Prediction of the effects of acceleration on the burning of AP/HTPB solid propellants

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

2014

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...

Section: Equations For Structural Motionmentioning

confidence: 99%

“…One needs to take care in setting the solid-phase spatial increment )y, to be in accordance with the Fourier stability limit, )y Fo = (2" s )t) 1/2 , which is a function of the chosen time increment )t [34]. The time increment itself must be coordinated between the flow and structural model solution systems [30].…”

Section: Equations For Propellant Burning Ratementioning

confidence: 99%

Use of Reactive Particles for Solid Rocket Combustion Instability Suppression

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

2014

“…Structural vibration can play a significant role in nonsteady SRM internal ballistic behavior, as evidenced by observed changes in combustion instability symptoms as allied to changes in the structure surrounding the internal flow (e.g., propellant grain configuration, wall thickness, material properties) [10,12,21]. The level of sophistication required for modeling the motor structure (propellant, casing, static-test sleeve, nozzle) and applicable boundary conditions (load cell on static test stand) can vary, depending on the particular application and motor design.…”

Section: Equations For Structural Motionmentioning

confidence: 99%

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

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

2012

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 ...

“…Structural vibration can potentially play a significant role in nonsteady HRE internal ballistic behavior, as evidenced by observed changes in combustion instability symptoms in solid-propellant rocket motors (SRMs) as allied to changes in the structure surrounding the internal flow (e.g., fuel grain configuration, wall thickness, material properties) [13][14][15]. The level of sophistication required for modeling the engine structure (fuel grain, combustor casing, nozzle) and applicable boundary conditions (load cell on static test stand) can vary, depending on the particular application and engine design.…”

Section: B Equations For Structural Motionmentioning

confidence: 99%

Hybrid Rocket Engine Transient Internal Ballistic Simulation

51st AIAA/SAE/ASEE Joint Propulsion Conference

2015

There is considerable interest in gaining an improved prediction capability for hybrid rocket engine (HRE) performance under quasi-steady and nonsteady (transient) operating conditions. Transient behavior during an engine firing's main phase can occur at lower frequencies (non-acoustic symptoms) or at higher frequencies (acoustic symptoms). The focus of the present investigation is on simulating the intrinsic low frequency (LF) symptoms that commonly appear in HRE firings, whether the oxidizer feed system is isolated (regulated) or not. One associates this category of combustion instability with LF pressure oscillations of significant magnitude and persistent duration in the combustion chamber. For the present simulation model, the utility of employing a generalized Zeldovich-Novozhilov (Z-N) approach for modeling the transient LF combustion response at the burning fuel surface is demonstrated. Initial development of the internal ballistic simulation model is guided by experimental test firing data for a conventional GOx/HTPB engine. The influence of stoichiometric length, and a higher fuel regression rate, on intrinsic LF behavior is examined, with guidance from experimental test firing data for a nitrous oxide/paraffin engine. 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 C p = gas specific heat, J/kg-K C s = specific heat, solid phase, J/kg-K d = local core hydraulic diameter, m E = local total specific energy of gas in core flow, J/kg f = frequency, Hz, or Darcy-Weisbach friction factor f LF = frequency of intrinsic LF pressure oscillations, Hz f r = resonant frequency, Hz G = axial mass flux, kg/s-m 2 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 L st = stoichiometric length, m R f = fuel grain length, m M R = limit magnitude, cyclic input o m  = oxidizer mass flow, kg/s p = local gas static pressure, Pa )p LF = peak-to-trough LF pressure oscillation magnitude, Pa R = specific gas constant, J/kg-K r b = instantaneous fuel regression rate, m/s r b,o = reference regression rate, m/s r b,qs = quasi-steady regression rate, m/s r b * = unconstrained regression rate, m/s r o = base fuel regression rate, m/s r st= stoichiometric mixture ratio (oxidizer-to-fuel mass) T ds = decomposition temperature of fuel under non-combustive ablation, K T f = flame temperature, gas phase, K T i = initial temperature, solid phase, K T ox = incoming oxidizer temperature, K T s = burning surface temperature, K T 4 = local core gas temperature, K )t = time increment, s u = core axial gas velocity, m/s v f = nominal flamefront velocity, m/s x = axial distance from head end, m )x = spatial increment in axial direction, m y = radial distance from burning surface, m )y = spatial increment in radial direction, solid phase, m )y Fo = Fourier limit spatia...