Premixed Swirl Burner Research Articles

The impact of N2 micro-jets on the V-to-M flame shape transition in a premixed swirl burner

Injection of N2 through micro-jets located on the dump plane of a lean premixed swirl stabilized combustor is investigated as a new method for mitigating combustion instabilities. This study focuses on the chemical and fluid dynamic processes by which the N2 micro-jets impact the flame dynamics. An experimental and numerical investigation is performed to characterize the combustion instability during the V-to-M flame shape transition in a swirl burner fueled with premixed CH4/air, at an equivalence ratio of 0.62. Reasonable agreements have been found between the experimental measurements and simulation results. Both of them present that the flame changes from V-shape to M-shape periodically, and a low-frequency instability around 10 Hz is observed accordingly. It is confirmed that intermittent flame extinction in the outer recirculation zone (ORZ) is the source of the combustion instability. Furthermore, injection of N2 through micro-jets located on the combustor dump plane, into the outer recirculation zone, results in a stable V shape flame. It is clearly seen that the ORZ dilution can eliminate the combustion instability without inhibiting the combustion efficiency. A special focus is placed on the impact of the diluent injection on the local flame-flow interaction. The nitrogen micro-jets increase the local nitrogen concentration by 7% on average, lowering the flame speed and extinction strain rates by 27% and 17% respectively. Moreover, the micro-jets increase the turbulence intensity in the ORZ, leading to a significant increase in the Karlovitz number and transferring the local combustion regime from the thin reaction zone regime to the broken reaction zone regime. Hence, the nitrogen micro-jets impact on both the turbulence and the chemical reaction rates prevents flame propagation into the ORZ and results in a stable flame.

Effects of scaling laws on flow and combustion characteristics of lean premixed swirl burners

Modern heavy gas turbine combustors are always huge, so it is difficult and costly to do experiment. Thus, geometry scaling method has come into sight. In this paper, based on a single lean premixed swirl burner, validated computational fluid dynamic (CFD) model was used to study the effects of different scaling laws on various scalling models from 1/2 to 1/10. Experimental study on prototype combustor and the 3/5 scale model under full operating condition is also carried out to verify the NOx emission under different laws. Results showed that DaI scaling law was able to maintain good similarity under combustion state when scaling factor = 1/2–1/5, while Re scaling law would bring significant changes on flow and flame characteristics. The emission of NOx is also similar to prototype by using Da<sc>i</sc> law. But Re law could keep flow characteristics under non-combustion state. It is suggested that Dai law is suitable for lean premixed swirl combustor geometry scaling.

Robust identification of flame frequency response via multi-fidelity Gaussian process approach

Accurate, robust, and efficient identification of flame frequency response (FFR) plays a crucial role in thermoacoustic instability prediction, analysis and control. In order to extract the FFR from high-fidelity numerical simulation time series data, two methods are currently used in the community, which are based on harmonic excitation or broadband excitation, respectively. The former can produce quite accurate FFR estimates even in the presence of significant noise, but only at discrete frequencies; the latter method, which combines broadband forcing and system identification techniques, provides the complete FFR over the frequency range of interest, but may introduce increased levels of uncertainties in the identified results. The present study aims to fully exploit the respective strengths, while avoiding the weaknesses of the two aforementioned methods by proposing a multi-fidelity approach that merges FFR identification results from a short time broadband excitation (low-fidelity) and harmonic excitations at a few select frequencies (high-fidelity). The proposed approach is realized via a machine-learning technique called “Multi-fidelity Gaussian Process.” Our case study demonstrates that the proposed multi-fidelity approach can effectively assimilate the global trend provided by the low-fidelity results and local estimates provided by the high-fidelity results, thus leading to a globally accurate and robust FFR identification even in the presence of strong noise. In addition, we investigate the impact of the number and locations of harmonic forcing frequencies on the performance of the proposed approach. Finally, we employ the proposed multi-fidelity framework to identify the FFR of a turbulent premixed swirl burner test rig based on previously published data, which further highlights the capability and flexibility of the proposed approach in real applications.

Selective Exhaust Gas Recycling in Gas Turbines with CO2 capture: A comprehensive technology assessment

Modern gas turbines operate with large amounts of excess air for cooling and dilution of the combustion gases, in order to maintain gas turbine blade integrity. Selective recycling of CO2 into the gas turbine compressor inlet, also referred as Selective Exhaust Gas Recirculation (SEGR), can reduce the large volumetric flow rate through a CO2 capture system caused by the gas turbine excess air requirements, by 70 - 77%. It also increases CO2 concentrations to 14-18 vol% from 3-4% vol, increasing the driving force for post-combustion capture systems. This paper provides a comprehensive assessment of the concept and presents research outcomes from the UK-funded SELECT project, including power plant and process modelling, techno-economic assessments, pilot-scale gas turbine experimental work and experimental combustion tests on a representative combustor. Using an integrated model of turbomachinery, power cycles and a generic post-combustion CO2 capture technology with a 30%wt MEA solvent, we show that a reduction of up to 50% of the absorber of the capture plant – the most capital intensive part of the process – can be achieved. The compressor and gas turbine operate without any significant deviation from their design point, and a marginal increase of 0.5% point in the net electrical efficiency can be achieved. Pilot-scale testing - conducted at the Pilot Scale Advanced Capture Technologies (PACT) facilities at the University of Sheffield - show that CO2 injection at the compressor inlet of a 100 kW micro gas turbine (mGT) connected to a 1 tonne per day CO2 capture plant reduces net electrical efficiency by 1-2 %point. This is caused by lower flame temperatures, and, unlike in larger gas turbines, the control system of the micro gas turbine. Combustion tests at Cardiff University’s Gas Turbine Research Centre (GTRC) in a pilot-scale high-pressure generic premixed swirl burner, representative of modern dry-low emissions (DLR) gas turbine burners, show the effect of CO2 as diluent on the operational premixed CH4/air flame stability, chemical kinetics and measured exhaust gas composition. CO2 acts as a combustor inhibitor, causing downstream migration of the premixed flame zone, leading to eventual blow-off, instability and extinction, requiring a change in the operation equivalence ratio. The effect of adding CO2 leads to a reduction in the adiabatic flame temperature due to thermal quenching, which results in higher CO emissions and smaller thermal NOx emissions. Increasing pressure has a significant reducing effect on CO emissions, yet it results in higher NOx production, which may require mitigation if this trend is found to continue towards pressures approaching that of the F-class gas turbine. Finally, a conceptual design assessment of a regenerative adsorption wheel with structured adsorbents is proposed for the selective recycling of CO2 in combined cycle gas turbine (CCGT) power plants. It has the advantage of a relatively small pressure drop to reduce the derating of the gas turbine compared to selective CO2 membrane systems. An equilibrium model of a rotary adsorber with commercially available activated carbon adsorbents shows that four rotary wheels of 24 m diameter and 2 m length would be required in an 820MW CCGT plant. A reduction of 50% in the mass of adsorbent would be possible with an adsorbent with a higher capacity, such as Zeolite X13, with upstream dehydration of the flue gases.

Numerical simulation of ammonia/methane/air combustion using reduced chemical kinetics models

Ammonia appears to be a potential alternative fuel that can be used as a hydrogen vector and fuel for gas turbines and internal combustion engines. Chemical mechanisms of ammonia combustion are important for the development of ammonia combustion systems, but also as a mean of investigation of harmful NOx emissions, so they can be minimized. Despite of large body of experimental and modelling work on the topic of ammonia combustion, there is still need for additional investigation of combustion kinetics.The object of this work is further numerical study of ammonia combustion chemistry under conditions resembling industrial ones. After literature review, three mechanisms of ammonia combustion that also include carbon chemistry are used for simulation of experimental premixed swirl burner with the aim of evaluating their performance. San Diego mechanism, that was also the most detailed one, proved to be the best in terms of emissions, but neither one of the models was able to accurately reproduce CO emission after equivalence ratio went beyond 0.81. It was also observed that oxygen is excessively consumed. This study contributes to the current knowledge by providing new insights in ammonia burning conditions closely resembling those in industrial applications, and consequently is expected that insights obtained will help in the design of real industrial burning systems.

Study of the effect of bluff body size on stability limits of a premixed natural gas swirl burner

Flame stabilization is highly important in lean premixed combustion which is considered a desirable technology for low-emission gas turbines. Swirl stabilization is one of the most common methods used for this purpose. Simple generation of swirl, however, is not enough to reach an acceptable operating range. A method of improving stability is using a bluff body in order to resist flame flashback caused by combustion-induced vortex breakdown at moderate to high swirl numbers. The present study aims to investigate the effect of bluff body size on the stability boundaries of flashback and blowout and also on flame shape. A premixed swirl burner is designed and built to operate with natural gas at atmospheric condition. In addition to gas and air flow rates at stability limits, normal and chemiluminescence flame images are documented. The non-reacting flow is also simulated to investigate the flow pattern out of the burner nozzle. It is found that bluff body size has a significant influence on flashback prevention and to a lesser extent on lean blowout limit while having minor effect on the shape of the flame. Just before blowout, low-frequency fluctuations are observed in the chemiluminescence radiations that are associated with the periodic changes in flame zone. Nonetheless, no warning signs are observed before flashback. Looking into the velocity profiles at the nozzle exit also shows an increase in axial velocity near the center of the nozzle with larger bluff bodies, revealing the mechanism of improvement of burner resistance to flame flashback.

Finite rate simulations and analyses of wet/distributed flame structure in swirl-stabilized combustion

Towards developing humidified gas turbines (HGT) capable of running at high electrical efficiencies and low emissions, wet/steam-diluted combustion in a premixed swirl burner is investigated using large eddy simulation and a partially stirred reactor method. Chemical explosive mode and extended combustion mode analyses are performed to promote the understanding of wet flame structures. The former identifies the key features of the wet methane oxidation processes, and the latter extends the flame regime classification method to describing the combustion status of fluid parcels using local properties. Three combustion regimes are extensively discussed: the swirl stabilized (SS), colorless distributed (CDC) and non-combustible. Using the combined analyses of the two approaches, it is found that compared to dry flames, wet flames present more fluid parcels defined in the practical CDC regime where local heat release is low and Damköhler number is smaller than unity. The wet fluid parcels are capable of self-igniting via radical explosion, while dry fluid parcels self-ignite via thermal runaway. The species CH2O and temperature are the first and second highest contributors towards the explosivity of dry flames, while temperature is insignificant to that of wet flames. The species C2H6 is found an important source to the self-ignitability of wet fluid parcels in the practical CDC regime due to the activation of the three-body ethane formation reaction R148: 2CH3 + M = C2H6 + M in the low O2% wet combustion environment. Proper use of proposed methods to quantify wet flame behavior guides stable and low emission operation of practical HGT.

Combustion instability analysis on a partially premixed swirl combustor by thermoacoustic experiments and modeling

The combustion instability of a partially premixed swirl burner is investigated by experimental tests and numerical modeling. The experimental results show that the combustion dynamics of the partially premixed swirl combustor under different thermal power rates and equivalence ratios can be classified into three regimes: combustion noise, intermittent oscillation and limit cycle oscillation. The characteristics of each combustion regime are clarified: combustion noises occur with small pressure oscillation amplitudes and unapparent frequencies when the equivalence ratio approaches 1; the limit cycle oscillations present in strong single frequencies within the relative lower (6223–8563) and higher (10,796–13536) ranges of Re number; the intermittent oscillations observed within a middle range (8634–10796) show multiple peaks in their spectrums. To obtain the relationship between flame transfer function and thermoacoustic modes of the combustor, the CFD/system identification and low order thermoacoustic network model are developed. The thermoacoustic modes are found to be influenced by the interactions between natural acoustic mode and flame response factors. The modeling results reveal that the intermittent oscillations show two modes with positive growth rates, while the limit cycle oscillations are dominated by one mode. Moreover, the combustion instability is found more sensitive to FTF but not acoustic boundary in the modeling.

Relationship of gain and phase in the transfer function of swirling flames

Gain and phase are two key characteristics of flame transfer function (FTF) in evaluating unsteady flame response. Few studies have investigated the correlation between gain and phase of FTF compared to the extensive literature on the gain characteristics. In this study, we measured the gain and phase of acoustic-excited swirling flames with different flow rates, fuels, equivalence ratios, and burner structures on a single nozzle premixed swirl burner. We identified, for the first time, the consistent variation of FTF gain and derivative of phase over a wide range of acoustic frequencies, and revealed an essential linear relationship between the extremal frequencies of gain and phase derivative, demonstrating that the gain and phase of FTF are not independent. We further proposed an analytical decomposition of the periodically oscillated swirling flame in which FTF equals the combined complex vector of all the perturbing mechanisms. The synchronized variation characteristics of the gain and phase derivative for different flames and acoustic excitations can be explained using a two vector model based on vector decomposition. The distinct time lags and angular velocities of the perturbing vectors were determined by the different spatial positions of the flame tip and base. The local extrema of the FTF modulus and phase derivative are caused by the phase interference of the sub-vectors. Multiple complex vectors affecting heat release rate should be considered under high frequency.

Experimental study of stratified swirl flame dynamics in a model gas turbine combustor

The flame structure and dynamic response of stratified swirl flames are investigated using a stratified premixed swirl burner. The change of swirl intensity is achieved by swirlers with different swirl angles. Stratification of the flow and mixtures is established by varying the bulk air flow rates and mixture equivalence ratios between the inner and outer annulus. Depending on operating conditions, four different flame structures are stabilized in the combustor: A V-shaped flame (V-flame), a stratified flame (S-flame), a lifted flame (L-flame) and a special plate-shaped flame (P-flame). Thermoacoustic instabilities are then investigated. Generally, the frequency and intensity of the pressure and heat release pulsation are coupled. The amplitude of the pressure and heat release pulsation are all sensitive to the swirl intensity, air split ratio (ASR) and stratification ratio (SR). Large amplitude limit cycles are found in the strong swirl, high ASR and high SR flame. The dominant frequency of pulsation is about 100 Hz in the cases with SR < 1, when SR > 1, the dominant frequency fluctuates between 400 Hz and 500 Hz. The hysteresis phenomenon is also observed in current experiments. Different flame structures can occur in the same operating condition by varying the operating routines.

Sound Pressure Level Analysis of a Liquid-Fueled Lean Premixed Swirl Burner with Various Quarls

Swirl burners are widely used in numerous practical applications since they are characterized by low pollutant emission and a wide operating range. Besides reliable operation, a burner must fulfill noise emission regulations, which is often a sound pressure level in dB(A) when people are affected. Therefore, the present paper evaluates the overall sound pressure level (OASPL) variation of a 15-kW liquid-fueled turbulent atmospheric swirl burner at various setups. Firstly, the combustion air flow rate was adjusted, which induced a swirl number modification due to the fixed swirl vanes. Secondly, the atomizing pressure of the plain-jet airblast atomizer was modified, which also affected the swirl number. High atomizing air jets notably increased combustion noise by intensifying the shear layer. Thirdly, a geometrical modification was performed; 0°–60° half cone angle quarls in 15° steps were installed on the lip of the baseline burner for extended flame stability. By filtering the OASPL to the V-shaped flames, a linearly decreasing trend was observed as a function of swirl number. Their derivative also has a linearly decreasing characteristic as a function of the atomizing pressure.

Prediction of Premixed Flame Dynamics Using Large Eddy Simulation With Tabulated Chemistry and Eulerian Stochastic Fields

Abstract This paper demonstrates that a large Eddy simulation (LES) combustion model based on tabulated chemistry and Eulerian stochastic fields can successfully describe the flame dynamics of a premixed turbulent swirl flame. The combustion chemistry is tabulated from one-dimensional burner-stabilized flamelet computations in dependence on progress variable and enthalpy. The progress variable allows to efficiently include a detailed reaction scheme, while the dependence on enthalpy describes the effect of heat losses on the reaction rate. The turbulence-chemistry interaction is modeled by eight Eulerian stochastic fields. An LES of a premixed swirl burner with a broadband velocity excitation is performed to investigate the flame dynamics, i.e., the response of heat release rate to upstream velocity perturbations. In particular, the flame impulse response and the flame transfer function (FTF) are identified from LES time series data. Simulation results for a range of power ratings are in good agreement with the experimental data.

Generation and transport of equivalence ratio fluctuations in an acoustically forced swirl burner

In the context of thermoacoustic instabilities, knowledge about the generation and transport of equivalence ratio fluctuations is highly important to correctly model their impact on the flame transfer function. In this work, spatially resolved equivalence ratio perturbations in the mixing section of an acoustically forced, partially premixed swirl burner typical of modern gas turbine combustors are investigated. Tunable diode laser absorption spectroscopy using a wavelength-modulation approach is applied to assess the spatially inhomogeneous equivalence ratio field in the radial direction. Particle image velocimetry is applied to measure the axial velocity field. Based on these results, a tomographic reconstruction is utilized to deduce the local fuel distribution at two axial locations. Integrated, global equivalence ratio fluctuations are calculated and compared to simple line-of-sight measurements. The influence of the forcing frequency and amplitude is investigated and good agreement was found between the different measurement approaches. Frequency dependent equivalence ratio perturbation generation mechanisms driven by air velocity fluctuations in the swirler, as well as pressure fluctuations at the fuel injector, are observed. Two different mixing transfer functions modeling diffusion and dispersion are compared to the results and reveal substantial differences, indicating a significant impact of coherent fluctuations of the transport velocity on the mixing that are not accounted for by either of the models.

Impact of Stretch and Heat Loss on Flame Stabilization in a Lean Premixed Flame approaching Blow-off

The accurate prediction of the turbulent combustion process in lean burn flames is of primary importance in the design of gas turbine low-emission combustors. In this framework, the correct account for high strain levels, combined with the heat loss of the flame, by numerical tools is of high technical relevance in order to improve the operational flexibility while reducing emissions. In fact, in high Reynolds lean combustion modelling, the quenching effects due to flame front distortion are expected to govern flame behaviour. The present work presents an assessment of the modelling strategies to introduce the stretch effects on the flame in Flamelet Generated Manifold (FGM) model, in both the framework of Reynolds-Averaged Navier-Stokes (RANS) and Large-Eddy Simulation (LES). At this purpose a premixed swirl burner experimentally studied at Cambridge University was chosen, consisting of a strongly swirling, confined natural gas flame. Results highlight that LES-FGM, coupled with an extended Turbulence Flame Closure model (TFC), succeeds in predicting the main characteristics of the flame at different operating conditions approaching blow-off, thus representing a valid tool to investigate lean burn flames in such context.

Measurement and Simulation of Combustion Noise and Dynamics of a Confined Swirl Flame

The combustion noise produced by a confined, turbulent, premixed swirl burner is predicted with large-eddy simulation of compressible, reacting flow. Characteristics-based state-space boundary conditions are coupled to the large-eddy simulation to impose precisely and independently from each other magnitude and phase of the acoustic reflection coefficients at the boundaries of the computational domain. The coupling approach proves to be accurate and flexible in regard to the estimation of sound pressure spectra in a confined swirl combustor for different operating conditions. The predicted sound pressure levels and its spectral distributions are compared to measurements. Excellent qualitative and quantitative agreement is achieved not only for a stable configuration but also for configurations that exhibit a thermoacoustic instability. This indicates that the flow and flame dynamics are reasonably well reproduced by the simulations.

3D Simulation of Ammonia Combustion in a Lean Premixed Swirl Burner

To date, a number of mechanical, electrical, thermal, and chemical approaches have been developed for storing electrical energy for utility-scale services. The only sufficiently flexible mechanism allowing large quantities of energy to be stored over long time periods is chemical energy storage in the form of carbon or hydrogen. One chemical considered for hydrogen carriage that can potentially be employed for storage is ammonia. Ammonia can substitute pure hydrogen for storage and be employed for power generation at large industrial scale if the molecule is efficiently burned through mature equipment such as gas turbines, thus providing not only a carbon free fuel, but also a chemical capable of being stored at low energy requirements. Thus, progress on the use of ammonia in gas turbines is a main priority for groups working on the area. Studies need to be conducted in experimental rigs with strong CFD analyses for further industrial implementation. In this paper, modelling of ammonia combustion in a generic gas turbine combustor is explored in order to provide an effective tool for future application. Large Eddy Simulation approach was used to develop a model for ammonia/hydrogen combustion in gas turbine combustors. To capture more details of the turbulent reacting flow, a detailed chemical mechanism was selected for a deep insight. A Partially Stirred Reactor framework was utilized to deal with the turbulence/chemistry interaction. The developed model was then applied to the simulation of lean premixed ammonia/hydrogen flames in a generic swirl burner. A preliminary validation for the model is performed by correlation of NOx emission with experimental data. Results show the model can provide detailed information of flow field, flame structure, emissions, etc. It can be used to optimize the procedure of utilizing ammonia as a fuel in future equipment design.

Swirl stability and emission characteristics of CO-enriched syngas/air flame in a premixed swirl burner

There is significant variation in the composition of synthesis gas derived from biomass, coal or waste. The inconsistency of syngas constituents poses challenges and requires thorough characterisation prior to use as alternative fuel in practical combustion system. The present study investigates the combustion and emission characteristics of CO-enriched syngases by using an atmospheric premixed swirl flame burner. High (CO/H2 = 3) and moderate (CO/H2 = 1.2) CO-enriched syngases were fully premixed with air and diluents of CH4 and CO2 prior to ignition at the burner outlet. Direct flame imaging shows that moderate CO-enriched syngas produces less luminous flames than high CO-rich syngas, signifying less tendency to form soot. Moderate CO-rich syngases show more compact flames with higher intensity owing to higher H2 contents. The blowout test shows that higher CO content syngases result in lean blowout at higher equivalence ratios, posing stability issues. High fractions of unreactive CO2 and reactive CH4 in syngases result in higher lean blowout limit. Emissions wise, high CO-rich syngases show evidently less NOx emissions as compared to baseline pure CO flames at increasing equivalence ratios. Moderate CO-rich flame exhibits higher NOx level than high CO-rich at ϕ < 0.8. However, at fuel-stoichiometric and fuel-rich regions they display similar levels of NOx. Higher fraction of CO2 dilution results in reduction of NOx emissions, with pronounced impact on fuel-rich cases. There was minimal effect on CO emissions with increased dilution of CO2.

The contribution of intrinsic thermoacoustic feedback to combustion noise and resonances of a confined turbulent premixed flame

The influence of Intrinsic Thermoacoustic (ITA) feedback on the combustion noise spectrum produced by a confined, turbulent, premixed, swirl flame is investigated. The analysis is based on the understanding that sound is generated by unsteady heat release resulting from turbulent fluctuations on the one hand, and from the response of the flame to incoming acoustic perturbations on the other. The former effect is described by a source term for combustion noise, i.e. a spectral distribution of unsteady heat release rate, the latter by the flame transfer function. Both quantities are identified from time series data for fluctuating velocity and heat release rate, generated with large eddy simulation of premix swirl burner. The combustion noise source term and the flame transfer function are then introduced in an acoustic network model of the test rig in order to compute the spectral distribution of the sound pressure level at a certain location in the combustion chamber. Results for the noise spectrum are in good agreement with experiment, showing a broadband component and well-defined peaks. The frequencies of the peaks correspond to either acoustic cavity or ITA resonances. The acoustic network model is used for parametric studies, where the acoustic reflection coefficient at the combustor exit is varied. Remarkably, it is found that the magnitude of the ITA peak increases with decreasing values of the acoustic reflection coefficient, and vice versa. Furthermore, the influence of combustion chamber length on resonance frequencies is explored. It is observed that the frequency of the ITA resonance is insensitive to combustor length. This behaviour is observed qualitatively also in experiments.

Flow Physics of a Bluff-Body Swirl Stabilized Flame and their Prediction by Means of a Joint Eulerian Stochastic Field and Tabulated Chemistry Approach

In the frame of this work a transported joint scalar probability density function (PDF) method is combined with the flamelet generated manifolds (FGM) tabulated chemistry approach for large eddy simulation (LES) modeling of a three-dimensional turbulent premixed swirl burner. This strategy accounts for the turbulence-chemistry interaction at reasonable computational costs. At the same time, it allows the usage of detailed chemistry mechanisms for the creation of the chemical database. The simulation results obtained are comparatively assessed along with complementary measurements. Furthermore, transient and time-averaged data are used to provide insight into the flow physics of the bluff-body swirl stabilized flame considered. The sensitivity of the results to different modeling approaches regarding the predicted flame shape and its dynamics is also investigated, where the implemented approach is compared with the well-established artificially thickened flame (ATF) combustion model. Consequently, the investigation conducted in this work aims to provide a complete picture on the ability of the proposed combustion model to reproduce the flow conditions within complex bluff-body swirl stabilized flames.

Uncertainty Quantification of Growth Rates of Thermoacoustic Instability by an Adjoint Helmholtz Solver

Thermoacoustic instabilities are often calculated with Helmholtz solvers combined with a low-order model for the flame dynamics. Typically, such a formulation leads to an eigenvalue problem in which the eigenvalue appears under nonlinear terms, such as exponentials related to the time delays that result from the flame model. The objective of the present paper is to quantify uncertainties in thermoacoustic stability analysis with a Helmholtz solver and its adjoint. This approach is applied to the model of a combustion test rig with a premixed swirl burner. The nonlinear eigenvalue problem and its adjoint are solved by an in-house adjoint Helmholtz solver, based on an axisymmetric finite-volume discretization. In addition to first-order correction terms of the adjoint formulation, as they are often used in the literature, second-order terms are also taken into account. It is found that one particular second-order term has significant impact on the accuracy of the predictions. Finally, the probability density function (PDF) of the growth rate in the presence of uncertainties in the input parameters is calculated with a Monte Carlo approach. The uncertainties considered concern the gain and phase of the flame response, the outlet acoustic reflection coefficient, and the plenum geometry. It is found that the second-order adjoint method gives quantitative agreement with results based on the full nonlinear eigenvalue problem, while requiring much fewer computations.