Finite-Element Analysis of Turbulent Flow in Annular Exhaust Diffusers of Gas Turbine Engines

Abstract

A finite-element model of the turbulent flow field in the annular exhaust diffuser of a gas turbine engine is developed. The analysis is based on a modified version of the Petrov-Galerkin weighted residual method, coupled with a highly accurate biquadratic finite element of the Lagrangian type. The elemental weight functions in the finite-element formulation are so defined to ensure upwinding of the convection terms in the flow-governing equations while reverting to the conventional Galerkin’s definition for all other terms. This approach is equivalent to altering the integration algorithm as the convection terms in the element equations are derived, with the exception that the latter technique is tailored for low-order elements of the linear and bilinear types. Numerical results of the current analysis indicate that spurious pressure modes associated with this type of inertia-dominated flow are alleviated while the false numerical diffusion in the finite-element equations is simultaneously minimized. Turbulence of the flow field is modeled using the two-layer algebraic turbulence closure of Baldwin and Lomax, and the eddy viscosity calculations are performed at variably spaced points which are different from those in the finite-element discretization model. This enhances the accuracy in computing the wall shear stress and the inner/outer layer interface location. The computational model is verified using a set of experimental data at design and off-design operation modes of the exhaust diffuser in a commercial gas turbine engine. Assessment of the results in this case is favorable and, as such, provides evidence of the model capability as an accurate predictive tool in the diffuser detailed design phase.