Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Combustor Noise”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 181 records · Page 10

Development of a High Frequency Class-A Amplifier for High Temperature Wireless Microsystems based on a Silicon Carbide Static Induction Transistor

Next generation gas turbine engine health monitoring for high performance jet engine-powered aircraft will incorporate integrated microelectronic sensors specifically designed to enhance aircraft functionality, engine efficiency, and safety. Temperature, air flow and pressure associated with the gas path as well as emissions from the engine correlate to the state of the combustor and other engine health conditions. Monitoring these parameters accurately requires positioning electronic sensors in the hot zone of the gas turbine engine, which exposes them to temperatures in excess of 400ºC. At these temperatures, signal amplification is needed at the transducer level to distinguish the desired measured signal from the significant electronic noise generated by the harsh environment. In this presentation, we report on the simulation, development, fabrication, and testing on a high temperature Class-A amplifier which utilizes a 4H-SiC Static Induction Transistor (SIT) as the active device and input/output matching and DC bias networks comprised of thin-film spiral inductors, metal-insulator-metal capacitors, and thick film chip resistors. A small signal model that emulates the operation of the 4H-SiC SIT from 25 to 400ºC, with an emphasis on operation at 400οC, was utilized. Measurements were performed from 25 to 400ºC to generate current-voltage curves, capacitive transistor characteristics and high frequency scattering parameters (S-parameters). The measured data was used to extrapolate the transconductance, gm, as a function of temperature for model development. Circuit simulation tools were used to generate S-parameters, which were compared to the measured values. At 400οC, a maximum difference between measured and simulated S-parameters for frequencies from 20 to 100 MHz were 3.84%, 0.68%, 10.61%, and 3.26% for S21, S12, S11, and S22, respectively. The average transit frequency, ft, was calculated from measured values to be 197.8 MHz, while the simulated value from the model was found to be 200 MHz. The Amplifier’s S-parameters were recorded at 20-100 MHz over a temperature range of 25-400ºC and show a gain of approximately 15.8 and 5.80 dBm at 25 and 400ºC, respectively. The input and output reflection coefficients at 50 MHz and 400ºC were -18.5 and -15.2 dB, respectively. The noise figure and phase noise were measured over the temperature range of 25-400ºC and recorded. The noise figure increased 21% at 50 MHz over the temperature range, while the 1 kHz offset of the phase noise remained below -110 dB. The stability factor, K, calculated with measured and simulated data demonstrates unconditional stability over the frequency range at 400ºC. Lastly, the 1-dB compression point was measured at 50 MHz and 400ºC with an approximated output of 9.5 dBm.

SiC↗

A theoretical model for the cross spectra between pressure and temperature downstream of a combustor

A theoretical model developed to calculate pressure-temperature cross spectra, pressure spectra, temperature spectra and pressure cross spectra in a ducted combustion system is presented. The model assumes the presence of a fluctuating-volumetric-heat-release-rate disk source and takes into account the spatial distribution of the steady-state volumetric-heat flux. Using the model, pressure, velocity, and temperature perturbation relationships can be obtained. The theoretical results show that, at a given air mass flow rate, the calculated pressure-temperature cross spectra phase angle at the combustor exit depends on the model selected for the steady-state volumetric-heat flux in the combustor. Using measurements of the phase angle, an appropriate source region model was selected. The model calculations are compared with the data. The comparison shows good agreement and indicates that with the use of this model the pressure-temperature cross spectra measurements provide useful information on the physical mechanisms active at the combustion noise source.

Miles, J. H.↗

Combustion noise and combustion instabilities in propulsion systems

This paper is concerned with some aspects of non-linear behavior of unsteady motions in combustion chambers. The emphasis is on conditions under which organized oscillations having discrete frequencies may exist in the presence of random motions. In order to treat the two types of motions together, and particularly to investigate coupling between noise and combustion instabilities, the unsteady field is represented as a synthesis of acoustic modes having time-varying amplitudes. Each of the amplitudes are written as the sum of two parts, one associated with the random field and the remainder representing the organized oscillations. After spatial averaging, the general problem is reduced to solution of a set of second-order ordinary differential equations whose structure depends on the sorts of nonlinear processes accounted for. This formulation accommodates any physical process; in particular, terms are included to represent noise sources, although only limited modeling is discussed. Our results suggest that random sources of noise have only small effects on combustion instabilities and seem not to be a cause of unstable motions. However, the coupling between the two sorts of unsteady motions may be important as an essential process in a proposed scheme for noise control. It is now a familiar observation that many nonlinear deterministic systems are capable of exhibiting apparently random motions called 'chaos.' This is a particularly interesting possibility for systems which also executed non-deterministic random motions. In combustion chambers, a nonlinear deterministic system (acoustical motions) exists in the presence of noise produced by flow separation, turbulent motions, and energy released by combustion processes. The last part of the paper is directed to the matter of discovering whether or not chaotic motions exist in combustion systems. Analysis has not progressed sufficiently far to answer the question. We report here recent results of processing data taken in one combustor to determine the dimensions of any attractors in the motions. No evidence has been found for chaos in the strict sense, but the method seems to be an important means of investigating the nonlinear behavior of combustion systems.

F. E. C. Culick↗

High Speed Research: Propulsion Project Accomplishments

This past year has been one of great accomplishment for the propulsion element of NASA's High Speed Research (HSR) Program. The HSR Program is a NASA/industry partnership to develop the high-risk/high-payoff airframe and propulsion technologies applicable to a second-generation supersonic commercial transport, or High Speed Civil Transport (HSCT). The propulsion element, which also involves industry partners, is managed by the NASA Lewis Research Center. These technologies will contribute greatly to U.S. industry's ability to make an informed product launch decision for an HSCT vehicle. Specific NASA Lewis accomplishments in 1997 include: 1. Small-scale combustor sector tests conducted in Lewis' Engine Research Building contributed to the evolution of approaches to developing a combustor with ultralow NOx emissions. 2. Components were tested in Lewis' CE-9 facility (in Lewis' Engine Research Building) to assess the performance of candidate ceramic matrix composite (CMC) materials in this realistic combustion environment. Test results were promising, and acceptable levels of structural durability were demonstrated for the ceramic matrix composite material tested. Ceramic matrix composites continue to show great promise for use in HSCT combustor liners. 3. Engine emissions tests in Lewis' Propulsion Systems Laboratory provided insight into other classes of emissions (e.g., particulates and aerosols) which will be important to control in HSCT propulsion system designs. 4. Small-scale nozzle tests conducted in Lewis' Aero-Acoustic Propulsion Laboratory are contributing to the design of a low-noise, high-performance mixer/ejector nozzle configuration for HSCT engines. Over 18,000 hours of durability testing were completed in Lewis' materials laboratories to evaluate superalloy and g-titanium aluminide performance for HSCT nozzle applications. A two-dimensional supersonic inlet concept was tested in Lewis' 10- by 10-Foot Supersonic Wind Tunnel. The extensive database and the knowledge gained contributed to the selection of a two-dimensional inlet as the preferred inlet concept for the HSR Program.

Shaw, Robert J.↗

Water Misting and Injection of Commercial Aircraft Engines to Reduce Airport NOx

This report provides the first high level look at system design, airplane performance, maintenance, and cost implications of using water misting and water injection technology in aircraft engines for takeoff and climb-out NOx emissions reduction. With an engine compressor inlet water misting rate of 2.2 percent water-to-air ratio, a 47 percent NOx reduction was calculated. Combustor water injection could achieve greater reductions of about 85 percent, but with some performance penalties. For the water misting system on days above 59 F, a fuel efficiency benefit of about 3.5 percent would be experienced. Reductions of up to 436 F in turbine inlet temperature were also estimated, which could lead to increased hot section life. A 0.61 db noise reduction will occur. A nominal airplane weight penalty of less than 360 lb (no water) was estimated for a 305 passenger airplane. The airplane system cost is initially estimated at $40.92 per takeoff giving an attractive NOx emissions reduction cost/benefit ratio of about $1,663/ton.

Daggett, David L.↗

Nonlinear dynamics of combustor azimuthal modes: Experiments and modeling

This paper provides an experimental and theoretical investigation of azimuthal instabilities in a lean, premixed combustor. It presents data from a high Reynolds number, industrial-scale facility with multiple fuel stages that enable variation of radial and azimuthal symmetries. The combustor exhibits a variety of behaviors – including standing, spinning, mixed waves, and intermittent behaviors, as well as periodic limit cycles and quasi-periodic oscillations – depending upon varying power and azimuthal symmetry. A second key objective of this paper is to present a weakly nonlinear framework that is used to understand and interpret these results, showing the influence of eigenmode degeneracy, background noise, and azimuthal non-uniformities in mean quantities such as temperature and flame-acoustic coupling. In particular, this analysis shows the importance of the linear instability growth/damping rate and azimuthal non-uniformities in controlling the relative prominence of standing, spinning, or mixed waves at the limit cycle, as well as the preference in the spinning direction. It also shows the conditions under which single frequency or quasi-periodic oscillations are dominant, and how these are more fundamentally influenced by azimuthal non-uniformities and background noise.

42 ENGINEERING↗

Sequence2Self: Self-supervised image sequence denoising of pixel-level spray breakup morphology

Optical imaging of fast and transient phenomena such as the turbulent breakup of liquid sprays exhibit low signal-to-noise ratios due to the limited illumination intensity relative to the short exposure time. Image denoising is required to facilitate physical studies over these data but is challenging due to the absence of clean ground-truths and the stringency of the denoising task (e.g., strong and complex noise, limited resolution, preserving physical fidelity), preventing supervised and existing un-/self-supervised deep learning methods. To this end, Sequence2Self (Seq2S) is proposed, an extension of Self2Self (S2S) to image sequences that leverages both the signal’s spatial and temporal correlation. Seq2S is demonstrated on time-resolved x-ray phase contrast imaging of liquid jet fuel sprays in a gas turbine combustor, which possesses all of challenges detailed above. Experiments are conducted across four fuels with different breakup morphology using various state-of-the-art methods. Overall, many of the methods failed and Seq2S was most successful: (1) Accurate spray structures were reconstructed with consistent evolution across frames void of artifacts. (2) The performance was robust, invariant to the hyperparameter choice. (3) Computational time is short and can be made eligible for real-time denoising. In particular, the images denoised by Seq2S showed spray droplet diameter distributions with near-zero Kullback–Leibler divergence (0.01 ± 0.01) to a cleaner reference, whereas the second best method yielded 0.06 ± 0.03. In conclusion, this suggests that Seq2S can be reliably used prior to subsequent quantitative spray analyses as it retains (if not, improves) the statistical physical properties of the data.

97 MATHEMATICS AND COMPUTING↗

High-Flow Jet Exit Rig Designed and Fabricated

The High-Flow Jet Exit Rig at the NASA Glenn Research Center is designed to test single flow jet nozzles and to measure the appropriate thrust and noise levels. The rig has been designed for the maximum hot condition of 16 lbm/sec of combustion air at 1960 R (maximum) and to produce a maximum thrust of 2000 lb. It was designed for cold flow of 29.1 lbm/sec of air at 530 R. In addition, it can test dual-flow nozzles (nozzles with bypass flow in addition to core flow) with independent control of each flow. The High- Flow Jet Exit Rig was successfully fabricated in late 2001 and is being readied for checkout tests. The rig will be installed in Glenn's Aeroacoustic Propulsion Laboratory. The High-Flow Jet Exit Rig consists of the following major components: a single component force balance, the natural-gas-fueled J-79 combustor assembly, the plenum and manifold assembly, an acoustic/instrumentation/seeding (A/I/S) section, a table, and the research nozzles. The rig will be unique in that it is designed to operate uncooled. The structure survives the 1960 R test condition because it uses carefully selected high temperature alloy materials such as Hastelloy-X. The lower plenum assembly was designed to operate at pressures to 450 psig at 1960 R, in accordance with the ASME B31.3 piping code. The natural gas-fueled combustor fires directly into the lower manifold. The hot air is directed through eight 1-1/2-in. supply pipes that supply the upper plenum. The flow is conditioned in the upper plenum prior to flowing to the research nozzle. The 1-1/2-in. supply lines are arranged in a U-shaped design to provide for a flexible piping system. The combustor assembly checkout was successfully conducted in Glenn's Engine Component Research Laboratory in the spring of 2001. The combustor is a low-smoke version of the J79 combustor used to power the F4 Phantom military aircraft. The natural gas-fueled combustor demonstrated high-efficiency combustion over a wide range of operating conditions. This wide operating envelope is required to support the testing of both single- and dual-flow nozzles. Key research goals include providing simultaneous, highly accurate acoustic, flow, and thrust measurements on jet nozzle models in realistic flight conditions, as well as providing scaleable acoustic results. The High-Flow Jet Exit Rig is a second-generation high-flow test rig. Improvements include cleaner flow with reduced levels of particulate, soot, and odor. Choked-flow metering is required with plus or minus 0.25-percent accuracy. Thrust measurements from 0 to 2000 lbf are required with plus or minus 0.25-percent accuracy. Improved acoustics will be achieved by minimizing noise through large pipe bend radii, lower internal flow velocities, and microdrilled choke plates with thousands of 0.040-in.- diameter holes.

Buehrle, Robert J.↗

Active Suppression of Instabilities in Engine Combustors

A method of feedback control has been proposed as a means of suppressing thermo-acoustic instabilities in a liquid- fueled combustor of a type used in an aircraft engine. The basic principle of the method is one of (1) sensing combustor pressure oscillations associated with instabilities and (2) modulating the rate of flow of fuel to the combustor with a control phase that is chosen adaptively so that the pressure oscillations caused by the modulation oppose the sensed pressure oscillations. The need for this method arises because of the planned introduction of advanced, lean-burning aircraft gas turbine engines, which promise to operate with higher efficiencies and to emit smaller quantities of nitrogen oxides, relative to those of present aircraft engines. Unfortunately, the advanced engines are more susceptible to thermoacoustic instabilities. These instabilities are hard to control because they include large dead-time phase shifts, wide-band noise characterized by amplitudes that are large relative to those of the instabilities, exponential growth of the instabilities, random net phase walks, and amplitude fluctuations. In this method (see figure), the output of a combustion-pressure sensor would be wide-band-pass filtered and then further processed to generate a control signal that would be applied to a fast-actuation valve to modulate the flow of fuel. Initially, the controller would rapidly take large phase steps in order to home in, within a fraction of a second, to a favorable phase region within which the instability would be reduced. Then the controller would restrict itself to operate within this phase region and would further restrict itself to operate within a region of stability, as long as the power in the instability signal was decreasing. In the phase-shifting scheme of this method, the phase of the control vector would be made to continuously bounce back and forth from one boundary of an effective stability region to the other. Computationally, this scheme would be implemented by the adaptive sliding phaser averaged control (ASPAC) algorithm, which requires very little detailed knowledge of the combustor dynamics. In the ASPAC algorithm, the power of the instability signal would be calculated from the wide-bandpass- filtered combustion-pressure signal and averaged over a period of time (typically of the order of a few hundredths of a second) corresponding to the controller updating cycle [not to be confused with the controller sampling cycle, which would be much shorter (typically of the order of 10(exp -4) second)].

Kopasakis, George↗

Liquid rocket spray combustion stability analysis

A computational approach to the analysis of spray combustion stability in liquid rocket combustors is proposed which is based on the unsteady quasi-two-dimensional Euler equations with interphase source terms derived from a Lagrangian treatment of the combusting spray. Based on a preliminary evaluation, the computational methodology presented here is a promising research tool and a potential design/development aid for investigating the stability characteristics of liquid rocket engines. The method is characterized by low numerical noise; the Lagrangian treatment of the spray offers improved flexibility for the direct modeling of spray combustion.

Litchford, Ron J.↗

An Overview of Low-Emission Combustion Research

An overview of research efforts at NASA Glenn Research Center (GRC) in low-emission combustion technology that have made a significant impact on the Nitrogen Oxides (NOx) emission reduction in aircraft propulsion will be presented. The technology advancements and their impact on aircraft emissions will be discussed in the context of NASAs Aeronautics Research Mission Directorate (ARMD) high-level goals in fuel burn, noise and emission reductions. The highlights of the research presented will show how the past and current efforts have laid the foundation for the engines that are flying today as well as how the continued technology advancements will significantly influence the next generation of aviation propulsion system designs.

Clean Energy↗

HSR Overview

The leading Aeronautics program within NASA is the High Speed Research Program (HSR). The HSR program's highest priorities are high pay-off technologies for airframe and propulsion systems required for a high speed civil transport (HSCT). These priorities have been developed collaboratively with NASA, FAA and the US Industry (Boeing-McDonnell Douglas, Pratt & Whitney and General Electric). Phase one of the HSR program started on 1990, and concentrated on the environmental challenges of minimizing NOx and noise. The first program goal is to reduce the NOx emission index to less than 5 (Concord NOx index is 20 and is unacceptable), in order to have little impact on the earth's ozone layer. The second goal is to reduce noise levels to FAR Stage 3 (or better), comparable to those of subsonic aircraft (far below the Concorde noise levels that require exemptions form less stringent standards). This requirement greatly impacts the nozzle design increasing its length and complexity and poses unique sealing challenges. Phase two started in 1993 and initiated work on the technologies required for an economical HSCT. Materials technologies under development include a ceramic-matrix-composite combustion liner, lightweight materials for the nozzle, as well long-life turbomachinery disk and blade alloys. Other required materials are being developed under the DOD-IHPTET program, where there is close cooperation. Economic goals translate into the development of technologies for tri-class service, 5000 nautical mile range aircraft with a ticket price no more than 20% over the subsonic ticket price. The potential market could be as large as 1500 aircraft, according to a Boeing study. Technology alone will not enable this airplane, yet without enabling technologies "on the shelf", it will not occur. The HSCT engine will be the largest engine ever built and operate at maximum conditions for long periods of time posing a number of challenges. The HSR engine mission requires that rotating equipment stay at take-off condition temperatures for hours not minutes per flight. Hence rotating equipment and seals must operate for many thousands of hours at extreme temperatures. It is anticipated that the nozzle will be 12 feet long and roughly 4 ft. by 5 ft. in cross-section with a nominal airflow of 800 lbs/sec. The complex function of the nozzle (including an ejector for noise attenuation) combined with long life place new demands on nozzle seal design. Three inlet configurations are under consideration with attendant sealing challenges, as will be illustrated herein. Four of these engines are required to propel a 5000 nautical mile class vehicle which demand that component reliability be at the highest possible level. In response, an HSR seals session was implemented as a part of the 1997-Seals and Secondary Flow Workshop. Overview presentations were given for each of the following areas: inlet, turbomachinery, combustor and nozzle. The HSCT seal issues center on durability and efficiency of rotating equipment seals (including brush seals), structural seals (including rope seals and other advanced concepts), and high-speed bearing and sump seals. Tighter clearances, propulsion system size and thermal requirements represent extremes that challenge the component designers. This document provides an initial step toward defining HSR seal needs. The overview for HSR seal designs includes, defining seal objectives, summarizing sealing and materials requirements, presenting relevant seal cross-sections, and identifying technology needs for the HSR office.

Hendricks, R. C.↗

Planar laser-induced fluorescence imaging of OH in the exhaust of a bi-propellant thruster

Planar laser-induced fluorescence imaging of the hydroxyl radical has been performed on the flow produced by the exhaust of a subscale H2/O2 fueled bi-propellant rocket engine. Measurements were made to test the feasibility of OH (0,0) and (3,0) excitation strategies by using injection seeded XeCl and KrF excimer lasers, respectively. The flow is produced with hydrogen and oxygen reacting at a combustor chamber pressure of 5 atm which then exhausts to the ambient. The hydroxyl concentration in the exhaust flow is approximately 8 percent. Fluorescence images obtained by pumping the Q1(3) transition in the (0,0) band exhibited very high signals but also showed the effect of laser beam absorption. To obtain images when pumping the P1(8) transition in the (3,0) band it was necessary to use exceptionally fast imaging optics and unacceptably high intensifier gains. The result was single-shot images which displayed a signal-to-noise ratio of order unity or less when measured on a per pixel basis.

Paul, Phillip H.↗

An overview of rotorcraft propulsion research at Lewis Research Center

Rotorcraft propulsion research at Lewis Research Center is discussed, stressing programs in four areas of component research: compressors, combustors, turbines and transmissions, and three developmental programs: the Small Turboshaft Engine Research (STER) Project, the Advanced Rotorcraft Transmission (ART) program, and the Compound Cycle Engine (CCE) program. The component research emphasizes special problems of turboshaft engines in the 5 lb/sec to 30 lb/sec range. The objectives of the STER program are to evaluate the application of advanced concepts to small turboshaft engine systems and to investigate system related phenomena, such as distortion effects and secondary flow phenomena. The goals of the ART program are to reduce transmission weight by 25 percent, noise generation by 10 dB and mean time between removal to 5,000 hrs. The CCE program is working to combine the airflow capacity and light-weight features of a gas turbine with the more efficient, but heavier diesel turbine.

Bill, Robert C.↗

In-situ measurement of moist flue gas under high pressure using a nafion dryer and FTIR

The formation of the main flue gas species (NOx, SOx, CO2, and CO) in pressurized oxy-fuel combustion can be fundamentally different from oxy-fuel combustion at atmospheric pressure. To accurately obtain the concentration of these gas species in a pressurized oxy-fuel combustor, a gas measurement which maintains the sampling pressure is needed. Very few published studies have accomplished this, and never under the conditions reported herein. In this work, we fire PRB coal in a 100 kWth staged pressurized oxy-fuel combustor (SPOC) under a pressure 15 bara. We utilize a state-of-the-art FTIR (Thermo Scientific Nicolet iS20) with a novel high-pressure gas cell that is under process pressure to measure the in-situ flue-gas concentration in a sampled flow. However, water vapor can significantly interfere with the FTIR measurement, particularly under pressure. To address this problem, we have developed a high-pressure nafion dryer to selectively remove the water vapor from the flue gas while retaining the flue gas species. This approach can significantly increase the signal-noise ratio for the FTIR. By integrating the nafion dryer and the high-pressure gas cell, we were able to successfully measure flue gas species at system pressure with the FTIR.

Cheng, Mao↗

Particle Streak Velocimetry of Supersonic Nozzle Flows

A novel velocimetry technique to probe the exhaust flow of a laboratory scale combustor is being developed. The technique combines the advantages of standard particle velocimetry techniques and the ultra-fast imaging capabilities of a streak camera to probe high speed flows near continuously with improved spatial and velocity resolution. This "Particle Streak Velocimetry" technique tracks laser illuminated seed particles at up to 236 picosecond temporal resolution allowing time-resolved measurement of one-dimensional flows exceeding 2000 m/s as are found in rocket nozzles and many other applications. Developmental tests with cold nitrogen have been performed to validate and troubleshoot the technique with supersonic flows of much lower velocity and without background noise due to combusting flow. Flow velocities on the order of 500 m/s have been probed with titanium dioxide particles and a continuous-wave laser diode. Single frame images containing multiple streaks are analyzed to find the average slope of all incident particles corresponding to the centerline axial flow velocity. Long term objectives for these tests are correlation of specific impulse to theoretical combustion predictions and direct comparisons between candidate green fuels and the industry standard, monomethylhydrazine, each tested under identical conditions.

Willits, J. D.↗

CARS Temperature Measurements in a Hypersonic Propulsion Test Facility

Nonintrusive diagnostic measurements were performed in the supersonic reacting flow of the Hypersonic Propulsion Test Cell 2 at NASA-Langley. A Coherent Anti-stokes Raman Spectroscopy (CARS) system was assembled specifically for the test cell environment. System design considerations were: (1) test cell noise and vibration; (2) contamination from flow field or atmospheric borne dust; (3) unwanted laser or electrically induced combustion (inside or outside the duct); (4) efficient signal collection; (5) signal splitting to span the wide dynamic range present throughout the flow field; (6) movement of the sampling volume in the flow; and (7) modification of the scramjet model duct to permit optical access to the reacting flow with the CARS system. The flow in the duct was a nominal Mach 2 flow with static pressure near one atmosphere. A single perpendicular injector introduced hydrogen into the flow behind a rearward facing step. CARS data was obtained in three planes downstream of the injection region. At least 20 CARS data points were collected at each of the regularly spaced sampling locations in each data plane. Contour plots of scramjet combustor static temperature in a reacting flow region are presented.

Jarrett, Olin, Jr.↗

Restricted Modal Analysis Applied to Internal Annular Combustor Autospectra and Cross-Spectra Measurements

A treatment of the modal decomposition of the pressure field in a combustor as determined by two pressure time history measurements is developed herein. It is applied to a Pratt and Whitney PW4098 engine combustor over a range of operating conditions. For modes other than the plane wave the assumption is made that there are distinct frequency bands in which the individual modes, including the plane wave mode, overlap such that if circumferential mode m and circumferential mode m-1 are present then circumferential mode m-2 is not. In the analysis used herein at frequencies above the first cutoff mode frequency, only pairs of circumferential modes are individually present at each frequency. Consequently, this is a restricted modal analysis. As part of the analysis one specifies mode cut-on frequencies. This creates a set of frequencies that each mode spans. One finding was the successful use of the same modal span frequencies over a range of operating conditions for this particular engine. This suggests that for this case the cut-on frequencies are in proximity at each operating condition. Consequently, the combustion noise spectrum related to the circumferential modes might not change much with operating condition.

Miles, Jeffrey Hilton↗