On the reflection of a plane shock wave from a rigid wall in a detonating gas

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Abstract

This study presents a physical-mathematical model, computational algorithms, and results of calculations for ignition and detonation in a combustible mixture behind a reflected shock wave. The problem is solved numerically using the Godunov method for two-dimensional unsteady gas dynamics equations coupled with chemical kinetics. Calculations of detonation wave initiation and propagation in a methane-air mixture are performed using a simplified kinetic mechanism for methane combustion. Two propagation regimes are identified: a steady regime with constant velocity and an unsteady oscillatory mode. It is demonstrated that, far from the wall, the average detonation velocity and the key flow parameters behind the wave front can be accurately determined from the solution of a self-similar problem of shock wave reflection from a wall, under the assumptions of frozen flow ahead of the wave and thermodynamic equilibrium behind it.

About the authors

Vladimir Yu. Gidaspov

Moscow Aviation Institute (National Research University)

Author for correspondence.
Email: gidaspov@mai.ru
ORCID iD: 0000-0002-5119-4488
SPIN-code: 9954-7270
Scopus Author ID: 6506396733
ResearcherId: B-4572-2019
https://www.mathnet.ru/rus/person26168

Dr. Phys. & Math. Sci., Senior Researcher; Professor; Dept. of Computational Mathematics and Programming

Russian Federation, 125993, Moscow, Volokolamskoe Shosse, 4

Natalya S. Severina

Moscow Aviation Institute (National Research University)

Email: severinans@mai.ru
ORCID iD: 0000-0001-5951-4629
SPIN-code: 5512-8170
Scopus Author ID: 56638598100
ResearcherId: T-4276-2018
https://www.mathnet.ru/rus/person51389

Cand. Phys. & Math. Sci., Associate Professor; Associate Professor; Dept. of Computational Mathematics and Programming

Russian Federation, 125993, Moscow, Volokolamskoe Shosse, 4

References

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2. Figure 1. Flow structure upon shock wave reflection from a wall in a detonating gas mixture. Notation: $O$ — incident shock impingement on the wall; $B$ — ignition event; $C$ — combustion wave and reflected shock interaction point. Waves: ISW—incident shock wave; RSW—reflected shock wave; CW—combustion wave; DW—detonation wave. Flow regions: 0—ahead of ISW; 1—behind ISW; 2—behind RSW; 3—behind DW

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3. Figure 2. Formation of a detonation wave upon shock wave reflection from a wall: a) overdriven detonation wave (ODW) regime; b) Chapman—Jouguet detonation wave (CJDW) regime with an adjacent expansion fan (EF). Flow regions: 0—ahead of ISW; 1—behind ISW; 3—immediately behind the detonation wave; 4—near-wall region (for case b)

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4. Figure 3. Color scales for contour visualization: a) pressure, Pa; b) temperature, K (online in color)

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5. Figure 4. Temperature contours at different time instants: a, b — $t = 1.411$ ms; c, d — $t = 2.538$ ms. Incident shock wave parameters: $M_{\text{ISW}} = 3.2$; initial conditions: $p = 10000$ Pa, $T = 300$ K (online in color)

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6. Figure 5. Pressure contours at different time instants: a, b — $t = 1.411$ ms; c, d — $t = 2.538$ ms. Incident shock wave parameters: $M_{\text{ISW}} = 3.2$; initial conditions: $p = 10000$ Pa, $T = 300$ K (online in color)

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7. Figure 6. Temperature vs. longitudinal coordinate: 1—$t = 1.411$ ms; 2—$t = 2.538$ ms; 3—$t = 3.353$ ms; 4—temperature behind the overdriven detonation wave; 5—temperature behind the Chapman—Jouguet detonation wave

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8. Figure 7. Pressure vs. longitudinal coordinate: 1—$t = 1.411$ ms; 2—$t = 2.538$ ms; 3—$t = 3.353$ ms; 4—pressure behind the overdriven detonation wave; 5—pressure behind the Chapman—Jouguet detonation wave

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9. Figure 8. Detonation wave velocity vs. incident shock wave Mach number $M_{\text{ISW}}$: markers—average velocity values calculated far from the wall; 1—equilibrium overdriven detonation wave velocity; 2—Chapman—Jouguet detonation wave velocity

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