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

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Astrometric Membership Tests for the Zinn–Newell–Gibson UV-bright Stars in Galactic Globular Clusters

In 1972, Zinn, Newell, & Gibson (ZNG) published a list of 156 candidate UV-bright stars they had found in 27 Galactic globular clusters (GCs), based on photographs in the U and V bands. UV-bright stars lie above the horizontal branch (HB) and blueward of the asymptotic giant branch (AGB) and red giant branch in the clusters’ color–magnitude diagrams. They are in rapid evolutionary phases—if they are members and not unrelated bright foreground stars. The ZNG list has inspired numerous follow-up studies, aimed at understanding late stages of stellar evolution. However, the ZNG candidates were presented only in finding charts, and celestial coordinates were not given. Using my own collection of CCD frames in u and V, I have identified all of the ZNG objects, and have assembled their coordinates, parallaxes, and proper motions from the recent Gaia Early Data Release 3 (EDR3). Based on the Gaia astrometry, I have determined which objects are probable cluster members (45% of the sample). For the members, using photometry from EDR3, I have assigned the stars to various evolutionary stages, including luminous post-AGB stars, and stars above the HB. I point out several ZNG stars of special interest that have still, to my knowledge, never been studied in detail. This study is an adjunct to a forthcoming survey of the Galactic GCs in the uBVI photometric system, designed for detection of low-gravity stars with large Balmer discontinuities.

47 OTHER INSTRUMENTATION↗
NASA NTRS1994

The Fornax-Leo-Sculptor stream revisited

Lynden-Bell first demonstrated that the satellites of the Milky Way appear situated along two great 'streams' in the sky: the 'Magellanic stream' and the 'Fornax-Leo-Sculptor (FLS) stream.' Further exploration of the three-dimensional distribution of Galactic satellites reveals that the recently discovered Sextans and Phoenix dwarf spheroidal galaxies also lie near the plane defined by the FLS galaxies, and therefore strengthens the evidence in favor of the FLS stream. Moreover, a specific group of globular clusters -- those exhibiting the reddest horizontal branches (HBs) among those identified as 'young halo' by Zinn -- appear to populate the FLS stream. As previously demonstrated by Zinn, the spatial distribution of old halo globulars appears to be flattened toward the Galactic plane, and therefore the old halo clusters are typically anti-correlated to the nearly orthogonal FLS stream. A scenario is postulated wherein the Galactic satellites of the FLS stream and the red HB, young halo globular clusters share a common origin in the accretion of a formerly larger, parent satellite galaxy or Searle & Zinn 'fragment.'

Majewski, Steven R.↗
DOE OSTI2013

The early development of neutron diffraction: science in the wings of the Manhattan Project

Early neutron diffraction experiments performed in 1944 using the first nuclear reactors are described. Although neutron diffraction was first observed using radioactive decay sources shortly after the discovery of the neutron, it was only with the availability of higher intensity neutron beams from the first nuclear reactors, constructed as part of the Manhattan Project, that systematic investigation of Bragg scattering became possible. Remarkably, at a time when the war effort was singularly focused on the development of the atomic bomb, groups working at Oak Ridge and Chicago carried out key measurements and recognized the future utility of neutron diffraction quite independent of its contributions to the measurement of nuclear cross sections. Ernest O. Wollan, Lyle B. Borst and Walter H. Zinn were all able to observe neutron diffraction in 1944 using the X-10 graphite reactor and the CP-3 heavy water reactor. Subsequent work by Wollan and Clifford G. Shull, who joined Wollan’s group at Oak Ridge in 1946, laid the foundations for widespread application of neutron diffraction as an important research tool.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1993

The Galactic bulge and halo

The relationship between the Galactic halo and bulge is discussed, with reference to early results from a survey for K giants in a field 2 kpc from the Galactic center and Zinn's (1992) data on globular-cluster kinematics. The data are currently too meager to decide whether the inner halo shades gradually into the bulge, although there are some interesting kinematical similarities between bulge stars and Zinn's Old Halo clusters in the inner Galaxy. Useful observations that would help decide this matter are also discussed.

Morrison, Heather L.↗
NASA NTRS1988

Integrated-light spectroscopy of globular clusters at the infrared Ca II lines

Integrated-light spectroscopy has been obtained for 27 globular clusters at the Ca II IR triplet. Line strengths and radial velocities have been measured from the spectra. For the well-studied clusters in the sample, the strength of the Ca II lines is very well correlated with previous metallicity estimates. Thus, the triplet is useful as a metallicity indicator in globular cluster integrated-light spectra. The greatly reduced effect of interstellar extinction at these wavelengths (compared to the blue region of the spectrum) has permitted observations of some of the most heavily reddened clusters in the Galaxy. For several such clusters, the Ca II triplet metallicities are in poor agreement with metallicity estimates from IR photometry by Malkan (1981). The strength of an interstellar band at 8621A has been used to estimate the amount of extinction towards these clusters. Using the new metallicity and radial-velocity data, the metallicity distribution, kinematics, and spatial distribution of the disk globular cluster system have been analyzed. Results very similar to those of Zinn (1985) have been found. The relation of the disk globulars to the stellar thick disk is discussed.

Armandroff, Taft E.↗
NASA NTRS1994

The horizontal-branch stars in globular clusters. 2: The second parameter phenomenon

Using synthetic horizontal-branch models, we have investigated the origin of the systematic variation in horizontal-branch (HB) morphology with galactocentric distance (R(sub G)) among globular clusters. The variations in He abundance, CNO abundance, and core mass required separately to explain this effect are inconsistent with either the observed properties of the RR Lyrae variables or the observed main-sequence turnoffs in the clusters. There is also no clear evidence that the trend with R(sub G) is related to the central concentrations, central densities, or absolute magnitudes of the clusters. The variations in cluster age required to explain this effect are not in conflict with any observations. A detailed comparison of our synthetic HB calculations with pairs of clusters of very different HB morphology but similar (Fe/H) reveals reasonably good agreement between the age differences inferred from HB morphology and the main-sequence turnoff. The major source of uncertainty is the need for ad hoc hypotheses in the modeling of the HB morphologies of a few peculiar clusters (e.g., NGC 6752). Nonetheless, there is firm evidence for age variations of several gigayears (as much as approximately 5 Gyr) among the halo globular clusters. Our results support the hypothesis of Searle & Zinn that the inner halo is more uniform in age and is older in the mean than the outer halo, and we estimate this difference to be approximately 2 Gyr.

Lee, Young-Wook↗
DOE OSTI2012

The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects

We study the dynamics of four dimensional gauge theories with adjoint fermions for all gauge groups, both in perturbation theory and non-perturbatively, by using circle compactification with periodic boundary conditions for the fermions. There are new gauge phenomena. We show that, to all orders in perturbation theory, many gauge groups are Higgsed by the gauge holonomy around the circle to a product of both abelian and nonabelian gauge group factors. Non-perturbatively there are monopole-instantons with fermion zero modes and two types of monopole-anti-monopole molecules, called bions. One type are magnetic bions which carry net magnetic charge and induce a mass gap for gauge fluctuations. Another type are neutral bions which are magnetically neutral, and their understanding requires a generalization of multi-instanton techniques in quantum mechanics — which we refer to as the Bogomolny-Zinn-Justin (BZJ) prescription — to compactified field theory. The BZJ prescription applied to bion-anti-bion topological molecules predicts a singularity on the positive real axis of the Borel plane (i.e., a divergence from summing large orders in peturbation theory) which is of order N times closer to the origin than the leading 4-d BPST instanton-anti-instanton singularity, where N is the rank of the gauge group. The position of the bion-anti-bion singularity is thus qualitatively similar to that of the 4-d IR renormalon singularity, and we conjecture that they are continuously related as the compactification radius is changed. By making use of transseries and Écalle’s resurgence theory we argue that a non-perturbative continuum definition of a class of field theories which admit semi-classical expansions may be possible.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

Renormalization group method based on the ionization energy theory

Proofs are developed to explicitly show that the ionization energy theory is a renormalized theory, which mathematically exactly satisfies the renormalization group formalisms developed by Gell-Mann-Low, Shankar and Zinn-Justin. However, the cutoff parameter for the ionization energy theory relies on the energy-level spacing, instead of lattice point spacing in k-space. Subsequently, we apply the earlier proofs to prove that the mathematical structure of the ionization-energy dressed electron-electron screened Coulomb potential is exactly the same as the ionization-energy dressed electron-phonon interaction potential. The latter proof is proven by means of the second-order time-independent perturbation theory with the heavier effective mass condition, as required by the electron-electron screened Coulomb potential. The outcome of this proof is that we can derive the heat capacity and the Debye frequency as a function of ionization energy, which can be applied in strongly correlated matter and nanostructures.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Continuous conditional generative adversarial networks for data-driven solutions of poroelasticity with heterogeneous material properties

Machine learning-based data-driven modeling can allow computationally efficient time-dependent solutions of PDEs, such as those that describe subsurface multiphysical problems. In this work, our previous approach (Kadeethum et al., 2021d) of conditional generative adversarial networks (cGAN) developed for the solution of steady-state problems involving highly heterogeneous material properties is extended to time-dependent problems by adopting the concept of continuous cGAN (CcGAN). The CcGAN that can condition continuous variables is developed to incorporate the time domain through either element-wise addition or conditional batch normalization. Moreover, this framework can handle training data that contain different timestamps and then predict timestamps that do not exist in the training data. As a numerical example, the transient response of the coupled poroelastic process is studied in two different permeability fields: Zinn & Harvey transformation and a bimodal transformation. The proposed CcGAN uses heterogeneous permeability fields as input parameters while pressure and displacement fields over time are model output. Our results show that the model provides sufficient accuracy with computational speed-up. This robust framework will enable us to perform real-time reservoir management and robust uncertainty quantification in poroelastic problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

A NEW CENSUS OF THE VARIABLE STAR POPULATION IN THE GLOBULAR CLUSTER NGC 2419

We present B, V, and I CCD light curves for 101 variable stars belonging to the globular cluster NGC 2419, 60 of which are new discoveries, based on data sets obtained at the Telescopio Nazionale Galileo, the Subaru telescope, and the Hubble Space Telescope. The sample includes 75 RR Lyrae stars (38 RRab, 36 RRc, and one RRd), one Population II Cepheid, 12 SX Phoenicis variables, two {delta} Scuti stars, three binary systems, five long-period variables, and three variables of uncertain classification. The pulsation properties of the RR Lyrae variables are close to those of Oosterhoff type II clusters, consistent with the low metal abundance and the cluster horizontal branch morphology, disfavoring (but not totally ruling out) an extragalactic hypothesis for the origin of NGC 2419. The observed properties of RR Lyrae and SX Phoenicis stars are used to estimate the cluster reddening and distance, using a number of different methods. Our final value is {mu}{sub 0} (NGC 2419) = 19.71 {+-} 0.08 mag (D = 87.5 {+-} 3.3 kpc), with E(B - V) = 0.08 {+-} 0.01 mag, [Fe/H] = -2.1 dex on the Zinn and West metallicity scale, and a value of M{sub V} that sets {mu}{sub 0} (LMC) = 18.52 mag. This value is in good agreement with the most recent literature estimates of the distance to NGC 2419.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

METALLICITY DISTRIBUTION FUNCTIONS OF THE OLD POPULATIONS OF THE MAGELLANIC CLOUDS FROM RR Lyrae STARS

We present the first metallicity distribution functions of the old field populations in the Magellanic Clouds (MCs). Our metallicities are based on the Fourier decomposition of Type ab RR Lyrae light curves from the Optical Gravitational Lensing Experiment. On the metallicity scale of Zinn and West, we find a mean metallicity of [Fe/H] = -1.50 {+-} 0.24 dex based on 16,776 RR Lyrae stars in the Large Magellanic Cloud (LMC). For the Small Magellanic Cloud (SMC) we obtain -1.70 {+-} 0.27 dex based on 1831 RR Lyrae stars. These uncertainties represent the intrinsic spread in the population rather than the standard deviation of the mean. Our results are in good agreement with the few existing spectroscopic metallicity determinations for LMC RR Lyrae stars from the literature. For both the LMC and the SMC the metallicity spread exceeds 1 dex in [Fe/H]. The distribution of metallicities in both Clouds is very uniform, and no significant metallicity gradient is detectable. We also do not find any pronounced populations of extremely metal-poor RR Lyrae candidates with metallicities well below -2 dex, although we need to caution that the photometric method used may overestimate the metallicities of metal-deficient stars. Moreover, because of stellar evolutionary effects one does not expect to observe many RR Lyrae stars among very metal-poor horizontal branch stars. We suggest that the MCs experienced fairly rapid and efficient early enrichment involving pre-enriched gas as well as possibly gas infall, while metal loss through outflows does not seem to have played a significant role. Moreover, we suggest that the differences in the metallicities of the old population of LMC and SMC make an origin from a single, common progenitor unlikely, unless the separation happened very early on.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

THE GLOBULAR CLUSTER NGC 6402 (M14). I. A NEW BV COLOR-MAGNITUDE DIAGRAM

We present BV photometry of the Galactic globular cluster NGC 6402 (M14), based on 65 V frames and 67 B frames, reaching two magnitudes below the turnoff level. This represents, to the best of our knowledge, the deepest color-magnitude diagram (CMD) of NGC 6402 available in the literature. Statistical decontamination of field stars as well as differential reddening corrections are performed in order to derive a precise ridgeline and hence physical parameters of the cluster. We discuss previous attempts at deriving a reddening value for the cluster, and argue in favor of a value E(B - V) = 0.57 {+-} 0.02, which is significantly higher than indicated by either the Burstein and Heiles or Schlegel et al. (corrected according to Bonifacio et al.) interstellar dust maps. Differential reddening across the face of the cluster, which we find to be present at the level of {Delta}E(B - V) Almost-Equal-To 0.17 mag, is taken into account in our analysis. We measure several metallicity indicators based on the position of the red giant branch (RGB) in the cluster CMD. These give a metallicity of [Fe/H] = -1.38 {+-} 0.07 on the Zinn and West scale and [Fe/H] = -1.28 {+-} 0.08 on the new Carretta et al. (UVES) scale. We also provide measurements of other important photometric parameters for this cluster, including the position of the RGB luminosity function ''bump'' and the horizontal branch morphology. We compare the NGC 6402 ridgeline with that of NGC 5904 (M5) derived by Sandquist et al., and find evidence that NGC 6402 and M5 have approximately the same age to within the uncertainties, although the possibility that M14 may be slightly older cannot be ruled out.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1992

The chronology of the formation of the Galaxy

Recent advances in our understanding of horizontal-branch (HB) stars and in precision CCD photometry make it possible to establish a chronology of the formation of the Galaxy from the fossil record. The Lee et al. HB evolutionary models and the inferred age-metallicity relation of the Galactic globular-cluster system are now strengthened by many pieces of supporting evidence. This provides valuable information regarding the formation chronology of the halo and disk. Moreover, there is strong evidence from RR Lyrae stars that the radial variation in HB morphology observed in the halo continues to the very center of the Galaxy, which suggests that the formation of the bulge and halo was an inside-out process. These two crucial pieces of information are combined to extend the Searle and Zinn picture of halo formation to include the formation of the bulge and disk. The emerging picture is consistent with the idea that galaxies formed as clusters and mergers of many small gas-rich subsystems, rather than by the rapid collapse of single large protogalactic clouds.

Lee, Young-Wook↗
NASA NTRS1994

Absolute proper motions to B approximately 22.5: Evidence for kimematical substructure in halo field stars

Radial velocities have been obtained for six of nine stars identified on the basis of similar distances and common, extreme transverse velocities in the proper motion survey of Majewski (1992) as a candidate halo moving group at the north Galactic pole. These radial velocities correspond to velocities perpendicular to the Galactic plane which span the range -48 +/- 21 to -128 +/- 9 km/sec (but a smaller range, -48 +/- 21 to -86 +/- 19 km/sec, when only our own measurements are considered), significantly different than the expected distribution, with mean 0 km/sec, for a random sample of either halo or thick disk stars. The probability of picking such a set of radial velocities at random is less than 1%. Thus the radial velocity data support the hypothesis that these stars constitute part of a halo moving group or star stream at a distance of approximately 4-5 kpc above the Galactic plane. If real, this moving group is evidence for halo phase space substructure which may be the fossil remains of a destroyed globular cluster, Galactic satellite, or Searle & Zinn (1978) 'fragment.'

Majewski, Steven R.↗
NASA NTRS1994

The galactic globular cluster system

We explore correlations between various properties of Galactic globular clusters, using a database on 143 objects. Our goal is identify correlations and trends which can be used to test and constrain theoretical models of cluster formation and evolution. We use a set of 13 cluster parameters, 9 of which are independently measured. Several arguments suggest that the number of clusters still missing in the obscured regions of the Galaxy is of the order of 10, and thus the selection effects are probably not severe for our sample. Known clusters follow a power-law density distribution with a slope approximately -3.5 to -4, and an apparent core with a core radius approximately 1 kpc. Clusters show a large dynamical range in many of their properties, more so for the core parameters (which are presumably more affected by dynamical evolution) than for the half-light parameters. There are no good correlations with luminosity, although more luminous clusters tend to be more concentrated. When data are binned in luminosity, several trends emerge: more luminous clusters tend to have smaller and denser cores. We interpret this as a differential survival effect, with more massive clusters surviving longer and reaching more evolved dynamical states. Cluster core parameters and concentrations also correlate with the position in the Galaxy, with clusters closer to the Galactic center or plane being more concentrated and having smaller and denser cores. These trends are more pronounced for the fainter (less massive) clusters. This is in agreement with a picture where tidal shocks form disk or bulge passages accelerate dynamical evolution of clusters. Cluster metallicities do not correlate with any other parameter, including luminosity and velocity dispersion; the only detectable trend is with the position in the Galaxy, probably reflecting Zinn's disk-halo dichotomy. This suggests that globular clusters were not self-enriched systems. Velocity dispersions show excellent correlations with luminosity and surface brightness. Their origin is not well understood, but they may well reflect initial conditions of cluster formation, and perhaps even be used to probe the initial density perturbation spectrum on a approximately 10(exp 6) solar mass scale. Core radii and concentrations play a role of a 'second parameter' in these correlations. While a global manifold of cluster properties has a high statistical dimensionality (D greater than 4), a subset of structural, photometric, and dynamical parameters forms a statistically three-dimensional family, as expected from objects following King models; we propose to call this set of quantities the King Manifold. Some of the observed correlations may be usable as distance indicator relations for globular clusters.

Djorgovski, S.↗
NASA NTRS1998

Standard Giant Branches in the Washington Photometric System

We have obtained CCD photometry in the Washington system C, T(sub 1) filters for some 850,000 objects associated with 10 Galactic globular clusters and 2 old open clusters. These clusters have well-known metal abundances, spanning a metallicity range of 2.5 dex from [Fe/H] approx -2.25 to +0.25 at a spacing of approx. 0.2 dex. Two independent observations were obtained for each cluster and internal checks, as well as external comparisons with existing photoelectric photometry, indicate that the final colors and magnitudes have overall uncertainties of 0.03 mag. Analogous to the method employed by Da Costa and Armandroff for V, I photometry , we then proceed to construct standard ((M(sub T),(C - T(sub 1))(sub 0)) giant branches for these clusters adopting the Lee et distance scale, using some 350 stars per globular cluster to define the giant branch. We then determine the metallicity sensitivity of the ((C - T(sub 1))(sub 0) color at a given M((sub T)(sub 1)) value. The Washington system technique is found to have three times the metallicity sensitivity of the V, I technique. At M((sub T)(sub 1)) = -2 (about a magnitude below the tip of the giant branch, roughly equivalent to M(sub I) = -3), the giant branches of 47 Tuc and M15 are separated by 1.16 magnitudes in (V - l)(sub 0) and only 0.38 magnitudes in (V - I)(sub 0). Thus, for a given photometric accuracy, metallicities can be determined three times more precisely with the Washington technique. We find a linear relationship between (C - T(sub l)(sub 0) (at M(sub T)(sub 1) = -2) and metallicity exists over the full metallicity range, with an rms of only 0.04 dex. We also derive metallicity calibrations for M(sub T)(sub 1) = -2.5 and -1.5, as well as for two other metallicity scales. The Washington technique retains almost the same metallicity sensitivity at faint magnitudes , and indeed the standard giant branches are still well separated even below the horizontal branch. The photometry is used to set upper limits in the range 0.03 - 0.09 dex for any intrinsic metallicity dispersion in the calibrating clusters. The calibrations are applicable to objects with ages approx. greater than 5 Gyr - any age effects are small or negligible for such objects. This new technique is found to have many advantages over the old two-color diagram technique for deriving metallicities from Washington photometry. In addition to only requiring 2 filters instead of 3 or 4, the new technique is generally much less sensitive to reddening and photometric errors, and the metallicity sensitivity is many times higher. The new technique is especially advantageous for metal-poor objects. The five metal-poor clusters determined by Geisler et al., using the old technique, to be much more metal-poor than previous indications, yield metallicities using the new technique which are in excellent agreement with the Zinn scale.

Geisler, Doug↗
NASA NTRS2003

Progress in Developing a New Field-theoretical Crossover Equation-of-State

A new field-theoretical crossover equation-of-state model is being developed. This model of a liquid-gas critical point provides a bridge between the asymptotic equation-of-state behavior close to the transition, obtained by the Guida and Zinn-Justin parametric model [J. Phys. A: Math. Gen. 31, 8103 (1998)], and the expected mean field behavior farther away. The crossover is based on the beta function for the renormalized fourth-order coupling constant and incorporates the correct crossover exponents and critical amplitude ratios in both regimes. A crossover model is now being developed that is consistent with predictions along the critical isochore and along the coexistence curve of the minimal subtraction renormalization approach developed by Dohm and co-workers and recently applied to the O(1) universality class [Phys. Rev. E, 67, 021106 (2003)]. Experimental measurements of the heat capacity at constant volume, isothermal susceptibility, and coexistence curve near the He-3 critical point are being compared to the predictions of this model. The results of these comparisons will be presented.

Rudnick, Joseph↗
NASA NTRS2014

Mean Flow Augmented Acoustics in Rocket Systems

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

Fischbach, Sean R.↗