Simulation of Cavitating Flow around a 2-D Hydrofoil

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流体空化热效应的实验研究

摘要我国稠油资源丰富，对其进行降黏开采对于我国国民经济发展意义重大。

目前常用的蒸汽驱、蒸汽吞吐、电加热等方法存在设备复杂、成本高、能量损耗大、安全性差等缺点，寻找新的开采方法势在必行。

空化是发生在液体介质中的一种物理现象。

空化发生时，会在空泡附近形成极端高温（1900-5000K）和高压（140MPa-170MPa），并伴有强烈的冲击波和微射流。

如何有效利用空化过程中的这种极端热效应成为部分专家学者关注的课题。

基于以上几点，本文对流体空化过程中的热效应问题开展了实验研究，得到以下结论：（1）总结分析了空化类型与作用机理，确定了以闭式叶轮为核心的水力空化发生方式。

（2）基于数值模拟的方法，使用CFX软件对不同叶轮结构内空化情况进行了对比分析，选定进口角为11.2、出口角为36的叶轮用于后续的实验研究。

（3）设计并制作了空化热效应室内实验装置，对空化发生器部件进行了机械强度校核。

（4）利用空化热效应实验装置，研究了不同参量（流体初始温度、流量、流体体积、粘度）对流体空化热效应的影响规律，结果发现：在当前实验条件下，随着流量的增加，流体空化热效应先增强后减弱，在流量为1.6m3/h时流体空化热效应最佳；随着黄原胶粘度的增加，空化热效应逐渐受到抑制；流体初始温度（0-40°C）、流体体积对空化热效应的影响可以忽略不计。

研究成果对于弄清空化热效应的内在规律，拓展空化技术在石油领域的应用具有重要意义。

关键词：空化，热效应，叶轮，数值模拟，实验研究Experimental Research on Thermal Effect of Cavitating FluidQiu Junjie (Oil & Gas Well Engineering)Directed by Prof. Wang MingboAbstractThere is abundant heavy oil resource in mainland China. Steam flooding, steam stimulation and electric heating are very popular to develop heavy oil reservoir. These methods have disadvantages of complex equipment, high cost, large energy loss and insecurity. It is necessary to find a new and economical method to enhance the recovery of heavy oil resources.Cavitation is a physical phenomenon occured in liquid media. When cavitation occurs, extremely high temperature(1900-5000K) and pressure(140MPa-170MPa) are formed around the tiny bubbles, accompanied by strong shock waves and microjets. How to use the extreme thermal effect of cavitation has gained more and more attention from experts and scholars.On the basis of the points above, experimental research on the thermal effect of cavitating fluid is carried out in this thesis. The following conclusions are drawn from the thesis:(1)With the summary and analysis of the cavitation modes and working mechanisms, the hydrodynamic cavitation mode with the shrouded impeller was applied to the experimental study.(2)The cavitating effects with different impeller structures were simulated and analysed by commercial software CFX and the impeller with inlet angle of 11.2° and outlet angle of 36°was chosen for subsequent experimental research.(3)An experimental facility for the thermal effect of cavitating fluid was designed and manufactured and its mechanical strength was validated.(4)The influence of different parameters(initial temperature, flow rate, flow volume and fluid viscosity) on the thermal effect of cavitating fluid was analysed and the following conclusions were drawn that: As the flow rate increases, the thermal effect of cavitation increases at first and decreases later, reaching its peak value when the flow rate is 1.6m3/h; With the increase of xanthan gum viscosity, the thermal effect of cavitation is supressed; The influence of fluid temperature(under 40°C) and flow volume on the thermal effect of cavitation can be ignored.The research results are of great significance to finding out the internal law of thermal effect of cavitating fluid and expanding the application of cavitation technology in the field ofpetroleum.Key Words:cavitation, thermal effect, impeller, numerical simulation, experimental research目录第一章绪论 (1)1.1 研究目的及意义 (1)1.2 国内外研究进展 (1)1.2.1 空化的分类与发生方式 (1)1.2.2 空化理论研究进展 (2)1.2.3 空化实验研究进展 (3)1.2.4 空化数值模拟研究进展 (5)1.3 研究内容与技术路线 (9)第二章叶轮空化场的数值模拟 (10)2.1 叶轮设计 (10)2.2 数学模型 (11)2.2.1 Mixture模型 (11)2.2.2 湍流模型 (12)2.2.3 空化模型 (13)2.3 建模求解 (14)2.3.1 物理模型的建立 (14)2.3.2 网格划分 (15)2.3.3 求解设置 (17)2.4 结果分析 (17)2.4.1 压力分布 (17)2.4.2 速度场分布 (18)2.4.3 汽含率分布 (20)2.5 本章小结 (22)第三章空化热效应实验装置的设计 (23)3.1 实验系统设计 (23)3.2 部件设计 (23)3.2.1 驱动电机的选择 (23)3.2.2 基座设计 (24)3.2.3 连接盘设计 (24)3.2.4 支撑盘设计 (25)3.2.5 叶轮设计 (25)3.2.6 空化罐设计 (25)3.2.7 配套组件设计 (26)3.3 强度校核 (27)3.4 本章小结 (34)第四章空化热效应的实验研究 (35)4.1 实验方案介绍 (35)4.2 流体初始温度对空化热效应的影响 (38)4.3 流量对空化热效应的影响 (39)4.4 流体体积对空化热效应的影响 (41)4.5 黄原胶溶液粘度实验 (41)4.5.1 空化对溶液粘度的影响 (41)4.5.2 溶液粘度对空化热效应的影响 (43)4.6 导热油加热实验 (44)4.7 本章小结 (45)结论 (46)参考文献 (47)致谢 (51)中国石油大学（华东）硕士学位论文第一章绪论1.1 研究目的及意义我国稠油资源丰富，占原油总储量的20%以上。

离心泵的空化流数值模拟与空化余量预测

离心泵的空化流数值模拟与空化余量预测赖喜德;廖功磊;曾维国【摘要】空化余量是泵非常重要的性能指标之一,目前主要依靠试验来确定.如何在离心泵设计过程中较为准确地预测出必须的空化余量对优化设计和提高运行稳定性等方面十分重要.针对离心泵运行过程中发生空化时的流动特点,基于Rayleigh-Plesset方程来描述空泡生长和溃灭过程的空泡动力学模型,采用混合空化两相流模型和三维全流道两相流流动数值模拟技术,探索通过数值试验来预测空化余量的方法.对一低比转速离心泵进行全流道空化流数值模拟,通过改变NPSHa来模拟试验工况,数值模拟预测出各模拟试验工况下的扬程、叶片表面压力分布、叶片表面空化发生区域以及流道内空泡体积率分布,从而预测该泵的NPSHr,其预测结果与试验值的误差小于10％.%NPSHr is one of the most important performance of a pump, which is mainly derived from hydraulic model tests. How to accurately predict a pump' s NPSHr is a great challenge to optimize design and enhance operating stability. Based on cavitating flow feature inside a centrifugal pump, bubble growth and implosion are calculated from the Rayleigh - Plesset equation which describes the dynamic behavior of spherical bubble, filled with vapor and gas, as a function of the local pressure. A numerical simulation of two -phase flow with a homogenous mixture of gas and liquid inside a centrifugal pump was employed to explore the methodology of predicting NPSHr with numerical test approach. A numerical simulation for cavitating flow inside a low specified speed centrifugal pump was conducted in whole passage. The numerical test was carried out for the centrifugal pump at different operatingconditions by varying NPSHa, which is similar to hydraulic tests, NPSHr for this pump can be predicted from the head -drop curves which were computed by numerical simulation. Meanwhile, the pressure distribution on blades surfaces, districts where cavitation occurred, and vapor volume fraction inside the flow passage of a pump could be used to investigate the cavitating flows and helpful to determine NPSHr value. It showed that the predicted result agreed with the measured results by hydraulic tests and the maximum error was within 10%.【期刊名称】《西华大学学报（自然科学版）》【年(卷),期】2013(032)002【总页数】4页(P29-32)【关键词】离心泵;空化流;两相流;数值模拟;性能预测【作者】赖喜德;廖功磊;曾维国【作者单位】西华大学能源与环境学院,四川成都610039【正文语种】中文【中图分类】TH311空化流动是水力机械运行过程中在流道中普遍存在的一种复杂的流动现象。

openfoam cavity算例

英文回答：The openFOAM cavity case represents a highly recognizedputational fluid dynamics (CFD) model, specifically designed to simulate the fluid flow within a 2D cavity. This case is extensively utilized for the validation and rigorous testing of CFD solvers, as well as for the in-depth analysis of fluid behavior within a confined space. The cavity geometryprises a rectangular domain featuring lid-driven cavity flow, where the constant velocity of the top boundary induces a circulating flow pattern within the cavity. The openFOAM cavity case offers users the opportunity to investigate andprehend the impact of various turbulence models, solver configurations, and boundary conditions on the flow dynamics.开放的FOAM腔外壳代表一种高度识别的流体动力学（CFD）模型，专门用来模拟2D腔内的流体流。

该案被广泛用于CFD解析器的验证和严格测试，以及深入分析封闭空间内的流体行为。

腔状几何特征是一个长方形域，以盖式驱动的腔流为特征，其中顶部边界的恒定速度在腔内诱导一个循环流模式。

flunt文献

[1] G. K. Batchelor.An Introduction to Fluid Dynamics.Cambridge Univ. Press, Cambridge, England, 1967.[2] D. Cokljat, V. A. Ivanov, and S. A. Vasquez.A Non-Equilibrium Two-Phase Model for Cavitating Flows.In Third International Conference on Multiphase Flow, Lyon, France, 1998. Available on ICMF98 CD-ROM, paper 224.[3] J. L. Ferzieger and M. Peric.Computational Methods for Fluid Dynamics.Springer-Verlag, Heidelberg, 1996.[4] J. Janicka and W. Kollmann.A Numerical Study of Oscillating Flow Around a Circular Cylinder.Combustion and Flame, 44:319--336, 1982.[5] W. P. Jones and J. H. Whitelaw.Calculation Methods for Reacting Turbulent Flows: A Review.Combust. Flame, 48:1--26, 1982.[6] W. M. Kays.Turbulent Prandtl Number - Where Are We?J. Heat Transfer, 116:284--295, 1994.[7] B. E. Launder.Second-Moment Closure and Its Use in Modeling Turbulent Industrial Flows. International Journal for Numerical Methods in Fluids, 9:963--985, 1989.[8] B. E. Launder.Second-Moment Closure: Present... and Future?Inter. J. Heat Fluid Flow, 10(4):282--300, 1989.[9] B. E. Launder, G. J. Reece, and W. Rodi.Progress in the Development of a Reynolds-Stress Turbulence Closure.J. Fluid Mech., 68(3):537--566, April 1975.[10] B. E. Launder and N. Shima.Second-Moment Closure for the Near-Wall Sublayer: Development and Application. AIAA Journal, 27(10):1319--1325, 1989.[11] B. E. Launder and D. B. Spalding.Lectures in Mathematical Models of Turbulence.Academic Press, London, England, 1972.[12] B. E. Launder and D. B. Spalding.The Numerical Computation of Turbulent Flows.Computer Methods in Applied Mechanics and Engineering, 3:269--289, 1974.[13] J. P. Vandoormaal and G. D. Raithby.Enhancements of the SIMPLE Method for Predicting Incompressible Fluid Flows. Numer. Heat Transfer, 7:147--163, 1984.[14] L. D. Smoot and P. J. Smith.NOx Pollutant Formation in a Turbulent Coal System.In Coal Combustion and Gasification, page 373, Plenum, Plenum, NY, 1985.[15] F. C. Lockwood and C. A. Romo-Millanes.Mathematical Modelling of Fuel - NO Emissions From PF Burners.J. Int. Energy, 65:144--152, September 1992.[16] R. K. Boyd and J. H. Kent.Three-dimensional furnace computer modeling.In 21stSymp. (Int'l.) on Combustion, pages 265--274. The Combustion Institute, 1986.[17] M. Manninen, V. Taivassalo, and S. Kallio.On the Mixture Model for Multiphase Flow.VIT Publications, Technical Research Centre of Finland, 1996.。

Method and system for simulating flow of fluid aro

专利名称：Method and system for simulating flow offluid around a body发明人：Toshihiro Kamatsuchi申请号：US12005381申请日：20071227公开号：US20080177511A1公开日：20080724专利内容由知识产权出版社提供专利附图：摘要：A simulation method for flow of fluid around a body, according to the present invention, comprising dividing a target domain of simulation into a plurality ofcomputational unit domains named cubes, generating an uniform number of Cartesianmesh elements named cells, in each of the cubes, performing computation in the cubes in each computational step, and exchanging data between adjacent cubes after completion of each computational step. In dividing the target domain of simulation into cubes, division is repeated while a ratio between adjacent cube sizes is maintained in a certain range until cubes including a boundary between the body and the fluid, is small enough to obtain a desired resolution so that sizes of the cubes are appropriately determined according to a shape of the body.申请人：Toshihiro Kamatsuchi地址：Saitama JP国籍：JP更多信息请下载全文后查看。

翻译

However they were unable to obtain the information about the velocity field inside the cavitationitself. The problem they faced was overexposure of the particles added to the water (they were not visible since thevapourstructure reflects much more light), so the velocity field inside the cavitation structure was notdetermined. The method appliedin the present study, which allows also the flow measurements inside thevapourstructure and the simultaneous acquisition ofthe shape of the cavitation structure, is a combination of PIV method, LIF (Laser Induced Fluorescence) technique and a use
simulationwas performed. Comparison between numerical and experimentalresults shows good correlation. The distribution
andsize ofvapourstructures and the velocity fields agree well. The distribution of pressure on the hydrofoil surfaceis correctly

通气超空泡多相流场数值仿真方法

通气超空泡多相流场数值仿真方法佚名【摘要】通气超空泡流动涉及多相流动、湍流、相变及可压缩等流体力学难点问题，流动机理非常复杂。

其中多相流模型是通气超空泡数值仿真研究工作的重点，将严重影响通气超空泡数值仿真结果的精度。

本文有针对性地对比了目前广泛采用的均质平衡流模型和欧拉双流体模型，结合作者所在课题组多年来在水洞试验和数值仿真方面的研究成果，从空泡形态和流体动力两方面分析了欧拉双流体模型在预测通气超空泡方面的优势。

随着研究的进一步深入，通气超空泡数值仿真方法有望成为超空泡减阻技术的重要研究手段，可以为工程设计提供参考。

%Ventilated supercavitating flow involves such topics in fluid mechanics as multiphase flow, turbulence, phase change and compressibility, its mechanism is very complex. The multiphase flow model has attracted much more atten-tion in the study of numerical simulation of supercavitating flow, however its accuracy in simulation is not satisfactory. In this paper, the homogeneous model, which are widely used in the world, are compared with the Euler two-fluid model by combining with the authors′ research by means of water tunnel experiments and numerical simulation. The advan-tages of the Euler two-fluid model in predicting ventilated supercavitation is analyzed in terms of cavity shape and hy-drodynamics of a vehicle. Numerical simulation of ventilated supercavitation is expected to become an important ap-proach of drag-reduction technology through supercavitation.【期刊名称】《鱼雷技术》【年(卷),期】2013(000)003【总页数】6页(P165-170)【关键词】通气超空泡;多相流;数值仿真方法;均值平衡流模型;欧拉双流体模型【正文语种】中文【中图分类】TJ630.1;O351.2对于通气超空泡流动的研究, 最早可以追溯到上个世纪40年代。

模拟弯道水流条件下丁坝对沿程水位影响的研究

《河南水利与南水北调》2023年第11期试验与研究模拟弯道水流条件下丁坝对沿程水位影响的研究徐锴（上饶信泽水利水电设计有限公司，江西上饶334000）摘要：丁坝的建设有调整水流方向的作用，为了改善弯道水流流场，文章进行了弯道水流模拟试验，分析丁坝对沿程水位的影响，结果表明：丁坝的设置位置及角度对弯道左岸、右岸水位有一定影响。

以上研究为丁坝布置工程提供参考。

关键词：弯道水流；丁坝；沿程水位；阻水作用中图分类号：TV64；TV131文献标识码：A文章编号：1673-8853（2023）11-0096-021引言丁坝是河道工程中应用较广泛的水工建筑之一，具有束狭河道，保护堤岸的作用。

由于天然河道部分为弯道，在弯曲河道中合理的布置丁坝，可避免堤岸遭受水流的冲蚀。

文章通过弯道水流模拟试验，研究丁坝对沿程水位的影响，并对不同丁坝尺寸条件下的沿程水位和丁坝不同位置条件下的沿程水位进行分析。

2试验材料和方法2.1试验材料此次弯道水流模拟试验采用高精度可变坡弯道矩形水槽，该水槽上游直水槽长度为15m ，处于中间的弧形水槽为180°弯道，弧形的中心线半径（圆心到水槽外侧的距离）为2.40m ，下游直水槽长度为15m ，水槽的纵向断面为1m×1m （宽×高），坡度可变范围为0%～1.50%。

水槽水位测量采用无线超声波自动水位测量系统，该系统水位测量仪在水槽弯道处沿程分布，分布位置分别为弯道水流进口、弯道水流出口、90°弯道处两侧，共计6个。

该水位测量仪位于水面上，采用超声波探测水位情况，与水槽内水流无任何接触，不会对水流进行任何干扰，并且各位置的水位可同步采集，显著提高了试验数据精确度。

试验采用的丁坝模型为普通玻璃制作，丁坝模型设置2种规格，长丁坝的长×高×厚分别为20cm×50cm×4cm ，短丁坝的长×高×厚分别为6cm×50cm×2cm 。

journal of fluid mechanics 文献

标题: Two-dimensional and axisymmetric viscous flow in apertures作者: Dabiri, Sadegh; Sirignano, William A.; Joseph, Daniel D.Flow Visualization Using Cavitation Within Blade Passage of an Axial Waterjet Pump RotorDavid Y. Tan,Rinaldo L. Miorini,Jens Keller and Joseph KatzCAVITATION PHENOMENA WITHIN REGIONS OF FLOW SEPARATION.Katz, Joseph Source:Journal of Fluid Mechanics, v 140, p 397-436, Mar 1984Two-dimensional and axisymmetric viscous flow in apertures作者: Dabiri, Sadegh; Sirignano, William A.; Joseph, Daniel D.Interaction between a cavitation bubble and shear flow作者: Dabiri, Sadegh; Sirignano, William A.; Joseph, Daniel D.Direct numerical evidence of stress-induced cavitation作者: Falcucci, G.; Jannelli, E.; Ubertini, S.; 等.标题: Non-spherical bubble dynamics in a compressible liquid. Part 1. Travelling acoustic wave作者: Wang, Q. X.; Blake, J. R.标题: Cavitation in linear bubbles作者: Brenner, Michael P.标题: Numerical simulations of non-spherical bubble collapse作者: Johnsen, Eric; Colonius, Tim标题: Simulation ofcavitationbubbles in a convergent-divergent nozzlewaterjet作者: Qin, Z.; Bremhorst, K.; Alehossein, H.; 等.The influence of the sleeve's orifices geometric patterns on the fluid flow through a hydraulic resistance作者:Sfarlea, I (Sfarlea, I.)[ 1 ] ; Bode, F (Bode, F.)[ 1 ] ; Opruta, D (Opruta, D.)[ 1 ]标题: NUMERICAL SIMULATION OF ORIFICE CAVITATING FLOWS USING TWO-FLUID AND THREE-FLUID CAVITATION MODELS作者: Darbandi, Masoud; Sadeghi, HamedFlow instability due to cryogenic cavitation in the downstream of orifice 作者: Lee, Changjin; Roh, Tae-Seong来源出版物: JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY标题: A STUDY ON FLOW THROUGH AN ORIFICE WITH PREDICTIONOF CAVITATION AND HYDRAULIC FLIP作者: Darbandi, Masoud; Sadeghi, Hamed书籍团体作者: ASME标题: ANALYSIS OF THERMAL EFFECTS IN ACAVITATING ORIFICE USING RAYLEIGH EQUATION AND EXPERIMENTS 作者: Grazia, De Giorgi Maria; Daniela, Bello; Ficarella, Antonio书籍团体作者: ASME会议: 17th International Conference on Nuclear Engineering 会议地点: Brussels, BELGIUM会议日期: JUL 12-16, 2009标题: Simulations of cavitation in orifice and venturis作者: Ahuja, Vineet; Hosangadi, Ashvin丛书编者: Moatamedi, M会议: Joint Conference of the ASME Pressure Vessels and Piping Division/8th International Conference on Creep and Fatigue at Elevated Temperatures会议地点: San Antonio, TX会议日期: JUL 22-26, 2007标题: Effects on pipe vibrations of cavitation in an orifice and inglobe-style valves作者: Caillaud, Sebastien; Gibert, Rene-Jean; Moussou, Pierre; 等.丛书编者: Paidoussis, MP会议: 6th Symposium on Fluid-Structure Interactions, Aeroelasticity and Flow-Induced Vibration and Noise 会议地点: Vancouver, CANADA会议日期: JUL 23-27, 2006会议赞助商: ASME, Pressure Vessels & Piping Div标题: Flow and cavitation characteristics of a damping orifice in water hydraulics作者: Liu Yinshui; Zhu Bihai; Zhu Yuquan; 等.来源出版物: PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART A-JOURNAL OF POWER AND ENERGY 卷: 220期: A8页: 933-942 DOI: 10.1243/09576509JPE323出版年: DEC 2006标题: Investigation of cavitation near the orifice of hydraulic valves作者: Gao, H.; Lin, W.; Tsukiji, T.来源出版物: PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART G-JOURNAL OF AEROSPACE ENGINEERING 卷: 220期: G4页:253-265 DOI: 10.1243/09544100JAER O26出版年: AUG 2006标题: Effects of orifice internal flow on breakup characteristics oflike-doublet injectors作者: Jung, K; Khil, T; Yoon, Y来源出版物: JOURNAL OF PROPULSION AND POWER 卷: 22期: 3页: 653-660 DOI: 10.2514/1.20362出版年: MAY-JUN 2006被引频次: 6 (来自所有数据库)标题: Visualization of cavitation in high-pressure diesel fuel injectororifices作者: Li, Haiyun; Collicott, Steven H.来源出版物: ATOMIZATION AND SPRAYS 卷: 16期: 8页: 875-886 DOI: 10.1615/AtomizSpr.v16.i8.20出版年: 2006被引频次: 8 (来自所有数据库)标题: Experimental study of thermal cavitation in an orifice作者: De Giorgi, Maria Grazia; Chiara, Fabio; Ficarella, Antonio书籍团体作者: ASME会议: 8th Biennial Conference on Engineering Systems Design and Analysis 会议地点: Turin, ITALY会议日期: JUL 04-07, 2006会议赞助商: ASME来源出版物: Proceedings of the 8th Biennial Conference on Engineering Systems Design and Analysis, Vol 1 页: 523-529出版年: 2006被引频次: 0 (来自所有数据库)Cavitation Inception and Head Loss Due to Liquid Flow Through Perforated Plates of Varying ThicknessD. 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T., 1987, ―A Method for Rheological Characterization of Tube Viscometer Data,‖ J. Pipelines, 7 , pp. 165–176.29Miller, D. S., 1996, "Internal Flow: A Guide to Losses in Pipe and Duct Systems", BHRA Group, Cranfield, Bedfordshire.30Lakshmana Rao, N. S., and Sridharan, K., 1972, ―Orifice Losses for Laminar Approach Flow,‖ J. Hydraul. Div., 98 (11), pp. 2015–2034. Available at/cgi/WWWdisplay.cgi?12791731Rangaraju, K. G. and Jain, A. K., 1978, ―Energ y Loss Due to Sharp Edged Orifice Meters,‖ Irrig. Power, 35 (3) pp. 401–406. Available at /Record/IND7903051232Shima, N., 1984, ―Loss and Discharge Characteristics of a Flow of Polymer Solutions Through Pipes Orifices,‖ Bu ll. JSME, 27 (225), pp. 443–449. [CrossRef]33Humpherys, A. S., 1987, ―Energy Dissipation in Low Pressure Irrigation Pipelines: II Orifices,‖ Trans. ASAE, 30 (1), pp. 176–182. Available at /473/1/596.pdfY. Tomita and A. Shima, “Mechanisms of impulsive pressure generation and damage pit formation by bubble collapse,”J. Fluid Mech.169, 535 (1986).C.-T. Hsiao, G. L. Chahine, and H.-L. Liu, ―Scaling effect on prediction of cavitation inception in a line vortex flow,‖J. Fluids Eng.125, 53 (2003)./10.1115/1.1521956Y. Kuhn de Chizelle, S. L. Ceccio, and C. E. Brennen, “Observations and scaling of traveling bubble cavitation,”J. Fluid Mech.293, 99 (1995).Cavitation Bubbles Near BoundariesAnnual Review of Fluid MechanicsS. Gopalan, J. Katz and O. Knio, ―The flow structure in the near field of jets and its effect on cavitation inception,‖J. Fluid Mech.398, 1 (1999)./10.1017/S0022112099006072G. L. Chahine and Y. T. Shen, “Cavitation bubbles near boundaries.”J. Fluids Eng.108, 99 (1986).标题: Growth, oscillation and collapse of vortex cavitation bubbles作者: Choi, Jaehyug; Hsiao, Chao-Tsung; Chahine, Georges; 等.来源出版物: JOURNAL OF FLUID MECHANICS 卷: 624页: 255-279 DOI: 10.1017/S0022112008005430出版年: APR 10 2009标题: Prediction of tip vortex cavitation inception using coupled spherical and nonspherical bubble models and Navier-Stokes computations作者: Hsiao, CT; Chahine, G79.I. D. Pearce and A. Lichtarowicz, ―Discharge performance of long orifices with cavitating flow,‖ Proceedings of Second Fluid Power Symposium, Guildford,UK, 1971.A. Yamaguchi and T. Suzuki, “Cavitation in hydraulic fluids. Part 3: Oncavitation in long orifices,”J. Fluid Control12, 21 (1980).J. P. Tullis, “Cavitation scale effects for valves,”J. Hydraul. Div., Am. Soc. Civ. Eng.99, 1109 (1973).Flow characteristics of a micro-orificeAmmourah, S.A.a, Benim, A.C.b, Maqableh, A.M.c, Khadrawi, A.F.c, Al-Nimr, M.A.dA criterion for flow mechanisms through vertical sharp-edged orifice and model for the orifice discharge coefficientCao, R., Liu, Y., Yan, C.Flow characteristics of a micro-orificeAmmourah, S.A.a, Benim, A.C.b, Maqableh, A.M.c, Khadrawi, A.F.c, Al-Nimr, M.A.dCharacteristics of R-123 two-phase flow through micro-scale short tube orifice for design of a small cooling systemJin, S.a, Sung, T.a, Seo, T.b, Kim, J.a∙Experimental study of discharge coefficient and cavitation for different nozzle geometries ∙Kim, S.R., Ku, K.W., Hong, J.G., Lee, C.W.CFD analysis of flowfield and cavitation in aSharp-Edged circular orificeKyparissis, S.D.a, Margaris, D.P.bOFFICE CAVITATION AND ITS EFFECT ON SPRAY MIXING.(1976) Journal of Fluids Engineering, Transactions of the ASME, 98 Ser 1 (4), pp.681-687. Cited 154 times.Cavitation indices for high pressure orifice plate energydissipators(1988) International Journal of Mechanical Sciences, 30 (9), pp. 637-657.The effect of orifice plate geometry upon discharge coefficient (1990) Flow Measurement and Instrumentation, 1 (3), pp. 133-140. Cited 12 times.Flow regime transitions due to cavitation in the flow through an orifice(1990) International Journal of Multiphase Flow, 16 (6), pp. 1023-1045. Cited 46 times.Andrews, K.A., Sabersky, R.H.Flow Through an Orifice From a Transverse Stream(1990) Journal of Fluids Engineering, 112 (4), pp. 524-526. Cited 4 times.DecemberAlajbegovic, A.Three-Dimensional Cavitation Calculations in Nozzles(1999) 2nd Annual Meeting Institute ForMultifluid Science and TechnologySanta Barbara, California, USA, MarchYuan, W., Sauer, J., Schnerr, G.H.Modeling and computation of unsteady cavitation flows in injection nozzles(2001) Mecaniqueet Industries, 2 (5), pp. 383-394. Cited 36 times.doi: 10.1016/S1296-2139(01)01120-4Sato, K., Saito, Y.(2001) Unstable Cavitation Behavior In a Circular-Cylindrical Orifice Flow4th International Symposium on Cavitation, Pasadena, California, USA, JuneBorutzky, W., Barnard, B., Thoma, J.An orifice flow model for laminar and turbulent conditions(2002) Simulation Modelling Practice and Theory, 10 (3-4), pp. 141-152. Cited 38 times. Archer, A.A predictive model for cavitation erosion downstream orifices (2002) American Society of Mechanical Engineers, Fluids Engineering Division (Publication) FED, 257 (1 A), pp. 403-409.doi: 10.1115/FEDSM2002-31012Vortmann, C., Schnerr, G.H., Seelecke, S.Thermodynamic modeling and simulation of cavitating nozzle flow (2003) International Journal of Heat and Fluid Flow, 24 (5), pp. 774-783. Cited 29 times.doi: 10.1016/S0142-727X(03)00003-1Yagi, Y., Murase, M., Sato, K., Hattori, S.Mechanism of cavitation erosion at the exit of a long orifice(2003) Proceedings of the ASME/JSME Joint Fluids Engineering Conference, 1 B, pp. 1359-1364. Cited 2 times.ISBN: 0791836967Chen, Y., Lu, C.-J., Wu, L.Modelling and computation of unsteady turbulent cavitation flows (2006) Journal of Hydrodynamics, 18 (5), pp. 559-566. Cited 21 times.doi: 10.1016/S1001-6058(06)60135-2De Giorgi, G.M., Chiara, F., Ficarella, A.Experimental Study of Thermal Cavitation in an Orifice(2006) 8th ASME Conference On Engineering Systems Design and Analysis, 1, pp. 523-529.。

三维扭曲水翼空化现象CFD模拟

CFD Simulation of the Cavitating Flow of a 3 D
Twisted Hydrofoil
作者：张晓曦[1];陈秋华[2]
作者机构： [1]厦门理工学院环境科学与工程学院,福建厦门361024 [2]厦门理工学院土木工程与建筑学院,福建厦门361024
出版物刊名：厦门理工学院学报
页码： 106-111页
年卷期： 2016年第1期
主题词：扭曲水翼空化 CFD模拟
摘要：为研究三维扭曲水翼在空化数σ=1.07时的空化现象,以CFD方法为手段,利用Fluent软件中的Schnerr and Sauer空化两相流模型和RNG k-ε湍流模型对Twist-N11扭曲水翼进行了模拟,得到了空泡形态及空泡周围流场细节.分析发现空泡的产生和大小与水翼各断面的攻角有关,攻角越大,产生空泡的可能性就越大.由于空泡的存在,水翼上表面的流线被抬高,并且在空泡后形成了回流漩涡区.这种现象一方面会增大水翼的阻力,另一方面漩涡的不稳定演化会进一步影响空泡的大小和形态,甚至可能导致空泡脱落.本研究可为扭曲水翼的非定常空化特性研究提供有力基础.。

Simulation of Cavity Flow by the Lattice Boltzmann Method

1 Center for Nonlinear Studies and Theoretical Division, Los Alamos Nationalmos, NM 87545
2 Department of Mathematics, Kansas State University, Manhattan, KS 66506. 3 Department of Mechanical Engineering, Kansas State University, Manhattan, KS 66506.
evolution equation, i.e. the lattice Boltzmann equation. The lattice Boltzmann equation as a numerical scheme was ﬁrst proposed by McNamara and Zanetti [6]. In their model, the collision operator is the same as in the LGA. Higuera, Jimenez and Succi [7, 8] introduce a linearized collision operator that is a matrix and has no correspondence to the detailed collision rules. Statistical noise is completely eliminated in both models; however, the other problems remain since the equilibrium distribution is still Fermi-Dirac. The lattice Boltzmann model proposed by Chen et al. [9, 11] and Qian et al.

翼型空化最新进展四

Lingjiu Zhou College of Water Conservancy and CivilEngineering,China Agricultural University,Beijing,China100083e-mail:zlj09@Zhengwei Wang Department of Thermal Engineering,Tsinghua University,Beijing,China100084 e-mail:wzw@ Numerical Simulation of Cavitation Around a Hydrofoil and Evaluation of a RNG␬-␧Model Cavitatingﬂow around a hydrofoil was simulated using a transport equation-based model with consideration of the inﬂuence of noncondensable gases.The cavity length and the pressure distributions on the suction side can be well predicted for stable cavities using the standard renormalization-group(RNG)␬-␧turbulence model with proper non-condensable gas mass fraction.The unstable cavity shedding at lower cavitation numbers was not well predicted by the standard RNG␬-␧turbulence model.A modiﬁed RNG␬-␧turbulence model was evaluated by comparing the calculated spatial-temporal pressure distributions on the suction wall with experimental data.The results showed that the predicted cavity growth and shedding cycle and its frequency agree well with the experi-mental data.However,the pressure increase caused by interaction of the reentrantﬂow and the cavity interface is overestimated,which caused the time-averaged pressure on the front part of the hydrofoil to be overestimated.The time-averaged pressure on the rear of the hydrofoil was low because the small cavity shedding on the rear part of the cavity was not predicted.͓DOI:10.1115/1.2816009͔IntroductionCavitation occurs in a wide variety ofﬂuid engineering systems including pumps,water turbines,propellers,and pipes.In most cases,cavitation is an undesirable phenomenon,causing signiﬁ-cant degradation in performance and damage as well as vibration and noises.Noticeable efforts have been made in numerical simu-lations of cavitatingﬂows in recent years.Most cavitation models are based on the pseudohomogeneousﬂow theory proposed by Kubota et al.͓1͔,which modeled the two phaseﬂuid as a mixture of liquid and its vapor sharing the same velocity and pressure. Reynolds-averaged Navier-Stokes͑RANS͒equations were solved for the mixture to obtain the velocity,pressure,and turbulence quantities.Additional equations were deduced to solve for the vapor and the liquid volume fractions.One of the methods used to model cavitation and condensation was to use a proper state law for the mixture.Delannoy and Kueny͓2͔proposed a barotropic state law that strongly links the mixture density to the static pressure,which describes the mixture density in the incompressible parts,in the pure vapor parts,and in the transition zone of theﬂowﬁeld.This model together with modiﬁcations of the turbulence viscosity was successfully adopted to simulate cloud cavity shedding in a Venturi-type duct͓3,4͔.Iga et al.͓5,6͔used a state law similar to the barotropic state law concept,which described the mixture density as function of pres-sure and vapor mass fraction.Their results also agreed with the experimental data.Another approach is the transport equation-based model ͑TEM͒,which solves an additional transport equation for either the mass or volume fraction.A source term is used to model the mass transfer caused by evaporation and condensation.Several models have been proposed for the source term.Senocak and Shyy͓7,8͔compared three models to develop an interfacial dynamics-based-cavitation model and pointed out that although pressure distributions predicted by different models agreed well with each other,the predicted density distributions differed.This implies that the compressibility characteristics embodied in each cavitation model differ.In practical cavitatingﬂows,in most engineering equipment, the operating liquid contains aﬁnite amount of noncondensable gases dissolved in the liquid due to leakage or aeration.Noncon-densable gases not only change the initial critical cavitation pres-sure but also affect theﬂowﬁeld through volume expansion and condensation.Different methods have been used to treat the non-condensable gases.Most methods have been based on a transportequation.Some methods have assumed that the densities of theliquid,vapor,and noncondensable gas are all constant.Kunz et al.͓9͔used an additional transport equation for the noncondensable gas.Unlike other pressure-correction-based methods,they used adual-time,preconditioned,implicit artiﬁcial compressibility algo-rithm.Yuan and Schnenn͓10͔used the same concept but solvedthe transport equations using a pressure-correction method.Sin-ghal et al.͓11͔also included the effect of noncondensable gases intheir“full cavitation model.”They considered the noncondensablegas to have a constant mass fraction and with an ideal gas density.This assumption seemed to be more reasonable since the effect ofvolume change of noncondensable gas was included.The modelof Singhal et al.was validated by many cases related toﬁxedcavities and was adopted by the commercial software FLUENT forcavitatingﬂows.However,the noncondensable gas mass fraction was then foundto excessively affect cavity behavior in practical calculations.Inaddition,the standard turbulence models failed to predict the in-stabilities for low cavitation numbers,as was also pointed out byDelgosha et al.͓3,4͔,who then modiﬁed the turbulent viscosity͑a modiﬁed renormalization-group͑RNG͒␬-␧model͒to simulate cloud cavity shedding in a Venturi-type duct.The barotropic state law concept was adopted in their calculations to deal with the cavitation precession.Inspired by their work,the present work combines the modiﬁed turbulent viscosity with the full cavitation model.Calculations were performed for various cavitation num-bers with emphasis on the inﬂuence of noncondensable gas mass fraction and the turbulence model in the simulations.The un-steady behavior of cloud cavity shedding is analyzed and the tur-bulence model is evaluated based on experimental data.Contributed by the Fluids Engineering Division of ASME for publication in the J OURNAL OF F LUIDS E NGINEERING.Manuscript received January17,2007;ﬁnal manu-script received June30,2007;published online December19,2007.Review con-ducted by Steven Ceccio.Governing Equations and Cavitation ModelTheﬂuid was assumed to be a mixture of liquid,vapor,and noncondensable gases.Theﬂow was assumed to be pseudohomo-geneous so the multiphaseﬂuid components were assumed to share the same velocity and pressure distributions.Therefore,only one set of Favre-averaged Navier–Stokes equations was used to describe theﬂow.The continuity and the momentum equations for the mixture areץ␳ץt+ٌ·͑␳V͒=0͑1͒ץ͑␳V͒ץt+ٌ·͑␳VV͒=−ٌP+ٌ·ͭ͑␮+␮tٌ͒ͫ͑V+ٌV T͒−23ٌ·V Iͬͮ͑2͒where P is the mixture pressure,␳is the mixture density,and V is the mixture velocity vector.The laminar viscosity␮is deﬁned as a density-weighted average of the three components.␮t is the turbulent viscosity closed by the RNG␬-␧model͓12͔.The mix-ture density␳is deﬁned by1␳=f v␳v+f ncg␳ncg+1−f v−f ncg␳l͑3͒withf v=a v␳v␳f ncg=a ncg␳ncg␳f l=a l␳l␳=1−f v−f ncg͑4͒where f v,f ncg,f l are the component mass fractions,␳v,␳ncg,␳l are the component densities,and a v,a ncg,a l are the component vol-ume fractions of the vapor,gas,and liquid components.During calculation,f ncg was assumed to be a very small constant.The cavitation model used to simulate vapor generation and conden-sation rates isץ͑a v␳v͒ץt+ٌ·͑a v ␳v V͒=ץ͑␳f v͒ץt+ٌ·͑␳f v V͒=−C cͱk␭␳l␳lͱ2max͑p−p v,0͒3␳lf v+C eͱk␭␳l␳vͱ2max͑p v−p,0͒3␳lϫ͑1−f v−f ncg͒͑5͒The noncondensable gases’density was calculated using the ideal gas law:␳ncg=WPRT͑6͒The combined vapor and gas volume fraction a v+a ncg is theﬁnal void fraction.The model uses the recommended empirical factors c e=0.02, c c=0.01and the surface tension coefﬁcient␭=0.0717N/m.Hydrofoil Geometry and DiscretizationThe effect of the noncondensable gas mass fraction and the turbulence model were assessed by modeling cavitatingﬂow around a hydrofoil,which was experimentally studied by Leroux et al.͓13͔.The hydrofoil used for the simulation was a two-dimensional cambered NACA66͑mod͒foil with the coordinates given by Leroux et al.͓13͔.The relative maximum thickness was 12%at45%from the leading edge and the relative maximum camber was2%at50%from the leading edge.The chord length was C=0.150m.The foil wasﬁxed within a1m long and 0.192m wide square cross test section.The angle of attack was 6deg.The freestream velocity was5.33m/s.Several pressures were monitored during calculations to study the pressure oscilla-tions caused by the cavitation.On suction side,these points werenamed P0,P05,P1–P9with P0located at x=0,P05at x=0.05C,P1at x=0.1C,P2at x=0.2C,etc.The geometry was simpliﬁed to a2D problem.The mesh was generated with seven block structured grid,as shown in Fig.1. The mesh size was carefully selected to ensure the nondimen-sional normal distance from the wall͑y*͒located in the log-law region since the standard wall function was adopted for near walltreatment.For a grid with27,961nodes,the distributions of y*of the wall-adjacent cell’s centroid were within30–300͑see Fig.2͒, so this grid was used for the following calculations.The time-dependent equations were discretized using the control-volume technique with the SIMPLEC scheme.The second-order upwind scheme was used for the convection terms with the central difference scheme used for the diffusion terms in the momentum equations and the transport equations for␬and␧. The pressure staggering option͑PRESTO͒was used for the pres-sure interpolation.The QUICK scheme was used for the vapor mass fraction transport equation.For above grid,several time steps,0.001s,0.0005s,and0.0001s,were tested with⌬t =0.0005s,found to give reasonable results with relatively short calculational times so it was used in the calculations. Calculated ResultsSimulations were performed for noncavitatingﬂows to verify the angle of attack.The pressure distribution at an attack angle of 6deg is plotted in Fig.3,which shows that the calculated results agree well with the experimental data͑all the experimental data in this paper are from Leroux et al.͓13͔͒.Inﬂuence of f ncg on the Simulation of Cavitating Flows With Stable Cavities.The standard RNG␬-␧turbulence model was used in calculations for cavitation numbers varying from1.25to 1.67with mass fraction f ncg from1ϫ10−8to1ϫ10−6.Theinﬂu-Fig.1Calculation domain and seven block structured grid with27,961nodesFig.2Distributions of y*of the wall-adjacent cell’s centroid for noncavitating and cavitatingﬂowence of the mass fraction,f ncg ,was investigated with the results shown in Fig.4.For a constant cavitation number,the cavity length and thickness increased with increasing noncondensable gas mass fraction up to f ncg of about 1ϫ10−7.The cavity length then increased more slowly with increasing noncondensable gas mass fraction from 1ϫ10−7to 1ϫ10−6͑see Fig.4͒;however,the cavity thickness increased faster.Higher noncondensable gas mass fractions ͑1ϫ10−5͒gave odd cavity shapes with the interface even reaching the upper wall of the test section,which were ob-viously wrong thus not presented.The noncondensable gas mass fraction is expected to greatly inﬂuence the calculated cavity length of the pressure distribution.In the model of Singhal et al.the combined vapor and gas volume fraction a v +a g was used as the ﬁnal void ing a g cal-culated using Eqs.͑4͒and ͑6͒:a ncg =␳f ncg ␳ncg =␳f ncg RTWP͑7͒Therefore,in this model,the noncondensable gases not onlyaffect the mass transfer rate between the liquid and vapor ͑in Eq.͑5͒,the vapor generation term ͒but also strongly affect the ﬂow ﬁeld as its volume increases with decreasing pressure ͑Eq.͑7͒͒.The calculated results show that in most of the cavity,noncon-densable gas volume fraction is quite high.This also explains the fact that Eq.͑5͒has much lower empirical factors,c e and c c ,than other models ͓7,8͔that do not include noncondensable gas effects.Figure 5compares pressure distributions on the suction side of the proﬁle,which shows that the cavity length and pressure dis-tribution on the wall can be reasonably predicted if the noncon-densable gas mass fraction is properly selected.For the case in Fig.5,f ncg =6ϫ10−8–8ϫ10−8give the best results with higher noncondensable gas for lower cavitation numbers.Lower f ncg ͑less than 6ϫ10−8͒experienced some convergence difﬁculties.The experimental data had more gradual pressure increases near the downstream end of the cavity than that shown in calculated results.Figure 5shows that the calculated pressure gradient was quite steep in the closure region of the cavity with a very stable cavity.These imply that the closure region is not well predicted.Katz and Gopalan ͓14͔observed that for sheet cavities,the cavity shapes in the closure region are highly irregular and unsteady.They indicated that cavity collapse in the closure region involves substantial increases in turbulence and momentum and displace-ment thickness in the boundary layer.However,the present model did not consider the interaction between the turbulence and the vapor collapse in the closure region,which might explain the lack of accuracy in the closure region.When the predicted cavity length exceeded half the chord,the cavity became unstable,as was also observed in the experiments.The results with f ncg =8ϫ10−8for ␴=1.25show that the standard RNG ␬-␧model predicted an unstable cavity expanding and shrinking within 0.35C –0.6C with a frequency of 4.5Hz.The typical vapor contours and velocity vectors are shown in Fig.6.The pressure at P4is shown in Fig.7.There was no cavity shed-ding in the calculated results but the experiments revealed cloud shedding for this condition with the main frequency of the pres-sure oscillations of 3.625Hz.Therefore,although the calculations predicted cavity instabilities for ␴=1.25,the unsteady behavior was not correctly simulated by the standard RNG ␬-␧model.Fig.3Comparison of calculated result and experimental data for a noncavitatingﬂowFig.4Calculated cavity shape for ␴=1.41using various f ncg with the standard RNG ␬-␧modelFig.5Predicted pressure distribution on the suction side for various noncondensable gas mass fractionsSimulations With a Modiﬁed Renormalization-Group ␬-␧Model.Delgosha et al.͓4͔suggested a modiﬁcation to the stan-dard RNG ␬-␧model,which simply reduced the mixture turbulent viscosity.In the standard RNG ␬-␧model,the turbulent viscosity is deﬁned as␮t =␳c ␮k 2␧͑8͒where c ␮=0.085.The modiﬁed turbulent viscosity is deﬁned as␮t =f ͑␳͒c ␮k 2␧͑9͒wheref ͑␳͒=␳v +͑a l ͒n ͑␳l −␳v ͒͑10͒This modiﬁcation was found to signiﬁcantly improved simula-tions of the cloud shedding.Various values of n were used in the modiﬁed RNG ␬-␧model.The results showed that with f ncg =8ϫ10−8,n =3–10gave similar results.The predicted shedding frequency was about 3.57Hz us-ing n =3and 3.75Hz using n =10,which are both close to the experimental frequency.The behavior and the development of the cavity cycle were also inspected in detail.The wall pressure ﬂuc-tuations at the various points are shown in Fig.8for n =3.Onlypart of numerical results is shown in order to compare with the experimental results.The time axis for numerical results was panned in such a way to align the beginning of a new cycle of numerical results at 0.17s,the initial point for the experimental cycle.Generally,the calculated pressure distributions agreed rea-sonably well with the experimental data and the cavity growth is predicted reasonably well.A detailed discussion is as follows.Discussion.The calculated cavity growth can be divided into three stages.Period A is the growth of the sheet cavity,which lasts for about 0.13s ͑from 0.17s to 0.30s ͒.Comparison of the spatial-temporal pressure distributions on the suction wall with experimental data shows that the sheet cavity growth period is well predicted in Period A.The sheet cavity before destabilization was about 0.7C long in agreement with the experimental data.Initially,the cavity has a smooth interface.Then,the reentrant ﬂow develops at the rear of the cavity ͑at about t =0.215s ͒.As the cavity length exceeds 1/3of the chord,the interface becomes wavy and the reentrant ﬂow pushes further toward the front ͑see Fig.8,t =0.255s ͒,which makes the cavity interface move upward and the cavity grow thicker.The main ﬂow above the interface accelerates and the pressure near the rear of the cavity decreases,which causes the cavity to grow further until the cavity length reaches about 0.7C .The pressure at points P 1–P 7decreases to the vaporization pressure in an orderly succession.However,some differences were noticeable.The calculated re-sults failed to predict the small shedding on the rear part of the sheet cavity ͑labels a and b in Fig.8͒observed in the experiments due to the fact that the interaction between the turbulence and the vapor collapse in the closure region was not included in the model,as mentioned earlier for the stable cavity results.For the same reason,the average pressure on the rear part was estimated to be lower,as shown in Fig.10.Both the calculated results and the experimental data showed the pressure perturbations,which cut the cavity into two parts ͑see Fig.8͒.Period B ͑from t =0.30s to 0.41s ͒in Fig.9showsthatFig.6Calculated void fraction contours and velocity vectors for ␴=1.25using the standard RNG ␬-␧model,f ncg =8Ã10−8…to get a clear view,every four vec-tor is displayed…Fig.7Calculated pressure variations at P4for ␴=1.25using the standard RNG ␬-␧model,f ncg =8Ã10−8this is related to the interaction between the reversed ﬂow and the cavity interface,which was conﬁrmed by other researchers ͓15,16͔.The standard RNG ␬-␧model failed to predict the un-stable cavity cycle,which was more accurately predicted by the modiﬁed RNG ␬-␧model since the modiﬁed RNG ␬-␧model reduced the turbulence viscosity within the high void fraction re-gion.Figures 6and 9show that both the standard RNG ␬-␧model and the modiﬁed RNG ␬-␧model predicted the reversed ﬂow in the bottom of the sheet cavity;however,the standard RNG ␬-␧model did not predict that the reverse ﬂow would reach the front of the hydrofoil.With the modiﬁed RNG ␬-␧model,the reversed ﬂow developed toward the front with negative velocities on most of the suction surface.This is consistent with the experimental results of George et al.͓17͔that longer partial cavities at larger attack angles showed consistently negative gas-phase velocities near the hydrofoil midchord.The reversed ﬂow perturbed the cav-ity interface near the front of the hydrofoil and caused rolling up of the cavity,with this process being closely related to the vortex movement,as shown in Fig.9.These results suggest that the interaction between the reversed ﬂow and the cavity interface is closely related to the reduction of the turbulent viscosity.Al-though Delgosha et al.͓4͔stated that the modiﬁed model included the compressibility effect,they also noticed that the ﬁnal effect of the modiﬁcation was to reduce the turbulent viscosity in the vapor/liquid mixture zone.As was pointed out by Ceccio and Iyer ͓18͔in their experiments on developed cavitation in a shear layer,the cavitation within the cores of streamwise vortices decoupled the stretching and rotation rate of these ﬂow structures and re-duced the Reynolds stresses and cross-stream velocity ﬂuctua-tions.Therefore,the presence of cavitation within the shear layer may change the effective rheology of the ﬂow.This effect may also exist in the present case with an obvious shear layer ͑Fig.9͒.Equation ͑10͒includes this effect in a simple way;thus,the results are improved regardless of which barotropic state law is used ͑the calculations of Delgosha et al.͓4͔͒or if the full cavitation model ͑the present calculations ͒is used.However,the modiﬁed RNG ␬-␧model tends to overestimate the pressure increase caused by the interaction between the reen-trant jet and the cavity interface.Figure 8shows that the calcu-lated pressure perturbations were much more violent on the front part of the surface and occurred a little earlier than in the experi-mental data.There is a small disturbance which lasts for about 0.02s ͑from 0.30s to 0.32s ͒with small irregular pressure ﬂuc-tuations from 0.1C to 0.4C ͑see Fig.8͒.Then,major pressure perturbations occur caused by the shedding of the rear part of the cavity.This is initiated near the head ͑at 0.05C ͒with a distinct pressure increase.However,in the experimental data,the major pressure perturbation was observed at approximately the middle of the cavity ͑at 0.4C ͒.In addition,the pressure perturbations lasted much longer in the calculated results than in the experimen-tal data.Both experimental and calculation results show that after the cavity is cut into two parts,the cavity near the head continues to grow and forms a sheet cavity while the rear part cavity moves downstream.Figure 9shows that the moving of the rear part of the cavity is related to the rolling up of the vortex,which readjusts the velocity and pressure in the middle part of the chord.So,Fig.8shows a small pressure increase at each point in order,which corresponds to the growth of the front part of the cavity and the shedding of the rear part of the cavity.The rear part of the cavity disappears in Period C.The overall pressure increase and cavity destabilization during the shedding of the rear part of cavity in Period C were predicted by the calcula-tions.When the rear part of the cavity totally disappears into wake behind the hydrofoil,the pressure over the whole suction surface suddenly increases,which collapses sheet cavity on the front part.For some time,the whole surface is free of cavities.This period lasts for about 0.05s ͑from t =0.41s to 0.445s ͒with another cycle then begins as the sheet cavity starts to grow again on the front part.A shock wave is believed to occur when the rear part of the cavity collapses in the high pressure region downstream ͓13͔.Since the present calculation assumed that the liquid phase was incompressible,the shock wave propagation could not be pre-dicted.Figure 8shows that the pressure increased suddenly at almost the same time ͑at t =0.42s ͒at all points.The velocity vectors in Fig.9indicate that the shedding of the rear part oftheFig.8Predicted pressure ﬂuctuations during cavity growth and destabilization for ␴=1.25using the modiﬁed RNG ␬-␧model,f ncg =8Ã10−8cavity is closely related to the vortex shedding.The vanishing of the cavity and the vortex reduced the blockage effects and caused the pressure increase,which quickly collapsed the remaining sheet cavity on the front part.The hydrofoil was then free of a cavita-tion region for a short period.The collapse of the main cavity near the back was the main reason for the pressure peak in this period.However,the predicted pressure peak was a little higher,which may due to the reason that the compressibility and bubble cloud effects were not included in the calculation:The experiments showed that the rear part cavity is bubble cloud,which can inﬂu-ence the ﬂuid compressibility and wave speed and affect the col-lapsing behavior,while Fig.9shows that the calculated rear part cavity is bumpy.Therefore,the pressure was overestimated on the front part of the hydrofoil,as shown in Fig.10because the pressure increase caused by interaction between the reentrant jet and the cavity interface was overestimated in Period B.The predicted pressure peak caused by the collapse of the main cavity near the back was also a little higher in Period C.The simpliﬁcation from 3D prob-lem to a 2D model can also lead to the differences of amplitude between the numerical and experimental pressure ﬂuctuations.Therefore,much more research work is needed in the future.Inﬂuence of n .The calculated results show that the index n had little inﬂuence on the frequency of the unstable cavity as long asnFig.10Comparison of the pressure distribution on the suc-tion surface for ␴=1.25.The calculated data were obtained us-ing the modiﬁed RNG ␬-␧model,f ncg =8Ã10−8.Fig.9Calculated void fraction contours and velocity vectors for ␴=1.25using the modiﬁed RNG ␬-␧model,f ncg =8Ã10−8…to get a clear view,every four vector is displayed …was larger than 3.The cavity growth cycle for n =10was also composed of three stages,the sheet cavity growth period,the pres-sure disturbance period with the cavity being cut into two parts,and the high pressure period after the shedding of the rear part of the cavity.The differences between the predictions for n =10and n =3in Fig.11are insigniﬁcant since the variations are similar to the variations in the experimentally measured cavity growth cycles,which were similar but not identical.ConclusionCavitating ﬂow around a hydrofoil was simulated using a TEM including noncondensable gas effects.The cavity length and the pressure distributions on the suction side were well predicted for stable cavities using the standard RNG ␬-␧turbulence model with proper noncondensable gas mass fraction.However,the interac-tion between turbulence and the vapor collapse in the closure region was not included in the model,so the results were less accurate there.The results showed that for lower cavitation numbers,the cav-ity was unstable when its length exceeded half the chord.The unstable cavity shedding at lower cavitation numbers was not well predicted by the standard RNG ␬-␧turbulence model.A modiﬁed RNG ␬-␧turbulence model was found to more accurately predict the shedding frequency by reducing the turbulent viscosity in the mixture region.The modiﬁed RNG ␬-␧turbulence model was evaluated based on a detailed comparison of the calculated spatial-temporal pressure distributions on the suction wall with experimental data.The results showed that the cavity growth/shedding cycle characteristics and frequency agreed well with ex-perimental data.The sheet cavity length before the rear cavity shedding was reasonably predicted.The calculated results also describe the interaction behavior between the reentrant ﬂow and the cavity interface,which is one reason for the cavity destabili-zation.The sudden pressure increase along the whole wall caused by the collapse of the main cavity in the rear,which is another reason for the cavity destabilization,was also seen in the results.However,the time-averaged pressure on the front part of the hy-drofoil was overestimated because the pressure increase caused by interaction between the reentrant ﬂow and the cavity interface was overestimated.The time-averaged pressure on the rear of the hy-drofoil was low because the small cavity shedding on the rear part of the cavity was not predicted.Nomenclaturea v ,a ncg ,a l ϭvapor,gas,and liquid volume fractionsC ϭhydrofoil chord ͑m ͒C p ϭpressure coefﬁcient deﬁned byC p =͑p −p r ͒/͑0.5␳u 2͒f v ,f ncg ,f lϭvapor,gas,and liquid mass fractions P ϭpressure ͑Pa ͒P r ϭpressure at reference point ͑Pa ͒P vϭvaporization pressure ͑Pa ͒,set as 3540Pa in the present study t ϭtime ͑s ͒u ϭfreestream velocity ͑m/s ͒V ϭvelocity vector ͑m/s ͒y *ϭthe nondimensional normal distance from thewall deﬁned by y *=͑␳c ␮1/4k 1/2/␮͒y d ,with y d the distance to the wall ␳ϭmixture density ͑kg /m 3͒␮ϭlaminar viscosity ͑N s /m 2͒␮tϭturbulent viscosity ͑N s /m 2͒␳v ,␳ncg ,␳lϭvapor,gas,and liquid densities ͑kg /m 3͒␴ϭcavitation number deﬁned by ␴=͑p r −p v ͒/͑0.5␳u 2͒AcknowledgmentThe authors gratefully acknowledge the support from Key Technologies R&D Program for China’s 11th Five-Year Plan ͑2006BAJ04B03͒.References͓1͔Kubota,A.,Kato,H.,and Yamaguti,H.,1992,“A New Modeling of Cavitat-ing Flows:A Numerical Study of Unsteady Cavitation on a Hydrofoil Sec-tion,”J.Fluid Mech.,240,pp.59–96.͓2͔Delannoy,Y .,and Kueny,J.L.,1990,“Two Phase Flow Approach in UnsteadyCavitation Modeling,”Cavitation and Multiphase Flow Forum ,V ol.98,pp.153–158.͓3͔Delgosha,C.O.,Reboud,J.L.,and Delannoy,Y .,2003,“Numerical Simula-tion of the Unsteady Behaviour of Cavitating Flows,”Int.J.Numer.Methods Fluids,42,pp.527–548.͓4͔Delgosha,C.O.,Patella,F.R.,and Reboud,J.L.,2003,“Evaluation of theTurbulence Model Inﬂuence on the Numerical Simulations of Unsteady Cavi-tation,”ASME J.Fluids Eng.,125,pp.38–45.͓5͔Iga,Y .,Nohml,M.,Goto,A.,and Ikohagi,T.,2004,“Numerical Analysis ofCavitation Instabilities Arising in the Three-Blade Cascade,”ASME J.Fluids Eng.,126,pp.419–429.͓6͔Iga,Y .,Nohml,M.,Goto,A.,Shin,B.R.,and Ikohagi,T.,2003,“NumericalStudy of Sheet Cavitation Breakoff Phenomenon on a Cascade Hydrofoil,”ASME J.Fluids Eng.,125,pp.643–651.͓7͔Senocak,I.,and Shyy,W.,2004,“Interfacial Dynamics-Based Modelling ofTurbulent Cavitating Flows,Part I:Model Development and Steady-State Computations,”Int.J.Numer.Methods Fluids,44,pp.975–995.͓8͔Senocak,I.,and Shyy,W.,2004,“Interfacial Dynamics-Based Modelling ofTurbulent Cavitating Flows,Part II:Time-Dependent Computations,”Int.J.Numer.Methods Fluids,44,pp.997–1016.͓9͔Kunz,R.F.,Boger,D.A.,Stinebring,D.R.,Chyczewski,T.S.,Lindau,J.W.,Gibeling,H.J.,Venkateswaran,S.,and Govindan,T.R.,2000,“A Precondi-tioned Navier-Stokes Method for Two-Phase Flows With Application to Cavi-tation Prediction,”Comput.Fluids,29,pp.849–875.͓10͔Yuan,W.,and Schnerr,G.H.,2003,“Numerical Simulation of Two-PhaseFlow in Injection Nozzles:Interaction of Cavitation and External Jet Forma-tion,”ASME J.Fluids Eng.,125,pp.964–969.͓11͔Singhal,A.K.,Athavale,M.M.,Li,H.Y .,and Jiang,Y .,2002,“MathematicalBasis and Validation of the Full Cavitation Model,”ASME J.Fluids Eng.,124,pp.617–624.͓12͔Yakhot,V .,Orszag,S.A.,Thangham,S.,Gatski,T.B.,and Speziale,C.G.,1992,“Development of Turbulence Models for Shear Flows by a Double Ex-pansion Technique,”Phys.Fluids A,4͑7͒,pp.1510–1520.͓13͔Leroux,J.B.,Astolﬁ,J.A.,and Billard,J.Y .,2004,“An Experimental Studyof Unsteady Partial Cavitation,”ASME J.Fluids Eng.,126,pp.94–101.͓14͔Katz,J.,and Gopalan,S.,2000,“Flow Structure and Modeling Issues in theClosure Region of Attached Cavitation,”Phys.Fluids,12͑4͒,pp.895–911.͓15͔Pham,T.M.,Larrarte,F.,and Fruman,D.H.,1999,“Investigation of UnsteadySheet Cavitation and Cloud Cavitation Mechanisms,”ASME J.Fluids Eng.,121,pp.289–296.͓16͔Kubota,S.,Kato,H.,Yamaguchi,H.,and Meada,M.,1987,“Unsteady Struc-ture Measurement of Cloud Cavitation on a Foil Section Using Conditional Sampling Technique,”International Symposium on Cavitation Research Fa-cilities and Techniques ,Boston,pp.161–168.͓17͔George,D.L.,Iyer,C.O.,and Ceccio,S.L.,2000,“Measurement of theBubbly Flow Beneath Partial Attached Cavities Using Electrical Impedance Probes,”ASME J.Fluids Eng.,122,pp.151–155.͓18͔Ceccio,S.L.,and Iyer,C.O.,2002,“The Inﬂuence of Developed Cavitationon the Flow of a Turbulent Shear Layer,”Phys.Fluids,14͑10͒,pp.3414–3431.Fig.11Inﬂuence of parameter n on the predicted pressures at P4and P7.f ncg =8Ã10−8was used for both n =3and n =10.。

金枪鱼自主波动游动的数值模拟

DOI：10.3969/j.issn1000-4874.2011.02.012
金枪鱼自主波动游动的数值模拟 *
徐晓锋, 万德成
（上海交通大学船舶海洋与建筑工程学院海洋工程国家重点实验室，上海 200240, Email: bradley_001@）
摘要：鱼类游动问题蕴含着复杂的流体力学机理，其仿生问题同时又有着重要应用背景。该文运用人工伪压缩
*
(3)
图1
整个流场网格
2.5 流体动力性能的计算流体运动控制方程为式方程(1)，仿生鱼自主游动的控制方程为
M d2r =F dt 2
上述方程中， t 表示计算域 (ξ ,η , ζ ) 中的时间，方程 (2)中的最后一项表示通过单元表面的净通量。 2.2 方程的离散本文采用有限体积法对方程进行离散，其中对流项采用三阶精度的 MUSCL 格式，黏性项利用有限体积法中高斯积分进行运算并采用二阶中心差分格式，对时间项则采用欧拉全隐格式进行离散。具体的方法可以参考文献[10,11]。
(2)
其中 f = ( F + Fv ,G + Gv , H + H v ) ，S (t ) 是单元的表面积， n = (nx , n y , nz ) 是外法向单位向量， u g 是网格速度。物理域和计算域的关系为如下
⎧ξ = ξ ( x, y, z ) ⎧ x = x(ξ ,η , ζ ) ⎪η = η ( x, y, z ) ⎪ y = y (ξ ,η , ζ ) ⎪ ⎪ ⎨ζ = ζ ( x, y, z ) ←→ ⎨ z = z (ξ ,η , ζ ) ⎪ ⎪ ⎪t * = t ⎪t = t * ⎩ ⎩
方法求解三维不可压缩非定常 Navier-Stokes 方程，计算分析金枪鱼从静止加速起动到巡游直至减速波动游动的全过程，得到鱼类游动时各状态的流场信息以及受力情况。同时结合计算结果，对鱼类游动过程进行了参数研究并且分析了鱼体推力产生的机理。计算结果分析表明：数值求解非定常 Navier-Stokes 方程能够模拟鱼体运动时的流场；鱼体摆动频率以及摆幅会影响鱼的游动；持续摆动产生的涡环形成反卡门涡街是鱼体游动时产生推力的重要因素。关键词：波动游动；数值三维鱼运动流场；金枪鱼文献标识码：A

空化模型在低温流体空化流动三维计算中的应用与评价

空化模型在低温流体空化流动三维计算中的应用与评价孙铁志;魏英杰;王聪;路中磊【摘要】This paper aims to evaluate the application of different cavitation models in three-dimensional computations of the cavitating flow characteristics of cryogenics liquids. The aim is realized by implanting the cavitation models and physical properties of liquid nitrogen and liquid hydrogen at different tempera-tures to the CFX solver code by using the secondary development of CFX software, and considering the ef-fect of latent heat of evaporation in the energy equation, then the 3D numerical simulation of cavitating flow is conducted around a hydrofoil in liquid nitrogen and ogive in liquid hydrogen.The results show that the liquid phase distribution characteristics of the three different cavitation modelsat the cavitation region are different,and the length and thickness of the cavity have some differences.Due to the difference of the mass transfer mechanism of the three cavitation models, which leads to the pressure distribution and temperature drop are different under the thermodynamic effects. The applicability of Kubota model is the strongest for predictingthe pressure distribution, and the Merkle model can reflect the temperature drop at the cavitation region well, whereas the differences between the numerical results and experimental data of Kunz model arethe biggest.%为评价不同空化模型对低温流体空化过程流场特性预测的适用性,文章通过对CFX软件的二次开发,将Kubota、Merkle和Kunz三种空化模型和液氮、液氢随温度变化的物性参数引入到CFX求解代码中,同时在求解的能量方程中添加汽化潜热影响,从而在考虑热力学效应条件下,开展了液氮绕水翼空化流动和尖顶拱在液氢中空化流动的三维数值模拟研究,并将计算结果与试验数据进行对比,实现了对不同空化模型适用性的评价.结果表明:三种空化模型计算的空化区域液相分布特性不同,空泡长度和厚度有差别;由于空化模型方程源相体现的质量传输机理不同,导致热力学效应下空化区域压强分布和温降存在差异;Kubota空化模型可有效预测液氮空化流场压强分布,Merkle模型可较好地反映空化区域温降,Kunz模型计算的结果与试验数据差别最大.【期刊名称】《船舶力学》【年(卷),期】2018(022)001【总页数】9页(P22-30)【关键词】空化模型;低温流体;空化流动;热力学效应【作者】孙铁志;魏英杰;王聪;路中磊【作者单位】大连理工大学船舶工程学院,辽宁大连116024;哈尔滨工业大学航天学院,哈尔滨150001;哈尔滨工业大学航天学院,哈尔滨150001;哈尔滨工业大学航天学院,哈尔滨150001【正文语种】中文【中图分类】TJ7630 引言当流场中液体的压强降到当地温度下的饱和蒸汽压强以下时，将会发生空化现象[1]。

如何使用SolidWorks Flow Simulation分析孔蚀现象

如何使用SolidWorks Flow Simulation分析孔蚀现象Cavitation in SolidWorks Flow Simulation –如何使用SolidWorks Flow Simulation分析孔蝕現象■實威國際/CAE產品事業部何謂孔蝕現象(Cavitation)孔蝕現象(Cavitation)也稱之為氣穴現象、空穴。

當液體進入管路或閥門時如果壓力低於流體之蒸發壓壓力(Vapor Saturation Pressure)，就會在管路或閥門的流道內產生氣泡。

這氣泡不是因為加熱而產生的，而是因為流動造成局部區域流速較快引起局部區域靜壓驟降，氣泡的產生會造成噪音或振動，而且通常是發生在實體表面上，因此會損壞管路或閥門的壁面，進而降低設備的使用壽命。

孔蝕現象也常常發生在其他常見的裝置如泵浦、葉輪……等流體機械。

若能透過分析軟體在產品設計階段模擬出此現象，則對於產品品質有非常大的保障。

(圖一) 發生孔蝕現象的渦輪葉片(圖片來源:參考資料2)(圖二) 葉輪模型範例，吸入端至吐出端的壓力曲線，上方曲線是正常的，下方曲線低於蒸發壓力會發生孔蝕現象。

孔蝕現象在SolidWorks Flow Simulation1.SolidWorks Flow Simulation 2006以前版本。

SolidWorks Flow Simulation無法直接模擬出孔蝕現象。

不過，可以藉由分析結果中負壓的區域指出有孔蝕現象的區域。

2.SolidWorks Flow Simulation 2007之後版本。

SolidWorks Flow Simulation有一項新增功能，可以應用來評估是否發生孔蝕現象。

(圖三) 在SolidWorks Flow Simulation 2007版本之後，在流體流動特性(Flow Characteristic)中，就可以指定要不要啟動Cavitation選項。

使用建議• 若是分析水的流動，在分析的區域中有可能局部區域的靜態將低於液體在環境溫度下的蒸發壓力值或者是液體流過劇烈加熱區域使溫度上升至沸點而引起孔蝕現象，建議在Wizard 或General Settings的Fluid設定頁面中啟用Cavitation選項。

天然气旋流脱水装置压力场性能分析

4 天然气作为最清洁的低碳化石能源，在当前能源消费体系中占有相当高的比例，截止2022年，全国天然气消费量超过3600亿立方米，并在未来较长时间继续保持稳步增长。

在天然气需求量大，需求质量高的要求下，对其开采、集输、净化加工等方面提出了更安全环保高效的要求。

天然气在使用过程中水分过高会造成天然气燃烧热值下降、形成水合物堵塞设备管线、加剧管道内腐蚀等重大安全隐患，因此天然气高效脱水尤为重要[1]。

目前天然气主要脱水技术有三甘醇脱水法、低温冷却分离法、膜分离脱水法、分子筛技术等，其中三甘醇脱水法应用广泛，但具有投资大、维护成本高、三甘醇贫液易被污染等缺点。

天然气旋流脱水是一种全新的物理脱水方法，该工艺利用含水天然气经Laval喷管后低温凝结、绝热膨胀、旋流分离等过程，具有成本低、能耗小、分离效率高等优点。

因此，以天然气旋流脱水装置为模型，进行了网格划分，对其内部流场的压力性能进行模拟与仿真分析，总结出内部压力场的影响因素与分布规律。

1 旋流脱水分离技术理论基础含水天然气在旋流分离前须将其内水蒸气组分凝结成液滴，并将其进入分离装置的旋流段入口进行加速，保证在旋流段产生的离心力可以甩出液滴进行干湿分离，因此含水天然气须经过具有增速降温功能的Laval喷管段，其中喷管直径最小处称为喉部。

天然气在Laval喷管前端速度达到0.3倍马赫数，在喷管末端加速至2倍马赫数以上，因此必须考虑密度变化情况，按照可压缩气体流动规律及流体力学三大控制方程[2]。

质量守恒方程： 0)(=+∂∂udivtρρ动量守恒方程：∂t程：xzxyxxx Fzyxxpu udivtu+∂∂+∂∂+∂∂+∂∂-=+∂∂τττρρ)(yzyyyxy Fzyxypudivt+∂∂+∂∂+∂∂+∂∂-=+∂∂τττρυρυ)(zzzyzxz Fzyxzpudivt+∂∂+∂∂+∂∂+∂∂-=+∂∂τττρωρω)(天然气旋流脱水装置压力场性能分析巢皓文冯碧阳朱盼陇东学院石油化工学院甘肃庆阳 745100 摘要：天然气含水量过高会导致燃烧效率降低，热值减少，同时易生成水合物阻塞设备及管线，因此天然气脱水是整个产业非常重要的环节。

螺旋桨梢涡及梢涡空泡数值模拟

螺旋桨梢涡及梢涡空泡数值模拟刘芳远1,2,傅慧萍1,2,李杰1(1.上海交通大学船舶海洋与建筑工程学院,上海200240;2.高新船舶与深海开发装备协同创新中心,上海200240)摘要:以PPTC (Potsdam Propeller Test Case )桨为研究对象,探索了螺旋桨梢涡及梢涡空泡的数值模拟方法。

通过梢涡区域的划分及网格加密,对螺旋桨无空化流场进行了数值模拟,成功捕获了梢涡;然后基于均质混合流模型和Zwart-Gerber-Belamri 空化模型对空化流场进行了数值模拟;并将计算结果与试验数据进行了广泛的比较和分析,以校验计算网格和计算方法。

研究表明:无论片空泡还是梢涡空泡的计算结果均与试验观测吻合良好;同时,所得螺旋桨推力和扭矩系数也与试验值符合良好;有效地实现了梢涡捕捉及梢涡空泡模拟。

同时指出,水中含气率对推力和扭矩系数的影响大于空泡形态。

关键词:梢涡;梢涡空泡;螺旋桨;数值模拟中图分类号:U661.1文献标识码:A doi:10.3969/j.issn.1007-7294.2019.04.002Numerical simulation of propeller tip vortex and TVCLIU Fang-yuan 1,2,FU Hui-ping 1,2,LI Jie 1(1.School of Naval Architecture,Ocean and Civil Engineering,Shanghai Jiao Tong University,Shanghai 200240,China;2.Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration,Shanghai 200240,China)Abstract :Numerical simulation method of propeller tip vortex and tip vortex cavitation (TVC)was researched by calculating the propeller model of Potsdam Propeller Test Case (PPTC).Through the partition of tip vor ⁃tex field and the refinement of the field gridding,non-cavitating flow around PPTC was simulated and tip vortex was successfully captured.Then the cavitating flows were calculated based on the homogeneous mix ⁃ture flow model and the Zwart-Gerber-Belamri cavitation prehensive analysis of computational results and comparisons with EFD data were done to validate the computational mesh and method.The good agreement between the calculated and observed cavitation was found for both tip vortex cavity and sheet cavity.The calculated thrust and torque coefficients agree with the EFD data as well.The tip vortex and tip vortex cavitation were both numerically captured.And it is shown that the nucleation site volume fraction has more effect on the thrust and torque coefficients than the cavity patterns.Key words:tip vortex;tip vortex cavitation;propeller;numerical simulation0引言螺旋桨空泡是一种汽化空泡,即水因降压到饱和蒸汽压力导致汽化,水汽通过界面,进入气核并使之膨胀。

水下爆炸船体结构响应间断伽辽金法数值模拟

水下爆炸船体结构响应间断伽辽金法数值模拟于福临;郭君;姚熊亮;任少飞【摘要】In order to solve the underwater explosion flow field with large discontinuities, Level Set method was applied to track the interface position of the multi⁃medium flow, Ghost Fluid method was used to calculate the physical parameter of both sides of the interface, time and space were discretized by Runge⁃Kutta Discontinuous Galerkin Method, Euler equations of the flow field were solved. One⁃dimensional andtwo⁃dimensional assessments were conducted by RKDG approach. The results reflect the phenomena of underwater explosion shock wave generation, propagation, reflection and explosion products expansion. Finally, the shock responses and damage characteristics of hull plates under shock load were simulated with the nonlinear FEM softeware ABAQUS. The RKDG method can be applied to simulate the hull plates response with high accuracy. The response of hull plates is inversely proportional to the blast center distance.%为求解水下爆炸强间断流场，采用Level Set方法定位多相流界面位置，应用虚拟流体方法处理邻近界面两侧物理量，并用RKDG方法进行空间和时间的离散，求解流场的Euler方程，并进行一维、二维评价，计算结果能够较好地反映水下爆炸冲击波产生、传播、反射和爆炸产物的膨胀等现象。