The rate of damping of perturbations on a shock wave reflected from a perturbed flat wall was measured in a shock tube. Incident shock wave Mach numbers of 1·45 and 1·09 in air together with sinusoidal and Gaussian wall perturbations were employed. These measurements were compared with a modified form of a linearized theory due to Zaidel (1960). The linearization was performed about the basic solution of a plane shock wave reflected normally from a flat wall.The rate of decay and the frequency and phase of oscillations agreed very well with the theoretical predictions; the amplitudes of the oscillations were some-what larger than predicted. The reflected shock shape was initially in good agreement with theory, but higher frequency perturbations on the reflected shock front caused deviations from the predicted shape after the shock front had travelled about one wall-wavelength away from the wall.The generally satisfactory agreement between theory and experiment supports the use of linearized analysis in predicting shock wave stability.
The initial value problem presented by mixing and chemical reaction in the wake of a flat plate is solved using the boundarylayer approximation. When a cool combustible mixture and its hot combustion products are separated by a finite, perfectly insulating flat plate, the velocity, temperature, and combustible concentration are determined in the vicinity of the trailing edge.The mixing problem without chemical reaction is solved in terms of a ‘universal solution’ for a given initial temperature ratio and Prandtl number from which the solution for arbitrary temperature ratios can be obtained.The mixing problem with chemical reaction is solved in terms of a ‘universal solution’ for the first two terms of an assumed series solution for the temperature. In this case the ‘universality’ is with respect to a parameter B characterizing the chemical and hydrodynamic initial conditions.The axial distance from the trailing edge to the first local temperature maximum is given in terms of the initial conditions and is shown to be greatly shortened by the presence of the viscous wake as compared with non-viscous mixing.
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