DIRECT NUMERICAL SIMULATION OF TURBULENT MIXING LAYERS WITH PERIODIC FORCING INDUCED INFLOW

Abstract

The direct numerical simulation of the turbulent mixing layer with periodically-forced inflow is performed. The angular frequency Ωc was set as a control parameter. To compare the experimental study of Naka et al. (2010), the angular frequency is set to be Ω = 0.83 (Case A) and 3.85 (Case B). In the present simulation, the momentum thickness shows the Case A achieved the mixing enhancement, while Case B achieves its suppression. Due to the both controls, the Reynolds normal shear stress, especially v′v′ increases behind the periodic forcing. The Reynolds shear stress u′v′ is suppressed in the Case B at downstream. This region is agree with that the mixing suppression is found in the momentum thickness. Furthermore, the anisotropic tensor indicates that two dimensional large coherent structure is generated in the Case B in which mixing was suppressed. Introduction A mixing layer is one of the fundamental free shear flow generated by the velocity gap (Brown & Roshko (2009)). In order to understand the vortex dynamics in shear flows, mixing layers have extensively been studied since Brown & Roshko (1974) experimentally visualized the coherent structure in turbulent mixing layers. Huang & Ho (1990) experimentally studied an acoustically perturbed laminar mixing layer and observed small-scale turbulence created due to interaction of spanwise and streamwise structures after the merging of spanwise vortices. Turbulent mixing layers can be found in various practical applications: e.g., inside combustion chambers and around the exhaust of turbo engines. Techniques for mixing enhancement or suppression are sometimes needed for efficient combustion or noise reduction. Ho (1982) attempted to control the mixing layer by perturbing the flow rates of inflows. They show that the spreading rate of a mixing layer can be manipulated at very low forcing level if the mixing layer is perturbed near a subharmonic of the most-amplified frequency. Naka et al. (2010) studied a mixing layer periodically forced by using a flap-type actuator made of piezoplastic (Polyvinylidene fluoride: PVDF) film aiming at both enhancement and suppression of mixing. They conclude that at some parameters of forcing mixing suppression can also be achieved. In the present study, direct numerical simulation (DNS) of turbulent mixing layers with periodic forcing, which mimics that by the flap-type actuator of Naka et al. (2010), is performed. The forcing by the flap-type actuator is modeled by transversely oscillating the inflow turbulent boundary layers. Direct numerical simulation The governing equations are the incompressible continuity and Navier-Stokes equations as following,