Paper 11: The Attenuation of Shock Waves in Rough Ducts

Abstract

The rule formulated by Whitham (1)† is briefly described and the application of this rule to the attenuation of shock waves in rough ducts is mentioned. A review of previous work on shock wave attenuation shows that most investigators have used smooth-walled ducts for their experiments and a steady-flow, flat-plate boundary-layer analogy for their theory. An alternative approach based upon one-dimensional flow is examined. Previous work concerned with this alternative approach is outlined and the present problem is then explained in detail. The attenuation of moving, one-dimensional shock waves in rough ducts is considered using the theory of characteristics applied to one-dimensional, unsteady, compressible flow, including friction and heat transfer effects and using Whitham's rule. In order to evaluate this, steady-flow friction coefficients and the Reynolds analogy between pipe friction and heat transfer are used. Comparison of the present theory with previous experimental results shows good agreement with half of them. It is suggested that at least part of the difference between the present theory and the other half of the experiments can be attributed to the method used by the previous investigators when evaluating their experimental results.