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 to Mirels' shock-tube boundary layer equations was the inclusion of a modern friction model based on empirical data for compressible, turbulent boundary layers (i.e, the Van Driest II and Spalding- Chi models). For easy inclusion into existing routines, the updated friction expressions were modified and incorporated into the original shock-tube boundary layer relations via simple changes to the constants and exponents. In the improved model, the turbulent shear stress term has an exponent of 0.14 as compared to 0.25 in the Blasius relation. The improved skin friction coefficient is close to the Blasius skin friction coefficient at low pressures (P2 < 1 atm) but can be a factor of two greater at high pressures (P2 > 5 atm). 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 JLLS 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. 2001 by The Aerospace Corporation.
