Chuhan Wang

We employ a hybrid computational fluid dynamics (CFD)/low-order framework to investigate the forced response of a self-excited conical flame. The framework resolves flame dynamics using CFD while describing the acoustic field with a low-order model, concentrating computational effort on the dominant source of thermoacoustic nonlinearity. When the flame is self-excited and unforced, heat release rate fluctuations, Q′, are governed by flame pinch-off: Q′ reaches a maximum near pinch-off and a minimum when detached flame pockets disappear. When the self-excited flame is forced, the hybrid framework reproduces the suppression region and attenuation levels of acoustic pressure fluctuations, p′, satisfactorily, as reported experimentally before. Oscillation suppression arises from weakened thermoacoustic coupling, as the phase relationship between p′ and Q′ shifts from in-phase to out-of-phase, reducing acoustic energy production. Rayleigh-index analysis shows that forcing primarily affects the upper flame region, where pinch-off dominates, whereas the wavepacket-like structure in the lower half of the flame remains largely unchanged. These results identify flame pinch-off as the key mechanism linking open-loop forcing to thermoacoustic suppression and demonstrate the importance of resolving flame dynamics when predicting the forced response of self-excited flames. The proposed framework provides an efficient tool for studying thermoacoustic instability.

Analyse globale des instabilités linéaires de flammes: Cette thèse vise à appliquer les développements récents de la méthodologie du domaine de la théorie de l'instabilité linéaire à l'étude de l'instabilité de combustion. L'instabilité de la flamme se réfère ici aux oscillations instables du champ d'écoulement réactif. L'analyse des modes propres pour la description des oscillations auto-entretenues et l'analyse entrée-sortie pour la caractérisation du comportement des amplificateurs sont mises en œuvre dans un cadre global. Les équations décrivant l'écoulement réactif sont linéarisées et résolues dans l'ensemble du domaine de calcul, y compris les schémas de réaction chimique linéarisés. Dans ce cadre, l'interaction entre la dynamique de l'écoulement, la réaction chimique et l'acoustique peut être intrinsèquement prise en compte et étudiée en détail. Dans cette thèse, nous nous concentrons sur la dynamique linéaire des flammes laminaires prémélangées, comprenant principalement une flamme à fente qui agit comme un amplificateur, et une flamme stabilisée à corps bluff qui agit comme un oscillateur.La réponse au forçage de la flamme à fente avec un schéma de réaction en deux étapes pour la combustion du méthane est étudiée dans le régime linéaire. La fonction de transfert de flamme est calculée à partir du modèle linéaire, en excellent accord avec les calculs non linéaires de référence. Le gain d'énergie entre le forçage appliqué de l'extérieur et la réponse globale de dégagement de chaleur est calculé, et les pics de gain sont liés aux modes thermoacoustiques intrinsèques. L'analyse résolvante est utilisée pour identifier les structures de forçage optimal et leur réponse de flamme associée, conduisant à une discussion des mécanismes dominants pour l'amplification des perturbations d'écoulement, qui déclenchent des oscillations de flamme. Ceux-ci semblent impliquer une résonance avec des modes d'instabilité thermoacoustique intrinsèques.La stabilité linéaire globale d'une flamme laminaire prémélangée ancrée sur un corps bluff est étudiée via une analyse modale. Le pas de temps non linéaire et l'analyse de stabilité démontrent que l'écoulement réactif est significativement stabilisé par rapport au cas non réactif, mais la flamme est à nouveau déstabilisée si le corps bluff est davantage chauffé. Par décomposition détaillée des modes propres dans l'écoulement en régime stationnaire, la région d'écoulement active qui entraîne l'instabilité est identifiée dans la région où la vorticité de l'écoulement de base est la plus grande, suggérant la région de cisaillement de sillage. L'analyse du champ temporellement moyenné d'une flamme oscillante dans le cycle limite capture avec précision la fréquence d’oscillation, ce qui peut être considéré comme un cas de référence pour l'analyse modale sur l'écoulement moyen réactif avec le schéma de chimie linéarisé.Afin de comprendre le rôle des structures cohérentes à grande échelle dans l'instabilité des flammes turbulentes, nous menons une étude fondamentale sur l'effet des stries sur l'instabilité des jets incompressibles non réactifs.

Fluid flows around hypersonic vehicles experience chemical non-equilibrium effects at extreme temperature conditions. Reynolds-averaged Navier–Stokes (RANS) equations are primarily used to simulate turbulent external flow at full vehicle scales. However, the turbulent closure of near-wall reactions related to gas dissociation is omitted in practice because it remains unknown how to close the associated mean reaction rate, despite research efforts in this direction for more than a decade. This paper aims to discover an appropriate turbulent closure strategy of the involved finite-rate dissociative reaction through direct numerical simulation of a hypersonic turbulent boundary at Mach 9.2 with an isothermal cold wall surface, computed using Park’s five-species air dissociation model. Three sets of calculations are conducted, including two sets with non-catalytic and catalytic wall surface conditions, and one set without chemical reaction. Results show that the involved endothermic reaction mainly affects the magnitude of mean temperature and its fluctuations, whereas it has a relatively slight influence on the velocity and wall surface statistics. Turbulence-chemistry interaction is analysed within the same probability density function (PDF) framework as Wang & Xu (2024 J. Fluid Mech. vol. 998, A1), which considers temperature and species compositions in sample space. We find that modelling only the PDF of temperature, with simple knowledge of the mean species concentrations, is sufficient to reasonably well close the turbulent reaction rates and heat absorption rates, except for quantitative errors in the reaction rate of atomic nitrogen. This finding avoids the need for a more complex multivariable PDF in closure and also eliminates the requirement to model species fluctuations in RANS. Assuming a log-normal distribution for temperature provides better results, owing to the strongly skewed temperature distribution near the wall surface. The dependence and sensitivity of the single model parameter, temperature skewness, are further investigated. It is shown that the accuracy of closure result is not highly sensitive to the exact skewness value, as long as a negative one within a relatively wide range is selected. The developed closure model is applied to a wall model with species balance equations, showing significant improvement over the laminar closure, while further closure modelling efforts in the atomic nitrogen are still needed to improve computation robustness.

We investigate self-excited axisymmetric oscillations of a lean premixed methane–air V-flame in a laminar annular jet. The flame is anchored near the rim of the centrebody, forming an inverted cone, while the strongest vorticity is concentrated along the outer shear layer of the annular jet. Consequently, the reaction and vorticity dynamics are largely separated, except where they coalesce near the flame tip. The global eigenmodes corresponding to the linearised reacting flow equations around the steady base state are computed in an axisymmetric setting. We identify an arc branch of eigenmodes exhibiting strong oscillations at the flame tip. The associated eigenvalues are robust with respect to domain truncation and numerical discretisation, and they become destabilised as the Reynolds number increases. The frequency of the leading eigenmode is found to correspond to the Lagrangian disturbance advection time from the nozzle outlet to the flame tip. The essential role of this convective mechanism is also supported by resolvent analysis, which finds that the same flame-tip disturbance structure and frequency are optimally amplified when the flame is subjected to external white noise forcing. Strong non-modal effects in the form of pseudo-resonance are not found. Nonlinear time-resolved simulation further reveals notable hysteresis phenomena in the subcritical regime prior to instability. Hence, even when the flame is linearly stable, perturbations of sufficient amplitude can trigger limit-cycle oscillations and higher-dimensional dynamics sustained by nonlinear feedback. A Monte Carlo simulation of passive tracers in the unsteady flame suggests a nonlinear non-local instability mechanism. Notably, linear analysis of the subcritical time-averaged limit-cycle state yields eigenvalues that do not match the nonlinear periodic oscillation frequencies. This mismatch is attributed to the fundamentally nonlinear dynamics of the subcritical V-flame instability, where the dichromatic, non-local interaction between the heat release rate along the flame surface and the vortex dynamics in the jet shear layer cannot be approximated as a simple distortion of the mean flow.

The complex behaviours of supersonic turbulent boundary-layer flows interacting with combustion is explored through the use of direct numerical simulations. The chosen flow model is a non-premixed hydrogen–air flame ignited within a three-dimensional supersonic turbulent flat-plate boundary layer operating at a Mach number of 2.33 and a friction Reynolds number of approximately 1000. The simulation involves a finite-rate model for the hydrogen–air reaction including 9 species and 19 steps with adiabatic non-catalytic wall conditions. The inlet flow consists of preheated air in the main stream and a hydrogen film injected in proximity to the cold wall, inducing mixing and ignition in the outer layer. The specific inlet configuration leads to two successive transition stages of distinct mechanisms, with the first stage related to the mixing-layer instability and the second one to the boundary-layer instability. The excess Reynolds stresses resulting from the transition exhibit a downstream decrease, with values being lower than canonical adiabatic profiles, particularly in the outer layer. This difference is attributed to the reduced local friction Reynolds numbers, associated with the non-classical wall-normal distributions of density and viscosity. The effect of combustion on the recovery process and skin friction is analysed in comparison with a supplemented chemistry-frozen setting. Velocity–temperature and velocity–species correlations are further examined. The wall-normal profiles of turbulent Prandtl number tend to classical non-reacting values and the turbulent Schmidt number is only slightly affected by the reaction. The strong Reynolds analogy linking velocity and temperature fluctuations is found to be invalid in the outer layer due to the presence of large-scale temperature fluctuations and the inhomogeneity of hydrogen gas distribution, as revealed by a spectrum analysis. A statistical analysis of elementary reactions at varying wall-normal distances is provided, highlighting the dominance of hydrogen atom depletion in the inner region and the prevalence of water vapour production in the outer region, together contributing to the chemical heat release across the boundary layer. Turbulence–chemistry interaction is assessed through a comparison of mean turbulent and laminar chemical heat release rates, showing significant differences of up to an order of magnitude. Using a simple diagnostic tool, the modelling of fluctuations associated with hydrogen gas and two intermediate products is found to be crucial for turbulent chemistry closure.

This study investigates the linear stability of a laminar premixed flame, anchored on a square cylinder and confined inside a channel. Many modern linear analysis concepts have been developed and validated around non-reacting bluff-body wake flows, and the objective of this paper is to explore whether those tools can be applied with the same success to the study of reacting flows in similar configurations. It is found that linear instability analysis of steady reacting flow states accurately predicts critical flow parameters for the onset of limit-cycle oscillations, when compared to direct numerical simulation performed with a simple one-step reaction scheme in the low Mach number limit. Furthermore, the linear analysis predicts a strong stabilising effect of flame ignition, consistent with documented experiments and numerical simulations. Instability in ignited wake flows is, however, found to set in at sufficiently high Reynolds number, and a linear wavemaker analysis characterises this instability as being driven by hydrodynamic mechanisms of a similar nature as in non-reacting wake flows. The frequency of nonlinear limit-cycle flame oscillations in this unstable regime is retrieved accurately by linear eigenmode analysis performed on the time-averaged mean flow, under the condition that the full set of the reacting flow equations is linearised. If, on the contrary, unsteadiness in the density and in the reaction rate are excluded from the linear model, then the congruence between linear and nonlinear dynamics is lost.

This study investigates the linear stability of a laminar premixed flame, anchored on a square cylinder and confined inside a channel. Many modern linear analysis concepts have been developed and validated around non-reacting bluff-body wake flows, and the objective of this paper is to explore whether those tools can be applied with the same success to the study of reacting flows in similar configurations. It is found that linear instability analysis of steady reacting flow states accurately predicts critical flow parameters for the onset of limit-cycle oscillations, when compared to direct numerical simulation performed with a simple one-step reaction scheme in the low Mach number limit. Furthermore, the linear analysis predicts a strong stabilising effect of flame ignition, consistent with documented experiments and numerical simulations. Instability in ignited wake flows is, however, found to set in at sufficiently high Reynolds number, and a linear wavemaker analysis characterises this instability as being driven by hydrodynamic mechanisms of a similar nature as in non-reacting wake flows. The frequency of nonlinear limit-cycle flame oscillations in this unstable regime is retrieved accurately by linear eigenmode analysis performed on the time-averaged mean flow, under the condition that the full set of the reacting flow equations is linearised. If, on the contrary, unsteadiness in the density and in the reaction rate are excluded from the linear model, then the congruence between linear and nonlinear dynamics is lost.