^{1,a)}, Chung K. Law

^{1}, Vitaly Bychkov

^{2}and Lars-Erik Eriksson

^{3}

### Abstract

Spontaneous flameacceleration leading to explosion triggering in open tubes/channels due to wall friction was analytically and computationally studied. It was first demonstrated that the acceleration is affected when the thermal expansion across the flame exceeds a critical value depending on the combustion configuration. For the axisymmetric flame propagation in cylindrical tubes with both ends open, a theory of the initial (exponential) stage of flameacceleration in the quasi-isobaric limit was developed and substantiated by extensive numerical simulation of the hydrodynamics and combustion with an Arrhenius reaction. The dynamics of the flame shape, velocity, and acceleration rate, as well as the velocity profile ahead and behind the flame, have been determined.

This work was supported by the U.S. Air Force Office of Scientific Research and by the Swedish Kempe Foundation.

I. INTRODUCTION

II. CRITERION FOR FLAMEACCELERATION

III. THEORY OF FLAMEACCELERATION IN OPEN CYLINDRICAL TUBES

A. Flame-generated flow

B. Flame shape and velocity

IV. DIRECT NUMERICAL SIMULATIONS

V. RESULTS AND DISCUSSION

VI. SUMMARY

### Key Topics

- Flames
- 230.0
- Kinematics
- 18.0
- Flame dynamics
- 16.0
- Thermal expansion
- 16.0
- Friction
- 15.0

## Figures

Accelerating or hypothetical steady flame in a tube/channel with nonslip walls and both ends open.

Accelerating or hypothetical steady flame in a tube/channel with nonslip walls and both ends open.

Scaled profile of the flow velocity, Eq. (25), for various .

Scaled profile of the flow velocity, Eq. (25), for various .

Scaled flame shape, Eq. (37), for and various .

Scaled flame shape, Eq. (37), for and various .

Flame acceleration in a cylindrical tube of radius (a) and (b) . Both ends of the tube are open. The flame isotherms are taken from 600 to 2100 K with the step of 300 K in each plot in both figures. (a) The positions (a)–(h) are related to the time instants , with equal time intervals . (b) The positions (a)–(g) are related to the time instants , with equal time intervals .

Flame acceleration in a cylindrical tube of radius (a) and (b) . Both ends of the tube are open. The flame isotherms are taken from 600 to 2100 K with the step of 300 K in each plot in both figures. (a) The positions (a)–(h) are related to the time instants , with equal time intervals . (b) The positions (a)–(g) are related to the time instants , with equal time intervals .

Flame oscillations in a 2D channel of width with both ends open (Ref. 27). The flame isotherms are taken from 600 to 2100 K with the step of 300 K in each plot. The positions (a)–(f) are related to the time instants .

Flame oscillations in a 2D channel of width with both ends open (Ref. 27). The flame isotherms are taken from 600 to 2100 K with the step of 300 K in each plot. The positions (a)–(f) are related to the time instants .

Flame acceleration in a cylindrical tube of radius with one end closed (Ref. 23). The flame isotherms are taken from 600 to 2100 K with the step of 300 K in each plot. The positions (a)–(g) are related to the time instants , with interval .

Flame acceleration in a cylindrical tube of radius with one end closed (Ref. 23). The flame isotherms are taken from 600 to 2100 K with the step of 300 K in each plot. The positions (a)–(g) are related to the time instants , with interval .

Evolution of the flame shape in a cylindrical tube of radius with both ends open. The colors designate the temperature: from 300 K in the cold gas to 2400 K in the burnt matter. The snapshots (a)–(g) are related to the time instants , with equal time intervals .

Evolution of the flame shape in a cylindrical tube of radius with both ends open. The colors designate the temperature: from 300 K in the cold gas to 2400 K in the burnt matter. The snapshots (a)–(g) are related to the time instants , with equal time intervals .

The scaled total flame velocity vs time for open cylindrical tubes with and . The plots are related to three main stages of the flame dynamics: (a) initial (concave), (b) intermediate (inversional), and [(c) and (d)] final (self-similar, convex). (d) is a counterpart of (c) in the semilogarithmic scale. The dashed plot is related to the test simulation run with and the simulation grid . Two dotted plots in (c) and (d) are related to a tube with a closed end (Ref. 23).

The scaled total flame velocity vs time for open cylindrical tubes with and . The plots are related to three main stages of the flame dynamics: (a) initial (concave), (b) intermediate (inversional), and [(c) and (d)] final (self-similar, convex). (d) is a counterpart of (c) in the semilogarithmic scale. The dashed plot is related to the test simulation run with and the simulation grid . Two dotted plots in (c) and (d) are related to a tube with a closed end (Ref. 23).

Acceleration rate vs the Peclet number for . The solid plot shows the numerical solution to Eq. (39). The dashed plot presents the zeroth-order approximation, Eq. (43). The simulation results are shown by symbols. The dotted plot is related to a tube with a closed end (Ref. 23).

Acceleration rate vs the Peclet number for . The solid plot shows the numerical solution to Eq. (39). The dashed plot presents the zeroth-order approximation, Eq. (43). The simulation results are shown by symbols. The dotted plot is related to a tube with a closed end (Ref. 23).

The scaled total burning rate vs time for an open cylindrical tube with and various expansion factors .

The scaled total burning rate vs time for an open cylindrical tube with and various expansion factors .

The scaled total burning rate vs time for an open cylindrical tube with and various expansion factors . The plots are related to (a) concave and (b) convex stages of the flame dynamics.

The scaled total burning rate vs time for an open cylindrical tube with and various expansion factors . The plots are related to (a) concave and (b) convex stages of the flame dynamics.

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