Improved Turbulent Boundary-Layer Model for Shock Tubes
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A viscous boundary-layer model was assembled to help describe the nonideal gas dynamics within shock tubes operating at high densities. The analytical model is based primarily on the landmark work of Mirels, who used the Blasius relation for the turbulent skin friction. The main improvement was the incorporation of a modern friction model for compressible, turbulent boundary layers via changes to the constants and exponents of Mirels's original boundary-layer relations. For example, the wall shear stress now depends on a Reynolds number to the -0.14 power as compared to 0.25 in the original model. As a result, the boundary layer at higher densities is thicker in the present model than in the original one, thus increasing the incident-shock attenuation and related nonuniformities. Even in borderline cases, the boundary-layer transitions to turbulent very quickly, usually within 100 s for incident-shock pressures greater than about 2 atm. Because a turbulent boundary layer is thicker than a laminar one at the same conditions, the boundary-layer thickness in higher-pressure shock tubes is expected to be a larger fraction of the tube diameter than normally seen in lower-pressure shock tubes. The turbulent boundary layer and elevated pressure also increase the heat transfer to the shock-tube walls.
