Numerical Solution of Solid Propellant Transient Combustion

Kooker, Douglas E.; Nelson, C.T.

doi:10.1115/1.3450974

Cited by 31 publications

(16 citation statements)

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“…One can argue that the use of Eq. (30) or some comparable damping function, while empirical, parallels the approach taken by past researchers in using a stipulated surface thermal gradient; both approaches act to constrain the exchange of energy through the burning surface interface, allow for some variability in better comparing to a given set of experimental data, and prevent so-called burning-rate "runaway" (unstable divergence of r b with time) [26]. As discussed in [25], the use of K b at a set value does allow for a converged solution that is independent of the increment size for )t and )y, as long as one respects the Fourier stability requirement noted earlier.…”

Section: Equations For Propellant Burning Ratementioning

confidence: 93%

“…The idealized "pre-heated" inert particle assumption, entering the central core flow at T f , is shown in Eq. (26). As outlined in [18], the viscous interaction between the gas and a particle from the i th particle set is represented by the drag force D i , and the heat transfer from the core flow to a particle from the i th set is defined by Q i .…”

Section: B Equations Of Motion Governing Two-phase Flowmentioning

confidence: 99%

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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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Section: Equations For Propellant Burning Ratementioning

confidence: 93%

Section: B Equations Of Motion Governing Two-phase Flowmentioning

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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“…The pressure-based burning component may be found through de St. Robert's law: (13) The flow-based erosive burning component (negative and positive) is established through the following expression [18]: (14) where at lower flow speeds, the negative component resulting from a stretched combustion zone thickness (δ r > δ o ) may cause an appreciable drop in the base pressuredependent burning rate r o . The stretching of the flame zone at low speed may be viewed as being the result of a laminar-like sliding process of the local axial flow in the boundary layer acting to extend and curve the path of a representative particle moving up from the burning surface towards the flame front, such that the effective reactive length is increased.…”

Section: Numerical Modelmentioning

confidence: 99%

“…The focus of this study will be on strong axial shock-wave-related symptoms; two-and three-dimensional instability symptoms of smaller magnitude, e.g., due to vortex shedding observed in segmented motors, will not be under consideration here. A more recent version of a transient burning rate model (based on the Zeldovich-Novozhilov [Z-N] approach [13][14][15][16], with specific modifications for the simulation model as described in [17]) is employed for the present study. The latest version of this Z-N model allows for the inclusion of a net surface heat of reaction term (∆H s ), that better enables a match to experimental response data.…”

Section: Introductionmentioning

confidence: 99%

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

Greatrix

2009

International Journal of Spray and Combustion Dynamics

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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 pressuredependent and acceleration-dependent burning, is applied to the investigation of instabilityrelated behaviour in a small cylindrical-grain motor. Pertinent key factors, like the initial pressure disturbance magnitude and the propellant's 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. NOMENCLATURE INTRODUCTIONOver the last fifty years or so, there has been a number of research efforts directed towards understanding the physical mechanisms, or at least the surrounding factors, behind the appearance of symptoms associated with nonlinear axial combustion instability [1-2] in solid rocket motors (SRMs). Traditionally, these symptoms are a sustained axial pressure wave presence in the combustion chamber, sometimes accompanied by a substantial rise in the base chamber pressure [dc shift]. The motivation for these past and present studies was and is of course to bring this better understanding to bear in more precisely suppressing, if not eliminating, these symptoms. Studies of nonlinear axial combustion instability have ranged from numerous experimental test firing series on the one hand [3], and linear/nonlinear acoustic theory modelling on the other [2,[4][5][6]. Largely, the acoustic analysis produces frequency-based standing wave solutions for a given chamber geometry, but typically without some useful quantitative information. On occasion, researchers have employed a numerical modelling approach, to work towards a more comprehensive quantitative understanding of the physics involved [7][8]. The numerical model would typically produce a travelling wave solution to a limit pressure wave amplitude and a corresponding small or larger dc shift in chamber pressure, a time-based result evolving from an initial pulse disturbance introduced into the chamber flow. Available computational power and associated result turnaround times commonly forced some simplifications in the given numerical model. A comprehensive numerical model for simulation of nonlinear dynamic flow and combustion conditions is ultimately essential in the quest for the ability to predict and quantify axial combustion instability symptoms in SRMs. An effective model combines the ef...

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“…[81][82][83][84][85][86][87], oscillatory burning (Refs. [88][89][90][91][92][93][94][95][96][97][98][99][100][101][102][103][104][105][106][107], deflagration and low pressure extinction of ammonium oerchlorate (Refs. [108][109][110][111][112][113][114][115][116][117][118][119][120][121][122], low pressure extinction of composite propellants (Refs.…”

Section: -Background or The Research Studymentioning

confidence: 99%