## A Basic Three-Dimensional Turbulent Boundary Layer Experiment To Test Second-Moment Closure Models

##### Abstract

In this work, a three-dimensional turbulent boundary layer experiment was set up with alternating stream-wise and span-wise pressure gradients. The pressure gradients are generated as a result of the test section wavy side wall shape. Each side had six sine waves with a trough to peak magnitude to wavelength ratio of 0.25. Boundary layer control was used so that the flow over the side walls remains attached. The mean flow velocity components, static and total pressures were measured at six plane along the stream-wise direction. The alternating mean span-wise and stream-wise pressure gradients created alternating stream-wise and span-wise vorticity fluxes, respectively, along the test section. As the flow developed downstream the vorticity created at the tunnel floor and ceiling diffused away from the wall.
The vorticity components in the stream-wise and span-wise directions are strengthened due to stretching and tilting terms in the vorticity transport equations. The positive-z half of the test section contains large areas that generate positive vorticity flux in the trough region and smaller areas generating negative vorticity around the wave peak. The opposite is true for the negative-z half of the test-section. This results in a large positive stream-wise vorticity in the positive-z half and negative stream-wise vorticity in the negative-z half of the test-section. The smaller regions of opposite sign vorticity in each half tend to mix the flow such that as they diffuse away from the wall, the turbulent stresses are more uniform.
Turbulent fluctuating velocity components were measured using Laser Doppler Velocimetery. Mean velocities as well as Reynolds stresses and triple velocity component correlations were measured at thirty stations along the last wave in the test section. Profiles at the center of the test section showed three dimensionality, but exhibited high turbulence intensities in the outer layer.
Profiles off the test section centerline are highly three dimensional with multiple peaks in the normal stress profiles. The flow also reaches a state where all the normal stresses have equal magnitudes while the shear stresses are non-zero.
Flow angles, flow gradient angles and shear stress angles show very large differences between wall values and outer layer vlaues. The shear stress angle lagged the flow gradient angle indicating non-equilibrium.
A turbulent kinetic energy transport budget is performed for all profiles and the turbulence kinetic energy dissipation rate is estimated. Spectral measurements were also made and an independent estimate of the kinetic energy dissipation rate is made. These estimates agree very well with those estimates made by balancing the turbulence kinetic energy transport equation.
Multiple turbulent diffusion models are compared to measured quantities. The models varied in agreement with experimental data. However, fair agreement with turbulence kinetic energy turbulent diffusion is observed. A model for the dissipation rate tensor anisotropy is used to extract estimates of the pressure-strain tensor from the Reynolds stress transport equations. The pressure-strain estimates are compared with some of the models in the literature. The comparison showed poor agreement with estimated pressure-strain values extracted from experimental data.
A tentative model for the turbulent Reynolds shear stress angle is developed that captures the shear stress angle near wall behavior to a very good extent. The model contains one constant that is related to mean flow variables. However, the developed expression needs modification so that the prediction is improved along the entire boundary layer thickness.

##### Collections

- Doctoral Dissertations [12912]

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