Steady Flow Simulation of Rotor-Stator Interactions with a New Unsteady Flow Model

Abstract

Numerical computations of the o w eld in turbomachines are largely used in an industrial context. Two categories of simulations are in competition: steady simulations, mainly used, and unsteady simulations, still too expensive for a systematic use. However, several studies of rotor-stator interactions showed that a steady simulation without supplementary source terms does not match well with those obtained by the timeaveraged unsteady simulation. This dierence is the consequence of the standard models, which do not take into account the unsteady part of the \deterministic stresses; these stresses are equivalent to the Reynolds’ stresses but account for the unsteady eects and particularly phenomena related to the radial diusion of the losses. Within this framework, the rst part of this study proposes a model for these kinematic deterministic stresses including the unsteady part of stresses. The model suggested is based on transport equations similar to those met in turbulence, but using deterministic stresses. In these equations, \the velocity-pressure gradient is a key parameter for all the components of deterministic stress. We thus propose a closure for this correlation term. The development of this closure is based on the results obtained using steady and unsteady numerical simulations for a transonic axial o w turbine stage. The comparisons between the original and the modelled terms show that we are able to reproduce the various concentrations of high value of \velocity-pressure gradient correlation. The last part of this study proposes the results obtained after integration of the transport of deterministic stresses model in a steady Navier-Stokes solver for the same transonic axial o w turbine stage. In a rst time, we use the deterministic stresses calculated with the results of the unsteady numerical simulation as source terms in the steady solver. This is to show the contribution of those stresses in the steady simulation. We use nally the complete model of kinematic deterministic stresses in the solver to validate the proposed model in this work.