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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 NTRS2009

Efficient Multidisciplinary Analysis Approach for Conceptual Design of Aircraft with Large Shape Change

The conceptual and preliminary design processes for aircraft with large shape changes are generally difficult and time-consuming, and the processes are often customized for a specific shape change concept to streamline the vehicle design effort. Accordingly, several existing reports show excellent results of assessing a particular shape change concept or perturbations of a concept. The goal of the current effort was to develop a multidisciplinary analysis tool and process that would enable an aircraft designer to assess several very different morphing concepts early in the design phase and yet obtain second-order performance results so that design decisions can be made with better confidence. The approach uses an efficient parametric model formulation that allows automatic model generation for systems undergoing radical shape changes as a function of aerodynamic parameters, geometry parameters, and shape change parameters. In contrast to other more self-contained approaches, the approach utilizes off-the-shelf analysis modules to reduce development time and to make it accessible to many users. Because the analysis is loosely coupled, discipline modules like a multibody code can be easily swapped for other modules with similar capabilities. One of the advantages of this loosely coupled system is the ability to use the medium- to high-fidelity tools early in the design stages when the information can significantly influence and improve overall vehicle design. Data transfer among the analysis modules are based on an accurate and automated general purpose data transfer tool. In general, setup time for the integrated system presented in this paper is 2-4 days for simple shape change concepts and 1-2 weeks for more mechanically complicated concepts. Some of the key elements briefly described in the paper include parametric model development, aerodynamic database generation, multibody analysis, and the required software modules as well as examples for a telescoping wing, a folding wing, and a bat-like wing. The paper also includes the verification of a medium-fidelity aerodynamic tool used for the aerodynamic database generation with a steady and unsteady high-fidelity CFD analysis tool for a folding wing example.

Chwalowski, Pawel↗
NASA NTRS2010

Optical Imaging and Radiometric Modeling and Simulation

OPTOOL software is a general-purpose optical systems analysis tool that was developed to offer a solution to problems associated with computational programs written for the James Webb Space Telescope optical system. It integrates existing routines into coherent processes, and provides a structure with reusable capabilities that allow additional processes to be quickly developed and integrated. It has an extensive graphical user interface, which makes the tool more intuitive and friendly. OPTOOL is implemented using MATLAB with a Fourier optics-based approach for point spread function (PSF) calculations. It features parametric and Monte Carlo simulation capabilities, and uses a direct integration calculation to permit high spatial sampling of the PSF. Exit pupil optical path difference (OPD) maps can be generated using combinations of Zernike polynomials or shaped power spectral densities. The graphical user interface allows rapid creation of arbitrary pupil geometries, and entry of all other modeling parameters to support basic imaging and radiometric analyses. OPTOOL provides the capability to generate wavefront-error (WFE) maps for arbitrary grid sizes. These maps are 2D arrays containing digital sampled versions of functions ranging from Zernike polynomials to combination of sinusoidal wave functions in 2D, to functions generated from a spatial frequency power spectral distribution (PSD). It also can generate optical transfer functions (OTFs), which are incorporated into the PSF calculation. The user can specify radiometrics for the target and sky background, and key performance parameters for the instrument s focal plane array (FPA). This radiometric and detector model setup is fairly extensive, and includes parameters such as zodiacal background, thermal emission noise, read noise, and dark current. The setup also includes target spectral energy distribution as a function of wavelength for polychromatic sources, detector pixel size, and the FPA s charge diffusion modulation transfer function (MTF).

Ha, Kong Q.↗
NASA NTRS1995

Analysis of gas absorption to a thin liquid film in the presence of a zero-order chemical reaction

The paper presents a detailed theoretical analysis of the process of gas absorption to a thin liquid film adjacent to a horizontal rotating disk. The film is formed by the impingement of a controlled liquid jet at the center of the disk and subsequent radial spreading of liquid along the disk. The chemical reaction between the gas and the liquid film can be expressed as a zero-order homogeneous reaction. The process was modeled by establishing equations for the conservation of mass, momentum, and species concentration and solving them analytically. A scaling analysis was used to determine dominant transport processes. Appropriate boundary conditions were used to solve these equations to develop expressions for the local concentration of gas across the thickness of the film and distributions of film height, bulk concentration, and Sherwood number along the radius of the disk. The partial differential equation for species concentration was solved using the separation of variables technique along with the Duhamel's theorem and the final analytical solution was expressed using confluent hypergeometric functions. Tables for eigenvalues and eigenfunctions are presented for a number of reaction rate constants. A parametric study was performed using Reynolds number, Ekman number, and dimensionless reaction rate as parameters. At all radial locations, Sherwood number increased with Reynolds number (flow rate) as well as Ekman number (rate of rotation). The enhancement of mass transfer due to chemical reaction was found to be small when compared to the case of no reaction (pure absorption), but the enhancement factor was very significant when compared to pure absorption in a stagnant liquid film. The zero-order reaction processes considered in the present investigation included the absorption of oxygen in aqueous alkaline solutions of sodiumdithionite and rhodium complex catalyzed carbonylation of methanol. Present analytical results were compared to previous theoretical results for limiting conditions, and were found to have very good agreement.

Rajagopalan, S.↗
DOE OSTI2021

Enhanced Data Efficiency Using Deep Neural Networks and Gaussian Processes for Aerodynamic Design Optimization

Adjoint-based optimization methods are attractive for aerodynamic shape design primarily due to their computational costs being independent of the dimensionality of the input space and their ability to generate high-fidelity gradients that can then be used in a gradient-based optimizer. This makes them very well suited for high-fidelity simulation based aerodynamic shape optimization of highly parametrized geometries such as aircraft wings. However, the development of adjoint-based solvers involve careful mathematical treatment and their implementation require detailed software development. Furthermore, they can become prohibitively expensive when multiple optimization problems are being solved, each requiring multiple restarts to circumvent local optima. In this work, we propose a machine learning enabled, surrogate-based framework that replaces the expensive adjoint solver, without compromising on predicting predictive accuracy. Specifically, we first train a deep neural network (DNN) from training data generated from evaluating the high-fidelity simulation model on a model-agnostic design of experiments on the geometry shape parameters. The optimum shape may then be computed by using a gradient-based optimizer coupled with the trained DNN. Subsequently, we also perform a gradient-free Bayesian optimization, where the trained DNN is used as the prior mean. We observe that the latter framework (DNN-BO) improves upon the DNN-only based optimization strategy for the same computational cost. Overall, this framework predicts the true optimum with very high accuracy, while requiring far fewer high-fidelity function calls compared to the adjoint-based method. Furthermore, we show that multiple optimization problems can be solved with the same machine learning model with high accuracy, to amortize the offline costs associated with constructing our models. Our methodology finds applications in the early stages of aerospace design. (C) 2021 Published by Elsevier Masson SAS.

Renganathan, S. Ashwin↗
NASA NTRS1980

Fluid dynamics of the unsteady two phase processes leading to DDT in granular solid propellants

Deflagration to Detonation (DDT) was predicted to occur in porous beds of high-energy solid propellants by solving the unsteady fluid mechanical convective heat transfer from hot gas products, obtained from the rapid burning at high pressures, provides the impetus to develop a narrow combustion zone and a resulting strong shock. A parametric study clearly indicates that DDT occurs only when a combination of the solids loading fraction, the burning rate constants, the propellant chemical energy, and the particle size provide for critical energy and gas release to support a detonation wave. Predictions for the run-up length to detonation as a function of these parameters are presented.

Krier, H.↗
DOE OSTI2020

A Data-Driven Nonparametric Approach for Probabilistic Load-Margin Assessment Considering Wind Power Penetration

A modern power system is characterized by an increasing penetration of wind power, which results in large uncertainties in its states. These uncertainties must be quantified properly; otherwise, the system security may be threatened. Facing this challenge, here we propose a cost-effective, data-driven approach to assessing a power system's load margin probabilistically. Using actual wind data, a kernel density estimator is applied to infer the nonparametric wind speed distributions, which are further merged into the framework of a vine copula. The latter enables us to simulate complex multivariate and highly dependent model inputs with a variety of bivariate copulae that precisely represent the tail dependence in the correlated samples. Furthermore, to reduce the prohibitive computational time of traditional Monte-Carlo simulations that process a large amount of samples, we propose to use a nonparametric, Gaussian-process-emulator-based reduced-order model to replace the original complicated continuation power-flow model through a Bayesian-learning framework. To accelerate the convergence rate of this Bayesian algorithm, a truncated polynomial chaos surrogate, which serves as a highly efficient, parametric Bayesian prior, is developed. This emulator allows us to execute the time-consuming continuation power-flow solver at the sampled values with a negligible computational cost. Results of simulations that are performed on several test systems reveal the impressive performance of the proposed method in the probabilistic load-margin assessment.

17 WIND ENERGY↗
NASA NTRS1966

Nonlinear Aspects of Combustion Instability in Liquid Propellant Rocket Motors Sixth Yearly Progress Report, 1 Jun. 1965 - 31 May 1966

This is the sixth yearly report on the research at Princeton University on the problem of combustion instability in liquid-propellant rocket motors. These investigations have been sponsored by the National Aeronautics and Space Administration under NASA Contract NASr-217 and, in the past, under NASA Grant NsG-99-60. The nonlinear aspects of the problem have been emphasized in both the theoretical and experimental portions of the program. Presently, the theoretical research primarily involves studies of possible mechanisms or forcing functions of the instabilities, the nonlinear gasdynamic oscillations associated with instability in rocket motors, the effect of the exhaust nozzle on the stability, and the effect of damping devices on the stability. In conjunction with the theoretical program, an experimental program of an equally broad range is being conducted. This program includes basic experiments both with rocket motors and "cold" chambers which have been designed to study various combustion processes in order to provide understanding which would be useful in the construction of a theoretical model. It also includes studies of the effects of exhaust nozzles and damping devices upon the instability as well as controlled testing of liquid rocket motors with parametric variations intended to determine the factors which strongly influence the incidence of nonlinear combustion instability.

Combustion instability↗
NASA NTRS1990

Selective removal of organics for water reclamation

Electrooxidation is a means of removing organic solutes directly from waste waters without the use of chemical expendables. The feasibility of the concept for oxidation of organic impurities common to urine, shower waters and space habitat humidity condensates was demonstrated. Electrooxidation of urine and waste water ersatz was experimentally demonstrated. The electrooxidation principle, reaction kinetics, efficiency, power, size, experimental test results and water reclamation applications are described. Process operating potentials and the use of anodic oxidation potentials that are sufficiently low to avoid oxygen formation and chloride oxidation are also described. The design of a novel electrochemical system that incorporates a proton exchange membrane (PEM) electrolyte is presented based on parametric test data and current fuel cell technology.

Murphy, Oliver J.↗
NASA NTRS2008

Design, Fabrication, and Performance of Foil Gas Thrust Bearings for Microturbomachinery Applications

A methodology for the design and construction of simple foil thrust bearings intended for parametric performance testing and low marginal costs is presented. Features drawn from a review of the open literature are discussed as they relate to bearing performance. The design of fixtures and tooling required to fabricate foil thrust bearings is presented, using conventional machining processes where possible. A prototype bearing with dimensions drawn from the literature is constructed, with all fabrication steps described. A load-deflection curve for the bearing is presented to illustrate structural stiffness characteristics. Start-top cycles are performed on the bearing at a temperature of 425 C to demonstrate early-life wear patterns. A test of bearing load capacity demonstrates useful performance when compared with data obtained from the open literature.

Dykas, Brian↗
NASA NTRS2018

Simulating Forest Dynamics of Lowland Rainforests in Eastern Madagascar

Ecological modeling and forecasting are essential tools for the understanding of complex vegetation dynamics. The parametric demands of some of these models are often lacking or scant for threatened ecosystems, particularly in diverse tropical ecosystems. One such ecosystem and also one of the world's biodiversity hotspots, Madagascar's lowland rainforests, have disappeared at an alarming rate. The processes that drive tree species growth and distribution remain as poorly understood as the species themselves. We investigated the application of the process-based individual-based FORMIND model to successfully simulate a Madagascar lowland rainforest using previously collected multi-year forest inventory plot data. We inspected the model's ability to characterize growth and species abundance distributions over the study site, and then validated the model with an independently collected forest-inventory dataset from another lowland rainforest in eastern Madagascar. Following a comparative analysis using inventory data from the two study sites, we found that FORMIND accurately captures the structure and biomass of the study forest, with r(squared) values of 0.976, 0.895, and 0.995 for 1:1 lines comparing observed and simulated values across all plant functional types for aboveground biomass (tonnes/ha), stem numbers, and basal area (m(squared)/ha), respectively. Further, in validation with a second study forest site, FORMIND also compared well, only slightly over-estimating shade-intermediate species as compared to the study site, and slightly under-representing shade-tolerant species in percentage of total aboveground biomass. As an important application of the FORMIND model, we measured the net ecosystem exchange (NEE, in tons of carbon per hectare per year) for 50 ha of simulated forest over a 1000-year run from bare ground. We found that NEE values ranged between 1 and -1 t Cha(exp -1)year(exp -1), consequently the study forest can be considered as a net neutral or a very slight carbon sink ecosystem, after the initial 130 years of growth. Our study found that FORMIND represents a valuable tool toward simulating forest dynamics in the immensely diverse Madagascar rainforests.

Forest Productivity↗
DOE OSTI2024

Photoproduction of K0K0-bar with the GlueX Experiment

In this dissertation, we study photoproduction of K0 ?K 0 through the KSKLp and KSKSp ?nal states with the GlueX Phase-I (GlueX-I) data set. We measure the spin-density matrix elements (SDMEs) and di?erential cross section of ?(1020) ! KSKL to better understand photoproduction of light vector mesons. A mass independent Partial Wave Analysis (PWA) of the KSKL and KSKS meson spectrum below 2 GeV is also undertaken to study the meson spectrum with JPC = even++ and odd??. The ?(1020) di?erential cross section is measured at E = 8:2 ? 8:8 GeV and ?t = 0:15 ? 1:00 GeV2. The di?erential cross section is well described by an exponential decay with slope 4:44?0:01 GeV?2 and the integrated cross section is determined to be 295:7?0:4 nb, only statistical uncertainties are quoted. Both measurements are consistent and far more precise than the previous measurement by Ballam et al. [1]. The ?(1020) SDMEs were measured in nine bins of ?t in the same range. At low ?t, we ?nd the data were consistent with s-channel helicity conservation, SCHC, i. e. the only non-zero SDMEs were ?1 1?1 = ?Im(?2 1?1) = 1=2. At higher ?t, the SDMEs deviate from SCHC and the measurements indicate this is due to natural parity exchange since we observe that the SDMEs are consistent with zero unnatural exchange. We also ?find that the contribution from helicity double-flip amplitudes is consistent with zero. The measured SDMEs are in poor agreement with theoretical predictions put forward by JPAC [35]. These measurements will serve as input to re?ne models of production processes, which will be essential for the interpretation of possible signals of exotic mesons in GlueX. Analysis of the spectrum above the ?(1020) indicates the presence of at least three particles at ? 1:50, ? 1:75, and 2:20 GeV. We employ simple parametrizations of the resonance line shape based on relativistic Breit-Wigner functions considering cases with and without interference. The resonance at ? 1:50 GeV is not identifi?ed as any specifi?c resonance, but could be due to interference between the ?(1450) and !(1420). Our models favor the resonance at ~1:75 GeV as the X(1750) rather than the ?(1680). We ?find that introducing a third Breit-Winger into the models improves the ?t quality with the ?2/ndf going from 1.75 to 1.59 and 1.41 to 1.18 for models without and with interference respectively. A PWA of the KSKL spectrum indicates that the spectrum is consistent with exclusively spin-1 contribution up to ? 1:6 GeV. Above ? 1:6 GeV we ?find evidence for a small spin-3 contribution. We also ?nd that the spectrum predominantly positive reflectivity up to ? 1:6 GeV, after which the spectrum becomes a nearly equal mix of both. The KSKS system shows a rich spectrum with multiple resonance structures but is more statistically limited than the KSKL system. Modelling the line shape we ?find evidence at greater than 10? level in favor of a resonance at ? 1:75 GeV. The model parameters suggest this resonance is the f0(1710). The PWA of the KSKS system was inconclusive. However, using a small set of amplitudes suggests that the spin-2 contribution to the spectrum is primarily in the range 1:2?1:6 GeV, where f2(1270), a2(1320) and f02 (1525) are expected.

Linera, Gabriel Rodriguez↗
DOE OSTI2022

Learning-Based Demand Response in Grid Interactive Buildings via Gaussian Processes

This paper presents a predictive controller for a grid-interactive multi-zone building where the temperature dynamics are learned via Gaussian Process (GP) regression. We investigate the development of a learning-based predictive control with two main objectives: (i) continuously learn the temperature dynamics of the building based on data; and, (ii) use the learned dynamics to solve a multi-objective predictive control problem to guarantee occupants' comfort and energy efficiency during normal conditions and demand response events. We leverage the probabilistic non-parametric properties of GPs to estimate the (unknown) non-linear temperature dynamics of the building and to incorporate the uncertainty of those predictions in a multi-objective optimization problem. The GP-based predictive control is solved via a zero-order primal-dual projected-gradient algorithm. We evaluate numerically the performance of the proposed controller using a five-zone commercial building.

demand response↗
DOE OSTI2025

Parametric and Robustness Studies of Qudit Mediated Quantum State Transfer and Entanglement Creation

The large number of available states participating in quantum state evolution in a system of qudits translates into better thermal resilience, for quantum state transfer (QST) and distributed entangled states, than a system of 2-level qubits. In this report we study the dependence of fidelities of the above processes on various system parameters. Sensitivity to modes of dissipation and errors is also studied. An alternative and potentially more efficient scheme to create Bell states is used.

Chao, Yu-Chiu [Fermilab] (ORCID:000900039584159X)↗
DOE OSTI2020

Validation of the Community Land Model Version 5 over the Contiguous United States (CONUS) using in-situ and remote sensing datasets

The Community Land Model (CLM) is an effective tool to simulate the biophysical and biogeochemical processes and their interactions with the atmosphere. Although CLM Version 5 (CLM5) constitutes various updates in these processes, its performance in simulating energy, water and carbon cycles over the Contiguous United States (CONUS) at scales which land surface changes and hydrometeorological and hydroclimatological applications are more locally relevant is yet to be assessed. In this study, we conducted three simulations at 0.125? during 1979-2018 over the CONUS using different configurations of CLM, namely CLM5-biogeochemistry (CLM5BGC), CLM4.5BGC, and CLM5-satellite phenology (CLM5SP). We validated and compared their simulations against multiple remote-sensed and in-situ datasets. Overall, the parametric and structural updates (e.g., carbon cost for nitrogen uptake, variable soil thickness, dry surface layer) in CLM5 improve its ability in capturing terrestrial biogeochemical dynamics. The low evapotranspiration in CLM5BGC is associated with biases in simulating vegetation phenological characteristics rather than soil water limitations. The mismatch between CLM5BGC-simulated peak leaf area index and reference data can be attributed to CLM5BGC's inability in simulating phenology of trees and grasses. The differences between CLM-simulated irrigation and reference estimates can be attributed to differences between processes represented in models and in reality, and uncertainties in input and validation datasets. Evaluation against observations at small catchments suggest that hydrologic parameters needed to be calibrated to improve simulations of runoff, especially subsurface runoff. Additional efforts are needed to incorporate spatially-distributed plant phenology and physiology parameters and regional-specific agricultural management practices (e.g., planting, harvest).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Piston geometry and stroke optimization for high efficiency propane spark ignition engines

Propane has unique properties and offers interesting characteristics for high-efficiency spark ignition engines. Its high volatility reduces or completely eliminates fuel-wall wetting and facilitates fuel air mixing. Furthermore, propane has a research octane number of 112 and a high octane sensitivity of 15. Finally, its laminar flame speed is on the same order as that of conventional gasoline, and it exhibits high dilution tolerance. Modern spark ignition internal combustion engines rely on fast combustion rates and high dilution to achieve high brake thermal efficiencies. To accomplish this, high stroke-to-bore ratios and high geometric compression ratios have been used in new engine designs. Therefore, propane’s relatively high laminar flame speeds, high knock resistance, and dilution tolerance make it an excellent candidate fuel for modern spark ignition engines. The objective of this work is to co-optimize the piston geometry and the engine stroke to maximize the efficiency of a spark-ignition engine fueled with propane. 3D computational fluid dynamics (CFD) simulations employing the extended coherent flamelet model were used to study the parametric effects of piston shape and stroke length. A piston geometry based on high performing pistons was parameterized using four controlling parameters. The piston geometry and engine stroke design space was explored using deterministic and quasi-random sampling techniques. In conclusion, a Gaussian process regression model was built using the simulation data to explain the results observed.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2024

Multiphysics Co-Optimization Design and Analysis of Double-Side Cooled Silicon Carbide-Based Power Module: Preprint

With the rapid growth of Electric Vehicles (EVs) and Hybrid Electric Vehicles (HEVs), much more rigorous design targets have been set for automotive power electronics, including high power density, high reliability, and low cost. Novel power module and inverter technologies based on wide bandgap (WEG) semiconductors have been developed to meet these design targets, while providing optimal power semiconductor operating temperature and promising thermomechanical performance. Compared with conventional cooling techniques which are normally applied only on one side of power module, double-side cooling approach is now believed to be the solution to enable high power density and low thermal resistance of WEG semiconductor-based power electronics. In this work, we develop a three-phase power module that is double-sided cooled using dielectric fluid jet impingement. In each phase, four silicon carbide (SiC) power semiconductors are bonded to copper busbars without electrical insulation layers. A finite element analysis (FEA) model is created for thermal and thermomechanical analysis. Based on FEA modeling results, we select particular dimensions for a parametric study to optimize thermal and mechanical performance. Using a multi-objective genetic algorithm (MOGA)-based optimization method, we have minimized the maximum junction temperature and thermal stresses within the power module. The multiphysics co-optimization approach has enabled an efficient design process of power modules with greatly reduced computational cost, as compared to conventional processes that rely on exhaustive numerical simulations and iterations.

ADVANCED PROPULSION SYSTEMS↗
NASA NTRS1995

Analytical investigation of the hygrothermal effects and parametric study of the Edge Crack Torsion (ECT) mode 3 test lay-ups

A shear deformation theory including residual thermal and moisture effects is developed for the analysis of either symmetric or unsymmetric laminates with mid-plane edge delamination under torsion loading. The theory is based on an assumed displacement field which includes shear deformation. The governing equations and boundary conditions are obtained from the principle of virtual work. The analysis of the (90/(+/- 45)(n)/(-/+ 45)(n)/90)(s) ECT mode 3 test lay-up indicates that there are no hygrothermal effects on the mode 3 strain energy release rate because the laminate, and both sublaminates above and below the delamination, are symmetric lay-ups. A further parametric study reveals that some other lay-ups can have negligible hygrothermal effects even when the sublaminates above and below the delamination are not symmetric about their own mid-planes. However, these lay-ups may suffer from distortion after the curing process. Another Interesting set of lay-ups investigated is a class of antisymmetric laminates with (+/-(theta/(theta -90)(2)/theta))(n) lay-ups. It is observed that when n takes on even numbers (2 and 4), both hygrothermal and mode 1 effects can be neglected. From this point of view, these lay-ups provide a way to determine the mode 3 toughness between two dissimilar layers. However, when n takes on odd numbers (1 and 3), both hygrothermal and mode 1 effects may be strong in these lay-ups. In particular, when theta equals 45 deg, the lay-ups are free from both hygrothermal and mode 1 effects irrespective of n.

Li, Jian↗
NASA NTRS2012

Physics of Acoustic Radiation from Jet Engine Inlets

Numerical simulations of acoustic radiation from a jet engine inlet are performed using advanced computational aeroacoustics (CAA) algorithms and high-quality numerical boundary treatments. As a model of modern commercial jet engine inlets, the inlet geometry of the NASA Source Diagnostic Test (SDT) is used. Fan noise consists of tones and broadband sound. This investigation considers the radiation of tones associated with upstream propagating duct modes. The primary objective is to identify the dominant physical processes that determine the directivity of the radiated sound. Two such processes have been identified. They are acoustic diffraction and refraction. Diffraction is the natural tendency for an acoustic wave to follow a curved solid surface as it propagates. Refraction is the turning of the direction of propagation of sound waves by mean flow gradients. Parametric studies on the changes in the directivity of radiated sound due to variations in forward flight Mach number and duct mode frequency, azimuthal mode number, and radial mode number are carried out. It is found there is a significant difference in directivity for the radiation of the same duct mode from an engine inlet when operating in static condition and in forward flight. It will be shown that the large change in directivity is the result of the combined effects of diffraction and refraction.

Tam, Christopher K. W.↗