A study has been conducted to evaluate the rotating valve method of measuring the combustion response of solid propellants to small amplitude pressure oscillations. The method is based on producing pressure oscillations in a small rocket motor by varying the area of a secondary exhaust nozzle in a periodic manner. This is accomplished by using a rotating valve as the secondary orifice. The valve apparatus operates concurrently with a primary nozzle which controls the steady-state pressure. The frequency of the oscillations is determined by the rotational speed of the valve. A theoretical analysis was conducted to relate the combustion response function to measurable ballistic properties of the combustion chamber. Assuming that the combustion chamber is small in comparison to the acoustic wavelength, the combustion response function can be calculated from the amplitude of the oscillating pressure and the phase angle between the oscillating pressure and oscillating nozzle area. Cold flow tests were conducted using nitrogen and helium to test the validity of the analysis. Excellent agreement was found between the measured and predicted amplitudes and phase angles. Combustion tests then were conducted using two aluminized propellant formulations and three nonaluminized formulations. There was excellent agreement between the T-burner and rotating valve tests conducted on the same batch of propellant. For two nonaluminized propellants, the comparisons were based on different batches of propellant. Differences in combustion response and variations in burning rate and characteristic exhaust velocity were observed for these two formulations. It was concluded that the rotating valve method is a valid substitute for the T-burner. Substantial reductions in the cost of characterizing propellants also were obtained using this new approach.

Combustion Response Function Measurements by the Rotating Valve Method

The three-dimensional nozzle admittance, an important parameter in combustion instability studies, was experimentally measured for several nozzle configurations. The admittance values were obtained using a modification of the classical impedance tube technique. The modified impedance tube method measures the admittance of a duct termination in the presence of one-dimensional mean flow and three-dimensional oscillations. Values of the nozzle admittance were obtained from pressure amplitude measurements taken at discrete points along the length of the tube. To determine the effects of nozzle geometry, nozzles were tested with half-angles of 15, 30, and 45 deg and entrance Mach numbers of 0.08, 0.16, and 0.20. The admittance results are presented as functions of nondimensional frequency for mixed first tangential-longitudinal modes. These results are compared with available theoretical predictions, and good agreement between theory and experiment is shown.

Experimental determination of three-dimensional liquid rocket nozzle admittances.

Numerical simulations are carried out to evaluate the nozzle damping of rocket motors. A subscale cold flow experimental condition where nozzle damping coefficients are evaluated through the pulse decay method is taken as a validation case. The flowfield of the motor is simulated by solving three-dimensional Reynolds-averaged Navier–Stokes equations using commercial computational fluid dynamics software. The trend of the pressure decay in the head end is well captured for different values of port-to-throat area ratios, and a very good match is obtained between the computed and experimental values of the nozzle decay coefficient. Validated methodology is used to evaluate the damping coefficient of a burning solid rocket motor with composite propellant.

Damping Coefficient Prediction of Solid Rocket Motor Nozzle Using Computational Fluid Dynamics

The method presented makes use of a division of the region of integration into closed rectangular elements. The velocity is taken to be constant in each element. The integral equation is reduced to a matrix equation which can be solved by an appropriate iteration approach. The derivation and solution of the matrix equation are discussed and the matrix elements are considered. The described concepts were implemented for a nonlifting parabolic-arc airfoil.

Numerical solution for subcritical flows by a transonic integral equation method

The damping of axial instabilities by a variety of small-scale solid rocket nozzles has been determined experimentally under cold-flow conditions using the modified impedance tube technique. The dependence of the damping upon the cavity depth and the secondary flow rate issuing from the cavity of a submerged nozzle, the geometry of the convergent section of a single-ported nozzle, and the number of nozzles present in a multipleported nozzle cluster has been determined. Measured data indicate that in the case of the submerged nozzle the cavity depth surrounding the nozzle has a significant effect upon the nozzle admittance while the secondary flow rate issuing from the cavity has negligible effect on the admittance. Tests conducted with conical, equal-radii-ofcurvature and linear-velocity-profile nozzles showed that conical nozzles provide the most damping. Tests with multiple-ported nozzles indicated that quadruple-ported nozzles provide less damping for axial instabilities than single and dual-ported nozzles whose damping capabilities are approximately the same.

Damping of Axial Instabilities by Small-Scale Nozzles Under Cold-Flow Conditions

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.

George L. Dehority

Papers

Analysis of Acoustic Waves in a Cold-Flow Rocket