k-ω SST湍流模式三维激波分离流动修正

Shock/boundary-layer separation is a typical turbulence non-equilibrium flow in the field of aeronautical aerodynamics. Accurate simulation of shock separated flow is of great significance for aerodynamic performance evaluation and optimization of transonic aircraft. The definition of eddy viscosity coefficient in conventional eddy-viscosity turbulence models (EVM), however, is not suitable for non-equilibrium flow. The Bradshaw assumption introduced by k-ω SST turbulence model for this purpose instead restricts the generation of Reynolds stress when applied to three-dimensional flow with strong adverse pressure gradient and large separation, which results in the invalidity of k-ω SST model as well as other commonly used EVMs for this kind of flow. Moreover, the existing nonlinear constitutive relation of Reynolds stress cannot effectively improve the simulation accuracy. To this end, two shock separated flow correction methods respectively based on Bradshaw assumption and length scale are proposed for k-ω SST model. The former correction relaxes the limitation of Reynolds stress generation by increasing Bradshaw constant. While based on the concept of turbulence length scale, the latter correction constructs a modified function for the dissipation term of the ω equation by using the mixing length theory, the generation-dissipation ratio of turbulent kinetic energy and a newly defined ratio of length scale to improve the modeling length scale in three-dimensional shock separated flow. The two methods both get better simulation results for the transonic flow of ONERA M6 wing at high angle of attack than those of Reynolds stress model. Further Reynolds stress analysis reveals that the concept of "major Reynolds-stress component" in three-dimensional shock separated flow is no longer tenable since the magnitude of each Reynolds-stress component is close. The grid convergence analysis, and verifications on other angles of attack and the wall-function law of turbulent boundary layer on the flat plate further confirm the validity, applicability and universality of the proposed correction methods.