Influence of dynamic boundary conditions on the computed flow patterns inside a coaxial rotating disk-cylinder system

In this paper, numerical solutions for the steady axisymmetric flow of an isothermal viscous fluid driven by moderate disk and/or cylinder coaxial rotation are presented. The influence of the two possible types of dynamic boundary conditions for the solid walls on the meridional flow features is discussed in detail using the computed Stokes streamfunction, angular momentum and vorticity distributions. Results show a clear dependence between the computed-generated flow patterns and the boundary conditions used.     

基于SPH 的雨滴打击不规则边界的模拟方法

为实现对雨滴打击树枝等不规则边界过程的模拟,研究了流体粒子在网格表示的 固体边界处的受力情况,提出了一种不需要粒子采样的边界受力模拟方法。采用高斯积分法则 对网格模型的三角面片进行积分,并就此对固液边界的粒子的密度进行修正,以积分的方法对 固体边界处的压力、粘性力等参数进行计算,从而保证边界粒子受力的连续性。同时,还提出 了一种吸引力模型,用来控制粒子在沿着物体表面滑落时的运动。实验结果表明,该方法在模 拟水滴铺展、收缩、沿着边界流动等现象时达到了较为真实的效果。     

Simulating the Stabilization Process by Boundary Conditions of a Quasi-Two-Dimensional Flow with a Four-Vortex Structure

A numerical stabilization problem by the boundary conditions of the given initial flow is considered for a two-dimensional system of Navier-Stokes equations that approximately describes the motion of a viscous incompressible fluid in a rectangular cell under an external electro-magnetic force and has an unstable quasi-stationary solution with a four-vortex structure for the selected values of the parameters. A mathematical statement of the problem, a method to solve it, and the results of the numerical computations are presented.     

A lattice Boltzmann based implicit immersed boundary method for fluid–structure interaction

The immersed boundary method is a practical and effective method for fluid–structure interaction problems. It has been applied to a variety of problems. Most of the time-stepping schemes used in the method are explicit, which suffer a drawback in terms of stability and restriction on the time step. We propose a lattice Boltzmann based implicit immersed boundary method where the immersed boundary force is computed at the unknown configuration of the structure at each time step. The fully nonlinear algebraic system resulting from discretizations is solved by an Inexact Newton–Krylov method in a Jacobian-free manner. The test problem of a flexible filament in a flowing viscous fluid is considered. Numerical results show that the proposed implicit immersed boundary method is much more stable with larger time steps and significantly outperforms the explicit version in terms of computational cost.     

Steady flow past a rotating cylinder

Numerical solutions have been obtained for steady viscous flow past a rotating circular cylinder. Results are presented for Reynolds numbers of 5 and 20 and ratios of the speed of the surface of the cylinder to the fluid speed at infinity from 0 to 0.5. The effects of using different boundary conditions on the stream function at large distances from the cylinder are presented and discussed.     

Accuracy of the Simultaneous-Approximation-Term Boundary Condition for Time-Dependent Problems

The simultaneous-approximation-term (SAT) approach to applying boundary conditions for the compressible Navier-Stokes equations is analyzed with respect to the errors associated with the formulation’s weak enforcement of the boundary data. Three numerical examples are presented which illustrate the relationship between the penalty parameters and the accuracy; two examples are fundamentally acoustic and the third is viscous. The viscous problem is further analyzed by a continuous model whose solution is known analytically and which approximates the discrete problem. From the analysis it is found that at early times an overshoot in the boundary values relative to the boundary data can be expected for all values of the penalty parameters but whose amplitude reduces with the inverse of the parameter. Likewise, the long-time behavior exhibits a t ^−1/2 relaxation towards the specified data, but with a very small amplitude. Based on these data it is evident that large values of the penalty parameters are not required for accuracies comparable to those obtained by a more traditional characteristics-based method. It is further found that for curvilinear boundaries the SAT approach is superior to the locally one-dimensional inviscid characteristic approach.     

Shedding of vortices behind a circular cylinder

The process of shedding of vortices from a circular cylinder is discussed by computing an unsteady viscous fluid flow at Reynolds number 200 under natural boundary conditions with a fine mesh near the surface of the cylinder. The phenomena of shedding of vortices is described by drawing streamlines patterns and the equivorticity lines at different times. The variations of the vorticity distribution, the pressure distribution and the drag coefficient at different times are shown by graphs. The Strouhal number for the shedding process is calculated and compared with the known results.     

Lubrication analysis of the viscous micro/nano pump with slip

A viscous pump is a device such that a cylindrical rotor is eccentrically placed in a channel, so that the viscous resistance between the small and large gaps between the cylinder and the channel walls generate a net flow along the channel. Assuming that the gaps between the cylinder and the channel walls are small compared to the radius of the rotor, the hydrodynamic theory of lubrication may be utilized to study the viscous pump. Here lubrication theory is used to obtain an analytical solution which relates the flowrate, rotation rate, pressure drop and applied torque as functions of two geometric parameters for a viscous pump. This analysis differs from a previous similar study in two ways. Firstly, certain integrals are evaluated explicitly, and secondly the standard no-slip boundary condition of fluid mechanics has been replaced with the Navier boundary condition which allows a degree of tangential velocity slip on all solid boundaries. Comparison with the prior known solution shows that the solution obtained in this study predicts a slightly improved pump performance for the case of no-slip. For the case of slip, our results demonstrate that the performance of the pump is significantly improved.

Output Feedback Boundary Control of a Ginzburg–Landau Model of Vortex Shedding

An exponentially convergent observer is designed for a linearized Ginzburg-Landau model of vortex shedding in viscous flow past a bluff body. Measurements are restricted to be taken collocated with the actuation which is applied on the cylinder surface. The observer is used in conjuction with a state feedback boundary controller designed in previous work to attenuate vortex shedding. While the theoretical results apply to the linearized system under sufficiently smooth initial data that satisfy the boundary conditions, simulations demonstrate the performance of the linear output feedback scheme on the nonlinear plant model     

SPH 流固耦合模拟自适应采样固壁虚粒子边界处理方法

固壁虚粒子边界处理方法是流体模拟中一种主要边界处理方法,但其不能确保流 体粒子不穿透固体边界,并且计算量较大。为防止流体粒子穿透边界,在边界附近设置一个阻 尼区,阻尼区内的流体粒子被边界施加一个弹性力和一个和流体粒子运动速度方向相反的阻尼 力,使得边界附近流体粒子更加稳定。为减少计算量,提出两种边界粒子自适应采样法：一种 是依据边界周围粒子数目的不同,边界粒子自适应地采样质量不同的大小粒子;另一种是依据 边界周围粒子数目的不同,边界粒子自适应的采样不同层数的相同质量粒子。与传统的固体边 界粒子采样方法相比,该方法减少了边界粒子数目,加快了模拟速度,节省了计算机内存,基 于GPU 加速技术实现的三维流体模拟,能够进行实时交互。     

Boundary control of a laminar flow of a viscous incompressible fluid in the generalized Couette cell. The asymptotic approach

In this paper, a limiting problem for an optimal boundary control problem of a laminar flow of a viscous incompressible fluid in the generalized Couette cell, when the number of inner cylinders unrestrictedly increases, is obtained.     

SPH particle boundary forces for arbitrary boundaries

This paper is concerned with approximating arbitrarily shaped boundaries in SPH simulations. We model the boundaries by means of boundary particles which exert forces on a fluid. We show that, when these forces are chosen correctly, and the boundary particle spacing is a factor of 2 (or more) less than the fluid particle spacing, the total boundary force on a fluid SPH particle is perpendicular to boundaries with negligible error. Furthermore, the variation in the force as a fluid particle moves, while keeping a fixed distance from the boundary, is also negligible. The method works equally well for convex or concave boundaries. The new boundary forces simplify SPH algorithms and are superior to other methods for simulating complicated boundaries. We apply the new method to (a) the rise of a cylinder contained in a curved basin, (b) the spin down of a fluid in a cylinder, and (c) the oscillation of a cylinder inside a larger fixed cylinder. The results of the simulations are in good agreement with those obtained using other methods, but with the advantage that they are very simple to implement.     

Fully explicit implementation of direct numerical simulation for a transient near-field methane/air diffusion jet flame

Direct numerical simulation (DNS) is a kind of ultimate numerical simulation tool for studying fundamental turbulent flows, mixing, chemical reactions and interactions among them. In the present work, a fully explicit method of implementing DNS is presented for investigating transient multi-component methane/air jet flame in the near field. The detailed methodology, enclosing non-dimensional governing equations, inlet velocity disturbance, chemical scheme and fluid property, was discussed. An explicit eighth-order finite-difference scheme was used combined with an explicit tenth-order filter. Conservative variables are temporally advanced in two segmented stages that handle Euler terms and viscous terms respectively. A modified non-reflecting boundary condition was used, which has better performance about the characteristic waves on boundary planes. The developed code was firstly tested with an air jet and evaluated in terms of accuracy and parallel efficiency. Then a methane/air combusting jet was simulated to study the characteristics of the chemical heat-release in turbulence.     

Boundary conditions in mixture theory and in CFD applications of higher order models

We discuss the importance of and the need for (additional) boundary conditions in Mixture Theory (also known as the Theory of Interacting Continua). Specifically, we will give an overview of the model due to Rajagopal and Massoudi which is appropriate for the flow of a linearly viscous fluid infused with solid particles. The solid particles are modeled as granular materials. In this formulation the need for additional boundary condition arises due to higher gradients of density (or volume fraction). The challenging issue of how to ‘split’ the total stress or the total velocity at the boundary is also discussed.     

改进的流体模拟固体边界处理算法

流体模拟是计算机图形学的一个重要研究分支,流体的固体边界处理一直是流体 模拟的研究重点,光滑粒子流体动力学(SPH)方法中的镜像粒子法是处理固体边界的一个重要方 法。镜像粒子法通过靠近边界的流体粒子在边界外动态生成对应的镜像粒子来处理固体边界问 题,但随着边界复杂程度的提高,传统的镜像粒子法生成镜像粒子的复杂度也随之提高,模拟 效率随之降低。为此,文章对镜像粒子法进行改进,提出一种新的镜像粒子场量求值方法,有 效地降低了复杂边界情况下生成镜像粒子的复杂度,且使靠近边界的流体粒子场量更加均匀。 仿真实验结果表明,随着流体模拟粒子数的增加以及边界复杂程度的提高,该方法比传统镜像 粒子法效率高的优势也更加明显。     

An Efficient Hybrid Incompressible SPH Solver with Interface Handling for Boundary Conditions

We propose a hybrid smoothed particle hydrodynamics solver for efficientlysimulating incompressible fluids using an interface handling method for boundary conditions in the pressure Poisson equation. We blend particle density computed with one smooth and one spiky kernel to improve the robustness against both fluid–fluid and fluid–solid collisions. To further improve the robustness and efficiency, we present a new interface handling method consisting of two components: free surface handling for Dirichlet boundary conditions and solid boundary handling for Neumann boundary conditions. Our free surface handling appropriately determines particles for Dirichlet boundary conditions using Jacobi‐based pressure prediction while our solid boundary handling introduces a new term to ensure the solvability of the linear system. We demonstrate that our method outperforms the state‐of‐the‐art particle‐based fluid solvers.     

Modified integral equation solution of viscous flows near sharp corners

Solutions of the biharmonic equation governing steady two dimensional viscous flow of an incompressible newtonian fluid are obtained by employing a direct biharmonic boundary integral equation (BBIE) method in which Green's Theorem is used to reformulate the differential equation as a pair of coupled integral equations. The classical BBIE gives poor convergence in the presence of singularities arising in the solution domain. The rate of convergence is improved dramatically by including the analytic behaviour of the flow in the neighbourhood of the singularities. The modified BBIE (MBBIE) effectively ‘subtracts out’ this analytic behaviour in terms of a series representation whose coefficients are initially unknown. In this way the modified flow variables are regular throughout the entire solution domain. Also presented is a method for including the asymptotic nature of the flow when the solution domain is unbounded.     

Size-dependent effects on critical flow velocity of a SWCNT conveying viscous fluid based on nonlocal strain gradient cylindrical shell model

This article investigates vibration and instability analysis of a single-walled carbon nanotube (SWCNT) conveying viscous fluid flow. For this purpose, the first-order shear deformation shell model is developed in the framework of nonlocal strain gradient theory (NSGT) for the first time. The proposed model is a conveying viscous fluid in which the external force of fluid flow is applied by the modified Navier–Stokes relation and considering slip boundary condition and Knudsen number. The NSGT can be reduced to the nonlocal elasticity theory, strain gradient theory or the classical elasticity theory by inserting their specific nonlocal parameters and material length scale parameters into the governing equations. Comparison of above-mentioned theories suggests that the NSGT predicts the greatest critical fluid flow velocity and stability region. The governing equations of motion and corresponding boundary conditions are discretized using the generalized differential quadrature method. Furthermore, the effects of the material length scale, nonlocal parameter, Winkler elastic foundation and Pasternak elastic foundation on vibration behavior and instability of a SWCNT conveying viscous fluid flow with simply supported and clamped–clamped boundary conditions are investigated.     

Least square finite element solution of stagnation point flow

A detailed analysis of the least square finite element solution of nonlinear boundary value problems is presented with reference to a particular example of nonlinear coupled differential equations governing the flow of an incompressible viscous fluid in the vicinity of a forward stagnation point at a blunt body. The numerical solutions are presented for different cases. The results obtained by the least square finite element method are in very good agreement with the results available in the literature confirming the versatility and usefulness of the application of the method to nonlinear boundary value problems governing the fluid flow problems.     

Non-coaxial rotating flow of viscous fluid with heat and mass transfer

Heat and mass transfer in unsteady non-coaxial rotating flow of viscous fluid over an infinite vertical disk is investigated. The motion in the fluid is induced due to two sources. Firstly, due to the buoyancy force which is caused because of temperature and concentration gradients. Secondly, because of non-coaxial rotation of a disk such that the disk executes cosine or since oscillation in its plane and the fluid is at infinity. The problem is modeled in terms of coupled partial differential equations with some physical boundary and initial conditions. The dimensionless form of the problem is solved via Laplace transform method for exact solutions. Expressions for velocity field, temperature and concentration distributions are obtained, satisfying all the initial and boundary conditions. Skin friction, Nusselt number and Sherwood number are also evaluated. The physical significance of the mathematical results is shown in various plots and is discussed for several embedded parameters. It is found that magnitude of primary velocity is less than secondary velocity. In limiting sense, the present solutions are found identical with published results.