COMPRESSIBILITY BOUNDARY LAYER THEORY AND ITS SIGNIFICANCE IN COMPUTATIONAL HYDRODYNAMICS

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A SIMILARITY METHOD FOR LAMINAR WAKE OF POWER-LAW FLUID FLOW AROUND A FLAT PLATE

Based on the characteristic equation for power-law fluid and the Prandtl boundary layer equation, using the similarity method similar to that of Newtonian fluids, two similarity variables were given and a normal differential equation was derived for the laminar wake of power-law fluid flow produced by a flat plate. And numerical results were obtained. The results show that the power-law index n has evident influence on the velocity distribution in the wake. In the wake, velocity gradient is larger, and the wake is narrower for larger n .     

粘性流中的二维兴波水翼水动力特性研究

本文采用边界层的概念来研究粘性流中的二维兴波水翼之水动力特性的数值计算方法。考虑到边界层与外部势流的相互干扰，运用了势流与边界层的相互迭代计算，从而求得两者相互匹配的解。用势流解求得的水翼升力系数往往比实验值明显偏大。而用本文的方法，从算例来看，计算结果比势流解减小１５％左右，而与实验值比较接近。本文还讨论了兴波阻力的计算方法，并有算例。     

用密度函数法对自由表面进行数值模拟

本文从二维非定常N-S方程出发，提出了一种处理自由表面问题的数值方法。引入密度函数法(density-function method)追踪自由表面，在密度函数的传输方程中采用TVD格式达到了二阶精度。对均匀来流中的非定常不可压方柱绕流进行了数值模拟。数值结果成功地捕捉了自由表面波动以及漩涡的生成、分离的时间发展历程。同时验证了本方法的有效性。     

STUDIES ON THE NUMERICAl SIMULATION OF UNSTEADY FLOWS

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Three-dimensional large eddy simulation and vorticity analysis of unsteady cavi- taring flow around a twisted hydrofoil

Large Eddy Simulation (LES) was coupled with a mass transfer cavitation model to predict unsteady 3-D turbulent cavitating flows around a twisted hydrofoil. The wall-adapting local eddy-viscosity (WALE) model was used to give the Sub-Grid Scale (SGS) stress term. The predicted 3-D cavitation evolutions, including the cavity growth, break-off and collapse downstream, and the shedding cycle as well as its frequency agree fairly well with experimental results. The mechanism for the interactions between the cavitation and the vortices was discussed based on the analysis of the vorticity transport equation related to the vortex stretching, volumetric expansion/contraction and baroclinic torque terms along the hydrofoil mid-plane. The vortical flow analysis demonstrates that cavitation promotes the vortex production and the flow unsteadiness. In non-cavitation conditions, the streamline smoothly passes along the upper wall of the hydrofoil with no boundary layer separation and the boundary layer is thin and attached to the foil except at the trailing edge. With decreasing cavitation number, the present case has σ= 1.07, and the attached sheet cavitation becomes highly unsteady, with periodic growth and break-off to form the cavitation cloud. The expansion due to cavitation induces boundary layer separation and significantly increases the vorticity magnitude at the cavity interface. A detailed analysis using the vorticity transport equation shows that the cavitation accelerates the vortex stretching and dilatation and increases the baroclinic torque as the major source of vorticity generation. Examination of the flow field shows that the vortex dilatation and baroclinic torque terms increase in the cavitating case to the same magnitude as the vortex stretching term, while for the non-cavitating case these two terms are zero.     

拖式吊舱螺旋桨定常性能理论计算

本文提出拖式吊舱螺旋桨(螺旋桨位于吊舱首部)定常水动力性能的势流理论计算方法。螺旋桨采用升力面理论涡格法、吊舱采用面元法分析计算，二者的相互干扰通过叠代计算来处理。考虑吊舱的影响，修改了尾涡模型。应用本方法，计算了拖式吊舱螺旋桨的定常性能，并与空泡水筒试验结果进行了比较，计算与试验吻合良好。     

Numerical simulation of viscous flow past an oscillating square cylinder using a CIP-based model

The flow past an in-line forced oscillating square cylinder at Reynolds number of 200 is studied using an in-house code, named constrained interpolation profile method developed in Zhejiang University(CIP-ZJU). The model is established in the Cartesian coordinate system using the CIP method to discretise the Navier-Stokes equations. The fluid-structure interaction is treated as a multiphase flow of the liquid and solid phases to be solved simultaneously. An immersed boundary method is used to deal with the boundary of the solid body. The CFD model is first applied to the computation of the flow past a fixed square cylinder for its validation. Computations are then performed for the flow past a square cylinder oscillating in the streamwise direction. Considerable attention is paid to the symmetric and anti-symmetric modes of the vortex shedding in the oscillating square cylinder wake. Various oscillation amplitudes and frequencies are simulated and their effects on the vortex shedding modes are analyzed via Lissajous patterns of the unsteady lift coefficient. The relationship among the lift coefficient, the drag coefficient and the lock-on range is also investigated quantitatively.     

绕圆柱非定常周期性涡旋脱落的数值模拟

利用非定常流函数涡量方程数值模拟圆柱突然起动尾流涡旋的形成及周期性脱落过程。对求解的流函数的一阶导数即速度项采用四阶精度的Hermitian公式，而方程的对流项则采用四阶精度的差分格式，并利用ADI方法迭代求解差分方程组。当雷诺数Re不大于40时，圆柱尾流为附体的两个对称涡，为定常解。当Re大于40后流动为非定常及非对称的，圆柱尾流呈现周期性涡旋交替脱落而形成著名的Karman涡街。选择Re=100为例，在初始条件未加任何扰动情况下，成功地模拟了圆柱非定常涡旋形成与脱落的完整过程（无量纲时间算到t=250及以上）。所计算的阻力系数与实验结果及其它数值方法的计算结果一致。约在t=200形成严格的Karman涡街。对涡量方程ADI求解方法的稳定性进行了分析。对流项采用四阶精度差分格式，若应用于定常问题，将极大提高数值求解的精度，若应用于非定常问题的求解，将对求解精度有所改善，其中时间空间两阶混合偏导数的处理是关键，有待进一步的数值实验。     

均匀流绕旋转圆柱分离流动的数值模拟

本文利用离散涡模型与边界层理论相结合的方法，研究了高雷诺数下，均匀流绕旋转圆柱的分离流动以及有关动力学特性，并验证了Magnus效应，数值模拟过程中，边界层方程用Keller盒式法求解，离散涡采用涡量均匀分布的圆形涡团模型并以涡核半径随时间增长来模拟涡旋的粘性扩散效应。在计算绕旋转圆柱的流动中，无须人为地引进非对称扰动，到一定时候就能自动形成交替脱落的涡街，旋转圆柱周向速度与来流速度比值α的变化范围为0.05-0.3。计算所得升阻系数、分离点的位置以及压力分布与理论和实验结果相符。     

两层黏性流体中直立圆柱体绕流的三维数值模拟

研究了两层流体中直立贯底圆柱体的三维黏性绕流问题.以不可压缩Navier-Stokes方程为控制方程,应用VOF方法追踪两层流体的内界面,建立了该问题的数值模拟方法.成功地数值模拟了两层流体中圆柱体黏性绕流产生的三维尾涡特征,表明了流体的密度分层效应对直立贯底圆柱体的尾涡特性和阻力系数都是有影响的.在海洋立管涡激振动的研究中,考虑流体的密度分层效应是重要的.     

采用新的结构—尾流反作用力耦合模型分析圆柱结构涡激共振

该文建立了一个新的结构-与尾流振子流固耦合模型.采用具有非线性阻尼的振子来模化、van der pol方程来描述流场近尾迹动力学.以结构与流体的受力互为反作用力的关系,建立了新的流固耦合模型.使用该文的模型对二维结构涡激振动问题进行研究,能很好地预计结构涡激共振的特性.计算结果表明,结构共振的最大振幅随着结构的数和质量阻尼参数的增大而减小,与实验结果规律一致、数值吻合.根据该文的模型计算结果给出了预测共振振幅值的拟合公式,并给出了共振情况下升力、相位等的变化规律.     

不可压缩旋转涡对的流噪声计算研究

相隔一定距离的两个同向旋涡相互诱导而形成绕中点旋转的涡对,进而诱发流噪声。该文基于不可压缩流场提供的非稳态流动信息,采用黏声分离法研究水流场中旋转涡对的声学特性。计算结果同理论值进行比较,并探讨了计算条件对计算稳定性和准确性的影响。计算结果表明:在选取合适的计算参数(人工阻尼、网格尺寸和时间步长)的情况下,黏声分离法方法适用于预测水流噪声。对不可压缩旋转涡对的声场特性进行分析,得到旋转涡对声压图案类似四极子,在远场接近圆柱波;随着旋转马赫数的增加,声压级增大。     

水力机械转轮中全三维势流的非线性混合边界元法

为求解水力机械(水轮机,水泵等)转轮中的全三维势流流动,本文提出了一种有效的计算方法,文中计入了转轮流场的一些实际特性,如叶片不均匀负荷,叶片出口的旋涡流动等。由于采用了非线性混合边界元,故本文所提出的方法精度高,简单易行,计算量小,可以较广泛地适用于偏离设计工况的运行情况,算例结果同实验值吻合很好。     

NUMERICAL SIMULATION OF A PODDED PROPULSOR IN VISCOUS FLOW

A podded propulsor in viscous flow is numerically simulated in this article.The region of fluid is divided into efficient calculation grids.The pressure and viscous force of blades,pod and strut are obtained as functions of an advance coefficient.The steady result is used as a base in the unsteady simulation to obtain a solution more quickly.The distributions of the thrust and torque fluctuations of the key blade in one revolution are obtained.The calculation results from the mixing plane on steady conditions are compared with those obtained from the sliding mesh model on unsteady conditions.The User-Defined Function(UDF)method is used to simulate the influence of ship hull on the non-uniform wake of the propeller.     

MHD flow of a visco-elastic fluid through a porous medium between infinite parallel plates with time dependent suction

This work provides a comprehensive theoretical analysis of MHD unsteady free convection viscoelastic fluid flow through a porous medium. The medium is treated as incompressible and optically transparent. The flow of the fluid is initiated by shearing action of the moving wall with time dependent suction. Radiative heat flow is considered in temperature equation. The coupled nonlinear problem has been solved asymptotically. Approximate solutions have been obtained for the mean velocity, mean temperature using multi parameter perturbation technique. The originality of the present study is to investigate the effect of viscoelastic property of the fluid(Walters B? model) on the flow and heat transfer phenomena when the flow is permeated through a porous medium with uniform porous matrix subject to transverse magnetic field and time dependent fluctuative suction at the boundary surface. The case of viscous flow has been discussed as a particular case on comparison with the result reported earlier and it is in good agreement. Flow reversal is indicated incase of viscoelastic fluid with high heat capacity in the presence of magnetic field. The higher cooling of the plate in case of viscoelastic flow also causes a flow reversal.     

3-D NUMERICAL SIMULATION OF FLOW THROUGH AN ORIFICE SPILLWAY TUNNEL

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Free-surface flow past a submerged cylinder

This study employs a Lagrangian frame numerical method to investigate two-dimensional free-surface flow induced by a submerged moving cylinder. This method combines the advantages of vortex methods and boundary integral methods, and is capable of capturing the complex motion of free surface and vortices. A series of computations are performed to investigate the effects of Froude number, the depth of submergence and still water depth on the flow motion. Free surface deformation, wake vortex and hydrodynamic forces are studied.

     

The effect of variable viscosity on the flow and heat transfer of a viscous Agwater and Cu-water nanofluids

A numerical study is carried out to study the effects of the temperature dependent viscosity on the flow and heat transfer of a nanofluid over a flat surface in the presence of viscous dissipation. The governing nonlinear partial differential equations are transformed into nonlinear ordinary differential equations, and are solved numerically by the Keller-box method. The numerical results indicate that the effect of nanoparticle volume fraction is to increase the heat transfer and hence enhance the thermal boundary layer thickness. This is true even in the presence of variable viscosity and the viscous dissipation. Furthermore, the results obtained for heat transfer characteristics with nanoparticles reveal many interesting behaviors that warrant further study on the effects of the "nano-solid-particles".     

NUMERICAL STUDY FOR THE NONLINEAR EVOLUTION OF VORTEX SHEET AND ITS APPLICATIONS: PART II. EVOLUTION OF WING SHEDDING VORTEX

1.　 INTRODUCTIONVortex sheet exists widely in a variety of nature and engineering problems,which isusually shed from airplane wing,ship propeller,swim ming fish,and so on.To study thebehaviour of vortex sheetevolution is much helpful to understand the physical mechanism ofthose flows.Therefore,many vortex m ethods[1 - 5 ] ,even involving viscous effects,weredeveloped to simulate the vortex sheet motion.As was discussed in Part I,asuperconvergence scheme based on Multhopp′s discretizati…