Large Eddy Simulation of Laminar and Turbulent Shock/Boundary Layer Interactions in a Transonic Passage

Shock/boundary layer interactions (SBLI) are a fundamental fluid mechanics problem, which is relevant in a wide range of applications including transonic rotors in turbomachinery.  This paper uses wall-resolved large eddy simulation (LES) to examine the interaction of transonic flow over a curved surface with laminar and turbulent boundary layers.   The LES calculations were performed using GENESIS, which is based on HpMusic and is a variable order (up to sixth) unstructured grid solver employing a discontinuous formulation known as flux reconstruction (FR) / correction procedure via reconstruction (CPR) (Huynh, 2007). The solution is advanced in time using a pre-conditioned implicit algorithm to allow for larger time steps and hence for more efficient computation of practically-relevant, high-Reynolds number flows. The geometry created for this analytical study is a transonic passage with a convergent-divergent nozzle that expands the flow to the desired Mach number upstream of the shock and then introduces constant radius curvature near the location of a normal shock to simulate local airfoil camber. The Mach numbers in the divergent section of the transonic passage simulate single stage commercial fan blades.  This configuration was designed to be the simplest test case that is able to demonstrate relevant SBLI physics using wall-resolved LES, which avoids the uncertainty related to boundary and flow conditions in available high Reynolds number experimental data.

The results predicted with the LES calculations show significant differences between laminar and turbulent SBLI in terms of shock structure, boundary layer separation and transition, and aerodynamic losses.   When the inflow boundary layer is laminar, an unsteady separation forms significantly upstream of the main normal shock leading to the formation of a first upstream oblique wave.  The flow then transitions to turbulence causing a second set of oblique waves to form a ‘lambda foot’ with the main normal shock.   However, when the boundary layer is tripped turbulent near the throat of the transonic passage a fundamentally different flow structure is observed: the first oblique wave that was due to laminar separation is absent and a single, spatially more confined ‘lambda foot’ is formed.   These changes in the shock structure and the associated changes in the location and extent of flow separation lead to a lower wake deficit for the turbulent case.  The results of the LES calculations presented here capture the laminar and turbulent SBLI physics consistent with the classical visualizations obtained by Liepmann (1946) of transonic flow over a biconvex airfoil as well as recent measurements reported by Hergt et al. (2018) in a transonic compressor cascade.