Analytical and Computational Study of Flame Acceleration in Tubes: Effect of Wall Friction

Flame dynamics in micro-pipes have been observed to be strongly affected by the wall boundary conditions. In this respect, two mechanisms of flame acceleration are related to the momentum transferred in these regions: 1) that associated with flame stretching produced by wall friction forces; and 2) when obstacles are placed at the walls, as a result of the delayed burning occurring between them, a jet-flow is formed, intensively promoting the flame spreading. Wall thermal conditions have usually been neglected, thus restricting the cases to adiabatic wall conditions. In contrast, in the present work, the effect of the boundary conditions on the flame propagation dynamics is investigated, computationally, with the effect of wall heat losses included in the consideration. In addition, the powerful flame acceleration attained in obstructed pipes is studied in relation to the obstacle size, which determines how different this mechanism is from the wall friction. A parametric study of two-dimensional (2D) channels and cylindrical tubes, of various radiuses, with one end open is performed. The walls are subjected to slip and non-slip, adiabatic and constant temperature conditions, with different fuel mixtures described by varying the thermal expansion coefficients. Results demonstrate that higher wall temperatures promote slower propagation as they reduce the thermal expansion rate, as a result of the post-cooling of the burn matter. In turn, smaller obstacle sizes generate weaker flame acceleration, although the mechanism is noticed to be stronger than the wall friction-driven, even for the smaller sizes considered.

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Flame acceleration due to wall friction: Accuracy and intrinsic limitations of the formulations

Modern Physics Letters B ◽

10.1142/s021798491550205x ◽

2015 ◽

Vol 29 (32) ◽

pp. 1550205 ◽

Cited By ~ 1

Author(s):

Berk Demirgok ◽

Hayri Sezer ◽

V’yacheslav Akkerman

Keyword(s):

Reynolds Number ◽

Thermal Expansion ◽

Order Approximation ◽

Combustion Process ◽

Wall Friction ◽

Zeroth Order ◽

First Order ◽

Flame Acceleration ◽

Wide Range ◽

Cylindrical Tubes

The analytical formulations on the premixed flame acceleration induced by wall friction in two-dimensional (2D) channels [Bychkov et al., Phys. Rev. E 72 (2005) 046307] and cylindrical tubes [Akkerman et al., Combust. Flame 145 (2006) 206] are revisited. Specifically, pipes with one end closed are considered, with a flame front propagating from the closed pipe end to the open one. The original studies provide the analytical formulas for the basic flame and fluid characteristics such as the flame acceleration rate, the flame shape and its propagation speed, as well as the flame-generated flow velocity profile. In the present work, the accuracy of these approaches is verified, computationally, and the intrinsic limitations and validity domains of the formulations are identified. Specifically, the error diagrams are presented to demonstrate how the accuracy of the formulations depends on the thermal expansion in the combustion process and the Reynolds number associated with the flame propagation. It is shown that the 2D theory is accurate enough for a wide range of parameters. In contrast, the zeroth-order approximation for the cylindrical configuration appeared to be quite inaccurate and had to be revisited. It is subsequently demonstrated that the first-order approximation for the cylindrical geometry is very accurate for realistically large thermal expansions and Reynolds numbers. Consequently, unlike the zeroth-order approach, the first-order formulation can constitute a backbone for the comprehensive theory of the flame acceleration and detonation initiation in cylindrical tubes. Cumulatively, the accuracy of the formulations deteriorates with the reduction of the Reynolds number and thermal expansion.

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Impacts of the Lewis and Markstein numbers on premixed flame acceleration in channels due to wall friction

Physics of Fluids ◽

10.1063/5.0067222 ◽

2022 ◽

Vol 34 (1) ◽

pp. 013604

Author(s):

Serdar Bilgili ◽

Vitaly Bychkov ◽

V'yacheslav Akkerman

Keyword(s):

Premixed Flame ◽

Wall Friction ◽

Flame Acceleration

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Computational Study of Premixed Flame Propagation in Micro-Channels with Nonslip Walls: Effect of Wall Temperature

Fluids ◽

10.3390/fluids6010036 ◽

2021 ◽

Vol 6 (1) ◽

pp. 36

Author(s):

Orlando J. Ugarte ◽

V’yacheslav Akkerman

Keyword(s):

Flame Propagation ◽

Computational Study ◽

Reacting Flow ◽

Narrow Channels ◽

Flow Equations ◽

Flame Acceleration ◽

Flame Dynamics ◽

Micro Channels ◽

Fuel Mixtures ◽

The Impact

This investigation evaluates the propagation of premixed flames in narrow channels with isothermal walls. The study is based on the numerical solution of the set of fully-compressible, reacting flow equations that includes viscosity, diffusion, thermal conduction and Arrhenius chemical kinetics. Specifically, channels and pipes with one extreme open and one extreme closed are considered such that a flame is sparked at the closed extreme and propagates towards the open one. The isothermal channel walls are kept at multiple constant temperatures in the range from Tw=300 K to 1200 K. The impact of these isothermal walls on the flame dynamics is studied for multiple radii of the channel (R) and for various thermal expansion ratios (Θ), which approximate the thermal behavior of different fuel mixtures in the system. The flame dynamics in isothermal channels is also compared to that with adiabatic walls, which were previously found to produce exponential flame acceleration at the initial stage of the burning process. The results show that the heat losses at the walls prevent strong acceleration and lead to much slower flame propagation in isothermal channels as compared to adiabatic ones. Four distinctive regimes of premixed burning in isothermal channels have been identified in the Θ−Tw−R space: (i) flame extinction; (ii) linear flame acceleration; (iii) steady or near-steady flame propagation; and (iv) flame oscillations. The physical processes in each of these regimes are discussed, and the corresponding regime diagrams are presented.

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