Effects of Exhaust Nozzle Recombination on Hypersonic Ramjet Performance

Abstract

Exhaust nozzle recombination studies are carried out for hydrogen-fueled subsonic combustion ramjet engines. Bray's criterion is used to determine a nozzle freezing point. Nozzle performance is calculated by assuming equilibrium conditions up to the freezing point and frozen flow from the freezing point to the nozzle exit. Several engine parameters are varied in order to determine their effect on recombination and specific impulse. These parameters include nozzle throat size, throat radius of curvature, nozzle shape, Mach number, altitude, equivalence ratio, and inlet kinetic energy efficiency. The study has shown that recombination losses are not expected to be serious for Mach numbers up to 9 and freestream dynamic pressures above 500 psf. Nomenclature A= cross-sectional area A c = combustion chamber exit area A * = critical flow or throat area CD = overall drag coefficient of combustion chamber Cy = velocity coefficient DC = combustion-chamber drag 3D = dissociation rate F n et = net stream thrust g -gravitational constant H = static enthalpy /net = net fuel specific impulse J = energy conversion factor k r = forward reaction rate for reaction r k-r = reverse reaction rate for reaction r I = length M = Mach number M = mean molecular weight m = mass-flow rate, slugs/sec N = number of moles per unit mass of mixture n = number of moles tl = number of species in rth reaction equation P = static pressure 0 = net rate of molar change go = freestream dynamic pressure, p a Fo 2 /2 RC = nozzle throat radius of curvature #o = universal gas constant RT = nozzle throat cross-sectional radius (R = recombination rate= fuel injection angle j = specific-heat ratio TIKE -inlet-kinetic-energy efficiency for subsonic combustion vi rf = stoichiometric coefficient, left side of reaction equation Vi rff = stoichiometric coefficient, right side of reaction equation P = mass density $ = equivalence ratio Subscripts a = air C = combustion chamber e -nozzle exit / -fuel Presented at the AIAA-ASME Hypersonic Ramjet Conference, White Oak, Md., April 23-25, 1963; revision received July 22, 1963. * Aerospace Engineer, Mission Analysis Branch. t Aeronautical Research Scientist. i = species j = species in rth equation m = number of molecular species P = constant static pressure S = constant static entropy T = constant static temperature 0 = freestream 1 = inlet entrance 2 = combustion-chamber entrance 3 = combustion-chamber exit

Effects of hydrogen–air non–equilibrium chemistry on the performance of a model scramjet thrust nozzle

“…5, the ratio was 0⋅956. This is in accord with previous investigations (3)(4)(5)(6)(7) , where nozzle freezing caused only a small loss in thrust.…”

“…An early study (3) of freezing of hydrogen-air chemical recombination in a ramjet thrust nozzle, where the expansion takes place from a low subsonic Mach number, showed that if equilibrium flow is maintained past the low supersonic area ratios the loss in thrust caused by chemical freezing is not exceedingly high. In later numerical studies of scramjet thrust nozzles at high flight Mach numbers, where the nozzle expansion takes place from supersonic Mach numbers, it was shown that although molecular vibration was in equilibrium throughout the nozzle, the chemical composition was not (4) , that at precombustion pressures of the order of an atmosphere there was little recombination in the nozzle (5) and that, in spite of this, the lack of complete recombination yielded an overall thrust which was only 1% less than the value for an equilibrium expansion (6) .…”

Some comparisons of turboramjet-powered hypersonic aircraft for cruise and boost missions.

“…The exhaust-nozzle flow was assumed to be in equilibrium. 11 As indicated in Fig. 1, the second stage was considered to be carried internally.…”

The Rate-Controlled Constrained-Equilibrium Approach to Far-From-Local-Equilibrium Thermodynamics

“…It is finally important to note that the thermodynamic-consistency condition (40), that the entropy generation rate be non-negative definite under the endogenous dynamics, is always satisfied, because in evaluating the ratesċ τ i we use the full internal dynamics (the detailed kinetic scheme), with forward and reverse rate constants k + and k − that depend on temperature and pressure only, a condition that we have seen in Section 4.6 warrants the nonnegativity of the entropy generation rate. As previously noted (see also [53,76]), whether or not there are kinetically-controlled constraints in addition to element conservation, all conceivable reactions contribute to the rate of entropy production.…”

“…Sugden and co-workers [37], Kaskan [38], Schott [39], and Franciscus and Lezberg [40] treated the hydrogen-oxygen combustion problem. Keck and Gillespie [41] (see also [42,43]) developed a general rate-controlled constrained-equilibrium method for reacting gas mixtures.…”