On the Simulation of Unsteady Turbulence and Transition Effects in a Multistage Low Pressure Turbine: Part I — Verification and Validation

Abstract

This is the first part of a series of three papers on the simulation of turbulence and transition effects in a multistage low pressure turbine. In this first part, the extension, verification and validation of a Harmonic Balance (HB) method recently proposed by the authors to fully include established turbulence and transition models in the method is presented. As an alternating frequency/time-domain type method the implemented HB solver has the advantage of being able to utilize models (e.g. boundary conditions or residual functions) formulated in either the frequency- or time-domain. On the one hand this allows highly accurate nonreflecting boundary conditions formulated in the frequency-domain to be used along entry, exit or interface boundaries, and on the other hand complex nonlinear terms formulated in the time-domain to be used to describe nonlinear effects. Nevertheless, the wish to minimize the number of harmonics used to describe a given time-periodic unsteady flow, coupled with the often highly nonlinear nature of turbulence and transition models makes the full inclusion of such models in the HB method challenging. In this work the integration of Menter’s SST two-equation k–ω turbulence model along with Menter and Langtry’s two-equation γ–Reθ transition model in the context of a general framework for transport equations in the CFD solver TRACE is described in detail. Following the basic verification of the underlying transport equation framework, the implemented models are used to compute the well known high lift, low pressure turbine airfoil T106C and results are compared with the available experimental data as well as results from more conventional time-domain simulations. Alongside the basic validation of the models this testcase is furthermore used to investigate the importance of including higher harmonics, as opposed to only the zeroth harmonic, of the turbulence and transition models for the accurate prediction of the time-mean flow.

Flutter Analysis of a Transonic Steam Turbine Blade with Frequency and Time-Domain Solvers

“…In this work, the steady and time-domain solvers were run in combination with Wilcox' twoequation turbulence model [18]. In the harmonic balance solver, resolving the unsteadiness of turbulence quantities by higher harmonics is optional [19]. The linearised solver is always based on the frozen turbulence assumption, i.e., the eddy viscosity is simply taken as the one from the steady solution.…”