Computation of shock/boundary-layer interactions in bump channels with transport-type turbulence models

Abstract

In this paper, an explicit time-marching finite-volume scheme has been used together with a number of convergence acceleration techniques such as the multigrid strategy. Two types of turbulence models, a Johnson—King (J—K) model and a two-layer k-ε/k-l model, have been incorporated and modified to model internal compressible flows with multiple walls. Some modifications have been made of the inner layer viscosity formulations of the J—K model in order to improve its predictive capability for flow separation. Partially implicit treatment of the transport-type equations of turbulence in the models is adopted, because the source terms in these equations can cause numerical stiffness when there are flow separation, sharp gradients and high cell-aspect ratio near the solid wall. A two-dimensional arc-bump flow investigated experimentally by Liu and Squire [X. Liu and L.C. Squire, Interaction on curved surface at transonic speed, in: Turbulent Shear/Shock Wave Interactions, IUTAM Symposium Palaiseau 1985 (Springer, Berlin Heidelberg 1985) 93–104.] was calculated using the J—K model with satisfactory agreement with the corresponding measurement. Although efficient and accurate, it is found that the J—K model lacks the theoretical generality to be extended to model three-dimensional (3D) complex internal flows with multiple walls. Therefore, a two-layer k-ε model is employed for 3D flow computation. Various measures are adopted to ensure stable and convergent numerical solution. A three-dimensional transonic channel flow with multiple shock/boundary layer interactions was studied with the aforementioned two-layer model and numerical methods. The results are compared with experimental measurements [J. Cahen, V. Couaillier, J. Delery and T. Pot, Validation of Navier—Stokes code using a k-ε turbulence model applied to a three-dimensional transonic tunnel, AIAA paper AIAA-93-0293, AIAA 1993] and numerical results obtained by using a Low-Reynolds-Number (LRN) k-ε model [VUB/FFA, Turbulence Models in EURANUS and the 3D Delery bump, Technical Report SNWP3.3/01, VUB, Pleinlaan 2, 1050 Brussels, Belgium and FFA, P.O. Box 11021, S-161 11 Bromma, Sweden 1993]. Compared with other (LRN) two-equation models, the two-layer model implemented is promising in modeling very complex 3D internal flows in terms of efficiency, robustness and accuracy. The two-layer model permits uniform distribution of flow properties to be specified as initial condition which makes the simulation easier to be carried out.