Fue-Sang Lien

Assessment of turbulence-transport models including non-linear rng eddy-viscosity formulation and second-moment closure for flow over a backward-facing step

Abstract A computational study is performed in which the predictive capabilities of a range of eddy-viscosity and second-moment-closure models are examined by reference to a separated flow behind a backward-facing step in an expanding channel. The models include three second-moment-closure variants, all being of the ‘Launder-Reece-Rodi’ type, two RNG k—ϵ forms, one combining the RNG approach with a non-linear eddy-viscosity formulation, and a low-Re k—ϵ model. The study demonstrates that to achieve a solution similar to that returned by second-moment closure, the RNG formulation needs to be implanted into a non-linear eddy-viscosity framework; neither returns, on its own, the correct behaviour, not even for mean-flow features. Moreover, relatively minor variations within second-moment closure—specifically, such relating to wall-induced effects on turbulence isotropisation and to stress diffusion—can significantly alter the overall performance of the closure. All models specifically designed to return realistic solutions for normal stresses seriously over-estimate anisotropy.

A general non-orthogonal collocated finite volume algorithm for turbulent flow at all speeds incorporating second-moment turbulence-transport closure, Part 1: Computational implementation

Abstract A computational procedure has been developed for predicting separated turbulent flows in complex two-dimensional and three-dimensional geometries. The procedure is based on the fully conservative, structured finite volume framework within which the volumes are non-orthogonal and collocated such that all flow variables are stored at one and the same set of nodes. To ease the task of discretization and to enhance the conservative property of the scheme, a Cartesian or datum-line-adapted decomposition of the velocity field has been used. The solution algorithm is iterative in nature, approaching the steady solution with the aid of a pressure-correction scheme. Convection is approximated with a range of schemes, among them higher-order upstream-weighted approximations and a TVD-type MUSCL form, the last applied principally to the transport equations governing turbulence properties. Effects of turbulence are represented either by two-equation eddy-viscosity models or by a full Reynolds-stress-transport closure. The former category includes both high- and low-Reynolds-number variants in two- as well as three-dimensional conditions. To achieve a stable implementation of the Reynolds-stress equations, a special interpolation practice, analogous to that of Rhie and Chow for momentum [1], has been introduced within the general framework. The procedure has been formulated so as to apply to both incompressible and compressible flows. The latter may contain shocks and highly supersonic regions. To achieve this range of applicability, the retarded-density concept has been combined with the basic pressure-based algorithm to capture shock waves. A ‘Full Approximation Multigrid’ scheme for convergence acceleration has been incorporated and applied in conjunction with all turbulence models including second-moment closure. The present first part of a twin paper focuses on numerical and turbulence-modelling issues. In Part 2, computational results are presented for six representative applications out of fifteen recently predicted with the algorithm within an extensive validation exercise.

Numerical modelling of the turbulent flow developing within and over A 3-D building array, part I: A high-resolution reynolds-averaged Navier-Stokes approach

A study of the neutrally-stratified flow within and over an array of three-dimensional buildings (cubes) was undertaken using simple Reynolds-averaged Navier—Stokes (RANS) flow models. These models consist of a general solution of the ensemble-averaged, steady-state, three-dimensional Navier—Stokes equations, where the k-ε turbulence model (k is turbulence kinetic energy and ε is viscous dissipation rate) has been used to close the system of equations. Two turbulence closure models were tested, namely, the standard and Kato—Launder k-ε models. The latter model is a modified k-ε model designed specifically to overcome the stagnation point anomaly in flows past a bluff body where the standard k-ε model overpredicts the production of turbulence kinetic energy near the stagnation point. Results of a detailed comparison between a wind-tunnel experiment and the RANS flow model predictions are presented. More specifically, vertical profiles of the predicted mean streamwise velocity, mean vertical velocity, and turbulence kinetic energy at a number of streamwise locations that extend from the impingement zone upstream of the array, through the array interior, to the exit region downstream of the array are presented and compared to those measured in the wind-tunnel experiment. Generally, the numerical predictions show good agreement for the mean flow velocities. The turbulence kinetic energy was underestimated by the two different closure models. After validation, the results of the high-resolution RANS flow model predictions were used to diagnose the dispersive stress, within and above the building array. The importance of dispersive stresses, which arise from point-to-point variations in the mean flow field, relative to the spatially-averaged Reynolds stresses are assessed for the building array.

A MULTIBLOCK IMPLEMENTATION OF A NON‐ORTHOGONAL, COLLOCATED FINITE VOLUME ALGORITHM FOR COMPLEX TURBULENT FLOWS

A multiblock algorithm for general 2D and 3D turbulent flows is introduced and applied to three cases : a compressor cascade passage, a two-element high-lift aerofoil and a round-to-square transition duct. The method is a generalization of a single-block scheme which is based on a non-orthogonal, fully collocated finite volume framework, applicable to incompressible and compressible flows and incorporating a range of turbulence transport models, including second-moment closure. The multiblock implementation is essentially block-unstructured, each block having its own local co-ordinate system unrelated to those of its neighbours. Any one block may interface with more than one neighbour along any one block face. Interblock communication is handled by connectivity matrices and effected via a two-cell overlap region along block boundaries in which halo data reside. The algorithm and the associated data communication are explained in detail, and its effectiveness is verified, with particular reference to improved numerical resolution and parallel computing.

A Pressure-Velocity Solution Strategy for Compressible Flow and Its Application to Shock/Boundary-Layer Interaction Using Second-Moment Turbulence Closure

A nonorthogonal, collocated finite-volume scheme, based on a pressure-correction strategy and originally devised for general-geometry incompressible turbulent recirculating flow, has been extended to compressible transonic conditions. The key elements of the extension are a solution for flux variables and the introduction of streamwise-directed density-retardation which is controlled by Mach-number-dependent monitor functions, and which is applied to all transported flow properties. Advective fluxes are approximated using the quadratic scheme QUICK or the secondorder TVD scheme MUSCL, the latter applied to all transport equations, including those for turbulence properties

A pressure-based unstructured grid method for all-speed flows

An all-speed algorithm based on the SIMPLE pressure-correction scheme and the ‘retarded-density’ approach has been formulated and implemented within an unstructured grid, finite volume (FV) scheme for both incompressible and compressible flows, the latter involving interaction of shock waves. The collocated storage arrangement for all variables is adopted, and the checkerboard oscillations are eliminated by using a pressure-weighted interpolation method, similar to that of Rhie and Chow [Numerical study of the turbulent flow past an airfoil with trailing edge separation. AIAA Journal 1983; 21: 1525]. The solution accuracy is greatly enhanced when a higher-order convection scheme combined with adaptive mesh refinement (AMR) are used. Copyright

Multigrid acceleration for recirculating laminar and turbulent flows computed with a non-orthogonal, collocated finite-volume scheme

Abstract A study has been undertaken of multigrid convergence acceleration in iterative calculations of recirculating laminar and turbulent flows. The basic numerical platform is a 2D/3D non-orthogonal, collocated finite-volume algorithm in which convection is approximated, optionally, by a non-monotonic upstream-weighted third-order scheme or by a monotonie second-order MUSCL/TVD formulation, and which iterates the solution towards the steady state by way of a pressure-correction scheme. The study investigates the performance of various multigrid implementations including the correction and full approximation multigrid variants, the latter operated within a variety of cycles, both with prescribed and residual-driven relaxation sweeps at each grid level. The multigrid implementation is documented in detail and includes a consideration of data-structure issues and special algorithmic measures necessary to secure robust convergence for turbulent flows. The performance characteristics of the multigrid variants are then exposed through a range of results arising from computations for laminar and turbulent conditions, with turbulence being represented by the k-ϵ model or full Reynolds-stress-transport closure.

Non-linear eddy-viscosity modelling of transitional boundary layers pertinent to turbomachine aerodynamics

Abstract The predictive performance of three low-Reynolds-number turbulence models, one based on the linear (Boussinesq) stress-strain relationship and two adopting cubic forms, is examined by reference to transitional flat-plate boundary layers subjected to streamwise pressure gradient and moderate free-stream turbulence, the latter causing bypass transition. One of the cubic models involves the solution of two transport equations, while the other involves three equations, one of which relates to the second invariant of turbulence anisotropy. The investigation demonstrates that, for the conditions examined, the non-linear models return a more credible representation of transition than the linear variant, although none of the models may be said to be entirely satisfactory. Thus, while non-linear modelling shows promise and offers inherent advantages through the use of a more general stress-strain linkage and elaborate calibration, further refinement is needed in the present cubic variants for transitional flows.

Computational prediction of flow around highly loaded compressor-cascade blades with non-linear eddy-viscosity models

A computational study is presented which examines the predictive performance of two variants of a cubic low-Re eddy-viscosity model when applied to the flow around two highly loaded compressor-cascade blades. Particular challenges are posed by the transitional nature of the flow and the presence of laminar leading-edge separation in oA-design conditions. Comparisons are presented for local as well as integral flow parameters, including turbulence intensity and losses. The study demonstrates that the cubic model is able to predict, in accord with experimental data and in contrast to a linear base-line model, the influential leading-edge separation preceding transition, due to the suppression of turbulence-energy generation in the impinging zone ahead of the leading edge. This attribute and a greater sensitivity to streamline curvature enable the model to give, in some flow conditions, a more realistic description of the development of the boundary layer after transition and a better prediction of the loss at oA-design incidence. However, the model also exhibits predictive weaknesses, among them an inappropriate delay in reattachment and transition to fully developed turbulence, resulting in insuAcient sensitivity to adverse pressure gradient once transition has occurred. ” 1998 Elsevier Science Inc. All rights reserved.

A general non-orthogonal collocated finite volume algorithm for turbulent flow at all speeds incorporating second-moment turbulence-transport closure, Part 2: Application

Abstract A general non-orthogonal finite-volume procedure, documented in a companion paper presented earlier, is applied to six flows, one 2D laminar, one 2D turbulent, two 3D turbulent, one inviscid transonic and one turbulent transonic. The principal aim is to convey the capabilities of the method, and this aim is pursued by choosing flows which feature a wide range of phenomena and processes. In some cases, a comparison is presented between two or more turbulence-modelling practices, and in these cases, considerable emphasis is put on an analysis of model performance and associated physical implications.