Linear Stability and Pressure-Driven Response Function of Solid Propellants with Phase Transition

Cozzi, Franco; DeLuca, Luigi T.; Novozhilov, B. V.

doi:10.2514/2.5500

Cited by 11 publications

(7 citation statements)

References 19 publications

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“…Therefore, as more accurate and detailed combustion validation results become available, it will become necessary to incorporate more detailed condensed-phase reaction kinetics into combustion simulations. Some combustion simulation models have been developed over the past decades to include more sophisticated condensed-phase phenomena, including multistep reactions [33], phase transition [34][35][36], melting [37,38], porosity of the granular material [39,40], etc. However, they are either computationally expensive (not applicable to large-scale engineering simulation codes for the time being) or do not give significantly better performance than the WSB model in transient combustion simulation.…”

Section: Discussionmentioning

confidence: 99%

Use of Condensed-Phase Reaction Models in Combustion Simulation of Energetic Materials

Wang

Wight

2008

Journal of Propulsion and Power

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The contribution of condensed-phase reaction kinetics to the overall combustion behavior of cyclotetramethylenetetranitramine is investigated in the context of a successful two-step chemical reaction scheme introduced by Ward, Son, and Brewster ("Role of Gas-and Condensed-We derive extensions of the activation energy asymptotics of the condensed-phase reaction from nthorder (0 n 1) kinetics to include 10 additional analytic reaction models. The results show that it is not possible to determine uniquely the condensed-phase reaction model by validating against steady-state burn rates and surface temperatures because the parameters of all models are sufficiently flexible to fit the experiments. However, the frequency-dependent transient response functions of mass burning rate to fluctuations in pressure and external radiation are somewhat more sensitive to the choice of kinetic model. The sensitivity of using different kinetic models to fit experimental T-burner data is more pronounced under conditions in which the surface temperature is low and no external radiation is applied. The power law model, which has the highest contribution to condensed-phase heat release, provides the best fit to transient combustion response functions. Nomenclature A c = Arrhenius preexponential factor B g = gas-phase frequency factor C p = heat capacity D g = gas-phase Damköhler number E = activation energy f = frequency of oscillating pressure/radiance f r = fraction of external radiation absorbed below surface reaction zone fY = condensed-phase reaction model K a = laser absorption coefficient of condensed phase k = nondimensional temperature sensitivity m = mass burning rate or mass flux m r = reference mass flux, 1 kg=m 2 s n = order of reaction P = pressure Q = heat release q = heat flux R = ideal gas constant R p = pressure-driven frequency response function R q = radiation-driven frequency response function r = @T s =@T 0 p r b = linear burn rate T = temperature W = molecular weight x = distance x g = gas flame characteristic thickness Y = mass fraction Y cc = critical mass fraction at burning surface = extent of conversion = r k, Jacobian parameter @ x y = @y=@x = thermal conductivity = homogeneous solution to energy equation with oscillating perturbation = pressure exponent or pressure sensitivity = solid density p = temperature sensitivity = nondimensional frequency c = rate of condensed-phase reaction ! = 2f, circular frequency Subscripts c = condensed phase f = flame g = gas l = liquid r = radiation s = surface = extent of conversion 0 = initial Superscript = nondimensional quantity

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Section: Discussionmentioning

confidence: 99%

Use of Condensed-Phase Reaction Models in Combustion Simulation of Energetic Materials

Wang

Wight

2008

Journal of Propulsion and Power

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“…. : (18) For velocity coupling the nonlinear forcing function can be calculated as follows. For n= 1,3,5,...: 5…”

Section: Higher Order Driving Termsmentioning

confidence: 99%

Experimental Combustion Instability Data Analysis using different theoretical Models

Knoetze

Rousseau

2013

49th AIAA/ASME/SAE/ASEE Joint Propulsion Conference

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Combustion instability (CI) is a problem that is often ignored during the design phase of a new solid rocket motor (SRM). When a project is plagued with its occurrence ad hoc solutions are often used to eliminate the problem at the cost of performance. This is due to two factors; the expense associated with obtaining combustion instability data for a propellant and secondly, the difficulty associated with making predictions, especially for complex grain geometries.This study focuses on the first problem namely to obtain useable data for predictions. The T-Burner has long been regarded as the industry standard for obtaining such data, but it is an expensive apparatus to operate and maintain. It requires a large test matrix and thus a large number of man-hours.A tubular grain motor that can be pulsed was developed. This allows for several frequencies to be evaluated simultaneously. Two sets of hardware were developed to perform pulse tests. A re-usable tubular grain motor that can be operated at a wide range of pressures as well as modular re-useable pulsers that can produce desired pressure disturbances over a wide range of motor pressures were developed. The pulsers were evaluated by performing cold flow tests. It was possible to predict their performance over a large range of pressures. This prediction capability allowed for fast pulser calibration for the motor used in this study.Several different propellants have been tested with success and high quality data have been obtained. Subsequent analysis of this data has shown that it is possible to obtain admittance/response functions from this data and vastly decrease the total number of tests required to quantify a propellants response. Hardware was shown to be reliable and the results reproducible.It has been shown that one pulse test can replace 30 T-Burner tests. This lead to a dramatic decrease in man-hours required. Though there is still some debate on which growth and loss terms should be included the analyst can decide which to include. As long as the analyst is consistent with the terms used to predict the full scale motor's stability it is possible to select the propellant least likely to go unstable. This study has also shown that it is possible to obtain the velocity coupled response allowing for the prediction of triggering. Regardless of the CI linear terms employed, this methodology provides the SRM designer in the tactical missile environment a tool to obtain admittance/response function for a propellant quickly and cheaply allowing for the selection of the best propellant for the specific design. NomenclatureA nondimensional function used in linear frequency response analysis A b Admittance function for the burning surface α Growth or decay constants [s −1 ] A n , B n Slowly varying amplitudes B nondimensional function used in linear frequency response analysis β c Non-linear gas dynamics term arising from Culick's method D Diameter [m] E s Activation energy, cal/mol η Thermal diffusivity (m 2 /s) η n Mode amplitude of the n th acoustic mode f Fre...

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“…Various aspects of the problem were analyzed in [5][6][7][8][9]. A fairly complete review of publications can be found in [10]. Obviously, the powder characteristics exert a strong effect on combustion instability.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear response functions of the burning rate of ballistite powders

Зенин

Finjakov

2008

Combust Explos Shock Waves

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Second-order nonlinear response functions to pressure oscillations are calculated for a group of ballistite powders with additives, based on results of microthermocouple measurements. A unified law of gasification of ballistite powders is refined. A classification of nonlinear response functions is proposed: viscous, normal, and critical response functions are identified. More than half of the burning regimes of these powders are demonstrated to have a viscous response type with a weak dependence on frequency and with a weakly expressed maximum in the case of a resonance. The effect of the powder composition on the nonlinear response functions is analyzed. Specific features of the nonlinear response as a function of a new parameter (phase shift between the interacting modes) are considered. It is shown that the errors in determining the nonlinear response functions depend on the response type and have low values for the majority of the burning regimes. Arguments in favor of the process one-dimensionality in the reactive layer of the condensed phase are given. A hypothesis of the near-critical state of some products of decomposition in this layer is proposed.

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Linear Stability and Pressure-Driven Response Function of Solid Propellants with Phase Transition

Cited by 11 publications

References 19 publications

Use of Condensed-Phase Reaction Models in Combustion Simulation of Energetic Materials

Use of Condensed-Phase Reaction Models in Combustion Simulation of Energetic Materials

Experimental Combustion Instability Data Analysis using different theoretical Models

Nonlinear response functions of the burning rate of ballistite powders

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