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SPECTRAL EDDY DIFFUSIVITY AND PRANDTL NUMBER DISTRIBUTIONS IN A HEATED TURBULENT WAKE

Hyung Suk Kang
Department of Mechanical Engineering, and Center for Environmental and Applied Fluid Mechanics, The Johns Hopkins University, Baltimore, Maryland 21218, USA

Charles Meneveau
Department of Mechanical Engineering, and Center for Environmental and Applied Fluid Mechanics, The Johns Hopkins University, Baltimore, Maryland 21218, USA

Resumo

For turbulent flows the subgrid-scale (SGS) scalar-variance dissipation spectrum can be expressed as the co-spectrum of negative SGS scalar flux and filtered scalar gradient. Using local isotropy, the radial SGS scalar-variance dissipation spectrum is expressed in terms of the streamwise components of the SGS scalar flux and filtered scalar gradient that can be measured in experiments. Using an array of four X-type hot-wire and four I-type cold-wire probes, two-dimensional box-filtered velocities and temperatures in the streamwise and cross-stream directions by invoking Taylor's hypothesis are obtained at the centerline of a heated wake flow, at a Reynolds number based on Taylor scale of 350. From the radial dissipation spectra the spectral eddy viscosity and Prandtl number are evaluated. Consistent with classical two-point closure predictions, when using box filters, the spectral eddy viscosity and diffusivity decrease near the filter wavenumber. Interestingly, the spectral Prandtl number (the ratio of the spectral eddy viscosity to diffusivity) has a longer plateau-behavior than the spectral eddy diffusivity and viscosity, with a range around 0.7.