Predictions of a Supersonic Turbulent Flow in a Square Duct

Abstract

In this paper we have confirmed that eddy viscosity turbulence models are inadequate to predict secondary vortical flows developed from corners in internal flows. To remedy this shortcoming, we have added the quadratic constitutive relation (QCR) of Spalart to the one- and two-equation SA and SST turbulence models, respectively. The results of QCR with the SA and SST turbulence models have been validated against experimental data of Davis and Gessner for supersonic flow through a square duct. The approach is shown to be simple to implement and overall agreement is seen to improve with the use of QCR. Introduction: Supersonic flow through a square duct is altered by secondary vortical flow developing from the corners. These secondary flows are generated by Reynolds stress gradients acting in the corner region and appear to have similar structure to those found in subsonic flow through square ducts (1-3). Such flow is representative of various airplane inlets and therefore it is important to understand and predict the impact of this secondary flow on inlet pressure recovery and distortion. An experimental study was performed at the University of Washington to gain a better understanding of how the secondary flow associated with corners affects local flow conditions in a square duct over the development length (3). This configuration was utilized in this study to validate and improve the RANS turbulence models utilized for corner flows at Boeing. Accurate prediction of the flow around and through the aircraft is essential for design improvement, risk mitigation, and wind-tunnel and flight test reduction. At Boeing, the RANS approach is used routinely for design and analysis of our configurations. While RANS has proven to be a powerful approach for flow-field prediction, it still has some shortcomings even for steady state flow predictions. The one- and two-equation SA (4) and SST (5) eddy viscosity turbulence models, respectively, are still the workhorses for routine applications. The Reynolds