Driven Cavity Flow Research Articles

A Neural Network-Based Poisson Solver for Fluid Simulation

The pressure Poisson equation is usually the most time-consuming problem in fluid simulation. To accelerate its solving process, we propose a deep neural network-based numerical method, termed Deep Residual Iteration Method (DRIM), in this paper. Firstly, the global equation is decomposed into multiple independent tridiagonal sub-equations, and DRIM is capable of solving all the sub-equations simultaneously. Moreover, we employed Residual Network and a correction iteration method to improve the precision of the solution achieved by the neural network in DRIM. The numerical results, including the Poiseuille flow, the backwards-facing step flow, and driven cavity flow, have proven that the numerical precision of DRIM is comparable to that of classic solvers. In these numerical cases, the DRIM-based algorithm is about 2–10 times faster than the conventional method, which indicates that DRIM has promising applications in large-scale problems.

Steady state regimes in lid driven cavity flows of magnetic fluids in the presence of an external magnetic field

In this work, we study the flow of magnetic fluids in a square top lid driven cavity in the presence of an applied magnetic field. The magnetic field is generated by a steady electric current flowing through a wire placed underneath the cavity. The magnetization of the magnetic fluid is described by an evolution equation that combines magnetization relaxation, advection and interaction with the flow via the vorticity. The governing equations are solved via a vorticity-streamfunction formulation implemented in a finite difference scheme. The main governing physical parameters of the examined cavity flow are the Reynolds number, ranging from 50 to 500, the magnetic pressure coefficient, which measures the relative importance between magnetic and inertial forces, ranging from 0 to 1000, and Péclet number which is O(1) and measures the ratio between the magnetization relaxation time and the flow time scale. We have examined the different mechanisms which cause changes in the local fluid magnetization, i.e., flow vorticity and advection. In particular, we examine how vorticity of the flow intensifies deviations of the magnetization of the fluid with respect to the local equilibrium of magnetization. In addition, we identify a complex topological structure of the flow inside the cavity characterized by the magnetic effects that dominate the generation of secondary structures of vorticity induced by the effect of field gradient, orientation and a non-uniformity in the fluid magnetization inside the cavity.

Lid driven cavity flow with two porous square obstacles

The flow of Newtonian incompressible fluid inside a two-dimensional lid-driven cavity with two non-adherent porous square blocks was numerically studied. The non-linear governing equations, Darcy-Forchheimer-Brinkman for the porous medium and Navier-Stokes for the free fluid region, were solved using the finite element method. The streamlines and velocity profile of the fluid inside the cavity, as well as the maximum value of the stream function and the coordinates of the main vortex created, are investigated to determine the effect of the Reynolds number, the different combinations of Darcy number and the different placements of the porous squares, on the behaviour of the fluid flow.

Application of Weighted Least Squares Meshless Method to Incompressible Flows

Meshless methods have been successfully applied to solve a large number of inviscid and viscous compressible flows in both two and three dimensional flow fields. However, the conventional methods of solution for compressible flow equations cannot be applied to incompressible flow equations. This is due to the basic difference in the nature of the pressure variable in the compressible and incompressible flows. Pressure acts as a thermodynamic variable in case of compressible flows and can be easily updated by using the equation of state. In contrast, in case of incompressible flows, the pressure is merely responsible for enforcing the incompressibility constraint and hence cannot be updated by the equation of state. This has led to the development of numerical methods based on Helmholtz Decomposition to solve for the fluid flows in the incompressible flow regimes. Here, we have applied weighted least squares meshless method to solve for the flows in the incompressible flow regime using the projection method based on Helmholtz Decomposition. The standard test cases of two dimensional lid driven cavity flow at Reynolds numbers of 100, 400 and 1000 have been solved using the weighted least squares meshless method. A good match between the results of the test case using the meshless methods and conventional CFD methods for the solution of the incompressible flows has been obtained.

Preliminary code development for single-phase liquid natural circulation flow simulation based on two-phase compressible model

It is of great significance to study the thermal-hydraulic characteristics of Lead-based Fast Reactor. In these years, the computational fluid dynamics method has become an attractive way in thermal-hydraulic and safety simulations of liquid metal cooled reactors. In order to investigate thermal-hydraulic characteristics of single-phase natural circulation flow in liquid metal cooled reactors, a self-developed CFD code was developed in this paper. The new code was proposed based on the two-phase compressible model, including liquid and vapor governing equations and a series of auxiliary models. The commercial CFD software ANSYS FLUENT was used to verify and validate the new code by comparing their simulation results under a typical heat driven cavity flow case. The comparison showed that the results simulated by the new code had good agreement with the ones calculated by ANSYS FLUENT. Furthermore, by coupling the above CFD model with the fuel pin heat transfer model, the application was conducted based on a full-scale reactor steady-state simulation of a natural circulation driven LBE-cooled fast reactor. From the results, it can be concluded that the new code can simulate and evaluate thermal-hydraulic behaviors of the LBE-cooled reactor well.

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.

Chaotic mixing in an acoustically driven cavity flow

We investigate the mixing properties of an acoustic driven flow in a parallelepipedic cavity with square basis. Relying on nonnormal reflections, an acoustic beam with a square path is obtained, generating a global complex flow in the cavity which enables chaotic advection. For a moderate power of the source, the chaotic region invades the whole cavity, illustrating that acoustic streaming can be used successfully as a nonintrusive tool to mix efficiently.

Second order unconditional linear energy stable, rotational velocity correction method for unsteady incompressible magneto-hydrodynamic equations

In this paper, we present a second order decoupled time discretization method for solving the unsteady incompressible magneto-hydrodynamic (MHD) equations. The method is mainly based on the rotational velocity correction projection scheme and extrapolation algorithm. The semi-implicit and extrapolation treatments are used to deal with the hydrodynamic equation and the magnetic equation nonlinear terms respectively. We prove the unconditional energy stability for the proposed scheme by means of a key technique Gauge–Uzawa format. To verify the effectiveness of the presented scheme, we test a series of numerical experiments: accuracy test, stability test, flow around a cylinder test and driven cavity flow problem.

Parallelization of lattice Boltzmann method for CFD using message passing interface

The lattice Boltzmann method has become a promising numerical technique and is now being considered as an alternative to the conventional CFD methods owing a possibility to simulate more complex geometries at relatively low computational costs. The simulations of complex and very fine resolution computational domains in CFD is challenging due to the lack of memory resources and long processing times, therefore parallel computing is being considered as a promising way to cope with this ever increasing mission of computational power. In this work parallelization of 2-D lattice Boltzmann model based CFD code using message passing interface was performed to increase speedup factor for parallel computing. Lattice Boltzmann approach based CFD code of a benchmark Lid driven cavity flow problem was parallelized using different message passing interface subroutines and made to run on a cluster system of processors. The time and speed up factor for execution of the benchmark problem was investigated. The results showed that these message passing communications have little influence on the performance of the parallel lattice Boltzmann method.

Study of fluid–structure interaction with undulating flow using channel driven cavity flow system

Study of fluid–structure interaction with undulating flow using channel driven cavity flow system

Stability of obliquely driven cavity flow

The linear stability of the incompressible flow in an infinitely extended cavity with rectangular cross-section is investigated numerically. The basic flow is driven by a lid which moves tangentially, but at yaw with respect to the edges of the cavity. As a result, the basic flow is a superposition of the classical recirculating two-dimensional lid-driven cavity flow orthogonal to a wall-bounded Couette flow. Critical Reynolds numbers computed by linear stability analysis are found to be significantly smaller than data previously reported in the literature. This finding is confirmed by independent nonlinear three-dimensional simulations. The critical Reynolds number as a function of the yaw angle is discussed for representative aspect ratios. Different instability modes are found. Independent of the yaw angle, the dominant instability mechanism is based on the local lift-up process, i.e. by the amplification of streamwise perturbations by advection of basic flow momentum perpendicular to the sheared basic flow. For small yaw angles, the instability is centrifugal, similar as for the classical lid-driven cavity. As the spanwise component of the lid velocity becomes dominant, the vortex structures of the critical mode become elongated in the direction of the bounded Couette flow with the lift-up process becoming even more important. In this case the instability is made possible by the residual recirculating part of the basic flow providing a feedback mechanism between the streamwise vortices and the streamwise velocity perturbations (streaks) they promote. In the limit when the basic flow approaches bounded Couette flow the critical Reynolds number increases very strongly.

Moments-based method for boundary conditions in the lattice Boltzmann framework: A comparative analysis for the lid driven cavity flow

Dealing with boundary conditions (BC) was ever considered a puzzling question in the lattice Boltzmann (LB) method. The most popular BC models are based on Ad-Hoc rules and, although these BC models were shown to be suitable for low-order LB equations, their extension to high-order LB was shown to be a very difficult problem and, at authors knowledge, never solved with satisfaction. The main question to be solved is how to deal with a problem when the number of unknowns (the particle populations coming from the outside part of the numerical domain) is greater than the number of equations at our disposal at each boundary site. Recently, BC models based on the regularization of the LB equation, or moments-based models, were proposed. These moments replace the discrete populations as unknowns, independently of the number of discrete velocities that are needed for solving a given problem. The full set of moments-based BC leads, nevertheless, to an overdetermined system of equations, and what distinguishes one model from another is the way this system is solved. In contrast with previous work, we base our approach on second-order moments. Four versions of this model are compared with previous moments-based models considering, in addition to the accuracy, some main model attributes such as global and local mass conservation, rates of convergence, and stability. For this purpose, the complex flow patterns displayed in a two-dimensional lid-driven cavity are investigated.

Numerical Simulation of Slip effect on Lid-Driven Cavity Flow Problem for High Reynolds Number: Vorticity – Stream Function Approach

Incompressible 2-D Navier-stokes equations for various values of Reynolds number with and without partial slip conditions are studied numerically. The Lid-Driven cavity (LDC) with uniform driven lid problem is employed with vorticity - Stream function (VSF) approach. The uniform mesh grid is used in finite difference approximation for solving the governing Navier-stokes equations and developed MATLAB code. The numerical method is validated with benchmark results. The present work is focused on the analysis of lid driven cavity flow of incompressible fluid with partial slip conditions (imposed on side walls of the cavity). The fluid flow patterns are studied with wide range of Reynolds number and slip parameters.

Memory-efficient Lattice Boltzmann Method for low Reynolds number flows

The Lattice Boltzmann Method algorithm is simplified by assuming constant numerical viscosity (the relaxation time is fixed at τ=1). This leads to the removal of the distribution function from the computer memory. To test the solver the Poiseuille and Driven Cavity flows are simulated and analyzed. The error of the solution decreases with the grid size L as L−2. Compared to the standard algorithm, the presented formulation is simpler and shorter in implementation. It is less error-prone and needs significantly less working memory in low Reynolds number flows. Our tests showed that the algorithm is less efficient in multiphase flows. To overcome this problem, further extension and the moments-only formulation was derived, inspired by the Multi-Relaxation Time (MRT) approach for single component multiphase flows.

A unified framework of continuous and discontinuous Galerkin methods for solving the incompressible Navier–Stokes equation

In this paper, we propose a unified numerical framework for the time-dependent incompressible Navier–Stokes equation which yields the H1-, H(div)-conforming, and discontinuous Galerkin methods with the use of different viscous stress tensors and penalty terms for pressure robustness. Under minimum assumption on Galerkin spaces, the semi- and fully-discrete stability is proved when a family of implicit Runge–Kutta methods are used for time discretization. Furthermore, we present a unified discussion on the penalty term. Numerical experiments are presented to compare our schemes with classical schemes in the literature in both unsteady and steady situations. It turns out that our scheme is competitive when applied to well-known benchmark problems such as Taylor–Green vortex, Kovasznay flow, potential flow, lid driven cavity flow, and the flow around a cylinder.

A Predictor–Corrector Meshless Based Scheme for Incompressible Navier–Stokes Flows

In this paper, a predictor–corrector scheme in meshless radial basis functions for solving incompressible Navier–Stokes equations in vorticity–streamfunction formulation is presented. The method is based on a local collocation formulation and does not require either a grid generation or evaluation of an integral. Predictor–corrector techniques are used to evaluate numerical fluxes in the forward–backward stencil parts and a relaxation scheme is investigated in order to reach high order accuracy. The main advantages of this approach are that no mesh generations nor Riemann problem solvers are required during the solution process. Numerical results are shown for several test examples including problems on driven cavity flows, backward-facing step flows and Rayleigh–Benard convection flows. The main focus is to examine the performance of the proposed meshless method for Navier–Stokes problems with high Reynolds number. The obtained results demonstrate its ability to capture the main solution features.

Hyperbolic cell-centered finite volume method for steady incompressible Navier-Stokes equations on unstructured grids

A hyperbolic method for incompressible Navier-Stokes equations is presented in a cell-centered finite volume framework on unstructured meshes. Solution algorithms were introduced on triangular meshes in 2D and on tetrahedral meshes in 3D. Justification of the absolute Jacobian approximation is discussed, and a solution reconstruction algorithm utilizing the robust and effective wrapping stencil is illustrated. The effectiveness of the unconditionally stable implicit solution strategy was demonstrated by comparison to an explicit scheme. A series of test cases are presented in order of study accuracy and as a comparison with other reference computational and experimental results, namely Kovasznay flow, driven cavity flow, and flow past a circular cylinder in 2D and a sphere in 3D. The equal order of accuracy feature of the hyperbolic method, namely the second order accuracy in solution and the gradient variables, was verified. The superior accuracy of the current hyperbolic scheme in terms of predicting the velocity gradient on a solid surface was emphasized by comparison with standard second order finite volume results.

Numerical investigation of the cascaded central moment lattice Boltzmann method for non-Newtonian fluid flows

We present a cascaded lattice Boltzmann (LB) method based on central moments and multiple relaxation times for the simulation of the non-Newtonian fluid flows. In this regard, we consider nonlinear constitutive relations for the power law fluids encompassing shear thinning and shear thickening characteristics and the Bingham fluids that model fluids with yield behavior. This involves local adjustment of the relaxation times during the collision step for the second order moments, which are related to the magnitude of the shear rate. The latter is related to the second invariant of the strain rate tensor whose components are computed locally based on non-equilibrium moments. Such relations also account for the additional corrections needed to eliminate the cubic velocity errors arising from the aliasing effects associated with the standard lattices to enable simulations of non-Newtonian flows with high fidelity. We then perform the validation of the resulting method for a variety of non-Newtonian flow problems, including the lid driven cavity flow, flow over a cylinder and a pair of cylinders in a tandem configuration. Results demonstrate accurate solutions, second order grid convergence and improvements in numerical stability to enable higher Reynolds number computations of non-Newtonian fluid flows achieved with the use of the cascaded LB method when compared to other collision models.

A novel Lagrangian finite element method with adaptive element-particle conversion ability for incompressible flows with free surfaces

When modeling fluid flows with the finite element method (FEM), a normal way is to implement the simulation in an Eulerian frame, as it is difficult for the Lagrangian FEM to deal with fluid flows with extremely large deformations, especially for incompressible flows with violent fluid-structure interactions along with changing free surfaces. In this paper, we developed a novel Lagrangian FEM for modeling incompressible flows with violently changing free surfaces. The Lagrangian FEM is an edge-based smoothed FEM (ES-FEM) which has special advantages over the conventional FEM due to the gradient smoothing technique. An artificial equation of state is used in the ES-FEM to treat the incompressible flow as weakly compressible. In order to simulate large fluid deformation, an adaptive algorithm is employed to convert the FEM elements in areas with large fluid deformation into particles in the smoothed particle hydrodynamics (SPH) as the SPH method is well suited for modeling fluid deformation and free surfaces. Some state-of-art algorithms including the kernel gradient correction and particle shift technique are integrated into the SPH method to ensure the computational accuracy of the fluid modeling. After such treatment, the Lagrangian ES-FEM is used for modeling fluid flows with small deformations while SPH is employed for areas with large fluid deformations where ES-FEM elements are automatically converted to SPH particles. Four numerical examples including still water, lid driven cavity flow, dam break and water entry are modeled using the present Lagrangian FEM. The numerical studies demonstrate that the present Lagrangian FEM with adaptive element-particle conversion ability is as accurate as SPH in modeling incompressible flows with violently changing free surfaces while it is much more efficient than SPH.

New applications of numerical simulation based on lattice Boltzmann method at high Reynolds numbers

In order to study the flow behavior at high Reynolds numbers, two modified models, known as the multiple-relaxation-time lattice Boltzmann method (MRT-LBM) and large-eddy-simulation lattice Boltzmann method (LES-LBM), have been employed in this paper. The MRT-LBM was designed to improve numerical stability at high Reynolds numbers, by introducing multiple relaxation time terms, which consider the variations of density, energy, momentum, energy flux and viscous stress tensor. As a result, MRT-LBM is capable of dealing with turbulent flows considering energy dispersion and dissipation. In the present paper, this model was employed to simulate the flow at turbulent Reynolds numbers in wall-driven cavities. Two-sided wall driven cavity flow was studied for the first time, based on MRT-LBM, at Reynolds numbers ranging from 2×104to1×106, and employing a very large resolution2048 × 2048. It is found that whenever top and bottom lids are moving in the opposite directions, and the Reynolds number is higher than 2×104, the flow is chaotic, although some quasi-symmetric properties still remain, fully disappearing at Reynolds numbers between 2×105 and 3×105. Furthermore, between this Reynolds numbers range, 2×105<Re<3×105, the quasi-symmetric structures turn into a much smaller and fully chaotic eddies. The LES-LBM model implements the large eddy simulation turbulent model into the conventional LBM, allowing to study the flow at turbulent Reynolds numbers. LES-LBM combined with Quadruple-tree Cartesian cutting grid (tree grid) was employed for the first time to characterize the flow dynamics over a cylinder and a hump, at relatively high Reynolds numbers. In order to construct the macroscopic quantities in the virtual boundaries separating two different grid levels, a set of new schemes were designed. The coupling of the LES-LBM and tree grid drastically reduced the computational time required to perform the simulations, thus, allowing to minimize the hardware requirements. LES-LBM model is shown to be much more efficient when combined with the tree grid instead of using the standard Cartesian grid.