorticityequation泊肃叶流Poiseuilleflow奥辛流Oseenflow剪切流shearflow粘性流[动]viscousflow层流laminarflow分离流separatedflow二次流secondaryflow近场流nearfieldflow远场流farfieldflow滞止流stagnationflow尾流wake[flow]回流backflow反流reverseflow射流jet自由射流freejet管流pipeflow,tubeflow内流internalflow拟序结构coherentstructure 猝发过程burstingprocess表观粘度apparentviscosity 运动粘性kinematicviscosity 动力粘性dynamicviscosity泊poise厘泊centipoise厘沱centistoke剪切层shearlayer次层sublayer流动分离flowseparation层流分离laminarseparation 湍流分离turbulentseparation 分离点separationpoint附着点attachmentpoint再附reattachment再层流化relaminarization起动涡startingvortex驻涡standingvortex涡旋破碎vortexbreakdown涡旋脱落vortexshedding压[力]降pressuredrop压差阻力pressuredrag压力能pressureenergy型阻profiledrag滑移速度slipvelocity无滑移条件non-slipcondition壁剪应力skinfriction,frictionaldrag壁剪切速度frictionvelocity磨擦损失frictionloss磨擦因子frictionfactor耗散dissipation滞后lag相似性解similarsolution局域相似localsimilarity气体润滑gaslubrication液体动力润滑hydrodynamiclubrication浆体slurry泰勒数Taylornumber纳维-斯托克斯方程Navier-Stokesequation 牛顿流体Newtonianfluid边界层理论boundarylatertheory边界层方程boundarylayerequation边界层boundarylayer附面层boundarylayer层流边界层laminarboundarylayer湍流边界层turbulentboundarylayer 温度边界层thermalboundarylayer边界层转捩boundarylayertransition 边界层分离boundarylayerseparation 边界层厚度boundarylayerthickness 位移厚度displacementthickness动量厚度momentumthickness能量厚度energythickness焓厚度enthalpythickness注入injection吸出suction泰勒涡Taylorvortex速度亏损律velocitydefectlaw形状因子shapefactor测速法anemometry粘度测定法visco[si]metry流动显示flowvisualization油烟显示oilsmokevisualization 孔板流量计orificemeter频率响应frequencyresponse油膜显示oilfilmvisualization阴影法shadowmethod纹影法schlierenmethod烟丝法smokewiremethod丝线法tuftmethod氢泡法nydrogenbubblemethod相似理论similaritytheory相似律similaritylaw部分相似partialsimilarity定理pitheorem,Buckinghamtheorem 静[态]校准staticcalibration动态校准dynamiccalibration风洞windtunnel激波管shocktube激波管风洞shocktubewindtunnel水洞watertunnel拖曳水池towingtank旋臂水池rotatingarmbasin扩散段diffuser测压孔pressuretap皮托管pitottube普雷斯顿管prestontube斯坦顿管Stantontube文丘里管VenturitubeU形管U-tube压强计manometer微压计micromanometer多管压强计multiplemanometer静压管static[pressure]tube流速计anemometer风速管Pitot-statictube激光多普勒测速计laserDoppleranemometer, laserDopplervelocimeter热线流速计hot-wireanemometer热膜流速计hot-filmanemometer流量计flowmeter粘度计visco[si]meter涡量计vorticitymeter传感器transducer,sensor压强传感器pressuretransducer 热敏电阻thermistor示踪物tracer时间线timeline脉线streakline尺度效应scaleeffect壁效应walleffect堵塞blockage堵寒效应blockageeffect动态响应dynamicresponse响应频率responsefrequency底压basepressure菲克定律Ficklaw巴塞特力Bassetforce埃克特数Eckertnumber格拉斯霍夫数Grashofnumber努塞特数Nusseltnumber普朗特数prandtlnumber雷诺比拟Reynoldsanalogy施密特数schmidtnumber斯坦顿数Stantonnumber对流convection自由对流naturalconvection,freeconvec-tion 强迫对流forcedconvection热对流heatconvection质量传递masstransfer传质系数masstransfercoefficient热量传递heattransfer传热系数heattransfercoefficient对流传热convectiveheattransfer辐射传热radiativeheattransfer动量交换momentumtransfer能量传递energytransfer传导conduction热传导conductiveheattransfer热交换heatexchange临界热通量criticalheatflux浓度concentration扩散diffusion扩散性diffusivity扩散率diffusivity扩散速度diffusionvelocity分子扩散moleculardiffusion沸腾boiling蒸发evaporation气化gasification凝结condensation成核nucleation计算流体力学computationalfluidmechanics多重尺度问题multiplescaleproblem伯格斯方程Burgersequation对流扩散方程convectiondiffusionequationKDU方程KDVequation 修正微分方程modifieddifferentialequation拉克斯等价定理Laxequivalencetheorem数值模拟numericalsimulation大涡模拟largeeddysimulation数值粘性numericalviscosity非线性不稳定性nonlinearinstability希尔特稳定性分析Hirtstabilityanalysis相容条件consistencyconditionCFL条件Courant-Friedrichs-Lewycondition,CFLcondition狄里克雷边界条件Dirichletboundarycondition熵条件entropycondition远场边界条件farfieldboundarycondition流入边界条件inflowboundarycondition无反射边界条件nonreflectingboundarycondition数值边界条件numericalboundarycondition流出边界条件outflowboundarycondition冯.诺伊曼条件vonNeumanncondition近似因子分解法approximatefactorizationmethod人工压缩artificialcompression人工粘性artificialviscosity边界元法boundaryelementmethod配置方法collocationmethod能量法energymethod有限体积法finitevolumemethod流体网格法fluidincellmethod,FLICmethod通量校正传输法flux-correctedtransportmethod 通量矢量分解法fluxvectorsplittingmethod伽辽金法Galerkinmethod积分方法integralmethod标记网格法markerandcellmethod,MACmethod特征线法methodofcharacteristics直线法methodoflines矩量法momentmethod多重网格法multi-gridmethod板块法panelmethod质点网格法particleincellmethod,PICmethod质点法particlemethod预估校正法predictor-correctormethod投影法projectionmethod准谱法pseudo-spectralmethod随机选取法randomchoicemethod激波捕捉法shock-capturingmethod激波拟合法shock-fittingmethod谱方法spectralmethod稀疏矩阵分解法splitcoefficientmatrixmethod不定常法time-dependentmethod时间分步法timesplittingmethod变分法variationalmethod涡方法vortexmethod隐格式implicitscheme显格式explicitscheme交替方向隐格式alternatingdirectionimplicitscheme,ADIscheme 反扩散差分格式anti-diffusiondifferencescheme紧差分格式compactdifferencescheme守恒差分格式conservationdifferencescheme克兰克-尼科尔森格式Crank-Nicolsonscheme杜福特-弗兰克尔格式Dufort-Frankelscheme指数格式exponentialscheme戈本诺夫格式Godunovscheme高分辨率格式highresolutionscheme拉克斯-温德罗夫格式Lax-Wendroffscheme蛙跳格式leap-frogscheme单调差分格式monotonedifferencescheme保单调差分格式monotonicitypreservingdiffe-rencescheme 穆曼-科尔格式Murman-Colescheme半隐格式semi-implicitscheme斜迎风格式skew-upstreamscheme全变差下降格式totalvariationdecreasingschemeTVDscheme 迎风格式upstreamscheme,upwindscheme计算区域computationaldomain物理区域physicaldomain影响域domainofinfluence依赖域domainofdependence区域分解domaindecomposition维数分解dimensionalsplit物理解physicalsolution弱解weaksolution黎曼解算子Riemannsolver守恒型conservationform弱守恒型weakconservationform强守恒型strongconservationform散度型divergenceform贴体曲线坐标body-fittedcurvilinearcoordi-nates [自]适应网格[self-]adaptivemesh适应网格生成adaptivegridgeneration自动网格生成automaticgridgeneration数值网格生成numericalgridgeneration交错网格staggeredmesh网格雷诺数cellReynoldsnumber数植扩散numericaldiffusion数值耗散numericaldissipation数值色散numericaldispersion数值通量numericalflux放大因子amplificationfactor放大矩阵amplificationmatrix阻尼误差dampingerror离散涡discretevortex熵通量entropyflux熵函数entropyfunction分步法fractionalstepmethod。

离心泵全三维流场的大涡数值模拟

鉴于此发现 ,将叶轮各通道所通过的流量值计算出并示于图 6中. 由图 6可见 ,最高流量值 (通道 1)与最低流量值 (通道 3)相差几倍. 上述现象的原因是因为通道 2～5 与泵壳壁面相距较近且离泵出口较远 ,叶轮出流被泵壳壁面堵塞使过流量减少. 相反 ,与泵壳壁面相距较远或离泵出口较近的通道 ,流量及流速就比较高.
离心泵在农业及民用等许多部门中有着广泛的应用. 实现离心泵的流动数值模拟 ,对于泵的优化设计以达到增效节能的目的具有重要的现实意义. 离心泵系统一般导入管、叶轮及泵壳等元件. 随着近年流体力学计算技术的迅速发展 ,离心泵的三维数值模拟已成为现实. 但离心泵湍流模拟多见于 κ2ε等双方程湍流模型的使用 [ 128 ]. 大涡模拟技术 (LES)是近年来才发展起来的湍流模型 ,它对流动中的较大尺度旋涡进行 Navier2Stokes (N 2S) 方程直接计算 (DNS ) , 对较小尺度旋涡进行平均近似处理 (RANS). 研究表明大涡模拟要优于通常的 κ2ε湍流模型 ,它不仅能够像 κ2ε模型那样计算出流动的时均规律 ,而且能够较准确地描述流动中的不对称特性. 受计算机硬件的限制 ,以往大涡模拟常见于简单几何体内的三维湍流计算中 ,近年来一些研究者尝试使用大涡模拟以较稀疏的计算网格应用于工程计算中 [9210 ]. 为此本文选取一低比转速 ( ns = 45)离心泵作为研究对象 ,以流动软件 FLUENT为工具 ,使用大涡模拟湍流模型对包括导入管、叶轮及泵壳在内的全流场进行设计工况下的三维计算.
L s —网格的混合长度 , m;
ns —离心泵比转速 ;
114
华南理工大学学报 (自然科学版 )

Large eddy simulation of flow around the Ahmed body

Large eddy simulation ofﬂow around the Ahmed bodyC.Hinterberger,M.Garc´ıa-Villalba,and W.RodiInstitute for Hydromechanics,University of Karlsruhe,Kaiserstrasse12,76128Karlsruhe,Germany1IntroductionThe automotive industry has a high demand for reliable simulation meth-ods capable of tackling the complex turbulent airﬂow around vehicles.The Ahmed reference model is a generic car-type bluﬀbody with a slant back.It is frequently used as a benchmark test case for this kind ofﬂow.In spite of the relatively simple geometry of the Ahmed body,theﬂow around it retains some main features of theﬂow around real cars.The Ahmed body,Fig.1,wasﬁrst deﬁned and its characteristics described in the experimental work of Ahmed et al[1].Therein,it is shown that most of the drag of the body is due to pressure drag,which is generated at the rear end.The structure of the wake is very complex,with a separation zone and counter-rotating vortices coming oﬀthe slant side edges,whose strength is mainly determined by the base slant angle.The maximum drag was found for a critical slant angle of30˚.Above this angle a sudden drop in drag occurs which corresponds to a change in the wake structure.Below this angle,strong counter-rotating vortices are present and theﬂow separates in the middle region of the top edge and reattaches at the sloping surface.For angles above the critical angle,the counter-rotating vortices are weaker,the separation occurs along the entire top and the side edges and there is no reattachment.More recently,Lienhart et al[2]performed more detailed experiments on the same body,albeit at a somewhat lower velocity.They measured the mean andﬂuctuating velocities by LDA and obtained surface oil-ﬂow pictures for two rear vehicle body slant angles(ϕ=25˚andϕ=35˚),i.e.just below and above the critical angle.Their results show the diﬀerences inﬂow behaviour for the two angles considered.In recent years,there have been several computational studies of thisﬂow. Han[3]and Gilli´e ron and Chometon[4]using the RANS approach obtained qualitatively good results in terms ofﬂow structures but they do not show velocity proﬁle comparisons.In two recent workshops[5,6]theﬂow around the Ahmed body was a test case and the results presented there have shown2 C.Hinterberger,M.Garc´ıa-Villalba,and W.Rodithat it is diﬃcult with classical RANS methods to obtain accurate predictions of mean velocitiy and turbulence intensitiy proﬁles for thisﬂow.With other approaches the results have been similar,for example,Kapadia et al[7]using DES(Detached Eddy Simulation).Finally,there is a Large Eddy Simulation reported in the literature,[8],however theﬂow conditions were diﬀerent(no ground was present)so that these results are not directly comparable with the experiments.In this paper we present two Large Eddy Simulations of theﬁrst conﬁg-uration(25˚)of the experiment of Lienhart et al[2],while the work for the second conﬁguration(35˚)is in progress.The outline of the paper is as follows.In section2the simulation details will be presented,the computational setup will be discussed and the grids will be described.In section3.1,some quantitave results will be presented,in terms of mean velocity and turbulent intensity proﬁles.Flow visualisation and turbulent coherent structures will be discussed in section3.2.Finally,some conclusions will be made in section4.Fig.1.Ahmed model.Dimensions are in mm2The simulated conﬁgurationThe present conﬁguration has been speciﬁcally chosen to match the experi-ment of Lienhart et al[2].The Ahmed body,whose shape and dimensions are shown in Fig.1,was mounted in a3/4open test section(ﬂoor,but no side walls or ceiling).The bulk velocity was40m/s.This results in a Reynolds number Re=2.8×106(based on the length of the body L=1.044m), which is of the same order of magnitude but somewhat lower as the one in the original experiment of Ahmed et al[1](Re=4.3×106).Large eddy simulation ofﬂow around the Ahmed body3 2.1Numerical methodThe simulations were performed with the Finite Volume Code LESOCC2 (Large Eddy Simulation On Curvilinear Coordinates)which is an enhanced fully-parallelized version of the code LESOCC[9],developed at the Institute for Hydromechanics.It solves the incompressible3D time-dependentﬁltered Navier-Stokes equations on body-ﬁtted curvilinear block-structured grids us-ing second order central diﬀerences for the discretisation of the convective and viscousﬂuxes.Time advancement is accomplished by an explicit,low-storage Runge-Kutta method.Conservation of mass is achieved by the SIMPLE algo-rithm,with the pressure-correction equation being solved by the SIP proce-dure.The momentum-interpolation method of Rhie and Chow[10]is employed to prevent pressure-velocity decoupling and associated oscillations.2.2Computational setupTheﬂow around the Ahmed body was a test case in two recent workshops [5,6],the computational domain was deﬁned in them.The domain extends to ﬁve body lengths behind the body to ensure that the outﬂow condition does not aﬀect the near-body wake.The inﬂow plane is placed at a distance of1.3 body lengths upstream of the body.This distance corresponds roughly to5 body heights where blocking eﬀects dissapear.At the inﬂow section a uniform axial velocity proﬁle is imposed.The width of1.87m(5body widths)and the height of1.4m(5body heights)are taken analogous to the experiments. At both side boundaries and at the top boundary,free-slip conditions are applied.At the outﬂow of the domain,a convective boundary condition for the velocities is used.Finally,wall functions are used because of the high Reynolds number which does not allow aﬁne resolution of the near wallﬂow down to the viscous sub-layer.The wall function is similar to the Werner-Wengle [11]approach but assuming an instantaneous logarithmic proﬁle instead of a power law proﬁle.It is applied at the walls of the vehicle and at the bottom of the channel.In order to account for the unresolved subgrid-scale motions, the Smagorinsky subgrid-scale model is employed with a model constant ofC s=0.13.2.3GridsIn this paper we present simulations of theﬂow around the25˚slant-back Ahmed body performed with two grids.They have been generated with the commercial software ICEM-CFD.Grid1consist of93blocks and8.8106 cells.Grid2consist of214blocks and18.5106cells.Both grids have an O-grid structure around the body,which is necessary due to the round body front.This allows for grid reﬁnement in the wall-normal direction near the body boundaries.The outer block structure of Grid1is orthogonal,Fig2(a). In order to get a concentration of grid points close to the body in spanwise4 C.Hinterberger,M.Garc´ıa-Villalba,and W.Rodiand streamwise direction,an outer O-grid structure was chosen in Grid2,Fig 2(b).In addition,Grid2includes more reﬁnement in the region of the slant back,especially close to the top and side edges,Fig2(c-h).For both grids, the near-wall cell centre has a wall distance on average of about40wall units (∆y P+),but it varies from approximately10in the separated regions along the slant back to150close to the top rear edge.The spanwise and streamwise extent of the grid cells is up to a factor of10larger for Grid2,except in the reﬁnement regions close to the edges.For Grid1this factor is even larger.This means that the boundary layer at the body surface is highly underresolved.Sketches of the block structure.(c-h)Slices in diﬀerent planes showing the grid point distribution in the body region.(c,d)Cut in xz-plane.(e,f)Cut in xy-plane. (g,h)Cut in yz-plane.Large eddy simulation ofﬂow around the Ahmed body5 3Results3.1Time averaged proﬁlesFor the front part,mean streamwise velocity proﬁles in the symmetry plane are compared with the experiment in Fig.3.It can be seen that theﬂow upstream of the body and in the free stream above it is properly represented in the simulation.This is because in this region the level of turbulence is so low that theﬂow is nearly potentialﬂow.Fig.3.Mean streamwise velocity proﬁles in the symmetry plane In Figures4and5,the mean streamwise velocity proﬁles and root mean square velocityﬂuctuations are compared with the experimental results in the rear body part and the near wake(in the symmetry plane).The general agreement with the experiment is reasonably good taking into account that neither grid isﬁne enough to resolve adequately the boundary layer develop-ing on the body up to the slant back.However there are some discrepancies between the computations and the experiment mainly concerning the velocity proﬁles on the slant back.In the experiment,theﬂow separates right at the corner of the sloping surface and it reattaches in the middle of the surface. In the simulation,theﬂowﬁrst stays attached before it separates somewhat downstream of the corner and no reattachment occurs on the slant back.This is most likely due to the poor resolution of both grids near the wall leading to an incorrect prediction of the approaching boundary layer.The main diﬀerences between the results of the two simulations are found at the beginning of the sloping surface.There,Grid2is muchﬁner than Grid 1,and it can be seen that the turbulence intensities are very close to the6 C.Hinterberger,M.Garc´ıa-Villalba,and W.RodiFig.4.Mean streamwise velocity proﬁles in the rear body and near wake(symmetry plane)experimental ones for Grid2while they are too low for Grid1,Fig.5.In addition,the prediction of the separation point is closer to the experiment in the simulation performed with theﬁner grid,in which theﬂow separates earlier,Fig.4.The complex unsteadyﬂow on the slant back leads to highﬂuctuation intensities which are very diﬃcult to predict.In fact,no RANS method has succeeded in predicting the high values observed in the experiments[5,6] while the present LES calculations(Fig.5)have.Figure6shows the mean velocity vectors in the symmetry plane,Fig. 6(a-b),and in three transverse yz-planes,Fig.6(c-h).The streamwise loca-tion of these transverse planes is indicated in Fig.6(a)by dashed lines.The colour of the vectors corresponds to turbulent kinetic energy.From the com-parison of the experiment,Figs.6(a,c,e,g)on the left,with the simulation, Figs.6(b,d,f,h)on the right,it is clear that the mainﬂow structures are well captured in the simulation.The size and the extent of the recirculation zone behind the body are well predicted,Fig.6(b).The development of the counter-rotating vortices,which can be seen from the secondaryﬂow vectors in theLarge eddy simulation ofﬂow around the Ahmed body7Fig.5.Root mean square streamwise velocityﬂuctuations in the rear body and near wake(symmetry plane)y−z planes,is also in close agreement with the experiment.In Fig.6(d),it can be seen that these vortices develope half-way down the slant back,they grow while they approach the end of the body,Fig.6(f),and they are strong and fully developed in the near wake,Fig.6(h).The level of turbulence obtained in the simulation is also in good agreement with the experiment,as can be seen from the coloured regions in Figure6.3.2Flow visualisation andﬂow structuresThe calculation results show complex time-dependentﬂow features in the wake region.In Fig.7,two typical instantaneous velocityﬁelds in the symmetry plane are shown.As discussed in section3.1,the prediction of theﬂow on the sloping surface is very diﬃcult.Thus,in Fig.7on the left,an instantaneous ﬁeld is captured in which theﬂow tends to reattach on the slant back.However, in Fig.7on the right,theﬂow in that zone is completely separated.Note that in the experiment theﬂow reattaches(at least in the mean).The unsteadiness of the near body-wake is clearly well captured.Theﬂow between the body and8 C.Hinterberger,M.Garc´ıa-Villalba,and W.RodiFig.6.Mean velocity vectors coloured by turbulent kinetic energy.(a,b)symmetry plane y=0mm.(c,d)Close to the middle of the slant back x=−88mm.(e,f)End of the body x=0mm.(g,h)Near-body wake x=200mm.(a,c,e,g)Experiment. (b,d,f,h)Simulation performed with Grid2.Large eddy simulation ofﬂow around the Ahmed body9 the ground plate has a rather strong inﬂuence on the shape of the recirculation zone.Fig.7.Instantaneous streamwise velocityﬁelds in the symmetry planeIn order to illustrate the presence of large-scale vortices in the recirculation zone,Fig.8shows the isosurfaces of pressureﬂuctuations p for three sequen-tial instants in time.The main part gives a perspective view while the three pictures on the left give the side view,top view and view from the back re-spectively.It can be seen that large spanwise vortex tubes are generated near the leading edge of the slanted face,which grow and roll down the surface. Furthermore,vortex tubes that wrap the counter-rotating vortices coming oﬀthe slant side edges can be detected.The sequential pictures show that these vortex tubes form helical structures as they move downstream.3.3Work in progressPreliminary simulations have been performed for the second case(ϕ=35˚)of the experiment of Lienhart et al[2].Theﬁrst results are not very satisfactory. In that case,theﬂow separates along the top and side edges and the counter-rotating vortices are weaker.In the preliminary simulations,this behaviour is not well captured.Furthermore,the drag coeﬃcient for this case is not well-predicted.The experiment of Ahmed et al[1]has shown that above a slant back angle of30˚,there is a drop in the drag coeﬃcient.While in the simulation for the25˚case the prediction of the drag was good,in the preliminary simulations for the35˚case,the drop in the drag does not take place,and the drag coeﬃcient is highly over-predicted.This may be due to the poor resolution of the near wall regions but further investigation is required. 4ConclusionsA Large Eddy Simulation of theﬂow around the Ahmed body with a slant-back angle of25˚was performed.Theﬂow around the Ahmed body is a very10 C.Hinterberger,M.Garc´ıa-Villalba,and W.RodiFig.8.Isosurface of pressureﬂuctuationsLarge eddy simulation ofﬂow around the Ahmed body11 challenging problem because of the complex geometry and the high Reynolds number.The results obtained by the simulation are promising;the comparison with the experiments shows that theﬂow structures are well captured.The agreement of the time-averaged quantities is good although some discrepancies are present,especially in the lower part of the slant back.The results also show that this is a good test case for further development.The calculations for the conﬁguration with a slant angle of35˚are in progress.Improvements of the method(subgrid-scale model,discretisation,wall modelling,etc)are required to obtain good results for the35˚case.AcknowledgmentsThis work was funded through the EU TMR-project”LES of Complex Flows”. The calculations were carried out on the IBM RS/6000SP-SMP high perfor-mance computer of the University of Karlsruhe,and the assistance of Mr. Gernert is gratefully acknowledged.The authors are also grateful to Dr.J. Fr¨o hlich for many helpful discussions.References1.S.R.Ahmed,G.Ramm,and G.Faltin.Some salient features of the time averagedground vehicle wake.SAE paper no.840300,1984.2.H.Lienhart,C.Stoots,and S.Becker.Flow and turbulence structures in thewake of a simpliﬁed car model(Ahmed model).In DGLR Fach Symp.der AG STAB,2000.putational analysis of three-dimensional turbulentﬂow around abluﬀbody in ground proximity.AIAA Journal,27:1213–1219,1989.4.P.Gilli´e ron and F.Chometon.Modelling of stationary three-dimensional sepa-rated airﬂows around an Ahmed reference model.In ESAIM proc.,volume7, pages173–182,1999.5.S.Jakirli´c,R.Jester-Z¨u rker,and C.Tropea,editors.Proceedings of9th ER-COFTAC IAHR COST Workshop on reﬁned turbulence modelling,2001.6.R.Manceau and J.P.Bonnet,editors.Proceedings of10th ERCOFTAC IAHRQNET-CFD Workshop on reﬁned turbulence modelling,2002.7.S.Kapadia,S.Roy,and K.Wurtzler.Detached eddy simulation over a referenceAhmed car model.AIAA paper no.2003-0857,2003.8.R.J.A.Howard and rge eddy simulation of an Ahmed referencemodel.Journal of Turbulence,3,2002.9.M.Breuer and rge eddy simulation of complex turbulentﬂows ofpractical interest.In E.H.Hirschel,editor,Flow simulation with high perfor-mance computers II,volume52of Notes on Numerical Fluid Mechanics,pages 258–274.Vieweg,Braunschweig,1996.10. C.M.Rhie and W.L.Chow.Numerical study of the turbulentﬂow past an airfoilwith trailing edge separation.AIAA Journal,21(11):1061–1068,1983.11.H.Werner and rge-eddy simulation of turbulentﬂow over andaround a cube in a plate channel.In8th Symp.on Turb.Shear Flows,1993.。

大涡模拟计算二维问题

大涡模拟计算二维问题在流体力学中，大涡模拟（Large Eddy Simulation，简称LES）是一种用于模拟流体中湍流现象的计算方法。

它能够更准确地捕捉湍流的涡旋结构和运动特性，从而提供更准确的流场预测。

大涡模拟计算在二维问题中也得到了广泛应用。

二维问题指的是流场变量只与空间的两个维度有关，而与时间无关。

这种情况下，大涡模拟计算方法可以通过对湍流流场进行二维数值模拟，来研究流体中的湍流现象。

在进行大涡模拟计算二维问题时，首先需要设定合适的初始条件和边界条件。

初始条件指定了流场在计算开始时的状态，而边界条件则规定了流体在计算区域的边界上的行为。

这两个条件的设置对计算结果的准确性和可靠性至关重要。

采用数值方法对流场进行离散化处理，将连续的流体运动转化为离散的数值计算。

常用的数值方法包括有限差分法、有限元法和谱方法等。

这些方法能够将流场分割成网格，并对网格上的流体守恒方程进行离散化。

在大涡模拟计算中，通过使用合适的模型来模拟湍流的能量传递和涡旋的产生与衰减过程。

常用的模型有壁面函数、雷诺平均模型等。

这些模型考虑了湍流的统计性质，以及湍流在不同尺度上的特点。

通过迭代求解离散化后的流体守恒方程，得到二维湍流的数值解。

这个数值解可以提供流场中湍流的各种特性，如湍流的动能、湍流的涡旋结构等。

总结而言，大涡模拟计算二维问题是一种用于模拟流体中湍流现象的计算方法，通过对流场进行离散化处理和采用合适的模型来模拟湍流的特性。

它在研究流体力学中的湍流行为以及流场的准确预测上起到了重要的作用。

JournalofHydraulicResearch

JOURNAL OF HYDRAULIC RESEARCHVol. 48 - 2010SPIS TREŚCINo. 1EDITORIAL1 JHR editorial newsRESEARCH PAPERS3 Temporal scour evolution at bridge piers: effect of wood debris roughnessand porosity / STEFANO PAGLIARA AND IACOPO CARNACINA14 Mechanism of rock-bed scour due to impinging jet / AIHUA LI ANDPEIQING LIU23 Flow movement and sediment transport in compound channels /CHUNHONG HU, ZUWEN JI AND QINGCHAO GUO33 Influence of cohesion on suspended load transport of non-uniformsediments / RAJESH K. JAIN AND UMESH C. KOTHYARI44 A robust two-equation model for transient-mixed flows / ARTUROS. LEON, MOHAMED S. GHIDAOUI, ARTHUR R. SCHMIDT ANDMARCELO H. GARCIA57 Effects of dimensionless parameters on air-entraining vortices / KEREMTAŞTAN AND NEVZAT YILDIRIM65 Pressure behaviour in riser tube of a short airlift pump / CHARALAMPOST. MOISIDIS AND ELEFTHERIOS G. KASTRINAKIS74 Cavitation characteristics of offset-into-flow and effect of aeration /ZHIYONG DONG, YIHONG WU AND DONG ZHANG81 Effect of inclined jet screen on turbidity current / CHRISTOPH D. OEHY,GIOVANNI DE CESARE AND ANTON J. SCHLEISS91 Mixing coefficients for longitudinal and vertical mixing in the near field ofa surface pollutant discharge / SARBJIT SINGH, ZULFEQUAR AHMADAND UMESH C. KOTHYARITECHNICAL NOTES100 Water budget model for a remnant northern Everglades wetland / EHABA. MESELHE, JEANNE C. ARCENEAUX AND MICHAEL G. WALDON106 Discharge equation of a circular sharp-crested orifice / PRABHATA K. SWAMEE AND NIMISHA SWAMEE108 Effect of intake head wall and trash rack on vortices / HAMED SARKARDEH, AMIR REZA ZARRATI AND REZA ROSHAN113 Experimental study of energy loss through submerged trashracks / SHAWN P. CLARK, JONATHAN M. TSIKATA AND MELISSAHARESIGN119 Numerical simulation of high-speed turbulent water jets in air / ANIRBAN GUHA, RONALD M. BARRON AND RAM BALACHANDAR125 Drop characteristics of free-falling nappe for aerated straight-drop spillway / YAO-MING HONG, HUNG-SHIN HUANG AND SHIUAN WAN131 AUTHOR INDEX139 LIST OF REVIEWERSRESEARCH PAPERS141 Two-dimensional free surface flow numerical model for vertical slot fishways / JACQUES CHORDA, MARIE MADELEINE MAUBOURGUET,HÉLÈNE ROUX, MICHEL LARINIER, LAURENT TARRADE ANDLAURENT DAVID152 A one-dimensional bedload transport model for steep slopes / MICHAEL CHIARI, KURT FRIEDL AND DIETER RICKENMANN161 Semi-empirical model for channel bed evolution due to lateral discharge withdrawal / BURKHARD ROSIER, JEAN-LOUIS BOILLAT AND ANTON J. SCHLEISS169 Apparent friction coefficient in straight compound channels / PEDRO J.M. MORETA AND JUAN PEDRO MARTIN-VIDE178 Restoration of an incised mountain stream using artificial step-pool system / GUO-AN YU, ZHAO-YIN WANG, KANG ZHANG, XUEHUA DUAN AND TUNG-CHIUNG CHANG188 Effect and design of an underminer structure / SIMO TAMMELA, HANNU MARTTILA, SUBHASISH DEY AND BJØRN KLØVE197 Classification of flow patterns in rectangular shallow reservoirs / MATTHIEU DUFRESNE, BENJAMIN J. DEWALS, SÉBASTIENERPICUM, PIERRE ARCHAMBEAU AND MICHEL PIROTTON205 Modelling secondary cells and sediment transport in rectangular channels / MAZEN OMRAN AND DONALD W. KNIGHT213 Approximate modelling of 2D curvilinear open channel flows / OSCAR CASTRO-ORGAZ225 Influence of time-dependent viscosity on wall shear stresses in unsteady pipe flows / ALAN E. VARDY AND JAMES M.B. BROWN238 On particle-based simulation of a dam break over a wet bed / ABBAS KHAYYER AND HITOSHI GOTOH250 Bias errors induced by cross-talk in two-phase flow measurements / DANXUN LI, XINGKUI WANG AND QIANG ZHONGTECHNICAL NOTES255 Modelling of periodic flows in pipelines by transfer function method /H. PRASHANTH REDDY, M. HANIF CHAUDHRY AND PRANABK. MOHAPATRA260 Modelling roughness in scale models / CHRISTOPHER B. WEBB, STEVEN L. BARFUSS AND MICHAEL C. JOHNSON265 Evaluation of 2D shallow-water model for spillway flow with a complex geometry / XINYA YING AND SAM S.Y. WANG269 Experimental investigation of air pockets in pumping pipeline systems / OSCAR POZOS, JUERGEN GIESECKE, WALTER MARX, EDUARDOA. RODAL AND ALEJANDRO SANCHEZ274 Analysis of gradually and spatially varied flow in sand-bed channels / GOPU SREENIVASULU, ACHANTA RAMAKRISHNA RAO, BIMLESHKUMAR AND SAURABH TRIPATHIDISCUSSION280 Hydraulic design of Khafagi flumes / OSCAR CASTRO-ORGAZ, WILLIH. HAGERRESEARCH PAPERS283 An experimental study of mounds formed by dumping coarse sediment in channel flow / FARUK BHUIYAN, NALLAMUTHU RAJARATNAM ANDDAVID Z. ZHU292 Buoyant jets with three-dimensional trajectories / GUSTAAF A. KIKKERT, MARK J. DAVIDSON AND ROGER I. NOKES302 Two-dimensional operator for bank failures induced by water-level rise in dam-break flows / C. SWARTENBROEKX, S. SOARES-FRAZÃO,R. STAQUET AND Y. ZECH315 Regime relationships of alluvial canal with seepage / BIMLESH KUMAR, GOPU SREENIVASULU AND ACHANTA RAMAKRISHNA RAO320 Flood debris filtering structure for urban storm water treatment / JUNGSEOK HO, TODD MARTI AND JULIE COONROD329 Stepped and smooth spillways: resistance effects on stilling basin lengths / ANDRÉ LUIZ ANDRADE SIMÕES, HARRY EDMAR SCHULZ ANDRODRIGO DE MELO PORTO338 Air entrapped in gravity pipeline systems / OSCAR POZOS, CARLOSA. GONZALEZ, JUERGEN GIESECKE, WALTER MARX AND EDUARDOA. RODAL348 Linear stability of the 1D Saint-Venant equations and dragparameterizations / OLIVIER THUAL, LOUIS-ROMAIN PLUMERAULTAND DOMINIQUE ASTRUC354 Unsteady friction and visco-elasticity in pipe fluid transients / HUAN-FENG DUAN, MOHAMED GHIDAOUI, PEDRO J. LEE AND YEOU-KOUNG TUNG363 Experimental database for non-Newtonian flow in four channel shapes / JOHAN BURGER, RAINER HALDENWANG AND NEIL ALDERMAN TECHNICAL NOTES371 Optimum leak detection and calibration of pipe networks by inverse transient analysis / HAMID SHAMLOO AND ALI HAGHIGHI377 A semi-permanent method for fixing sand beds in laboratory flumes / SHALINI KASHYAP, BENOÎT DOUTRELEAU, GEORGES BOU-BOTROS, COLIN D. RENNIE AND RONALD TOWNSEND383 Predicting contraction scour with a two-dimensional depth-averaged model / YONG G. LAI AND BLAIR P. GREIMANN388 Universal probability distributions of turbulence in open channel flows / SUJIT K. BOSE AND SUBHASISH DEY395 Turbulence characteristics of the transition region from hydraulic jump to open channel flow / A.T.M. HASAN ZOBEYER, NASREEN JAHAN,ZAHIDUL ISLAM, GAUTAM SINGH AND NALLAMUTHU RAJARATNAM 400 Effect of a standing baffle on the flow structure in a rectangular open channel / HAMIDREZA JAMSHIDNIA, YASUSHI TAKEDA AND BAHAR FIROOZABADI405 Equations for plane, highly curved open channel flows / OSCAR CASTRO-ORGAZ409 Recovery factor for non-equilibrium sedimentation processes / CHIH TED YANG AND REZA MARSOOLIRESEARCH PAPERS415 Large eddy simulation of vortex flow in intake channel of hydropower facility / AKIHIKO NAKAYAMA AND NOBUYUKI HISASUE428 Adaptation of Preissmann's scheme for transcritical open channel flows / CAROLINE SART, JEAN-PIERRE BAUME, PIERRE-OLIVIERMALATERRE AND VINCENT GUINOT441 Flow-altering countermeasures against scour at bridge piers: a review / ALI TAFAROJNORUZ, ROBERTO GAUDIO AND SUBHASISH DEY453 Weakly undular hydraulic jump: effects of friction / OSCAR CASTRO-ORGAZ466 A two-layer approach for depth-limited open-channel flows with submerged vegetation / WONJUN YANG AND SUNG-UK CHOI476 Flow characteristics of bottom outlets with moving gates / BIJAN DARGAHI483 Pressure extrema in energy-dissipating structure using block maxima: case study / SIMONE M. CEREZER, DANIELA MÜLLER, ROBINT. CLARKE AND MARCELO G. MARQUES491 Toe protection for spill-through and vertical-wall abutments / ANTÓNIOH. CARDOSO, GONZALO SIMARRO, CRISTINA FAEL, OLIVIER LEDOUCEN AND ANTON J. SCHLEISSTECHNICAL NOTES499 On elongated air pockets in downward sloping pipes / IVO POTHOF AND FRANCOIS CLEMENS504 Effect of Froude number on bubble clustering in a hydraulic jump / CARLO GUALTIERI AND HUBERT CHANSON509 Physical modelling of pressure flushing for desilting of non-cohesive sediment / MANOOCHEHR FATHI-MOGHADAM, SAMADEMAMGHOLIZADEH, MAHMOUD BINA AND MEHDI GHOMESHI515 Overflow characteristics of circular-crested weirs / SARA BAGHERI AND MANOUCHEHR HEIDARPOUR521 3D model for prediction of flow profiles around bridges / SELAHATTIN KOCAMAN, GALIP SECKIN AND KUTSI S. ERDURAN526 Head loss coefficient of orifice plate energy dissipater / WU JIANHUA, AI WANZHENG AND ZHOU QI531 Computation of critical tractive stress of scaling sizes in non-uniform sediments / PREM LAL PATEL, PRAKASH DEVIDAS POREY ANDSHAILESHKUMAR B. PATEL538 Local scour at open-channel junctions / S. MAHMOOD BORGHEI AND AIDIN JABBARI SAHEBARIDISCUSSION543 Application of potential flow to circular-crested weir / MANOUCHEHR HEIDARPOUR, JAHANSHIR MOHAMMADZADEH HABILI AND AMIRHAMZEH HAGHIABI. Discusser: OSCAR CASTRO-ORGAZ547 Modelling dike breaching due to overtopping / LUKAS SCHMOCKER AND WILLI H. HAGER. Discusser: MIODRAG JOVANOVIĆ550 Effect of spacing of two offset jets on scouring phenomenon / DIPA DEY AND T.I. ELDHO. Discusser: B. S. PANI; ADRIAN C. H. LAIBOOK REVIEW553 River training and sediment management with submerged vanes / JOCHEN ABERLE555 Constructions hydrauliques: ecoulements stationnaires (Hydraulic structures – steady flows) / YVES ZECH557 Hydraulic modelling – an introduction: principles, methods and applications / WILLI H. HAGER AND MICHAEL PFISTERNo. 5RESEARCH PAPERS559 A model to simulate the transport and fate of gas and hydrates released in deepwater / POOJITHA D. YAPA, LALITH K. DASANAYAKA, UDITHAC. BANDARA AND KISABURO NAKATA573 1D numerical evaluation of dike erosion due to overtopping / MARIANEVE PONTILLO, LUKAS SCHMOCKER, MASSIMO GRECO AND WILLI H.HAGER583 Nappe flow over horizontal stepped chutes / FLORIANA MARIA RENNA AND UMBERTO FRATINO591 Drawdown curve and turbulent boundary layer development for chute flow / OSCAR CASTRO-ORGAZ AND WILLI H. HAGER603 Dam-break flows during initial stage using SWE and RANS approaches / HATICE OZMEN-CAGATAY AND SELAHATTIN KOCAMAN612 Discharge estimation in open channels by means of water level hydrograph analysis / COSTANZA ARICÒ, GIOVANNI CORATO, TULLIO TUCCIARELLI, MOULDI BEN MEFTAH, ANTONIO FELICE PETRILLOAND MICHELE MOSSA620 Moment of momentum equation for curvilinear free-surface flow / OSCAR CASTRO-ORGAZ AND WILLI H. HAGER632 Mixing and re-entrainment in a negatively buoyant jet / SIMONE FERRARI AND GIORGIO QUERZOLI641 Turbulent mixing of particles under tidal bores: an experimental analysis / HUBERT CHANSON AND KOK-KENG TAN650 Essential system response information for transient-based leak detection methods / HUAN-FENG DUAN, PEDRO J. LEE, MOHAMEDS. GHIDAOUI AND YEOU-KOUNG TUNGTECHNICAL NOTES658 Non-universality of von Kármán's κ in fluvial streams / ROBERTO GAUDIO, ANTONIO MIGLIO AND SUBHASISH DEY664 Exploratory study on the roller effect of direct hydraulic jumps / OSCAR CASTRO-ORGAZ, MICHAEL PFISTER AND WILLI H. HAGER669 Hydraulic behaviour of flow over an oblique weir / ABDORREZA KABIRI-SAMANI, AHMAD ANSARI AND S. MAHMOOD BORGHEI674 Generalized Coles' law and outer layer conformal mapping / ALDO RONA AND MARCO GROTTADAUREA680 Two-phase flow pattern transitions of short airlift pumps /CHARALAMPOS T. MOISIDIS AND ELEFTHERIOS G. KASTRINAKIS DISCUSSION686 Application of Godunov-type schemes to transient mixed flows / ARTURO S. LEÓN, MOHAMED S. GHIDAOUI, ARTHUR R. SCHMIDT ANDMARCEL H. GARCÍA. Discusser: A. G. BARNETT690 Investigation of circular jets in shallow water / JOHN P. RAIFORD and ABDUL A. KHAN. Discusser: BIDYA S. PANI; ADRIAN C. H. LAI694 Discharge coefficient of sharp-crested weirs using potential flow / HOSSEIN AFZALIMEHR AND SARA BAGHERI. Discusser: OSCARCASTRO-ORGAZ697 Numerical modelling of flow over a chute spillway / MEHMET SALIH KIRKGOZ, MEVLUT SAMI AKOZ AND AHMET ALPER ONER.Discusser: OSCAR CASTRO-ORGAZ699 Curved-streamline transitional flow from mild to steep slopes / O. CASTRO-ORGAZ AND W.H. HAGER. Discusser: CARMINE DI NUCCI; ANIELLO RUSSO SPENANo. 6FORUM PAPER703 New hydropower converters for very low-head differences / JAMES SENIOR, NICOLE SAENGER AND GERALD MÜLLERRESEARCH PAPERS715 River morphodynamics with creation/consumption of grain size stratigraphy 1: laboratory experiments / ENRICA VIPARELLI, ROBERT HAYDEL, MARTINO SALVARO, PETER R. WILCOCK AND GARYPARKER727 River morphodynamics with creation/consumption of grain size stratigraphy 2: numerical model / ENRICA VIPARELLI, OCTAVIOE. SEQUEIROS, ALESSANDRO CANTELLI, PETER R. WILCOCK ANDGARY PARKER742 Hydrodynamic instability of hyperconcentrated flows of the Yellow River / YUCHUAN BAI AND HAIJUE XU754 Advances in sediment transport modelling / SCOTT C. JAMES, CRAIGA. JONES, MATTHEW D. GRACE AND JESSE D. ROBERTS764 Sills and gabions as countermeasures at bridge pier in presence of debris accumulations / STEFANO PAGLIARA, IACOPO CARNACINA ANDFABRIZIO CIGNI775 Modelling vegetation effects in irregular meandering river / XIN SUN, KOJI SHIONO, PONNAMBALAM RAMESHWARAN AND JIMH. CHANDLER784 Predicting near-field dam-break flow and impact force using a 3D model / CHEN YANG, BINLIANG LIN, CHUNBO JIANG AND YING LIU793 Physically-consistent wall boundary conditions for the k-ω turbulence model / DAVID R. FUHRMAN, MARTIN DIXEN AND NIELS GJØLJACOBSEN801 Double-averaging turbulence characteristics in flows over a gravel bed / SANKAR SARKAR AND SUBHASISH DEY810 Wall friction and turbulence dynamics in decelerating pipe flows / CHANCHALA ARIYARATNE, SHUISHENG HE AND ALAN E. VARDY DISCUSSION822 Prototype measurements of pressure fluctuations in The Dalles Dam stilling basin / ZHIQUN DENG, GREGORY R. GUENSCH, MARSHALLC. RICHMOND, MARK A. WEILAND AND THOMAS J. CARLSON.Discusser: RAÚL A. LOPARDO824 Three-dimensional (3D) modeling of non-uniform sediment transport ina channel bend with unsteady flow / TIM FISCHER-ANTZE, NILSRÜTHER, NILS R.B. OLSEN AND DIETER GUTKNECHT. Discusser:ERIK MOSSELMAN826 Experimental and numerical modelling of symmetrical four-branch supercritical cross junction flow / EMMANUEL MIGNOT, ANDRÉPAQUIER AND NICOLAS RIVIÈRE. Discusser: LEONARDO S. NANÍA, MANUEL GÓMEZ, JOSÉ DOLZ AND ARTURO S. LEÓN829 Drag coefficient of unsubmerged rigid vegetation stems in open channel flows / U.C. KOTHYARI, K. HAYASHI, AND H. HASHIMOTO.Discusser: MANOOCHEHR FATHI-MOGHADAM AND SAMADEMAMGHOLIZADEH831 Effect of tall vegetation on sediment transport by channel flows / U.C. KOTHYARI, H. HASHIMOTO AND K. HAYASHI. Discusser:MANOOCHEHR FATHI-MOGHADAM, BABAK LASHKARARA, SADEGH HAGHIGHIPOUR AND MEHDI BEHDARVANDBOOK REVIEW834 Fluvial hydraulics. S. Lawrence Dingman / Reviewer: ALITAFAROJNORUZ836 Erosion and sedimentation, second edition. Pierre Y. Julien / Reviewer: WILLI H. HAGER AND VOLKER WEITBRECHTOprac. BPK。

大涡模拟简单介绍

大涡模拟简单介绍大涡模拟（Large Eddy Simulation，简称LES）是一种流体动力学数值模拟方法，用于模拟湍流流动。

相比于传统的雷诺平均Navier-Stokes方程（RANS）模拟方法，LES可以更准确地捕捉流动中的湍流结构和湍流涡旋，并且消除了能量储存和耗散的子网格模型假设。

LES的基本原理是在Navier-Stokes方程的基础上，通过滤波器将流动变量划分为长时间和空间尺度下的平均分量和湍流分量。

经过充分滤波的方程组被认为是LES方程组，其中长时间和空间尺度下的平均分量由RANS求解，湍流分量则采用直接数值模拟（DNS）或者更为常见的子网格模型进行近似。

LES方程组通常采用基于物理的平滑学习系数（Smagorinsky模型）或者基于数值的子网格尺度计算方法来估计湍流涡旋的剪切应力。

与传统的RANS模拟相比，LES能够提供更多细节的湍流结构信息，从而更好地预测湍流流动中的流场特性，比如涡旋结构、湍流能量传递、湍流耗散等。

这些信息对于工程问题的分析和设计有着重要的意义，比如风力发电机翼型的气动性能、船舶外形的水动力性能等。

LES的优势主要体现在以下几个方面：1.湍流结构预测能力：LES可以更准确地模拟湍流结构，包括涡旋的生成、演化和消散过程，因此能够提供更详尽的湍流流场信息。

2.湍流能量传递和耗散特性：LES能够有效地预测湍流能量的传递和耗散特性，对于评估流动中的湍流耗散和能量损失有着重要的意义。

3.均匀流动和非均匀流动的统一模拟：与传统的RANS方法相比，LES对均匀流动和非均匀流动有着较好的统一模拟能力。

对于非均匀流动，LES能够更好地预测局部湍流结构的分布和演化。

4.对涡旋缩放和旋转的准确模拟：LES能够模拟涡旋的缩放和旋转过程，能够提供更真实的细节湍流结构信息。

尽管LES在提供细节湍流结构信息方面具有优势，但其计算成本较高，主要体现在网格分辨率和时间步长上。

由于需要考虑到湍流结构的空间和时间变化，LES所需的网格分辨率通常较高，这对计算资源的要求较高。

Large eddy simulation of unsteady flow in gas

Large eddy simulation of unsteady ﬂow in gas–liquid separator applied in thorium molten salt reactorJing-Jing Li 1•Ya-Lan Qian 1•Jun-Lian Yin 1•Hua Li 2•Wei Liu 2•De-Zhong Wang 1Received:14June 2017/Revised:18August 2017/Accepted:6October 2017ÓShanghai Institute of Applied Physics,Chinese Academy of Sciences,Chinese Nuclear Society,Science Press China and Springer Nature Singapore Pte Ltd.2018Abstract Axial gas–liquid separators have been adopted in ﬁssion gas removal systems for the development of thorium molten salt reactors.In our previous study,we observed an unsteady ﬂow phenomenon in which the ﬂow pattern is directly dependent on the backpressure in a gas–liquid separator;however,the underlying ﬂow mechanism is still unknown.In order to move a step further in clarifying how the ﬂow pattern evolves with a variation in backpressure,a large eddy simulation (LES)was adopted to study the ﬂow ﬁeld evolution.In the simulation,an artiﬁcial boundary was applied at the separator outlet under the assumption that the backpressure increases linearly.The numerical results indicate that the unsteady ﬂow feature is captured by the LES approach,and the ﬂow transition is mainly due to the axial velocity proﬁle redistribution induced by the backpressure variation.With the increase in backpressure,the axial velocity near the downstream oriﬁce transits from negative to positive.This change in the axial velocity sign forces the unstable spiral vortex to become a stable recti-linear vortex.Keywords Swirl ﬂow ÁThorium molten salt reactor ÁComputational ﬂuid dynamics ÁLarge eddy simulationList of symbols P out Backpressure Re Reynolds number r *Non-dimensional radial coordinates r *=r /R S Swirl number t Time t *Non-dimensional time T Total time of ﬂow evolution V in Average velocity at separator inlet v Ãa Non-dimensional axial velocity v Ãa ¼v a =V in v Ãt Non-dimensional tangential velocity v Ãt ¼v t =V in1IntroductionIn the development of the ﬁssion gas removal system applied in thorium molten salt reactors (TMSRs),an axial-type swirl tube is used as a gas–liquid separator (Fig.1).The separator consists of the swirl vane,swirl chamber,and recovery vane.When a bubbling ﬂow moves though the separator from the right-hand side to the left-hand side,bubbles concentrate in the center of the swirl chamber and coalesce into an air core;the concentrated gas–liquid mixture is removed from the upstream and downstream oriﬁces.In previous experiments [1,2],during the air core establishment process,the authors observed that the two-phase ﬂow regime illustrated in Fig.2exhibits a three-stage phase as the separator outlet backpressure increases.The ﬂow development is similar to the well-known pro-cession vortex core (PVC)phenomenon [3],which is encountered in various swirl ﬂow applications such as the swirl combustor [4],cyclone [5],vortex ampliﬁer,andThis work was supported by the National Natural Science Foundation of China (Nos.11535009and 51406114).&Jun-Lian Yinjlyin@1School of Mechanical Engineering,Shanghai Jiao Tong University,Shanghai 200240,China2Shanghai Institute of Applied Physics,Shanghai 201800,ChinaNUCL SCI TECH (2018) 29:62https:///10.1007/s41365-018-0411-3vortex diode [6].In the PVC,the center of the swirl vortex deviates from the geometric center of the swirl device concerned and rotates like a helix.Because the PVC plays a key role in swirl ﬂow devices,the underlying mechanism dominating the ﬂow transition has attracted the interest of several researchers.A comprehensive review of oscillation mechanisms and the role of the PVC in swirl combustion systems was reported in a study by Nicholas [3];it stated that the occurrence of the PVC is related to the swirl number (S )and the presence of a central recirculation zone,as well as the mode of the fuel entry,combustor conﬁgu-ration,and equivalence ratio.Pisarev et al.[5]studied the ‘‘end of vortex’’phenomenon in a reversed ﬂow centrifugal separator and concluded that the instability observed could be related to Reynolds number and swirl chamber length.Experimental studies conducted by Shtork et al.[7],using a high-speed camera and laser Doppler velocimetry on swirl ﬂows in a lean premixed swirl-stabilized combustor,and a gas–liquid cylindrical cyclone separator observed by Hreiz et al.[8],conﬁrmed that the occurrence of PVC is strongly related to a variation in the axial velocity proﬁle.Fur-thermore,Alekseenko et al.[9]pointed out that the com-monly used swirl ﬂow parameters (Reynolds and swirl numbers)do not uniquely characterize the ﬂow structure and the axial velocity proﬁle is another key parameter affecting swirl ﬂow pattern evolution.Moreover,RagabFig.12D geometry of axial gas–liquidseparatorFig.2(Color online)Two-phase ﬂow evolution with S =1.17and Re =119,891.a P out =23.0kPa,b P out =105.0kPa,c P out =186.0kPa62 Page 2of 9J.-J.Li et al.and Sreedhar[10]used a numerical simulation to demon-strate that large-scale helical sheets of vorticity will be produced when a swirl vortex that has axial velocity deﬁ-cits is affected by little disturbances.Based on the above review,a common qualitative con-clusion for explaining the PVC phenomenon is the varia-tion in the axial velocity component[11].Inspired by this concept,the authors felt that by conducting a numerical study on the evolution ofﬂowﬁeld in the gas–liquid sep-arator with increasing backpressure,they could produce results that will be signiﬁcant in interpretingﬂow unsteadiness.Due to this hypothesis,an unsteadyﬂow simulation based on the large eddy simulation(LES) method was carried out.2Numerical modeling2.1Geometry,grid,and boundary conditionsComputationalﬂuid dynamics(CFD)models were constructed in order to conform to the conﬁguration of swirl tubes used in the experiments.All geometrical and operational parameters of the swirl tube,including the shapes of swirl and recovery vanes,were carefully copied in the CFD models.The3D models were built using a commercial program called‘‘universal graphics(UG) Graphix,’’and discretization was carried out using inte-grated computer engineering and manufacturing(ICEM) computationalﬂuid dynamics(CFD).Figure3provides an overview of the grid geometry.The grid density was controlled in such a manner that the y?value of theﬁrst grid point of all the walls con-cerned was less than1,while the swirl chamber’s core zone was reﬁned in order to resolve the vortex motion more accurately.The total number of cells was approximately 10,000,000,including approximately2,000,000cells in the swirl vane domain,2,000,000in the recovery vane domain, and6,000,000in the swirl chamber domain.Pure water was selected as the workingﬂuid for the simulations.The temperature was taken as293K,and the properties of the water were as follows:density=997kg/m3;dynamic viscosity=8.899910-4Pa s;and molecular mass= 18.02kg/kmol.By considering a state of an unsteady simulation,the time step was set to0.0005s;this guaran-tees that the Courant number is around1.A simulation of 0.25s of real time is sufﬁcient for obtaining a regular unsteadyﬂow.In terms of the boundary conditions,a velocity inlet with V in=2.41m/s(Re=119,891)was set at the separator inlet,while the opening boundary condi-tions with atmospheric static pressures were set at the outlets of the upstream and downstream oriﬁces.At the separator outlet,a linear pressure outlet assumed by Eq.1 was adopted:P out¼1013250Ât Pa½ :ð1Þ2.2Turbulence modelingAppropriate turbulence model selection is a crucial factor in numerical simulations of conﬁned swirling tur-bulentﬂows.Based on comprehensive CFD studies [12–16]on gas–solid cyclones,it has been established that standard eddy viscosity-based models cannot predict the velocity proﬁles for swirlﬂows;this is as a result of their isotropic modeling of Reynolds stresses.Second-order closure models like the Reynolds stress model(RSM)can predict the averaged velocity proﬁles,which conform to some reasonable degree with experiments.Regarding the capability of predicting unsteady characteristics,no models can achieve better performance than LES,which was val-idated by Pisarev et al.[5]during their unsteady numerical simulations at the end of vortex evolution in cyclones.LES involves a3D time-dependent computation of the large-scale turbulent motions that are mainly responsible for turbulent mixing,while those with scales smaller than the computational grid are parameterized;that is,LES solves in theﬁltered velocityﬁeld where theﬁltering operation allows for separation of theﬂuid motion scales at the grid level,with small motion scales being considered by a subgrid-scale model.Theﬁltered velocityﬁeld is computed as the solution of theﬁltered Navier–Stokes equations: o u io x i¼0;o u io tþo u i u jo x i¼À1qo po x iþoo x jmþm sgsÀÁo u io x j8>><>>:;ð2Þwhere the additional eddy viscosity m sgs must be modeled in order to close the system.The localized dynamic Smagorinsky model was used in this study,in which the eddy viscosity is calculated as follows:m sgs¼C DðÞ2 S x;tðÞj j;ð3Þwhere S x;tðÞj j denotes the norm of theﬁltered strain rate tensor.The grid size is deﬁned as D¼VolðÞ1=3;‘‘Vol’’is the cell volume,and the coefﬁcient,C,is dynamically computed following Germano’s deﬁnition[17].2.3ComputationA three-stage calculation procedure was applied to implement the unsteady simulation.In order to obtain appropriate initialﬂow conditions,ﬁrst,a steady CFDLarge eddy simulation of unsteadyﬂow in gas–liquid separator applied in thorium molten…Page3of9 62result was computed by the RSM turbulence model and taken as the initial condition for the unsteady LES simu-lation with a constant backpressure at t =0.A total time of D t 1=0.15s was used for the ﬁrst LES simulation in order to obtain a permanent ﬂow regime.Then,the linear varying pressure outlet was activated and the unsteady ﬂow simu-lation was initiated,with a time step of 0.0001s and a total time of 0.25s.The computation running in parallel mode in a cluster with 20CPUs (2.4GHz)and 96GB RAM typically required 168h for the entire process.3Results and discussionPost-processing of the transient results obtained during the total computed time indicates that the time scale used to capture the ﬂow transition is T =0.15s.Therefore,four points with an equivalent time step of 0.05s were deﬁned to describe the unsteady process,and the non-dimensional time was deﬁned as t *=t /T (where t *=0;t =0.33;t *=0.67;t *=1).The following results are discussed from part to whole.The swirl ﬂow regime was characterized by the vortex region detected by the Q-criterion,which is deﬁned as the second invariant of the velocity gradient tensor and has been widely adopted to illustrate spatial vortices [18].In order to validate the numerical model,a comparison between the calculated vortex andexperimental results obtained by means of visualization [1]is illustrated in Fig.4.A qualitative agreement can be observed in terms of the vortex core shape.Figure 5pre-sents the vortex region evolution with increasing back-pressure,from which we can observe a signiﬁcant change in the vortex core,transiting from a cylindrical shape (t *=0)to a double and single helix.Another observation of Fig.2reveals that the basic ﬂow phenomenon in terms of the air core shape representing the vortex core shape is captured;again,this validates that backpressure plays a key role in vortex dynamics.From the perspective of a gas–liquid separator’s separation function,we can conclude that unstable vortex patterns,such as the cylindrical shape,double helix,and single helix,prevent the bubbles from being separated.In order to bring more clarity on the mode in which the ﬂow ﬁeld dominates vortex dynamics,the ﬂow ﬁeld downstream of the vortex region,near the recovery vane,is illustrated by the velocity vector ﬁeld,streamlines,and a zero axial velocity isosurface in Fig.6.It can be observed that the velocity ﬁeld experiences complex ﬂow unsteadiness.With the increase in back-pressure,the axial velocity sign changes from negative to positive,which is also depicted by the change in area of the zero axial velocity isosurface.As noted in our previous study,when the initial backpressure approaches the atmo-spheric pressure level,air entrainment occurs at both the upstream and downstream oriﬁces.In the simulation,theFig.3(Color online)Grid geometry and boundary conditions in LES computation62 Page 4of 9J.-J.Li et al.water entrainment results in a negative axial velocity,which initiates prominent secondary vortices near the zero axial velocity surface (Fig.6a).The axial velocity magni-tude is reduced with increasing backpressure,as indicated in Fig.6b.The zero axial velocity isosurface transforms into a spiral style,which in turn induces the secondary vortices into an oscillatory mode.The existence of the oscillating secondary vortices explains the periodic double helix.The further increase in backpressure shrinks the negative axial velocity zone from a continuous spiral to dispersed pieces close to the downstream oriﬁce where a single helix is formed (Fig.6c).The vanishing of the zero axial velocity surface in Fig.6d simultaneously drives the periodic single helix into a rectilinear air core.It can be concluded from the above analysis that the axial velocity sign dominates the vortex dynamics.The vortex shape evolution represented by the variation in the air core shape in Fig.2is strongly dependent on the change in axial velocity.In order to elucidate the details of the variation in the velocity vector,the velocity distribution extracted from four axial positions (Fig.7)with an equivalentaxialFig.4(Color online)Comparison of CFD and experimental result ﬂow patterns.a Instantaneous ﬂow pattern by visualization,b instantaneous ﬂow pattern byCFDFig.5(Color online)Vortex region evolution illustrated by the Q -criterion.a t *=0,b t *=0.33,c t *=0.67,d t *=1Large eddy simulation of unsteady ﬂow in gas–liquid separator applied in thorium molten …Page 5of 9 62distance of 0.5D near the downstream oriﬁce is illustrated in Fig.8.Qualitatively,with increasing backpressure,the prominent change in velocity is in the axial velocity component,the sign of which varies from negative to positive.In order to obtain a quantitative comparison of the variation in velocity,both the axial and tangentialvelocityFig.6Velocity distribution evolution near downstream oriﬁce.a t *=0,b t *=0.33,c t *=0.67,d t *=1Fig.7(Color online)Four axial positions used to extract velocity vectors62 Page 6of 9J.-J.Li et al.components normalized by the average velocity at the separator inlet are shown in Figs.9and 10.It can be clearly identiﬁed from Fig.9that the initial zone (t *=0)with negative axial velocity occupies the range of -0.15\r *\0.15and gradually decreases and dimin-ishes when t *=1.The transition of the axial velocity sign results in the vortex motion shown in Fig.10.When the axial velocity is negative,the vortex center wraps around the centerline;when the axial velocity is positive,the vortex center is conﬁned to the geometrical center of the swirl chamber.4ConclusionIn this paper,we presented a numerical study to inves-tigate the unsteady ﬂow phenomenon in a gas–liquid sep-arator.During the experiment,we observed that the air core in the swirl chamber of the separator exhibited a cylindrical shape,a double helix,a single helix,and a rectilinear shape when the backpressure at the separator outlet gradually increased.In order to explain the underlying mechanism dominating the ﬂow regime transition,a single-phase LES simulation with an artiﬁcial boundary conditionwasFig.8(Color online)Variation in velocity vector at four axial locations.a t *=0,b t *=0.33,c t *=0.67,d t *=1Large eddy simulation of unsteady ﬂow in gas–liquid separator applied in thorium molten …Page 7of 9 62carried out to represent the varying backpressure.The vortex region evolution indicated that the change in the ﬂow pattern observed in the experiment can be captured via a numerical approach.The variation in the vortex region was analyzed using the velocity vector distribution.We found that the vortex dynamics are dependent on the change in the axial velocity distribution,which can induce unsteady secondary vortices and an inner counter-rotating vortex.When the axial velocity is positive,the vortex approaches a steady state.It should be noted that,in the numerical study,the assumed boundary condition for backpressure is not based on experimental data because a transient experiment with aﬁxed Reynolds number and increasing backpressure is not available.Moreover,a comparison between the vortex shape evolution and air core was not presented because a single-phase medium was used in the simulation.A two-phase simulation,which can predict the dispersedﬂow corresponding to the separation process and gas–liquid interface simultaneously,would be more appropriate and provide highﬁdelity;however,this simulation is currently very difﬁcult to carry out. References1.J.Yin,J.Li,Y.Ma et al.,Study on the air core formation of agas–liquid separator.J.Fluid.Eng.T.ASME.137,91301(2015).https:///10.1115/1.40301982.J.Yin,Y.Ma,Y.Qian et al.,Experimental investigation of thebubble separation route for an axial gas–liquid separator for TMSR.Ann.Nucl.Energy97,1–6(2016).https:///10.1016/j.anucene.2016.06.0183.N.Syred,A review of oscillation mechanisms and the role of theprecessing vortex core(PVC)in swirl combustion systems.Prog.Energy Combust.32,93–161(2006).https:///10.1016/j.pecs.2005.10.0024.D.Durox,J.P.Moeck,J.Bourgouin et al.,Flame dynamics of avariable swirl number system and instability bust.Flame160,1729–1742(2013).https:///10.1016/ bustﬂame.2013.03.0045.G.I.Pisarev,V.Gjerde,B.V.Balakin et al.,Experimental andcomputational study of the‘‘end of the vortex’’phenomenon in reverse-ﬂow centrifugal separators.AIChE J.58,1371–1380 (2012).https:///10.1002/aic.126956.J.L.Yin,L.Jiao,L.Wang,Large eddy simulation of unsteadyﬂow in vortex diode.Nucl.Eng.Des.240,970–974(2010).https:///10.1016/j.nucengdes.2010.01.0107.S.I.Shtork,N.F.Vieira,E.C.Fernandes,On the identiﬁcation ofhelical instabilities in a reacting swirlingﬂow.Fuel87, 2314–2321(2008).https:///10.1016/j.fuel.2007.10.016 8.R.Hreiz, C.Gentric,N.Midoux et al.,Hydrodynamics andvelocity measurements in gas-liquid swirlingﬂows in cylindrical cyclones.Chem.Eng.Res.Des.92,2231–2246(2014).https:// /10.1016/j.cherd.2014.02.0299.S.V.Alekseenko,P.A.Kuibin,V.L.Okulov et al.,Helical vor-tices in swirlﬂow.J.Fluid Mech.382,195–243(1999).https:// /10.1017/S002211209800377210.S.Ragab,M.Sreedhar,Numerical simulation of vortices withaxial velocity deﬁcits.Phys.Fluids7,549–558(1995).https://doi.org/10.1063/1.86858211.O.Lucca-Negro,T.O’Doherty,Vortex breakdown:a review.Prog.Energy Combust.27,431–481(2001).https:///10.1016/S0360-1285(00)00022-812.J.L.Yin,J.J.Li,Y.F.Ma et al.,Numerical approach on theperformance prediction of a gas–liquid separator for TMSR.J.Nucl.Sci.Technol.(2015).https:///10.1080/00223131.2015.109239913.B.C.Cai,J.J.Wang,L.C.Sun et al.,Experimental study andnumerical optimization on a vane-type separator for bubble separation in TMSR.Prog.Nucl.Energy74,1–13(2014).https:// /10.1016/j.pnucene.2014.02.00714.Y.Xu,X.Song,Z.Sun et al.,Numerical investigation of theeffect of the ratio of the vortex-ﬁnder diameter to the spigot diameter on the steady state of the air core in a hydrocyclone.Ind.Eng.Chem.Res.52,5470–5478(2013).https:///10.1021/ ie302081v15.M.Narasimha, A.N.Mainza,P.N.Holtham et al.,Air-coremodelling for hydrocyclones operating with solids.Int.J.Miner.Process.102,19–24(2012).https:///10.1016/j.minpro.2011.09.00462 Page8of9J.-J.Li et al.16.R.Hreiz,C.Gentric,N.Midoux,Numerical investigation ofswirlingﬂow in cylindrical cyclones.Chem.Eng.Res.Des.89, 2521–2539(2011).https:///10.1016/j.cherd.2011.05.001 17.M.Germano,U.Piomelli,P.Moin et al.,A dynamic subgrid-scale eddy viscosity model.Phys.Fluids Fluid Dyn.3, 1760–1765(1991).https:///10.1063/1.85795518.A.Favrel,A.Mueller,ndry et al.,Study of the vortex-induced pressure excitation source in a Francis turbine draft tube by particle image velocimetry.Exp.Fluids56,1–15(2015).https:///10.1007/s00348-015-2085-5Large eddy simulation of unsteadyﬂow in gas–liquid separator applied in thorium molten…Page9of9 62。

某型破拆机器人臂架系统运动仿真及变幅液压缸参数设计

某型破拆机器人臂架系统运动仿真及变幅液压缸参数设计王大洪1，张文帅2，滕儒民2，范子剑2，曾卉帆2（1. 深圳市先进智能技术研究所，广东深圳 518049；2. 大连理工大学机械工程学院，辽宁大连 116023）［摘要］某型破拆机器人臂架系统采用3节工作臂、4个液压缸进行变幅动作，以实现臂架端部破拆装置的合理运动及精准定位，正确计算出破拆装置的作业范围以及液压缸的参数是设计该产品的关键。

本文通过臂架系统的运动仿真给出了该产品的作业范围以及液压缸的参数，为合理设计臂架系统提供了准确数据。

该方法和手段为同类产品的设计提供了借鉴。

［关键词］破拆机器人；臂架；运动学仿真；液压缸参数计算［中图分类号］TU689 ［文献标识码］B ［文章编号］1001-554X（2022）02-0118-04Motion simulation and parameter design of luffing hydraulic cylinder forboom system of a demolition robotWANG Da-hong，ZHANG Wen-shuai，TENG Ru-min，FAN Zi-jian，ZENG Hui-fan特殊环境下破拆机器人是结合高危环境特点开发的一种遥控多功能作业机器人。

破拆机器人最早由瑞典brokk公司于20世纪70年代开发、研制和生产，经过不断地改进，朝着标准化、系列化、自动化和智能化的方向发展［1］。

进入21世纪，随着人力成本的不断提升和工人要求对工作环境的不断改善，破拆机器人在建筑改造和拆除、桥梁隧道地铁施工、抢险救援及排爆、冶金工业炉窑打渣、水泥工业回转窑拆除等应用场所使用越来越广泛。

王旭［2］以新型拆除机器人工作装置为研究对象，采用矩阵法得到拆除机器人工作装置的运动轨迹方程，为研究拆除机器人工作装置的优化设计提供了新方法；赵家宏［3］用CATIA软件建立了破拆机器人模型，利用ADAMS软件对拆除机器人的工作装置进行了运动学仿真分析，获得了液压锤的工作范围包络图。

蓄水坑灌单坑土壤水分运动模型的有限体积法求解

( 5)坑底边界 CcB c, 为了减少水分的深层渗漏, 坑底为不透水, 故其水分通量为零, 即
-
K
(
h
)
5h 5z
+
K
(
h
)
=0
n
( t\0, 0[ r[ R1, z = H 0 )
( 8)
2 模型求解
图 1 蓄水单坑入渗剖面示意图 F ig. 1 Profile o fw ate r storage pits irr iga tion
关键词: 蓄水坑灌土壤水分运动有限体积法数值模拟中图分类号: S2751 2 文献标识码: A 文章编号: 1000-1298( 2011) 05-0063-05
Num erical Simulation for Single P it SoilW ater M ovem ent ofW ater Storage P it Irrigation
有限体积法的基本思想 [ 11 ~ 12 ] 是将计算区域划分为一系列不重复的控制容积 (控制体 ), 把变量存在单元的中心, 单元的边界为控制体。通过将待解的微分方程对控制体作积分导出离散方程, 因其严格满足控制体内及整个计算区域的积分守恒, 由此建立的离散格式在计算连续流时可保证无守恒误差。
为了得到式 ( 10)的积分结果, 非稳态项中, H随 r 和 z 变化的型线取为阶梯式, 对流项和扩散项随时
间而变的型线处理为
Qt+ $t
It =
TP dt= [ aTPt+ $ t + ( 1- a)TPt ] $t
t
( 0显式格式; 当 a = 1 /2时, 为
hw = hi ( t\ 0, r = R 1, H 1 [ z [ H 0 ) ( 7) 式中 hi ) ) ) 入渗面 i点的压力势, cm

WRF-LES（LargeEddySimulation）模拟结果的分析与讨论理想案例

WRF-LES（LargeEddySimulation）模拟结果的分析与讨论理想案例國立中央大學大氣物理研究所書報討論時間：2013/04/12地點：S1-713講員：李忠剛指導教授：鄭芳怡老師WRF-LES(Large Eddy Simulation)模擬結果的分析與討論:理想案例與真實案例摘要本篇文章主要研究目地為評估WRF在不同網格解析度下，對理想個案與真實個案的模擬結果，進行分析與評估。

對於理想個案，進行了以下的敏感度測試：(1)垂直解析度的改變；(2)水平解析度的改變；(3)次網格模式的選取。

理想個案的模擬結果顯示，改變水平網格解析度所帶來的改善會比改變垂直解析度有作用；而次網格模式的選取對模擬結果則沒有太大的影響。

真實個案的實驗設計，包含了六層網格嵌套，水平網格解析度如下: d1(12150公尺), d2(4050公尺), d3(1350公尺), d4(450公尺), d5(150公尺), d6(50公尺)，其中d1~d3使用WRF中尺度氣象模式進行模擬。

而d4~d6使用WRF turbulence-resolving large-eddy simulation (WRF-LES)來進行模擬。

d1~d3的敏感度測試包括：(1)再分析資料的選取(NARR vs. GCIP)；(2)horizontal turbulence參數化的選取。

而d4~d6的敏感度測試包括：(1)水平網格解析度的改變；(2)再分析資料與次網格模式的選取。

將真實個案的模擬結果與觀測資料進行比對，發現使用與觀測場較相近的再分析資料，其改善影響程度高於horizontal turbulence 參數話的選取。

而WRF-LES模擬結果則顯示提高水平網格解析度對模擬結果有一定程度的改善，而對於再分析資料的敏感度依舊高於次網格模式上的選取。

關鍵字Large-Eddy Simulation, LESSub-grid scale model參考文獻Charles Talbot, Elie Bou-Zeid, and Jim Smith, Nested Mesoscale Large-Eddy Simulations with WRF: Performance in Real Test Cases. J.of Hydrometeorology, 13, DOI: 10.1175/JHM-D-11-048.1, 2012.。

低雷诺数圆柱绕流的大涡模拟分析

低雷诺数圆柱绕流的大涡模拟分析李霖;张志国;王先洲;冯大奎【摘要】以二维圆柱为研究对象,采用大涡模拟的方法对圆柱绕流进行数值模拟.计算的雷诺数Re=400.计算结果能够清晰地反映卡门涡街的周期性脱落.通过对圆柱表面压力分布的深入探究,揭示圆柱尾流中产生周期性旋涡脱落的原因.研究结果中的阻力、升力呈周期性变化规律以及斯特劳哈尔数(St)都与前人实验结果较好吻合,说明大涡模拟能够对低雷诺数的圆柱绕流进行准确的模拟.%In this paper large eddy simulation is used to simulate the flow cross a 2D cylinder. The Reynolds number of the simulation is 400. The alternate eddy formation and shedding is captured precisely in this paper. The analysis of pressure distribution on cylinder reveals the mechanism of Karman vortex street. The drag, lift and Strouhal number obtained by simulation shows a good match with available data from the reference and literature. The large eddy simulation method shows a high quality on the flow field simulating and more attention should be paid on in the future.【期刊名称】《舰船科学技术》【年(卷),期】2013(035)001【总页数】5页(P22-26)【关键词】大涡模拟;圆柱绕流;卡门涡街;压力分布【作者】李霖;张志国;王先洲;冯大奎【作者单位】华中科技大学船舶与海洋工程学院,湖北武汉430074;华中科技大学船舶与海洋工程学院,湖北武汉430074;华中科技大学船舶与海洋工程学院,湖北武汉430074;华中科技大学船舶与海洋工程学院,湖北武汉430074【正文语种】中文【中图分类】O351.30 引言一个世纪以来，圆柱绕流问题一直是经典的流体力学问题之一，也是众多理论分析、数值模拟以及实验研究的对象［1-2］。

大涡模拟的FLUENT算例2D

Tutorial:Modeling Aeroacoustics for a Helmholtz Resonator Using the Direct Method(CAA)IntroductionThe purpose of this tutorial is to provide guidelines and recommendations for the basic setup and solution procedure for a typical aeroacoustic application using computational aeroacoustic(CAA)method.In this tutorial you will learn how to:•Model a Helmholtz resonator.•Use the transient k-epsilon model and the large eddy simulation(LES)model foraeroacoustic application.•Set up,run,and perform postprocessing in FLUENT.PrerequisitesThis tutorial assumes that you are familiar with the user interface,basic setup and solution procedures in FLUENT.This tutorial does not cover mechanics of using acoustics model,but focuses on setting up the problem for Helmholtz-Resonator and solving it.It also assumes that you have basic understanding of aeroacoustic physics.If you have not used FLUENT before,it would be helpful toﬁrst review FLUENT6.3User’s Guide and FLUENT6.3Tutorial Guide.Problem DescriptionA Helmholtz resonator consists of a cavity in a rigid structure that communicates through anarrow neck or slit to the outside air.The frequency of resonance is determined by the mass of air in the neck resonating in conjunction with the compliance of the air in the cavity.The physics behind the Helmholtz resonator is similar to wind noise applications like sun roof buﬀeting.We assume that out of the two cavities that are present,smaller one is the resonator.The motion of theﬂuid takes place because of the inlet velocity of27.78m/s(100km/h).The ﬂow separates into a highly unsteady motion from the opening to the small cavity.This unsteady motion leads to a pressureﬂuctuations.Two monitor points(Point-1and Point-2) act as microphone points to record the generated sound.The acoustic signal is calculated within FLUENT.Theﬂow exits the domain through the pressure outlet.Modeling Aeroacoustics for a Helmholtz Resonator Using the Direct Method(CAA) Preparation1.Copy theﬁles steady.cas.gz,steady.dat.gz,execute-by-name.scm,stptmstp4.scm,ti-to-scm-jos.scm and stptmstp.txt into your working directory.2.Start the2D double precision(2ddp)version of FLUENT.Setup and SolutionStep1:Grid1.Read the initial case and dataﬁles for steady-state(steady.cas.gz and steady.dat.gz).File−→Read−→Case&Data...Ignore the warning that is displayed in the FLUENT console while reading theseﬁles.2.Keep default scale for the grid.Grid−→Scale...3.Display the grid and observe the locations of the two monitor points,Point-1andPoint-2(Figure1).Figure1:Graphics Display of the Grid4.Display and observe the contours of static pressure(Figure2)and velocity magnitude(Figure3)for the initial steady-state solution.Display−→Contours..Modeling Aeroacoustics for a Helmholtz Resonator Using the Direct Method(CAA)Figure2:Contours of Static Pressure(Steady State)Figure3:Contours of Velocity Magnitude(Steady State)Modeling Aeroacoustics for a Helmholtz Resonator Using the Direct Method(CAA) Step2:Models1.Select unsteady solver.Deﬁne−→Models−→Solver...(a)Select Unsteady in the Time list.(b)Select2nd-order-implicit in the Unsteady formulation list.(c)Retain the default settings for other parameters.(d)Click OK to close the Solver panel.2.Deﬁne the viscous model.Deﬁne−→Models−→Viscous...(a)Select Non-Equilibrium Wall Functions in the Near-Wall Treatment list.(b)Retain the default settigns for other parameters.(c)Click OK to close the Viscous Model panel.Near-Wall Treatment predicts good separation and re-attachment points.Step3:MaterialsDeﬁne−→Materials...1.Select ideal-gas from the Density drop-down list.2.Retain the default values for other parameters.3.Click Change/Create and close the Materials panel.Ideal gas law is good in predicting the small changes in the pressure.Step4:Solution1.Monitor the static pressure on point-1and point-2.Solve−→Monitors−→Surface...(a)Enter2for the Surface Monitors.(b)Enable Plot and Print options for monitor-1and monitor-2.(c)Select Time Step from the When list.(d)Click Deﬁne...for monitor-1to open Deﬁne Surface Monitor panel.Modeling Aeroacoustics for a Helmholtz Resonator Using the Direct Method(CAA)i.Select Vertex Average from the Report Type drop-down list.ii.Select Flow Time from the X Axis drop-down list.iii.Enter1for Plot Window.iv.Select point-1from the Surfaces selection list.(e)Similarly,specify the surface monitor parameters for point-2.2.Start the calculations using the following settings.Solve−→Iterate...(a)Enter3e-04s for Time Step Size.The expected time step size for this problem is of the size of about1/10th of thetime period.The time period depends on the frequency(f)which is calculatedusing the following equation:f=c2πSV[L+π2.D h2]where,c=Speed of soundS=Area of the oriﬁce of the resonatorV=Volume of the resonatorL=Length of the connection between the resonator and the freeﬂow areaD h=Hydraulic diameter of the oriﬁceFor this geometry,the estimated frequency is about120Hz.(b)Enter250for the Number of Time Steps.(c)Enter50for Max Iterations per Time Step.(d)Click Apply.Modeling Aeroacoustics for a Helmholtz Resonator Using the Direct Method(CAA)(e)Read the schemeﬁle(stptmstp4.scm).File−→Read−→Scheme...Thisﬁle activates a alternative convergence criteria.For acoustic simulationswith CAA it is obligatory that the pressure is completely converged at the recieverposition.FLUENT compares the monitor quantities within the last n-deﬁned it-erations to judge if the deviation is smaller than a y-deﬁned deviation.(f)Specify the number of previous iterations from which monitor values of eachquantity used are saved and compared to the current(latest)value(include theparanthesis):(set!stptmstp-n5)(g)Specify the relative(the smaller of two values in any comparison)diﬀerenceby which any of the older monitor values(for a selected monitor qauntity)maydiﬀer from the newest value:(set!stptmstp-maxrelchng1.e-02)(h)Deﬁne the execute commands.Solve−→Execute Commandsi.Enter(stptmstp-resetvalues)for theﬁrst command and select Time Stepfrom the drop-down list.ii.Enter(stptmstp-chckcnvrg"/report/surface-integrals vertex-avg point-1 ()pressure")and select Iteration from the drop-down list.iii.Click OK.(i)Click Iterate to start the calculations.The iterations will take a long time to complete.You can skip this simulation af-ter few time steps and read theﬁles(transient.cas.gz and transient.dat.gz)provided with this tutorial.Theseﬁles contain the data for theﬂow time of0.22seconds.As seen in Figures4and5,no pressureﬂuctuations are present at thisstage.The oscillations of the static pressure at both monitor points has reacheda constant value.The RANS-simulation is a good starting point for Large Eddy Simulation.Ifyou choose to use the steady solution as initial condition for LES,use the TUIcommand/solve/initialize/init-instantaneous-vel provides to get a more realisticinstantaneous velocityﬁeld.The usage of LES for acoustic simulations is obliga-tory.The next two pictures compare the static pressure obtained with RANS andLarge Eddy Simulation for a complete simulation until0.525seconds.Obviously,the k-epsilon model underpredicts the strong pressure oscillation after reachinga dynamically steady state(>0.3s)due to its dissipative character.Under-predicted pressure oscillations lead to underpredicted sound pressure level whichmeans the acoustic noise is more gentle.Modeling Aeroacoustics for a Helmholtz Resonator Using the Direct Method(CAA)Figure4:Convergence History of Static Pressure on Point-1(Transient)Figure5:Convergence History of Static Pressure on Point-2(Transient)Modeling Aeroacoustics for a Helmholtz Resonator Using the Direct Method(CAA) Step5:Enable Large Eddy Simulation1.Enter the following TUI command in the FLUENT console:(rpsetvar’les-2d?#t)2.Enable large eddy simulation eﬀects.The k-epsilon model cannot resolve very small pressureﬂuctuations for aeroacousticdue to its dissipative e Large Eddy Simulation to overcome this problem.Deﬁne−→Models−→Viscous...(a)Enable Large Eddy Simulation(LES)in the Model list.(b)Enable WALE in the Subgrid-Scale Model list.(c)Click OK to close the Viscous Model panel.An Information panel will appear,warning about bounded central-deferencing be-ing default for momentum with LES/DES.Modeling Aeroacoustics for a Helmholtz Resonator Using the Direct Method(CAA)(d)Click OK to close the Information panel.3.Retain default discretization schemes and under-relaxation factors.Solve−→Controls−→Solution...4.Enable writing of two surface monitors and specifyﬁle names as monitor-les-1.out andmonitor-les-2.out for monitor plots of point-1and point-2respectively.Solve−→Monitors−→Surface...To account for stochastic components of theﬂow,FLUENT provides two algorithms.These algorithms model theﬂuctuating velocity at velocity inlets.With the spec-tral synthesizer theﬂuctuating velocity components are computed by synthesizing adivergence-free velocity-vectorﬁeld from the summation of Fourier harmonics.5.Enable the spectral synthesizer.Deﬁne−→Boundary Conditions...(a)Select inlet in the Zone list and click Set....i.Select Spectral Synthesizer from the Fluctuating Velocity Algorithm drop-downlist.ii.Retain the default values for other parameters.iii.Click OK to close the Velocity Inlet panel.(b)Close the Boundary Conditions panel.Modeling Aeroacoustics for a Helmholtz Resonator Using the Direct Method(CAA) Typically it takes a long time to get a dynamically steady state.Additionally,thesimulated(and recorded for FFT)ﬂow time depends on the minimum frequency in thefollowing relationship:flowtime=10minimumfrequency(1)The standard transient scheme(iterative time advancement)requires a considerable amount of computaional eﬀort due to a large number of outer iterations performed for each time-step.To accelerate the simulation,the NITA(non-iterative time advance-ment)scheme is an alternative.6.Set the solver parameters.Deﬁne−→Models−→Solver...(a)Enable Non-Iterative Time Advancement in the Transient Controls list.(b)Click OK to close the Solver panel.7.Set the solution parameters.Solve−→Controls−→Solution...(a)Select Fractional Step from the Pressure-Velocity Coupling drop-down list.(b)Click OK to close the Solution Controls panel.8.Disable both the execute commands.Solve−→Execute Commands...9.Continue the simulation with the same time step size for1500time steps to get adynamically steady solution.10.Write the case and dataﬁles(unsteady-ﬁnal.cas.gz and unsteady-ﬁnal.dat.gz).File−→Write−→Case&Data...Figure6:Convergence History of Static Pressure on Point-1(Transient)Figure7:Convergence History of Static Pressure on Point-2(Transient)Step6:Postprocessing1.Display the contours of static pressure to visualize the eddies near the oriﬁce.2.Enable the acoustics model.Deﬁne−→Models−→Acoustics...(a)Enable Ffowcs-Williams&Hawkings from the Model selection list.(b)Retain the default value of2e-05Pa for Reference Acoustic Pressure.To specify a value for the acoustic reference pressure,it is necessary to activatethe acoustic model before starting postprocessing.(c)Retain default settings for other parameters.(d)Click OK to accept the settings.A Warning dialog box appears.This is an informative panel and will not aﬀectthe postprocessing results.(e)Click OK to acknowledge the information and close the Warning panel.3.Plot the sound pressure level(SPL).Plot−→FFT...(a)Click Load Input File...button.(b)Select monitor plotﬁle for Point-1(monitor-les-1.out).(c)Click Plot/Modify Input Signal....i.Select Clip to Range,in the Options list.ii.Enter0.3for Min and0.5for Max in the X Axis Range group box.iii.Select Hanning in the Window drop-down list.Hanning shows good performance in frequency resolution.It cuts the timerecord more smoothly,eliminating discontinuities that occur when data iscut oﬀ.iv.Click Apply/Plot and close the Plot/Modify Input Signal panel.(d)Select Sound Pressure Level(dB)from the Y Axis Function drop-down list.(e)Select Frequency(Hz)in the X Axis Function drop-down list.(f)Click Plot FFT to visualize the frequency distribution at Point-1.(g)Select Write FFT to File in the Options list.Note:Plot FFT button will change to Write FFT.(h)Click Write FFT and specify the name of the FFTﬁle in the resulting Select Filepanel.(i)Similarly write the FFTﬁle for monitor plot for point-2(Figure9).Figure8:Spectral Analysis of Convergence History of Static Pressure on Point-1Figure9:Spectral Analysis of Convergence History of Static Pressure on Point-2In Figures8and9,the sound pressure level(SPL)peak occurs at125Hz which is close to the analytical estimation.Considering that this tutorial uses a slightly large time step and a2D geometry,the result isﬁne.pare the frequency spectra at point-1and point-2.Plot−→File...(a)Click Add...and select two FFTﬁles(point-1-fft.xy and point-2-fft.xy)that you have saved in the previous step.(b)Click Plot to visualize both spectra in the same window(Figure10).Note that the peak for Point-1is a little higher than for Point-2.This is due to the dissipative behaviour of the sound in the domain.The bigger the distance between the reciever point and the noise source,the bigger is the dissipation of sound.This is the reason,why we use CAA method only for nearﬁeld calculations.Figure10:Comparison of Frequency Spectra at Point-1and Point-2A second issue is the dissipation of sound due to the inﬂuence of the grid size.This applies especially for which the wave lengths are very short.Thus,a too coarse mesh is not capable of resolving high frequencies correctly.In the present example,the mesh is rather coarse in the far-ﬁeld.Thus,the discrepancy between both spectra is more evident in the high frequency range.This behaviour can be seen in Figure11.For high frequencies,the monitor for Point-1generates much fewer noise than monitor for Point-2due to coarse grid resolution.Figure11:Spectral Analysis of Convergence history of Static PressureThe deviation of sound pressure level between theﬁrst two maximum peaks(50Hz and132 Hz)is quite small.The postprocessing function magnitude in fourier transform panel is similar to the root mean square value(RMS)of the static pressure at these frequencies. We can use the RMS value to derive the amplitude of the pressureﬂuctuation which is responsible for the SPL-peak.The resolution of frequency spectra is limited by the temporal discretization.With the temporal discretization,the maximum frequency isf max=12 t(2)This frequency is deﬁned as Nyquist frequency.It is the maximum educible frequency.To resolve up to f max the maximum allowable time step size isf max=12×f max(3)Figure12:Spectral Analysis of Convergence History of Static Pressure on Point-1An instability of theﬂuid motion coupled with an acoustic resonance of the cavity(helmholtz resonator)produces large pressureﬂuctuations(at132Hz).Compared to this dominant helmholtz resonance the pressureﬂuctuation at50Hz is quite small.Figure13:Spectral Analysis of Convergence History of Static Pressure on Point-2SummaryAeroacoustic simulation of Helmholtz resonator has been performed using k-epsilon model and Large Eddy Simulation model.The advantage of using LES model has been demon-strated.You also learned how the sound dissipation occurs in the domain by monitoring sound pressure level at two diﬀerent points in the domain.The importance of using CAA method has also been explained.。

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Advanced Materials Research Vols. 255-260
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∂ρτ ij ∂ρu i ∂ρu i u j ∂u ∂P ∂ + =− + (µ i ) + + ρg i ∂t ∂x j ∂xi ∂x j xj ∂x j
(2)
1 where “—” is the solvable scale varible, P = p + ρδ ijτ kk is the correction pressure, ρ is the fluid 3 density, τ ij is the subgrid-scale sress. In this article, the Smagorinsky’s model:
3468
Advances in Civil Engineering, CEBM 2011
vertical drop is placed at the end of reversion curve. Figure 1 shows the numerical model. The numerical grid used the structured grid because the numerical model was simple.
Abstract: The simulation of hydraulic characteristics was carried out with Larger Eddy Simulation (LES) and Volume of Fluid (VOF) method. The numerical results show that the flow condition is smooth, the length of lateral cavity gradually increases with the size of lateral enlargement increases, the maximum pressure value on the lateral wall appears after the bottom cavity, the upper part of the lateral cavity region was longer than the lower part due to gravity and the backwater does not intrude into bottom cavity. The numerical results agree well with the experimental date. The new lateral aerator has good hydraulic characteristics and the LES with VOF method can well predict the hydraulic characteristics after the new lateral aerator. Introduction In recent years, the aerator of a deflector and vertical drop was placed at the end of reversion curve of spillway to prevent cavitation damage. But the size of deflector weakly changes makes the flow condition deteriorates rapidly and the length of the lateral cavity increases rapidly[1-2]. This aerator has a badly hydraulic characteristics and difficultly applies the similar future engineering projects. In this article, a sudden lateral enlargement and vertical drop was placed at the end of reversion curve of spillway. The simulation of hydraulic characteristics was carried out by the Large Eddy Simulation (LES) with Volume of Fluid (VOF) method. The flow conditions, the variation laws of the length of the lateral cavity, the maximum value of pressure on the lateral wall and the form of lateral cavity were obtained. The numerical results agree well with the experiment. The research results provide reference to design and scientific research. Mathematical Formula and Boundry Condition Large Eddy Simulation. The governing equations of LES are obtained by filtering the N-S equations use box filter in this artical. The filtering N-S equations of incompressible water-air two phase flow as
Large Eddy Simulation of Hydraulic Characteristics after New Lateral Aerator Guojing Lia, Guangqing Daib, Qing Yangc, Xudong Mad
State Key Laboratory of Hydraulics and Mountain River Engineering，Sichuan University, Chengdu 610065, China
∆=
13
V
(5)
where S ij is the resolved rate-of-strain tensor defined by:
S ij =
∂u 1 ∂u i + j 2 ∂x j ∂xi

(6)
VOF Method. The VOF methord is the water-air phase use the same velocity and pressure field, the water free surface is get only by adding a continuous equation of water volume fraction in
∂ρ ∂ρu i +erved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP, . (ID: 130.113.151.253, McMaster University, Hamilton, Canada-24/03/15,20:21:29)
a
lengbingshuang01@, b daigq01@, c youngking411@,
d
yanyangma@
Keywords: Large Eddy Simulation; VOF method; Lateral enlargement and vertical drop; Aeration to prevent cavitation damage; Lateral cavity.
Fig.1 The numerical model The water inlet boundary used velocity-inlet boundary. The wall boundary used no-slip and no-penetration boundary. The water outlet boundary used outflow boundary, grad(u)=0. The air inlet boundary used pressure inlte boundary and pressure value was atmospheric pressure. Reference pressure used atmospheric pressure. Results Analysis and Discussion Flow Condition and Length of Lateral Cavity. The flow condition and the length of lateral cavity is the important assessment indexes for a sudden lateral enlargement and vertical drop. When a deflector was installed on the lateral wall, the size of deflector weakly increases makes the flow condition deteriorate rapidly and the length of lateal cavity increases rapidly[3]. The reasion is that the flow line is contracted by the defletor and the flow is jeted out at the end of deflector, the size of deflector increases make the outflow angle of jet flow increases, the length of lateral cavity rapidly becomes larger than bottom cavity and makes the flow condition deteriorate rapidly. But when the lateral enlargement is placed at the end of reversion curve, the flow condition is very smooth and the length of lateral cavity gradually with the size of lateral enlargement, Table 1 shows the length of cavity of four schemes, Figure 2 shows the flow condition of four schemes. When the size of lateral enlargement gradually increases, the weakly water-wing gradually appears after the bottom cavity, Figure 2 (d) shows the weakly water-wing after the bottom cavity. The reasion is that spread angle of jet flow is mainly affected by the pressure change at the end of reversion curve, when the pressure change is fixed, the increase of lateral enlargement make the length of lateral cavity gradually increases. From the Table 1, it can be founded that the length of cavity obtained by the numerical simulation with LES and VOF method agrees well with the experiment. Pressurelaw along Lateral Wall and Bottom. The pressurelaw along the lateral wall and bottom is one of the important assessment indexes for a sudden lateral enlargement and vertical drop. The weakly negative pressure appears on the lateral and bottom in the cavity. The maximu pressure on the lateral wall and bottom appears after the bottom cavity and the maximum pressure on the lateral wall has nothing with the length of the lateral cavity, Figure 3 show the maximu pressure on the lateral wall and bottom. The pressure gradually becomes stationary distribution after the zone of the maximum pressure. Figure 4 shows the pressurelaw along the lateral wall, Figure 5 shows the pressure along the bottom. It can be found from Figure 4 and Fifure 5 that the satisfactory agreements between numerical and experimental results for the pressurelaw along the lateral wall and bottom.