Modeling of nonlinear longitudinal instability in solid rocket motors

Baum, Joseph D.; Levine, J.

doi:10.1016/0094-5765(86)90089-5

Cited by 23 publications

(8 citation statements)

References 16 publications

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“…Studies of nonlinear axial combustion instability have ranged from numerous experimental test firing series on the one hand [1][2][3], and linear/nonlinear acoustic theory modeling on the other (largely, the analysis producing frequency-based standing wave solutions for a given chamber geometry, but without some useful quantitative information) [4][5][6][7]. On occasion, researchers have employed a numerical modeling approach, to work towards a more comprehensive quantitative understanding of the physics involved (the numerical model producing a traveling wave solution to a limit wave amplitude and corresponding small or larger dc shift, typically a time-based result evolving from an initial pulse disturbance introduced into the chamber flow) [8,9]. Available computational power and associated result turnaround times commonly forced some simplifications in the given numerical model.…”

Section: Introductionmentioning

confidence: 99%

Use of Reactive Particles for Solid Rocket Combustion Instability Suppression

Greatrix¹

2014

50th AIAA/ASME/SAE/ASEE Joint Propulsion Conference

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Research towards predicting and quantifying undesirable transient axial combustion instability symptoms in solid-propellant rocket motors necessitates a comprehensive numerical model for internal ballistic simulation under dynamic flow and combustion conditions. In the present investigation, a numerical evaluation of the usage of reactive aluminum particles for the suppression of axial shock wave development is brought forward, for a motor whose instability symptom driving mechanisms are based on transient combustion response and structural-vibration-induced normal acceleration. A primary focus is placed on evaluating the qualitative trends associated with the use of aluminum particles that in general diminish in size as they move downstream in the central internal flow. The particle size regression is stipulated to occur at a nonuniform rate, through an evaporation law that is governed by the particle's current diameter. Individual transient internal ballistic simulation runs for a reference composite-propellant cylindrical-grain motor show the evolution of the axial pressure wave for a given initiating pressure disturbance, particle loading, and initial particle size. The limit pressure wave magnitudes at a later reference time in a given firing simulation run are collected for a series of runs, in order to assist in the evaluation of identifiable trends. The numerical results demonstrate that the ability of the particles to suppress axial wave development can be effective, but in general, not nearly as effective when comparing to the constant-diameter inert particle case, for the same particle loading. There may be some advantage in using a larger starting reactive particle size relative to the reference inert case, for improved overall symptom suppression, to a certain extent. However, increasing the reactive particle loading may ultimately be the only feasible means for reaching a desired symptom suppression level. Nomenclature A= local core cross-sectional area, m 2 a = gas sound speed, m/s a R = longitudinal (or lateral) acceleration, m/s 2 a n = normal acceleration, m/s 2 b = nonequilibrium sound speed of two-phase mixture C = de St. Robert coefficient, m/s-Pa n C m = particle solid specific heat, J/kg-K C p = gas specific heat, J/kg-K C pp = reactive particle gas specific heat, J/kg-K C s = specific heat, solid phase, J/kg-K D i = drag of gas on a particle from i th particle set, N d = local core hydraulic diameter, m d mi = mean particle diameter for i th particle set, m d m,o = initial particle diameter, m E = local total specific energy of gas in core flow, J/kg E pi = local total specific energy, i th particle set in flow, J/kg f = frequency, Hz, or Darcy-Weisbach friction factor Propulsion and Energy Forum G a = accelerative mass flux, kg/m 2 -s h = convective heat transfer coefficient, W/m 2 -K )H s = net surface heat of reaction, J/kg K b = burn rate limiting coefficient, s -1 k = gas thermal conductivity, W/m-K k r = particle evaporation coefficient, s m / p n k s = thermal conductivity, solid ph...

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Section: Introductionmentioning

confidence: 99%

Use of Reactive Particles for Solid Rocket Combustion Instability Suppression

Greatrix¹

2014

50th AIAA/ASME/SAE/ASEE Joint Propulsion Conference

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“…Such an approach has been derived from the classical non linear mechanics text by Krylov and Bogoliubov [4]. All the above approaches have been supplemented by rigorous analytical modelling by Fletcher [5] and Levine [6], by external ballistic pulsing (Solanki [7]) and the effect of propellant geometry on the combustion stability [8]. Experimentally, the T-burner has been employed by researchers [7], to study the propellant response to incoming pressure oscillations.…”

Section: Introductionmentioning

confidence: 99%

Investigation of Intermittent Oscillations in Composite Propellant

Selvakumaran

Kadiresh

2017

Propellants Explo Pyrotec

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A pressurized window bomb arrangement for AP-HTPB combustion is studied using high speed images to analyze for unsteady combustion, resulting in combustion instability. The base combustion is unsteady and non-stationary. The base filtered heat release rate pattern displays intermittency, seldom observed in prior literature. The intermittency observed is of type 1, and subsequent analysis leads to questions on conventional amplitude spectra as a measure of instability. A novel indicator, the intermittency factor is defined to understand the role of intermittency. It is seen that intermittency is marked by fluctuating intermittency factor values, implying a large deviation in phase values.

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“…Studies of nonlinear axial combustion instability have ranged from numerous experimental test firing series on the one hand [1], and linear/nonlinear acoustic theory modeling on the other (largely, the analysis producing frequency-based standing wave solutions for a given chamber geometry, but without some useful quantitative information) [2][3][4][5]. On occasion, researchers have employed a numerical modeling approach, to work towards a more comprehensive quantitative understanding of the physics involved (the numerical model producing a traveling wave solution to a limit wave amplitude and corresponding small or larger dc shift, typically a time-based result evolving from an initial pulse disturbance introduced into the chamber flow) [6,7]. Available computational power and associated result turnaround times commonly forced some simplifications in the given numerical model.…”

Section: Introductionmentioning

confidence: 99%

Effect of Diminishing Particle Size on Solid Rocket Combustion Instability Symptom Suppression

Greatrix¹

2012

48th AIAA/ASME/SAE/ASEE Joint Propulsion Conference &Amp;amp; Exhibit

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Research towards predicting and quantifying undesirable transient axial combustion instability symptoms in solid-propellant rocket motors necessitates a comprehensive numerical model for internal ballistic simulation under dynamic flow and combustion conditions. In the present investigation, important elements of the framework for numerically evaluating the usage of reactive aluminum particles for the suppression of axial shock wave development are brought forward. A primary focus is placed on evaluating the qualitative trends associated with the time-dependent reduction in size of the aluminum particles as they move downstream in the central internal flow. In order to simplify the scope of this preliminary study, the reactive particle size regression is stipulated to occur at a designated uniform rate for a given simulated firing. Individual transient internal ballistic simulation runs for a reference composite-propellant cylindrical-grain motor show the evolution of the axial pressure wave for a given initiating pressure disturbance, and particle loading and size diminishment rate. Particle loading distributions at various locations in the motor chamber's internal flow, at different times into the given firing (pre-and postdisturbance), are presented. The limit pressure wave magnitudes at a later reference time in a given firing simulation run are collected for a series of runs at different particle size reduction rates, in order to assist in the evaluation of identifiable trends. The numerical results demonstrate that the ability of the particles to suppress axial wave development improves as the nominal particle regression rate becomes lower. Nomenclature A= local core cross-sectional area, m 2 a = gas sound speed, m/s a R = longitudinal (or lateral) acceleration, m/s 2 a n = normal acceleration, m/s 2 b = nonequilibrium sound speed of two-phase mixture C = de St. Robert coefficient, m/s-Pa n C m = particle solid specific heat, J/kg-K C p = gas specific heat, J/kg-K C pp = reactive particle gas specific heat, J/kg-K C s = specific heat, solid phase, J/kg-K D i = drag of gas on a particle from i th particle set, N d = local core hydraulic diameter, m d mi = mean particle diameter for i th particle set, m E = local total specific energy of gas in core flow, J/kg E pi = local total specific energy, i th particle set in flow, J/kg f = frequency, Hz, or Darcy-Weisbach friction factor G a = accelerative mass flux, kg/m 2 -s h = convective heat transfer coefficient, W/m 2 -K )H s = net surface heat of reaction, J/kg K b = burn rate limiting coefficient, s -1 k = gas thermal conductivity, W/m-K k s = thermal conductivity, solid phase, W/m-K M a = magnitude of attenuation M R = limit magnitude, cyclic input m pi = mean mass of a particle from i th particle set, kg N i = number of particles from the i th set in a given volume N set = total number of particle sets N tot = total number of particles in a given volume n = exponent, de St. Robert's law p = local gas static pressure, Pa )p d = initial pulse disturbance step ...

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Modeling of nonlinear longitudinal instability in solid rocket motors

Cited by 23 publications

References 16 publications

Use of Reactive Particles for Solid Rocket Combustion Instability Suppression

Use of Reactive Particles for Solid Rocket Combustion Instability Suppression

Investigation of Intermittent Oscillations in Composite Propellant

Effect of Diminishing Particle Size on Solid Rocket Combustion Instability Symptom Suppression

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