David R. Greatrix

Structural Vibration Considerations for Solid Rocket Internal Ballistics Modeling

*† ‡ § The coupling of structural vibrations with the nonlinear internal ballistic flow and burning rate of a sleeved cylindrical-grain motor is investigated through numerically simulated motor firings configured for the evaluation of pulse-triggered combustion instability behavior. The predicted results illustrate the significant impact of the threedimensional structural acceleration field on the burning rate and axial wave development during unsteady motor operation. Parameters such as the structural damping have been found to significantly influence the axial shock wave development and base chamber pressure rise during simulated firings. Instability-related symptoms are demonstrated through this study to be dependent at least in part on the motor structural vibrations.

Transient Burning Rate Model for Solid Rocket Motor Internal Ballistic Simulations

A general numerical model based on the Zeldovich-Novozhilov solid-phase energy conservation result for unsteady solid-propellant burning is presented in this paper. Unlike past models, the integrated temperature distribution in the solid phase is utilized directly for estimating instantaneous burning rate (rather than the thermal gradient at the burning surface). The burning model is general in the sense that the model may be incorporated for various propellant burning-rate mechanisms. Given the availability of pressure-related experimental data in the open literature, varying static pressure is the principal mechanism of interest in this study. The example predicted results presented in this paper are to a substantial extent consistent with the corresponding experimental firing response data.

Simulation of Axial Combustion Instability Development and Suppression in Solid Rocket Motors

In the design of solid-propellant rocket motors, the ability to understand and predict the expected behaviour of a given motor under unsteady conditions is important. Research towards predicting, quantifying, and ultimately suppressing undesirable strong transient axial combustion instability symptoms necessitates a comprehensive numerical model for internal ballistic simulation under dynamic flow and combustion conditions. An updated numerical model incorporating recent developments in predicting negative and positive erosive burning, and transient, frequency-dependent combustion response, in conjunction with pressure-dependent and acceleration-dependent burning, is applied to the investigation of instability-related behaviour in a small cylindrical-grain motor. Pertinent key factors, like the initial pressure disturbance magnitude and the propellants net surface heat release, are evaluated with respect to their influence on the production of instability symptoms. Two traditional suppression techniques, axial transitions in grain geometry and inert particle loading, are in turn evaluated with respect to suppressing these axial instability symptoms.

Steepness of Grain Geometry Transitions on Instability Symptom Suppression in Solid Rocket Motor

Research towards predicting and quantifying undesirable transient nonlinear axial combustion instability symptoms in solid rocket motors, and the various means for suppressing these symptoms, is being undertaken through the use of a comprehensive numerical model for internal ballistic simulation under dynamic flow, combustion and structural vibration conditions. In the present paper, as a follow-on study of area transition effects, the effect of the steepness of left-to-right internal propellant grain port geometry transitions in suppressing instability symptoms is comprehensively examined. Individual transient simulation runs for unstable cases show the evolution of the axial pressure wave and associated dc shift for the given grain geometry of a reference motor, as initiated by a given pressure disturbance. Limit pressure wave magnitudes are collected for a number of simulation runs for different grain area transition gradients, and mapped on an attenuation trend chart. Within the context of the present study, for one reference motor design and size, it is clear that steeper area transitions are more effective in suppressing wave development. When the effect of acceleration (through structural vibration of the propellant surface) on the combustion process is included in the numerical calculations, one observes substantial differences in burning and internal flow behavior in the presence of axial pressure wave activity, as reflected in individual firing simulations and the corresponding attenuation map.

Hybrid Rocket Engines

The hybrid rocket engine utilizes a combination of solid rocket and liquid rocket technology to meet some flight mission applications. In terms of performance, cost, availability of materials and safety, the hybrid approach does potentially have some advantages. A number of design issues are covered in this chapter, including the implications of solid fuel regression rate and stoichiometric length on engine performance. Modeling of solid fuel surface regression as a function of mass flux is presented. The framework for steady and nonsteady internal ballistic analysis is discussed.

Dual Particle Loading for Solid Rocket Instability Symptom Suppression

Research towards predicting and quantifying undesirable transient axial combustion instability symptoms in solid rocket motors necessitates a comprehensive numerical model for internal ballistic simulation under dynamic flow and combustion conditions. Once some confidence is gained in a given model’s ability to adequately predict such symptoms under a given driving mechanism, or mechanisms if more than one at play, one can turn to modeling various techniques that might be employed toward symptom suppression. In the present investigation, various factors and trends, related to the usage of two sets of inert particles comprised of the same material (aluminum) but at different diameters for the suppression of axial shock wave development, are numerically predicted for a composite-propellant cylindrical-grain motor.

Numerical Transient Burning Rate Model for Solid Rocket Motor Simulations

*The incorporation of time- and frequency-dependent effects on solid propellant burning behavior is important in the developing of more sophisticated solid rocket internal ballistic simulation models. A general numerical model based on the Zeldovich-Novozhilov solidphase energy conservation result for transient solid-propellant burning is presented in this study. A burning rate limiting function enables numerical stability at representative spatial and temporal increments, and with adjustment allows for an applicable alignment with observed experimental combustion response characteristics for a given propellant.

Regression Rate Estimation for Swirling-Flow Hybrid Rocket Engines

In the present study, an analytical model based on convective heat feedback is developed for the estimation of the solid fuel surface regression rate of hybrid rocket engines with head-end swirling-flow oxidizer injection. The convective heat transfer between the axial core flow and the burning fuel surface, coupled with the convective heat feedback between the effective tangential flow and the burning fuel surface, is the means by which the fuel regression rate is presumed to be increased by swirl, above that due to the axial mass flux. The representation of the effective boundary layers used in this study includes the influence of transpiration, effective hydraulic diameters (for flows in the axial and tangential direction), and fuel surface roughness. From the literature, a variety of propellant combinations, engine sizes, and flow swirl numbers are evaluated for engines having circular-port fuel grains, with sample model results provided. The predicted fuel regression rates for the most part compare q...

Numerical Modeling Considerations for Transient Burning of Solid Propellants

Timeand frequency-dependent effects on solid propellant burning behavior is of concern when developing nonsteady solid rocket internal ballistic simulation models. A general numerical model based on the Zeldovich-Novozhilov solid-phase energy conservation result for transient solid-propellant burning is presented in this study. An empirical burning rate limiting function allows for an applicable alignment with observed experimental combustion response characteristics for a given propellant, with the solution independent of time and spatial increment sizing below a certain threshold sizing. The effects arising from a variable propellant surface temperature on propellant burning response are examined.

Combined structural oscillation effects on solid rocket internal ballistics

The combined effects of radial and axial vibration of the surrounding structure on the internal ballistics of a solid rocket motor are investigated via numerical simulation. A finite-difference model is applied for the radial deformation dynamics of the propellant/casing assembly along the length of the motor, while the nonsteady internal core flow is modelled using a primarily second-order, finite-volume random-choice technique. Predicted nonsteady combustion and flow behavior resulting from an initial pressure pulse within the flow, allied to the free axial and radial oscillation behavior of the surrounding structure, is consistent with experimentally observed trends associated with axial and transverse combustion instability. Instability-related phenomena such as the dc pressure rise and axial pressure wave strength development are demonstrated to be dependent in part on the motor structural characteristics.