By Theory and Experiment Fickett Davis
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The rarefaction behind the front is thus stronger than expected in any treatment that neglects the boundary layer, and the flow Mach number increases more than expected. Fay (1959) offers a qualitative treatment of this effect in the quasione-dimensional (nozzle) approximation. He notes that the strictly onedimensional theory of Zeldovich (1940), in which the wall forces are considered to be distributed uniformly across the tube, is inadequate. With average wall forces determined from pipe flow measurements, this theory gives velocity deficits a thousand times smaller than those measured experimentally.
This property has been directly verified by observations of the Mach angle, and of the failure of following waves to overtake the front. 3A1. Experiment Detonation velocities have been measured and compared with the calculated values in a number of systems. Typical studies are those of Peek and Thrap (1957), Brochet, Manson, Rouze, and Struck (1963), Getzinger, Bowen, Oppenheim, and Boudart (1965), and Strauss and Scott (1972). The tube must be long enough to ensure a steady velocity in the measurement section.
5G, except that there the rate of area increase is related to the shock-front curvature, whereas Fay 66 Sec. 3A GASES assumes a plane front and uses his boundary-layer estimate of equivalent rate of area increase. Although the set of ordinary differential equations defining the channel flow could be integrated directly, it is simpler to formulate the problem in terms of the usual one-dimensional equations with a small but unknown correction term containing an integral of the true pressure over the length of the reaction.