Integral Theory for Turbulent Base Flows at Subsonic and Supersonic Speeds

Citation

Alber, Irwin Emanuel (1967) Integral Theory for Turbulent Base Flows at Subsonic and Supersonic Speeds. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/0YEZ-H062. https://resolver.caltech.edu/CaltechETD:etd-10302003-141417

Abstract

The integral near wake analysis of Reeves and Lees developed for supersonic laminar base flows is extended to the case of fully turbulent separated adiabatic flow behind a rearward facing step at both subsonic and supersonic speeds. A turbulent eddy viscosity model is formulated for the shear stress scaling of the dissipation integral in the mechanical energy equation. It is shown that the eddy viscosity can be described simply by one incompressible constant (valid for both shear layers and wakes) and one reference density ρ_r. Using a compressibility transformation, theoretical solutions for the spreading rates of free shear layers are found to agree with experiment when the reference density is chosen to be the centerline density for the wake flow.

Two alternate methods are presented for joining the wake flow solution to the body first, through a turbulent free shear layer mixing solution, and then through the use of a two parameter family of velocity profiles valid near the body. A simple conservation model is presented to relate the viscous sublayer after expansion to the initial boundary layer ahead of the step.

For free stream Mach numbers M₁ ≤ 2.3, the integral theory is found to give good estimates for the length scales and centerline pressure variations measured experimentally for both wake flows and step flows (where reattachment is to a solid surface).

An iterative method of solution for the incompressible wake flow problem is presented as an extension of the work of Green. The calculation proposes the proper criteria for obtaining a convergent solution. The base pressure coefficient is found to be equal to the difference between the momentum thicknesses in the far wake and at the base.

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