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Acoustic dissipation studies were undertaken using a subscale, cold-flow rocket motor model to determine the effect of purely geometric variables on the acoustic performance leadi~ng to axial mode combustion instability. Cold air served as the working fluid to simulate the internal flow and to obtain a critical nozzle throat condition. Using interchangeable metal parts, it was possible to simulate the geometry of a cylindrical-bore grain at various real motor burn times and also to vary the nozzle throat diameter. The results confirmed the speculation that, for practical motor designs, the radiation of acoustic energy through the nozzle is the largest source of loss for the axial mode and increases with the J of the motor. In view of the change in J with time during burning, this loss can vary-conspicuously during the motor burn time. SU.

A promising method for determining the losses in a rocket chamber during (combustioninstability is based on acoustic measurements at room temperature. This method permits the losses to be determined from experiments in a small-scale model of the actual chamber. The calculations presented here treat the acoustics of a chamber with mean flow; they are intended to be used in the design of such experiments and in the interpretation of data. NomenclatureA = admittance at boundary, defined by Eq. (9) a = sonic velocity D = tan 2 ft + 20 tanfi + X t t -unit axial vector / = dimensional frequency; also nonhomogeneous part of pressure boundary equation [Eq. (8)] h = nonhomogeneous part of pressure wave equation [Eq. (7)]k -nondimensional wave number for steady oscillations, 6>L/a ki = nondimensional wave number for purely axial mode classical oscillations kN = nondimensional wave number for classical mode oscillations I = axial mode number (ki/ir) Mo = magnitude of Mach number perturbation at head end of chamber N = X tan 2 ft -26 tanfi + 1 n = normal unit vector r = dimensionless radius, r/L S c = cross-sectional area of chamber S p = nozzle entrance area s = dimensionless entropy, v\ -P'/P t = time; nondimensional following Eq. (2) [(real time)/ (£/«)] X = square of the absolute value of complex nondimensional nozzle admittance, X = A* 2 + 0 2 Z -dimensionless head-end impedance, 17/M 0 ' t\ = nondimensional pressure, p'/yp 0 = imaginary part of nondimensional nozzle admittance A = imaginary part of k p -real part of nondimensional nozzle admittance = a. + ip; tanh<£ = -A n 12 = real part of k n = nondimensional frequency, fl/(l -M c ) 2

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