Linearized k-ε Analysis of Free Turbulent Mixing in Streamwise Pressure Gradients With Experimental Verification

The equations of momentum, turbulent kinetic energy, and dissipation are subjected to a coordinate transformation and linearized to obtain approximate closed-form solutions of free mixing problems. The linearization involves not only an assumption regarding the relative transverse uniformity of free mixing flow fields, but also a turbulence modeling approach in which a preliminary estimate of the length scale is a necessary input. As a by-product of this linearization, the equations partially decouple from one another and may, therefore, be solved sequentially. In order to provide the length scale and free-stream velocity dependence upon the transformed streamwise coordinate, a temporary transformation from the physical to the mathematical plane is developed on the basis of a classical eddy viscosity formula. Due to the analytical nature of the process, the input velocity and length scale thus obtained may be adjusted to conform with the desired velocity distribution in physical space, and the appropriate length scale computed from the solution of the equations. The analysis is favorably compared to experimental data on the turbulent mixing of two-dimensional wakes in adverse pressure gradients.