Experiments investigation of the effects of surface roughness on laminar flow in macro tubes

Experiments investigation of the effects of surface roughness on laminar flow in macro tubesK.Huang a ,J.W.Wan a ,⇑,C.X.Chen a ,D.F.Mao b ,Y.Q.Li caSchool of Environmental Studies,China University of Geosciences,430074Wuhan,China bWISDRI Engineering &Research Incorporation Limited,Wuhan,China cThree Gorges Survey Research Institute Company Limited,Wuhan,Chinaa r t i c l e i n f o Article history:Received 14September 2012Received in revised form 11October 2012Accepted 14October 2012Available online 27November 2012Keywords:Laminar flowSurface roughness Friction factor Head dropa b s t r a c tThis paper experimentally investigated the effects of surface roughness on laminar flow in macro tubes (d =19mm).Head drop experiments were conducted in six organic glass tubes with relative roughness (D /d )ranging from 1/118.75to 1/6.66.Water head drop data were used to characterize the friction factor over a Reynolds number ranging from 300to 25000.The experimental results for tubes with relative roughness (D /d <5%)were in good agreement with Nikuradse’study.The friction factor could be well predicted by theoretical correlation fRe in laminar flow.Obvious deviation of the friction factor from the classical theory was observed for tubes with large relative roughness (D /d >5%).The product of fRe was larger than 64and increased with an increase in relative roughness.Earlier transition from laminar to turbulent flow was also confirmed.The critical Reynolds number linearly deceased as the relative roughness increased.Ó2012Elsevier Inc.All rights reserved.1.IntroductionThe effects of surface roughness on flow in pipes have been studied over a century.Several of experiments were carried out to investigate the exact effects roughness has on water flow,but whether there were deviation from conventional theory in laminar flow and an early transition from laminar to turbulence flow are still controversial.The pioneering work on effects of surface roughness were stud-ied by Darcy [1]and Fanning [2]in the nineteenth century,how-ever the systematic work on understanding the relationship between surface roughness and pressure drop was conducted by Nikuradse [3].The results of Nikuradse’experiments showed that the value of fRe was equal to 64for laminar flow and the transition Reynolds number from laminar to turbulent flow was around 2000.These were the classical theory on flow in rough pipes and have been used for over a century.In recently years,experimental results in micro scale level have found some new characters in laminar flow.Peiyi and Little [4]are ones of the pioneer investigators who studied the deviation in lam-inar flow in microchannels with high ‘‘relative roughness’’(D /d =0.2–0.3).They studied different gases flow in rectangular and trapezoidal channels (d =55.8–72.4l m).The friction factor ob-tained were larger (10–30%)than those predicted by the classicaltheory and an earlier transition from laminar to turbulent flow oc-curred at Reynolds number from 400to 900.Li [5]experimentally investigated water flow in glass,silicon,and stainless steel micro-tubes with diameters ranging from 80lm to 205l m to studied the effect of surface roughness on flow characteristics.The experimen-tal results showed that the frictional factor measured in smooth tubes made of glass and silicon was in good agreement with the conventional theory.For stainless steel tubes with higher rough-ness,the value of fRe was 15%higher than the theoretical predic-tions in laminar flow when ‘‘relative roughness’’was larger than 5%.An earlier transition also was observed at lower Reynolds num-ber (1700–1900).Tang et al.[6]experimentally investigated flow characteristics for gas in stainless steel and fused silica microtubes with diameter ranging from 50to 200l m.The authors found that the friction fac-tor in silica channels were well predicted by the conventional the-ory while for stainless steel tubes the friction factors were much higher than theoretical values.They explained the phenomenon due to larger relative roughness of stainless steel tubes.When the relative surface roughness was larger than 5%,the friction fac-tor would deviate from the theoretical value.Mala and Li [7]con-ducted experiments on water flow in microtubes with diameters ranging from 50to 254l m.The authors found that for larger diam-eter tubes the experimental results were in good agreement with classic theory,while for smaller tubes the friction factor gradually deviated from the conventional theory and the product fRe in-creased as the diameter of the tubes decrease.The measured fric-0894-1777/$-see front matter Ó2012Elsevier Inc.All rights reserved./10.1016/j.expthermflusci.2012.10.022Corresponding author.E-mail address:cugwanjw@ (J.W.Wan).tion factor may be due to the effects of surface roughness of the microtubes.Xu et al.[8]experimentally investigated waterflow in microchannels with hydraulic diameter ranging from50l m to 300l m.They observed that the experimental results deviated from classical theory for tube diameters lower than100.Judy et al.[9]investigated theflow characteristics of three differentflu-ids(water,hexane,and isopropanol)in capillaries with diameters ranging from20to150l m.The results also revealed that friction factor deviated from conventional theory when the diameter was below100l m.Similar conclusions were given by other investiga-tors[10–12].To investigating the specific effects of relative tough-ness on liquidflow in rough tubes,Kandlikar[13]reassessing Nikuradse’s experiments and proposed a new definition of average roughness[14–16].Brackbill and Kandlikar[17]experimentally determined the effect of roughness and friction factor in micro-tubes.They confirmed that the roughness effect in laminar region and the friction factor could be well predicted by Kandlikar’s con-strictedflow parameters.Schmitt and Kandlikar[18]determined the laminar friction factor by using constricted diameter and ob-tained a correlation between relative roughness and relative roughness.The above results indicated that the relative roughness may be the cause of deviation from conventional theory,but contra-dictory results were gotten by other investigators.Judy et al.[19]conducted experiments on different liquidflow in micro-channels made of fused silica and stainless steel with diameters ranging from15l m to150l m.All experimental data were in good agreement with classic theory and no deviation was ob-served for diameter or material of the tubes.Hwang and Kim [20]investigatedflow characteristics in microtubes with diame-ter of0.244,0.430,and0.792mm.The results could be well pre-dicted by theory within an average deviation of8.9%.The authors considered that the diversity deviation on friction factor may be caused by the inaccuracy measurement of the inner diameter of the tubes.Dutkowski[21]experimentally studied water and airflow in stainless steel tubes with inner diameters of0.55,0.64and 1.1mm.The friction factor obtained from experiments was well predicted by conventional theory.Sara et al.[22]conducted experiments with water in tubes with the diameter of0.2mm and their results showed good agreements with the classic theory.Lorenzini et al.[23]reviewed the past experimental investigations,and then theoretically and experi-mentally studied airflow characteristics in circular channels from26l m to508l m in diameter with different surface rough-ness.The results showed friction factor in laminar regime was in good agreement with the conventional theory.For both smooth and rough tubes.The authors consider that the deviation from the Poiseuille law for microchannel with diameter less than 100l m was due to compressibility effects but not surface roughness effects.Barlak et al.[24]investigated friction factor and pressure drop in tubes from0.2mm to0.589mm in diame-ter and the length-to-diameter ratios ranging from16to265. The experimental data also well agreed with the conventional theory.Although many experimental studies have found large relative roughness may cause the deviation from conventional theory in laminar regime,it’s still a controversial issue and required further investigation.All the above-mentioned experiments were con-ducted in microchannels with different diameters and the surface roughness was only determined by the material of tubes,so the ef-fects of roughness onflow characteristics haven’t been systematic investigated.Nikuradse conducted experiments in tubes with low relative roughness,but deviation in laminarflow was always ob-served in tubes with large relative roughness(D/d>%5).The focus of this paper is to present a comprehensive experimental investiga-tion on pressure drop and friction factor of laminarflow through tubes with relative roughness ranging from1/118.75to1/6.66. The tubes with lower roughness were used to verify the accuracy of Nikuradse’s experiments,and the larger roughness tubes were to explore the relationship between relative roughness andflow characteristics in laminar regime.Further,the experimental results will be compared with the past work.Possible reason for the phe-nomenon of laminarflow in rough tubes will be proposed.Espe-cially,the follow two questions will be discussed:(1)Whether the value of fRe is large than64in rough tubes?(2)Whether there is an earlier transition to turbulentflow inrough tubes?2.Experimental setup and data reduction2.1.Experimental setupThe experimental apparatus used in this investigation is de-picted schematically in Fig.1.It mainly consists of three parts: an adjustment valve,test section(rough tubes)and measurement equipment.Water was supplied by the centrifugal pump to the test tube andflow rate was adjusted by the inflow valve.After passing through the test tube,water was collected by a tank.Thefluidflow rate was calculated by water volume collected over a correspond-ing measured elapsed time.To minimize errors,flow rate were ob-served three times for a certain head drop and mean value was adopted.Three piezometer tubes were used to measure the water head drop.The location of the piezometer tubes was shown in Fig.1.Piezometer tubes were500mm away from both ends of the test tube to decrease the inlet and outlet effects.Meanwhile, water temperature was also measured by thermometer.In this study,the sections included six organic glass tubes with different relative roughness(D/d).Each test tube is3000mm in length,19mm in inner diameter(d).Method to create roughness on the inside walls of the tubes was similar with Nikuradse’exper-iments.To keep uniform roughness throughout the tubes,sifted sand was chosen to create the surface roughness(D).For example, in order to obtain surface roughness of0.16mm,sand was sifted in sieves having opening of0.15–0.17mm diameter.The information of rough tubes with different relative roughness is shown in Table1.But the method to stick the sand grains to the walls of the tubes in this study was different from Nikuradse’experiments. In Nikuradse’experiments,Japanese lacquer was chosen as binder. The tubes werefirstfilled with Japanese lacquer and then emptied, and thenfilled with sifted sand grain and emptied.To assure good adherence of sand grains to the wall,the tubes were refilled with lacquer and again emptied after a drying period of2–3weeks.This resulted in a thin coat of lacquer on the surface of the particles which caused the relative roughness values ranged between0% and3.3%[13].Therefore,Chloroform was used to stick the sand grains to the walls of the tubes and the refilled process was not adapted in this study.2.2.Data reductionReynolds number(Re)and friction factor(f),were defined as the same with Nikuradse.Reynolds number was calculated from equa-tion with the following form:Re¼udmð1Þin which m is the kinematic viscosity,u is the averageflow velocity which can be determined by the following formula:u¼QÁ4p dð2Þ244K.Huang et al./Experimental Thermal and Fluid Science45(2013)243–248where Q is the measured flow rate,d is the diameter of the tube.Once the average flow velocity has been determined from Eq.(2),Reynolds number could be obtained by putting u in Eq.(1).The friction factor f is determined as the following equation:f ¼2gdu 2J ð3ÞWhere J is the hydraulic gradient which means the head drop re-ferred to a length unit of the tube.The experimental uncertainties of the parameters were listed in Table 2.The uncertainty of the Reynolds number and the friction factor is determined by equation using the method described by Abernethy et al.[25].y ¼f ðx 1;x 2;...;x N Þd y ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi@f @x 1d x 1 2þÁÁÁþ@f@x Nd x N 2"#v u u tð4ÞBy applying Eq.(4),the calculated mean uncertainty for theReynolds number and friction factor are 3.2%and 5.9%,respectively.3.Results and discussionWater head drop was measured with the tubes had different surface roughness at various flow rates.Reynolds number is calcu-lated by Eq.(1).Fig.2shows the experimental results of hydraulicgradient (J )depending of Reynolds number for water flow in six rough tubes with relative roughness D /d =1/118.75,1/61.79,1/30.89,1/14.18,1/10.56,1/6.66.Fig.2a presents that the value ofJTable 1Relative roughness results.Number d (mm)D (mm)Sieves diameter (mm)D /d R1190.160.15–0.171/118.75R20.30750.3–0.3151/61.79R30.6150.6–0.631/30.89R4 1.34 1.25–1.431/14.18R5 1.8 1.6–21/10.56R62.852.5–3.21/6.66Table 2Experimental uncertainties of the major parameters.Parameter Uncertainty ParameterUncertainty Diameter (d )±1%Time (t )±0.1s Temperature (T )±0.1°C Volume (V )±1%Head (H )±1mm Reynolds number (Re )±3.2%Length (L )±1mmFriction factor (f )±5.9%K.Huang et al./Experimental Thermal and Fluid Science 45(2013)243–248245increased as the value of Re increased.With the same value of Re, the hydraulic gradient value was greater for tubes having larger relative roughness.On the transition from laminarflow into turbu-lentflow,the relationship between Re and J shows a non-linear behavior.Fig.2b shows the slope of the curve on J versus Re rise rapidly at Re=2000for tubes R1-4.However,it seems that the transition for tubes R5-6occurred a little earlier for Re in the range of1500–1800(Fig.2c).Besides,the hydraulic gradient values of R1 are sometimes slightly higher than the hydraulic gradient values of R2when Re is larger than about2100(Fig.2b).This phenomenon occurred in the region called thefirst portion of turbulentflow by Nikuradse,where the waterflow became unstable with the streamlinefluctuating stochastically.Considering that the value of J was close in this region,theflowfluctuation may influence the measurement of water head drop and the experiments results.In order to ascertain whether the experimental results deviated from classical theory for tubes with large surface roughness,theMoody chart was used to plot the experimental data.The theoret-ical value of fRe is equal to64for incompressible laminarflow in circular tube.In Fig.3,friction factor is plotted as a function of Re by experi-mental data from both Nikuradse’study with relative roughness D/ d=1/120,1/60,1/30and this study with D/d=1/118.75,1/61.79, 1/30.89.Fig.3shows the results of experimental investigations were in good agreement with Nikuradse’in laminarflow.It can be noted that the experimental data follow with the theoretical lin-ear law at low Reynolds number within the range of 300<Re<2000.The roughness had no effects on the friction in laminarflow and the value of friction factor is equal to64/Re. The deviation from laminar to turbulentflow occurred around Re=2000.However,the friction factors of this research were high-er than the friction factors of Nikuradse’research when Re is larger than about6000,although the relative roughness is almost the same(1/30.89and1/30,1/61.79and1/60,1/118.75and1/120). This could be explained by the different method for sticking the sand grains.The process that refilled lacquer in the test tubes by Nikuradse would result in the relative roughness less than actual value which caused the friction factors decreasing as well in tran-sitional and turbulent region.Fig.4presents the friction factor as a function of Reynolds num-ber for tubes with larger value of relative roughness(D/d=1/14.18, 1/10.56,1/6.66).In the laminar region,the diagram still shows lin-ear relationship between friction factor and Reynolds number,but the product of fRe is no longer equal to64.The value of friction fac-tor increased with an increase in relative roughness for the same value of Reynolds number.In attempt to investigate the roughness effect on friction factor, product of fRe is plotted as a function of D/d by experimental results(Fig.5).Fig.5shows that the value of fRe slowly rose as the relative roughness increased for laminarflow when the relative roughness is less than1/30.89and the value of fRe increase qua-dratic as the Re increased when the relative roughness is larger than5%.The correlation of experimental data gave the following equation with R2=0.9985.It can be seen that surface roughness caused a sharp increase of fRe for laminarflow when the relative roughness is larger than5%.Similar conclusion was also obtained by Kandlikar et al.[26],Brackbill and Kandlikar[17].Constricted flow was used to explain the deviation from theoretical law in lam-inarflow in tubes with large surface roughness in Kandlikar’s study.The constrictedflow parameter is defined as follows:d cf¼dÀ2Dð5Þwhere d cf is the constrictedflow diameter,d is the inner diameter of the tube,and D is the surface roughness.The Reynolds number and friction factor were accordingly defined based on the constricted flow diameter as follows:Re cf¼u cf d cfm¼dcfÁReð6Þf cf¼2gdcfu2ÁJ¼fÁd5cfdð7ÞThe product of fRe can be written as Eq.(8):fRe¼f cf Re cfÁd4d4cf¼f cf Re cfÁd4ðdÀ2DÞ4ð8ÞThe value of f cf Re cf in laminarflow is equal to64,so Eq.(8)can be written as follows:246K.Huang et al./Experimental Thermal and Fluid Science45(2013)243–248fRe¼64Ád4ðdÀ2DÞ4ð9ÞEq.(9)indicated that the value of fRe is equal to64in laminar flow region for smooth tubes(D=0).As the surface roughness in-creased,the product of fRe increased accordingly.When the surface roughness is small enough(D/d<5%),the deviation from laminar flow can be neglected.The above analysis has been verified by the experimental results.It can be seen from Fig.4that the effect of roughness on transi-tion to turbulence was also confirmed by experimental results.The critical Reynolds number Re c decreased with an increase of surface roughness,for the increased roughness would provide larger inter-acted area on the surface roughness.The surface roughness would bend theflow line near the inner surface,causing earlier transition to turbulence.The critical Reynolds number was plotted as a func-tion of relative roughness in Fig.6.As what mentioned before,the critical Reynolds number Re c for tubes with relative roughness less than1/30was well predicted by the theoretical law,with the value of Re c around2000.But for tubes with relative roughness larger than0.06,the critical Rey-nolds number dramatically decreased.The critical Reynolds num-ber has been modeled as a linefit and is given as Re c=2277.7À5965(D/d)with a coefficient of determination(R2) of0.9986.Brackbill and Kandlikar proposed similar linear correla-tion to predict the critical Reynolds number forflow in microchan-nel,which agreed with constricted model well[27].But the slope of the correlation presented by Brackbill and Kandlikar is higher than that in this study.The correlation to predict the critical Rey-nolds number forflow in macro tubes should be investigated by more experiments.4.ConclusionsThe paper presents experimental results of effect of roughness on waterflow in macro tubes with inner diameter d=19mm. The test tubes were made in organic glass with relative roughness ranging from1/118.75to1/6.66.The main conclusions can be summarized as follows:–The results of experimental investigations were in good agree-ment with Nikuradse’in laminarflow for tubes with D/d<1/ 30;transition from laminarflow to turbulentflow occurred around Re=2000and the product of fRe was equal to64.–Constrictedflow model could explain the deviation from theo-retical law in laminarflow in tubes with large surface roughness and experimental results in this paper also agreed with the model.–Earlier transition was observed when relative roughness D/d>5%;the critical Reynolds number could be calculated byequation:Re c¼2277:7À5965ðD=dÞ.–Friction factor of laminarflow deviated from theoretical corre-lation f Re when relative roughness D/d>5%;the product of fRe could be predicted by equation when relative roughness D/d>5%:fRe=10217(D/d)2À888.86(D/d)+83.454. 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