Imperial College London


Faculty of Natural SciencesDepartment of Mathematics

Chair in Applied Mathematics







753Huxley BuildingSouth Kensington Campus






BibTex format

author = {Skene, CS and Schmid, PJ},
doi = {10.1017/jfm.2018.793},
journal = {Journal of Fluid Mechanics},
pages = {516--542},
title = {Adjoint-based parametric sensitivity analysis for swirling M-flames},
url = {},
volume = {859},
year = {2018}

RIS format (EndNote, RefMan)

AB - A linear numerical study is conducted to quantify the effect of swirl on the response behaviour of premixed lean flames to general harmonic excitation in the inlet, upstream of combustion. This study considers axisymmetric M-flames and is based on the linearised compressible Navier–Stokes equations augmented by a simple one-step irreversible chemical reaction. Optimal frequency response gains for both axisymmetric and non-axisymmetric perturbations are computed via a direct–adjoint methodology and singular value decompositions. The high-dimensional parameter space, containing perturbation and base-flow parameters, is explored by taking advantage of generic sensitivity information gained from the adjoint solutions. This information is then tailored to specific parametric sensitivities by first-order perturbation expansions of the singular triplets about the respective parameters. Valuable flow information, at a negligible computational cost, is gained by simple weighted scalar products between direct and adjoint solutions. We find that for non-swirling flows, a mode with azimuthal wavenumber is the most efficiently driven structure. The structural mechanism underlying the optimal gains is shown to be the Orr mechanism for and a blend of Orr and other mechanisms, such as lift-up, for other azimuthal wavenumbers. Further to this, velocity and pressure perturbations are shown to make up the optimal input and output showing that the thermoacoustic mechanism is crucial in large energy amplifications. For these velocity perturbations are mainly longitudinal, but for higher wavenumbers azimuthal velocity fluctuations become prominent, especially in the non-swirling case. Sensitivity analyses are carried out with respect to the Mach number, Reynolds number and swirl number, and the accuracy of parametric gradients of the frequency response curve is assessed. The sensitivity analysis reveals that increases in Reynolds and Mach numbers yield higher gains, through a
AU - Skene,CS
AU - Schmid,PJ
DO - 10.1017/jfm.2018.793
EP - 542
PY - 2018///
SN - 0022-1120
SP - 516
TI - Adjoint-based parametric sensitivity analysis for swirling M-flames
T2 - Journal of Fluid Mechanics
UR -
UR -
UR -
VL - 859
ER -