Effect of Wall Boundary Conditions on Flame Propagation in Micro-Chambers

2015 ◽  
Author(s):  
Orlando Ugarte ◽  
Sinan Demir ◽  
Berk Demirgok ◽  
V’yacheslav Akkerman ◽  
Vitaly Bychkov ◽  
...  
Keyword(s):  
Thermal Expansion ◽  
Boundary Conditions ◽  
Flame Propagation ◽  
Thermal Conditions ◽  
Wall Friction ◽  
Adiabatic Wall ◽  
Friction Forces ◽  
Flame Acceleration ◽  
Wall Boundary ◽  
Wall Boundary Conditions

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.

Effect of Thermal Boundary Conditions on Propagation of Non-Equidiffusive Flames

2020 ◽  
Author(s):  
Vyacheslav (Slava) Akkerman
Keyword(s):  
Boundary Conditions ◽  
Flame Front ◽  
Surface Area ◽  
Thermal Conditions ◽  
Lewis Number ◽  
Wall Friction ◽  
Adiabatic Wall ◽  
Narrow Channels ◽  
Flame Instability ◽  
Aspect Ratios

Abstract Boundary conditions constitute one of the key factors influencing combustion in chambers with large aspect ratios such as narrow channels or pipes. Specifically, the flame shape and propagation velocity are impacted by wall friction and wall heat transfer. Both factors continuously influence the shape of the flame front, thereby resulting in its larger surface area as compared to a planar flame front. Such a corrugated flame consumes more fuel per unit time and thereby propagates faster than the planar flame at the same thermal-chemical conditions. Consequently, a flame accelerates due to the boundary conditions. In the recent years, there have been many studies scrutinizing the role of boundary conditions in flame acceleration scenario by means of analytical formulations, numerical studies or experimental measurements. However, the majority of these works was limited to equidiffusive flames, where the thermal-to-mass diffusivity ratio (the Lewis number; Le) is unity. In this respect, the present work removes this limitation by analyzing non-equidiffusive (Le < 1 or Le > 1) flames propagating in pipes of various widths. Specifically, a parametric study has been conducted by means of simulations of the basic hydrodynamic and combustion equations. In this particular study, two-dimensional channels with smooth walls and different thermal conditions such as isothermal and adiabatic walls, have been employed for various Lewis numbers in the range 0.2 ≤ Le ≤ 2.0, and for various Reynolds number associated with the flame propagation in the range 5 ≤ Re ≤ 30. As a result, a strong coupling between the wall conditions and the variations of the Lewis and Reynolds numbers is demonstrated. Specifically, it is observed that the increase in the Lewis number results in moderation of flame tip acceleration. It is also found that there is a change in the burning rate and surface area of the flame front at the lower Lewis numbers, where flames appear unstable against the diffusional-thermal flame instability. Moreover, a substantial difference between the cases of isothermal and adiabatic wall conditions is demonstrated.

Extension of classical stability theory to viscous planar wall-bounded shear flows

2019 ◽  
Vol 877 ◽  
pp. 1134-1162 ◽  
Author(s):  
Harry Lee ◽  
Shixiao Wang
Keyword(s):  
Boundary Conditions ◽  
Shear Flows ◽  
Early Stage ◽  
Linear Instability ◽  
Slip Condition ◽  
Translation Invariant ◽  
Alternative Derivation ◽  
Wall Boundary ◽  
Wall Boundary Conditions ◽  
Parallel Shear Flows

A viscous extension of Arnold’s inviscid theory for planar parallel non-inflectional shear flows is developed and a viscous Arnold’s identity is obtained. Special forms of the viscous Arnold’s identity have been revealed that are closely related to the perturbation’s enstrophy identity derived by Synge (Proceedings of the Fifth International Congress for Applied Mechanics, 1938, pp. 326–332, John Wiley) (see also Fraternale et al., Phys. Rev. E, vol. 97, 2018, 063102). Firstly, an alternative derivation of the perturbation’s enstrophy identity for strictly parallel shear flows is acquired based on the viscous Arnold’s identity. The alternative derivation induces a weight function. Thereby, a novel weighted perturbation’s enstrophy identity is established, which extends the previously known enstrophy identity to include general streamwise translation-invariant shear flows. Finally, the validity of the enstrophy identity for parallel shear flows is rigorously examined and established under global nonlinear dynamics imposed with two classes of wall boundary conditions. As an application of the enstrophy identity, we quantitatively investigate the mechanism of linear instability/stability within the normal modal framework. The investigation reveals a subtle interaction between a critical layer and its adjacent boundary layer, which determines the stability nature of the disturbance. As an implementation of the relaxed wall boundary conditions imposed for the enstrophy identity, a control scheme is proposed that transitions the wall settings from the no-slip condition to the free-slip condition, through which a flow is stabilized quickly in an early stage of the transition.

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