In this work, we develop an analytical model to describe laminar premixed flame response to an oscillating flow and use this model to predict the relationship between the heat release rate and the instantaneous flow field. Fully developed pulsating flow through a channel is considered. The flow is driven by pressure gradients. To facilitate direct comparison with experiments, the transient velocity profile is obtained in terms of mass flow rate fluctuations. The flame is anchored at the channel wall. The flame is assumed to be a thin surface, separating the reactants and the products. Flame displacement speed is assumed to be constant. The flame displacement is described by a single-valued function of the transverse coordinate. The flame dynamics is represented by a kinematic equation describing the displacement of the surface. The assumption of constant flame speed and fully developed flow allows closed-form solution of the flame response. The temporal variation of the mass flow rate and the flame surface area are compared to determine the gain and phase difference of the flame transfer function, relating the fluctuations in flame surface area to fluctuations in the mass flow rate.

1.
Fleifil
M.
,
Annaswamy
A. M.
,
Ghoneim
Z. A.
and
Ghoniem
A. F.
,
Response of a laminar premixed flame to flow oscillations: A kinematic model and thermoacoustic instability Results
,
Combust. Flame
,
106
,
487
510
,
1996
.
2.
Dowling
A. P.
,
A kinematic model of a ducted flame
,
J. Fluid Mech
.,
394
,
51
72
,
1999
.
3.
Ducruix
S.
,
Durox
D.
and
Candel
S.
,
Theoretical and experimental determinations of the Transfer function of a laminar premixed flame
,
Proc. Combust. Inst.
,
28
,
765
773
,
2000
.
4.
Schuller
T.
,
Durox
D.
and
Candel
S.
,
A unified model for the prediction of laminar flame transfer functions: comparisons between conical and V-flame dynamics
,
Combust. Flame
,
134
,
21
34
,
2003
.
5.
Cho
J. H.
and
Lieuwen
T
,
Laminar premixed flame response to equivalence ratio oscillations
,
Combust. Flame
,
140
,
116
129
,
2005
.
6.
Unsal
B.
,
Ray
S.
,
Durst
F.
,
Ertunc
O.
,
Pulsating laminar pipe flows with sinusoidal mass flux variations
,
Fluid Dynamics Research
,
37
,
317
333
,
2005
.
7.
Ray
S.
,
Unsal
B.
,
Durst
F.
,
Ertunc
O.
, and
Bayoumi
O. A.
,
Mass flow rate controlled fully developed laminar pulsating pipe flows
,
Trans. ASME J. Heat Transfer
,
127
,
405
418
,
2005
.
8.
Birkhoff, G. and Rota, G.-C., Ordinary Differential Equations, Fourth Edition, John Wiley and Sons, 1989.
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