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TECHNICAL PAPERS

# Computations of Flow Field and Heat Transfer in a Stator Vane Passage Using the $v2¯−f$ Turbulence Model

[+] Author and Article Information
A. Sveningsson1

Division of Thermo and Fluid Dynamics, Department of Mechanical Engineering,  Chalmers University of Technology, SE-412 96, Gothenburg, Swedenandreas.sveningsson@chalmers.se

L. Davidson

Division of Thermo and Fluid Dynamics, Department of Mechanical Engineering,  Chalmers University of Technology, SE-412 96, Gothenburg, Sweden

1

To whom correspondence should be addressed.

J. Turbomach 127(3), 627-634 (Jan 13, 2005) (8 pages) doi:10.1115/1.1929820 History: Received May 17, 2004; Revised January 13, 2005

## Abstract

In this study three-dimensional simulations of a stator vane passage flow have been performed using the $v2¯−f$ turbulence model. Both an in-house code (CALC-BFC ) and the commercial software FLUENT are used. The main objective is to investigate the $v2¯−f$ model’s ability to predict the secondary fluid motion in the passage and its influence on the heat transfer to the end walls between two stator vanes. Results of two versions of the $v2¯−f$ model are presented and compared to detailed mean flow field, turbulence, and heat transfer measurements. The performance of the $v2¯−f$ model is also compared with other eddy-viscosity-based turbulence models, including a version of the $v2¯−f$ model, available in FLUENT . The importance of preventing unphysical growth of turbulence kinetic energy in stator vane flows, here by use of the realizability constraint, is illustrated. It is also shown that the $v2¯−f$ model predictions of the vane passage flow agree well with experiments and that, among the eddy-viscosity closures investigated, the $v2¯−f$ model, in general, performs the best. Good agreement between the two different implementations of the $v2¯−f$ model (CALC-BFC and FLUENT ) was obtained.

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## Figures

Figure 1

Computational domain and the location of the stagnation plane and the plane SS that will be used for plotting. When the coordinate η is used η=0 is located on the suction side, η=1 on the pressure side.

Figure 2

End-wall Stanton number along the stagnation line (Y=0) and spanwise velocity along a line crossing the center of the horseshoe vortex roll-up (Y=0,Z=0.014S)

Figure 3

Contours of k∕Uin2. Inlet FBW from left. Left: v2¯−f Model 1 without realizability constraint; Right: As left but with relizability constraint. Contour intervals of 0.001.

Figure 4

Measured and predicted (v2¯−f model 1 and realizable k−ε model) Stanton number along the midspan of the vane. s∕C⩾0: suction side. s∕C⩽0: pressure side.

Figure 5

Contours of k∕Uin2×102 in the stagnation plane (contour interval of 0.01k∕Uin2)

Figure 6

Velocity vectors in the stagnation plane showing the horseshoe vortex roll-up

Figure 7

Top: Streamlines of FLUENT v2¯−f computation illustrating the horseshoe and leading-edge corner vortices in the stagnation plane. Middle: Measured and predicted (FLUENT ) Stanton number along the end-wall stagnation line. Bottom: CALC-BFC predictions.

Figure 8

Predicted secondary velocities in the lower half of plane SS (cf. Fig. 1). The reference arrows correspond to 20% of the maximum total velocity in the plane. Bottom: Endwall Stanton number along the bottom of plane SS.

Figure 9

Streamlines illustrating the secondary fluid motion responsible for the increase in end-wall heat transfer between two stator vanes. Streamlines A indicate the center of the pressure leg of the horseshoe vortex. Streamlines B, entering well above the end wall, are convected downward and spread along the endwall. Plane SS is colored with helicity, light region indicating clockwise rotation (passage vortex), dark region indicating anti-clockwise rotation (suction-side leg of horseshoe vortex).

Figure 10

Stanton number at the end wall along lines A-C

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