Wind Tunnel Studies of Decay and Spatial Diffusion of Turbulence

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Johns Hopkins University
The study of homogeneous isotropic turbulence is one of the founding blocks of turbulence theory. It helps understanding the behavior of the Navier-Stokes equation in its most fundamental form and contributes to the development of numerical mod- els. The first part of this thesis is dedicated to the study of decaying homogeneous isotropic turbulence generated by fractal active grids. The motivation for this study comes from previous studies of fractal-generated decaying turbulence which argued the existence of unusual decay behaviors. Specifically, exponential or very fast power law decays were reported instead of the widely accepted power-laws in times with decay exponents ranging between 1.0 and 1.4, approximately. These non-classical decays were later argued by other researchers to be limited to regions near the grid or perhaps to be due to low Reynolds numbers. In order to provide more definitive answers, in this work measurements are performed in the far field of a fractal grid at high Reynolds numbers. The results presented here exhibit power-law decays with decay exponents ranging approximately between 1.0 and 1.3, confirming that even fractal-generated grid turbulence conforms to classical decay laws. The second part of the work also explores the decay of the turbulent kinetic energy, but including possible effects of spatial diffusion. An initial nearly-uniform gradient of kinetic energy of the form k ∼ β(y − y0) is introduced in a flow with zero mean shear (y is the spanwise direction). In the wind tunnel this type of flow is achieved by combining spatially varying winglet geometries in the active grid placed downstream of a mesh with spatially varying solidity. The measurements taken in the test section with in-house built hot-wire anemometers show that at all spanwise locations the decay in the streamwise direction follows a power-law but with exponents n(y) that depend upon the spanwise location. The third part of this thesis revisits the previous problem while using different instruments. The Princeton-made nanoscale thermal anemometers (NSTAP) are used to study the decay and achieve full resolution of viscous range to accurately determine dissipation. These data then enable us to evaluate the gradient of the transverse spatial flux of the turbulent kinetic energy. The same dependence between the initial distribution of kinetic energy and the decay exponent were recovered. The results presented also suggest (but do no prove) the presence of a strong lateral flux of turbulent kinetic energy going up-gradient, from the low kinetic energy side to the high kinetic energy side of the initial distribution. The measurements do not prove up-gradient transport since another possibility to explain the measurements is down-gradient transport, but with a diffusion coefficient that increases in the direction of decreasing turbulent kinetic energy. We comment on other possible reasons for the surprising findings and on the need for Direct Numerical Simulations of this flow to provide simultaneous pressure-velocity data.
Fluid Mechanics, Turbulence, Wind Tunnel