Deterministic Stress Modeling of Hot Gas Segregation in a Turbine

Abstract

Simulation of unsteady viscous turbomachinery flowfields is presently impractical as a design tool due to the long run times required. Designers rely predominantly on steady-state simulations, but these simulations do not account for some of the important unsteady flow physics. Unsteady flow effects can be modeled as source terms in the steady flow equations. These source terms, referred to as Lumped Deterministic Stresses (LDS), can be used to drive steady flow solution procedures to reproduce the time-average of an unsteady flow solution. The goal of this work is to investigate the feasibility of using inviscid lumped deterministic stresses to model unsteady combustion hot streak migration effects on the turbine blade tip and outer air seal heat loads. The LDS model is obtained from an unsteady inviscid calculation. The inviscid LDS model is then used with a steady viscous computation to simulate the time-averaged viscous solution. The feasibility of the inviscid LDS model is demonstrated on a single-stage, three-dimensional, vane-blade turbine with a hot streak entering the vane passage at midpitch and midspan. The steady viscous solution with the LDS model is compared to the time-averaged viscous, steady viscous, and time-averaged inviscid computations. The LDS model reproduces the time-averaged viscous temperature distribution on the outer air seal to within 2.3 percent, while the steady viscous has an error of 8.4 percent, and the time-averaged inviscid calculation has an error of 17.2 percent. The solution using the LDS model is obtained at a cost in CPU time that is 26 percent of that required for a time-averaged viscous computation. [S0889-504X(00)00601-2]

Linear Deterministic Source Terms for Hot Streak Simulations

“…Previous researchers 2 have shown that the LDS approach works when derived from the exact nonlinear unsteady viscous equations and also when inviscid nonlinear unsteady solutions are used in fully viscous problems. 3 Hence, it is suf cient to compare the time averaged nonlinear unsteady inviscid solution to the source term augmented steady state inviscid solution. That comparison is presented in this section.…”

“…This approach is particularly convenient because it involves only the calculation of a single residual function. This essentially is the approach taken by Busby et al 3 and was the route chosen in the current work for nding the LDS obtained from the nonlinear unsteady TURBO code.…”

“…7 The purpose of this paper is to compare how well the linear solvers work as compared to the nonlinear unsteady approaches. In light of the recent work reported by Busby et al, 3 it is suf cient to demonstrate the technique through comparisons of results obtained with inviscid solutions.…”

“…A variationof this approachhas been employed recently by Busby et al, 3 who used a lower-delity (inviscid) set of equations to compute approximate source terms in a relatively short time. Their work showed that inviscid analyses faithfully approximate the hot streak unsteadiness source terms.…”

Neural Network Modeling of Deterministic Unsteadiness Source Terms

“…The LDST technique has been used in this latter fashion by Sondak et al 1 and Busby et al 2 to model rotor-stator interaction unsteadiness in turbomachinery. They performed unsteady inviscid simulations to extract the lumped deterministic stress field and then applied it as a source term in steady viscous calculations to model unsteady flow effects.…”