Simulating high Reynolds number flow in two-dimensional lid-driven cavity by multi-relaxation-time lattice Boltzmann method

By coupling the non-equilibrium extrapolation scheme for boundary condition with the multi-relaxation-time lattice Boltzmann method, this paper finds that the stability of the multi-relaxation-time model can be improved greatly, especially on simulating high Reynolds number （Re） flow. As a discovery, the super-stability analysed by Lallemand and Luo is verified and the complex structure of the cavity flow is also exhibited in our numerical simulation when Re is high enough. To the best knowledge of the authors, the maximum of Re which has been investigated by direct numerical simulation is only around 50 000 in the literature; however, this paper can readily extend the maximum to 1000 000 with the above combination.

Control of mean and fluctuating forces on a circular cylinder at high Reynolds numbers

A narrow strip is used to control mean and fluctuating forces on a circular cylinder at Reynolds numbers from 2.0 ×10^4 to 1.0 ×^ 10^5. The axes of the strip and cylinder are parallel. The control parameters are strip width ratio and strip position characterized by angle of attack and distance from the cylinder. Wind tunnel tests show that the vortex shedding from both sides of the cylinder can be suppressed, and mean drag and fluctuating lift on the cylinder can be reduced if the strip is installed in an effective zone downstream of the cylinder. A phenomenon of mono-side vortex shedding is found. The strip-induced local changes of velocity profiles in the near wake of the cylinder are measured, and the relation between base suction and peak value in the power spectrum of fluctuating lift is studied. The control mechanism is then discussed from different points of view.

NUMERICAL STUDY OF PARTICLE DISTRIBUTION IN THE WAKE OF GAS-PARTICLE TWO-PHASE FLOWS PAST A CIRCULAR CYLINDER AT HIGH REYNOLDS NUMBER

Particle-laden gas flows past a circular cylinder at the Reynolds number of 2×10^(5) were numerically investigated. The Discrete Vortex Method (DVM) was employed to evaluate the unsteady gas flow fields and a Lagrangian approach was applied for tracking individual solid particles. The vortex patterns and the distributions of particles with different Stokes numbers were obtained. Numerical results show that: (1) at small Stokes number (St=0.01) the particles move with the fluid and could be found evenly throughout the flow, (2) the regions around the vortex cores, where few particles exist, become wider as the stokes number of particles increases from 0.01 to 1.0, (3) at middle Stokes number (St=1.0, 10) centrifugal forces throw the particles out of the wake vortices, (4) at high Stokes number (St=100, 1000) the particles are not affected by the vortices,and their motion is determined by their inertia effects.

A NEW STABILIZED FINITE ELEMENT METHOD FOR SOLVING TRANSIENT NAVIER-STOKES EQUATIONS WITH HIGH REYNOLDS NUMBER

In this paper,we present a new stabilized finite element method for transient Navier-Stokes equations with high Reynolds number based on the projection of the velocity and pressure.We use Taylor-Hood elements and the equal order elements in space and second order difference in time to get the fully discrete scheme.The scheme is proven to possess the absolute stability and the optimal error estimates.Numerical experiments show that our method is effective for transient Navier-Stokes equations with high Reynolds number and the results are in good agreement with the value of subgrid-scale eddy viscosity methods,Pet ro-Galerkin finite element method and st reamline diffusion method.

Characteristics of settling of dilute suspension of particles with different density at high Reynolds numbers

Dilute suspension of particles with same density and size develops clusters when settle at high Reynolds number(≥250).It is due to particles entrapment in the wakes produced by upstream particles.In this work,this phenomenon is studied for suspension having particles with different densities by numerical simulations.The particle-fluid interactions are modelled using immersed boundary method and inter-particle collisions are modelled using discrete element method.In simulations,settling Reynolds number is always kept above 250 and the suspension solid volume fraction is nearly 0.1 percent.Two particle density ratios(i.e.density of heavy particles to lighter particles)equal to 4:1 and 2:1 and particles with same density are studied.For each density ratio,the percentage volume fraction of each particle density is nearly varied from 0.8 to 0.2.Settling characteristics such as microstructures of settling particle,average settling velocity and velocity fluctuations of settling particles are studied.Simulations show that for different density particles settling characteristics of suspension is largely dominated by heavy particles.At the end of paper,the underlying physics is explained for the anomalies observed in simulation.

An artificial viscosity augmented physics-informed neural network for incompressible flow

Physics-informed neural networks(PINNs)are proved methods that are effective in solving some strongly nonlinear partial differential equations(PDEs),e.g.,Navier-Stokes equations,with a small amount of boundary or interior data.However,the feasibility of applying PINNs to the flow at moderate or high Reynolds numbers has rarely been reported.The present paper proposes an artificial viscosity(AV)-based PINN for solving the forward and inverse flow problems.Specifically,the AV used in PINNs is inspired by the entropy viscosity method developed in conventional computational fluid dynamics(CFD)to stabilize the simulation of flow at high Reynolds numbers.The newly developed PINN is used to solve the forward problem of the two-dimensional steady cavity flow at Re=1000 and the inverse problem derived from two-dimensional film boiling.The results show that the AV augmented PINN can solve both problems with good accuracy and substantially reduce the inference errors in the forward problem.

SUPG finite element method based on penalty function for lid-driven cavity flow up to Re = 27500

A streamline upwind/Petrov-Galerkin （SUPG） finite element method based on a penalty function is pro- posed for steady incompressible Navier-Stokes equations. The SUPG stabilization technique is employed for the for- mulation of momentum equations. Using the penalty function method, the continuity equation is simplified and the pres- sure of the momentum equations is eliminated. The lid-driven cavity flow problem is solved using the present model. It is shown that steady flow simulations are computable up to Re = 27500, and the present results agree well with previous solutions. Tabulated results for the properties of the primary vortex are also provided for benchmarking purposes.

Finite difference streamline diffusion method using nonconforming space for incompressible time-dependent Navier-Stokes equations

This paper proposes a new nonconforming finite difference streamline diffusion method to solve incompressible time-dependent Navier-Stokes equations with a high Reynolds number. The backwards difference in time and the Crouzeix-Raviart （CR） element combined with the P0 element in space are used. The result shows that this scheme has good stabilities and error estimates independent of the viscosity coefficient.

NUMERICAL STUDY OF PARTICLE DISTRIBUTION IN WAKE OF LIQUID-PARTICLE FLOWS PAST A CIRCULAR CYLINDER USING DISCRETE VORTEX METHOD

Particle-laden water flows past a circular cylinder were numerically investigated. The discrete vortex method （DVM） was employed to evaluate the unsteady water flow fields and a Lagrangian approach was applied for tracking individual solid particles. A dispersion function was defined to represent the dispersion scale of the particle. The wake vortex patterns, the distributions and the time series of dispersion functions of particles with different Stokes numbers were obtained. Numerical results show that the particle distribution in the wake of the circular cylinder is closely related to the particle＇s Stokes number and the structure of wake vortices： （1） the intermediate sized particles with Stokes numbers, St, of 0.25, 1.0 and 4.0 can not enter the vortex cores and concen- trate near the peripheries of the vortex structures, （2） in the circular cylinder wake, the dispersion intensity of particles decreases as St is increased from 0.25 to 4.0.

ACCURATE COMPUTATION AND INTERPOLATION TECHNIQUE OF FINITE ANALYTIC COEFFICIENTS

The finite analytic method (FA) developed in the last decade is an effective numerical method for solving fluid flow problems. However, because of the limitation in the present computer, large round-off errors are found in calculating FA coefficients when Reynolds number is large. This paper investigates the cause of this difficulty and presents a special programming technique in making an accurate computation of FA coefficients. Then a fundamental function known as 'Pe' is tabulated by the accurate computation. In practical application the interpolation technique is employed so that the FA coefficients can be obtained reliably and quickly.

Study of poly-disperse aerosols deposition in turbulent flow with different Reynolds numbers

The turbulent deposition mechanism is one of the main mechanisms of aerosol deposition in nuclear power plant tubes.An experimental study of poly-disperse aerosol deposition in a horizontal tube is conducted,where the nominal Reynolds number(Re)is in a range of 3600–200,000.The aerosol deposition velocity first increases and then decreases with the increase of Res,and at high Re,particle rebound occurs during aerosol deposition in the tube.When the Re is low,the aerosol deposition velocity increases with the increase of aerosol diameter.When the Re is greater than 60,000,the deposition velocity first increases and then decreases with the increase of aerosol diameter due to particle surface rebound.A new aerosol deposition model has been developed by establishing the energy conservation equation of the rebounded particles in the viscous sublayer.The calculated results of the new model are in good agreement with these experimental results,and the error between the aerosol deposition velocity calculated by the model and experimental results is between−60%and 150%.

A Finite Element Variational Multiscale Method for Stationary Incompressible Magnetohydrodynamics Equations

In this paper,we propose a variational multiscale method(VMM)for the stationary incompressible magnetohydrodynamics equations.This method is defined by large-scale spaces for the velocity field and the magnetic field,which aims to solve flows at high Reynolds numbers.We provide a new VMM formulation and prove its stability and convergence.Finally,some numerical experiments are presented to indicate the optimal convergence of our method.

3-D numerical investigation of the wall-bounded concentric annulus flow around a cylindrical body with a special array of cylinders

Concentric annulus flow around a combinational cylindrical body with a special array of cylinders at five high Reynolds numbers is investigated numerically using Fluent 6.3.26 in this paper. The numerical results show a good agreement with the experimental data in regard to the axial velocity of the flow. This study focuses on the flow structure and the hydrodynamic characteristics based on the velocity distribution, the pressure distribution, streamlines and vectors under I-D, 2-D and 3-D condi- tions. Meanwhile, some global parameters including the pressure coefficient, the drag coefficient and the lift coefficient are analyzed. Numerical results show that the high velocity region and the reverse wake zone with low velocity exist in some spaces due to the disturbance of the cylindrical body. Negative pressures appear in some regions. Neither a wide area vortex nor the vortex shedding appears in the wall-bounded domain. The drag along the axial direction is the main force acting on the cylindrical body in the pipe domain. The annulus flow around the cylindrical body is analyzed to reveal the hydrodynamic characteristics of the complex turbule- nt concentric annulus flow field due to the multi-effects in the pipeline.

A FULL DISCRETE STABILIZED METHOD FOR THE OPTIMAL CONTROL OF THE UNSTEADY NAVIER-STOKES EQUATIONS

In this paper, a full discrete local projection stabilized （LPS） method is proposed to solve the optimal control problems of the unsteady Navier-Stokes equations with equal order elements. Convective effects and pressure are both stabilized by using the LPS method. A priori error estimates uniformly with respect to the Reynolds number are obtained, providing the true solutions are sufficient smooth. Numerical experiments are implemented to illustrate and confirm our theoretical analysis.

STUDY OF 2-D LARGE EDDY SIMULATION WITH VORTICITY DISSIPATION FOR FLOW PAST A CIRCULAR CYLINDER

An analysis is made on the numerical results of the vortex-shedding flow about a circular cylinder in the subcritical regime( R, = 1. 4× 105) obtained by using the LES approach with a hybrid boundary condition at the cylinder wall. A new method is presented to model the vorticity-dissipation mechanism of the real 3-D flow by introducing momentum-sink terms into the 2-D flow equations of primitive variables. TO show the effects of the added sink terms, a comparison is given between the flow behaviors produced by the 2-D models with and without vorticity-dissipation mechanism.

Improving the Stability of theMultiple-Relaxation-Time Lattice Boltzmann Method by a Viscosity Counteracting Approach

Numerical instability may occur when simulating high Reynolds number flows by the lattice Boltzmann method(LBM).The multiple-relaxation-time(MRT)model of the LBM can improve the accuracy and stability,but is still subject to numerical instability when simulating flows with large single-grid Reynolds number(Reynolds number/grid number).The viscosity counteracting approach proposed recently is a method of enhancing the stability of the LBM.However,its effectiveness was only verified in the single-relaxation-time model of the LBM(SRT-LBM).This paper aims to propose the viscosity counteracting approach for the multiple-relaxationtime model(MRT-LBM)and analyze its numerical characteristics.The verification is conducted by simulating some benchmark cases:the two-dimensional(2D)lid-driven cavity flow,Poiseuille flow,Taylor-Green vortex flow and Couette flow,and threedimensional(3D)rectangular jet.Qualitative and Quantitative comparisons show that the viscosity counteracting approach for the MRT-LBMhas better accuracy and stability than that for the SRT-LBM.