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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Large eddy simulation of a pressurized reactive fluid–particle system: single-particle dynamics analysis

Pressurized oxy-combustion (POC) is a promising candidate to reduce carbon emissions in power generation. Designing an effective burner plays a vital role in developing new combustion technologies. Because of the high pressure, the volume fraction of particles in a pressurized oxy-combustor could be higher than that in the conventional combustor, therefore, the particle dynamics in the pressurized vessel need to be evaluated accordingly. The present computational work is to predict the influence of the particle size and particle injection location on the particle trajectory. The Stokes number based on turbulence fluctuation, St, is adopted to evaluate the impact of the gas phase on the particulate phase. A large eddy simulation (LES) with the environment pressure of 15 bar and the thermal input of the fuel particle of 100 kWth has been performed by means of the commercial CFD package. It is shown that that in this pressurized environment St << 1 for the 25 µm particles, St ~ 1 for the 100 µm particles, while for the particles exceeding 200 µm St >> 1. The trajectories of the sampling particles from the LES results support this conclusion: the particles less than 100 µm tend to be uniformly distributed in the space while the particles exceeding 200 µm tend to concentrate in the combustor.

Li, Lei↗
DOE OSTI2021

Dynamics of Product Branching from Radical Intermediates in Elementary Combustion Reactions (Final Technical Report)

While the total rate constant for many elementary reactions is well-characterized, understanding the product branching in complex reactions presents a formidable challenge. To gain an incisive probe of such reactions, our experiments investigate the dynamics of the product channels that arise from transient radical intermediates along the bimolecular reaction coordinates. Our recent published work uses the methodology developed in my group in the last fifteen years, using both imaging and scattering apparatuses. The experiments generate a particular isomeric form of an unstable radical intermediate along a bimolecular reaction coordinate and study the branching between the ensuing product channels of the energized radical as a function of its internal rotational and vibrational energy under collision-less conditions. The experiments use a combination of: 1) measurement of product velocity and angular distributions in a crossed laser-molecular beam apparatus, with electron bombardment detection in my lab in Chicago or 2) with tunable vacuum ultraviolet photoionization detection at Taiwan's National Synchrotron Radiation Research Center (NSRRC), and 3) velocity map imaging using state-selective REMPI and single photon VUV ionization of radical intermediates and reaction products. We also employ tunable VUV photoionization detection in our imaging apparatus, using difference frequency four-wave mixing to produce photoionization light tunable from 8 to 10.8 eV. This year of support funded our work to photolytically generate the radical intermediate important in the OH + propene reaction when OH adds to an end carbon. Our other major result this past year was on the photoionization detection of vinoxy radicals. Our experiments at the NSRRC definitively show that vinoxy dissociatively ionizes to both CH 3 + and HCO + , and establishes the absolute partial photoionization cross section of vinoxy to CH 3 + at 10.5 and 11.44 eV. This should allow experimentalists detecting vinoxy radicals produced in bimolecular reactions such as OH + propene to get good branching fractions to that product channel. Finally we initiated studies of the photodissociation of 1-bromo-2-chloroethane and 1,1-bromochloroethane at 193 nm at the NSRRC.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1995

Excitable dynamics in high-Lewis number premixed gas combustion at normal and microgravity

Freely-propagating, premixed gas flames in high-Lewis (Le) number, quiescent mixtures are studied experimentally in tubes of various diameter at normal (lg) and microgravity (mu g). A premixture of lean butane and oxygen diluted with helium, argon, neon, nitrogen or a mixture of multiple diluents is examined such that the thermal diffusivity of the mixture (and to a lesser extent, the mass diffusivity of the rate-limiting component) is systematically varied. In effect, different diluents allow variation of the Le without changing the chemistry. The flames are recorded with high speed cinematography and their stability is visually assessed. Different modes of propagation were observed depending on the diameter of the tubes (different conductive heat loss), the composition of the mixture and the g-level. At 1g, four modes of propagation were observed in small and intermediate diameter tubes (large conductive heat loss): (1) steadily propagating flames, (2) radial and longitudinal pulsating flames, (3) 'wavering' flames, and (4) rotating spiral flames. As the diameter of the tube increases, the radial modes become more pronounced while the longitudinal modes systematically disappear. Also, multiple, simultaneous, spatially-separated 'pacemaker' sites are observed in intermediate and large diameter tubes. Each site starts as a small region of high luminosity and develops into a flamelet which assumes the form of one of the fore mentioned modes. These flamelets eventually interact, annihilate each other in their regions of intersection and merge at their newly created free-ends. For very large tubes, radially-propagating wave-trains (believed to be 'trigger waves') are observed. These are analogous to the radial pulsations observed in the smaller diameter tubes. At mu g, three modes of propagation have been observed: (1) steadily propagating flames, (2) radial and longitudinal pulsating flames, and (3) multi-armed, rotating flames. Since the pulsating mode exists at mu g and 1g, buoyant flicker is not the mechanism which drives the pulsations. Moreover, all of the instabilities at 1g and mu g have characteristic frequencies on the O(100Hz). This value is lower than the fundamental, longitudinal acoustic frequencies of the tubes which suggests that the instabilities are not acoustically driven. The patterns formed by this reaction bear remarkable similarities with the patterns formed in most excitable media when the behavior of the system is driven by couplings between chemical reaction and diffusion (e.g., Belousov-Zhabotinsky reaction, Patterns in slime molds, spiral waves in the retina of a bird's eye). While it is recognized that the chemical mechanism associated with this premixed gas reaction is exponentially sensitive to temperature and undoubtedly different from those which govern previously observed excitable media (most are isothermal, or weakly exothermic, liquid phase reactions), similar spatial and temporal patterns should not come as a complete surprise considering heat and mass diffusion are self similar. It is concluded that this premixed gas system is a definitive example of a diffusive-thermal, gas-phase oscillator based on these experimental results and their favorable comparison with theory.

Pearlman, Howard↗
NASA NTRS1995

Computing Instability In Combustion Of Liquid Propellants

Computational fluid dynamics (CFD) code developed for use in design analyses of flow instabilities associated with combustion of sprayed liquid propellants in rocket engines. Code also contributes to design of improved commercial sprayed-fuel combustors in furnaces and jet engines. Proves robust, user-friendly software tool with comprehensive analysis capability. Enables characterization of stability or instability of engine in terms of such physically meaningful parameters as initial conditions of spray, spatial distribution of ratio between concentrations of fuel and oxidizer at injector faces, geometry of combustor, and configurations of baffles.

Chen, Yen-Sen↗
NASA NTRS1993

Laser diagnostics for microgravity droplet studies

Rapid advances have recently been made in numerical simulation of droplet combustion under microgravity conditions, while experimental capabilities remain relatively primitive. Calculations can now provide detailed information on mass and energy transport, complex gas-phase chemistry, multi-component molecular diffusion, surface evaporation and heterogeneous reaction, which provides a clearer picture of both quasi-steady as well as dynamic behavior of droplet combustion. Experiments concerning these phenomena typically result in pictures of the burning droplets, and the data therefrom describe droplet surface regression along with flame and soot shell position. With much more precise, detailed, experimental diagnostics, significant gains could be made on the dynamics and flame structural changes which occur during droplet combustion. Since microgravity experiments become increasingly more expensive as they progress from drop towers and flights to spaceborne experiments, there is a great need to maximize the information content from these experiments. Sophisticated measurements using laser diagnostics on individual droplets and combustion phenomena are now possible. These include measuring flow patterns and temperature fields within droplets, vaporization rates and vaporization enhancement, radical species profiling in flames and gas-phase flow-tagging velocimetry. Although these measurements are sophisticated, they have undergone maturation to the degree where with some development, they are applicable to studies of microgravity droplet combustion. This program beginning in September of 1992, will include a series of measurements in the NASA Learjet, KC-135 and Drop Tower facilities for investigating the range of applicability of these diagnostics while generating and providing fundamental data to ongoing NASA research programs in this area. This program is being conducted in collaboration with other microgravity investigators and is aimed toward supplementing their experimental efforts.

Winter, Michael↗
DOE OSTI2020

Inertial dynamics of an interface with interfacial mass flux: Stability and flow fields’ structure, inertial stabilization mechanism, degeneracy of Landau’s solution, effect of energy fluctuations, and chemistry-induced instabilities

This work focuses on the long-standing problem of inertial dynamics of an interface with interfacial mass flux and reports new mechanisms for the interface stabilization and destabilization. The interface is a phase boundary separating fluids of different densities and having interfacial mass flux. To analyze the interface dynamics from a far field, we develop and apply the general matrix method to rigorously solve the boundary value problem involving the governing equations in the fluid bulk and the boundary conditions at the interface and at the outside boundaries of the domain. We find the fundamental solutions for the linearized system of equations and analyze the interplay of interface stability with flow fields’ structure by directly linking rigorous mathematical attributes to physical observables. We find that the interface is stable when the dynamics conserves the fluxes of mass, momentum, and energy; the stabilization is due to an inertial mechanism causing small oscillations of the interface velocity. In the classic Landau’s dynamics, the postulate of perfect constancy of the interface velocity leads to the development of Landau–Darrieus instability. This destabilization is also linked to the imbalance of the perturbed energy at the interface. The classic Landau’s solution is found to have degeneracy; lifting of the degeneracy may lead to singularity and self-similar dynamics. Our results compare well with traditional theories of combustion and propose new experiments to study the dynamics of the interface and the flow fields in combustible systems. We further conduct reactive molecular dynamics simulations to elucidate the complexity of chemical processes, to study the destabilizing effect of energy fluctuations on the interface stability, and to illustrate the chemistry-induced instabilities. In summary, we identify the extreme sensitivity of the interface dynamics to the interfacial boundary conditions, including the formal properties of fundamental solutions and the qualitative and quantitative properties of the flow fields. This provides new opportunities for studies, diagnostics, and control of multiphase flows in a broad range of processes in nature and technology.

42 ENGINEERING↗
DOE OSTI2020

A phenomenological rate of injection model for predicting fuel injection with application to mixture formation in light-duty diesel engines

Fuel injection rate laws are one of the most important pieces of information needed when modeling engine combustion with computational fluid dynamics. In this study, a simple phenomenological model of a common-rail injector was developed and calibrated for the Bosch CRI2.2 platform. The model requires three tunable parameter fits, making it relatively easy to calibrate and suitable for injector modeling when high-fidelity information about the internal injector’s geometry and electrical circuit details are not available. Each injection pulse is modeled as a sequence of up to four stages: an injection needle mechanical opening transient, a full-lift viscous flow inertial transient, a Bernoulli steady-state stage, and a needle descent transient. Parameters for each stage are obtained as polynomial fits from measured injection rate properties. The model enforces total injected mass, and the intermediate stages are only introduced if the injection pulse duration is long enough. Experimental rates of injection from two separate campaigns on the same injector were used to calibrate the model. The model was first validated against measured injection rate laws featuring pilot injections, short partially premixed combustion pulses, and conventional diesel combustion injection strategies. Then, it was employed as an input to engine computational fluid dynamics simulations, which were run to simulate experiments of mixture formation in an optically accessible light-duty diesel engine. It was found that, though simple, this model is capable of predicting both pilot and main injection pulse mass flow rates well: the simulations yielded accurate predictions of in-cylinder equivalence ratio distributions from injection strategies for both partially premixed combustion and pilot injections. Also, once calibrated, the model produced appropriate results for a wide range of injected mass and rail pressure values. Finally, it was observed that usage of such a relatively simple model can be a good choice when high-fidelity injection rate input and highly detailed information of the injector’s geometry and operation are not available, particularly as noticeable discrepancies can be present also among different experimental campaigns on similar hardware.

42 ENGINEERING↗
NASA NTRS1992

Multi-phase simulations of coaxial injector combustion

A multiphase computational fluid dynamics code (ARICC-3D) is presented and results of two simulations are discussed. The numerical framework of the CFD code is reviewed as well as some of the two-phase physical submodels. The simulations performed include a single coaxial element injector and a multielement injector using LOX/Hydrogen reactants. The single element injector simulation verified the interaction among the code's submodels. The multielement injector simulation transient results include the chamber response to a transverse pressure wave with and without a chamber baffle. The results of these simulations demonstrate the current capabilities and their limitations to model complex two-phase combustion phenomena. Possible ways to exceed these limitations are suggested.

Liang, P. Y.↗
NASA NTRS2014

Mean Flow Augmented Acoustics in Rocket Systems

Oscillatory motion in solid rocket motors and liquid engines has long been a subject of concern. Many rockets display violent fluctuations in pressure, velocity, and temperature originating from the complex interactions between the combustion process and gas dynamics. The customary approach to modeling acoustic waves inside a rocket chamber is to apply the classical inhomogeneous wave equation to the combustion gas. The assumption of a linear, non-dissipative wave in a quiescent fluid remains valid while the acoustic amplitudes are small and local gas velocities stay below Mach 0.2. The converging section of a rocket nozzle, where gradients in pressure, density, and velocity become large, is a notable region where this approach is not applicable. The expulsion of unsteady energy through the nozzle of a rocket is identified as the predominate source of acoustic damping for most rocket systems. An accurate model of the acoustic behavior within this region where acoustic modes are influenced by the presence of a steady mean flow is required for reliable stability predictions. Recently, an approach to address nozzle damping with mean flow effects was implemented by French [1]. This new approach extends the work originated by Sigman and Zinn [2] by solving the acoustic velocity potential equation (AVPE) formulated by perturbing the Euler equations [3]. The acoustic velocity potential (psi) describing the acoustic wave motion in the presence of an inhomogeneous steady high-speed flow is defined by, (del squared)(psi) − (lambda/c)(exp 2)(psi) − M(dot)[M(dot)(del)(del(psi))] − 2(lambda(M/c) + (M(dot)del(M))(dot)del(psi)−2(lambda)(psi)[M(dot)del(1/c)]=0 (1) with M as the Mach vector, c as the speed of sound, and lambda as the complex eigenvalue. French apply the finite volume method to solve the steady flow field within the combustion chamber and nozzle with inviscid walls. The complex eigenvalues and eigenvector are determined with the use of the ARPACK eigensolver. The present study employs the COMSOL Multphysics framework to solve the coupled eigenvalue problem using the finite element approach. The study requires one way coupling of the CFD High Mach Number Flow (HMNF) and mathematics module. The HMNF module evaluated the gas flow inside of a solid rocket motor using St. Robert's law modeling solid propellant burn rate, slip boundary conditions, and the supersonic outflow condition. Results from the HMNF model are used by the coefficient form of the mathematics module to determine the eigenvalues of the AVPE. The mathematics model is truncated at the nozzle sonic line, where a zero flux boundary condition is self-satisfying. The remaining boundaries are modeled with a zero flux boundary condition, assuming zero acoustic absorption on all surfaces. Pertinent results from these analyses are the complex valued eigenvalue and eigenvectors. Comparisons are made to the French results to evaluate the modeling approach. A comparison of the French results with that of the present analysis is displayed in figures 1 and 2, respectively. The graphic shows the first tangential eigenvector's real (a) and imaginary (b) values.

Fischbach, Sean R.↗
NASA NTRS2003

A Design Methodology for Rapid Implementation of Active Control Systems Across Lean Direct Injection Combustor Platforms

The VACCG team is comprised of engineers at Virginia Tech who specialize in the subject areas of combustion physics, chemical kinetics, dynamics and controls, and signal processing. Currently, the team's work on this NRA research grant is designed to determine key factors that influence combustion control performance through a blend of theoretical and experimental investigations targeting design and demonstration of active control for three different combustors. To validiate the accuracy of conclusions about control effectiveness, a sequence of experimental verifications on increasingly complex lean, direct injection combustors is underway. During the work period January 1, 2002 through October 15, 2002, work has focused on two different laboratory-scale combustors that allow access for a wide variety of measurements. As the grant work proceeds, one key goal will be to obtain certain knowledge about a particular combustor process using a minimum of sophisticated measurements, due to the practical limitations of measurements on full-scale combustors. In the second year, results obtained in the first year will be validated on test combustors to be identified in the first quarter of that year. In the third year, it is proposed to validate the results at more realistic pressure and power levels by utilizing the facilities at the Glenn Research Center.

Baumann, William T.↗
NASA NTRS2000

Computational Analysis of the Combustion Processes in an Axisymmetric, RBCC Flowpath

Computational fluid dynamic simulations have been used to study the combustion processes within an axisymmetric, RBCC flowpath. Two distinct operating modes have been analyzed to date, including the independent ramjet stream (IRS) cycle and the supersonic combustion ramjet (scramjet) cycle. The IRS cycle investigation examined the influence of fuel-air ratio, fuel distribution, and rocket chamber pressure upon the combustion physics and thermal choke characteristics. Results indicate that adjustment of the amount and radial distribution of fuel can control the thermal choke point The secondary mass flow rate was very sensitive to the fuel-air ratio and the rocket chamber pressure. The scramjet investigation examined the influence of fuel-air ratio and fuel injection schedule upon combustion performance estimates An analysis of the mesh-dependence of these calculations was presented. Jet penetration data was extracted from the three-dimensional simulations and compared favorably with experimental correlations of similar flows. Results indicate that combustion efficiency was very sensitive to the fuel schedule.

Steffen, Christopher J., Jr.↗
NASA NTRS2001

Computational Analysis of the Combustion Processes in an Axisymmetric, RBCC Flowpath

Computational fluid dynamic simulations have been used to study the combustion processes within an axisymmetric, RBCC flowpath. Two distinct operating modes have been analyzed to date, including the independent ramjet stream (IRS) cycle and the supersonic combustion ramjet (scramJet) cycle. The IRS cycle investigation examined the influence of fuel-air ratio, fuel distribution, and rocket chamber pressure upon the combustion physics and thermal choke characteristics. Results indicate that adjustment of the amount and radial distribution of fuel can control the thermal choke point. The secondary massflow rate was very sensitive to the fuel-air ratio and the rocket chamber pressure. The scramjet investigation examined the influence of fuel-air ratio and fuel injection schedule upon combustion performance estimates. An analysis of the mesh-dependence of these calculations was presented. Jet penetration data was extracted from the three-dimensional simulations and compared favorably with experimental correlations of similar flows. Results indicate that combustion efficiency was very sensitive to the fuel schedule.

Steffen, Christopher J., Jr.↗
NASA NTRS2015

Advanced Booster Liquid Engine Combustion Stability

Combustion instability is a phenomenon in liquid rocket engines caused by complex coupling between the time-varying combustion processes and the fluid dynamics in the combustor. Consequences of the large pressure oscillations associated with combustion instability often cause significant hardware damage and can be catastrophic. The current combustion stability assessment tools are limited by the level of empiricism in many inputs and embedded models. This limited predictive capability creates significant uncertainty in stability assessments. This large uncertainty then increases hardware development costs due to heavy reliance on expensive and time-consuming testing.

Tucker, Kevin↗
NASA NTRS1997

Effects of Buoyancy on Laminar and Turbulent Premixed V-Flame

Turbulent combustion occurs naturally in almost all combustion systems and involves complex dynamic coupling of chemical and fluid mechanical processes. It is considered as one of the most challenging combustion research problems today. Though buoyancy has little effect on power generating systems operating under high pressures (e.g., IC engines and turbines), flames in atmospheric burners and the operation of small to medium furnaces and boilers are profoundly affected by buoyancy. Changes in burner orientation impacts on their blow-off, flash-back and extinction limits, and their range of operation, burning rate, heat transfer, and emissions. Theoretically, buoyancy is often neglected in turbulent combustion models. Yet the modeling results are routinely compared with experiments of open laboratory flames that are obviously affected by buoyancy. This inconsistency is an obstacle to reconciling experiments and theories. Consequently, a fundamental understanding of the coupling between turbulent flames and buoyancy is significant to both turbulent combustion science and applications. The overall effect of buoyancy relates to the dynamic interaction between the flame and its surrounding, i.e., the so-called elliptical problem. The overall flame shape, its flowfield, stability, and mean and local burning rates are dictated by both upstream and downstream boundary conditions. In steady propagating premixed flames, buoyancy affects the products region downstream of the flame zone. These effects are manifested upstream through the mean and fluctuating pressure fields to influence flame stretch and flame wrinkling. Intuitively, the effects buoyancy should diminish with increasing flow momentum. This is the justification for excluding buoyancy in turbulent combustion models that treats high Reynolds number flows. The objectives of our experimental research program is to elucidate flame-buoyancy coupling processes in laminar and turbulent premixed flames, and to characterize microgravity (micro g) premixed flames. The results are used to derive appropriate scaling parameters for guiding the development of theoretical models to include the effects of buoyancy. Knowledge gain from the analysis will also contribute to further understanding of the elliptical nature of premixed flames. Our current emphasis is to examine the momentum limit above which the effects of buoyancy would become insignificant. This is accomplished by comparing the flowfields and the mean properties of normal gravity flames (+g), and reversed gravity flames (-g, up-side-down flames) at different flow velocities and turbulence intensities. Microgravity (micro g) flames experiments provide the key reference data to reconcile the differences between flames in +g and -g. As flame configuration has significant impact on premixed flames characteristics we have studied axi-symmetric conical flames and plane-symmetric rod-stabilized v-flames. The two configurations produce distinct features that dictates how the flames couple with buoyancy. In a conical flame, the hot products plume completely envelopes the flame cone and shields the flame from direct interaction with the ambient air. The plume originates at the burner rim and generates a divergent flowfield. In comparison, the products region of v-flames forms between the twin flame sheets and it is convergent towards the center-plane. Interaction with ambient air is limited to the two end regions of the stabilized rod and beyond the flame sheets.

Cheng, Robert K.↗
NASA NTRS2012

Performance Evaluation of a High Bandwidth Liquid Fuel Modulation Valve for Active Combustion Control

At the NASA Glenn Research Center, a characterization rig was designed and constructed for the purpose of evaluating high bandwidth liquid fuel modulation devices to determine their suitability for active combustion control research. Incorporated into the rig s design are features that approximate conditions similar to those that would be encountered by a candidate device if it were installed on an actual combustion research rig. The characterized dynamic performance measures obtained through testing in the rig are planned to be accurate indicators of expected performance in an actual combustion testing environment. To evaluate how well the characterization rig predicts fuel modulator dynamic performance, characterization rig data was compared with performance data for a fuel modulator candidate when the candidate was in operation during combustion testing. Specifically, the nominal and off-nominal performance data for a magnetostrictive-actuated proportional fuel modulation valve is described. Valve performance data were collected with the characterization rig configured to emulate two different combustion rig fuel feed systems. Fuel mass flows and pressures, fuel feed line lengths, and fuel injector orifice size was approximated in the characterization rig. Valve performance data were also collected with the valve modulating the fuel into the two combustor rigs. Comparison of the predicted and actual valve performance data show that when the valve is operated near its design condition the characterization rig can appropriately predict the installed performance of the valve. Improvements to the characterization rig and accompanying modeling activities are underway to more accurately predict performance, especially for the devices under development to modulate fuel into the much smaller fuel injectors anticipated in future lean-burning low-emissions aircraft engine combustors.

Saus, Joseph R.↗
DOE OSTI2022

Experimental Investigation of Interactions Between Two Closely Spaced Azimuthal Modes in a Multinozzle Can Combustor

Thermoacoustic instabilities in annular or circular combustors are often coupled with azimuthal modes. These modes can be characterized by a spin ratio (SR), which quantifies the dominant mode between two counter-rotating waves, and a phase difference between them, which is directly related to the orientation of the antinodal line. This study investigates the instability amplitudes, SR, and phase difference of two closely spaced (3% of their mean frequency), yet distinct azimuthal modes; one is the first azimuthal (1A) mode, and the other is a combination of first azimuthal and first longitudinal (1A1L) mode. Each mode itself consists of two peaks that are spaced even more closely in frequency (0.8%). Furthermore, distinct harmonics at 2× and 3× of these frequencies, presumably associated with nonlinearities, are also evident in the spectra. Each mode is bandpass filtered in spectrum to analyze them separately. For the 1A mode, the SR and phase difference exhibit a variety of behaviors—including quasi-periodic standing waves, spinning waves, and intermittency—depending on operating conditions such as thermal power and azimuthal fuel staging. Similar trends are observed for the 1A1 L mode. Moreover, there is clear coupling between the 1A and 1A1 L modes, as their SRs are almost synchronized during the quasi-periodic standing wave. This synchronization is observed in phase differences as well, but not in the instability amplitude. For spinning dominant wave conditions, the SRs of each mode have similar average values, but they fluctuate in a seemingly random fashion. For the phase difference, both average and fluctuation are not correlated. In contrast, the instability amplitudes are strongly correlated, with modulation of the 1A mode leading to that of the 1A1 L mode. Furthermore, these results clearly indicate that complex coupling occurs across closely spaced frequencies under instability conditions, coupling that must be understood in order to capture limit cycle dynamics.

33 ADVANCED PROPULSION SYSTEMS↗