Backward-facing Step Flow Problem Research Articles

Newton linearization of the Navier–Stokes equations for flow computations using a fully coupled finite volume method

Newton linearization is implemented for the discretized advection terms in the Navier-Stokes momentum equations. A modified Newton linearization algorithm is developed by analyzing how to properly account for mass conservation implicitly in the linearization. The numerical performance of the modified Newton linearization algorithm is investigated in terms of solution stability, convergence behaviour, and accuracy. A set of standard fluid flow test problems is solved using a pressure-based cell-centered fully coupled finite volume solver linearized by Picard, standard Newton, and modified Newton methods. The accuracy of numerical solutions is assessed by comparisons with provided benchmark solutions and those obtained by the present coupled solver linearized by the Picard method. The numerical results showed the modified Newton linearization algorithm converged to a solution with a rate up to 22 times higher than that of Picard linearization algorithm for the steady flow fields for lid-driven cavity test problems. The modified Newton linearization technique is also evaluated by computations of steady flow over a backward facing step and unsteady flow around a circular cylinder. The developed algorithm reduces the iteration number of the linearization cycle required up to 10 times for the backward facing step flow problem. Also, the unsteady flow computations are performed by modified Newton linearization algorithm with a lower number of iterations in comparison with the Picard linearization algorithm. The numerical experiments indicate that the modified Newton linearization algorithm maintains the solution accuracy with respect to the Picard linearization algorithm.

ADAPTIVE GRID REFINEMENT USING THE GENERALISED FINITE-DIFFERENCE METHOD

The combination of the Generalised Finite Difference Method (GFDM), and adaptive grid refinement is applied to solve 2D fluid flow problems. The accuracy of this combination is demonstrated by solving the 2D lid-driven cavity flow, and 2D backward-facing step flow problems, and comparing the results against the benchmarks. This new Computational Fluid Dynamics (CFD) formulation is applied to solve a 2D meter flow application to determine the velocity profiles through the centre of the meter for higher Reynolds numbers. To verify the accuracy of this combnation, analytical 2D and 3D Laplace partial differential equations (PDE's) are solved by two methods. The first method uses the Finite Difference Method (FDM) over a uniform grid of nodes, and the second method uses the GFDM over a non-uniform grid of nodes. Computational cost and accuracy comparisons are made for both methods.

A two-level variational multiscale meshless local Petrov-Galerkin (VMS-MLPG) method for incompressible Navier-Stokes equations

A two-level variational multiscale meshless local Petrov-Galerkin (VMS-MLPG) method is presented for incompressible Navier-Stokes equations based on two local Gauss integrations which effectively replace a unit operator (first level) and an orthogonal project operator (second level). The present VMS-MLPG method allows arbitrary combinations of interpolation functions for the velocity and pressure fields, specifically the equal-order interpolations that are easy to implement and satisfy the Babuska-Breezi (B-B) condition. The prediction accuracy and the numerical stability of the proposed method for the lid-driven cavity flow and the backward facing step flow problems are analyzed and validated by comparing with the SUMLPG method and the benchmark solutions. It is shown that the present VMS-MLPG method can guarantee the numerical stability and obtain the reasonable solutions for incompressible Navier-Stokes equation.

A benchmark test for room air distribution: the backward facing step flow

This paper concerns the use of Computational Fluid Dynamics (CFD) for the prediction of room air movement and provide a guide on selecting of the proper turbulence model. The benchmark which developed here for the first time is a backward-facing step flow problem. The measurements is performed in a small-scale model and the velocity filed is measured by Particle Image Velocimetry (PIV). The measurements focus on transitional flow and fully developed turbulent flow at isothermal condition. The PIV measurements and different CFD predictions are compared. The CFD predictions are generally slightly diverse, and this is, among other things, the result of using different turbulence models as well as using different software codes, grid distribution and boundary values etc. The k-ε family of turbulence models is an option for fully developed flow, and the k-ω family does work for transitional low turbulent flow in this backward-facing step flow.

Computational fluid dynamics predictions of non‐isothermal ventilation flow—How can the user factor be minimized?

The use of computational fluid dynamics (CFD) to solve indoor airflow problems has increased tremendously in the last decades. However, the accuracy of CFD simulations depends greatly on user experience, the available validation data, and the effort made to verify solutions. This study presents the results of a conference workshop, which assessed user influence on the CFD results obtained for a generic non-isothermal flow problem; ie, a backward-facing step flow problem with a heated wall below the supply. Fifty-five simulation sets were submitted by 32 teams. The results showed a very large spread in predicted penetration length (xre /(H-h)), location of maximum velocity in the lower part of the recirculation cell (xrm /(H-h)), and maximum velocity at this location (urm /u0 ). The turbulence model seemed to very strongly influence the results, with a statistically significant difference in the predictions yielded by the k-ε and k-ω models. The results obtained using a single turbulence model generally also showed a spread in results; the level of spread depended on factors such as grid size and near-wall treatment. The statistical data strongly indicate the need for validation studies using experimental data (benchmarks) to ensure the accuracy, reliability, and trustworthiness of CFD simulations for indoor airflow problems.

An improved particle smoothing procedure for Laplacian operator in a randomly scattered cloud

ABSTRACTIn the present study, an improved particle smoothing (IPS) procedure is proposed to imitate the Laplacian operator in a randomly scattered particle cloud. It is devised to provide a more accurate mathematical representation of diffusion term in the moving particle methods. From the numerical analyses, the major source of conventional particle smoothing (PS) schemes leading to solution inaccuracy can be attributed to the intrinsic artificial convection term, whose accuracy order is of O(δ−1). Spatial accuracy can be improved by eliminating the numerically induced artificial velocity in the proposed IPS scheme. Verification studies are performed by testing the proposed scheme in pure diffusion problems. Benchmark lid-driven cavity and backward-facing step flow problems are solved to demonstrate the superiority of the proposed scheme. In the light of numerical analysis and computational results, it is concluded that the proposed IPS scheme is effective to simulate fluid flow problems in the context of moving particle methods.

A global meshless collocation particular solution method (integrated Radial Basis Function) for two-dimensional Stokes flow problems

A global version of the Method of Approximate Particular Solutions (MAPS) is developed to solve two-dimensional Stokes flow problems in bounded domains. The velocity components and the pressure are approximated by a linear superposition of particular solutions of the non-homogeneous Stokes system of equations with a Multiquadric Radial Basis Function as forcing term. Although, the continuity equation is not explicitly imposed in the resulting formulation, the scheme is mass conservative since the particular solutions exactly satisfy the mass conservation equation. The present scheme is validated by comparing the obtained numerical result with the analytical solution of two boundary value problems constructed from the Stokeson exterior fundamental solution, i.e. regular everywhere except at infinity. For these two cases, convergence of the method and the influence of the value of the Multiquadric’s shape parameter on the numerical results are studied by computing the relative Root Mean Square (RMS) error for several homogeneous distributions of collocation points and values of the shape parameter. From this analysis is observed that the proposed MAPS results are stable and accurate for a wide range of shape parameter values. In addition, the lid-driven cavity and backward-facing step flow problems are solved and the obtained results compared with the solutions found with more conventional numerical schemes, showing good agreement between them.

The localized differential quadrature method for two-dimensional stream function formulation of Navier–Stokes equations

Localized differential quadrature (LDQ) method is employed to solve two-dimensional stream function formulation of incompressible Navier–Stokes equations. Being developed by introducing the localization concept to the general differential quadrature (GDQ) method, the employment of LDQ method becomes efficient and flexible, especially for the simulations of large scale computations. By introducing the Lagrange stream function to vorticity transport equation, the governing equation—the fourth-order partial differential equation (PDE)—is derived. To stably obtain the solutions of the fourth-order PDE, a fictitious point method is included to treat the boundary conditions. To examine the present scheme, two different types of classic benchmark fluid flow problems are proposed, including driven cavity flow problems and backward-facing step flow problems. The good agreement of solutions demonstrate the robustness and feasibility of the proposed scheme. Conclusively, the LDQ method is sufficient and appropriate enough to simulate the solutions of stream function formulation of Navier–Stokes equations with various Reynolds numbers.

Conjugate heat transfer study of backward-facing step flow – A benchmark problem

The conjugate heat transfer characteristics are studied for backward-facing step flow problem. Alternating direction implicit (ADI) method is used to find the steady state results for hydrodynamic solution using stream function–vorticity formulation. The energy equation in the fluid region and in the solid region are solved simultaneously. The conjugate effects are studied in connection with four parameters viz. Re, Pr, k and b. Effect of four parameters on local Nusselt number, interface temperature and average Nusselt number are presented in detail. The results are compared with non-conjugate case.

Stratified flow over a backward‐facing step: hybrid solution by integral transforms

The generalized integral transform technique (GITT) is employed in the hybrid numerical–analytical solution of the stratified backward-facing step flow problem, with automatic global accuracy control towards a user-prescribed accuracy target. The present paper is aimed at extending the available database on benchmark results in heat and fluid flow, which were progressively obtained through integral transforms, for the co-validation of more flexible fully discrete approaches. Numerical results are presented for the situations more frequently encountered in the literature Copyright © 2001 John Wiley & Sons, Ltd.

Backward-Facing Step Flow Analysis Using the Fourth-Order Finite-Difference Method.

In the incompressible viscous fluid flow analyses, the backward-facing step flow problem has been investigated as a benchmark problem with the inflow and outflow boundary conditions for testing the effectiveness of a new numerical scheme. In this research, the corrected fourth-order finite difference method is employed for this fluid flow analysis. This method was originally proposed by authors through the error analysis approach and has been successfully applied for viscous fluid flow and natural convection problems in a square cavity. In this study, the backward-facing step now was simulated for the Reynolds numbers of 800 and 1000, and the steady solutions were obtained. The effects of the sizes of computational meshes to the reattachment lengths are investigated, and the mesh-independent solutions are obtained. We confirm the agreement of our results with other research works and the effectiveness of our corrected fourth-order finite difference method for viscous fluid flow analyses with inflow and outflow boundary conditions.

Stratified flow over a backward-facing step: hybrid solution by integral transforms

The generalized integral transform technique (GITT) is employed in the hybrid numerical–analytical solution of the stratified backward-facing step flow problem, with automatic global accuracy control towards a user-prescribed accuracy target. The present paper is aimed at extending the available database on benchmark results in heat and fluid flow, which were progressively obtained through integral transforms, for the co-validation of more flexible fully discrete approaches. Numerical results are presented for the situations more frequently encountered in the literature Copyright © 2001 John Wiley & Sons, Ltd.

BOUNDARY ELEMENT ANALYSIS OF VISCOUS CHANNEL FLOW

The boundary element method (BEM) is used to investigate laminar viscous flows in internal channels. A direct iterative scheme is used to cope with the nonlinear character of the integral equations. To achieve convergence, an underrelaxation technique is employed at relatively high Reynolds numbers. Numerical examples of Poisseuille and backward-facing step flow problems are considered. It is found that BEM gives accurate solutions up to a certain Reynolds number for each case.

A numerical revisit of backward-facing step flow problem

In the present study we take a fresh look at a laminar flow evolving into a larger channel through a step configured in a backward-facing format. We conduct steady three-dimensional Navier–Stokes flow analysis in the channel using the step geometry and flow conditions reported by Armaly et al. This allows a direct comparison with the results of physical experiments, thus serving to validate the numerical results computed in the range of 100⩽Re⩽1000. Results show that there is generally excellent agreement between the present results and the experimental data for Re=100 and 389. Fair agreement for Re=1000 is also achieved, except in the streamwise range of 15⩽x⩽25. The main difference stems from the fact that the roof eddy is not extended toward the midspan in the channel with a span width 35 times of the height of the upstream channel. In the present study we also reveal that the flow at the plane of symmetry develops into a two-dimensional-like profile only when the channel width is increased up to 100 times of the upstream step height for the case with Re=800. The present computational results allow the topological features of the flow to be identified using critical point theory. The insight thus gained is useful in revealing a mechanism for the development of an end-wall-induced three-dimensional vortical flow with increasing Reynolds number.