0

### Research Papers: Gas Turbines: Structures and Dynamics

J. Eng. Gas Turbines Power. 2013;135(9):092501-092501-9. doi:10.1115/1.4024381.

In this paper, Carrera's unified formulation (CUF) is used to perform free-vibrational analyses of rotating structures. The CUF is a hierarchical formulation which offers a procedure to obtain refined structural theories that account for variable kinematic description. These theories are obtained by expanding the unknown displacement variables over the beam section axes by adopting Taylor's polynomials of N-order, in which N is a free parameter. Linear case (N = 1) permits us to obtain classical beam theories while higher order expansions could lead to three-dimensional description of dynamic response of rotors. The finite element method is used to derive the governing equations in weak form. These equations are written in terms of few fundamental nuclei, whose forms do not depend on the approximation used (N). In order to assess the new theory, several analyses are carried out and the results are compared with solutions presented in the literature in graphical and numerical form. Among the considered test cases, a rotor with deformable disk is considered and the results show the convenience of using refined models since that are able to include the in plane deformability of disks.

Commentary by Dr. Valentin Fuster

### Research Papers: Gas Turbines: Aircraft Engine

J. Eng. Gas Turbines Power. 2013;135(9):091201-091201-11. doi:10.1115/1.4024869.

This paper presents an integrated approach, targeting the comprehensive assessment of combined helicopter engine designs within designated operations. The developed methodology comprises a series of individual modeling theories, each applicable to a different aspect of helicopter flight dynamics and performance. These relate to rotor blade modal analysis, three-dimensional flight path definition, flight dynamics trim solution, aeroelasticity, and engine performance. The individual mathematical models are elaborately integrated within a numerical procedure, solving for the total mission fuel consumption. The overall simulation framework is applied to the performance analysis of the Aérospatiale SA330 helicopter within two generic, twin-engine medium helicopter missions. An extensive comparison with flight test data on main rotor trim controls, power requirements, and unsteady blade structural loads is presented. It is shown that, for the typical range of operating conditions encountered by modern twin-engine medium civil helicopters, the effect of operational altitude on fuel consumption is predominantly influenced by the corresponding effects induced on the engine rather than on airframe rotor performance. The implications associated with the implicit coupling between aircraft and engine performance are discussed in the context of mission analysis. The potential to comprehensively evaluate integrated helicopter engine systems within complete three-dimensional operations using modeling fidelity designated for main rotor design applications is demonstrated. The proposed method essentially constitutes an enabler in terms of focusing the rotorcraft design process on designated operation types rather than on specific sets of flight conditions.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 2013;135(9):091202-091202-10. doi:10.1115/1.4024870.

This work investigates the potential to reduce fuel consumption associated with civil rotorcraft operations at mission level, through optimization of the engine design point cycle parameters. An integrated simulation framework, comprising models applicable to rotorcraft flight dynamics, rotor blade aeroelasticity, and gas turbine performance, has been deployed. A comprehensive and computationally efficient optimization strategy, utilizing a novel particle-swarm method, has been structured. The developed methodology has been applied on a twin-engine light and a twin-engine medium rotorcraft configuration. The potential reduction in fuel consumption has been evaluated in the context of designated missions, representative of modern rotorcraft operations. Optimal engine design point cycle parameters, in terms of total mission fuel consumption, have been obtained. Pareto front models have been structured, describing the optimum interrelationship between maximum shaft power and mission fuel consumption. The acquired results suggest that, with respect to technological limitations, mission fuel economy can be improved with the deployment of design specifications leading to increased thermal efficiency, while simultaneously catering for sufficient performance to satisfy airworthiness certification requirements. The developed methodology enables the identification of optimum engine design specifications using a single design criterion; the respective trade-off between fuel economy and payload–range capacity, through maximum contingency shaft power, that the designer is prepared to accept.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 2013;135(9):091203-091203-7. doi:10.1115/1.4024954.

Microgas turbine (MGT) based combined heat and power (CHP) units provide a highly efficient, low-pollutant technology to supply heat and electrical power from fossil and renewable energy sources; however, pressurized MGT systems in an electrical power range from 1 to 5 $kWel$ utilize very small turbocharger components. These components suffer from higher losses, like seal and tip leakages, resulting in a reduced electrical efficiency. This drawback is avoided by an inverted Brayton cycle (IBC) based system. In an IBC hot gas is produced in a combustion chamber at atmospheric pressure. Subsequently, the exhaust gas is expanded in a turbine from an atmospheric to a subatmospheric pressure level. In order to increase electrical efficiency, heat from the turbine exhaust gas is recuperated to the combustion air. After recuperation, the gas is compressed to atmospheric pressure and is discharged from the cycle. To decrease the power demand of the compressor, and thereby increasing the electrical cycle efficiency, it is crucial to further extract residual thermal power from the gas before compression. Coolant flows provided by heating applications can use this heat supply combined with heat from the discharged exhaust gas. The low pressure levels of the IBC result in high volumetric gas flows, enabling the use of large, highly efficient turbocharger components. Because of this efficiency benefit and the described cooling demand, micro-CHP applications provide an ideal field for utilization of the IBC. To further increase the total efficiency, discharged exhaust gas can be partially recirculated to the air inlet of the cycle. In the present paper a steady state analysis of an IBC with exhaust gas recirculation (EGR) is shown, and compared to the performance of a conventional Brayton cycle with equivalent component properties. Using EGR, it could be found that the sensitivity of the electrical cycle efficiency to the coolant temperature further increases. The sequent discussion focuses on the trade-off between total efficiency and electrical efficiency, depending on coolant temperature and EGR rate. The results show that EGR can increase the total efficiency by 10% to 15% points, while electrical efficiency decreases by 0.5% to 1% point. If the coolant temperature is below 35 °C, condensation of water vapor in the exhaust gas leads to a further increase of heat recovery efficiency. A validated in-house simulation tool based on turbocharger maps has been used for the calculations.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 2013;135(9):091204-091204-10. doi:10.1115/1.4024949.

In the past several years, the traditional fourth year “hands-on” requirement for engineering programs in the U.S. is being satisfied by what is now called the capstone senior design project (herein referred to as CSDP). The engineering CSDP program director sends a call to the local industries within the state for solicitation of project proposals that will be worked on by the interdisciplinary engineering student team. Each industrial participant will have to contribute a preset budget defined by the program to the engineering school for each submitted proposal that has been selected by the student team. Honeywell has been an avid participant in the University of Arizona CSDP program for the past several years. Rather than define a simple CSDP that can be fully completed in the first attempt, the author has sought the value of teaching iterative design to the student team by defining a multiyear CSDP scope, in that after the first year, each successive team learns from the past design and implements its own improvement to the design it inherits. This paper gives an overview of Honeywell's CSDP titled “Measuring Heat Transfer in Annular Flow Between Co-Rotating or Counter-Rotating Cylinders.” Now in its fourth iteration, each wave of student team has been able to understand the complexity of the design, the challenge of testing for structural integrity, the controllability of implementing a balanced system of heat gain and loss to reach steady state operation, the evolution of starting with slip ring temperature measurements and ending at wireless telemetry, DOE testing to rank influencing variables, and heat transfer correlation of the data relating Nusselt versus Reynolds number. Beginning with the first year CSDP team, this paper covers the design approach selected by that team, its results, and the lessons learned as a result of failure in meeting the full requirements, which is then taken on by the next group of students the following year.

Commentary by Dr. Valentin Fuster

### Research Papers: Gas Turbines: Combustion, Fuels, and Emissions

J. Eng. Gas Turbines Power. 2013;135(9):091501-091501-5. doi:10.1115/1.4024798.

The laminar burning velocity of liquefied petroleum gas (LPG) air mixtures at high temperatures is extracted from the planar flames stabilized in the preheated mesoscale diverging channel. The experiments were carried out for a range of equivalence ratios and mixture temperatures. Computational predictions of the burning velocity and detailed flame structure were performed using the PREMIX code with USC mech 2.0. The present data are in very good agreement with both the recent experimental and computational results available. A peak burning velocity was observed for slightly rich mixtures, even at higher mixture temperatures. The minimum value of th temperature exponent is observed for slightly rich mixtures.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 2013;135(9):091502-091502-7. doi:10.1115/1.4024380.

The soot/nitric oxides (NOx) trade-off of diesel, biodiesel, and biodiesel–ethanol in a moderate exhaust gas recirculation (EGR) premixed low temperature combustion (LTC) mode is investigated in this study. Compared to diesel, biodiesel demonstrates poorer spray behavior and shorter ignition delay, but its oxygen content results in less soot. Blending ethanol into biodiesel enhances spray behavior, prolongs ignition delay, and further increases fuel oxygen fraction, resulting in a larger reduction in soot. In the moderate EGR premixed low temperature combustion mode, an obvious soot/NOx trade-off is demonstrated with diesel fuel. The soot/NOx trade-off is improved by biodiesel fuel and defeated by the biodiesel–ethanol blend. Low soot, low NOx, and high combustion efficiency are achieved with the biodiesel–ethanol blend and proper EGR rate.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 2013;135(9):091503-091503-10. doi:10.1115/1.4024868.

Large-eddy simulation (LES) is applied to turbulent spray combustion fields in a subscale (1/2) aircraft jet engine combustor with an air-blast type swirl fuel nozzle and validity is examined by comparing with measurements. In the LES, Jet-A is used as liquid fuel, and individual droplet motion is tracked in a Lagrangian manner with a parcel model. As a turbulent combustion model, the extended flamelet/progress-variable approach, in which heat transfer between droplets and ambient gas including radiation and heat loss from walls can be taken into account, is employed. A detailed chemistry mechanism of Jet-A with 1537 reactions and 274 chemical species is used. The radiative heat transfer is computed by the discrete ordinate (DO) method. The equivalence ratio ranges from 0.91 to 1.29. The comparisons of the predicted droplet velocity and size, gaseous temperature, NO, and soot emissions with the measurements show that the present LES is capable of capturing the general features of the turbulent spray combustion fields in the subscale (1/2) aircraft jet engine combustor.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 2013;135(9):091504-091504-9. doi:10.1115/1.4024757.

A thermodynamics-based computationally efficient mean value engine model that computes ignition delay, combustion phases, exhaust temperature, and indicated mean effective pressure has been developed for the use of control strategy development. The model is derived from the thermodynamic principles of ideal gas standard limited pressure cycle. In order to improve the fidelity of the model, assumptions that are typically used to idealize the cycle are modified or replaced with ones that more realistically replicate the physical process such as exhaust valve timing, in-cylinder heat transfer, and the combustion characteristics that change under varying engine operating conditions. The model is calibrated and validated with the test data from a Ford 6.7 liter diesel engine. The mean value model developed in this study is a flexible simulation tool that provides excellent computational efficiency without sacrificing critical details of the underlying physics of the diesel combustion process.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 2013;135(9):091505-091505-10. doi:10.1115/1.4024589.

This paper presents a detailed exergy analysis of homogeneous charge compression ignition (HCCI) engines, including a crank-angle resolved breakdown of mixture exergy and exergy destruction. Exergy analysis is applied to a multizone HCCI simulation including detailed chemical kinetics. The HCCI simulation is validated against engine experiments for ethanol-fueled operation. The exergy analysis quantifies the relative importance of different loss mechanisms within HCCI engines over a range of engine operating conditions. Specifically, four loss mechanisms are studied for their relative impact on exergy losses, including (1) the irreversible combustion process (16.4%–21.5%), (2) physical exergy lost to exhaust gases (12.0%–18.7%), (3) heat losses (3.9%–17.1%), and (4) chemical exergy lost to incomplete combustion (4.7%–37.8%). The trends in each loss mechanism are studied in relation to changes in intake pressure, equivalence ratio, and engine speed as these parameters are directly used to vary engine power output. This exergy analysis methodology is proposed as a tool to inform research and design processes, particularly by identifying the relative importance of each loss mechanism in determining engine operating efficiency.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 2013;135(9):091506-091506-8. doi:10.1115/1.4024421.

Lean NOx trap (LNT) catalytic aftertreatment devices are one potential option for the reduction of oxides of nitrogen (NOx) in the exhaust of compression ignition engines. They work through a controlled modulation between a storage phase that captures NOx over an alkali earth metal and a regeneration phase that reduces the stored nitrates on the surface using a rich pulse of injected fuel or via stoichiometric engine operation. This rich phase has an associated fuel penalty while being relatively difficult to control through temperature and chemical species. In order to improve system efficiency, a number of researchers have proposed dual leg LNT systems using two LNTs, one of which is always storing while the other is undergoing regeneration. The majority of the exhaust flows through the storage LNT while only a small fraction (low space velocity) advects across the regeneration LNT. This increases the regeneration residence time, improving effectiveness and decreasing the amount of fuel used. From an LNT simulation standpoint, most researchers utilize the classical one-dimensional (1D) aftertreatment model constructed from the Euler equations of motion that neglect axial conduction and diffusion. This paper explores the applicability of this model under low flow situations prevalent in a dual leg LNT system through a carbon monoxide light-off experiment. The authors chose this type of experiment in order to focus purely on fluid mechanics and not the choice of LNT reaction mechanism. The results suggest that a Navier–Stokes (N–S) version of the 1D aftertreatment model is preferred for the regeneration leg of a dual LNT system. Moreover, the authors provide the solution of such a model within this paper.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 2013;135(9):091507-091507-9. doi:10.1115/1.4024951.

Bluff body stabilized nonpremixed flames are usually used as pilot flames in lean-premixed combustors. Experiments are conducted to investigate the characteristics of the flame. Typical flame modes are investigated in both stable and unstable conditions. The flow structures, the reaction zone, and the dynamics of unstable flames are measured with particle image velocimetry (PIV), intensified charge-coupled device (ICCD) and a high-speed camera, respectively, based on which the inherent mechanisms that influence the configuration and stabilization of the flame are analyzed. Stable flames are apparently influenced by the mixing characteristics in the recirculation zone. Flame detachment, a typical phenomenon of stable flames in a turbulent air flow, can be explained by the distribution of fuel concentration in the recirculation zone. The Reynolds number of air has different effects on different parts of the flame, which results in three unstable flame modes at different Reynolds numbers of air. These results could be helpful for the design of stable burners in practice.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 2013;135(9):091508-091508-9. doi:10.1115/1.4024940.

The response of a perfectly premixed, turbulent jet flame at elevated inflow temperature to high frequency flow perturbations is investigated. A generic reheat burner geometry is considered, where the spatial distribution of heat release is controlled by autoignition in the jet core on the one hand, and kinematic balance between flow and flame propagation in the shear layers between the jet and the external recirculation zones on the other. To model autoignition and heat release in compressible turbulent flow, a progress variable/stochastic fields formulation adapted for the LES context is used. Flow field perturbations corresponding to transverse acoustic modes are imposed by harmonic excitation of velocity at the combustor boundaries. Simulations with single-frequency excitation are carried out in order to study the flame response to transverse fluctuations of velocity. Heat release fluctuations are observed predominantly in the shear layers, where flame propagation is important. The flow-flame coupling in these regions is analyzed in detail with a filter-based postprocessing approach, invoking a local Rayleigh index and providing insight into the interactions of flame wrinkling by vorticity and convection due to mean and fluctuating velocity.

Commentary by Dr. Valentin Fuster

### Research Papers: Gas Turbines: Cycle Innovations

J. Eng. Gas Turbines Power. 2013;135(9):091701-091701-10. doi:10.1115/1.4024419.

Data reconciliation is widely used in the chemical process industry to suppress the influence of random errors in process data and help detect gross errors. Data reconciliation is currently seeing increased use in the power industry. Here, we use data from a recently constructed cogeneration system to show the data reconciliation process and the difficulties associated with gross error detection and suspect measurement identification. Problems in gross error detection and suspect measurement identification are often traced to weak variable redundancy, which can be characterized by variable adjustability and threshold value. Proper suspect measurement identification is accomplished using a variable measurement test coupled with the variable adjustability. Cogeneration and power systems provide a unique opportunity to include performance equations in the problem formulation. Gross error detection and suspect measurement identification can be significantly enhanced by increasing variable redundancy through the use of performance equations. Cogeneration system models are nonlinear, but a detailed analysis of gross error detection and suspect measurement identification is based on model linearization. A Monte Carlo study was used to verify results from the linearized models.

Commentary by Dr. Valentin Fuster

### Research Papers: Gas Turbines: Turbomachinery

J. Eng. Gas Turbines Power. 2013;135(9):092601-092601-7. doi:10.1115/1.4024735.

During recent decades, artificial intelligence has been employed as a powerful tool for identification of complex industrial systems with nonlinear dynamics, such as gas turbines (GT). In this study, a methodology based on artificial neural network (ANN) techniques was developed for offline system identification of a low-power gas turbine. The processed data was obtained from a SIMULINK model of a gas turbine in matlab environment. A comprehensive computer program code was generated and run in matlab for creating and training different ANN models with feed-forward multilayer perceptron (MLP) structure. The code consisted of various training functions, different number of neurons as well as a variety of transfer (activation) functions for hidden and output layers of the network. It was shown that the optimal model for a two-layer network with MLP structure consisted of 20 neurons in its hidden layer and used trainlm as its training function, as well as tansig and logsid as its transfer functions for the hidden and output layers. It was also observed that trainlm has a superior performance in terms of minimum mean squared error (MSE) compared with each of the other training functions. The resulting model could predict performance of the system with high accuracy. The methodology provides a comprehensive view of the performance of over 18,720 ANN models for system identification of the single-shaft gas turbine. One can use the optimal ANN model from this study when training from real data obtained from this type of GT. This is particularly useful when real data is only available over a limited operational range.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 2013;135(9):092602-092602-7. doi:10.1115/1.4024953.

A combustion instability in a combustor typical of aero-engines is analyzed and modeled thanks to a low order Helmholtz solver. A dynamic mode decomposition (DMD) is first applied to the large eddy simulation (LES) database. The mode with the highest amplitude shares the same frequency of oscillation as the experiment (approximately 350 Hz) and it shows the presence of large entropy spots generated within the combustion chamber and convected down to the exit nozzle. With the lowest purely acoustic mode being in the range 650–700 Hz, it is postulated that the instability observed around 350 Hz stems from a mixed entropy/acoustic mode where the acoustic generation associated with the entropy spots being convected throughout the choked nozzle plays a key role. A delayed entropy coupled boundary condition is then derived in order to account for this interaction in the framework of a Helmholtz solver where the baseline flow is assumed to be at rest. When fed with the appropriate transfer functions to model the entropy generation and convection from the flame to the exit, the Helmholtz solver proves able to predict the presence of an unstable mode around $350$ Hz, which is in agreement with both the LES and the experiments. This finding supports the idea that the instability observed in the combustor is indeed driven by the entropy/acoustic coupling.

Commentary by Dr. Valentin Fuster

### Research Papers: Gas Turbines: Coal, Biomass, and Alternative Fuels

J. Eng. Gas Turbines Power. 2013;135(9):091401-091401-13. doi:10.1115/1.4024948.

Many proposed clean coal technologies for power generation couple a gasification process with a gas turbine combined cycle unit. In the gasifier, the coal is converted into a syngas which is then cleaned and fired before entering the turbine. A problem is that coal-derived syngases may contain alkali metal impurities that combine with the sulfur and chlorine from the coal to form salts that deposit on the turbine blades, causing corrosion. This paper describes a new model, applicable to most types of coal, for predicting the dewpoint temperatures and deposition rates of these sodium and potassium salts. When chlorine is present the main alkali species in the mainstream gas flow are the chlorides; but when chlorine is absent, the superoxides dominate. However, because the high-pressure turbine blades are film-cooled, they are at much lower temperatures than the mainstream gas flow and analysis then shows that the deposit is composed almost entirely of the sulfates in either liquid or solid form. This is true whether or not chlorine is present. Detailed calculations using the new model to predict the alkali salt deposition rates on three stages of an example utility turbine are presented. The calculations show how the dewpoint temperatures and deposition rates vary with the gas-phase chlorine and sulfur levels as well as with the concentrations of sodium and potassium. It is shown that the locations where corrosion is to be expected vary considerably with the type of coal and the levels of impurities present.

Commentary by Dr. Valentin Fuster

### Research Papers: Gas Turbines: Controls, Diagnostics, and Instrumentation

J. Eng. Gas Turbines Power. 2013;135(9):091601-091601-6. doi:10.1115/1.4024420.

A new nickel based thermocouple for high temperature applications in gas turbines has been devised at the Department of Material Science and Metallurgy of the University of Cambridge. This paper describes the new features of the thermocouple, the drift tests on the first prototype, and compares the behavior of the new sensor with conventional mineral insulated metal sheathed Type K thermocouples: the new thermocouple has a significant improvement in terms of drift and temperature capabilities. Metallurgical analysis has been undertaken on selected sections of the thermocouples exposed at high temperatures, which rationalizes the reduced drift of the new sensor. A second prototype will be tested in subsequent research, from which further improvements in drift and temperature capabilities are expected.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 2013;135(9):091602-091602-6. doi:10.1115/1.4024950.

The effects of tip shape on Reynolds number sensitivity of a seven hole pressure probe are studied over a range of flows associated with practical use of turbomachinery. It is shown that at low flow angles the response of a conical or hemispherical tipped probe is independent of a Reynolds number above Re = 3000, and at high flow angles Re = 6000. Despite there not being a discernible difference in the average error in flow properties at different Reynolds numbers between the two tip shapes, it is shown that the hemispherical tip is preferred because the pressure distributions around the tip are more consistent.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 2013;135(9):091603-091603-10. doi:10.1115/1.4024952.

In this paper, a prognostic methodology is applied to gas turbine field data to assess its capability as a predictive tool for degradation effects. On the basis of the recordings of past behavior, the methodology provides a prediction of future performance, i.e., the probability that degradation effects are at an acceptable level in future operations. The analyses carried out in this paper consider two different parameters (power output and compressor efficiency) of three different Alstom gas turbine power plants (gas turbine type GT13E2, GT24, and GT26). To apply the prognostic methodology, site specific degradation threshold values were defined, to identify the time periods with acceptable degradation (i.e., higher-than-threshold operation) and the time periods where maintenance activities are recommended (i.e., lower-than-threshold operation). This paper compares the actual distribution of the time points until the degradation limit is reached (discrete by nature) to the continuously varying distribution of the time points simulated by the probability density functions obtained through the prognostic methodology. Moreover, the reliability of the methodology prediction is assessed for all the available field data of the three gas turbines and for two values of the threshold. For this analysis, the prognostic methodology is applied by considering different numbers of degradation periods for methodology calibration and the accuracy of the next forecasted trends is compared to the real data. Finally, this paper compares the prognostic methodology prediction to a “purely deterministic” prediction chosen to be the average of the past time points of higher-than-threshold operations. The results show that, in almost all cases, the prognostic methodology allows a better prediction than the “purely deterministic” approach for both power and compressor efficiency degradation. Therefore, the prognostic methodology seems to be a robust and reliable tool to predict gas turbine power plant “probabilistic” degradation.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 2013;135(9):091604-091604-9. doi:10.1115/1.4024957.

In this paper, we develop a linear technique that predicts how the stability of a thermoacoustic system changes due to the action of a generic passive feedback device or a generic change in the base state. From this, one can calculate the passive device or base state change that most stabilizes the system. This theoretical framework, based on adjoint equations, is applied to two types of Rijke tube. The first contains an electrically heated hot wire, and the second contains a diffusion flame. Both heat sources are assumed to be compact, so that the acoustic and heat release models can be decoupled. We find that the most effective passive control device is an adiabatic mesh placed at the downstream end of the Rijke tube. We also investigate the effects of a second hot wire and a local variation of the cross-sectional area but find that both affect the frequency more than the growth rate. This application of adjoint sensitivity analysis opens up new possibilities for the passive control of thermoacoustic oscillations. For example, the influence of base state changes can be combined with other constraints, such as that the total heat release rate remains constant, in order to show how an unstable thermoacoustic system should be changed in order to make it stable.

Commentary by Dr. Valentin Fuster