### Abstract

Classical Quasi-Steady Homogeneous One-Dimensional (QSHOD) transient propellant combustion theory is revisited with the objective of extending it to heterogeneous propellants through a statistical averaging technique. The linearized QSHOD response of burning rate to pressure is rederived. Throughout the derivation, the response function is viewed as a relation among the boundary conditions at the propellant surface. This viewpoint helps clarify how the properties of the response function arise from the mathematics. Heterogeneous propellants are treated as a statistical ensemble of small, quasi-one- dimensional pieces, each having a QSHOD-like response. Including compositional fluctuations at the burning surface in the local response function is briefly discussed. However, modeling these sorts of fluctuations as linear perturbations about some mean surface composition is probably not representative of typical heterogeneous propellants, because local compositional fluctuations are not infinitesimal and can be quite large depending on the length scale one is considering. For situations in which the time scale of the oscillatory perturbation is smaller than the time scale of the local fluctuations in burning rate inherent to the steady-state burning of a heterogeneous propellant, the framework can be used to examine the effects that local scaling can have of the burning-rate response. Some elementary calculations are performed to show how the bulk-mode response can differ significantly from the local response when the burning rate is not constant over the propellant surface.

Original language | English (US) |
---|---|

Pages (from-to) | 2343-2350 |

Number of pages | 8 |

Journal | Symposium (International) on Combustion |

Volume | 27 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1998 |

Event | 27th International Symposium on Combustion - Boulder, CO, United States Duration: Aug 2 1998 → Aug 7 1998 |

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### ASJC Scopus subject areas

- Chemical Engineering(all)
- Fuel Technology
- Energy Engineering and Power Technology
- Mechanical Engineering
- Physical and Theoretical Chemistry
- Fluid Flow and Transfer Processes

### Cite this

*Symposium (International) on Combustion*,

*27*(2), 2343-2350. https://doi.org/10.1016/S0082-0784(98)80085-4

**Linear pressure coupled frequency response of heterogeneous solid propellants.** / Murphy, Jeffrey J.; Krier, Herman.

Research output: Contribution to journal › Conference article

*Symposium (International) on Combustion*, vol. 27, no. 2, pp. 2343-2350. https://doi.org/10.1016/S0082-0784(98)80085-4

}

TY - JOUR

T1 - Linear pressure coupled frequency response of heterogeneous solid propellants

AU - Murphy, Jeffrey J.

AU - Krier, Herman

PY - 1998/1/1

Y1 - 1998/1/1

N2 - Classical Quasi-Steady Homogeneous One-Dimensional (QSHOD) transient propellant combustion theory is revisited with the objective of extending it to heterogeneous propellants through a statistical averaging technique. The linearized QSHOD response of burning rate to pressure is rederived. Throughout the derivation, the response function is viewed as a relation among the boundary conditions at the propellant surface. This viewpoint helps clarify how the properties of the response function arise from the mathematics. Heterogeneous propellants are treated as a statistical ensemble of small, quasi-one- dimensional pieces, each having a QSHOD-like response. Including compositional fluctuations at the burning surface in the local response function is briefly discussed. However, modeling these sorts of fluctuations as linear perturbations about some mean surface composition is probably not representative of typical heterogeneous propellants, because local compositional fluctuations are not infinitesimal and can be quite large depending on the length scale one is considering. For situations in which the time scale of the oscillatory perturbation is smaller than the time scale of the local fluctuations in burning rate inherent to the steady-state burning of a heterogeneous propellant, the framework can be used to examine the effects that local scaling can have of the burning-rate response. Some elementary calculations are performed to show how the bulk-mode response can differ significantly from the local response when the burning rate is not constant over the propellant surface.

AB - Classical Quasi-Steady Homogeneous One-Dimensional (QSHOD) transient propellant combustion theory is revisited with the objective of extending it to heterogeneous propellants through a statistical averaging technique. The linearized QSHOD response of burning rate to pressure is rederived. Throughout the derivation, the response function is viewed as a relation among the boundary conditions at the propellant surface. This viewpoint helps clarify how the properties of the response function arise from the mathematics. Heterogeneous propellants are treated as a statistical ensemble of small, quasi-one- dimensional pieces, each having a QSHOD-like response. Including compositional fluctuations at the burning surface in the local response function is briefly discussed. However, modeling these sorts of fluctuations as linear perturbations about some mean surface composition is probably not representative of typical heterogeneous propellants, because local compositional fluctuations are not infinitesimal and can be quite large depending on the length scale one is considering. For situations in which the time scale of the oscillatory perturbation is smaller than the time scale of the local fluctuations in burning rate inherent to the steady-state burning of a heterogeneous propellant, the framework can be used to examine the effects that local scaling can have of the burning-rate response. Some elementary calculations are performed to show how the bulk-mode response can differ significantly from the local response when the burning rate is not constant over the propellant surface.

UR - http://www.scopus.com/inward/record.url?scp=0032265630&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032265630&partnerID=8YFLogxK

U2 - 10.1016/S0082-0784(98)80085-4

DO - 10.1016/S0082-0784(98)80085-4

M3 - Conference article

AN - SCOPUS:0032265630

VL - 27

SP - 2343

EP - 2350

JO - Proceedings of the Combustion Institute

JF - Proceedings of the Combustion Institute

SN - 1540-7489

IS - 2

ER -