Direct Numerical Simulation of Spatially Evolving Statistically Stationary Planar Mixing Layers
Victor Zendejas Lopez, California Institute of Technology
Turbulent planar mixing layers (PML) are among the most studied free shear layers, often serving as proxies for understanding complex physical mechanisms in engineering and science applications such as combustion, aerodynamics, and atmospheric flows.
The simulation of turbulent PML has traditionally been studied in two configurations. The first configuration is a spatially evolving PML where a computational box contains an inlet, injecting two fluid streams moving in the same streamwise direction at different velocities, and an outlet where the developed flow exits. Due to the initial velocity discontinuity, the flow will become unstable, causing the flow to transition from a laminar to a fully turbulent flow downstream. This setup requires a long streamwise and tall domain to accommodate the growth and drift of the PML and is classified as statistically stationary since turbulence statistics do not vary in time but depend on the streamwise direction.
The second approach shifts the streamwise velocity by the average imposed free stream velocity, leading to symmetry in the streamwise baseflow and results in a statistically homogeneous PML. This homogeneity allows the use of periodic boundary conditions along the streamwise direction, reducing the need for a long streamwise domain and decreasing simulation costs. However, in this configuration, the PML develops over time and is no longer statistically stationary.
This work introduces a third method for simulating turbulent PML. By applying a mathematical transformation that rescales the vertical coordinate in space to the incompressible Navier-Stokes equations, which describe the evolution of PML, we obtain a set of transformed conservation equations with additional unclosed source terms that are closed on the fly. This transformation results in simulations that are both statistically stationary and homogeneous.