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At least 757 records · Page 42
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Decoding the B → K ν ν excess at Belle II: Kinematics, operators, and masses

An excess in the branching fraction for B + → K + ν ν recently measured at Belle II may be a hint of new physics. We perform thorough likelihood analyses for different new physics scenarios such as B → K X with a new invisible particle X , or B → K χ χ through a scalar, vector, or tensor current with χ being a new invisible particle or a neutrino. We find that vector-current three-body decay with m X ≃ 0.6 GeV—which may be dark matter—is most favored, while two-body decay with m X ≃ 2 GeV is also competitive. The best-fit branching fractions for the scalar and tensor cases are a few times larger than for the two-body and vector cases. Past measurements provide further discrimination, although the best-fit parameters stay similar. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1988

Conditions for the validity of unmagnetized-plasma theory in describing weakly magnetized plasmas

The application of the unmagnetized-plasma theory to the derivation of the expression for the dielectric tensor for weakly magnetized plasmas is examined. The analysis of Baldwin et. al. (1969) is employed to determine the conditions under which the magnetic effects on the dielectric tensor of a plasma are small. The relation between wave and plasma parameters and the plasma distribution function is studied. Axisymmetric distribution functions in magnetized plasma are considered. The derived conditions are analyzed in terms of resonance ellipses of the cyclotron maser theory. Examples are presented in which the conditions are applied to a nonrelativistic Maxwellian distribution and the dispersion and instability of Langmuir and Bernstein waves in weakly magnetized plasma. The data reveal that the conditions under which the magnetic field can be completely neglected depend on the forms of the distribution function.

Robinson, P. A.↗
NASA NTRSDate not supplied

Towards Surrogate Modeling of Subgrid Turbulent Transport for 3D Radiative Hydrodynamic Simulations of the Quiet Sun

In this work, we investigate the use of deep learn-ing techniques as surrogate models, to enhance the estimationof effects of subgrid turbulent transport for 3D radiatuve hy-drodynamic simulations of the quiet Sun. We develop two dis-tinct 3D Convolutional Neural Networks (3DCNNs) to capturespatio-temporal dependencies in 3D velocity fields, leveragingdifferent activation functions and architectural designs. Thesemodels integrate both averaged velocity vector components andscalar features such as plasma density to enhance predictionaccuracy. Additionally, a Multilayer Perceptron (MLP) modelis employed to approximate complex nonlinear relationships,offering a comparison in performance between convolutionaland fully connected architectures. Logarithmic transformationis applied to the targets to handle heavily skewed data, im-proving model performance. All models are compared againsta physics-based Gradient Model. Results show that the 3DCNNmodels excel at approximating Reynolds stress tensors, makingthem a candidate for assisting in producing reduced resolutionsimulations, and thereby reducing computational overheadwhile maintaining higher accuracy than the baseline. Thesefindings demonstrate the potential of deep learning, particu-larly CNNs, to advance scalable and accurate simulations ofsolar dynamics, offering a promising alternative to traditionalturbulence models.

Heliophysics↗
DOE OSTI2024

Scalable learning of potentials to predict time-dependent Hartree–Fock dynamics

We propose a framework to learn the time-dependent Hartree–Fock (TDHF) inter-electronic potential of a molecule from its electron density dynamics. Although the entire TDHF Hamiltonian, including the inter-electronic potential, can be computed from first principles, we use this problem as a testbed to develop strategies that can be applied to learn a priori unknown terms that arise in other methods/approaches to quantum dynamics, e.g., emerging problems such as learning exchange–correlation potentials for time-dependent density functional theory. We develop, train, and test three models of the TDHF inter-electronic potential, each parameterized by a four-index tensor of size up to 60 × 60 × 60 × 60. Two of the models preserve Hermitian symmetry, while one model preserves an eight-fold permutation symmetry that implies Hermitian symmetry. Across seven different molecular systems, we find that accounting for the deeper eight-fold symmetry leads to the best-performing model across three metrics: training efficiency, test set predictive power, and direct comparison of true and learned inter-electronic potentials. All three models, when trained on ensembles of field-free trajectories, generate accurate electron dynamics predictions even in a field-on regime that lies outside the training set. To enable our models to scale to large molecular systems, we derive expressions for Jacobian-vector products that enable iterative, matrix-free training.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2001

Statistical Ensemble of Large Eddy Simulations

A statistical ensemble of large eddy simulations (LES) is run simultaneously for the same flow. The information provided by the different large scale velocity fields is used to propose an ensemble averaged version of the dynamic model. This produces local model parameters that only depend on the statistical properties of the flow. An important property of the ensemble averaged dynamic procedure is that it does not require any spatial averaging and can thus be used in fully inhomogeneous flows. Also, the ensemble of LES's provides statistics of the large scale velocity that can be used for building new models for the subgrid-scale stress tensor. The ensemble averaged dynamic procedure has been implemented with various models for three flows: decaying isotropic turbulence, forced isotropic turbulence, and the time developing plane wake. It is found that the results are almost independent of the number of LES's in the statistical ensemble provided that the ensemble contains at least 16 realizations.

Carati, Daniele↗
DOE OSTI2023

Local position-space two-nucleon potentials from leading to fourth order of chiral effective field theory

We present local, position-space chiral NN potentials through four orders of chiral effective field theory ranging from leading order (LO) to next-to-next-to-next-to-leading order (N 3 LO, fourth order) of the Δ-less version of the theory. The long-range parts of these potentials are fixed by the very accurate πN LECs as determined in the Roy-Steiner equations analysis. At the highest order (N 3 LO), the NN data below 190 MeV laboratory energy are reproduced with the respectable χ 2 /datum of 1.45. A comparison of the N 3 LO potential with the phenomenological Argonne v 18 (AV18) potential reveals substantial agreement between the two potentials in the intermediate range ruled by chiral symmetry, thus, providing a chiral underpinning for the phenomenological AV18 potential. Our chiral NN potentials may serve as a solid basis for systematic ab initio calculations of nuclear structure and reactions that allow for a comprehensive error analysis. In particular, the order by order development of the potentials will make possible a reliable determination of the truncation error at each order. Our new family of local position-space potentials differs from existing potentials of this kind by a weaker tensor force as reflected in relatively low D-state probabilities of the deuteron (P D ≲ 4.0 % for our N 3 LO potentials) and predictions for the triton binding energy above 8.00 MeV (from two-body forces alone). As a consequence, our potentials may lead to different predictions when applied to light and intermediate-mass nuclei in ab initio calculations and, potentially, help solve some of the outstanding problems in microscopic nuclear structure.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

A Novel Solid Form of Erlotinib: Synthesis by Heterogeneous Complexation and Characterization by NMR Crystallography

We describe the synthesis of a novel complex of the anticancer "active pharmaceutical ingredient erlotinib (ERL) via heterogeneous nucleation on polished zinc tiles. The resulting product, ERL 2 ·ZnCl 2 , is characterized by single-crystal X-ray diffraction, multinuclear solid-state NMR (ssNMR) spectroscopy, and density functional theory (DFT) calculations. Also characterized are the hydrochloride salt (ERL·HCl) and monohydrate free base (ERL·H 2 O) forms of erlotinib. 13 C ssNMR spectroscopy is useful for site-by-site assignment and rapid fingerprinting, while also providing preliminary structural interpretations, such as the number of molecules in the asymmetric unit. 35 Cl ssNMR can readily differentiate between the chloride ions in ERL·HCl and the covalently bonded chlorine in ERL 2 ·ZnCl 2 . 15 N ssNMR proves to be critical here because of the large isotropic chemical shift differences between ERL·H 2 O, ERL·HCl, and ERL 2 ·ZnCl 2 . The 15 N chemical shift tensors are linked directly to differences in structure and bonding with the aid of DFT calculations. Together, these results demonstrate the utility of multinuclear NMR crystallography for the characterization of solid forms of APIs, especially when other analytical techniques face significant challenges.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2003

Macroscopic Models of Radiative Transfer as Applied to Computation of the Radiation Field in the Solar Atmosphere

In this paper a new three dimensional half-moment model for radiative transfer is presented for a gray medium. It describes the evolution of the zeroth and first directional half moments of the radiative intensity. The closure is provided, similarly to Dubroca and Klar, by the maximum entropy concept. This work generalizes that model to three dimensions. The model presented here (the derivation being done in Ripoll and Wray, called the M(sup 1/2)(sub 1) model, is a hyperbolic system consisting of a total of eight equations in three dimensions, four equations for each direction. Each half model has the classical form of a macroscopic moment model in which the pressure tensor is constructed from the well-known Eddington tensor with a particular Eddington factor. Moreover, different source and border terms occur. The latter introduce couplings between the macroscopic and microscopic quantities and between the + and - streams, through the intensity in the plane perpendicular to the flux. The main theoretical application of the half moment model, treated in this paper, is its reduction to a full moment model, called M(sup +)(sub 1), for the particular but important case of a hot, opaque source radiating in a cold transparent (or semi-transparent) medium for very specific applications, such as stellar interiors or atmospheres, or combustion problems. The structure of the paper is as follows. In section 2, the model M(sup 1/2)(sub 1) is presented. In section 3, for the particular case of a hot, opaque source radiating into a cold medium, the half moment model is reduced to the M(sup +)(sub 1) model. In section 4, we first solve a simple and academic problem to validate the models, followed by a simplified solar atmosphere.

Ripoll, J.-F.↗
DOE OSTI2020

The well-tempered cosmological constant: the Horndeski variations

Well tempering is one of the few classical field theory methods for solving the original cosmological constant problem, dynamically canceling a large (possibly Planck scale) vacuum energy and leaving the matter component intact, while providing a viable cosmology with late time cosmic acceleration and an end de Sitter state. We present the general constraints that variations of Horndeski gravity models with different combinations of terms must satisfy to admit an exact de Sitter spacetime that does not respond to an arbitrarily large cosmological constant. We explicitly derive several specific scalar-tensor models that well temper and can deliver a standard cosmic history including current cosmic acceleration. Stability criteria, attractor behavior of the de Sitter state, and the response of the models to pressureless matter are considered. The well tempered conditions can be used to focus on particular models of modified gravity that have special interest— not only removing the original cosmological constant problem but providing relations between the free Horndeski functions and reducing them to a couple of parameters, suitable for testing gravity and cosmological data analysis.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Stability, electronic quantum states, and magnetic interactions of Er 3+ ions in Ga 2 ⁢O 3

Here, we report an ab initio study of phase stability, defect formation, electronic structure, and multiple magnetic, Dzyaloshinskii-Moriya, optical, hyperfine, and crystal field interactions in erbium (Er)-doped wide band gap 𝛼- and 𝛽-gallium oxides (Ga 2 ⁢O 3 ), critically important to make a foundation for both optoelectronic and quantum information applications. The chemical, structural, mechanical, and dynamical stabilities of the pristine phases are confirmed from respective negative formation energies, negative cohesive energies, favorable elastic constants, and positive phonon frequencies. The phonon dispersions indicate that the Ga-O bonds are uniform in the 𝛼-phase, while they vary in the 𝛽-phase due to the anisotropic polyhedral movement. The defect formation energy analysis confirms that both Er-doped 𝛼- and 𝛽−Ga 2 ⁢O 3 prefer Er 3+ (neutral) state. The underestimated band gaps of the pristine phases from standard density functional theory (DFT) calculations as compared to experimental values are corrected by employing the hybrid functional calculations, resulting in the indirect band gaps of 5.21 eV in 𝛼−Ga 2 ⁢O 3 and 4.94 eV in 𝛽−Ga 2 ⁢O 3 . The site preference energy analysis indicates partial occupation of Er in the octahedral site of Ga. The anisotropic nature of hyperfine tensor coefficients of Er is similar in both phases, which may be due to the occupation of Er in the same octahedral Ga site. On the other hand, the calculated magnetic exchange interaction between two Er dopants is negative for 𝛼 and positive for 𝛽, indicating an antiferromagnetic (AFM) ground state in the former and a ferromagnetic (FM) ground state in the latter. Large values of Dzyaloshinskii-Moriya interactions (DMIs) are obtained along the 𝑥 direction in the 𝛼 and along the 𝑦 direction in the 𝛽. The large DMI may support exotic magnetic textures, a promising direction for spintronic applications. The analysis of dielectric constants and refractive indices of both pristine and Er-doped phases shows a good agreement with available experimental values. The calculated optical anisotropy is slightly higher in 𝛽 than those in 𝛼, which is due to the involvement of lower symmetry in 𝛽. The crystal field coefficients (CFCs) calculated from DFT are used to analyze 4⁢𝑓 multiplets and 4⁢𝑓 −4⁢𝑓 transitions. Thus calculated lowest energy level of the first excited state to the lowest energy level of the ground state is about 1.53 µ⁢m, which is in a good agreement with available experiments, and it falls within the quantum telecommunication wavelength range.

3-dimensional systems↗
DOE OSTI2022

Far-from-equilibrium slow modes and momentum anisotropy in expanding plasma

The momentum distribution of particle production in heavy-ion collisions encodes information about thermalization processes in the early-stage quark-gluon plasma. We use kinetic theory to study the far-from-equilibrium evolution of an expanding plasma with an anisotropic momentumspace distribution. We identify slow and fast degrees of freedom in the far-from-equilibrium plasma from the evolution of moments of this distribution. At late times, the slow modes correspond to hydrodynamic degrees of freedom and are naturally gapped from the fast modes by the inverse of the relaxation time, $τ$$^{–1}_{R}$. At early times, however, there are an infinite number of slow modes with a gap inversely proportional to time, τ –1 . From the evolution of the slow modes we generalize the paradigm of the far-from-equilibrium attractor to vector and tensor components of the energy momentum tensor, and even to higher moments of the distribution function that are not part of the hydrodynamic evolution. We predict that initial-state momentum anisotropy decays slowly in the far-from-equilibrium phase and may persist until the relaxation time.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Type II Seesaw leptogenesis

The Type II Seesaw Mechanism provides a minimal framework to explain the neutrino masses involving the introduction of a single triplet Higgs to the Standard Model. However, this simple extension was believed to be unable to successfully explain the observed baryon asymmetry of the universe through Leptogenesis. In our previous work (Phys. Rev. Lett. 128 (2022) 141801), we demonstrated that the triplet Higgs of the Type II Seesaw Mechanism alone can simultaneously generate the observed baryon asymmetry of the universe and the neutrino masses while playing a role in setting up Inflation. This is achievable with a triplet Higgs mass as low as 1 TeV, and predicts that the neutral component obtains a small vacuum expectation value $v_Δ$ < 10 keV. We find that our model has very rich phenomenology and can be tested by various terrestrial experiments as well as by astronomical observations. Particularly, we show that the successful parameter region may be probed at a future 100 TeV collider, upcoming lepton flavor violation experiments such as Mu3e, and neutrinoless double beta decay experiments. Additionally, the tensor-to-scalar ratio from the inflationary scenario will be probed by the LiteBIRD telescope, and observable isocurvature perturbations may be produced for some parameter choices. In this article, we present all the technical details of our calculations and further discussion of its phenomenological implications.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Exponential acceleration of macroscopic quantum tunneling in a Floquet Ising model

The exponential suppression of macroscopic quantum tunneling (MQT) in the number of elements to be reconfigured is an essential element of broken symmetry phases. This suppression is also a core bottleneck in quantum algorithms, such as traversing an energy landscape in optimization, and adiabatic state preparation more generally. In this work, we demonstrate exponential acceleration of MQT through Floquet engineering with the application of a uniform, high frequency transverse drive field. Using the ferromagnetic phase of the transverse field Ising model in one and two dimensions as a prototypical example, we identify three phenomenological regimes as a function of drive strength. For weak drives, the system exhibits exponentially decaying tunneling rates but robust magnetic order; in the crossover regime at intermediate drive strength, we find polynomial decay of tunnelling alongside vanishing magnetic order; and at very strong drive strengths both the Rabi frequency and time-averaged magnetic order are approximately constant with increasing system size. We support these claims with extensive full wavefunction and tensor network numerical simulations, and theoretical analysis. An experimental test of these results presents a technologically important and novel scientific question accessible on NISQ-era quantum computers.

Grattan, George↗
DOE OSTI2022

Geothermal Fault Zone and Fluid Imaging through Joint Airborne ZTEM and Ground MT Data Inversion Analysis

This project has aimed to achieve detailed electrical resistivity resolution at geothermal reservoir scales by combining airborne natural electromagnetic (EM) field surveying (ZTEM) with ground magnetotelluric (MT) measurements to approximate an airborne MT geophysical method. MT alone is relatively expensive and may have permitting challenges in sensitive areas. Airborne ZTEM field data contains only the magnetic field, requires a background assumption, and has been limited to relatively high frequencies, thus suffering uniqueness problems. Based on proto-type 2D simulations, ZTEM ambiguities may be reduced through formal incorporation with possibly sparse ground MT soundings, which we pursued in full 3D for this project. The methodology was tested at the high-temperature Roosevelt Hot Springs geothermal system, Utah, which was considered advantageous given the near total exposure of crystalline reservoir rocks across the project area. ZTEM and ground MT survey data were acquired in 2017, subcontracted to outside parties with which we have worked in the past. These included 80 remote-referenced tensor MT soundings over the Mineral Mountains and adjacent Roosevelt Hot Spring producing geothermal system. These MT stations abut later coverage of a similar number of MT stations taken for the Utah FORGE project providing excellent total data aperture to re-solve structure beneath both project areas better than either set alone. The airborne ZTEM survey covered 704 line kilometers in E-W flight lines with a 250 m line spacing. Although this survey was timed during a maintenance-related shutdown of power production at the Roosevelt Hot Springs, other noise sources difficult to identify but including two high-voltage state-scale transmission lines compromised the ZTEM survey badly leading to unusable responses. Thus, with DOE management concurrence, the project proceeded to emphasize inversion and interpretation of the joint SubTER-FORGE MT data sets with regard to the Roosevelt Hot Springs reservoir recharge and to deep heat sources for both it and the Utah FORGE EGS project area. We also investigated the joint ZTEM-MT sampling concept with data sets from the Eleven Mile Canyon prospect area donated by the U.S. Navy (A. Sabin, PoC). Inversion of the SubTER-FORGE MT data using the HexMT 3D finite element algorithm reveals a large, low-resistivity anomaly extending sub-vertically through the depth range of the crust beneath the western Mineral Mountains. The steep conductive zone connects in the lower crust to a more tabular conductor characteristic of much of the Great Basin that generally is ascribed to current mafic magmatic underplating, hybridization and fluid release. The location of the resolved anomaly relative to the recent (0.5-0.8 Ma) eruptive centers of the Mineral Mountains implicates it as remnants of the magma body which fed these centers. This structure appears to be currently feeding heat and fluids upward into the Roosevelt Hot Springs hydrothermal system, as well as heat laterally to the FORGE project area. Separate and joint inversion models were carried out for the donated Eleven Mile Canyon MT-ZTEM data set to demonstrate concept. ZTEM only inversion showed two main alteration zones in the western portion of the project area known from geological mapping. Joint inversion including an E-W profile of MT soundings sharpened these features considerably. It also resolved in much greater detail the graben related normal faulting structure of the central project area which lies at depths exceeding the sensitivity of ZTEM alone. The sparse number of MT da-ta relative to the ZTEM required upweighting the former by a factor of several, but an exact procedure awaits future research. Our final impression is that sparse MT data can improve resolution of the subsurface over that of ZTEM alone. However, well sampled MT data are to be preferred and offer the simplicity of interpreting just one data type, and possess the superior resolution capability coming with the electric field everywhere, and from their high bandwidth.

15 GEOTHERMAL ENERGY↗
DOE OSTI2025

A Unified Perspective on Poincaré and Galilei Relativity: II. General Relativity: A. Kinematics

Building on the first paper in this series (Paper I), a unified perspective on Poincaré and Galilei physics in a 5-dimensional spacetime setting is further pursued through a consideration of the kinematics of general relativity, with the gravitational dynamics to be addressed separately. The metric of the 5-dimensional affine spacetimes governed by the Bargmann groups considered in Paper I (central extensions of the Poincaré and Galilei groups) is generalized to curved spacetime by extending the usual 1 + 3 (traditionally ‘3 + 1’) formalism of general relativity on 4-dimensional spacetime to a 1 + 3 + 1 formalism, whose spacetime kinematics is shown to be consistent with that of the usual 1 + 3 formalism. Spacetime tensor laws governing the motion of an elementary classical material particle and the dynamics of a simple fluid are presented, along with their 1 + 3 + 1 decompositions; these reference the foliation of spacetime in a manner that partially reverts the Einstein perspective (accelerated fiducial observers, and geodesic material particles and fluid elements) to a Newton-like perspective (geodesic fiducial observers, and accelerated material particles and fluid elements subject to a gravitational force). These spacetime laws of motion for particles and fluids also suggest that a strong-field Galilei general relativity would involve a limit in which not only 𝑐 → ∞ but also 𝐺 → ∞ , such that 𝐺/𝑐 2 remains constant.

Bargmann group↗
DOE OSTI2026

From Weibel seeds to dynamo beyond pair-plasmas

Bridging the spatiotemporal scales of magnetic seed field generation and subsequent dynamo amplification in the weakly collisional intracluster medium presents an extreme numerical challenge. We perform collisionless turbulence simulations with initially unmagnetised electrons that capture both magnetic seed generation via the electron Weibel instability and the ensuing dynamo amplification. Going beyond existing pair-plasma studies, we use an ion-to-electron mass ratio of 100 for which we find electron and ion dynamics are sufficiently decoupled. These simulations are enabled by the 10-moment collisionless fluid solver of Gkeyll, which evolves the full pressure tensor for all species. The electron heat-flux closure regulates pressure isotropisation and effectively sets the magnetic Reynolds number. We investigate how the strength of the closure influences the transition between a regime reminiscent of previous kinetic pair-plasma simulations and a regime exhibiting dynamo behaviour qualitatively similar to magnetohydrodynamics.

astrophysical plasmas↗
DOE OSTI2021

Demonstration of CFD to support the coupled analysis of a reactor pressure vessel subjected to pressurized thermal shock

The structural components that comprise nuclear reactors and their supporting structures are subjected to harsh operating environments that can challenge their integrity, especially after exposure for extended duration or under accident condition. As one of the most significant components of a reactor, the Reactor Pressure Vessel (RPV) is exposed to an aggressive environment during the operation time (e.g. more than 40 years). Aging degradation mechanisms (e.g. thermo-fatigue) could grow initial defects up to a critical size, increasing the susceptibility to failure in the RPV. The conventional methods are mostly based on simple crack and structure geometries. Very limited studies consider the real conditions of the RPV subjected to a thermal shock due to a Loss of Coolant Accident (LOCA). During a LOCA event, the most severe conditions take place when the emergency core cooling (ECC) water is injected inside the cold legs filled initially with hotter water and/or steam. The rapid cooling of the down-comer and the internal RPV surface followed probably by re-pressurization of the RPV causes large temperature gradients and variation of pressure which induces thermal-mechanical stresses. In order to develop the model for integrity assessment of a reactor pressure vessel (RPV) subjected to pressurized thermal shock (PTS), a multi-physics simulation, which includes the thermo-hydraulic, thermo-mechanical and fracture mechanics analyses is necessary. The prediction of the temperature field is achieved by using computational fluid dynamics (CFD) simulation. In this report, a demonstration CFD standalone simulation is performed to support coupled analysis for Reactor Pressure Vessel (RPV) subjected to Pressurized Thermal Shock (PTS). The study use a simplified computational domain to represents a real RPV. The purpose of the study is to demonstrate the transient temperature response of RPV to ECC injection. The CFD model is built in a robust and efficient way for further coupled calculation. The next steps of this work, including the coupled thermal and tensor mechanics capabilities using Cardinal are expected to be complete by the end of FY21 for the demo problem. After this, into FY22, the capability will be demonstrated for a realistic RPV.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1977

Identification and measurement of combustion noise from a turbofan engine using correlation and coherence techniques

Fluctuating pressure measurements within the combustor and tailpipe of a turbofan engine are made simultaneously with far field acoustic measurements. The pressure measurements within the engine are accomplished with cooled semi-infinite waveguide probes utilizing conventional condenser microphones as the transducers. The measurements are taken over a broad range of engine operating conditions and for 16 far field microphone positions between 10 deg and 160 deg relative to the engine inlet axis. Correlation and coherence techniques are used to determine the relative phase and amplitude relationships between the internal pressures and far field acoustic pressures. The results indicate that the combustor is a low frequency source region for acoustic propagation through the tailpipe and out to the far field. Specifically, it is found that the relation between source pressure and the resulting sound pressure involves a 180 deg phase shift. The latter result is obtained by Fourier transforming the cross correlation function between the source pressure and acoustic pressure after removing the propagation delay time. Further, it is found that the transfer function between the source pressure and acoustic pressure has a magnitude approximately proportional to frequency squared. These results are shown to be consistent with a model using a modified source term in Lighthill's turbulence stress tensor, wherein the fluctuating Reynolds stresses are replaced with the pressure fluctuations due to fluctuating entropy.

Karchmer, A. M.↗