Reynolds averaged simulation of flow and heat transfer in ribbed ducts

Abstract

The accuracy of modern eddy-viscosity type turbulence models in predicting turbulent flows and heat transfer in complex passages is investigated. The particular geometries of interest here are those related to turbine blade cooling systems. This paper presents numerical data from the calculation of the turbulent flow field and heat transfer in two-dimensional (2D) cavities and three-dimensional (3D) ribbed ducts. It is found that heat transfer predictions obtained using the v²–f turbulence model for the 2D cavity are in good agreement with experimental data. However, there is only fair agreement with experimental data for the 3D ribbed duct. On the wall of the duct where ribs exist, predicted heat transfer agrees well with experimental data for all configurations (different streamwise rib spacing and the cavity depth) considered in this paper. But heat transfer predictions on the smooth-side wall do not concur with the experimental data. Evidence is provided that this is mainly due to the presence of strong secondary flow structures which might not be properly simulated with turbulence models based on eddy viscosity.

Introduction

Accurate evaluation of heat loads in the components of a gas-turbine engine is a key factor in the development of new, efficient engines. Common design techniques utilize experimental data correlations to quickly estimate the heat transfer coefficients (Webb et al., 1971). These methods do not reveal the underlying mechanism of turbulence and heat transfer for the device in question. They often are inaccurate. Owing to advances in available computer resources, elaborate numerical techniques, based on the solution of the full 3D Reynolds averaged Navier–Stokes (RANS) equations, are now being used to shed light on the flow phenomena and to provide guidelines to improve design methodology. In the RANS approach, the Navier–Stokes equations are averaged and the Reynolds stresses are computed with a turbulence model. The choice of turbulence model is crucial, as it directly affects the computational requirements and the accuracy of the predictions. In particular, because most of the gas turbine cooling systems promote turbulence close to the walls to enhance heat transfer, precise near-wall turbulence modeling is crucial to ensure accurate heat transfer predictions.

In this paper, the ability to predict heat transfer coefficients in ducts with artificial roughness elements (ribs) is investigated. To evaluate the accuracy of the predictions, numerical solutions are compared to the experimental data of Rau et al. (1998). This particular data set was chosen because both flow field and heat transfer data are available. Additional experimental data that can be used to assess the accuracy of the numerical predictions are available from Han et al., 1978, Han et al., 1985, Chyu and Wu (1989), Hirota et al. (1992) and Liou et al. (1993b).

Numerical predictions of the flow and heat transfer in rib-roughened passages have been conducted previously by several investigators: Simoneau and Simon (1992) showed that the conventional k–ϵ turbulence model with wall functions does not accurately predict the heat transfer level, due to the presence of massive separation in the flow field; Stephens (1995) found that the k–ω model showed only reasonable qualitative agreement with experimental data; Liou et al. (1993a) obtained good agreement with experimental data (on the symmetry plane) in a 2D Navier–Stokes calculation with the k–ϵ–A algebraic stress and heat flux model––however, the application of this model to complex 3D problems is computationally expensive and the model is numerically stiff (Gatski and Speziale, 1993; Speziale, 1997). More recently, it has been shown by Iacovides (1998) that two-layer k–ϵ with the effective viscosity model gives unsatisfactory heat transfer predictions in rotating ribbed passages. Better results were obtained with the two-layer approach coupled to a low-Re differential stress model. Computations with low-Re models were carried out by Iacovides and Raisee (1999), who found that improved heat transfer predictions could be obtained by introducing a differential version of the Yap length scale correction term which is independent of the wall distance.

Here, we revisit the ribbed duct problem. Since it has been shown that simplified wall treatments (wall functions, two layer, etc.) or methods that use empirical correlations (low-Re models) cannot correctly capture the separation and reattachment that takes place between successive ribs, we will examine the predictive capability of two more recent turbulence models: v²–f and Spalart–Allmaras (S–A).

The v²–f turbulence model was developed around the elliptic relaxation method for representing near-wall phenomena (Durbin and Pettersson-Reif, 2001). Unlike the low-Re approach, this is done without the aid of damping functions. It has been successfully applied to separated flow (Durbin, 1995), 3D boundary layers (Parneix et al., 1998) and impinging jets (Behnia et al., 1998, Behnia et al., 1999). In the present work, v²–f is used to predict flow and heat transfer in a 3D duct with ribs and in a model configuration resembling the tip of an axial turbine blade (Metzger et al., 1989).

Simulations have also been carried out with the S–A model. This is a one-equation, eddy-viscosity transport formulation, developed by Spalart and Allmaras (1992) and has proven to be both robust and accurate in aerodynamic applications (Bardina et al., 1997). Its accuracy for predicting internal flows has been largely untested, but is now addressed in this paper and in Kalitzin and Iaccarino (1999) (see also Durbin and Pettersson-Reif, 2001). Results from the standard two-layer k–ϵ model (Chen and Patel, 1988) are also included here for comparison.