Numerical investigation of forced transitional and turbulent wall jets

Abstract

The generation and development of large 2D vortical disturbances (coherent structures) in forced transitional and turbulent wall jets is investigated using several numerical techniques. For the early and late transition stages, 2D Numerical Simulation (2D-NS) and Direct Numerical Simulation (DNS) are employed, while for the forced turbulent flow Unsteady Reynolds-Averaged Navier-Stokes (URANS) calculations are used including a new, simplified approach called "Stability" RANS (SRANS) which substantially reduces the computational effort when compared to URANS. As base flows for the investigations, three prototypical wall jets are considered: Low and high Reynolds number laminar wall jets, represented by the Glauert similarity solution, and a turbulent wall jet (Rej = 10,000), modeled using a nearly self-preserving RANS solution starting at a virtual nozzle. The investigations of 2D vortical disturbances in both the transitional and the turbulent wall jet follow the 2D stages of shear flow transition, beginning with receptivity to harmonic forcing, followed by linear and nonlinear disturbance development, and 2D secondary instability. It is shown that the disturbance development in the turbulent flow parallels the one in the transitional flow in many respects. In particular, a 2D subharmonic resonance is found in both flows leading to a subharmonic resonance cascade with repeated vortex merging. Competing 3D fundamental and subharmonic resonances in the transitional wall jet are studied using a linearized Navier-Stokes code and 3D DNS. These 3D secondary instabilities weaken or diminish the 2D disturbances and lead to turbulent breakdown. Yet, for large amplitude forcing, the 3D resonances are surpassed by the 2D subharmonic resonance which leads to vortex merging upstream of the breakdown. With a 3D DNS of bypass transition, where a high Reynolds number laminar wall jet is tripped with large amplitude 3D forcing, it is demonstrated that 2D vortical structures persist in the presence of 3D turbulent fluctuations. In this simulation, 2D vortical structures emerge during transition and undergo repeated merging in the turbulent flow downstream.