非正交网格控制容积法分析复杂形状池内的流动

介绍一种基于非正交网格控制容积法的数学模型，及其在圆形沉沙池流动研究中的应用．该模型求解轴对称流动的连续方程及时均Ｎ－Ｓ方程，并采用标准ｋ－ε紊流模型，模拟圆形池内的流动．由于采用非正交网格，此计算模型可精确模拟几何形状较复杂的沉沙池内的流动，利用上述模型对某实际沉沙池进行了流场计算，计算所得流场与模型试验实测值符合良好．     

高阶紧致格式求解二维粘性不可压缩复杂流场

提出了一种求解二维不可压缩复杂流场的高精度算法．控制方程为原始变量、压力Ｐｏｉｓｓｏｎ方程提法．在任意曲线坐标下，采用四阶紧致格式求解Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程组，时间推进采用交替方向隐式（ＡＤＩ）格式，在非交错网格上用松弛法求解压力Ｐｏｉｓｓｏｎ方程．对于复杂的流场，采用了区域分解方法，并在每一时间步对各子域实施松弛迭代使之能精确地反映非定常流场．利用该算法计算了二维受驱空腔流动，弯管流动和垂直平板的突然起动问题．计算结果与实验结果和其他研究者的计算结果相比较吻合良好．对于平板起动流动，成功地模拟了流场中旋涡的生成以及Ｋａｒｍａｎ涡街的形成     

燃烧室两相流场亚网格燃烧模型的研究

在三维任意曲线坐标系下采用不同的亚网格燃烧模型对环形燃烧室火焰筒气液两相湍流瞬态反应流进行大涡模拟．计算中所采用的数学度模型有：k方程亚网格尺度模型估算亚网格湍流黏性；热通量辐射模型估算辐射换热，分别采用亚网格EBU燃烧模型（E-A model）、亚网格二阶矩输运方程模型（SOM）和亚网格二阶矩代数模型（SOM-A）估算化学反应速率．并在非交错网格系统下气相采用SIMPLE算法和混合差分格式求解，液相采用Lagrange处理，并用PSIC算法对其进行求解．通过实验结果和计算结果的比较，表明在三维任意曲线坐标系下对燃烧室火焰简两相湍流油雾燃烧流场进行大涡模拟，3种不同的亚网格燃烧模型都能真实反映两相湍流化学反应流流动及实际燃烧过程，而采用亚网格二阶矩输运方程模型稍优于其他两种亚网格燃烧模型．     

反应堆三角形通道棒束间二次流动的数值研究

采用非线性Ｋ－ε湍流模式数值模拟三角形通道棒束中的二次流动，并考察其对流动和传热的影响。数值方法采用非正交曲线坐标系下求解控制方程的非交错网格方法。计算结果表明该模式能够较为有效地反映棒束中的二次流动，进一步分析表明二次流动有利于改善棒束中的流动和传热特性。     

模型燃烧室内瞬态紊流的大涡模拟

本文采用三种不同亚网格尺度模型对带有V型稳定器的模型燃烧室二维瞬态紊流流动进行了大涡模拟。并在交错网格系下用SIMPLE算法和混合差分格式求解离散方程。数值研究拟不同型式入口速度分布和不同亚网格尺度模型下模型燃烧室二维瞬态紊流流场。计算结果表明不同入口速度分布和不同亚网格尺度模型对瞬态流场和出口速度分布有一定的影响。本文通过数值模拟,揭示了V型稳定器后旋涡的产生和脱落过程。通过计算结果及实验数据的比较可知,本文采用的亚网格尺度模型可以用来模拟模型燃烧室紊流流场及稳定器后面回流区的流动情况。     

跨音速大迎角绕流的Euler方程数值模拟

采用保角变换与代数方法相结合，生成全场统一的贴体、正交Ｏ－Ｈ型网格．采用有限体积法求解Ｅｕｌｅｒ方程，模拟具有歼击机外形的全机及翼身组合体大迎角跨音速绕流．计算表明，法向力系数、气动中心位置及压力分布的计算结果与实验结果吻合良好     

轴对称再入舱模型气动热特性数值模拟研究

应用基于块结构网格的有限体积求解方法,对热化学非平衡环境下轴对称再入舱模型的气动热特性进行了数值模拟。控制方程为带化学反应的多组元轴对称N-S方程,空间离散采用VanLeer迎风格式,时间推进为隐式LU-SGS格式;采用7组元7化学反应模型及Park双温模型模拟再入流场的热化学非平衡效应。对Hollis MP-1模型的气动热特性进行了数值模拟,分别就网格效应、湍流模型、流场的热力学性质对流场的气动力、热环境的影响进行了深入研究。研究结果表明:SST模型与k-w1998模型能更准确地计算再入流场热流峰值的位置与大小;在再入舱模型的局部区域,采用热力学非平衡模型计算的物面压强与热流结果要明显低于热力学平衡模型的结果。     

基于实体的注射成型流动模拟

提出了应用中面模型技术模拟实体模型的注射成型流动过程的新方法。对实体模型的表面进行二维网格划分，将结点在厚度方向上配对．配对点之间添加虚拟热流道单元，建立二维有限元分析的网格模型。将HeleShaw流动应用于非等温条件下的粘性、不可压缩流体，建立基于中面模型流动分析的数学模型，用充填园子的输运方程描述流动前沿。用有限元计算充填过程的压力场．有限差分计算温度场，高阶的Taylor展开式计算每一时间步长的充填因子。针对Han设计的试验模具，用相同的材料及工艺条件，比较中面模型和实体模型的模拟结果。算例分析表明，这种方法可以有效地模拟基于实体模型的注射成型流动过程。     

多相流动的直接数值模拟进展

多相流动的直接数值模拟的讨论就是把流场中颗粒周围计算网格缩小到颗粒尺寸以下进行流动的计算,颗粒的受力不是通过模型计算,而是通过积分表面的黏性力与压力获得.直接模拟方法的出现标志着人们对多相流动的认识从宏观扩展到微观层次.主要介绍了几种先进的直接模拟的方法:基于体适应的非结构化移动网格方法;基于固定网格方法;其它方法.      

非结构混合网格高超声速绕流与磁场干扰数值模拟

对均匀磁场干扰下的二维钝头体无粘高超声速流场进行了基于非结构混合网格的数值模拟.受磁流体力学方程组高度非线性的影响及考虑到数值模拟格式的精度,目前在此类流场的数值模拟中大多使用结构网格及有限差分方法,因而在三维复杂外形及复杂流场方面的研究受到限制.本文主要探索使用非结构网格(含混合网格)技术时的数值模拟方法.控制方程为耦合了Maxwell方程及无粘流体力学方程的磁流体力学方程组,数值离散格式采用Jameson有限体积格心格式,5步Runge-Kutta显式时间推进.计算模型为二维钝头体,初始磁场均匀分布.对不同磁感应强度影响下的高超声速流场进行了数值模拟,并与有限的资料进行了对比,得到了较符合的结果.     

River and reservoir flow modelling using the transformed shallow water equations

This paper describes a versatile finite difference scheme for the solution of the two-dimensional shallow water equations on boundary-fitted non-orthogonal curvilinear meshes. It is believed that this is the first non-orthogonal shallow water equation model incorporating the advective acceleration terms to have been developed in the United Kingdom. The numerical scheme has been validated against the severe condition of jet-forced flow in a circular reservoir with vertical side walls, where reflections of the initial free surface waves pose major problems in achieving a stable solution. Furthermore, the validation exercises are designed to test the computer model for artificial diffusion, which may be a consequence of the numerical scheme adopted to stabilize the shallow water equations. The model is shown to be capable of simulating the flow conditions in an irregularly shaped domain typical of the geometries frequently encountered in civil engineering river basin management.     

A Coupled Level Set and Volume of Fluid method for automotive exterior water management applications

Motivated by the need for practical, high fidelity, simulation of water over surface features of road vehicles a Coupled Level Set Volume of Fluid (CLSVOF) method has been implemented into a general purpose CFD code. It has been implemented such that it can be used with unstructured and non-orthogonal meshes. The interface reconstruction step needed for CLSVOF has been implemented using an iterative ‘clipping and capping’ algorithm for arbitrary cell shapes and a re-initialisation algorithm suitable for unstructured meshes is also presented. Successful verification tests of interface capturing on orthogonal and tetrahedral meshes are presented. Two macroscopic contact angle models have been implemented and the method is seen to give very good agreement with experimental data for a droplet impinging on a flat plate for both orthogonal and non-orthogonal meshes. Finally the flow of a droplet over a round edged channel is simulated in order to demonstrate the ability of the method developed to simulate surface flows over the sort of curved geometry that makes the use of a non-orthogonal grid desirable.     

A study on the extension of a VOF/PLIC based method to a curvilinear co-ordinate system

The conventional volume-of-fluid method has the potential to deal with large free surface deformation on a fixed Cartesian grid. However, when free-surface flows are within or over complex geometries of industrial relevance, such as free-surface flows over offshore oil platforms, it is advantageous to extend the method originally written in Cartesian forms into non-Cartesian forms. In the present study, an algorithm similar to the algorithm described by Rudman in 1997 is proposed for use with curvilinear co-ordinates. This extension results in the ability to model complex geometries which could not be modelled using the original algorithm. Excellent agreement between the solutions obtained on both orthogonal and non-orthogonal meshes is achieved, although in general the L ₁ error, based on the exact solution, on the non-orthogonal mesh is slightly higher than that on the orthogonal mesh. The extended fluid flow solving capacity of the present method is demonstrated through its application to a non-orthogonal Rayleigh–Taylor instability problem.     

Numerical solution of 2D and 3D turbulent internal flow problems

The paper describes a method for solving numerically two-dimensional or axisymmetric, and three-dimensional turbulent internal flow problems. The method is based on an implicit upwinding relaxation scheme with an arbitrarily shaped conservative control volume. The compressible Reynolds-averaged Navier-Stokes equations are solved with a two-equation turbulence model. All these equations are expressed by using a non-orthogonal curvilinear co-ordinate system. The method is applied to study the compressible internal flow in modern power installations. It has been observed that predictions for two-dimensional and three-dimensional channels show very good agreement with experimental results.     

A miniature triple hot-wire probe for wall bounded flows

 Four orthogonal and one non-orthogonal miniature triple hot-wire probes have been developed and tested in a two-dimensional turbulent boundary layer. The influence of the different wire configurations on measurements of the Reynolds stresses has been studied. A directional calibration with an analytical solution for the wire response equations was used for the measurements of the non-orthogonal probe and was tested for the orthogonal probes in order to correct their possible geometrical imperfections. It is shown that a directional calibration does not significantly improve the quality of the measurements for precisely manufactured orthogonal probes and that measuring errors are related rather to the measuring volume, the size of the domain of unique solutions for the instantaneous velocity vector and interference effects, i.e. the wire configuration itself. Received: 7 February 1997/Accepted: 18 November 1997     

Measurement of velocity vectors with orthogonal and non-orthogonal triple-sensor probes

A new method of interpreting the signals from triple-sensor thermal anemometer probes has been developed based on fast solution for all the roots of the non-linear Jorgensen (1971) equations describing the directional response of each cylindrical sensor. The sensors can be oriented at arbitrary angles to each other, but always within a range of probe geometries that keep prong interference and thermal wake interference below acceptable levels. The properties of a class of non-orthogonal symmetric tetrahedral probe geometries are studied in relation to the range of flow vector angles that can be measured, the sensitivity of the probe with respect to changes in flow angle, and the sensitivity of the computed velocity components due to angular errors associated with the construction of the probe. The solutions of Jorgensen's equations are inherently multiple-valued, but if the velocity vector is restricted to be within a cone of angles, they are unique. It is shown that measurements with non-orthogonal triple sensor signals are sensitive to angular deviations of a few degrees of the sensor angles from the nominally orthogonal probe geometry, indicating the need of a non-orthogonal algorithm. The mean, rms, Reynolds stress, and power spectrum of the velocity in fully developed turbulent pipe flow were measured using a specially designed triple sensor probe and the proposed algorithm.Presently with the Dept. of Mechanical Engineering at The University of Iowa     

Cryosurgery of a biological tissue with multiprobe: effect of central cryoprobe

In this paper a three-dimensional numerical model for cryosurgery is developed to study the effect of central probe on the cryosurgery process. The irregular boundary resulting due to the presence of cryoprobes is taken care by body-fitted multi-block non-orthogonal grids. The thermo-physical properties of biological tissue are considered as a function of temperature as phase change takes place over a wide temperature range for the biological tissue. It has been found that the cooling power requirement by the single offset cryoprobe is greater than that of the central cryoprobe. However, the presence of central cryoprobe markedly influenced the cryosurgery process, resulting in an increase in the ablation ratio by 57 % with an insignificant increase in cooling power by 4.5 %. This information can be utilised effectively in computerised planning of a cryosurgery protocol.     

Magnetohydrodynamic steady flow computations in three dimensions

A complete three-dimensional mathematical model has been developed governing the steady, laminar flow of an incompressible fluid subjected to a magnetic field and including internal heating due to the Joule effect, heat transfer due to conduction, and thermally induced buoyancy forces. The thermally induced buoyancy was accounted for via the Boussinesq approximation. The entire system of eight partial differential equations was solved by integrating intermittently a system of five fluid flow equations and a system of three magnetic field equations and transferring the information through source-like terms. An explicit Runge-Kutta time-stepping algorithm and a finite difference scheme with artificial compressibility were used in the general non-orthogonal curvilinear boundary-conforming co-ordinate system. Comparison of computational results and known analytical solutions in two and three dimensions demonstrates high accuracy and smooth monotone convergence of the iterative algorithm. Results of test cases with thermally induced buoyancy demonstrate the stabilizing effect of the magnetic field on the recirculating flows.     

A Lagrangian Mixed Subgrid-Scale Model in Generalized Coordinates

This paper presents the formulation of a mixed dynamic subgrid-scale model in non-Cartesian geometries suitable for the study of complex flows. Following the approach developed by Jordan [J. Comput. Phys. 148, 322 (1999)], the variables are first transformed into a contravariant form and then filtered in the computational space. A dynamic localized mixed model, previously developed within the Cartesian framework has been entirely re-formulated for non-orthogonal meshes. The model performance was evaluated by carrying out two tests. First, a plane channel flow at Re_τ = 395 was simulated using both Cartesian and curvilinear grids; the results show that the model formulation is consistent and insensitive to grid distortion, and compares well with the reference data. Then, computations of the turbulent flow over a two-dimensional channel with a wavy wall were performed. Accurate first- and second-order statistics were obtained using relatively coarse grids. This revised version was published online in July 2006 with corrections to the Cover Date.