A proper understanding of the intake starting process of supersonic airbreathing engines is crucial for a successful operation of the supersonic aircraft, especially for three-dimensional geometries in which no reliable starting prediction for a broad Mach number range exists, and the widespread Kantrowitz criterion only provides a conservative prediction. Experimental investigations from the literature are reviewed and put into the perspective of the Kantrowitz theory. First, an empirical relation is developed that is valid for a wide Mach number range, and that can be calibrated to certain classes of intakes by the user. Second, the Kantrowitz assumptions are modified and a semiempirical relation is derived. The semiempirical relation turned out to be an optimistic limit for self-starting.
NomenclatureA = area, m 2 a = speed of sound, m∕s C 1 = constant h = specific enthalpy, J∕kg k = constant M = Mach number _ m = mass flow, kg∕s p = pressure, N∕m 2 T = temperature, K β = shock angle, deg γ = ratio of specific heats θ = deflection angle, deg Π = pressure ratio ρ = density, kg∕m 3 Subscripts cl = cowl closure i = internal portion isentr. = isentropic Kantr. = Kantrowitz m = modified max = maximum poly. = polynomial semiemp. = semiempirical t, tot = total th = throat ∞ = freestream condition Superscript = chocked conditions
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