Mathematical modeling of detonation of an aluminum dust in oxygen with allowance for velocity nonequilibrium of the particles

Theoretical and numerical study of detonation processes in gas suspensions with aluminum particles

“…In solving a system of ordinary differential equations, all final states cannot be reached because the solution may contain a "choking line" [16,17] consisting of points where the derivatives of the main parameters become infinite. This situation may occur even for detonation velocities higher than the theoretical CJ velocity.…”

“…2a (the points are the results of numerical experiments) [16]. Similarly, in the two-velocity model, the domain of existence of steady solutions in the phase space (M 0 , α, β) is separated by the surface M 0 =M(α, β) [17]; here M 0 is determined by the frozen velocity of sound. There are no steady solutions for M 0 <M(α, β), and overdriven detonation is reached for M 0 >M(α, β).…”

“…An analysis of the model and numerical results obtained with the use of the latter can be found in [16][17][18][19][20][21][22][23][24][25]. Other mathematical models that describe detonation of aluminum-gas mixtures are also available in the literature; in particular, a model of aluminum-dust detonation with allowance for the kinetic mechanism of nucleation of the condensed oxide was proposed in [26].…”

“…The initial data for the computations were described in [17]. Figure 3a shows the distributions of pressure and density of the gas and particles in the weak detonation regime with α = 10 and β = 20 (solid curves).…”

“…To solve the problem of propagation of a traveling planar wave of heterogeneous detonation in a gas suspension and to determine the wave structure, we use a steady variant of equations of system A in a front-fitted coordinate system [7,8,16,17]. The initial state is the undisturbed state ahead of the front, and the final state is determined from the condition of equilibrium after termination of relaxation processes and chemical reactions.…”