Further Development of a Dynamic Intermittency Model For Wake-Induced Transition

Abstract

The transition model studied in this paper uses an equation for free-stream intermittency and one for near-wall intermittency, combined with the SST turbulence model. The model was already assessed in earlier work for wake-induced transition in boundary layers in separated state and in attached state. For separated state transition, the model predicts the start and growth of transition very well, except for the impossibility to describe the breakdown of the roll-up vortices in a 2D RANS simulation. In attached state transition, the model has the tendency to generate a delayed start of transition and a too slow growth rate in the initial phase of transition. We demonstrate that a delayed start of transition is inherent for a RANS simulation. We propose a repair for the too slow growth rate in the initial stage of the transition. Additionally, both for wake-induced transition in separated state and in attached state, the original model has the tendency to predict a state too near to laminar in between wakes at the trailing edge. We demonstrate that this is caused by the too rapid destruction of the near-wall intermittency during relaminarization and in the lack of activation of near-wall intermittency for low turbulence level in the free stream. We propose a repair for both deficiencies. The fourth improvement is that we take into account the influence of the free stream turbulence length scale in the criteria for onset of transition. We demonstrate the high quality of the improved model for wake-induced transition on a steam turbine stator blade for outlet Reynolds number 600,000 and two levels of turbulence in the background flow: 3% and 0.4%. Nomenclature γnear-wall intermittency factor ζ free-stream intermittency factor τ turbulence weighting factor, τ = γ + ζ β γ growth factor for near-wall intermittency k turbulent kinetic energy (m 2 /s 2 ) ω specific dissipation rate (s −1 ) θ momentum thickness (mm) F s starting function for intermittency H 12 shape factor S magnitude of the shear rate (s −1 ) S s space, scaled with suction side length τ /T time, scaled with wake period TKE turbulent kinetic energy, scaled with square of exit velocity Tu local free stream turbulence intensity U ∞ velocity at edge of boundary layer (m/s)

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].…”

“…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).…”

“…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 the version described in [123] the old criterion of 2.12% was left active. This is not necessary and it was later switched off.…”

“…Geometric characteristics of the N3-60 cascade are: blade chord 300 mm, axial blade chord 203.65 mm, blade pitch 240 mm. Full details on the blade geometry are specified in [123]. In the experiments, the wake generator was a wheel of pitch diameter D p = 1950 mm with cylindrical bars rotating in a plane perpendicular to the flow direction.…”

Simulation of transitional flows through a turbine blade cascade with heat transfer for various flow conditions

“…The bypass transition models come out mostly from the intermittency concept using the algebraic and/or transport equation for the intermittency coefficient, see e.g. Thermann and Niehuis [5], Straka and PĜíhoda [2] and/or Langtry and Menter [6], Kubacki et al [7], and Menter et al [8]. Besides, the three-equation k-kL-Z model by Walters and Cokljat [3] with the equation for the energy of non-turbulent fluctuations can be used for transition modelling as well.…”