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The purpose of this paper is to present a new eddy‐viscosity formulation designed to exhibit a correct response to streamline curvature and flow rotation. The formulation is implemented into a linear k‐ ε turbulence model with a two‐layer near‐wall treatment in a commercial computational fluid dynamics (CFD) solver.

A simple, robust formula is developed for the eddy‐viscosity that is curvature/rotation sensitive and also satisfies realizability and invariance principles. The new model is tested on several two‐ and three‐dimensional problems, including rotating channel flow, U‐bend flow and internally cooled turbine airfoil conjugate heat transfer. Predictions are compared to those with popular eddy‐viscosity models.

Converged solutions to a variety of turbulent flow problems are obtained with no additional computational expense over existing two‐equation models. In all cases, results with the new model are superior to two other popular k‐ ε model variants, especially for regions in which rapid rotation or strong streamline curvature exists.

The approach adopted here for linear eddy‐viscosity models may be extended in a straightforward manner to non‐linear eddy‐viscosity or explicit algebraic stress models.

The new model is a simple “plug‐in” formula that contains important physics not included in most linear eddy‐viscosity models and is easy to implement in most flow solvers.

The present model for curved and rotating flows is developed without the need for second derivatives of velocity in the formulation, which are known to present difficulties with unstructured meshes.

In recent years, the partially averaged Navier–Stokes (PANS) methodology has earned acceptability as a viable scale-resolving bridging method of turbulence. To further enhance its capabilities, especially for simulating separated flows past bluff bodies, this paper aims to combine PANS with a non-linear eddy viscosity model (NLEVM).

The authors first extract a PANS closure model using the Shih’s quadratic eddy viscosity closure model [originally proposed for Reynolds-averaged Navier–Stokes (RANS) paradigm (Shih et al., 1993)]. Subsequently, they perform an extensive evaluation of the combination (PANS + NLEVM).

The NLEVM + PANS combination shows promising result in terms of reduction of the anisotropy tensor when the filter parameter (f_k) is reduced. Further, the influence of PANS filter parameter f on the magnitude and orientation of the non-linear part of the stress tensor is closely scrutinized. Evaluation of the NLEVM + PANS combination is subsequently performed for flow past a square cylinder at Reynolds number of 22,000. The results show that for the same level of reduction in f_k, the PANS + NLEVM methodology releases significantly more scales of motion and unsteadiness as compared to the traditional linear eddy viscosity model (LEVM) of Boussinesq (PANS + LEVM). The authors further demonstrate that with this enhanced ability the NLEVM + PANS combination shows much-improved predictions of almost all the mean quantities compared to those observed in simulations using LEVM + PANS.

Based on these results, the authors propose the NLEVM + PANS combination as a more potent methodology for reliable prediction of highly separated flow fields.

Combination of a quadratic eddy viscosity closure model with PANS framework for simulating flow past bluff bodies.

Performance of various k‐ε models on turbulent forced convection in a channel with periodic ribs is assessed.

The influence of the Yap correction and the non‐linear stress‐strain relation on the predictions of mean‐flow, turbulence quantities and local heat transfer rate is examined. The effect of thermal boundary conditions on the heat transfer predictions is investigated by employing both the prescribed heat flux approach and the conjugate heat transfer approach.

It was found that the inclusion of the Yap correction in the ε‐equation significantly improves the predictions of mean velocity and wall heat transfer for both high‐Reynolds number and low‐Reynolds number k‐ε models in the present ribbed channel flow with massive flow separation. The employment of the non‐linear stress‐strain relation only marginally improves the predictions of turbulence quantities: the turbulence anisotropy is reproduced although the level of turbulence intensity is still too low. In general, the conjugate heat transfer approach predicts better average Nusselt number than the prescribed heat flux approach. However, both approaches under‐predict the experimental value by about 28‐33 percent when the low‐Reynolds number k‐ε model of Lien and Leschziner (1999) with the Yap term is adopted.

Thorough numerical treatments of the thermal boundary conditions at the solid‐liquid interface, and detailed periodic condition in the periodic regime, were given in the paper to benefit researchers interested in solving similar problems.

The purpose of this paper is to investigate turbulent fluid flow and heat transfer through passages with an array of either detached or alternative attached‐detached ribs of square cross‐section.

The finite‐volume method in a partially staggered grid system has been applied. For the modeling of turbulence, the zonal as well as the linear and non‐linear low‐Reynolds number k  −  ε models have been employed.

The numerical results show that the presence of the ribs produces a very complex flow in the channel. The mean flow predictions for the channel with detached ribs show that the low‐Re k  −  ε models are able to reproduce most of the experimentally observed flow features away from the ribbed wall, but return lower stream‐wise velocities close to the wall. Additionally, all low‐Re k  −  ε models underpredict the stream‐wise turbulence intensity whilst producing correct cross‐stream turbulence intensity levels close to the measured data. All three turbulence models fail to completely reproduce the distribution of Nusselt number. Among three turbulence models examined in this work, the zonal k  −  ε model produces the best heat transfer predictions.

The work contributes in understanding of the flow and thermal development in passages with detached ribs. The present set of 2D and steady heat and fluid flow comparisons establishes a base‐level for more realistic three‐dimensional and unsteady computations. The results of this study may be of interest to engineers attempting to re‐design the internal cooling system of gas turbine blades and to researchers interested in the turbulent flow‐modification aspects of heat transfer enhancement of forced convection in ribbed passages.

A numerical scheme that has already proved to be efficient and accurate for laminar heat transfer is extended for turbulent, axisymmetric heat transfer calculations. The extended scheme is applied to the steady‐state heat transfer of axisymmetric turbulent jets, impinging onto a flat plate. Firstly, the low‐Reynolds version of the standard k‐ε model is employed. As is well known, the classical k‐ε turbulence model fails to predict the heat transfer of impinging jets adequately. A non‐linear k‐ε model, with improved ε‐equation, yields much better results. The numerical treatment of the higher order terms in this model is described. The effect on the heat transfer predictions of a variable turbulent Prandtl number is shown to be small. It is also verified that the energy equation can be simplified, without affecting the results. Results are presented for the flow field and the local Nusselt number profiles on the plate for impinging jets with different distances between the pipe exit and the flat plate.

A numerical investigation has been undertaken to study fluid flow and heat transfer through artificially rib‐roughened channels. Such flows are of particular interest in internal cooling of advanced gas turbine blades. The main objective is to test the suitability of recently developed variants of the cubic non‐linear k‐ε model for the prediction of cooling flows through ribbed passages. The numerical approach used in this study is the finite‐volume method together with the SIMPLE algorithm. For the modelling of turbulence, the Launder and Sharma low‐Re k‐ε model and a new version of the non‐linear low‐Re two equation model that have been recently shown to produce reliable thermal predictions in impinging jet flows and also flows through pipe expansions, have been employed. Both models have been used with the form of the length‐scale correction term to the dissipation rate originally proposed by Yap and also more recently developed differential version, NYap. The numerical results over a range of flow parameters have been compared with the reported experimental data. The mean flow predictions show that both linear and non‐linear k‐ε models with NYap can successfully reproduce the distribution of the measured streamwise velocity component, including the length and width of the separation bubble, formed downstream of each rib. As far as heat transfer predictions are concerned, the recent variant of the non‐linear k‐ε leads to marked improvements in comparison to the original version of Craft et al. Further improvements in the thermal prediction result through the introduction of a differential form of the turbulent length scale correction term to the dissipation rate equation. The version of the non‐linear k‐ε that has been shown in earlier studies to improve thermal predictions in pipe expansions and impinging jets; it is thus found to also produce reasonable heat transfer predictions in ribbed passages.

An original finite element scheme for advection‐diffusion‐reaction problems is presented. The new method, called spotted Petrov‐Galerkin (SPG), is a quadratic Petrov‐Galerkin (PG) formulation developed for the solution of equations where either reaction (associated to zero‐order derivatives of the unknown) and/or advection (proportional to first‐order derivatives) dominates on diffusion (associated to second‐order derivatives). The addressed issues are turbulence and advective‐reactive features in modelling turbomachinery flows.

The present work addresses the definition of a new PG stabilization scheme for the reactive flow limit, formulated on a quadratic finite element space of approximation. We advocate the use of a higher order stabilized formulation that guarantees the best compromise between solution stability and accuracy. The formulation is first presented for linear scalar one‐dimensional advective‐diffusive‐reactive problems and then extended to quadrangular Q2 elements.

The proposed advective‐diffusive‐reactive PG formulation improves the solution accuracy with respect to a standard streamline driven stabilization schemes, e.g. the streamline upwind or Galerkin, in that it properly accounts for the boundary layer region flow phenomena in presence of non‐equilibrium effects.

The numerical method here proposed has been designed for second‐order quadrangular finite‐elements. In particular, the Reynolds‐Averaged Navier‐Stokes equations with a non‐linear turbulence closure have been modelled using the stable mixed element pair Q2‐Q1.

This paper investigated the predicting capabilities of a finite element method stabilized formulation developed for the purpose of solving advection‐reaction‐diffusion problems. The new method, called SPG, demonstrates its suitability in solving the typical equations of turbulence eddy viscosity models.

Hybrid Reynolds-averaged Navier–Stokes large eddy simulation (RANS-LES) methods have become popular for simulation of massively separated flows at high Reynolds numbers due to their reduced computational cost and good accuracy. The current study aims to examine the performance of LES and hybrid RANS-LES model for a given grid resolution.

For better assessment and contrast of model performance, both mean and instantaneous flow fields have been investigated. For studying instantaneous flow, proper orthogonal decomposition has been used.

Current analysis shows that hybrid RANS-LES is capable of achieving similar accuracy in prediction of both mean and instantaneous flow fields at a very coarse grid as compared to LES.

Focusing mostly on the practical applications of computation, most of the attention has been given to the prediction of one-point flow statistics and little consideration has been put to two-point statistics. Here, two-point statistics has been considered using POD to investigate unsteady turbulent flow.

This paper aims to predict turbulent flow and heat transfer through different channels with periodic dimple/protrusion walls. More specifically, the performance of various low-Re k-ε turbulence models in prediction of local heat transfer coefficient is evaluated.

Three low-Re number k-ε turbulence models (the zonal k-ε, the linear k-ε and the nonlinear k-ε) are used. Computations are performed for three geometries, namely, a channel with a single dimpled wall, a channel with double dimpled walls and a channel with a single dimple/protrusion wall. The predictions are obtained using an in house finite volume code.

The numerical predictions indicate that the nonlinear k-ε model predicts a larger recirculation bubble inside the dimple with stronger impingement and upwash flow than the zonal and linear k-ε models. The heat transfer results show that the zonal k-ε model returns weak thermal predictions in all test cases in comparison to other turbulence models. Use of the linear k-ε model leads to improvement in heat transfer predictions inside the dimples and their back rim. However, the most accurate thermal predictions are obtained via the nonlinear k-ε model. As expected, the replacement of the algebraic length-scale correction term with the differential version improves the heat transfer predictions of both linear and nonlinear k-ε models.

The most reliable turbulence model of the current study (i.e. nonlinear k-ε model) may be used for design and optimization of various thermal systems using dimples for heat transfer enhancement (e.g. heat exchangers and internal cooling system of gas turbine blades).

To perform 3D unsteady Reynolds Averaged Navier‐Stokes (URANS) simulations to predict turbulent flow over bluff body.

Turbulence closure is achieved through a non‐linear k−ε model. This model is incorporated in commercial FLUENT software, through user defined functions (UDF).

The study shows that the present URANS with standard wall functions predicts all the major unsteady phenomena, with a good improvement over other URANS reported so far, which incorporate linear eddy viscosity models. The results are also comparable with those obtained by LES for the same test case.

When comparing the computational time required by the present model and by LES, the accuracy achieved is significant and can be used for simulating 3D unsteady complex engineering flows with reasonable success.