Simulation Of Lid-driven Cavity Flow Research Articles

A Review Study of Numerical Simulation of Lid-Driven Cavity Flow with Nanofluids

Perhaps the most deliberated fluid problem in the field of Computational Fluid Dynamics is the lid driven cavity flow whose simple geometry is used to study the thermal behavior of many engineering applications such as cooling of electronic equipment, solar collectors, thermal storage systems, food processing, solar ponds, crystal growth, lubrication technologies and cooling of electrical and mechanical components. Researchers have been devoting much of their time in order to discover innovative methods to enhance the thermal conductivity of conventional fluids. With the development of nanotechnology, the concept of nanofluids has gained ground considerably as a new kind of heat transfer fluid. Nanofluid is a new kind of fluid with high thermal conductivity is a mixture of solid nanoparticles and a liquid. This review recapitulates the recent progress of the various numerical methods that are used in predicting the influence of several parameters such as type of nanoparticle and host liquid, particle volume concentration, particle size and shape, Brownian diffusion and thermophoresis effect on hydrodynamic and thermal characteristics of convective heat transfer using nanofluids in a lid driven cavity.

Numerical Study of Lid-Driven Square Cavity Flow with Embedded Circular Obstacles Using Spectral/hp Element Methods

We show a successful numerical study of lid-driven square cavity flow with embedded circular obstacles based on the spectral/hp element methods. Various diameters of embedded two-dimensional circular obstacles inside the cavity and Reynolds numbers Re (from 100 to 5000) are considered. In order to verify the effectiveness and accuracy of the current methods, numerical results are investigated by comparing with those available in the literature obtained by the moving immersed boundary method (MIBM) and the lattice Boltzmann method (LBM). The present spectral/hp element methods have been not only successfully applied to study and visualize the primary and induced vortices but also capture new vortices on the lower right, upper left and upper right positions of the circular obstacle when Reynolds number Re = 100 and Re = 5000, which is not observed in the lattice Boltzmann method. The current data and figures are in good agreement with the published results. The results of the present study show that the spectral/hp element methods are effective and accurate in simulation of lid-driven cavity flow with embedded circular obstacles, and the present methods have the following advantages: less preprocesses required and high-resolution characteristics.

Simulation of Lid-Driven Cavity Flow with Internal Circular Obstacles

The Lattice Boltzmann method (LBM) has been applied for the simulation of lid-driven flows inside cavities with internal two-dimensional circular obstacles of various diameters under Reynolds numbers ranging from 100 to 5000. With the LBM, a simplified square cross-sectional cavity was used and a single relaxation time model was employed to simulate complex fluid flow around the obstacles inside the cavity. In order to made better convergence, well-posed boundary conditions should be defined in the domain, such as no-slip conditions on the side and bottom solid-wall surfaces as well as the surface of obstacles and uniform horizontal velocity at the top of the cavity. This study focused on the flow inside a square cavity with internal obstacles with the objective of observing the effect of the Reynolds number and size of the internal obstacles on the flow characteristics and primary/secondary vortex formation. The current LBM has been successfully used to precisely simulate and visualize the primary and secondary vortices inside the cavity. In order to validate the results of this study, the results were compared with existing data. In the case of a cavity without any obstacles, as the Reynolds number increases, the primary vortices move toward the center of the cavity, and the secondary vortices at the bottom corners increase in size. In the case of the cavity with internal obstacles, as the Reynolds number increases, the secondary vortices close to the internal obstacle become smaller owing to the strong primary vortices. In contrast, depending on the sizes of the obstacles ( R / L = 1/16, 1/6, 1/4, and 2/5), secondary vortices are induced at each corner of the cavity and remain stationary, but the secondary vortices close to the top of the obstacle become larger as the size of the obstacle increases.

A finite volume method for the simulation of elastoviscoplastic flows and its application to the lid-driven cavity case

We propose a Finite Volume Method for the simulation of elastoviscoplastic (EVP) flows, modelled after the extension to the Herschel-Bulkley model by Saramito [J. Non-Newton. Fluid Mech. 158 (2009) 154–161]. The method is applicable to cell-centred grids of arbitrary geometry by the introduction of new stabilisation techniques of the “momentum interpolation” and “both sides diffusion” types, for pressure and velocity, respectively. Adaptive time stepping is employed. The method is used to perform benchmark simulations of lid-driven cavity flow, which also serve to explore certain aspects of this EVP constitutive equation in a two-dimensional setting. The model parameters are chosen so as to represent Carbopol, and simulations are performed for different lid velocities and with either slip or no-slip wall boundaries. The results are compared against those obtained with the classic Herschel-Bulkley model. It is noticed that different initial conditions for stress lead to different steady states. Furthermore, we investigate the cessation of the flow, once the lid is suddenly halted; it is found that, contrary to the classic Herschel-Bulkley predictions, the EVP flow does not cease in finite time. Rather, the flow decays very slowly while the material oscillates as kinetic energy is converted to elastic energy and vice versa. Flow decay is much faster under slip conditions due to the friction between the material and the walls.

Numerical simulation of lid-driven cavity flow of micropolar fluid

Incompressible unsteady laminar flow of a micropolar fluid in a lid driven square cavity has been examined numerically with finite difference scheme. In this paper, we verify the code validation of Newtonian incompressible fluid (K = 0) with standard bench mark problem in the literature and then proceed the present computation. The vorticity-stream function formulation of Navier-Stokes equations and angular momentum equation is solved by the Euler’s explicit method. The effect of various values of Reynolds number (Re) and vortex viscosity parameter (K) of the flow characteristics is studied and discussed through several graphs.

Data Partitioning on Multicore and Multi-GPU Platforms Using Functional Performance Models

Heterogeneous multiprocessor systems, which are composed of a mix of processing elements, such as commodity multicore processors, graphics processing units (GPUs), and others, have been widely used in scientific computing community. Software applications incorporate the code designed and optimized for different types of processing elements in order to exploit the computing power of such heterogeneous computing systems. In this paper, we consider the problem of optimal distribution of the workload of data-parallel scientific applications between processing elements of such heterogeneous computing systems. We present a solution that uses functional performance models (FPMs) of processing elements and FPM-based data partitioning algorithms. Efficiency of this approach is demonstrated by experiments with parallel matrix multiplication and numerical simulation of lid-driven cavity flow on hybrid servers and clusters.

A hybrid solution method for CFD applications on GPU-accelerated hybrid HPC platforms

Heterogeneous multiprocessor systems, where commodity multicore processors are coupled with graphics processing units (GPUs), have been widely used in high performance computing (HPC). In this work, we focus on the design and optimization of Computational Fluid Dynamics (CFD) applications on such HPC platforms. In order to fully utilize the computational power of such heterogeneous platforms, we propose to design the performance-critical part of CFD applications, namely the linear equation solvers, in a hybrid way. A hybrid linear solver includes both one CPU version and one GPU version of code for solving a linear equations system. When a hybrid linear equation solver is invoked during the CFD simulation, the CPU portion and the GPU portion will be run on corresponding processing devices respectively in parallel according to the execution configuration. Furthermore, we propose to build functional performance models (FPMs) of processing devices and use FPM-based heterogeneous decomposition method to distribute workload between heterogeneous processing devices, in order to ensure balanced workload and optimized communication overhead. Efficiency of this approach is demonstrated by experiments with numerical simulation of lid-driven cavity flow on both a hybrid server and a hybrid cluster.

A Semi-Implicit Scheme of Lattice Boltzmann Method for Two Dimensional Cavity Flow Simulation

The calculation sequence of collision, propagation and macroscopic variables is not very clear in lattice Boltzmann method (LBM) code implementation. According to the definition, three steps should be computed on all nodes respectively, which mean three loops are needed. While the “pull” scheme makes the only one loop possible for coding, this is called semi-implicit scheme in this study. The accuracy and efficiency of semi-implicit scheme are discussed in detail through the simulation of lid-driven cavity flow. Non-equilibrium extrapolation scheme is adopted on the boundary of simulation area. The results are compared with two classic articles, which show that semi-implicit scheme has good agreement with the classic scheme. When Re is less than 3000, the iterations steps of semi-scheme can be decreased by about 30% though comparing the semi-implicit scheme with standard scheme containing three loops. As the Re increases into more than 3400, the standard scheme is not converged. On the contrary, the iterations of semi-implicit scheme are approximately linear to Re.

Simulation of dynamic fluid–solid interactions with an improved direct-forcing immersed boundary method

Dynamic fluid–solid interactions are widely found in chemical engineering, such as in particle-laden flows, which usually contain complex moving boundaries. The immersed boundary method (IBM) is a convenient approach to handle fluid–solid interactions with complex geometries. In this work, Uhlmann's direct-forcing IBM is improved and implemented on a supercomputer with CPU–GPU hybrid architecture. The direct-forcing IBM is modified as follows: the Poisson's equation for pressure is solved before evaluation of the body force, and the force is only distributed to the Cartesian grids inside the immersed boundary. A multidirect forcing scheme is used to evaluate the body force. These modifications result in a divergence-free flow field in the fluid domain and the no-slip boundary condition at the immersed boundary simultaneously. This method is implemented in an explicit finite-difference fractional-step scheme, and validated by 2D simulations of lid-driven cavity flow, Couette flow between two concentric cylinders and flow over a circular cylinder. Finally, the method is used to simulate the sedimentation of two circular particles in a channel. The results agree very well with previous experimental and numerical data, and are more accurate than the conventional direct-forcing method, especially in the vicinity of a moving boundary.

Lattice Boltzmann simulation of flow in porous media on non-uniform grids

In this paper, the Lattice Boltzmann method (LBM) is adopted to simulate the incompressible flow in porous media on non-uniform grids. The flow through porous media was simulated by including the porosity into the equilibrium distribution function and adding a force term to the evolution equation to account for the linear and non-linear drag forces of the porous medium. Besides, non-uniform grids are adopted by using the interpolation-supplemented Lattice Boltzmann equation. Numerical simulations of lid-driven cavity flow, flow in a 2D symmetric sudden expansion channel, and cavity flow in polar coordinates are carried out. The results agree well with benchmark solutions, experimental data or traditional computational fluid dynamics method solutions. The present results demonstrate the potential of the Lattice Boltzmann algorithm for numerical simulation of fluid through porous media.

Mixing and available potential energy in stratified flows

Mixing plays an important role in atmospheric and oceanic flows. It occurs on the small scales, is due to molecular diffusion, and is irreversible. On the other hand, stirring is a kinematic process that enhances mixing but is reversible. Budgets of the available potential energy, which require that the reference potential energy be computed, are used to study these processes. We develop an approach for calculating the available potential energy from the probability density function that is more efficient than existing methods, especially in two and three dimensions. It is suitable for application to both numerical simulations and experiments. A new length scale is defined which quantifies stirring and provides a measure of the strength of overturns resulting from stirring as well as their size. Simulations of lid-driven cavity flow and stratified homogeneous turbulent shear flow provide illustrations of the method. The new length scale is similar to Thorpe scale in lid-driven cavity flow and closely related to the Ellison scale in homogeneous sheared turbulence.

SOLUTION OF THE PRESSURE CORRECTION EQUATION BY THE PRECONDITIONED CONJUGATE GRADIENT METHOD

The purpose of this work is to study the use of a preconditioned conjugate gradient method for solving the pressure correction equation in the simulation of incompressible flows. The preconditioned considered in this work include SSOR, ILU, and MIL.U. In addition, a new preconditioner based on an ADI-type iterative scheme is presented. The AD1 scheme uses the concept of the splitting of matrix via local one-dimensionality and is economical in memory requirement. A guideline for choosing the optimum parameter of ADI preconditioner is offered and tested. These preconditioned are tested in the simulation of lid-driven cavity flow and backward-facing step flows. The test results show that both ILU- and SSOR-precon-ditioned conjugate gradient methods have very irregular early-stage convergence. Both MILV- and ADI-precanditioned CC methods can be made very stable by choosing adequate parameters. The good convergence stability comes with lower asymptotic convergence rate.