Prediction Of Combustion Instabilities Research Articles

Multiphysics Modeling for Combustion Instability in Paraffin-Fueled Hybrid Rocket Engines

The use of paraffin-based fuels is a promising approach to a low regression rate in hybrid rocket engines, and the capability to describe and predict combustion instability in the presence of liquefying fuels becomes an enabling step towards the application of hybrid rockets in a wide range of space transportation systems. In this work, a multiphysics model having this purpose is presented and discussed. The model is based on a network of submodels in which chamber gas dynamics is described by a quasi-1D Euler model for reacting flows while thermal diffusion in the grain is described by the 1D heat equation in the radial direction. An artificial neural network is introduced to reduce the computational cost required by the chemical submodel. A sensitivity analysis is performed to identify the key parameters, which have the largest influence on combustion instability and to evaluate the predictive capability of the model despite the uncertainty introduced with the necessary modeling simplifications. Results are presented considering two test cases with different oxidizers: hydrogen peroxide and gaseous oxygen. The procedure shows good agreement with the experimental results available in the literature.

Predicting combustion behavior in rotating detonation engines using an interpretable deep learning method

As rotating detonation engine (RDE) is maturing toward engineering implementation, it is a crucial step in developing real-time diagnostics capable of monitoring the combustion state therein to prevent combustion instability, such as detonation quenching, re-initiation, and mode switch. However, previous studies rarely consider monitoring combustion behavior in RDEs, let alone predicting the impending combustion instabilities based on the warning signals. Given active control requirements, a novel Transformer-based neural network, RDE-Transformer, is proposed for monitoring and predicting the combustion states in advance. RDE-Transformer is a multi-horizon forecasting model fed by univariate or multivariate time series data including pressure signals and aft-end photographs. Model hyper-parameters, namely, the number of encoder and decoder layers, the number of attention heads, implementation of positional encoding, and prediction length, are investigated for performance improvements. The results show that the optimal architecture can reliably predict pressures up to 5 detonation periods ahead of the current time, with a mean squared error of 0.0057 and 0.0231 for the training and validation set, respectively. Moreover, the feasibility of predicting combustion instability is validated, and the decision-making process through the attention mechanism is visualized by attention maps, making the model interpretable and superior to other “black-box” deep learning methods. In summary, the high performance and high interpretability of RDE-Transformer make it a promising diagnostics functional component for RDEs toward applied technology.

Prediction of combustion instabilities based on the Green's function in a three-dimensional annular combustor with multiple flames

The prediction of combustion instabilities is essential for modern annular combustors fed by multiple flames. This paper develops a model based on Green's function to study the interaction of multiple flame responses with different types in a three-dimensional (3D) geometry. The flame responses are described by flame transfer functions and are recognized as monopole sources in 3D cavities. Then the dispersion relation equation in the form of matrix is performed with the condition of equality of pressure. Thermoacoustic complex frequencies, mode structure, as well as the stability behaviors in combustor can be obtained in this model and the analysis is accomplished using Rayleigh index. The results are compared to the values of existing theoretical models and a good agreement is achieved. Furthermore, the effects of non-identical flame responses on complicated slanted mode under the condition of asymmetric are studied. In addition, the combustion instabilities of radial mode can be predicted by this model when the radial position distributions of the heat sources move in the case of small ratio of inner wall to outer wall.

AP/HTPB combustion response simulation with a new equivalent linear system method

In the study of solid rocket motor (SRM) combustion instability, modeling and analyzing the combustion response of the solid propellant is a laborious task. We propose a new idea, an equivalent linear system method, for modeling solid propellant combustion response with three steps: first, simulating the transient combustion process under pulse pressure excitation for only one CFD case; then, treating the combustion process as a black-box and obtaining the transfer function of the combustion process from the CFD result; finally, predicting and analyzing the combustion response based on the transfer functions. For the AP/HTPB sandwich propellant withp¯=3MPa, the amplitude, duration, and direction of excitation pulses are studied. The new method is also verified, with a maximum relative error of 4.3% for burning rate response under p˜≤1MPa (as high as one-third of the pressure DC). Applicability of this new method is demonstrated for another two AP/HTPB sandwich propellants with different configuration under p¯=8MPa and p¯=10MPa, showing that the system-simulated combustion responses of burning surface temperature and burning rate are consisted well with the CFD results and the maximum relative error of burning rate response is 2.1%. Asymmetric combustion response for positive and negative pressure perturbations is a new finding based on the CFD and simulation results. Besides, a new approach using dual transfer functions is proposed to ensure high accuracy for the simulation of solid propellant combustion. The pressure-coupled response function is predicted by this method for the sandwich propellant under p¯=5MPa and p˜=20kPa within a wide continuous frequency range (0–3000 Hz). The comparison with CFD results indicates that the relative bias of Rp is less than 2%. With the proposed method, the combustion response to arbitrary pressure excitations can be simulated with high accuracy, high time-resolution, and high speed. The method shows great advantage and potential in simulating and predicting combustion instability.

Effect of flame motion on longitudinal combustion instabilities

In the analysis of combustion instabilities, especially for the longitudinal modes, the flame typically is regarded as a discontinuity at rest and the flame motion is usually ignored. However, this may lead to errors in the prediction of combustion instabilities for certain conditions. This paper investigates the effect of flame motion on the longitudinal combustion instabilities in a simple ducted combustion chamber. An analytical model considering the flame motion is incorporated into the thermoacoustic system. The dispersion relation is established, and the eigenvalues of thermoacoustic system can be obtained by solving it. The present study considers the cases with and without entropy noise produced at the outlet boundary. The effect of flame motion on longitudinal combustion instabilities is evaluated by consider it and not. When there is no entropy noise, the effect of the flame motion remains small. However, when the entropy noise is considered, the flame motion can have a large effect on different longitudinal modes. Furthermore, the presence of the flame motion can dissipate the entropy wave generated from the flame and further the corresponding combustion instability for the present configuration.

Prediction of combustion instability by combining transfer functions in a model rocket combustor

The flame transfer function (FTF) and acoustic transfer function (ATF) are estimated experimentally and numerically, respectively, and both are combined to predict combustion instability of a model rocket combustor with a single coaxial jet–swirl injector. FTF of the injector is measured experimentally by imposing external velocity excitation on the injector. ATF, i.e., model-chamber response to heat-release fluctuation from flames, is difficult to measure, and alternatively, an idea of numerical evaluation method is suggested by applying an equivalence-ratio perturbation to flames. Then, ATF is calculated by numerical simulations with a three-dimensional model and compared with ATF from the one-dimensional analytic equation. Results show that ATF estimated by the 3-D numerical model improves accuracy in predicting resonant frequencies and growth rates of pressure oscillations in the model chamber. Finally, a closed-loop system transfer function describing dynamic behaviors of the model chamber is formulated by combining FTF with ATF and it is applied to predict combustion instability of the chamber. This prediction is compared with experimental observation, which shows good agreement between them.

In-situ measurement of reflection coefficient and its application to predicting combustion instability in a gas turbine combustor

In-situ measurement of reflection coefficient and its application to predicting combustion instability in a gas turbine combustor

Investigation of flame surface density modeling for large eddy simulation of turbulent premixed flames by comparison with a prescribed reference solution

A framework is proposed to investigate the behavior of LES flame surface density models for simple academic cases, here the development of a statistically one-dimensional flame in an homogenous and isotropic turbulence, by comparison with a prescribed reference solution. First, a set of zero-dimensional equations is derived to reproduce a fractal flame surface evolving from an initially planar shape up to equilibrium. Then, a balance equation including a sub-grid scale contribution is solved to mimic the evolution of the overall resolved flame surface in an actual large eddy simulation.Non-dynamic and dynamic versions of an algebraic sub-grid scale flame surface wrinkling factor model are investigated. The non-dynamic model overestimates the total flame surface in early stages of the flame development while under (respectively over) estimation of unresolved surfaces are partly compensated by larger (respectively lower) resolved surfaces. Moreover, model parameters strongly affect flame response times possibly compromising the prediction of combustion instabilities. Results are improved using a dynamic flame surface wrinkling factor model.The generality of conclusions are limited by the enforcement of the reference solution but the proposed approach is well-suited to qualitative investigations of sub-grid scale models at negligible computational costs, to support direct numerical simulation studies or to help in analyzing LES results. It also suggests new possible closures for future developments.

Numerical Investigation of Combustion Instabilities in a Single-Element Lean Direct Inject Combustor Using Flamelet Based Approaches

Abstract In this paper, high-fidelity large eddy simulations (LES) along with flamelet-based combustion models are assessed to predict combustion dynamics in low-emission gas turbine combustor. A model configuration of a single-element lean direct injection (LDI) combustor from Purdue University (Huang et al., 2014, “Combustion Dynamics Behavior in a Single-Element Lean Direct Injection (LDI) Gas Turbine Combustor,” 50th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Cleveland, OH, July 28–30.) is used for the validation of simulation results. Two combustion models based on the flamelet concept, i.e., steady diffusion flamelet (SDF) model and flamelet generated manifold (FGM) model are employed to predict combustion instabilities. Simulations are carried out for two equivalence ratios of φ = 0.6, and 0.4. The results in the form of mode shapes, peak to peak pressure amplitude and power spectrum density (PSD) are compared with the experimental data of Huang et al. (2014, “Combustion Dynamics Behavior in a Single-Element Lean Direct Injection (LDI) Gas Turbine Combustor,” 50th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Cleveland, OH, July 28–30.). The effect of variation in the time-step size hence acoustic courant number is studied. Further, two numerical solver options, i.e., pressure-based segregated solver and pressure-based coupled solver, are used to understand their effect on the solution convergence regarding the number of time-steps required to reach the limit cycle of the pressure oscillations. A truncated (half) domain simulation is performed by applying an appropriate acoustic impedance boundary condition at the truncated location. Overall, the simulation results compare well with the experimental data and trends are captured accurately in all simulations. It builds confidence in flamelet-based combustion models for the use in combustion instability modeling which is traditionally done using finite rate chemistry models based on reduced kinetics.

Chemiluminescence as a diagnostic in studying combustion instability in a practical combustor

Prediction of combustion instability is essential in reducing development costs of large scale rocket engines. Recently, high fidelity CFD models have shown some ability to represent the stability characteristics of sub-scale experimental combustors. A challenge remains in acquiring experimental measurements of critical combusting flow properties, especially measurements of the unsteady heat addition field, for comparison to models. The chemiluminescent emission of radicals OH* and CH*, although commonly employed, may fall short due to its known dependence on pressure, strain rate, equivalence ratio, and turbulence level. Since these flame properties have large variations in an unstable rocket combustor, it is difficult to decouple the emission from all other variables except the heat release. Computations capture the local variations, and therefore can be used for a direct comparison with the measurements. The present study investigates the relationship between chemiluminescent species and heat release rate of the flame using simulations that employ detailed kinetics including the emitting species. This relationship is then compared to experimental spectral measurements captured with a fiber optic probe to check the validity of the model and to provide insight on the ability of the chemiluminescent light emission to indicate heat release in a high pressure unstable flame.

A novel modal expansion method for low-order modeling of thermoacoustic instabilities in complex geometries

This work proposes an improvement to existing methods based on modal expansions used for the prediction of thermoacoustic instabilities in zero Mach number flow conditions. Whereas the orthogonal basis made of the acoustic eigenmodes of the domain bounded by rigid walls is classically used, an alternative method based on a modal expansion onto an over-complete set of acoustic eigenmodes is proposed. This allows avoiding the misrepresentation of the acoustic velocity field often observed near non rigid-wall boundaries. A Low Order Model network utilizing a state-space framework is then built upon this novel type of modal expansion. Several test cases, going from non reacting ducts to a complex geometry with combustion, are studied to assess the potential of the approach. The methodology not only successfully mitigates the misrepresentation in the acoustic field in the presence of non-rigid-wall boundaries, but it also drastically improves the convergence speed. The modularity of the method and its ability to handle complex geometries are illustrated by considering a configuration featuring an annular chamber, an annular plenum, as well as multiple burners. This novel technique is expected to bring worthy improvements to existing Low Order Models using modal expansions for the prediction of combustion instabilities.

Reduced-Order Modeling Framework for Combustor Instabilities Using Truncated Domain Training

A multifidelity framework is established and demonstrated for the prediction of combustion instabilities in rocket engines. The main idea is to adapt appropriate fidelity modeling approaches for different components in a rocket engine to ensure accurate and efficient predictions. Specifically, the proposed framework integrates projection-based reduced-order models (ROMs) that are developed using bases generated on truncated domain simulations. The ROM training is performed on truncated domains, and thus does not require full-order model solutions on the full rocket geometry, thus demonstrating the potential to greatly reduce training costs. Geometry-specific training is replaced by the response generated by perturbing the characteristics at the boundary of the truncated domain. This training method is shown to enhance the predictive capabilities and robustness of the resulting ROMs, including at conditions outside the training range. Numerical tests are conducted on a quasi-one-dimensional model of a single-element rocket combustor, and the present framework is compared to traditional ROM development approaches.

Reduced Order Modeling Approach to Combustion Instabilities of Liquid Rocket Engines

This paper describes one possible approach to a numerical framework for a reduced order tool that aims to simulate combustion instabilities in liquid rocket engines. The numerical framework relies on the projection of the pressure fluctuations on the eigenmodes of the system. The pressure fluctuations are solutions of the wave equation of the system. After projection on the eigenmodes, the wave equation takes the form of a series of second-order harmonic equations with source terms that drive combustion instabilities and damping terms that attenuate them. A test rig was developed to study cavity interactions, injector impedance, and damping effects. The damping rates that were measured on the test rig show a trend that is consistent with observations in liquid rocket engines. On the whole, the test rig can be used to validate simplified models of combustion instabilities. The global framework of the reduced order approach that was developed to predict combustion instabilities was first validated by comparing the data from simulations against experimental results from the test rig in a series of nonreacting experiments. Our approach was then applied to a case study of a full-scale rocket engine. This engine, under certain operating conditions, exhibits instabilities. Stable and unstable behaviors have been revealed by the temporal evolution of calculated pressure amplitudes.

WKB solutions to the quasi 1-D acoustic wave equation in ducts with non-uniform cross-section and inhomogeneous mean flow properties – Acoustic field and combustion instability

Linear modal analysis based on the spatio-temporal harmonic representation of acoustic fluctuations is a well-known reduced order method to predict combustion instability frequencies. However, a limitation of this method is that it is only applicable to domains with homogeneous mean properties. The Wentzel-Kramers-Brillouin (WKB) method facilitates the development of approximate analytical solutions to the one-dimensional (1-D) acoustic wave equation in domains with inhomogeneous mean properties. The “classical” form of the WKB solution to the wave equation is based on the assumption of high frequency (or, short wavelength), and is applicable to uniform cross-section ducts with a mean temperature gradient, but no mean flow. Subsequently, the WKB method was extended to include uniform mean velocity as well. In the current study, we derive a WKB-type solution to the generalized Helmholtz equation in quasi 1-D ducts with non-uniform cross-sectional areas and inhomogeneities in mean flow properties such as the velocity, temperature, density, and pressure. The WKB solution is applicable under the assumptions of high frequency and slowly varying mean properties. In deriving this solution, a novel approach has been developed to relate the first and second spatial derivatives of the axial velocity fluctuations to the pressure fluctuations (and its derivatives).A second WKB-type solution (referred to as the WKB2 solution) is also obtained by relaxing the slowly-varying mean property assumption, but retaining the high frequency approximation. Thirdly, the Helmholtz equation for pressure is solved numerically without invoking the two WKB assumptions. The WKB, WKB2 and numerical solutions are compared for a number of cases involving combinations of non-uniform duct areas and axially varying mean properties. Finally, we apply the WKB solution to predict the longitudinal combustion instabilities in a 1-D combustor characterized by a sudden expansion, with uniform mean flow in each of the two ducts comprising the combustor, and a linear temperature profile downstream of a compact, planar flame.

Development of a comprehensive flame transfer function and its application to predict combustion instabilities in a dump combustor

ABSTRACTIn combustion instability analysis, a flame transfer function (FTF) is used to describe the response of a premixed flame to incident acoustic oscillations. A comprehensive FTF is developed that relates the fluctuations in flame heat-release rate to those in density, heat of reaction, turbulent flame speed, and the flame surface area. Each of these four contributions is eventually expressed in terms of the fluctuations in acoustic pressure and velocity through the respective response functions. The flame surface-area response to acoustic oscillations is incorporated into the FTF through the -equation level-set method. In this method, we directly solve for the level-set fluctuations in terms of the velocity fluctuations and then relate the flame surface-area oscillations to . In the absence of turbulent flame-speed fluctuations, the response functions from the present -equation approach are in good agreement with those from the conventional -equation approach (where one writes ). However, when the turbulent flame-speed fluctuations are included, the two approaches differ, principally in the flame response to axial velocity fluctuations. The current FTF, generalized for any mean flame shape, is applied to analyze the response of a V-shaped mean flame located at the cross-sectional interface of a 2D dump combustor. For this flame, the effects of variation in acoustic frequency, mean Mach number, mean temperature, and mean equivalence ratio on the FTF magnitude and phase are investigated. Both axial and mixed mode acoustic perturbations are considered. For the purely axial modes, the response-function amplitudes of density and heat of reaction are seen to be independent of frequency, while those of flame speed and axial velocity exhibit harmonic-like oscillations as a function of frequency. For the mixed-mode fluctuations, the response-function amplitude of density decays monotonically with frequency, whereas the response-function amplitudes of the heat of reaction, turbulent flame speed, and velocity components show decaying oscillatory behavior in frequency. Further, it is observed that the flame-speed response function contributes the most to the overall FTF. Phase analysis of the FTF shows that the transverse velocity response is nearly in phase with the heat-release fluctuations. In addition, density and transverse velocity fluctuations always show constructive interference with pressure fluctuations. The current FTF is also incorporated into a linear modal analysis framework to predict the combustion instabilities in a 2D dump combustor, and the model predictions validated against experiments. Three mean velocity profiles—uniform, parabolic, and turbulent power law—are considered. For the three flames, the first three longitudinal and fundamental transverse unstable modes are predicted.

Experimental study of nonlinear acoustic effects of orifices in duct systems

Researchers focused on reduced emissions hydrocarbon fuel combustion systems have developed new high-efficiency furnace and gas turbine engine technologies that, unfortunately, regularly suffer from detrimental combustion instabilities. Engineering design tools developed to predict these instabilities in combustion systems frequently neglect nonlinear acoustic effects. However, boundaries and duct junctions, e.g., area changes, valves, and orifices, often exhibit nonlinear effects even at low acoustic pressure amplitudes. Experimental data of these nonlinear effects are required to accurately model engine and duct acoustics and to predict combustion instabilities. This experimental investigation focuses on understanding the nonlinear acoustic response of an orifice with and without steady flow. Various orifices were mounted in a multiple-microphone impedance tube and the acoustic impedance of the combination was used to measure the nonlinear acoustic response and impedance of the orifices at amplitudes from 114 to 190 dB and over frequencies from 100 to 1500 Hz. The preliminary results of the experimental study suggest that the impedance is dependent on the acoustic velocity amplitude. This indicates significant nonlinear effects. These experimental data will assist the development of nonlinear acoustic models of orifices in combustion systems.

Application of a three-step approach for prediction of combustion instabilities in industrial gas turbine burners

Abstract Recently, because of environmental regulations, gas turbine manufacturers are restricted to produce machines that work in the lean combustion regime. Gas turbines operating in this regime are prone to combustion-driven acoustic oscillations referred as combustion instabilities. These oscillations could have such high amplitude that they can damage gas turbine hardware. In this study, the three-step approach for combustion instabilities prediction is applied to an industrial test rig. As the first step, the flame transfer function (FTF) of the burner is obtained performing unsteady computational fluid dynamics (CFD) simulations. As the second step, the obtained FTF is approximated with an analytical time-lag-distributed model. The third step is the time-domain simulations using a network model. The obtained results are compared against the experimental data. The obtained results show a good agreement with the experimental ones and the developed approach is able to predict thermoacoustic instabilities in gas turbines combustion chambers.

Numerical prediction of combustion instability limit cycle oscillations for a combustor with a long flame

A coupled numerical approach is investigated for predicting combustion instability limit cycle characteristics when the combustor contains a long flame. The test case is the ORACLES combustor, with a turbulent premixed flame a metre long: it exhibits limit cycle oscillations at ∼ 50 Hz and normalised velocity amplitude ahead of the flame of ∼ 0.29. The approach obtains the flame response to acoustic excitation using Large Eddy Simulations (LES), and couples this with a low-order wave-based network representation for the acoustic waves within the combustor. The flame cannot be treated as acoustically compact; the spatial distribution of both its response and the subsequent effect on the acoustics must be accounted for. The long flame is uniformly segmented axially, each segment being much shorter than the flow wavelengths at play. A series of “local” flame describing functions, one for the heat release rate response within each segment to velocity forcing at a fixed reference location, are extracted from the LES. These use the Computational Fluid Dynamics toolbox, OpenFOAM, with an incompressible approximation for the flow-field and combustion modelled using the Partially Stirred Reactor model with a global one-step reaction mechanism. For coupling with the low-order acoustic network modelling, compact acoustic jump conditions are derived and applied across each flame segment, while between flame segments, wave propagation occurs. Limit cycle predictions from the proposed coupled method agree well with those predicted using the continuous 1-D linearised Euler equations, validating the flame segmentation implementation. Limit cycle predictions (frequency 51.6 Hz and amplitude 0.38) also agree well with experimental measurements, validating the low-order coupled method as a prediction tool for combustors with long flames. A sensitivity analysis shows that the predicted limit cycle amplitude decreases rapidly when acoustic losses at boundaries are accounted for, and increases if combustor heat losses downstream of the flame are accounted for. This motivates more accurate determination of combustor boundary and temperature behaviour for thermoacoustic predictions.

Large eddy simulation of a turbulent swirling premixed flame coupling the TFLES model with a dynamic wrinkling formulation

Dynamic models that take advantage of the known resolved scales to automatically adjust the model parameters have proved to be very effective in large eddy simulations (LES). Global (uniform parameter evolving only with time) and local (parameter evolving both in space and time) dynamic formulations for the flame wrinkling factor are combined with the Thickened Flame (TFLES) model and simulations of the semi-industrial PRECCINSTA burner studied experimentally by Meier et al. (2007) are performed for the stable and unstable configurations. The global formulation predicts a time-dependent model exponent that remains close to 0.5 for the stable flame and oscillates strongly around 0.8 for the pulsating flame. The local formulation adapts the model parameter locally and automatically damps the wrinkling factor in the vicinity of walls, contrary to the global formulation requiring a wall law. The usual non-dynamic approach with an appropriate parameter is found to capture flow statistics of the stable flame with good accuracy, both in terms of Favre and quasi-Reynolds averages. However, the self-excited mode of the pulsating flame is predicted only with the dynamic formalism. The fractal dimension of the unstable flame is found to vary locally and depends on the phase within the period of oscillation. Dynamic models may then play an important role in the prediction of combustion instabilities.

Effects of High-harmonic Components on the Rayleigh Indices in Multi-mode Thermo-acoustic Combustion Instability

This paper presents the characteristics of non-fundamental multi-mode combustion instability and the effects of high-harmonic components on the Rayleigh criterion. Phenomenological observations of multi-harmonic-mode dynamic pressure waves regarding the intensity of harmonic components and the source of wave distortion have been explained by introducing examples of second- and third-order harmonics at various amplitudes. The amplitude and order of the harmonic components distorted the wave shapes, including the peak and the amplitude, of the dynamic pressure and heat release, and consequently the temporal Rayleigh index and its integrals. A cause-and-effect analysis was used to identify the root causes of the phase delay and the amplification of the Rayleigh index. From this analysis, the skewness of the dynamic pressure turned out to be a major source in determining whether multi-mode instability is driving or damping, as well as in optimizing the combustor design, such as the mixing length and the combustor length, to avoid unstable regions. The results can be used to minimize errors in predicting combustion instability in cases of high multi-mode combustion instability. In the future, the amount of research and the number of applications will increase because new fuels, such as fast-burning syngases, are prone to generating multi-mode instabilities.