INHOMOGENEOUS TWO-STREAM TURBULENT MIXING USING THE TURBULENT KINETIC ENERGY EQUATION
Final technical rept.
ARNOLD ENGINEERING DEVELOPMENT CENTER ARNOLD AFB TN
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A study was made on applying the turbulent kinetic energy approach to inhomogeneous two-stream turbulent mixing calculations and to calculations of a two-dimensional symmetric wake. Mixing calculations are made and compared with experimental data for coaxial hydrogen-air and air-air mixing flows. The turbulent kinetic energy equation is transformed into a transport equation for the turbulent shear stress by assuming that the turbulent shear stress is directly proportional to the turbulent kinetic energy. A flux model is assumed for the lateral diffusion of turbulent kinetic energy. The energy dissipation is modeled to a form similar to that derived for isotropic turbulence. Mass and energy transport are incorporated to the analysis by assuming the Prandtl and Lewis numbers to be unity. The resulting set of partial differential equations is hyperbolic and the method of characteristics are chosen for their solution. The theoretical method inherently incorporates history of the turbulent structure in the calculations which is physically more acceptable than turbulent structure models based on local flow properties. The results show that the turbulent kinetic energy approach is quite applicable to two-stream mixing problems, although the method requires further development before it is useful for routine engineering calculations. Calculations for a wake behind a flat plate are made and found to compare well with experimental data. The flux model for the diffusion of turbulent kinetic energy and the energy dissipation model were found to produce results which agree well with experimental data for both the mixing jet and the wake.
- Fluid Mechanics