A separated two-phase flow analysis to study deflagration-to-detonation transition (DDT) in granulated propellant

Krier, Herman; Kezerle, J. A.

doi:10.1016/s0082-0784(79)80006-5

Cited by 6 publications

(13 citation statements)

References 12 publications

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“…propellant and explosives. The theoretical models that have been developed, jshow there are constitutive relations which are "rate-determining" functions [7,8]. In addition, these relations are generally not well defined…”

Section: )mentioning

confidence: 99%

Gas Flow Resistance Measurements Through Packed Beds at High Reynolds Numbers

Jones

Krier

1983

Journal of Fluids Engineering

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This research study indicates that the classical Reynolds number dependency of the coefficient of drag for gases forced into packed beds is not correct at high Reynolds numbers. Care must also be taken to account for boundary layer wall effects that occur when the ratio of test chamber diameter to bead particle diameter is too small. Included is a review of the literature pertaining to gaseous flow resistance in packed beds. An existing test facility used in a previous study was found unsatisfactory, and necessary corrections were made to obtain normalized pressure gradient measurements at increasingly high Reynolds numbers. The resultant data was organized into a new correlation for the coefficient of drag, that is Fv=150+3.89Re1−φ0.87 This formula was developed for air flowing over spherical particles at Reynolds numbers ranging from 103–105.

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Section: )mentioning

confidence: 99%

Gas Flow Resistance Measurements Through Packed Beds at High Reynolds Numbers

Jones

Krier

1983

Journal of Fluids Engineering

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“…where T is the temperature, µ g,0 is the value of viscosity at 2000 K, and T g,0 is 2000 K [12]. As for the interfacial heat transfer coefficient, the heat expression form, in the case of having spherical particles…”

Section: Physical Model Descriptionmentioning

confidence: 99%

“…However, as presented in Equation 7, there is a solid pressure defined as the addition of gas pressure and the intergranular stress (τ p ), understood as the resistance of the particles to be compacted under the critical porosity. In this study, the authors consider the expressions proposed in several works, such as the ones from Krier and Kezerle [12], Hoffman and Krier [11], and Gokhale and Krier [30]:…”

Section: Physical Model Descriptionmentioning

confidence: 99%

“…As for the numerical methods used in the modeling of detonation of granular solid energetic materials, most of the authors used finite-difference schemes [10] although with distinct approaches. Hoffman and Krier [11] and Krier and Kezerle [12] used the MacCormack method [13] with a predictor-corrector scheme. Sheu et al [14][15][16] and Krier et al [17] also used a finite-different scheme with the Lax-Wendroff approach [18] whereas Baer and Nunziato [19] and Butler [20] applied the method of lines [21,22].…”

Section: Introductionmentioning

confidence: 99%

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An Energetic Model for Detonation of Granulated Solid Propellants

et al. 2019

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Unexpected detonation of granular solid energetic materials is a key safety issue in the propellants manufacturing industry. In this work, a model developed for the characterization of the early stages of the detonation process of granular solid energetic materials is presented. The model relies on a two-phase approach which considers the conservation equations of mass, momentum, and energy and constitutive relations for mass generation, gas-solid particle interaction, interphase heat transfer, and particle-particle stress. The work considers an extension of approximated Riemann solvers and Total Variation Diminishing (TVD) schemes to the solid phase for the numerical integration of the problem. The results obtained with this model show a good agreement with data available in the literature and confirm the potential of the numerical schemes applied to this type of model. The results also permit to assess the effectiveness of different numerical schemes to predict the early stages of this transient combustion process.

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“…15 A number of empirical correlations were altered for use beyond the ranges for which these correlations were developed. The lack of suitable constitutive relationships under DDT conditions were noted.…”

Section: Introductionmentioning

confidence: 99%

Boundary Condition Specification for Mobile Granular Propellant Bed Combustion Processes

Chen

Kuo

1981

AIAA Journal

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In the modeling of transient one-dimensional, two-phase combustion of granular propellants in gun interior ballistics, the boundary conditions at both the breech end and the base of the projectile must be specified adequately. The form and the total number of the boundary conditions required depend upon the relative velocities of the gases and solid particles with respect to the solid boundary and the condition of fluidization. In the study of a simulated gun system, the flow properties at the boundary are obtained by considering 1) the local balances of mass, momentum, and energy over a small control volume adjacent to the boundary; 2) the compatibility relationships along the characteristic lines; and 3) the number of algebraic relationships according to the instantaneous flow conditions. These considerations are necessary to provide the extraneous boundary conditions required for solving the partial differential equations with a second-order numerical scheme. Numerical results were compared and found in agreement with test-firing data. Nomenclature A= cross-sectional area of cylindrical combustion chamber A s = specific surface area of granular propellants, the surface exposed to fluid per unit volume C = speed of sound in particle phase C L = combustion chamber length C v = specific heat at constant volume C p = specific heat at constant pressure dx/dt = slope of characteristic equations D p = drag force due to porosity gradient D t = total drag force between gas and particle phases,=drag force acting on gases by particles per unit wetted area of particles (evaluated from KuoNydegger correlation) D/Dt -Lagrangian time derivative when observer follows motion of the bullet, (d/dt) +u B (d/dx) E = total stored energy (internal plus kinetic energy) per unit mass h c = average convection heat-transfer coefficient over pelletŝ chem = enthalpy of propellant gas at flame temperature /z ign = enthalpy of igniter gas h ( = total heat transfer coefficient, the unit-surface conductance k -thermal conductivity of gases k p = thermal conductivity of particles K = coefficient of characteristic equations M ign = igniter mass flow rate P = pressure (? wg -wetter perimeter between chamber wall and gas phase ($> wp = wetter perimeter between chamber wall and particle phase q = rate of conduction heat transfer per unit area Q w = rate of heat loss to chamber wall per unit spatial volume of gas-particle system r b -burning rate of solid propellant r p -radius of pellets R = gas constant t = time T = temperature T abl = ablation temperature of solid propellant Tf = adiabatic flame temperature of pellets r hg = temperature of hot igniter gas T ps -particle surface temperature r ign = ignition temperature of solid propellant U = velocity with respect to laboratory coordinates U B = projectile velocity with respect to laboratory coordinateŝ feign ~ igniter gas velocity x = distance from beginning of granular propellant bed X B = instantaneous location of base of projectile X L =left boundary of partial-differential-equation solution ...

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A separated two-phase flow analysis to study deflagration-to-detonation transition (DDT) in granulated propellant

Cited by 6 publications

References 12 publications

Gas Flow Resistance Measurements Through Packed Beds at High Reynolds Numbers

Gas Flow Resistance Measurements Through Packed Beds at High Reynolds Numbers

An Energetic Model for Detonation of Granulated Solid Propellants

Boundary Condition Specification for Mobile Granular Propellant Bed Combustion Processes

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