DOI: 10.1017/jfm.2026.11710 ISSN: 0022-1120
Nonlinear responses of the premixed V-flame subjected to dual-frequency disturbances
Xiaozhen Jiang, Xiaokang Liu, Aimee S. Morgans, Jiaqi Nan, Lei Li, Tengyu Liu, Lijun Yang, Jingxuan Li
The two-way interaction between the unsteady flame heat release rate (HRR) and acoustic waves can lead to combustion instability within combustors. Previous studies have typically characterised premixed flame responses to pure harmonic forcing, assuming dynamically linear or weakly nonlinear behaviour, to quantify flame–acoustic interactions. By combining third-order asymptotic analysis with numerical simulations of the
upper G
G
$G$
-equation, this study investigates the nonlinear response of laminar premixed V-flames subjected to dual-frequency velocity perturbations (
upper S t 1
S
t
1
$St_1$
and
upper S t 2
S
t
2
$St_2$
, dimensionless frequencies). The positive correlation between disturbance propagation speed
u Subscript c
u
c
$u_c$
and frequency
upper S t
S
t
$St$
is captured by integrating a velocity-potential model with calibration against existing experimental data. The mechanism by which the disturbance at one forcing frequency, say
upper S t 2
S
t
2
$St_2$
, affects the flame dynamic response at the other forcing frequency,
upper S t 1
S
t
1
$St_1$
, is studied in detail. The perturbation at
upper S t 2
S
t
2
$St_2$
couples with that at
upper S t 1
S
t
1
$St_1$
to induce third-order nonlinear terms, giving rise to a non-monotonic suppression mechanism that smooths out the flame’s spatial wrinkling owing to the positive correlation between
u Subscript c
u
c
$u_c$
and
upper S t
S
t
$St$
. As a result, excitation at
upper S t 2
S
t
2
$St_2$
modifies the HRR response at
upper S t 1
S
t
1
$St_1$
, delineating an effective region bounded on the left by the frequency threshold of the linear response and on the right by the aforementioned non-monotonicity. Within this region, excitation at
upper S t 2
S
t
2
$St_2$
can markedly attenuate the HRR gain at
upper S t 1
S
t
1
$St_1$
compared with the case where the flame is driven solely by the perturbation at
upper S t 1
S
t
1
$St_1$
. For instance, once both perturbation amplitudes exceed a certain threshold, excitation at
upper S t 2
S
t
2
$St_2$
can attenuate the flame response at
upper S t 1
S
t
1
$St_1$
by more than 40 % compared with the case without excitation at
upper S t 2
S
t
2
$St_2$
. These findings contribute to the development of a quantitative framework for understanding how targeted frequency perturbations modulate the flame dynamics via nonlinear interactions, which may inform open-loop approaches for mitigating thermoacoustic instabilities in combustion chambers.