Three-step approach for prediction of limit cycle pressure oscillations in combustion chambers of gas turbines

Currently, gas turbine manufacturers frequently face the problem of strong acoustic combustion driven oscillations inside combustion chambers. These combustion instabilities can cause extensive wear and sometimes even catastrophic damages to combustion hardware. This requires prevention of combustion instabilities, which, in turn, requires reliable and fast predictive tools. This work presents a three-step method to find stability margins within which gas turbines can be operated without going into self-excited pressure oscillations. As a first step, a set of unsteady Reynolds-averaged Navier–Stokes simulations with the Flame Speed Closure (FSC) model implemented in the OpenFOAM® environment are performed to obtain the flame describing function of the combustor set-up. The standard FSC model is extended in this work to take into account the combined effect of strain and heat losses on the flame. As a second step, a linear three-time-lag-distributed model for a perfectly premixed swirl-stabilized flame is extended to the nonlinear regime. The factors causing changes in the model parameters when applying high-amplitude velocity perturbations are analysed. As a third step, time-domain simulations employing a low-order network model implemented in Simulink® are performed. In this work, the proposed method is applied to a laboratory test rig. The proposed method permits not only the unsteady frequencies of acoustic oscillations to be computed, but the amplitudes of such oscillations as well. Knowing the amplitudes of unstable pressure oscillations, it is possible to determine how these oscillations are harmful to the combustor equipment. The proposed method has a low cost because it does not require any license for computational fluid dynamics software.     

Influence of nitrogen in aluminum droplet combustion

The influence of nitrogen on the aluminum droplet combustion under forced convection conditions has been studied. An aerodynamic levitation technique of millimetric size liquid droplets heated with a CO₂ laser has been adopted to characterize the combustion of aluminum droplets and, in particular, to observe the surface phenomena. The determination of the burning rate and of the droplet temperature in several atmospheres (H₂O/O₂, H₂O/Ar, H₂O/N₂, and air) has shown that they depend only on the nature and concentration of the oxidizers (O₂ and H₂O); a comparison of experiments in nitrogen and in argon containing mixtures demonstrated that N₂ did not influence the gas phase combustion. However, for nitrogen containing atmospheres we observed the formation of solid aluminum nitride (AlN) at the droplet surface after a latency time depending on the nitrogen pressure. AlN first interacts with the oxide cap producing an aluminum oxynitride, then completely covers the droplet, and finally prevents combustion. The existence of a latency time varying with the nitrogen pressure suggests that the AlN formation is controlled by heterogeneous kinetics. The phenomenon of oxide cap regression during combustion was also observed in all gases, and it is attributed to a chemical decomposition process of alumina by aluminum forming gaseous Al_xO_y species. Therefore, nitrogen effects are significant at the droplet surface rather than in the gas phase, and it is suggested that N₂ is probably one of the main species causing the manifestation of unsteady processes during aluminum droplet burning.     

Examination of mode shapes in an unstable model combustor

The coupling between the fluid dynamics, heat addition, and the acoustics of a combustor system determine whether it is prone toward combustion instability. This paper presents results from a benchmark study of the eigenmodes in an unstable experimental combustor. The axisymmetric combustor configuration is representative of a number of practical systems and comprises an injector tube, geometric expansion into a combustion chamber, and a short converging nozzle. Instability limit cycle amplitudes ranged from 5% to nearly 50% of the mean 2.2 MPa pressure. Multiple harmonics were measured for the highly unstable cases. The model combustor was designed to provide a fairly comprehensive set of tested effects: sonic vs subsonic inlets; oxidizer tube lengths that were either quarter-wave, half-wave, or off-resonant acoustic equivalents to the combustion chamber; a significant injector mean flow with Ma∼0.4; and a varied combustion chamber length. The measured mode shape data were analyzed and reduced to provide comparison with results from a linearized one-dimensional Euler model, which included the effects of real boundary conditions, entropy generation, area change, and heat and mass addition, but did not include a model for unsteady heat addition. For low-amplitude instabilities, the measured resonance frequencies agreed with those calculated by the model for the injector tube-combustion chamber system. Resonance frequencies for the high-amplitude oscillation cases corresponded to the first longitudinal frequency of the combustion chamber and its integer multiples. Good quantitative agreement was obtained between computed and measured phase difference profiles, and mode envelopes agreed qualitatively. These results provide a basis for subsequent combustion response studies on the effects of unsteady heat addition.     

Ethanol turbulent spray flame response to gas velocity modulation

A numerical investigation of the interaction between a spray flame and an acoustic forcing of the velocity field is presented in this paper. In combustion systems, a thermoacoustic instability is the result of a process of coupling between oscillations in heat released and acoustic waves. When liquid fuels are used, the atomisation and the evaporation process also undergo the effects of such instabilities, and the computational fluid dynamics of these complex phenomena becomes a challenging task. In this paper, an acoustic perturbation is applied to the mass flow of the gas phase at the inlet and its effect on the evaporating fuel spray and on the flame front is investigated with unsteady Reynolds averaged Navier-Stokes numerical simulations. Two flames are simulated: a partially premixed ethanol/air spray flame and a premixed pre-vaporised ethanol/air flame, with and without acoustic forcing. The frequencies used to perturb the flames are 200 and 2500 Hz, which are representative for two different regimes. Those regimes are classified based on the Strouhal number St = (D/U)f_f: at 200 Hz, St = 0.07, and at 2500 Hz, St = 0.8. The exposure of the flame to a 200 Hz signal results in a stretching of the flame which causes gas field fluctuations, a delay of the evaporation and an increase of the reaction rate. The coupling between the flame and the flow excitation is such that the flame breaks up periodically. At 2500 Hz, the evaporation rate increases but the response of the gas field is weak and the flame is more stable. The presence of droplets does not play a crucial role at 2500 Hz, as shown by a comparison of the discrete flame function in the case of spray and pre-vaporised flame. At low Strouhal number, the forced response of the pre-vaporised flame is much higher compared to that of the spray flame.     

An a priori assessment of the Partially Stirred Reactor (PaSR) model for MILD combustion

Moderate or Intense Low-oxygen Dilution (MILD) combustion has drawn increasing attention as it allows to avoid the thermo-chemical conditions prone to the formation of pollutant species while ensuring high energy efficiency and fuel flexibility. MILD combustion is characterized by a strong competition between turbulent mixing and chemical kinetics so that turbulence-chemistry interactions are naturally strengthened and unsteady phenomena such as local extinction and re-ignition may occur. The underlying physical mechanisms are not fully understood yet and the validation of combustion models featuring enhanced predictive capabilities is required. Within this context, high-fidelity data from Direct Numerical Simulation (DNS) represent a great opportunity for the assessment and the validation of combustion closure formulations. In this study, the performance of the Partially Stirred Reactor (PaSR) combustion model in MILD conditions is a priori assessed on Direct Numerical Simulations (DNS) of turbulent combustion of MILD mixtures in a cubical domain. Modeled quantities of interest, such as heat release rate and reaction rates of major and minor species, are compared to the corresponding filtered quantities extracted from the DNS. Different submodels for the key model parameters, i.e., the chemical time scale τ_c and the mixing time scale τ_mix, are considered and their influence on the results is evaluated. The results show that the mixing time scale is the leading scale in the investigated cases. The best agreement with the DNS data regarding the prediction of heat release rate and chemical source terms is achieved by the PaSR model that employs a local dynamic approach for the estimation of the mixing time scale. An overestimation of the OH species source terms occurs in limited zones of the computational domain, characterized by low heat release rates.     

Convective amplification of gas turbine engine internal noise sources

The acoustic field of a noise source is altered when the source is in motion. The change in the acoustic field introduced by the source motion, caused by source alteration and propagation effects, is defined as convective amplification. Previous studies of this phenomenon have been based on analytical models that did not incorporate the physical features necessary for calculation of the convective amplification factor for the internal noise sources of a gas turbine engine, which is required to predict in-flight noise levels from static engine noise measurements. An improved theoretical model was developed. At low frequencies, this model resulted in a convective amplification factor of (1?M₀ cos θ_e)^?4, which is identical with the factor established in earlier studies. At high frequencies, however, convective amplification is a function of flight speed, radiation angle, and source geometry.     

Flame–wall interaction effects on the flame root stabilization mechanisms of a doubly-transcritical LO2/LCH4 cryogenic flame

High-fidelity numerical simulations are used to study flame root stabilization mechanisms of cryogenic flames, where both reactants (O₂ and CH₄) are injected in transcritical conditions in the geometry of the laboratory scale test rig Mascotte operated by ONERA (France). Simulations provide a detailed insight into flame root stabilization mechanisms for these diffusion flames: they show that the large wall heat losses at the lips of the coaxial injector are of primary importance, and require to solve for the fully coupled conjugate heat transfer problem. In order to account for flame–wall interaction (FWI) at the injector lip, detailed chemistry effects are also prevalent and a detailed kinetic mechanism for CH₄ oxycombustion at high pressure is derived and validated. This kinetic scheme is used in a real-gas fluid solver, coupled with a solid thermal solver in the splitter plate to calculate the unsteady temperature field in the lip. A simulation with adiabatic boundary conditions, an hypothesis that is often used in real-gas combustion, is also performed for comparison. It is found that adiabatic walls simulations lead to enhanced cryogenic reactants vaporization and mixing, and to a quasi-steady flame, which anchors within the oxidizer stream. On the other hand, FWI simulations produce self-sustained oscillations of both lip temperature and flame root location at similar frequencies: the flame root moves from the CH₄ to the O₂ streams at approximately 450 Hz, affecting the whole flame structure.     

Scaling of the viscoelastic shell properties of phospholipid encapsulated microbubbles with ultrasound frequency

Phospholipid encapsulated microbubbles are widely employed as clinical diagnostic ultrasound contrast agents in the 1–5 MHz range, and are increasingly employed at higher ultrasound transmit frequencies. The stiffness and viscosity of the encapsulating “shells” have been shown to play a central role in determining both the linear and nonlinear response of microbubbles to ultrasound. At lower frequencies, recent studies have suggested that shell properties can be frequency dependent. At present, there is only limited knowledge of how the viscoelastic properties of phospholipid shells scale at higher frequencies. In this study, four batches of in-house phospholipid encapsulated microbubbles were fabricated with decreasing volume-weighted mean diameters of 3.20, 2.07, 1.82 and 1.61 μm. Attenuation experiments were conducted in order to assess the frequency-dependent response of each batch, resulting in resonant peaks in response at 4.2, 8.9, 12.6 and 19.5 MHz, respectively. With knowledge of the size measurements, the attenuation spectra were then fitted with a standard linearized bubble model in order to estimate the microbubble shell stiffness S_p and shell viscosity S_f, resulting in a slight increase in S_p (1.53–1.76 N/m) and a substantial decrease in S_f (0.29 × 10⁻⁶–0.08 × 10⁻⁶ kg/s) with increasing frequency. These results performed on a single phospholipid agent show that frequency dependent shell properties persist at high frequencies (up to 19.5 MHz).     

On the interplay of chemical and physical processes during the combustion of aluminum in water vapor

A model is considered, and the results of numerical calculations of the dynamics of the combustion of pre-prepared gas mixtures of Al and H₂O under adiabatic conditions are presented. The formation of the condensed phase is modeled taking into account the homogeneous nucleation of Al₂O₃ molecules and the processes of condensation, evaporation, and coagulation. The time dependences of the gas composition of the system, the concentration of aerosol particles, and their size distribution during the process are simulated. Details of the mechanism of the interplay of the gas-phase reactions and the formation of aerosol particles during aluminum combustion are discussed.     

Fixed-grid method for the modelling of unsteady partial oxidation of a spherical coal particle

The main goal of this work is the development of a fixed-grid method to model unsteady partial oxidation of a solid with implicit tracking of the interface. As a first step diffusive oxidation of a spherical coal particle is considered. The energy and species conservation equations formulated in spherical coordinates are discretised using the finite-volume approach. The boundary conditions for the temperature and species mass fractions at the solid–gas interface are modelled via special source terms activated in the interface cells. The numerical model was validated against analytic one- and two-film models for coal combustion in a dry-air atmosphere. Very good agreement was obtained. Based on the model developed a numerical study was carried out on the influence of water vapour on the partial oxidation of a spherical coal particle. Numerous numerical simulations were performed for particle diameters in the range 200×10^?6 m to 2×10^?2 m. The ambient temperature was varied in the range between 700 and 3000 K. The analysis of results showed that the addition of H₂O has an influence on the solution convergence due to the catalytic effect of water in the coal monoxide oxidation reaction making the whole system stiffer. However, at the same time, it was found that if the ambient mass fraction of water vapour is below 1×10^?3, its influence on combustion rates is minimal. The results of numerical simulations obtained for higher H₂O concentration (>1×10^?3) are discussed.     

Plasmons and their damping in a doped semiconductor superlattice

The complex zeroes of dielectric response function of a doped GaAs superlattice are computed to study the frequencies and damping rates of oscillations in coupled electron-hole plasma. The real part of a complex zero describes the plasma frequency, whereas imaginary part of it yields the damping rate. Strong scattering of charge carriers from random impurity potentials in a doped GaAs superlattice gives rise to a large value of damping rate which causes over-damping of plasma oscillations of coupled electron-hole gas below q_c, a critical value of wave vector component (q) along the plane of a layer of electrons (holes). The plasma oscillations which correspond to electrons gas enter into over-damped regime for the case of weak coupling between layers. Whereas, plasma oscillations which belong to hole gas go to over-damped regime of oscillations for both strong as well as weak coupling between layers. The damping rate shows strongq-dependence forq < q_c, whereas it weakly depends onq forq ≥q _c . The damping rate exhibits a sudden change atq =q _c , indicating a transition from non-diffusive regime (where collective excitation can be excited) to diffusive regime (over-damped oscillations).     

Fully compressible simulations of the impact of acoustic waves on the dynamics of laminar premixed flames for engine-relevant conditions

Thermo-acoustic instabilities remain problematic in the design of propulsion systems such as gas turbine engines, rocket motors, and ramjets. They arise from the constructive interaction of heat release rate and acoustic pressure oscillations, and can result in increased noise and mechanical fatigue. In the present work, we are concerned with the flame response to the thermodynamic fluctuations that accompany an incident acoustic wave. The objective is to investigate the flame dynamics under engine-relevant conditions using high-fidelity numerical simulations and detailed chemical kinetics. The focus is placed on the combustion of hydrogen and n-heptane, as they are both of practical interest and behave very differently when subjected to acoustic waves. We extract the phase and gain of the unsteady heat release response, which are directly related to the Rayleigh criterion and thus the stability of the system. We highlight the differences between results obtained using the fully compressible Navier-Stokes equations and the low Mach number approximation. The two simulation frameworks agree very well for acoustic wavelengths much larger than the flame thickness. However, they differ significantly at high frequencies. The gain erroneously reaches a plateau under the low Mach number approximation, while it decays to zero using the fully compressible framework. This difference is attributed to the spatial variations in the acoustic pressure, which are not captured by the low Mach number approximation.     

Unsteady deflagration speed of an auto-ignitive dimethyl-ether (DME)/air mixture at stratified conditions

The propagation speed of an auto-ignitive dimethyl-ether (DME)/air mixture at elevated pressures and subjected to monochromatic temperature oscillations is numerically evaluated in a one-dimensional statistically stationary configuration using fully resolved numerical simulations with reduced kinetics and transport. Two sets of conditions with temperatures within and slightly above the negative temperature coefficient (NTC) regime are simulated to investigate the fundamental aspects of auto-ignition and flame propagation along with the transition from auto-ignitive deflagration to spontaneous propagation regimes under thermal stratification. Contrary to the standard laminar flame speed, the steady propagation speed of an auto-ignitive front is observed to scale proportionally to its level of upstream reactivity. It is shown that this interdependence is primarily influenced by the characteristic residence time and the homogeneous auto-ignition delay. Furthermore, the unsteady reaction front in either of the two cases responds distinctly to the imposed stratification. Specifically, the results in both cases show that the dynamic flame response depends on the mean temperature at the flame base T_b and the time-scale of thermal stratification. It is also found that, based on T_b and the propensity of the mixture to two-stage chemistry, the instantaneous peak propagation speed and the overall time taken to achieve that speed differs considerably. A displacement speed analysis is carried out to elucidate the underlying combustion modes that are responsible for such a variation in flame response.     

Temperature behavior of the photovoltaic and pyroelectric responses of Sn2P2S6 semiconductor ferroelectric films

The electric response of Sn₂P₂S₆ semiconductor ferroelectric films to focused laser radiation (λ = 6328 Å) with a modulation frequency of 24 Hz is studied experimentally. It is shown that the signal involves an initial spike of current (an unsteady component) followed by the relaxation decrease to a certain value (a quasisteady component). The most significant changes in the shape and amplitude of the film response is observed near the Sn₂P₂S₆ monocrystal phase transition point of T _C = 66°C. The behavior of the unsteady component of the response is related to the behavior of the spontaneous polarization. This component decreases with increasing temperature. The quasi-steady component reaches its maximum at T = C _C. It is revealed that the behavior of relaxation processes corresponding to the decreasing response undergoes a change near the phase transition temperature.     

Combustion oscillations in gas fired appliances: Eigen-frequencies and stability regimes

This paper presents a one-dimensional acoustic model for prediction of the frequencies of self-excited oscillation and acoustic mode shapes in combustion systems. The impedance of the combustion system is represented in terms of a frequency response function (FRF). Impedances of the settling and combustion chambers are predicted by using the acoustic model, taking into account the temperature distribution in the combustion chamber. Reasonably good agreement between measured and predicted acoustic resonance frequencies and mode shapes was achieved. Some data on stability regimes are discussed.     

Aeroacoustics of duct junction flows merging at different angles

This paper reports an exploratory study of the aeroacoustics of a merging flow at a duct junction with the same width in all branches and different merging angles. The focus is put on the acoustic generation due to the flow unsteadiness. The study is carried out by the direct aeroacoustic simulation (DAS) approach, which solves the unsteady compressible Navier–Stokes equations and the perfect gas equation of state simultaneously using the conservation element and solution element (CE/SE) method. The Mach number based on the maximum inlet velocity of side branch is 0.1 and the Reynolds number of the flow based on duct width and this velocity is 2.3×10⁵. The numerical simulations are performed in two dimensions and the aeroacoustics at different merging angles (30°, 45°, 60° and 90°) are studied. Both the levels of unsteady interactions of merging flow structures and the efficiency of the acoustic generation are observed to increase with the merging angles, where the increase in acoustic efficiency can be up to three orders of magnitude. The major acoustic source is found to be the fluctuating wall pressure induced by the flow unsteadiness in the downstream branch. A scaling law between the wall fluctuating force and the acoustic efficiency is also derived.     

Experimental verification of the quasi-steady approximation for aerodynamic sound generation by pulsating jets in tubes

Voice production involves sound generation by a confined jet flow through an orifice (the glottis) with a time-varying area. Predictive models of speech production are usually based on the so-called quasi-steady approximation. The flow rate through the time-varying orifice is assumed to be the same as a sequence of steady flows through stationary orifices for wall geometries and flow boundary conditions that instantaneously match those of the dynamic, nonstationary problem. Either the flow rate or the pressure drop can then be used to calculate the radiated sound using conventional acoustic radiation models. The quasi-steady approximation allows complex unsteady flows to be modeled as steady flows, which is more cost effective. It has been verified for pulsating open jet flows. The quasi-steady approximation, however, has not yet been rigorously validated for the full range of flows encountered in voice production. To further investigate the range of validity of the quasi-steady approximation for voice production applications, a dynamic mechanical model of the larynx was designed and built. The model dimensions approximated those of human vocal folds. Airflow was supplied by a pressurized, quiet air storage facility and modulated by a driven rubber orifice. The acoustic pressure of waves radiated upstream and downstream of the orifice was measured, along with the orifice area and other time-averaged flow variables. Calculated and measured radiated acoustic pressures were compared. A good agreement was obtained over a range of operating frequencies, flow rates, and orifice shapes, confirming the validity of the quasi-steady approximation for a class of relevant pulsating jet flows.     

Specific features of the BCS-BEC crossover and thermodynamics in the 2D resonant Fermi gas with p-wave pairing

The 2D resonant Fermi gas with p-wave pairing is considered n the BCS-BEC regime. For the 2D analog of the superfluid A1 phase, the Leggett equations [1] for superfluid gap Δ and chemical potential μ are analytically solved at T = 0 and the spectrum of the collective excitations (acoustic waves) is analyzed in the BCS regime (μ > 0), where the triplet Cooper pairs emerge; in the BEC regime (μ < 0), where the triplet local pairs (molecules) emerge; and in the transition region, where μ → 0. At low temperatures, the contribution of the superfluid Fermi quasiparticles of the resonant gas to heat capacity C _v and the density of normal component ρ_n is also calculated. At μ = 0, the fermionic contribution to ρ_n and C _v are represented as power functions of temperature (ρ_n ～ T ³ and C _v ～ T ²). However, similar power contributions to these quantities are related to phonons (bosonic acoustic oscillations). The possibility of the experimental observation of the nontrivial topological term with the charge Q = 1 in the BCS regime of the 2D A1 phase is briefly discussed.     

Erosive burning of a propellant in the field of a traveling acoustic wave

The response of the propellant burning rate to periodically varied pressure and the tangential mass flow of the combustion products is examined within the framework of the phenomenological theory of unsteady combustion. The effect of an elementary acoustic disturbance, a plane monochromatic traveling acoustic wave, is examined. The analytical and numerical results are obtained for the simplest propellant model with a minimum number of parameters. The roles of the steady and unsteady components of erosion at low and high values of the erosion ratio are established.