Simulation Of Cavity Flow Research Articles

High‐order detached eddy simulation, zonal LES and URANS of cavity and labyrinth seal flows

SUMMARYHybrid numerical large eddy simulation (NLES), detached eddy simulation (DES) and URANS methods are assessed on a cavity and a labyrinth seal geometry. A high sixth‐order discretization scheme is used and is validated using the test case of a two‐dimensional vortex. The hybrid approach adopts a new blending function. For the URANS simulations, the flow within the cavity remains steady, and the results show significant variation between models. Surprisingly, low levels of resolved turbulence are observed in the cavity for the DES simulation, and the cavity shear layer remains two dimensional. The hybrid RANS–NLES approach does not suffer from this trait.For the labyrinth seal, both the URANS and DES approaches give low levels of resolved turbulence. The zonal Hamilton–Jacobi approach on the other had given significantly more resolved content. Both DES and hybrid RANS–NLES give good agreement with the experimentally measured velocity profiles. Again, there is significant variation between the URANS models, and swirl velocities are overpredicted. Copyright © 2013 John Wiley & Sons, Ltd.

Numerical Simulation of Cavity Flow within the Flow Field

Analysis of numerical simulation was used on flow field and temperature field in mechanical seal cavity. It borrowed a new calculation method, which was more visual and simpler than before. And this method analysed the change in temperature field of mechanical seal ring and the distribution of temperature and pressure in the flow field when mechanical seal was working. The result showed that the numerical simulation method was effect to the flow field in centrifugal pump.

CUDA Based Numerical Simulation of Cavity Flow and Performance Analysis

Cuda has been widely used in computational fluid dynamics due to the powerful abilities of floating point arithmetic on gpu.This paper solved the Navier-Stokes equations of two dimensional incompressible flow using parallel programming on cuda. The finite volume method and the second-order upwind discretization scheme were used in the simulation.The speed of serial c program and the cuda based program were compared and we also compared the two programs on different hardware.The simulations got high precision results,which showed that the cuda based parallel computing is much more efficiency,and the parallel algorithm could get a more than 10 times the acceleration.

Simulations of Three-dimensional Cavity Flows with Multi Relaxation Time Lattice Boltzmann Method and Graphic Processing Units

Three-dimensional square cavity flows are simulated using multi-relaxation lattice Boltzmann method and graphic processing units. It was found that transition takes place between 1700 < Re < 2000. Parallel computations are conducted on a single node multi graphic processing unit (GPU) system, consisting of three nVIDIA M2070 or GTX560 devices using OpenMP. Results show that the speedup performance is strongly dependent on problem size and the precision adopted. For single precision computation with 2403 grid density, about 159 times speedup can be obtained, while for double precision computation, this is slightly degraded to 112. Both are achieved with three Tesla M2070.

Regressing the Size and Cost of Turbulent Cavity Flow Simulations

A successful model of high Reynolds number cavity flows involves reproducing the flow physics with adequate accuracy, given the available computational resources. The process of planning high Reynolds number cavity flow simulations is systematically reviewed to extract the dependence of different programmer's choices on the CFD mesh size and on the cost of the computation. This process has been broken down into five phases: i) description of the problem in the continuous domain, ii) problem order reduction by turbulence modelling, iii) discretization in space and time, iv) integration of the governing equations, v) costing the numerical operations of the flow solver. This paper examines the influence of each phase on the spectral width and the grid density, which are the key CFD indicators that determine the cost of the computation. A dimensional analysis was conducted to separate the effects of the geometry of the enclosure, the boundary layer resolution, the turbulence model, and the numerical scheme order of accuracy. Regression analysis on the non-dimensional groups of published cavity CFD simulations determined the range of practical values used by current state-of-the-art computations. This analysis is a useful tool for obtaining design trade-offs by a multivariate optimization in cavity flow CFD and for estimating the order of magnitude of the computational resources required by the simulations.

Globally conservative high-order filters for large-eddy simulation and computational aero-acoustics

In computational aero-acoustics, large-eddy simulations (LES) or direct numerical simulations (DNS) are often employed for flow computations in the source region. As part of the numerical implementation or required modeling, explicit spatial filters are frequently employed. For instance, in LES spatial filters are employed in the formulation of various subgrid-scale (SGS) models such as the dynamic model or the variational multi-scale (VMS) Smagorinsky model; both in LES or DNS, spatial high-pass filters are often used to remove undesired grid-to-grid oscillations. Though these type of spatial filters adhere to local accuracy requirements, in practice, they often destroy global conservation properties in the presence of non-periodic boundaries conditions. This leads to the incorrect prediction of the flow properties near hard boundaries, such as walls. In the current work, we present globally conservative high-order accurate filters, which combine traditional filters at the internal points with one-sided conservative filters near the wall boundary. We test these filters to remove grid-to-grid oscillations both in a channel-flow case and in 2D cavity flow. We find that the use of a non-conservative filter leads to erroneous predictions of the skin friction in channel flows up to 30%. In the cavity-flow simulations, the use of non-conservative filters to remove grid-to-grid oscillations leads to important shifts in the Strouhal number of the dominant mode, and a change of the flow pattern inside the cavity. In all cases, the use of conservative high-order filter formulations to remove grid-to-grid oscillations lead to very satisfactory results. Finally, in our channel-flow test case, we also illustrate the importance of using conservative filters for the formulation of the VMS Smagorinsky model.

Immersed Boundary Method for Liquid-Solid Two-Phase Flow with Heat Transfer

In this paper, extended immersed boundary method (IBM) for liquid-solid two-phase flow with heat transfer is proposed. The velocity and pressure field are solved based on IBM of body force type. To treat heat transfer at the interphase, the temperature field is computed with the thermal conductivity modelled by considering the direction of interface and heat flux. Present heat conduction model is validated by heat conduction problem of compound cylinder. In addition, the numerical stability is improved by the predictor-corrector method. It enables the simulation of flow laden with solid particles of neutral density. Then, the applicability of present method is shown by direct numerical simulation of two-dimensional cavity flow including multiple particles, and the influences of particle size, layout and behavior for heat transfer properties are investigated.

Numerical simulation of cavity flow induced noise by LES and FW-H acoustic analogy

The predictions of cavity flow and flow-induced noise are two important and complex issues in fluid-acoustic coupling field. Numerical studies for these issues are performed in the paper by large eddy simulation (LES) and FW-H acoustic analogy. Firstly, the wall pressure fluctuations of plate, foil, shutter hole are computed and compared with experimental results. The robustness of large eddy simulation in unsteady flow calculation is analyzed. Secondly, the calculation of a 2-D cavity flow are accomplished. The power spectrum of pressure fluctuations is compared with measured data and the vorticity distribution is analyzed. Finally, the flow induced noises of two 3D cavities are predicted. The computed results are compared with experimental data of Large Circulation Channel in CSSRC. It shows that the numerical prediction method in the paper is credible.

Application of polynomial chaos on numerical simulation of stochastic cavity flow

In present paper, the mathematic background of intrusive polynomial chaos (IPC) method and coupling process with one dimension Euler equation were introduced. The IPC method was implemented for the 2D compressible stochastic Navier-Stokes equations to simulate the non-deterministic behavior of a lid driven cavity flow under the influence of uncertainties. The driven velocity and fluid viscosity were supposed respectively to be the uncertain variable which has Gaussian probability distribution. Based on the validation with benchmark results, discussions were mainly focused on the statistic properties of velocity distribution. The results indicated the effect of IPC method on the simulation of propagation of uncertainty in the flow field. For the simulated results of 2D cavity flow, influence of the driven velocity uncertainty is larger than that of viscosity.

Skew-symmetric form of convective terms and fully conservative finite difference schemes for variable density low-Mach number flows

The form of convective terms for compressible flow equations is discussed in the same way as for an incompressible one by Morinishi et al. [Y. Morinishi, T.S. Lund, O.V. Vasilyev, P. Moin, Fully conservative higher order finite difference schemes for incompressible flow, J. Comput. Phys. 124 (1998) 90], and fully conservative finite difference schemes suitable for shock-free unsteady compressible flow simulations are proposed. Commutable divergence, advective, and skew-symmetric forms of convective terms are defined by including the temporal derivative term for compressible flow. These forms are analytically equivalent if the continuity is satisfied, and the skew-symmetric form is secondary conservative without the aid of the continuity, while the divergence form is primary conservative. The relations between the present and existing quasi-skew-symmetric forms are also revealed. Commutable fully discrete finite difference schemes of convection are then derived in a staggered grid system, and they are fully conservative provided that the corresponding discrete continuity is satisfied. In addition, a semi-discrete convection scheme suitable for compact finite difference is presented based on the skew-symmetric form. The conservation properties of the present schemes are demonstrated numerically in a three-dimensional periodic inviscid flow. The proposed fully discrete fully conservative second-order accurate scheme is also used to perform the DNS of compressible isotropic turbulence and the simulation of open cavity flow.

Cavity flow simulation of Carreau–Yasuda non-Newtonian fluids using PIM meshfree method

Lid-driven cavity flow of a purely-viscous non-Newtonian fluid obeying Carreau–Yasuda rheological model is studied numerically using the PIM meshfree method combined with the Characteristic-Based Split-A algorithm. Results are reported for the velocity and pressure profiles at Reynolds numbers as high as 1000 for a non-Newtonian fluid obeying Carreau–Yasuda rheological model. For Newtonian fluids, results obtained from our PIM–CBS-A method show good agreement with benchmark results published in the literature and obtained using finite difference and/or Finite Element Methods. Our numerical results are also consistent with recent published results obtained using another meshfree method called LSM with the advantage that PIM needs less “points” to achieve the same degree of accuracy. Results obtained for the Carreau–Yasuda model reveals the strong effect of the shear-thinning behavior of a fluid on its flow kinematics within the cavity.

Molecular dynamics simulation of complex multiphase flow on a computer cluster with GPUs

Compute Unified Device Architecture (CUDA) was used to design and implement molecular dynamics (MD) simulations on graphics processing units (GPU). With an NVIDIA Tesla C870, a 20-60 fold speedup over that of one core of the Intel Xeon 5430 CPU was achieved, reaching up to 150 Gflops. MD simulation of cavity flow and particle-bubble interaction in liquid was implemented on multiple GPUs using a message passing interface (MPI). Up to 200 GPUs were tested on a special network topology, which achieves good scalability. The capability of GPU clusters for large-scale molecular dynamics simulation of meso-scale flow behavior was, therefore, uncovered.

LATTICE BOLTZMANN DYNAMICS AND DYNAMICAL SYSTEM SUB-GRID MODELS

The dynamics sub-grid scale (SGS) models and the dynamical system SGS model are introduced into the lattice Boltzmann method (LBM), and applied to numerical simulation of turbulent cavity flows. The results are compared with those of direct numerical simulation of turbulence and Smagorinsky SGS model. A new average method of eliminating the inherent unphysical oscillation of LBM is also given.

A reduced finite difference scheme based on singular value decomposition and proper orthogonal decomposition for Burgers equation

In this article, a reduced optimizing finite difference scheme (FDS) based on singular value decomposition (SVD) and proper orthogonal decomposition (POD) for Burgers equation is presented. Also the error estimates between the usual finite difference solution and the POD solution of reduced optimizing FDS are analyzed. It is shown by considering the results obtained for numerical simulations of cavity flows that the error between the POD solution of reduced optimizing FDS and the solution of the usual FDS is consistent with theoretical results. Moreover, it is also shown that the reduced optimizing FDS is feasible and efficient.

A dynamic procedure based on the scale-similarity hypotheses for large-eddy simulation

Current dynamic procedures in large-eddy simulation treat the two subgrid-scale stresses in the Germano identity with the same subgrid base model. Thus to get the base model coefficient, the coefficient must be assumed to be constant for test filter operation. However, since the coefficient has sharp fluctuations, this assumption causes some inconsistence. A new dynamic procedure was developed in which these two stresses are modeled by the base model and the scale-similarity hypotheses respectively. Thus the need for the assumption is removed and consistence is restored. The new procedure is tested in the large-eddy simulation of a lid-driven cavity flow at Reynolds number of 10,000. The results show that the new procedure can both improve the prediction of statistics of the flow and effectively relieve the singularity of subgrid-scale (SGS) model coefficient.

Finite difference scheme based on proper orthogonal decomposition for the nonstationary Navier-Stokes equations

The proper orthogonal decomposition (POD) and the singular value decomposition (SVD) are used to study the finite difference scheme (FDS) for the nonstationary Navier-Stokes equations. Ensembles of data are compiled from the transient solutions computed from the discrete equation system derived from the FDS for the nonstationary Navier-Stokes equations. The optimal orthogonal bases are reconstructed by the elements of the ensemble with POD and SVD. Combining the above procedures with a Galerkin projection approach yields a new optimizing FDS model with lower dimensions and a high accuracy for the nonstationary Navier-Stokes equations. The errors between POD approximate solutions and FDS solutions are analyzed. It is shown by considering the results obtained for numerical simulations of cavity flows that the error between POD approximate solution and FDS solution is consistent with theoretical results. Moreover, it is also shown that this validates the feasibility and efficiency of POD method.

A high accuracy hybrid method for two-dimensional Navier–Stokes equations

A dual-mesh hybrid numerical method is proposed for high Reynolds and high Rayleigh number flows. The scheme is of high accuracy because of the use of a fourth-order finite-difference scheme for the time-dependent convection and diffusion equations on a non-uniform mesh and a fast Poisson solver DFPS2H based on the HODIE finite-difference scheme and algorithm HFFT [R.A. Boisvert, Fourth order accurate fast direct method for the Helmholtz equation, in: G. Birkhoff, A. Schoenstadt (Eds.), Elliptic Problem Solvers II, Academic Press, Orlando, FL, 1984, pp. 35–44] for the stream function equation on a uniform mesh. To combine the fast Poisson solver DFPS2H and the high-order upwind-biased finite-difference method on the two different meshes, Chebyshev polynomials have been used to transfer the data between the uniform and non-uniform meshes. Because of the adoption of a hybrid grid system, the proposed numerical model can handle the steep spatial gradients of the dependent variables by using very fine resolutions in the boundary layers at reasonable computational cost. The successful simulation of lid-driven cavity flows and differentially heated cavity flows demonstrates that the proposed numerical model is very stable and accurate within the range of applicability of the governing equations.

Numerical simulation of cavity flows based on transformed equations

A new numerical algorithm is applied to simulate two-dimensional lid-driven cavity flows. In this new algorithm, the momentum equations are first transformed using an exponential function to eliminate the convection terms in the equations. Then a central differencing scheme is employed to discretize the transformed equations. The cavity flows studied in this work include those with non-zero velocity component in the y-direction on the upper and lower boundaries. The results for the velocity components along the geometric centerline, stream function patterns, and vorticity contours are presented and discussed. The predicted results are in excellent agreement with benchmark solutions.

Recent advances of Lattice Boltzmann techniques on unstructured grids

Further research on both theoretical and practical aspects of a previously defined finite-volume formulation to integrate the Lattice Boltzmann equation (LBE) on unstructured grids is presented. Moreover, additional explicit schemes for time discretisation are proposed. The method is tested on an impulsively started channel flow with the aim of exactly locating solid boundaries. Cavity flow simulations are used to measure the inaccuracies due to compressibility, grid and time discretisation effects. Finally, the proposed method has been tested against a laminar flow over a backward facing step in order to assess the effectiveness of open outlet boundary treatment.

Large Eddy Simulation of Turbulent Convective Cavity Flow

The large eddy simulation model with Smagorinsky subgrid-scale model was applied to two-dimensional turbulent convective cavity flow. The Reynolds number is lying from 1×104 to 4×105 and Archimedes number from 0 to 0.4. The simulation results were compared with the k−ϵ model results and experimental results wherever possible. Flow results were in good agreement with experimental data across the mid-planes. Effects of Smagorinsky constant and grid resolution were investigated.