The Effects of Turbulence Length Scale on Turbulence and Transition Prediction in Turbomachinery Flows

Abstract

An approach for estimation of the turbulence length scale at the inflow boundary is proposed and presented. This estimation yields reasonable turbulence decay, supporting the transition model in accurately predicting the laminar-turbulent transition location and development. As an additional element of the approach, the sensitivity of the turbulence model to free-stream values is suppressed by limiting the eddy viscosity in non-viscous regions. Therefore the well known realizability constraint after Durbin [1] is modified. The method is implemented in DLR’s turbomachinery flow solver TRACE in the framework of the k–ω turbulence model by Wilcox [2] and the γ–Reθ transition model by Langtry and Menter [3]. The improved model is tested to the T106A turbine testcase and validated at the T161 turbine cascade under low speed conditions and T170 turbine cascade at high speed conditions.

Improved Turbulence Prediction in Turbomachinery Flows and the Effect on Three-Dimensional Boundary Layer Transition

“…Thus, it will undergo a laminar-turbulent transition process in the cross-flow direction [17]. For this purpose, the recently extended γ-Re Θ transition model after Menter and Langtry [3] in combination with the improved turbulence prediction [10] shows its capability to better predict these kinds of flows and will now be shown as a follow up to Bode et al [7] in more detail on the Durham and Langston cascades. Later on, the ability of the improved numerical method on multistage test-cases will be shown, too.…”

“…Turbulence length scale effects on turbulence and transition prediction have been incorporated into the respective models, cf. Bode et al [10]. The validation of today's CFD-solvers especially against experimental cascade data with medium or high inflow turbulence intensity from 3 ≤ Tu ≤ 10% and in combination with moderate turbulence length scales (l T ∼ 0.01 m), (l T /l∼ 0.1 with l ∼ 0.1 m chord of a typical turbine cascade) ends up in an unphysical, too high eddy viscosity, leading to a false prediction of the turbulence and, hence, boundary layer flow due to the violation of the realizability constraint.…”

“…For this reason, a criterion for the determination of viscous regions (boundary layers and wakes) has been developed as an additional element of the implemented approach (cf. [10]). This criterion is based on the large values of turbulent dissipation rate ω in the vicinity of viscous walls.…”

“…The time-scale bound is only applied in these viscous regions, effectively preventing the eddy viscosity destruction in non-viscous areas by multiplying the time-scale bound by a factor b v , which is 1.0 in the boundary layer and the wake region and 0.1 in the free stream (cf. [10])…”

“…In the present paper, the k-ω turbulence model after Wilcox (1988) [2] with a modification after Bode et al [10] to improve the turbulence prediction in combination with the transition model after Menter and Langtry [3] and its extension to three-dimensional boundary layer transition after Menter and Smirnov [8] will be used to further improve the turbulence prediction and hence, the transitional behavior and its impact on the loss prediction. Therefore, the improved numerical method will be validated against test-cases with increasing complexity and will present the ability of the used numerical method to accurately predict the turbulence and transitional behavior of three-dimensional single and multistage turbomachinery test-cases.…”