Modelling of Unsteady Transition in Low-Pressure Turbine Blade Flows with Two Dynamic Intermittency Equations

Abstract

A transition model for describing wake-induced transition is presented based on the SST turbulence model by Menter and two dynamic equations for intermittency: one for near-wall intermittency and one for free-stream intermittency. In the Navier-Stokes equations, the total intermittency factor, which is the sum of the two, multiplies the turbulent viscosity computed by the turbulence model. The quality of the transition model is illustrated on the T106A test cascade for two Reynolds numbers, using experimental results by Stieger and Hodson for transition mainly due to kinematic wake impact on a separation bubble. The quality of the model is also revealed on the T106D test cascade using experimental results from Hilgenfeld, Stadtmuller and Fottner for wake turbulence induced transition. The test cases differ in pitch to chord ratio, Reynolds number and inlet free-stream turbulence intensity, causing different transition mechanisms. The unsteady results are presented in space-time diagrams of shape factor and wall shear stress on the suction side. The results show the capability of the model to capture the physics of unsteady transition in separated state. Inevitable shortcomings are revealed as well.Nomenclature F s = starting function for intermittency U = local velocity (m/s) U ∞ = free-stream velocity (m/s) γ = near-wall intermittency factor ζ = free-stream intermittency factor τ = turbulence weighting factor μ = molecular viscosity (Pa s) μ t = turbulent viscosity (Pa s) θ = momentum thickness Re θ = momentum thickness Reynolds number ρ ∞ U ∞ θ/μ

Transition Models for Turbomachinery Boundary Layer Flows: A Review

“…It is the version described in [123], with one further small modification. The version of [123] constitutes a repair of an earlier version [124]. The major differences are better description of relaminarisation, replacement of the ad-hoc criterion for detection of strong wake impact in separated boundary layer state (free-stream turbulence level above 2.12% together with separated state) by a more rational criterion and use of the same criterion for strong wake impact in attached boundary layer state (there was no criterion for this type of transition in the earlier version).…”

“…In [145], Piotrowski et al tested the PUIM [118] and the dynamic intermittency model of Lodefier and Dick [124] on the N3-60 for background inflow turbulence level 3%. PUIM generates quite good results, except that the relaxation to laminar state after the wake passage is incomplete, which means that the boundary layer does not return to fully laminar state, as it is the case in the experiments.…”

“…This deficiency was repaired in a later version by Kubacki et al [123] by the introduction of an onset for strong wake impact, as described before. In [122], Piotrowski et al tested the PUIM [118], the dynamic intermittency model of Lodefier and Dick [124] and the γ-Re θ model, but combined with their own correlations, on the N3-60 for background inflow turbulence level 0.4%. All models produce very good predictions of the time-varying intermittency and momentum thickness, but with a time lag of about 15% of the wake impact with respect to the experiments.…”

Numerical modelling of turbulent transition in complex geometries

“…Although there are new attempts to improve upon these models, their reliability remains to be confirmed. In this work we apply a more conservative γ-ζ model of Lodefier, Dick [5] and Kubacki et al [6] instead. The model contains transition criteria explicitly and any new criterion can be added easily.…”

Modelling of natural and bypass transition in aerodynamics

“…Langtry and Menter [1], Lodefier and Dick [2], Straka and PĜíhoda [3]). Nevertheless, these models need empirical correlations for the onset and length of the transition region and their application is limited for low free-stream turbulence.…”