A large eddy simulation of flows around an underwater vehicle model using an immersed boundary method

A large eddy simulation(LES) of the flows around an underwater vehicle model at intermediate Reynolds numbers is performed. The underwater vehicle model is taken as the DARPA SUBOFF with full appendages,where the Reynolds number based on the hull length is 1.0×105. An immersed boundary method based on the moving-least-squares reconstruction is used to handle the complex geometric boundaries. The adaptive mesh refinement is utilized to resolve the flows near the hull. The parallel scalabilities of the flow solver are tested on meshes with the number of cells varying from 50 million to 3.2 billion. The parallel solver reaches nearly linear scalability for the flows around the underwater vehicle model. The present simulation captures the essential features of the vortex structures near the hull and in the wake.Both of the time-averaged pressure coefficients and streamwise velocity profiles obtained from the LES are consistent with the characteristics of the flows pass an appended axisymmetric body. The code efficiency and its correct predictions on flow features allow us to perform the full-scale simulations on tens of thousands of cores with billions of grid points for higher-Reynolds-number flows around the underwater vehicles.     

A diffuse-interface immersed boundary method for simulation of compressible viscous flows with stationary and moving boundaries

In this paper, a diffuse-interface immersed boundary method (IBM) is proposed for simulation of compressible viscous flows with stationary and moving boundaries. In the method, the solution of flow field and the implementation of boundary conditions are decoupled into two steps by applying the fractional step technique, ie, the predictor step and the corrector step. Firstly, in the predictor step, the intermediate flow field is resolved by a recently developed gas kinetic flux solver (GKFS) without consideration of the solid boundary. The GKFS is a finite volume approach that solves the Navier-Stokes equations for the flow variables at cell centers. In GKFS, the inviscid and viscous fluxes are evaluated as a single entity by reconstructing the local solution of continuous Boltzmann equation. Secondly, in the corrector step, the intermediate flow field is corrected by the present diffuse-interface IBM. During this process, the velocity field is firstly corrected by the implicit boundary condition–enforced IBM so that the no-slip boundary condition can be accurately satisfied. After that, the density correction is made by an iterative approach with the help of the continuity equation. Finally, the correction of the temperature field is made in the same way as that of the velocity field. Good agreements between the present simulations and the reference data in literature demonstrate the reliability of the proposed method.     

一种模拟动边界绕流的锐利界面浸入边界法

为避免复杂贴体网格的更新和畸形对动边界流场计算效率、精度的影响,以充分掌握结构场的受力特性,采用一种改进的锐利界面（sharp-interface）浸入边界法模拟具有动边界绕流的流动问题。该方法将计算域中的固体视为流体,固体边界离散为若干个拉格朗日网格点,通过在界面单元处插值重构流动参数（速度）,将其直接作为流动求解器的边界条件,由此来反映固体边界的影响。即通过构造“虚拟点—受力点—垂足点”的计算结构,借助双线性插值得到虚拟点的速度,再通过强制满足固体边界的无滑移条件计算出受力点的速度,以此为边界条件,最终求解基于浸入边界法的耦合系统方程,实现复杂动边界的流动数值模拟。采用C++编写该浸入边界法的数值程序,以单圆柱绕流为验证算例,通过与文献和实验结果的对比,验证了该方法的准确性和可靠性。在此基础上,对主动运动椭圆柱绕流问题进行了精细计算,探讨了不同轴长比(A_R)、不同攻角($ \theta $)下的椭圆柱对尾涡结构分布特征和水力不稳定现象的影响。捕捉到了反对称S型、“P+S” Ⅰ型、“P+S” Ⅱ型尾涡脱落模态,漩涡强度、涡脱频率和升阻比随A_R和$ \theta $的变化规律,以及确定了升阻比临界攻角(25°)。

     

A ghost-cell immersed boundary method for large-eddy simulations of compressible turbulent flows

A methodology to perform a ghost-cell-based immersed boundary method (GCIBM) is presented for simulating compressible turbulent flows around complex geometries. In this method, the boundary condition on the immersed boundary is enforced through the use of ‘ghost cells’ that are located inside the solid body. The computations of variables on these ghost cells are achieved using linear interpolation schemes. The validity and applicability of the proposed method is verified using a three-dimensional (3D) flow over a circular cylinder, and a large-eddy simulation of fully developed 3D turbulent flow in a channel with a wavy surface. The results agree well with the previous numerical and experimental results, given that the grid resolution is reasonably fine. To demonstrate the capability of the method for higher Mach numbers, supersonic turbulent flow over a circular cylinder is presented. While more work still needs to be done to demonstrate higher robustness and accuracy, the present work provides interesting insights using the GCIBM for the compressible flows.     

An immersed boundary method for incompressible flows using volume of body function

A simple and effective immersed boundary method using volume of body (VOB) function is implemented on unstructured Cartesian meshes. The flow solver is a second‐order accurate implicit pressure‐correction method for the incompressible Navier–Stokes equations. The domain inside the immersed body is viewed as being occupied by the same fluid as outside with a prescribed divergence‐free velocity field. Under this view a fluid–body interface is similar to a fluid–fluid interface encountered in the volume of fluid (VOF) method for the two‐fluid flow problems. The body can thus be identified by the VOB function similar to the VOF function. In fluid–body interface cells the velocity is obtained by a volume‐averaged mixture of body and fluid velocities. The pressure inside the immersed body satisfies the same pressure Poisson equation as outside. To enhance stability and convergence, multigrid methods are developed to solve the difference equations for both pressure and velocity. Various steady and unsteady flows with stationary and moving bodies are computed to validate and to demonstrate the capability of the current method. Copyright © 2005 John Wiley & Sons, Ltd.     

An immersed boundary method for fluid flows around rigid objects

In this paper, we present an immersed boundary method for solving fluid flow problems in the presence of static and moving rigid objects. A FEM is used starting from a base mesh that does not represent exactly rigid objects (non?body?conforming mesh). At each time step, the base mesh is locally modified to provide a new mesh fitting the boundary of the rigid objects. The mesh is also locally improved using edge swapping to enhance the quality of the elements. The Navier–Stokes equations are then solved on this new mesh. The velocity of moving objects is imposed through standard Dirichlet boundary conditions. We consider a number of test problems and compare the numerical solutions with those obtained on classical body?fitted meshes whenever possible. Copyright © 2014 John Wiley & Sons, Ltd.     

An immersed boundary method for simulation of inviscid compressible flows

In this paper, an immersed boundary method for simulating inviscid compressible flows governed by Euler equations is presented. All the mesh points are classified as interior computed points, immersed boundary points (interior points closest to the solid boundary), and exterior points that are blanked out of computation. The flow variables at an immersed boundary point are determined via the approximate form of solution in the direction normal to the wall boundary. The normal velocity is evaluated by applying the no‐penetration boundary condition, and therefore, the influence of solid wall in the inviscid flow is taken into account. The pressure is computed with the local simplified momentum equation, and the density and the tangential velocity are evaluated by using the constant‐entropy relation and the constant‐total‐enthalpy relation, respectively. With a local coordinate system, the present method has been extended easily to the three‐dimensional case. The present work is the first endeavor to extend the idea of hybrid Cartesian/immersed boundary approach to compressible inviscid flows. The tedious task of handling multi‐valued points can be eliminated, and the overshoot resulting from the extrapolation for the evaluation of flow variables at exterior points can also be avoided. In order to validate the present method, inviscid compressible flows over fixed and moving bodies have been simulated. All the obtained numerical results show good agreement with available data in the literature. Copyright © 2014 John Wiley & Sons, Ltd.     

基于浸入边界算法的振动钝体绕流模拟研究

传统CFD方法在振动钝体绕流计算中常借助动网格技术,网格再生任务繁重。针对于此,本文利用可在静止网格中计算动边界绕流问题的浸入边界算法(IBM),编写数值模拟程序,分别对竖向强迫正弦振动方柱(Re=UD/v=103、振幅恒定、振动频率变化)以及桥梁断面(Re=UB/v=7.5×103、振幅、振动频率均变化)展开气动特性和流场特征结构分析。初步研究结果表明,振幅恒定为方柱高度的14%时,其涡脱锁定区长度为0.06~0.2,锁定区后端(Stc0.2)振动方柱涡脱频率回归静止涡脱频率;不同振幅下的桥梁断面阻力系数均在静止涡脱频率处产生峰值,桥梁断面升力系数则在此处均出现归零效应,且振幅越大,归零效应愈明显。     

Hydromagnetic boundary layer flow around an oscillating axisymmetric body

Boundary layer flow due to rotational oscillations of an axisymmetric body in the presence of a constant magnetic field is analysed by a process of successive approximations. The induced steady flow is confined only to the meridian place. The effect of the magnetic field is to decrease this steady flow.     

Numerical solution of axisymmetric cavity flows using the boundary element method

This paper presents a formulation of the boundary element method (BEM) for solution of axisymmetric cavity flow problems. The governing equation is written in terms of Stokes' stream function, requiring a new fundamental solution to be found. The iterative procedure for adjusting the free-surface position is similar to that used for planar cavity flows. Numerical results are compared with finite difference and finite element solutions, showing the robustness of the BEM model.     

Towards simulation of flapping wings using immersed boundary method

In this work the immersed boundary method is applied to simulate incompressible turbulent flows around stationary and moving objects. The goal is to demonstrate that the immersed boundary technique along with a large eddy simulation approach is capable of simulating the effect of the so‐called leading edge vortex (LEV), which can be found in flapping wing aerodynamics. A Lagrangian method is used to approximate the solutions in the freshly cleared cells that lay within solid objects at one time step and emerge into fluid domain at the next time step. Flow around a stationary cylinder at Re_D = 20, 40, and 3900 (based on cylinder diameter D) is first studied to validate the immersed boundary solver based on the finite volume scheme using a staggered grid. Then, a harmonically oscillating cylinder at Re_D = 10 000 is considered to test the solver after the Lagrangian method is implemented to interpolate the solution in the freshly cleared cells. Finally, this approach is used to study flows around a stationary flat‐plate at several angles of attack and fast pitching flat‐plate. The rapidly pitching plate creates a dynamic LEV that can be used to improve the efficiency of flapping wings of micro air vehicle and to determine the optimum flapping frequency. Copyright © 2012 John Wiley & Sons, Ltd.     

An immersed boundary/wall modeling method for RANS simulation of compressible turbulent flows

In this paper, an immersed boundary (IB) method is developed to simulate compressible turbulent flows governed by the Reynolds‐averaged Navier‐Stokes equations. The flow variables at the IB nodes (interior nodes in the immediate vicinity of the solid wall) are evaluated via linear interpolation in the normal direction to close the discrete form of the governing equations. An adaptive wall function and a 2‐layer wall model are introduced to reduce the near‐wall mesh density required by the high resolution of the turbulent boundary layers. The wall shear stress modified by the wall modeling technique and the no‐penetration condition are enforced to evaluate the velocity at an IB node. The pressure and temperature at an IB node are obtained via the local simplified momentum equation and the Crocco‐Busemann relation, respectively. The SST k ? ω and S‐A turbulence models are adopted in the framework of the present IB approach. For the Shear‐Stress Transport (SST) k ? ω model, analytical solutions in near‐wall region are utilized to enforce the boundary conditions of the turbulence equations and evaluate the turbulence variables at an IB node. For the S‐A model, the turbulence variable at an IB node is calculated by using the near‐wall profile of the eddy viscosity. In order to validate the present IB approach, numerical experiments for compressible turbulent flows over stationary and moving bodies have been performed. The predictions show good agreements with the referenced experimental data and numerical results.     

A ghost-cell immersed boundary method for large eddy simulation of flows in complex geometries

An efficient ghost-cell immersed boundary (IB) method is proposed for large eddy simulations of three-dimensional incompressible flow in complex geometries. In the framework of finite volume method, the Navier–Stokes equations are integrated using an explicit time advancement scheme on a collocated mesh. Since the IB method is known to generate an unphysical velocity field inside the IB that violates the mass conservation of the cells near the IB, a new IB treatment is devised to eliminate the unphysical velocity generated near the IB and to improve the pressure distribution on the body surface. To validate the proposed method, both laminar and turbulent flow cases are presented. In particular, large eddy simulations were performed to simulate the turbulent flows over a circular cylinder and a sphere at subcritical Reynolds numbers. The computed results show good agreements with the published numerical and experimental data.     

基于反馈力浸入边界法模拟复杂动边界流动

浸入边界法是模拟流固耦合的重要数值方法之一。本文采用反馈力浸入边界方法,对旋转圆柱和水轮机活动导叶旋转摆动绕流后的动边界流场进行数值模拟。其中,固体边界采用一系列离散的点近似代替,流体为不可压缩牛顿流体,使用笛卡尔自适应加密网格,利用有限差分法进行求解。固体对流场的作用通过构造适宜的反馈力函数实现。本文首先通过旋转圆柱绕流的计算结果同实验结果进行对比,吻合较好,验证了该计算方法的可靠性。然后针对水电站水力过渡过程中水轮机活动导叶旋转摆动绕流后的动边界流场进行数值模拟,得到导叶动态绕流后的流场分布特性和涡结构的演化特性。     

适用于浸入边界法的大涡模拟紊流壁面模型

基于近壁定常剪切应力假设,提出了一种新的适用于浸入边界法的大涡模拟紊流壁面模型。通过引入壁面滑移速度,修正了线性速度剖面计算得到的壁面剪切应力,使之满足Werner-Wengle模型。将其应用于平板紊流和高Re数圆管紊流的数值模拟,对比采用和不采用壁面模型的结果得知,采用此模型的速度剖面与实验值吻合良好,验证了此模型的有效性。研究了不同欧拉/拉格朗日网格相对位置对结果的影响,证明了此模型具有较好的鲁棒性,以及可根据局部流动状态和网格精度自动开闭的特点。     

A simple collision algorithm for arbitrarily shaped objects in particle-resolved flow simulation using an immersed boundary method

In the present study, we proposed a simple collision algorithm, which can be handled arbitrarily shaped objects, for flow solvers using the immersed boundary method (IBM) based on the level set and ghost cell methods. The proposed algorithm can handle the collision of the arbitrarily shaped object with little additional computational costs for the collision calculation because collision detection and calculation are performed using the level set function and image point, which are incorporated into the original IBM solver. The proposed algorithm was implemented on the solid-liquid IBM flow solver and validated by simulations of the flow over an isolated cylinder and sphere. Also, grid and time step size sensitivity on the total energy conservation of objects were investigated in cylinder-cylinder, cylinder-red-blood-cells-shaped (RBC-shaped) objects, sphere-sphere, and sphere-flat plate interaction problems. Through validation, good agreement with previous studies, grid and time step size convergence, and sufficient total energy conservation were confirmed. As a demonstration, the drafting, kissing, and tumbling processes were computed, and it was confirmed that the present result by the proposed method is similar to the previous computations. In addition, particle-laden flow in a channel including obstacles with collision and adhesion phenomena and the interaction of cylinders and wavy-wall were computed. The results of these simulations reveal the capability of solving a flow containing arbitrarily shaped moving objects with collision phenomena by a simple proposed method.     

A combined Lagrangian method for simulation of axisymmetric gas-particle vortex flows

A combined fully Lagrangian approach for meshless modeling of unsteady axisymmetric vortex flows of a gas-particle mixture with an incompressible carrier phase is developed. The approach proposed is based on the combination of a meshless vortex method for calculating axisymmetric flows of the carrier phase described by the Navier–Stokes (or Euler) equations and the full Lagrangian method for calculating the parameters of the dispersed phase. The combination of these methods reduces the problem of modeling the two phase flows to the solution of a high-order system of ordinary differential equations for the coordinates of toroidal vortex elements in the carrier phase and the particle trajectories, the velocity components, and the components of the Jacobian of transformation from the Eulerian to the Lagrangian variables in the dispersed phase. The application of the method is illustrated by modeling the behavior of an admixture of inertial Stokes particles with a small mass concentration in unsteady flows like solitary vortex rings in a viscous carrier phase and groups of vortex rings in an effectively inviscid carrier phase.     

A finite element immersed boundary method for fluid flow around rigid objects

This paper proposes a new immersed boundary (IB) method for solving fluid flow problems in the presence of rigid objects which are not represented by the mesh. Solving the flow around objects with complex shapes may involve extensive meshing work that has to be repeated each time a change in the geometry is needed. Important benefit would be reached if we are able to solve the flow without the need of generating a mesh that fits the shape of the immersed objects. This work presents a finite element IB method using a discretization covering the entire domain of interest, including the volume occupied by immersed objects, and which produces solutions of the flow satisfying accurately the boundary conditions at the surface of immersed bodies. In other words the finite element solution represents accurately the presence of immersed bodies while the mesh does not. This is done by including additional degrees of freedom on interface cut elements which are then eliminated at element level. The boundary of immersed objects is defined using a level set function. Solutions are shown for various flow problems and the accuracy of the present approach is measured with respect to solutions obtained on body‐fitted meshes. Copyright © 2010 Crown in the right of Canada.