Boundary layers interaction with shock waves

Another possible source of pressure fluctuations are transverse velocity fluctuations driven by shock wave-boundary layer interactions. A boundary layer will be produced in the near-wall fluid behind the detonation just as in the more well-studied case of a shock wave in a tube. While initially laminar, this boundary layer is expected to rapidly become turbulent and then fill the tube to produce a turbulent channel flow. Measurements behind nonreacting shock waves demonstrate that transition occurs within 10 tube diameters for 2000 m/s shock velocities, comparable to the detonation velocities of the present experiments. Smeets and Mathieu have measured the velocity fluctuations in turbulent boundary layers behind incident shocks and find fluctuation levels of 1-5% with characteristic frequencies close to U2I Dy where 2 is the postshock velocity in the lab frame and D is the tube diameter. 

The attenuation of the reflected shock wave over 12 cycles of reflection within cylindrical and spherical vessels has been examined. Computations without added dissipation simulate the qualitative features of the measured pressure histories, but the shock amplitudes and decay rates are incorrect. Computations using turbulent channel flow dissipation models have been compared with measurements in a cylindrical vessel. These comparisons indicate that the nonideal aspects of the experiments result in a much more rapid decay of the shock wave than predicted by the simple channel flow model. Dissipation mechanisms not directly accounted for in the present model include multidimensional flow associated with transverse shock waves (originating in detonation or shock instability) separated flow due to shock wave-boundary layer interactions the influence of flow in the initiator tube arrangement and real gas (dissociation and ionization) effects and fluid dynamic instabilities near the shock focus in cylindrical and spherical geometries. 

Mark, H., The Interaction of a Reflected Shock Wave with the Boundary Layer in a Shock Tubef NAG A TM 1418, 1958. 

Another possible source of nonideal behavior and large pressure fluctuations would be boundary layer separation caused by the interaction with the reflected shock wave. Boundary layer separation and bifurcated reflected shock waves are observed under certain conditions in shock tubes with nonreactive flows. Mark formulated a simple model that predicts the occurrence of bifurcation shock bifurcation and boundary layer separation will occur when the pressure jump across the reflected shock exceeds the maximum stagnation pressure possible in the cold boundary layer fluid. Numerical calculation for the present situation reveals bifurcation would not be expected when the detonation first reflects. This is a situation peculiar to detonations and is due to the much lower reflected-shock pressure ratio relative to that which would be produced by reflecting a shock wave of comparable strength. Consideration of the reflected shock motion at later times indicates that bifurcation would not occur until after the shock had reflected from the far end of the tube. 

Chapter II, Blast Wave Reflections and Interactions, presents a number of articles on the interaction of blast waves with real surfaces. For example, Rayevsky et al. have studied the normal reflection of a blast wave from a rigid wall coated with polyurethane foam. They found that, contrary to intuition, the foam layer significantly increased the peak reflected pressure on the wall. Lyakhov and coworkers report on shock reflections from a body with a hot or cold gas layer. Kuhl et al. present a detailed simulation of a double-Mach reflection from a dusty wall. By using a nondiffusive numerical scheme and adaptive mesh refinement, they were able to directly calculate the mixing in the unstable wall jet and dusty boundary layer flow. Similarity coordinates were used to average the fluctuating flow and thereby determine the dusty boundary layer profiles. Shepherd et al. report on the repeated reflections of detonation-driven blast waves in containers. 

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