Combustion, Explosion, and Shock Waves, Vol. 38, No. 2, pp. 206–214, 2002
Interaction of a Shock Wave with a Cloud of Aluminum Particles in a Channel T. A. Khmel’1 and A. V. Fedorov2
UDC 532.529+541.126
Translated from Fizika Goreniya i Vzryva, Vol. 38, No. 2, pp. 89–98, March–April, 2002. Original article submitted February 15, 2001.
Interaction of an incident shock wave (with a rectangular or triangular profile behind its front) with a finite-width semi-infinite cloud of aluminum particles located in a channel along the plane of symmetry is numerically simulated. Shock-wave interaction with the leading edge of the cloud results in the formation of a vortex that leads to cloud dispersion. Reflection of the curved shock wave from the plane of symmetry may be regular or may include the formation of the Mach stem. If the cloud is loaded by a rather strong shock wave, a detonation wave is formed in the cloud. In this case, the flow is periodic, which is caused by passing of transverse waves and their reflection from the walls.
INTRODUCTION The study of the behavior of suspensions of reactive particles in air under conditions of dynamic loading is of both theoretical and practical interest, in particular, for ensuring explosion and fire safety of industrial and civil buildings. One of the key problems is to determine conditions of initiation of detonation combustion of dust–gas mixtures. Initiation of detonation of suspensions of aluminum particles in air and oxygen was studied experimentally [1–4] and theoretically [5–12]. The mathematical model for detonation processes in a suspension of aluminum particles in oxygen was developed in [5] and later was applied to analyze steady detonation structures [7, 8] and unsteady processes [6, 9–11]. The calculation results are in agreement with experimental data on the detonation velocity [1] and correspond to the data of Borisov et al. [4] in terms of the estimated necessary energy of initiation. In [12], the processes of interaction of a shock wave (SW) with a cloud of particles are studied in a one-dimensional 1
Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090;
[email protected]. 2 Novosibirsk State University of Architecture and Construction, Novosibirsk 630008;
[email protected]; Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090.
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unsteady formulation, and conditions and scenarios of initiation of detonation waves depending on the amplitude and profile of the incident SW were determined. One of the specific features of initiation of the detonation wave in the cloud is the influence of the ρ-layer (layer of an elevated concentration of particles at the detonation-wave front) whose formation was predicted in [13] on the behavior of the combustion front at low amplitudes of the initiating SW. In this case, ignition of particles occurs at the cloud edge, and the detonation wave is formed as a result of acceleration of the combustion front due to its interaction with the ρ-layer. Two-dimensional effects in problems of propagation of detonation waves in a suspension of aluminum particles were studied by Khasainov et al. [14] who obtained a cellular structure of the steady detonation front by means of direct numerical simulation. SW interaction with a layer of inert particles was studied numerically in [15], which was associated with the problem of dust lift-up. The following specific features of the behavior of the layer were observed experimentally: delay in the lift-up of particles after SW passage and establishment of the limiting width of the cloud of particles. Korobeinikov et al. [16] considered a similar problem for reacting particles, where the introduction of a local two-dimensional perturbation of particle density led to the development of oscillatory modes of detonation propagation that did not decay under certain conditions. The reasons for this phenomenon have
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Interaction of a Shock Wave with a Cloud of Aluminum Particles in a Channel not been clearly understood; the authors only noted that the ρ-layer participates in the processes considered. The objective of the present paper is to study the edge effects at the boundary of an aerosuspension cloud under the action and passage of shock waves and also to study the effect of the finite transverse size of the cloud on excitation and propagation of detonation waves. Thus, the action of shock waves on a finite-width cloud of aluminum particles located in a plane channel is studied on the basis of the physicomathematical model of heterogeneous detonation of the suspension of aluminum particles in air [5, 8, 12] in a two-dimensional formulation.
1. FORMULATION OF THE PROBLEM We consider a plane channel with a symmetrically located cloud of aluminum particles in the form of a semi-infinite rectangle. The remaining space of the channel is filled by a gas (oxygen). The initiating action is a planar shock wave propagating over the gas along the channel and hitting the cloud. The profile of the initiating SW may be rectangular (supported SW), triangular, or trapezoid (SW accompanied by a rarefaction wave). In SW–cloud interaction, crossflow effects are manifested in deformation of the SW front, a change in the cloud shape, and dispersion of particles. The problem is to study these effects and determine their influence on excitation and propagation of detonation waves. SW interaction with a cloud of reacting solid particles is described within the framework of mechanics of interpenetrating continua with allowance for chemical reactions in the mixture. The channel walls are assumed to be ideally smooth and heat-non-conducting, and viscous effects are taken into account only in forces of interphase interaction. The particle concentration is assumed to be close to a stoichiometric value, which allows us to neglect the influence of the volume fraction of particles on the motion of the mixture. Equations that follow from the laws of conservation of mass, momentum, and energy have a divergent form (a complete description of the physicomathematical model that describes a one-dimensional unsteady detonation flow can be found in [12]): ∂ρi ui ∂ρi vi ∂ρi + + = (−1)i−1 J, ∂t ∂x ∂y ∂ρi ui + ∂t
∂[ρi u2i
+ (2 − i)p] ∂ρi ui vi + ∂x ∂y = (−1)i−1 (−fx + Ju2 ),
(1)
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∂(ρi ui vi ) ∂[ρi vi2 + (2 − i)p] ∂ρi vi + + ∂t ∂x ∂y i−1
= ( − 1)
(−fy + Jv2 ),
∂ρi Ei ∂[ρi ui (Ei + (2 − i)p/ρ1 )] + ∂t ∂x +
∂[ρi vi (Ei + (2 − i)p/ρ1 )] ∂y
= (−1)i−1 (−q − fx u2 − fy v2 + JE2 ). Hereinafter, p is the pressure, ρi = mi ρii is the mean density, mi is the volume concentration of the ith phase (i = 1, 2), m1 + m2 = 1, ρii is the true density of the phases, ρ22 = const, ui and vi are the velocity components, Ei is the total energy per unit mass, and cv,i is the heat capacity; the subscripts 1 and 2 refer to the gas and particles, respectively. The system is closed by the equations of state p = ρ11 RT1 , Ei = (u2i + vi2 )/2 + cv,i Ti + (i − 1)Q and global law of the chemical reaction: ρ Ea J = max(0, (ξ − ξk ))exp − , τξ RT2 T2 > Tign ;
J = 0,
(2)
(3)
T2 < Tign .
Here T1 and T2 are the gas and particle temperatures, Q is the heat release in the chemical reaction, ξ = ρ2 /ρ is the relative mass concentration of particles, ρ = ρ1 +ρ2 , ξk is the minimum admissible (residual after burning) fraction of particles, Ea is the activation energy, Tign is the ignition temperature, and τξ is the characteristic time of combustion. The processes of interphase interaction are determined by the following formulas [12, 17, 18]: f=
3m2 ρ11 cD |u1 − u2 |(u1 − u2 ), 4d q=
6m2 λ1 Nu(T1 − T2 ), d2
(4)
Nu = 2 + 0.6Re1/2 Pr1/3 , 0.43 cD (Re, M12 ) = 1 + exp − 4.67 M12 24 4 , × 0.38 + +√ Re Re √ |u1 − u2 | ρ11 ρ11 d|u1 − u2 | Re = , M12 = . √ µ γ1 p
(5)
208 Here d is the particle diameter, cD is the drag coefficient of particles, λ1 is the thermal conductivity of the gas, Re, Nu, and Pr are the Reynolds, Nusselt, and Prandtl numbers, respectively, µ is the viscosity of the gas, and γ1 = R/cv,1 is the ratio of specific heats of the gas. The initial-boundary problem for system (1)–(5) is formed similar to [12] but with allowance for the finite transverse size of the cloud: ϕSW , 0 6 x < XSW , 0 6 y 6 Y, ϕ0 , XSW 6 x < Xcl , 0 6 y 6 Y, t = 0, ϕ = (6) ϕ cl , Xcl 6 x < +∞, 0 6 y < D, ϕ0 , Xcl 6 x < +∞, D 6 y 6 Y.
Here ϕ = {ρ1 , ρ1 u1 , ρ1 v1 , ρ1 E1 , ρ2 , ρ2 u2 , ρ2 v2 , ρ2 E2 } is the vector of the solution, ϕSW (x) describes the planar shock wave in the gas (supported or accompanied by a rarefaction wave), XSW is the initial position of the front of the incident SW, ϕ0 and ϕcl refer to the state ahead of the SW front in the gas and the initial state of the mixture in the cloud, respectively, Xcl determines the front boundary of the cloud, 2D is the cloud width, 2Y is the channel width, and y = 0 is the plane of symmetry. The boundary conditions at the channel wall y = Y were set in accordance with the no-slip and heatinsulation conditions; conditions of symmetry were imposed for y = 0. The state behind the supported SW or the state after the passage of the rarefaction wave adjacent to the SW was sustained at the left boundary x = 0. Initial conditions were set at the right boundary, which was always at a certain distance ahead of the shock (detonation) front in computations. The initial conditions of the mixture were set in accordance with the data of [12]: p0 = 1 atm, T10 = T20 = 300 K, Tign = 900 K, ξcl = 0.55, Ea = 106 J/kg, Q = 2.94 · 106 J/kg, cv,1 = 914 J/(kg · K), and cv,2 = 880 J/(kg · K). The computations were performed for particles 5 and 1 µm in diameter. The value of Y was varied from 2 to 9 cm for D = 10 cm. The problem was solved on a uniform twodimensional finite-difference grid with the use of a TVD scheme for the gas and MacCormack scheme for the particles [10–12]. The computational domain was expanded in the course of propagation of the transient SW or initiated detonation wave over the mixture, including the undisturbed flow region. In the problem of propagation of an already formed detonation wave in a steady regime, the computational domain was bounded by the zone of equilibrium flow in detonation products, which was greater than the relaxation region by more than an order of magnitude. In this case, “soft” boundary conditions (zero values of the second derivatives of the parameters of the mixture) were set at the left boundary.
Khmel’ and Fedorov 2. NUMERICAL RESULTS 2.1. Interaction of a Supported SW with a Could of Nonreacting Particles. Regular and Mach Reflection. Vortex Structure Let the incident shock wave be characterized by a rectangular profile of parameters and its amplitude be lower than the critical value [12] at which the particles in the cloud can exceed the ignition threshold. Entering the cloud, the SW is decelerated, and refraction of the SW front is observed at the longitudinal boundary of the cloud. Figure 1 shows the shadow relief of pressure at the times t = 0.2, 0.4, and 0.5 msec for a propagation velocity of the incident SW equal to 1.037 km/sec (M0 = 3, the SW Mach number is determined by the velocity of sound of the initial state of the gas). The regions of negative and positive pressure gradients along the x axis are marked by the dark and light colors. For a rather small width of the cloud (Y = 2 cm), SW propagation in the channel is characterized by a strongly curved front inside the cloud for large particles (d = 5 µm) and by an inclined front for small particles (d = 1 µm). The arc-shaped SW reflected from the cloud (denoted by the letter R) is clearly seen at t = 0.2 msec. A small pressure shock that disappears outside the cloud (B) arises between the fronts of the reflected SW and leading SW as a result of turning over of the compression wave. The velocity and amplitude of this shock decrease, and it disappears after a certain time. As is seen from Fig. 1, SW propagation over the layer acquires a steady character. The SW velocity determined by the position of the maximum pressure gradient at y = 0 is approximately 0.97 km/sec. This value is greater than that for a cloud occupying the entire cross section of the channel (0.78 km/sec) but smaller than the SW velocity in the gas ahead of the cloud (1.037 km/sec). An increase in the relative width of the cloud leads to a greater deceleration of the SW in the channel. Thus, the front velocity reaches 0.94 km/sec for D = 5 cm and 0.84 km/sec for D = 8 cm. The behavior of the density of particles and the ρ-layer (the possibility of appearance of the latter in relaxing disperse media was predicted in [13]) was studied in a one-dimensional formulation [12]. In the case of a supported SW, a constant extension of the region of elevated density of particles is observed. In our case, the mixture behind the SW front becomes more compacted not only due to the longitudinal motion of the particles but also as a result of transverse compression of the layer upon refraction of the SW front at the in-
Interaction of a Shock Wave with a Cloud of Aluminum Particles in a Channel
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Fig. 1. Entrance of an SW (M0 = 3) into a layer of particles of diameter 5 (left) and 1 µm (right): shadow diagram of pressure for D = 2 cm and t = 0.2, 0.4, and 0.5 msec (from top to bottom on the left and on the right).
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Fig. 2. Dispersion of the cloud. Shadow image of particle density (M0 = 3 and D = 2 cm): on the left, d = 5 µm and t = 0.2, 0.3, 0.4, and 0.7 msec (from top to bottom); on the right, d = 1 µm and t = 0.2, 0.3, 0.4, and 0.5 msec (from top to bottom).
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Fig. 3. Flow structure at the time t = 0.7 msec for M0 = 3, D = 8 cm, and d = 5 µm.
terface between the gas and the aerosuspension. This can be seen in Fig. 2, which shows the shadow image of the particle density at various times for fractions with d = 5 and 1 µm (D = 2 cm). The dark color indicates high values of ρ2 , and the light color shows the absence of particles. Interaction of the incident SW with the edge of the cloud generates a vortex responsible for the crossflow motion of the mixture. The front edge of the cloud acquires a shape typical of the gas flow around clouds [18]. In a mixture of small particles, the crossflow motion toward the plane of symmetry leads to a significant compression of the cloud, but the vortex flow increases its width again. As a result, the maximum lift-up of the particles (the upper edge of the cloud) is identical both for d = 5 µm and for d = 1 µm. It is also seen that several regions of compaction of the layer behind the SW front are formed in a mixture of small particles as a result of multiple reflection of the SW from the plane of symmetry and the upper edge of the cloud. There are three such regions in Fig. 2 for the parameters d = 1 µm and t = 0.4 and 0.5 msec: directly behind the shock wave, at the left edge of the cloud, and in the region between them. The lift-up of particles under the action of the SW reflected from the plane of symmetry does not increase the cloud width to an extent greater than the initial value, i.e., it is not as significant as that caused by the vortex flow in the region of the front edge of the cloud. Figure 3 shows the flow parameters behind the SW front for M0 = 3, D = 8 cm, and d = 5 µm at the time t = 0.7 msec. Two upper fragments of the figure show the shadow relief of pressure and the shadow image of the particle density, respectively. High-pressure and low-pressure regions are marked by the light and dark color, respectively. The dark spot indicated by the letter V shows the vortex center. The distribution
of the particle density is similar to Fig. 2 for d = 1 µm and t = 0.2 msec; one can also see the refraction of the SW front at the gas–cloud interface and the refraction of the slip surface. The letter C on the shadow relief of the longitudinal velocity of the gas in Fig. 3 indicates a triangular region with clear boundaries between the SW front and the slip surface, where the longitudinal velocity of the mixture is smaller, but the crossflow velocity has a nonzero (negative) value. In this triangle, sharp turning of the flow toward the plane of symmetry is observed, which leads to compression of the cloud. The character of reflection of the refracted SW from the plane of symmetry inside the cloud depends on the particle size and cloud width. For large particles (d = 5 µm) for D = 2 cm, refraction has no clear structure, since the width of the relaxation regions is 2–3 cm and is comparable with the cloud width. For small particles (d = 1 µm), regular reflection from the plane of symmetry is observed (see Fig. 1). For d = 5 µm and D = 8 cm, the formation of the Mach stem is observed in the shadow relief of pressure (see Fig. 3). The Mach stem thickness here is determined by the large length of the relaxation regions. The reflected SW adjacent to the Mach stem is almost perpendicular to the slip surface, and no more reflections are observed. The flow patterns in Fig. 3 are similar to those in [19], where the cloud of particles was modeled by a layer of a denser gas in a similar problem. The transition from regular to Mach reflection in [19] was associated with the change in the initial density of the layer; the influence of other factors on the appearance of the Mach stem and its height was not studied. It was possible to establish some features of the dependence of the Mach stem height on the SW amplitude and layer thickness only for small particles for which the size of the velocity and temperature relaxation regions is much
Interaction of a Shock Wave with a Cloud of Aluminum Particles in a Channel smaller than the layer thickness (d = 1 µm). The computations for M0 = 1.5, 2, 3, and 5 (without burning of particles) show that the emergence of the Mach stem is almost independent of the amplitude of the incident SW but depends on the thickness of the layer of the mixture for a fixed initial concentration of particles in the cloud. Thus, regular reflection of the SW from the plane of symmetry is observed for D = 2 and 4 cm, and Mach reflection is observed for D = 6 and 8 cm. The height of the Mach stem formed when the SW enters the cloud decreases with time and tends to a constant value as the SW propagation becomes steady. The limiting height depends also on the layer width and particle size and slightly varies with changing amplitude of the incident SW. For example, for d = 5 µm and M0 = 3, it varies from 1.7 cm for D = 6 cm to 2 cm for D = 8 cm; for d = 1 µm and M0 = 3, it varies from 1.4 cm for D = 6 cm to 1.8 cm for D = 8 cm and reaches 1.2 cm for M0 = 2 and D = 6 cm. A model computation was performed, where particle ignition and combustion were eliminated, and only the influence of the SW amplitude on the formation of the shock-wave structure in the channel was examined. The results for M0 = 5 (velocity of the incident SW is 1.73 km/sec), D = 6 cm, and d = 5 µm under the action of a supported SW are shown in Fig. 4 for the times t = 0.3 and 0.45 msec. The distributions of the particle density and gas temperature are shown as shadow images (an inverse color scale is used for temperatures: the low and high values are shown by the dark and light color, respectively). The flow structure is similar to that shown in Fig. 3. In addition, one can see that a configuration with a Mach stem height of 1.25 cm is formed in the case of SW reflection from the plane of symmetry. The vortex flow of the gas is manifested here in temperature distributions: intense mixing of the less heated layer of the mixture in the cloud and the more heated gas behind the SW outside the cloud is observed. The crossflow compression of the cloud for the SW with M0 = 5 is stronger, but the maximum of the particle density 3 (≈23 kg/m ) corresponds to the volume concentration equal to 0.008, which is still within the accepted assumption of the small influence of the particle volume on the flow. 2.2. Interaction of a Real SW Attenuated by a Rarefaction Wave with a Cloud of Inert Particles The incident SW was assumed to be a structure consisting of an SW with a rectangular profile of a given amplitude (given Mach number) and a centered rarefac-
211
tion wave accompanying the SW at a certain distance from the front. The zone of the constant flow of the mixture is adjacent to the last characteristic of the rarefaction wave determined from the condition of pressure decrease to the atmospheric value. Thus, the gas-velocity profile has the form of a trapezium at the initial time. In the long run, the rarefaction wave first catches up the SW (the profile becomes triangular), and then the attenuated SW is decelerated and decays. SW decay is also observed when it enters the cloud; nevertheless, for a certain time, the SW interacts with the cloud approximately in the same manner as the supported SW. The flow pattern is shown in Fig. 5 as the distributions of the particle density and velocity components of the gas (the upper fragment for u1 shows the shadow relief and the lower fragment shows the shadow image, where the low and high values are marked by the dark and light color, respectively). The formation of a characteristic triangle bounded by the SW front in the mixture, slip surface, and reflected SW that rests on the Mach stem is also seen. In this region, the flow turns toward the plane of symmetry (dark triangle in the fragment for the crossflow velocity). The light spot on the shadow image for v1 indicates the region of lift-up of the particles. As in the one-dimensional case, the main difference in the action of attenuated and supported SW on the cloud is the fact that deceleration of the mixture in the rarefaction wave leads to longitudinal smearing of the ρ-layer whose amplitude also decreases with time. A comparison of the particle-density distributions in Figs. 4 and 5 shows that the front part of the cloud in Fig. 5 is smeared. The flow immediately behind the SW front in Figs. 4 and 5 remains almost identical until the amplitude of the transient SW becomes strongly attenuated by the rarefaction wave. Nevertheless, the rarefaction wave exerts some additional effect on the crossflow motion of particles: the layer is less compressed behind the SW but more mixed with the gas and extends over the entire cross section up to the channel walls.
2.3. Interaction of a Supported SW with a Cloud of Reacting Particles Conditions of detonation initiation in a cloud of aluminum particles that fills the entire cross section of the channel were studied in a one-dimensional formulation in [12]. It was found that a supported SW of a sufficient amplitude (M0 = 5 and velocity 1.73 km/sec) entering the cloud creates conditions for particle ignition and rapid formation of a detonation wave. Then the regime of steady overdriven detonation with a propagation velocity equal to 1.74 km/sec is established. The
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Fig. 4. Action of a strong SW on an inert mixture for M0 = 5, D = 6 cm, d = 5 µm, and t = 0.3 msec (left) and 0.45 msec (right). y, m 0.10
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Fig. 5. Action of an attenuated SW on an inert mixture for M0 = 5, D = 6 cm, and t = 0.45 msec.
influence of the limited transverse size of the cloud on the flow is manifested as follows. The SW that enters the cloud is inflected and refracted in accordance with the above-considered cases of an inert mixture. As the combustion zone develops, the front inside the cloud is accelerated, the ρ-layer behind the front of the leading SW transforms to the ρ-layer of the detonation structure, and the remaining region is filled by detonation products containing particles that have not been completely burned. The onset of a combustion site gives birth to a pressure wave, which propagates over the channel and, due to its multiple reflections from the upper wall and the plane of symmetry, leads to flow fluctuations at the front and behind the front of the
leading SW. This process is plotted in Fig. 6, which shows the shadow reliefs of pressure at the times within 0.2 to 0.4 msec with a period of 0.05 msec. It is seen in Fig. 6 that the curved SW is reflected from the plane of symmetry with the formation of the Mach stem. In contrast to the inert mixture, subsequent reflections from the upper boundary of the layer and the plane of symmetry with the formation of another shock front in detonation products are also noticeable for large particles (d = 5 µm). It is seen from Fig. 6 that the flow behind the front of the detonation wave adjacent to the SW in the gas cannot be considered as completely steady: the length, amplitude, and slope of the second shock adjacent to
Interaction of a Shock Wave with a Cloud of Aluminum Particles in a Channel
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Fig. 7. Oscillations of the detonation flow formed. Pressure profiles for y = 0, M0 = 5, D = 6 cm, and ∆t = 0.05 msec. y, m 0.10
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Fig. 6. Propagation of the detonation front in the cloud for M0 = 5, D = 2 cm, and t = 0.2–0.4 msec (from top to bottom; a step ∆t = 0.05 msec).
the combustion region are not constant. The line of the SW front also experiences fluctuations. Nevertheless, the time-averaged velocity of the SW front reached a constant value corresponding to the overdriven steady detonation regime. Since the SW velocity for M0 = 5 outside the cloud and the detonation-wave velocity in the cloud are almost identical, the cloud width has almost no effect on the velocity of the steady (on the average) detonation regime, but flow stabilization occurs faster in a narrow cloud. At the time of 0.4 msec, the mean velocity of the detonation wave formed is 1.78 km/sec for D = 2 cm, 1.8 km/sec for D = 6 cm, and 1.84 km/sec for D = 8 cm. For D = 6 cm, the mean velocity of 1.78 km/sec is reached only at t = 1.3 msec, which still exceeds the steady detonation-wave velocity (1.73 km/sec). Figure 7 shows the pressure distributions on the lower wall of the channel with a time step of 0.05 msec, which confirm the periodic character of detonation-wave propagation. The reason for that is multiple reflections of the pressure wave arising at the moment the combustion region is formed from the channel walls and the plane of symmetry. The oscillatory regime of propagation of the detonation front in [16] seems to be caused by similar processes. The crossflow motion of the mixture behind the detonation-wave front is more intense than behind the SW front in the inert mixture. However, since the
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Fig. 8. Dispersion of unburned particles for M0 = 5, d = 5 µm, D = 6 cm, and t = 0.05 msec.
main mass of particles burns down, the detonation products and the remaining unburned particles participate in mixing (Fig. 8, shadow image of the particle density). The cloud shape is similar to structures formed behind the SW without combustion of particles (see Figs. 2–4).
CONCLUSIONS • It has been found that the passage of a shock wave over a cloud of inert particles that occupies part of the cross section of a plane channel leads to refraction of the SW front and compression of the cloud behind the front. For shock waves with a rectangular profile and those accompanied by a rarefaction wave, the resultant compaction of the cloud extends to the channel cross section with the formation of a characteristic vortex structure at the edge of the cloud. • Reflection of an oblique SW inside the cloud from the plane of symmetry may be regular (if the relative width of the cloud is small) and involve the Mach stem formation. For the coarse-particle fraction, interaction of relaxation regions leads to smearing of the pattern of SW reflection from the plane of symmetry inside the cloud. • Interaction of a strong SW with a cloud of aluminum aerosuspension leads to the ignition of particles and formation of a detonation wave in the cloud.
214 • The steady detonation regime for a supported SW is characterized by periodic fluctuations of the flow, which is caused by the passage and reflection of transverse waves from the channel walls (plane of symmetry). The time-averaged propagation of the detonation wave corresponds to the overdriven steady detonation regime. This work was supported by the Russian Foundation for Fundamental Research (Grant Nos. 99–01– 00587 and 00–01–00891) and INTAS OPEN (Grant No. 97–2027).
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