A second‐order time accurate finite element method for quasi‐incompressible viscous flows

A finite element method for quasi‐incompressible viscous flows is presented. An equation for pressure is derived from a second‐order time accurate Taylor–Galerkin procedure that combines the mass and the momentum conservation laws. At each time step, once the pressure has been determined, the velocity field is computed solving discretized equations obtained from another second‐order time accurate scheme and a least‐squares minimization of spatial momentum residuals. The terms that stabilize the finite element method (controlling wiggles and circumventing the Babuska–Brezzi condition) arise naturally from the process, rather than being introduced a priori in the variational formulation. A comparison between the present second‐order accurate method and our previous first‐order accurate formulation is shown. The method is also demonstrated in the computation of the leaky‐lid driven cavity flow and in the simulation of a crossflow past a circular cylinder. In both cases, good agreement with previously published experimental and computational results has been obtained. Copyright © 2010 John Wiley & Sons, Ltd.     

Derivation and characteristics analysis of an acoustics–convection upstream resolution algorithm for the two‐dimensional Euler and Navier–Stokes equations

The first of a two‐paper series, this paper introduces a new decomposition not of the hyperbolic flux vector but of the flux vector Jacobian. The paper then details for the Euler and Navier–Stokes equations an intrinsically infinite directional upstream‐bias formulation that rests on the mathematics and physics of multi‐dimensional acoustics and convection. Based upon characteristic velocities, this formulation introduces the upstream bias directly at the differential equation level, before the spatial discretization, within a characteristics‐bias governing system. Through a decomposition of the Euler flux divergence into multi‐dimensional acoustics and convection–acoustics components, this characteristics‐bias system induces consistent upstream bias along all directions of spatial wave propagation, with anisotropic variable‐strength upstreaming that correlates with the spatial distribution of characteristic velocities. Copyright © 2005 John Wiley & Sons, Ltd.     

A new multi‐domain/multi‐resolution method for large‐eddy simulation

A new multi‐domain/multi‐resolution method is presented in the framework of the large‐eddy simulation (LES). The proposed treatment at the interfaces is conceived to deal with the problem of discontinuities on the characteristic length scales met in the case of two domains having different resolutions. It gives rise to an original approach taking into account not only the discontinuous aspect on the flow fields values but also, consequently, the non‐conservative aspect of transfer of fluxes through the interfaces. This new treatment at the interfaces has been assessed successfully in the case of a subsonic compressible channel flow. Copyright © 2001 John Wiley & Sons, Ltd.     

Progresses in application of computational fluid dynamic methods to large scale wind turbine aerodynamics

The computational fluid dynamics (CFD) methods are applied to aerodynamic problems for large scale wind turbines. The progresses including the aerodynamic analyses of wind turbine profiles, numerical flow simulation of wind turbine blades, evaluation of aerodynamic performance, and multi-objective blade optimization are discussed. Based on the CFD methods, significant improvements are obtained to predict two/three dimensional aerodynamic characteristics of wind turbine airfoils and blades, and the vortical structure in their wake flows is accurately captured. Combining with a multi-objective genetic algorithm, a 1.5 MW NH-1500 optimized blade is designed with high efficiency in wind energy conversion.     

铁路空调硬卧车内气流分布的数值模拟

建立了铁路空调硬卧车内CFD仿真模型,对车厢内流场、温度场和热舒适性评价指标进行了分析。采用稳态不可压缩雷诺时均N-S方程、k-ε湍流模型,应用控制容积法和交错网格进行离散。计算了空调硬卧车内三维空气流场和温度场,并与实验结果进行了对照,两者吻合较好。在此基础上分析了车厢内人体热舒适性,结果表明车厢中部和端部铺位PMV分布不同,端部人体热舒适感较好,中部较差;而且同一计算断面不同铺位的人体热舒适感差异较大:上铺有较大区域PMV<-1.0,人体感觉较凉;中铺大部分区域-0.51.0,人体感觉偏暖。     

空气炮碰撞实验台发射过程的数值模拟

利用计算流体动力学方法对单级空气炮碰撞实验台的发射过程进行了数值仿真,所得碰撞车发射速度与实验结果吻合。在此基础上,对碰撞车发射过程的流场变化、车体前后压力以及储气罐压力变化进行分析。结果表明,泄漏气体先于碰撞车充满整个发射空间,形成初始流场,使得车前压力出现正负交替现象,但其数值较小,对车体加速过程的影响可以忽略。当碰撞车进入泄压段后,受冲击射流作用,碰撞车仍处于加速状态,且速度增量约为2 m/s。

     

某调距导管桨系泊工况水力性能和流激直发声预报

采用经验证的计算流体力学方法,对某艏辅推调距导管桨设计螺距和系泊工况螺距的水动力性能进行了有效预报,并对系泊工况装船桨流激噪声进行了分析。系泊工况下,由于导管桨的抽吸作用在导管外壁近壁面区域存在与导管内部流动方向相反的逆向流动,且导管桨尾流场速度梯度分布不均匀、流动紊乱,此时桨叶与导管的推力之比约为1.2∶1。系泊工况船+桨的瞬态流场脉动信息表明,导管桨各部件噪声源强度均表现出从1倍到4倍叶频依次下降的规律,最强幅值集中在桨叶导边和导管内壁;在远场声源级频谱曲线中轴向测点线谱较高峰值位置体现出导管桨进流流场的流动特性。对比分析该艏辅推整体和各部件宽带声源级指向性,可知旋转部件(桨叶、桨榖)对总噪声级的贡献较大,静止部件是径向测点噪声的主要贡献源。     

Compact high‐resolution algorithms for time‐dependent advection on unstructured grids

A technique for constructing monotone, high resolution, multi‐dimensional upwind fluctuation distribution schemes for the scalar advection equation is presented. The method combines the second‐order Lax–Wendroff scheme with the upwind positive streamwise invariant (PSI) scheme via a fluctuation redistribution step, which ensures monotonicity (and which is a generalization of the flux‐corrected transport approach for fluctuation distribution schemes). Furthermore, the concept of a distribution point is introduced, which, when related to the equivalent equation for the scheme, leads to a ‘preferred direction’ for the limiting procedure, and hence to a new distribution of the fluctuation, which retains second‐order accuracy from the Lax–Wendroff scheme, even when the solution contains turning points. Experimental comparisons show that the new method compares favourably in terms of speed, accuracy and robustness with other, similar, techniques. Copyright © 2000 John Wiley & Sons, Ltd.     

Finite element and implicit Runge–Kutta implementation of an acoustics–convection upstream resolution algorithm for the time‐dependent two‐dimensional Euler equations

The second of a two‐paper series, this paper details a solver for the characteristics‐bias system from the acoustics–convection upstream resolution algorithm for the Euler and Navier–Stokes equations. An integral formulation leads to several surface integrals that allow effective enforcement of boundary conditions. Also presented is a new multi‐dimensional procedure to enforce a pressure boundary condition at a subsonic outlet, a procedure that remains accurate and stable. A classical finite element Galerkin discretization of the integral formulation on any prescribed grid directly yields an optimal discretely conservative upstream approximation for the Euler and Navier–Stokes equations, an approximation that remains multi‐dimensional independently of the orientation of the reference axes and computational cells. The time‐dependent discrete equations are then integrated in time via an implicit Runge–Kutta procedure that in this paper is proven to remain absolutely non‐linearly stable for the spatially‐discrete Euler and Navier–Stokes equations and shown to converge rapidly to steady states, with maximum Courant number exceeding 100 for the linearized version. Even on relatively coarse grids, the acoustics–convection upstream resolution algorithm generates essentially non‐oscillatory solutions for subsonic, transonic and supersonic flows, encompassing oblique‐ and interacting‐shock fields that converge within 40 time steps and reflect reference exact solutions. Copyright © 2005 John Wiley & Sons, Ltd.     

A novel interface‐tracking method based on Lagrangian particles for deformation analysis of a red blood cell in a capillary

A novel efficient interface‐tracking method is developed to gain an insight into the interface in a multiphase or multifluid system, called the modified particle binary level set (MPBLS) method, in which the binary level set function is defined to distinguish the different phases or fluids and further modified by Lagrangian particles scattered along the interface for achieving higher accuracy. The validation of the MPBLS method is carried out first by simulating the free motion of a red blood cell (RBC) in the rotating, shear and Poiseuille flows, respectively. Subsequently, further validations are performed by comparing with the experimental and numerical results published previously. As one of important applications, the MPBLS method is employed to investigate the deformation behaviors of RBCs with different shapes in a capillary. The simulations show that the healthy RBC gradually changes the geometric shape from a biconcave to a steady parachute shape. It is thus guaranteed that the RBC successfully traverses through the smaller capillaries compared with undeformed RBC. However, the unhealthy RBC with the circular or elliptical shape has different deformation behaviors, in which the steady parachute shape is much less concave at the rear and more convex in the front. Copyright © 2011 John Wiley & Sons, Ltd.     

A correction for Reynolds-averaged-Navier–Stokes turbulence model under the effect of shock waves in hypersonic flows

Studies on the unphysical increase of turbulent quantities for RANS simulation induced by shock waves in hypersonic flows are carried out. Numerical experiments on the hypersonic flow over a blunt body reveal that the phenomenon of unphysical increase of turbulent quantities across the detached shock wave is induced by the strain-rate-based production terms of the k-$\omega$ and k-$\omega$ SST turbulence models, which leads to the over-prediction of aerothermal prediction. While this phenomenon does not occur for Spalart–Allmaras (S–A) turbulence model because of its vorticity-based production term. In order to eliminate this unphysical phenomenon, and to maintain the accuracy of the original models for boundary layer and separation flows, a new correction method for the k-$\omega$ and k-$\omega$ SST models is proposed: by comparing the orders of magnitude between the strain-rate-based and vorticity-based production terms, the vorticity-based production term is used near the shock waves, while the original strain-rate-based production term is still used in other regions. Finally, the correction method is applied to turbulence and transition flows over blunt bodies, and the numerical results show that the correction method effectively eliminates the unphysical increase of turbulent quantities across shock waves and improves the accuracy of aerothermal and transition onset location prediction.     

CFD/NHT教学中若干易混淆概念的综合辨析教学方法

《计算流体力学》及《数值传热学》系列课程知识体系复杂、概念抽象且分散、易混淆概念较多;若教学方法不当,学生学完课程内容后往往对一些重要的概念似懂非懂,对概念相互之间的区别与联系亦是云里雾里,甚至对一些重要概念理解错误,导致面对数值仿真关键难题时不得要领。立足于此系列课程的特点,本文提出了一种综合辨析教学方法：通过典型案例引出概念,化抽象为具体,通过对照式、综合式、追根溯源式等辨析方法对概念进行综合辨析教学。该方法有助于学生辨析易混淆知识点,明晰零散概念间的区别与内在联系,从而实现对知识点的融会贯通和灵活运用,起到了拨云见日、升华理解的作用。文中以误差、稳定性和收敛性三方面相关易混淆概念的教学为例,介绍了该综合辨析教学方法的实施要点。该教学方法可为《计算流体力学》和《数值传热学》系列课程的教学或自学提供参考。

     

建筑风压场数值模拟中压力波动的平抑

在以同位网格为基础的简单流场压力计算中,通常采用动量插值方法来平抑流场中的压力波动现象;但是对于建筑风场等复杂的钝体绕流问题,由该平抑方法得到的收敛风压场仍可能存在小幅波动。为彻底解决同位网格格式下的压力波动,除采用动量插值方法外,本文提出了在压力校正方程的界面流速中添加压力梯度差值项的方法。算例分析表明,该方法计算得到的建筑风压场完全避免了压力波动现象,风压解与试验结果吻合良好。     

不同风场下TNT炸药爆炸烟云的扩散模型及特性

为获取不同风场下TNT爆炸烟云扩散时空分布规律与高度变化模型,本文理论描述了爆炸烟云扩散过程与机理,开展了不同水平风速下烟云扩散的计算流体力学（computational fluid dynamics, CFD）仿真和外场时空分布实验,建立了不同水平风速下烟云高度随时间变化模型及烟云最终高度计算模型,分析了烟云扩散过程中形态、温度、密度、速度变化规律。研究结果显示：CFD方法仿真烟云分布结果与实验结果基本一致,大气稳定且无风条件下烟云高度随时间呈指数0.5的幂函数关系,最终高度与爆炸当量可拟合为指数0.47的幂函数模型;水平风会加快烟云与空气混合的速度,导致幂函数模型中指数参数随风速变大而呈线性减小规律,风速越大烟云上升速度衰减越快、上升时间越短、最终高度越低。

     

带自由表面水流与离散颗粒耦合模型研究

基于考察泥沙运动的细观行为特征,采用离散单元法(DEM)模拟泥沙颗粒运动,结合带自由表面的水动力学计算模型,建立了CFD-DEM耦合数值模型。计算程序开发基于Fortran语言来实现。耦合模型中实现了硬球模型和软球模型两种颗粒碰撞模型,应用范围较广。作为自由表面水流与泥沙颗粒流数值模型的初步研究,在模型建立的基础上,对模型做了基本的验证。分别通过单颗粒静水沉降和混合颗粒群分选两个计算工况,验证了模型的正确性及模拟精度。该耦合模型可进一步丰富带自由表面水流条件下泥沙运动的研究手段。     

A two‐step monolithic method for the efficient simulation of incompressible flows

We propose a simple technique for improving computationally the efficiency of monolithic velocity–pressure solvers for incompressible flow problems. The idea consists in solving the discrete nonlinear system of governing equations in two steps: introducing ‘artificial’ compressibility first and afterwards correcting the solution by solving the original incompressible system. The speed‐up is obtained because of a better conditioning of the modified discrete system solved at the prediction step. The formulation can be easily implemented into existing monolithic codes requiring minor modification only. The paper concludes with two examples validating the formulation and facilitating the estimation of the obtained speed‐up. For the tests chosen, an average speed‐up is approximately double, suggesting that the method is a feasible approach for incompressible flows' simulation. Copyright © 2014 John Wiley & Sons, Ltd.     

SPH computation of plunging waves using a 2‐D sub‐particle scale (SPS) turbulence model

The paper presents a 2‐D large eddy simulation (LES) modelling approach to investigate the properties of the plunging waves. The numerical model is based on the smoothed particle hydrodynamics (SPH) method. SPH is a mesh‐free Lagrangian particle approach which is capable of tracking the free surfaces of large deformation in an easy and accurate way. The Smagorinsky model is used as the turbulence model due to its simplicity and effectiveness. The proposed 2‐D SPH–LES model is applied to a cnoidal wave breaking and plunging over a mild slope. The computations are in good agreement with the documented data. Especially the computed turbulence quantities under the breaking waves agree better with the experiments as compared with the numerical results obtained by using the k–ε model. The sensitivity analyses of the SPH–LES computations indicate that both the turbulence model and the spatial resolution play an important role in the model predictions and the contributions from the sub‐particle scale (SPS) turbulence decrease with the particle size refinement. Copyright © 2006 John Wiley & Sons, Ltd.     

An improved unstructured WENO method for compressible multi‐fluids flow

An improved high‐order accurate WENO finite volume method based on unstructured grids for compressible multi‐fluids flow is proposed in this paper. The third‐order accuracy WENO finite volume method based on triangle cell is used to discretize the governing equations. To have higher order of accuracy, the P1 polynomial is reconstructed firstly. After that, the P2 polynomial is reconstructed from the combination of the P1. The reconstructed coefficients are calculated by analytical form of inverse matrix rather than the numerical inversion. This greatly improved the efficiency and the robustness. Four examples are presented to examine this algorithm. Numerical results show that there is no spurious oscillation of velocity and pressure across the interface and high‐order accurate result can be achieved. Copyright © 2016 John Wiley & Sons, Ltd.