Direct Numerical Simulation of Laminar-to-Turbulence Transition in a Compressible Supersonic Channel Flow at Mach ۳

This work presents a direct numerical simulation (DNS) of laminar-to-turbulence transition in a compressible supersonic channel flow at Mach ۳ with a friction Reynolds number of ۴۵۰. A fully parallelized solver has been developed for this purpose, using a characteristic-type pressure-velocity-entropy formulation of full compressible Navier-Stokes equations. The initial flow field consists of a laminar channel profile perturbed by a large-scale, small-amplitude sinusoidal wave together with weak, small-scale random noise which acts as a trigger for transition. As the simulation progresses, the flow evolves from laminar to turbulent. During this process, Tollmien-Schlichting waves emerge in the linear instability phase, leading to a nonlinear transition and ultimately to the eventual development of fully developed turbulent flow. The statistical properties of the resulting fully developed turbulence are compared against existing reference data, showing very good agreement.

Keywords:

laminar-to-turbulence transition , direct numerical simulation , compressible supersonic channel flow , viscous (first-mode) instability , Tollmien-Schlichting waves