On the Stability of Planar Premixed Flames Under Nonadiabatic Conditions and Preferential Diffusion

2017 ◽  
Vol 9 (3) ◽  
Author(s):  
Eman Al-Sarairah ◽  
Bilal Al-Hasanat ◽  
Ahmed Hachicha
Keyword(s):  
Heat Loss ◽  
Numerical Study ◽  
Lewis Number ◽  
Premixed Flame ◽  
Constant Density ◽  
Damkohler Number ◽  
Damköhler Number ◽  
Number Ratio ◽  
Preferential Diffusion ◽  
The Stability

In this paper, we provide a numerical study of the stability analysis of a planar premixed flame. The interaction of preferential diffusion and heat loss for a planar premixed flame is investigated using a thermodiffusive (constant density) model. The flame is studied as a function of three nondimensional parameters, namely, Damköhler number (ratio of diffusion time to chemical time), Lewis number (ratio of thermal to species diffusivity), and heat loss. A maximum of four solutions are identified in some cases, two of which are stable. The behavior of the eigenvalues of the linearized system of stabilty is also discussed. For low Lewis number, the heat loss plays a major role in stabilizing the flame for some moderately high values of Damköhler number. The results show the effect of increasing or decreasing Lewis number on adiabatic and nonadiabatic flames temperature and reaction rate as well as the range of heat loss at which flames can survive.

A General Study of Counterflow Diffusion Flames for Supercritical CO2 Combustion

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
K. R. V. Manikantachari ◽  
Scott Martin ◽  
Ramees K. Rahman ◽  
Carlos Velez ◽  
Subith Vasu
Keyword(s):  
Prandtl Number ◽  
Supercritical Co2 ◽  
Diffusion Flames ◽  
Lewis Number ◽  
Dilution Effect ◽  
Scalar Dissipation ◽  
Damkohler Number ◽  
Nonpremixed Combustion ◽  
Flame Thickness ◽  
Damköhler Number

Abstract A counterflow diffusion flame for supercritical CO2 combustion is investigated at various CO2 dilution levels and pressures by accounting for real gas effects into both thermal and transport properties. The UCF 1.1 24-species mechanism is used to account the chemistry. The nature of important nonpremixed combustion characteristics such as Prandtl number, thermal diffusivity, Lewis number, stoichiometric scalar dissipation rate, flame thickness, and Damköhler number are investigated with respect to CO2 dilution and pressure. The results show that the aforementioned parameters are influenced by both dilution and pressure; the dilution effect is more dominant. Further, the result shows that Prandtl number increases with CO2 dilution and at 90% CO2 dilution, the difference between the Prandtl number of the inlet jets and the flame is minimal. Also, the common assumption of unity Lewis number in the theory and modeling of nonpremixed combustion does not hold reasonable for sCO2 applications due to large difference of Lewis number across the flame and the Lewis number on the flame drop significantly with an increase in the CO2 dilution. An interesting relation between Lewis number and CO2 dilution is observed. The Lewis number of species drops by 15% when increasing the CO2 dilution by 30%. Increasing the CO2 dilution increases both the flow and chemical timescales; however, chemical timescale increases faster than the flow timescales. The magnitudes of the Damköhler number signify the need to consider finite rate chemistry for sCO2 applications. Further, the Damköhler numbers at 90% sCO2 dilution are very small; hence, laminar flamelet assumptions in turbulent combustion simulations are not physically correct for this application. Also, it is observed that the Damköhler number drops nonlinearly with increasing CO2 dilution in the oxidizer stream. This is a very important observation for the operation of sCO2 combustors. Further, the flame thickness is found to increase with CO2 dilution and reduce with pressure.

Effect of Damkohler Number and Non-Unity Lewis Number on a Laminar Diffusion Flame

2003 ◽  
Author(s):  
Bassem H. Ramadan
Keyword(s):  
Diffusion Flame ◽  
Rectangular Channel ◽  
Flame Structure ◽  
Lewis Number ◽  
Damkohler Number ◽  
Laminar Diffusion Flame ◽  
Damköhler Number ◽  
Laminar Diffusion ◽  
Adi Schemes ◽  
Steady Laminar

The effect of the Damkohler number (Da) and non-unity Lewis number on a two-dimensional, steady, laminar diffusion flame anchored by a dividing plate in a rectangular channel was considered. The governing equations were solved numerically, using the SIMPLE and ADI schemes. The results for non-unity Lewis number were compared with those for a unity Lewis number, and Da a was also varied in order to determine their effect on the flame structure. The results show that an increase in the Da causes the flame to exist closer to the trailing edge of the divider and to increase the reactivity. A non-unity Lewis number creates a non-symmetrical flame by forcing the flame to exist on the fuel side.

The Combined Effects of Heat Loss and Reversibility on the Propagation of Planar Premixed Counterflow Flames

2018 ◽  
Vol 10 (6) ◽  
Author(s):  
Faisal Al-Malki
Keyword(s):  
Activation Energy ◽  
Finite Elements ◽  
Strain Rate ◽  
Heat Loss ◽  
Constant Density ◽  
Combined Effects ◽  
Stability Of Solutions ◽  
Counterflow Flames ◽  
The Stability ◽  
The Impact

Abstract We study in this paper the combined effect of heat loss and reversibility on the propagation of planar flames formed within the counterflow configuration. The problem has been formulated first using the thermodiffusive model with constant density and then solved numerically using finite elements. The impact of four main parameters, namely the reversibility r, the heat loss κ, the strain rate ε, and the activation energy β, on the propagation of planar flames has been discussed in details. The study has shown that planar flames under reversible conditions behave qualitatively similar to those observed for irreversible reactions, which agree with the asymptotic findings. In the presence of heat loss, the problem exhibits multiplicity of solutions whose number and stability were found to vary according to the strain rate ε. In addition, the study has predicted the existence of a certain value of the reversibility parameter r beyond which the impact of reversibility becomes negligible. Finally, we have examined the stability of the solutions and determined the domain of stability of solutions and their multiplicity for this problem.

Numerical Study of the Onset of Double-Diffusive Cellular Convection Due to a Uniform Lateral Heat Flux

1982 ◽  
Vol 104 (4) ◽  
pp. 649-655 ◽  
Author(s):  
S. Takao ◽  
M. Tsuchiya ◽  
U. Narusawa
Keyword(s):  
Heat Flux ◽  
Numerical Study ◽  
Vertical Wall ◽  
Lewis Number ◽  
Double Diffusive Convection ◽  
Physical Experiments ◽  
Diffusive Convection ◽  
The Stability ◽  
Double Diffusive ◽  
Lateral Heat

When a fluid with a vertical solute gradient of (−dS/dy)0 is heated laterally, roll cells start to form at the boundary, developing into a series of convective layers. Numerical experiments were performed to investigate the onset of the abovementioned double-diffusive convection under the application of a uniform lateral heat flux. The paper reports the results and discussion of the following aspects of the stability of double-diffusive convection; (i) the relationship between the critical value, (Ra/Rs)c, above which convection cells form along the vertical wall and the nondimensional slot width, (d/L), (ii) the effect of the Lewis number on (Ra/Rs)c. It was also confirmed that values of (Ra/Rs)c as well as H/L (the nondimensional vertical size of incipient cells) obtained in this numerical experiment for wide slot widths (d/L>∼30), agreed well with those obtained previously by physical experiments.

Lewis-number effects on edge-flame propagation

2002 ◽  
Vol 458 ◽  
pp. 219-228 ◽  
Author(s):  
VEDHA NAYAGAM ◽  
F. A. WILLIAMS
Keyword(s):  
Activation Energy ◽  
Propagation Velocity ◽  
Steady Motion ◽  
Lewis Number ◽  
Diffusion Time ◽  
Damkohler Number ◽  
Dimensional Model ◽  
One Dimensional ◽  
Damköhler Number ◽  
Propagation Velocities

Activation-energy asymptotics is employed to explore effects of the Lewis number, the ratio of thermal to fuel diffusivity, in a one-dimensional model of steady motion of edges of reaction sheets. The propagation velocity of the edge is obtained as a function of the relevant Damköhler number, the ratio of the diffusion time to the chemical time. The results show how Lewis numbers different from unity can increase or decrease propagation velocities. Increasing the Lewis number increases the propagation velocity at large Damköhler numbers and decreases it at small Damköhler numbers. Advancing-edge and retreating-edge solutions are shown to exist simultaneously, at the same Damköhler number, if the Lewis number is sufficiently large. This multiplicity of solutions has a bearing on potential edge-flame configurations in non-uniform flows.

Heat Rejection to the Surface Layer of a Solar Pond

1985 ◽  
Vol 107 (1) ◽  
pp. 99-106 ◽  
Author(s):  
Y. Jaluria ◽  
C. K. Cha
Keyword(s):  
Surface Layer ◽  
Heat Loss ◽  
Numerical Study ◽  
Surface Zone ◽  
Conductive Heat ◽  
Heat Rejection ◽  
Recirculating Flow ◽  
Solar Pond ◽  
Flow Effects ◽  
The Stability

An analytical and numerical study of the thermal and fluid flow effects of heat rejection to the surface layer of a salt-gradient solar pond, by means of a recirculating thermal discharge, is carried out. The use of solar ponds for power generation involves heat rejection, for which the surface zone may be employed. However, it is very important to determine the effect of the discharge of hot fluid on the temperature field in the surface zone and on the stability of the non-convective zone, which lies between the surface and storage zones. Of particular interest is the dependence of this flow on the inflow conditions, on heat loss at the surface and on the inflow-outflow configuration. The downward penetration of the flow is strongly governed by the buoyancy effects, and the study considers both the transient and the steady-state circumstances. The effect of the surface energy loss and of the conductive heat gained from below the surface zone is also studied. The flow is found to be strongly dependent on the inflow and outflow conditions and on the surface heat loss. The disturbance to the nonconvective zone is also studied. The basic physical processes involved are considered in detail, and the relevance of the results obtained in the design of the corresponding recirculating flow is outlined.

scholarly journals A New Mathematical Framework for Describing Thin-Reaction-Zone Regime of Turbulent Reacting Flows at Low Damköhler Number

Fluids ◽  
2020 ◽  
Vol 5 (3) ◽  
pp. 109
Author(s):  
Vladimir A. Sabelnikov ◽  
Andrei N. Lipatnikov
Keyword(s):  
Molecular Transport ◽  
Characteristic Functions ◽  
Constant Density ◽  
Mathematical Framework ◽  
Damkohler Number ◽  
Field Equations ◽  
Conditioned Reaction ◽  
Reaction Progress ◽  
Progress Variable ◽  
Damköhler Number

Recently, Sabelnikov et al. (2019) developed a phenomenological theory of propagation of an infinitely thin reaction sheet, which is adjacent to a mixing layer, in a constant-density turbulent flow in the case of a low Damköhler number. In the cited paper, the theory is also supported by Direct Numerical Simulation data and relevance of such a physical scenario to highly turbulent premixed combustion is argued. The present work aims at complementing the theory with a new mathematical framework that allows for appearance of thick mixing zones adjacent to an infinitely thin reaction sheet. For this purpose, the instantaneous reaction-progress-variable c ( x , t ) is considered to consist of two qualitatively different zones, that is, (i) mixture of products and reactants, c ( x , t ) < 1 , where molecular transport plays an important role, and (ii) equilibrium products, c ( x , t ) = 1 . The two zones are separated by an infinitely thin reaction sheet, where c ( x , t ) = 1 and | ∇ c | is fixed in order for the molecular flux into the sheet to yield a constant local consumption velocity equal to the speed of the unperturbed laminar reaction wave. Exact local instantaneous field equations valid in the entire spaceare derived for the conditioned (to the former, mixing, zone) reaction progress variable, its second moment, and instantaneous characteristic functions. Averaging of these equations yields exact, unclosed transport equations for the conditioned reaction-progress-variable moments and Probability Density Function (PDF), as well as a boundary condition for the PDF at the reaction sheet. The closure problem for the derived equations is beyond the scope of the paper.

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