Direct Numerical Simulation of Thermoacoustically Unstable Flames Via Non-Drifting Acoustic Delay Characteristic Boundary Conditions
Abstract
Thermoacoustic instability in premixed flames results from the coupling between the flame's heat release, as determined by combustion parameters, and surrounding acoustics, as determined by combustor geometry. A primary instability results in flame flattening as intrinsic flame instability modes are stabilised. Secondary thermoacoustic instability results in a parametric flame instability and drastic growth of acoustic amplitudes. Due to their relative expense, numerical simulations of these phenomena remain scarce. In this work, Direct Numerical Simulations (DNS) of thermoacoustically unstable idealised premixed flames in a tube with acoustically closed upstream and open downstream ends are presented. Results herein demonstrate nonlinear saturation of the primary instability as the flame flattens as well as an oscillating flame fingering characteristic of the unsteady Rayleigh-Taylor effect. To reduce computational cost, we perform DNS only on the region surrounding the flame. Acoustics at in- and outflows are described using the Navier-Stokes Characteristic Boundary Condition (NSCBC) method to model their delayed reentry into the domain in a formulation referred to as the Acoustic Delay Characteristic Boundary Condition (ADCBC) method. A new Averaged Proportional and Integral Linear Relaxation (APILR) method is also introduced, which modifies the Classic Linear Relaxation (CLR) method to maintain time-averaged values of inflow velocity and outflow pressure. Here, an integral control term is used to remove non-zero equilibrium time-averaged inflow velocities which impinge control over flame position. Both new methods demonstrate their capability in inert and counterflow flames test cases. These methods enable the numerical simulation of combustion instabilities at significantly reduced computational expense.
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BibTeX
@misc{cookman2026direct,
title = {{Direct Numerical Simulation of Thermoacoustically Unstable Flames Via Non-Drifting Acoustic Delay Characteristic Boundary Conditions}},
author = {Benjamin L. Cookman and Jack R. C. King and Raphaël C. Assier and Steven J. Lind},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05656},
eprint = {2609.05656},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05656},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Direct Numerical Simulation of Thermoacoustically Unstable Flames Via Non-Drifting Acoustic Delay Characteristic Boundary Conditions
AU - Benjamin L. Cookman
AU - Jack R. C. King
AU - Raphaël C. Assier
AU - Steven J. Lind
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.05656
UR - https://arxiv.org/abs/2609.05656
AB - Thermoacoustic instability in premixed flames results from the coupling between the flame's heat release, as determined by combustion parameters, and surrounding acoustics, as determined by combustor geometry. A primary instability results in flame flattening as intrinsic flame instability modes are stabilised. Secondary thermoacoustic instability results in a parametric flame instability and drastic growth of acoustic amplitudes. Due to their relative expense, numerical simulations of these phenomena remain scarce. In this work, Direct Numerical Simulations (DNS) of thermoacoustically unstable idealised premixed flames in a tube with acoustically closed upstream and open downstream ends are presented. Results herein demonstrate nonlinear saturation of the primary instability as the flame flattens as well as an oscillating flame fingering characteristic of the unsteady Rayleigh-Taylor effect. To reduce computational cost, we perform DNS only on the region surrounding the flame. Acoustics at in- and outflows are described using the Navier-Stokes Characteristic Boundary Condition (NSCBC) method to model their delayed reentry into the domain in a formulation referred to as the Acoustic Delay Characteristic Boundary Condition (ADCBC) method. A new Averaged Proportional and Integral Linear Relaxation (APILR) method is also introduced, which modifies the Classic Linear Relaxation (CLR) method to maintain time-averaged values of inflow velocity and outflow pressure. Here, an integral control term is used to remove non-zero equilibrium time-averaged inflow velocities which impinge control over flame position. Both new methods demonstrate their capability in inert and counterflow flames test cases. These methods enable the numerical simulation of combustion instabilities at significantly reduced computational expense.
ER -