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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS2012

Radar Scattering and Block Size Properties of Lunar Crater Ejecta From Mini-RF and LROC NAC Data

A major objective of the Mini-RF experiment is to distinguish lunar surfaces that may contain water/ice deposits [1,2]. Better understanding of the backscattering properties of craters of varying age and size is crucial for interpreting data received from the Mini-RF. The Mini-RF transmits a circularly polarized RF electromagnetic energy and coherently receives orthogonal linear polarization echoes [1]. The Mini- RF maps in two separate bands ( =12.6 and 4.5 cm) at a high resolution mode of 30 m/pixel [1]. Given the variables mentioned, the four stokes parameters are reconstructed. The Circular Polarization Ratio (CPR) is calculated for the purposes of understanding subsurface and surface roughness. The CPR is determined from reflections acquired from the ratio of power of the transmitted radio wave in same sense to the reflected radio wave in the opposite sense [1]. Ice in the permanently shadowed regions (PSRs) would be transparent to radar, but the inclusions of materials and imperfections would cause the radio wave to reflect multiple times [3], enhancing the number of same sense reflections and increasing the CPR. In addition, ice also displays the coherent backscatter opposition effect (CBOE), an interferrometric addition of same sense backscatter that further increases the CPR of ice targets [7]. High CPR values also correlate to multiple reflections and are typically associated with very rough surfaces [3]. The average dry lunar surface has a CPR in the range of 0.2-0.4 at 48deg incidence [3]. The purpose of this study is to begin to quantify degrees of surface wavelength-scale roughness with CPR and to understand how such surface roughness is created and gradually destroyed by erosion on the lunar surface. Another goal is to identify and isolate the possible causes of high CPR within the shadowed areas of anomalous polar craters [3]. All the studied craters are non-polar, so that we can see into their interiors in NAC images. The idea is to understand what controls blockiness in these craters so that we can rule out rocks (and rule in ice) for the anomalous polar dark ones [3].

Spudis, P. D.↗
NASA NTRS1993

Extrapolation of space weathering processes to other small solar system bodies

A diverse range of processes were invoked as the dominant factor or as important contributory factors in the modification of the optical surface and regolith of the moon. These include impact vitrification by large and small projectiles, solar wind implantation and the reduction of oxidized iron during energetic events, sputtering and crystal lattice damage by energetic cosmic rays, shock metamorphism of minerals, mixing of diverse lithologies by impacts, and contamination by external materials. These processes are also potentially important on the rocky surfaces of other small solar system bodies. For icy bodies, several additional processes are also possible, including formation of complex organic compounds from methane and ammonia-bearing ices by ultraviolet irradiation and the condensation of vapor species to form frost layers in the polar or cooler regions of objects at appropriate heliocentric distances. The lunar case, even when completely understood, will not extend in a simple linear fashion to other small rocky objects, nor will the optical surfaces of those objects all be affected to the same degree by each process. The major factors that will control the relative efficacy of a possible mechanism include the efficiency of ejecta retention and the degree to which the regolith materials experience multiple events (primarily a function of body size, escape velocity, and impactor velocities); the mean duration of typical regolith particle exposure at the optical surface and within reach of the micrometeorite, cosmic ray, solar wind, or UV fluxes (a function of the rate and scale of regolith mixing, production, and removal processes); the incident flux of solar (low energy) cosmic rays, solar wind, or UV radiation (inverse square of heliocentric distance) or of galactic (high energy) cosmic rays (slowly increasing flux with heliocentric distance); and the compositional and mineralogical nature of the surface being affected. In general, those processes that depend upon either the retention of impact ejecta or on the presence of multigenerational regoliths should be substantially less effective on smaller bodies with lower escape velocities. However, there are important exceptions to this generalization. For example, a process that involves the hypervelocity impact of small particles into a fine-grained regolith may be able to effectively retain highly shocked or melted material due to the nature of shock wave propagation in such a heterogeneous material.

Gaffey, M. J.↗
DOE OSTI2020

Electron beam injection from a hollow cathode plasma into a downstream reactive environment: Characterization of secondary plasma production and Si 3 N 4 and Si etching

A material etching system was developed by combining beam electron injection from a direct current (DC) hollow-cathode (HC) electron source with the downstream reactive environment of a remote CF 4 /O 2 low temperature plasma. The energy of the injected beam electrons is controlled using an acceleration electrode biased positively relative to the HC Argon discharge. For an acceleration voltage greater than the ionization potential of Ar, the extracted primary electrons can produce a secondary plasma in the process chamber. We characterized the properties of the secondary plasma by performing Langmuir probe measurements of the electron energy probability function (EEPF) 2.5 cm below the extraction ring. The data indicate the existence of two major groups of electrons, including electrons with a primary beam electron energy which varies as the acceleration voltage is varied, along with low energy electrons produced by ionization of the Ar gas atoms in the process chamber by the injected beam electrons. When combining the HC Ar beam electron with a remote CF 4 /O 2 electron cyclotron wave resonance (ECWR) plasma, the EEPF of both the low energy plasma electron and beam electron components decreases. Additionally, we studied surface etching of Si3N4 and poly-crystalline Si (poly-Si) thin films as a function of process parameters, including the acceleration voltage (0-70 V), discharge current of the HC discharge (1-2 A), pressure (2- 100 mTorr), source to substrate distance (2.5 to 5 cm), and feed gas composition (with or without CF 4 /O 2 ). The direction of the incident beam electrons was perpendicular to the surface. Si 3 N 4 and poly-crystalline silicon etching are seen and indicate an electronneutral synergy effect. No/little remote plasma spontaneous etching was observed for the conditions used in this study, and the etching is confined to the substrate area irradiated by the injected beam electrons. The electron etched Si 3 N 4 surface etching rate profile distribution is confined within a ~30 mm diameter circle, which is slightly broader than the area for which poly-Si etching is seen, and coincides closely with the spatial profile of beam electrons as determined by the Langmuir probe measurements. The magnitude of poly-Si etching rate is by a factor of two times smaller than the Si 3 N 4 etching rate. In this paper, we discuss possible explanations of the data and the role of surface charging.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1994

Experimental studies of shock-wave/wall-jet interaction in hypersonic flow

Experimental studies have been conducted to examine slot film cooling effectiveness and the interaction between the cooling film and an incident planar shock wave in turbulent hypersonic flow. The experimental studies were conducted in the 48-inch shock tunnel at Calspan at a freestream Mach number of close to 6.4 and at a Reynolds number of 35 x 10(exp 6) based on the length of the model at the injection point. The Mach 2.3 planar wall jet was generated from 40 transverse nozzles (with heights of both 0.080 inch and 0.120 inch), producing a film that extended the full width of the model. The nozzles were operated at pressures and velocities close to matching the freestream, as well as at conditions where the nozzle flows were over- and under-expanded. A two-dimensional shock generator was used to generate oblique shocks that deflected the flow through total turnings of 11, 16, and 21 degrees; the flows impinged downstream of the nozzle exits. Detailed measurements of heat transfer and pressure were made both ahead and downstream of the injection station, with the greatest concentration of measurements in the regions of shock-wave/boundary layer interaction. The major objectives of these experimental studies were to explore the effectiveness of film cooling in the presence of regions of shock-wave/boundary layer interaction and, more specifically, to determine how boundary layer separation and the large recompression heating rates were modified by film cooling. Detailed distributions of heat transfer and pressure were obtained in the incident shock/wall-jet interaction region for a series of shock strengths and impingement positions for each of the two nozzle heights. Measurements were also made to examine the effects of nozzle lip thickness on cooling effectiveness. The major conclusion from these studies was that the effect of the cooling film could be readily dispersed by relatively weak incident shocks, so the peak heating in the recompression region was not significantly reduced by even the largest levels of film cooling. For the case studies in the absence of film cooling, the interaction regions were unseparated. However, adding film cooling resulted in regions of boundary layer separation induced in the film cooling layer -- the size of which regions first increased and then decreased with increased film cooling. Surprisingly, the size of the separated regions and the magnitude of the recompression heating were not strongly influenced by the thickness of the cooling film, nor by the point of shock impingement relative to the exit plane of the nozzles. The lip thickness was found to have little effect on cooling effectiveness. Measurements with and in the absence of shock interaction were compared with the results of earlier experimental studies and correlated in terms of the major parameters controlling these flows.

Holden, Michael S.↗
NASA NTRS1994

Experimental studies of shock-wave/wall-jet interaction in hypersonic flow, part A

Experimental studies have been conducted to examine slot film cooling effectiveness and the interaction between the cooling film and an incident planar shock wave in turbulent hypersonic flow. The experimental studies were conducted in the 48-inch shock tunnel at Calspan at a freestream Mach number of close to 6.4 and at a Reynolds number of 35 x 10(exp 6) based on the length of the model at the injection point. The Mach 2.3 planar wall jet was generated from 40 transverse nozzles (with heights of both 0.080 inch and 0.120 inch), producing a film that extended the full width of the model. The nozzles were operated at pressures and velocities close to matching the freestream, as well as at conditions where the nozzle flows were over- and under-expanded. A two-dimensional shock generator was used to generate oblique shocks that deflected the flow through total turnings of 11, 16, and 21 degrees; the flows impinged downstream of the nozzle exits. Detailed measurements of heat transfer and pressure were made both ahead and downstream of the injection station, with the greatest concentration of measurements in the regions of shock-wave/boundary layer interaction. The major objectives of these experimental studies were to explore the effectiveness of film cooling in the presence of regions of shock-wave/boundary layer interaction and, more specifically, to determine how boundary layer separation and the large recompression heating rates were modified by film cooling. Detailed distributions of heat transfer and pressure were obtained in the incident-shock/wall-jet interaction region for a series of shock strengths and impingement positions for each of the two nozzle heights. Measurements were also made to examine the effects of nozzle lip thickness on cooling effectiveness. The major conclusion from these studies was that the effect of the cooling film could be readily dispersed by relatively weak incident shocks, so the peak heating in the recompression region was not significantly reduced by even the largest levels of film cooling. For the case studies in the absence of film cooling, the interaction regions were unseparated. However, adding film cooling resulted in regions of boundary layer separation induced in the film cooling layer, the size of which regions first increased and then decreased with increased film cooling. Surprisingly, the size of the separated regions and the magnitude of the recompression heating were not strongly influenced by the thickness of the cooling film, nor by the point of shock impingement relative to the exit plane of the nozzles. The lip thickness was found to have little effect on cooling effectiveness. Measurements with and in the absence of shock interaction were compared with the results of earlier experimental studies and correlated in terms of the major parameters controlling these flows.

Holden, Michael S.↗
NASA NTRS2015

Detection of CFRP Composite Manufacturing Defects Using a Guided Wave Approach

NASA Langley Research Center is investigating a guided-wave based defect detection technique for as-fabricated carbon fiber reinforced polymer (CFRP) composites. This technique will be extended to perform in-process cure monitoring, defect detection and size determination, and ultimately a closed-loop process control to maximize composite part quality and consistency. The overall objective of this work is to determine the capability and limitations of the proposed defect detection technique, as well as the number and types of sensors needed to identify the size, type, and location of the predominant types of manufacturing defects associated with laminate layup and cure. This includes, porosity, gaps, overlaps, through-the-thickness fiber waviness, and in-plane fiber waviness. The present study focuses on detection of the porosity formed from variations in the matrix curing process, and on local overlaps intentionally introduced during layup of the prepreg. By terminating the cycle prematurely, three 24-ply unidirectional composite panels were manufactured such that each subsequent panel had a higher final degree of cure, and lower level of porosity. It was demonstrated that the group velocity, normal to the fiber direction, of a guided wave mode increased by 5.52 percent from the first panel to the second panel and 1.26 percent from the second panel to the third panel. Therefore, group velocity was utilized as a metric for degree of cure and porosity measurements. A fully non-contact guided wave hybrid system composed of an air-coupled transducer and a laser Doppler vibrometer (LDV) was used for the detection and size determination of an overlap By transforming the plate response from the time-space domain to the frequency-wavenumber domain, the total wavefield was then separated into the incident and backscatter waves. The overlap region was accurately imaged by using a zero-lag cross-correlation (ZLCC) imaging condition, implying the incident and backscattered waves are in phase over the overlap boundaries.

Hudson, Tyler B.↗
NASA NTRS2012

NASA Tech Briefs, March 2012

The topics include: 1) Spectral Profiler Probe for In Situ Snow Grain Size and Composition Stratigraphy; 2) Portable Fourier Transform Spectroscopy for Analysis of Surface Contamination and Quality Control; 3) In Situ Geochemical Analysis and Age Dating of Rocks Using Laser Ablation-Miniature Mass Spectrometer; 4) Physics Mining of Multi-Source Data Sets; 5) Photogrammetry Tool for Forensic Analysis; 6) Connect Global Positioning System RF Module; 7) Simple Cell Balance Circuit; 8) Miniature EVA Software Defined Radio; 9) Remotely Accessible Testbed for Software Defined Radio Development; 10) System-of-Systems Technology-Portfolio-Analysis Tool; 11) VESGEN Software for Mapping and Quantification of Vascular Regulators; 12) Constructing a Database From Multiple 2D Images for Camera Pose Estimation and Robot Localization; 13) Adaption of G-TAG Software for Validating Touch and Go Asteroid Sample Return Design Methodology; 14) 3D Visualization for Phoenix Mars Lander Science Operations; 15) RxGen General Optical Model Prescription Generator; 16) Carbon Nanotube Bonding Strength Enhancement Using Metal Wicking Process; 17) Multi-Layer Far-Infrared Component Technology; 18) Germanium Lift-Off Masks for Thin Metal Film Patterning; 19) Sealing Materials for Use in Vacuum at High Temperatures; 20) Radiation Shielding System Using a Composite of Carbon Nanotubes Loaded With Electropolymers; 21) Nano Sponges for Drug Delivery and Medicinal Applications; 22) Molecular Technique to Understand Deep Microbial Diversity; 23) Methods and Compositions Based on Culturing Microorganisms in Low Sedimental Fluid Shear Conditions; 24) Secure Peer-to-Peer Networks for Scientific Information Sharing; 25) Multiplexer/Demultiplexer Loading Tool (MDMLT); 26) High-Rate Data-Capture for an Airborne Lidar System; 27) Wavefront Sensing Analysis of Grazing Incidence Optical Systems; 28) Foam-on-Tile Damage Model; 29) Instrument Package Manipulation Through the Generation and Use of an Attenuated-Fluent Gas Fold; 30) Multicolor Detectors for Ultrasensitive Long-Wave Imaging Cameras; 31) Lunar Reconnaissance Orbiter (LRO) Command and Data Handling Flight Electronics Subsystem; and 32) Electro-Optic Segment-Segment Sensors for Radio and Optical Telescopes.

Source record↗
NASA NTRS2016

Single-Event Latchup Testing of the Micrel MIC4424 Dual Power MOSFET Driver

We conducted 47 exposures of four different MIC4424 devices and did not observe any SEL or high-current events. This included worst-case conditions with a LET of 81 MeV-sq cm/mg, applied voltage of 18.5 V, a case temperature greater than 120 C, and a final fluence of 1x10(exp 7)/sq cm. We also monitored both the outputs for the presence of SETs. While the period of the 1 MHz square wave was slightly altered in some cases, no pulses were added or deleted. 1. Purpose: The purpose of this testing is to characterize the BiCMOS/DMOS Micrel MIC4424 dual, non-inverting MOSFET driver for single-event latchup (SEL) susceptibility. These data will be used for flight lot evaluation purposes. 2. Devices Tested: The MIC4423/4424/4425 family are highly reliable BiCMOS/DMOS buffer/driver MOSFET drivers. They are higher output current versions of the MIC4426/4427/4428. They can survive up to 5V of noise spiking, of either polarity, on the ground pin. They can accept, without either damage or logic upset, up to half an amp of reverse current (either polarity) forced back into their outputs. Primarily intended for driving power MOSFETs, the MIC4423/4424/4425 drivers are suitable for driving other loads (capacitive, resistive, or inductive) which require low-impedance, high peak currents, and fast switching times. Heavily loaded clock lines, coaxial cables, or piezoelectric transducers are some examples. The only known limitation on loading is that total power dissipated in the driver must be kept within the maximum power dissipation limits of the package. Five (5) parts were provided for SEL testing. We prepared four parts for irradiation and reserved one piece as an un-irradiated control. More information about the devices can be found in Table 1. The parts were prepared for testing by removing the lid from the CDIP package to expose the target die. The parts were then soldered to small copper circuit adapter boards for easy handling. These parts are fabricated in a bulk BiCMOS/DMOS technology. Since we do not know the number of overlayers used in the fabrication processes, linear energy transfer calculations are determined based on the top-surface incident ion species and kinetic energy.

Power MOSFET↗
NASA NTRS2017

Chapter 8: Droughts, Floods, and Wildfires

Recent droughts and associated heat waves have reached record intensity in some regions of the United States; however, by geographical scale and duration, the Dust Bowl era of the 1930s remains the benchmark drought and extreme heat event in the historical record (very high confidence). While by some measures drought has decreased over much of the continental United States in association with long-term increases in precipitation, neither the precipitation increases nor inferred drought decreases have been confidently attributed to anthropogenic forcing. The human effect on recent major U.S. droughts is complicated. Little evidence is found for a human influence on observed precipitation deficits, but much evidence is found for a human influence on surface soil moisture deficits due to increased evapotranspiration caused by higher temperatures. Future decreases in surface (top 10 cm) soil moisture from anthropogenic forcing over most of the United States are likely as the climate warms under higher scenarios. Substantial reductions in western U.S. winter and spring snowpack are projected as the climate warms. Earlier spring melt and reduced snow water equivalent have been formally attributed to human-induced warming (high confidence) and will very likely be exacerbated as the climate continues to warm (very high confidence). Under higher scenarios, and assuming no change to current water resources management, chronic, long-duration hydrological drought is increasingly possible by the end of this century. Detectable changes in some classes of flood frequency have occurred in parts of the United States and are a mix of increases and decreases. Extreme precipitation, one of the controlling factors in flood statistics, is observed to have generally increased and is projected to continue to do so across the United States in a warming atmosphere. However, formal attribution approaches have not established a significant connection of increased riverine flooding to human-induced climate change, and the timing of any emergence of a future detectable anthropogenic change in flooding is unclear. The incidence of large forest fires in the western United States and Alaska has increased since the early 1980s and is projected to further increase in those regions as the climate warms, with profound changes to certain ecosystems.

Wehner, M. F.↗
NASA NTRS1997

Clinical utility of T-wave alternans

Electrical alternans represents a variation in the morphology of electrocardiographic complexes on an every-other-beat basis in an ABABAB... pattern. Apparent electrical alternans associated with pericardial effusion results from rotation of the heart in the pericardial sac, and not true alternation in electrical conduction patterns. In contrast, true electrical alternans results from an alternation in electrical conduction patterns in the heart itself. Repolarization alternans is true electrical alternans associated with the ST segment and T wave of the electrocardiogram (ECG). Here we will focus on T-wave alternans (TWA) and its association with susceptibility to ventricular tachyarrhythmias. Electrical alternans was reported in the literature as early as 1909. Historically, electrical alternans has been regarded as a fairly rare electrocardiographic abnormality. Case reports of electrical alternans have been associated with a variety of disease states, including acute ischemia, Prinzmetal's angina, a variety of electrolyte abnormalities, and the long QT syndrome. Interestingly, patients born with the prolonged QT syndrome have a very high incidence of sudden cardiac death at an early age. Schwartz and Malliani showed that patients with the prolonged QT syndrome who do not demonstrate alternans at rest, may evidence alternans during stress such as emotional excitement. Thus, over the years electrical alternans has been associated anecdotally with conditions associated with an increased risk of ventricular arrhythmias. In 1948, Kalter reviewed the world literature on electrical alternans and found a total of 41 reported cases. In addition, he reviewed clinical ectrocardiograms from 6059 patients and found five new cases (incidence of less than 1 in 1000 patients). Interestingly, he found a very high mortality, 62%, associated with this condition. Despite the clinical associations reported in the literature, the consensus view of electrical alternans until recent years has been that alternans is an electrocardiographic curiosity rarely encountered in clinical practice which, when identified, does not have specific clinical significance.

Review, Tutorial↗
NASA NTRS2025

Photophoretic Propulsion Enabling Mesosphere Exploration NIAC Phase I Final Report

This Phase I report presents a comprehensive study on photophoretic flyers—innovative, ultralight, solar-powered vehicles that harness photophoretic forces generated via Knudsen pumping to achieve sustained flight in the mesosphere (50–80 km altitude). By integrating advanced materials such as nanocardboard— characterized by its extremely low areal density (~1 g/m²) and high bending stiffness—with ultrathin light-absorbing coatings, the project converts incident solar radiation directly into a directed thrust. Extensive experimental investigations, coupled with high-fidelity computational fluid dynamics (CFD) simulations using ANSYS Fluent, validate the concept across various three-dimensional geometries, including spherical, conical, and rocket-shaped configurations. These simulations bridge the gap between free-molecular and continuum flow regimes, demonstrating that optimized designs can generate lift forces sufficient to support kilogram-scale payloads even in low-pressure environments. At the heart of this innovation is the use of Knudsen pumping, where temperature gradients across porous surfaces induce directional gas flow, creating a modest overpressure that provides lift. The report introduces an analytical framework that interpolates between the well-known low-Reynolds number drag regime and the high-Reynolds number momentum theory. This model accurately predicts lift based on design parameters such as microchannel dimensions, porous wall geometry, areal density, and nozzle exit area. For instance, simulations indicate that 10-meter-scale structures with carefully engineered porous walls can achieve the necessary pressure differential to support scientifically significant payloads (~1 kg). The study also explores a hybrid propulsion approach that combines solar buoyancy with photophoretic lift. Initially, solar heating creates a buoyant force that elevates the flyer to mesospheric altitudes. Once in the optimal pressure range, the photophoretic mechanism—powered by Knudsen pumping—takes over as the primary source of lift, ensuring stable, long-duration flight. This dual-mode operation not only facilitates the deployment of photophoretic flyers but also broadens the potential applications for mesospheric exploration. In addition to propulsion, the report investigates the integration of photophoretic thrusters for trajectory control of existing research balloons in the upper stratosphere. By dynamically adjusting the nozzle orientation and controlling the flow-through velocity, these thrusters provide precise maneuverability, enabling the flyers to counteract atmospheric disturbances and adjust their flight paths in real time. For example, a photophoretic thruster approximately 7.5 by 7.5 meters in size could be unfolded below a payload gondola of a 60 million-cubic-foot zero-pressure balloon. Such a thruster can provide horizontal speed control of approximately 1 m/s using only sunlight and no moving parts (except those needed to track the Sun and control the jet direction). Importantly, photophoretic thrusters operate more efficiently at higher altitudes, which is complementary to known trajectory control techniques, such as propellers and tethered wings, which are more effective at lower altitudes. Finally, the report identifies three scientific research thrusts where mesospheric aircraft technology can have a profound impact: atmospheric tides, characterization of gravity waves, and investigation of mesospheric instabilities. Overall, the findings of this Phase I project represent a significant advancement in photophoretic propulsion technology. By demonstrating that large-scale, ultralight structures can be powered solely by solar radiation—via carefully engineered Knudsen pumping—this work lays a robust foundation for scalable, near-space flight architectures. Future refinements in material fabrication, structural optimization, and integrated trajectory control are expected to further enhance performance, paving the way for operational demonstrations that could revolutionize atmospheric science, remote sensing, and communication networks.

Knudsen Pump↗
NASA NTRS2005

Control of Combustion-Instabilities Through Various Passive Devices

It is well known that under some operating conditions, rocket engines (using solid or liquid fuels) exhibit unstable modes of operation that can lead to engine malfunction and shutdown. The sources of these instabilities are diverse and are dependent on fuel, chamber geometry and various upstream sources such as pumps, valves and injection mechanism. It is believed that combustion-acoustic instabilities occur when the acoustic energy increase due to the unsteady heat release of the flame is greater than the losses of acoustic energy from the system [1, 2]. Giammar and Putnam [3] performed a comprehensive study of noise generated by gasfired industrial burners and made several key observations; flow noise was sometimes more intense than combustion roar, which tended to have a characteristic frequency spectrum. Turbulence was amplified by the flame. The noise power varied directly with combustion intensity and also with the product of pressure drop and heat release rate. Karchmer [4] correlated the noise emitted from a turbofan jet engine with that in the combustion chamber. This is important, since it quantified how much of the noise from an engine originates in the combustor. A physical interpretation of the interchange of energy between sound waves and unsteady heat release rates was given by Rayleigh [5] for inviscid, linear perturbations. Bloxidge et al [6] extended Rayleigh s criterion to describe the interaction of unsteady combustion with one-dimensional acoustic waves in a duct. Solutions to the mass, momentum and energy conservation equations in the pre- and post-flame zones were matched by making several assumptions about the combustion process. They concluded that changes in boundary conditions affect the energy balance of acoustic waves in the combustor. Abouseif et al [7] also solved the one-dimensional flow equations, but they used a onestep reaction to evaluate the unsteady heat release rate by relating it to temperature and velocity perturbations. Their analysis showed that oscillations arise from coupling between entropy waves produced at the flame and pressure waves originating from the nozzle. Yang and Culick [8] assumed a thin flame sheet, which is distorted by velocity and pressure oscillations. Conservation equations were expressed in integral form and solutions for the acoustic wave equations and complex frequencies were obtained. The imaginary part of the frequency indicated stability regions of the flame. Activation energy asymptotics together with a one-step reaction were used by McIntosh [9] to study the effects of acoustic forcing and feedback on unsteady, one-dimensional flames. He found that the flame stability was altered by the upstream acoustic feedback. Shyy et al [10] used a high-accuracy TVD scheme to simulate unsteady, one-dimensional longitudinal, combustion instabilities. However, numerical diffusion was not completely eliminated. Recently, Prasad [11] investigated numerically the interactions of pressure perturbations with premixed flames. He used complex chemistry to study responses of pressure perturbations in one-dimensional combustors. His results indicated that reflected and transmitted waves differed significantly from incident waves.

Frendi, Kader↗