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At least 109 records · Page 6

On damping mechanisms in beams

A partial differential equation model of a cantilevered beam with a tip mass at its free end is used to study damping in a composite. Four separate damping mechanisms consisting of air damping, strain rate damping, spatial hysteresis and time hysteresis are considered experimentally. Dynamic tests were performed to produce time histories. The time history data is then used along with an approximate model to form a sequence of least squares problems. The solution of the least squares problem yields the estimated damping coefficients. The resulting experimentally determined analytical model is compared with the time histories via numerical simulation of the dynamic response. The procedure suggested here is compared with a standard modal damping ratio model commonly used in experimental modal analysis.

Banks, H. T.↗

On damping mechanisms in beams

A partial differential equation model of a cantilevered beam with a tip mass at its free end is used to study damping in a composite. Four separate damping mechanisms consisting of air damping, strain rate damping, spatial hysteresis and time hysteresis are considered experimentally. Dynamic tests were performed to produce time histories. The time history data is then used along with an approximate model to form a sequence of least squares problems. The solution of the least squares problem yields the estimated damping coefficients. The resulting experimentally determined analytical model is compared with the time histories via numerical simulation of the dynamic response. The procedure suggested here is compared with a standard modal damping ratio model commonly used in experimental modal analysis.

Banks, H. T.↗

A least-squares finite element method for 3D incompressible Navier-Stokes equations

The least-squares finite element method (LSFEM) based on the velocity-pressure-vorticity formulation is applied to three-dimensional steady incompressible Navier-Stokes problems. This method can accommodate equal-order interpolations, and results in symmetric, positive definite algebraic system. An additional compatibility equation, i.e., the divergence of vorticity vector should be zero, is included to make the first-order system elliptic. The Newton's method is employed to linearize the partial differential equations, the LSFEM is used to obtain discretized equations, and the system of algebraic equations is solved using the Jacobi preconditioned conjugate gradient method which avoids formation of either element or global matrices (matrix-free) to achieve high efficiency. The flow in a half of 3D cubic cavity is calculated at Re = 100, 400, and 1,000 with 50 x 52 x 25 trilinear elements. The Taylor-Gortler-like vortices are observed at Re = 1,000.

Jiang, Bo-Nan↗

Comparative Studies for the Sodium and Potassium Atmospheres of the Moon and Mercury

A summary discussion of recent sodium and potassium observations for the atmospheres of the Moon and Mercury is presented with primary emphasis on new full-disk images that have become available for sodium. For the sodium atmosphere, image observations for both the Moon and Mercury are fitted with model calculations (1) that have the same source speed distribution, one recently measured for electron-stimulated desorption and thought to apply equally well to photon-stimulated desorption, (2) that have similar average surface sodium fluxes, about 2.8 x 10(exp 5) to 8.9 x 10(exp 5) atoms cm(exp -2)s(exp -1) for the Moon and approximately 3.5 x 10(exp 5) to 1.4 x 10(exp 6) atoms cm(exp -2)s(exp -1) for Mercury, but (3) that have very different distributions for the source surface area. For the Moon, a sunlit hemispherical surface source of between approximately 5.3 x 10(exp 22) to 1.2 x 10(exp 23) atoms/s is required with a spatial dependence at least as sharp as the square of the cosine of the solar zenith angle. For Mercury, a time dependent source that varies from 1.5 x 10(exp 22) to 5.8 x l0(exp 22) atoms/s is required which is confined to a small surface area located at, but asymmetrically distributed about, the subsolar point. The nature of the Mercury source suggest that the planetary magnetopause near the subsolar point acts as a time varying and partially protective shield through which charged particles may pass to interact with and liberate gas from the planetary surface. Suggested directions for future research activities are discussed.

Smyth, William H.↗

A linear aerodynamic analysis for unsteady transonic cascades

A potential flow analysis to predict unsteady airloads produced by the vibrations of turbomachinery blades operating at transonic Mach numbers is presented. The unsteady aerodynamic model includes the effects of blade geometry, finite mean pressure variation across the blade row, high frequency blade motion, and shock motion within the framework of a linearized, frequency domain formulation. The unsteady equations are solved implicit, least squares, finite difference approximation which is applicable on arbitrary grids. A numerical solution for the entire unsteady field is determined by matching a solution determined on a rectilinear type cascade mesh, which covers an extended blade passage region, to a solution determined on a detailed polar type local mesh, which covers and extends well beyond the supersonic region(s) adjacent to a blade surface. Cascades of double circular arc and flat plate blades demonstrate the unsteady analysis, and partially illustrate the effects of blade geometry, inlet Mach number, blade vibration frequency and shock motion on unsteady response.

Verdon, J. M.↗

A Wind-Driven Snow Redistribution Module for Alpine3d V3.3.0: Adaptations Designed for Downscaling Ice Sheet Surface Mass Balance

Ice sheets gain mass via snow accumulation at the ice sheet surface, which is the primary component of surface mass balance. On the Antarctic ice sheet, winds redistribute snow resulting in surface mass balance that is variable in both space and time. Representing wind-driven snow redistribution processes in models is critical for local assessments of surface mass balance, repeat altimetry studies, and interpretation of ice core accumulation records. To this end, we have adapted Alpine3D, an existing distributed snow modeling framework, to downscale Antarctic surface mass balance to horizontal resolutions up to 1 km. In particular, we have introduced a new two-dimensional advection-based wind-driven snow redistribution module that is driven by an offline coupling between WindNinja, a wind downscaling model, and Alpine3D. We then show that large accumulation variability can be at least partially explained by terrain-induced wind speed variations which subsequently redistribute snow around rolling topography. By comparing Alpine3D to airborne-derived snow accumulation measurements within a testing domain over Pine Island Glacier in West Antarctica, we demonstrate that our Alpine3D downscaling approach improves surface mass balance estimates when compared to MERRA-2, a global atmospheric reanalysis which we use as atmospheric forcing. In particular, when compared to MERRA-2, Alpine3D reduces simulated surface mass balance root mean squared error by 23.4 mm w.e.yr−1 (13%) and increases variance explained by 24%. Despite these improvements, Alpine3D still underestimates observed accumulation variability, thus providing an opportunity for future model improvement.

Eric Keenan↗

Parameter identification in distributed systems

This paper describes a method for the identification of the parameters entering into the equations of motion of distributed systems. Because the motion of distributed systems is described in terms of partial differential equations, these parameters are in general continuous functions of the spatial variables. For vibrating systems, these parameters ordinarily represent the mass, stiffness and damping distributions. In this paper, these distributions are expanded in terms of finite series of known functions of the spatial variables multiplied by undetermined coefficients. It is assumed that the nature of the equations of motion is known and that a limited number of eigenvalues and eigenfunctions is identified in advance. Use is then made of the least squares method, in conjunction with the eigenfunctions' orthogonality, to compute the undetermined coefficients, thus identifying the system distributed parameters. A method for the identification of the eigensolution is also presented. The procedure for the identification of the eigensolution and of the system parameters is demonstrated via a numerical example.

Baruh, H.↗

Well-posedness of one-way wave equations and absorbing boundary conditions

A one-way wave equation is a partial differential which, in some approximate sense, behaves like the wave equation in one direction but permits no propagation in the opposite one. The construction of such equations can be reduced to the approximation of the square root of (1-s sup 2) on -1, 1 by a rational function r(s) = p sub m (s)/q sub n(s). Those rational functions r for which the corresponding one-way wave equation is well-posed are characterized both as a partial differential equation and as an absorbing boundary condition for the wave equation. We find that if r(s) interpolates the square root of (1-s sup 2) at sufficiently many points in (-1,1), then well-posedness is assured. It follows that absorbing boundary conditions based on Pade approximation are well-posed if and only if (m, n) lies in one of two distinct diagonals in the Pade table, the two proposed by Engquist and Majda. Analogous results also hold for one-way wave equations derived from Chebyshev or least-squares approximation.

Trefethen, L. N.↗

Simultaneous quaternion estimation (QUEST) and bias determination

Tests of a new method for the simultaneous estimation of spacecraft attitude and sensor biases, based on a quaternion estimation algorithm minimizing Wahba's loss function are presented. The new method is compared with a conventional batch least-squares differential correction algorithm. The estimates are based on data from strapdown gyros and star trackers, simulated with varying levels of Gaussian noise for both inertially-fixed and Earth-pointing reference attitudes. Both algorithms solve for the spacecraft attitude and the gyro drift rate biases. They converge to the same estimates at the same rate for inertially-fixed attitude, but the new algorithm converges more slowly than the differential correction for Earth-pointing attitude. The slower convergence of the new method for non-zero attitude rates is believed to be due to the use of an inadequate approximation for a partial derivative matrix. The new method requires about twice the computational effort of the differential correction. Improving the approximation for the partial derivative matrix in the new method is expected to improve its convergence at the cost of increased computational effort.

Markley, F. Landis↗

Archaean megacrystic plagioclase units and the tectonic setting of greenstones

Large (up to 20 cm), equidimensional, commonly euhedral, plagioclase megacrysts of highly calcic composition (An sub 80-90) occur commonly in all Archean cratons in one or more of three distinct associations: (1) as cumulate crystal segregations of anorthosite or as megacrysts in basaltic dikes, sills, and flows in greenstone belts that vary in metamorphic grade from greenschist to granulite. Throughout 100's of thousands of square kilometers of northwestern Ontario and Manitoba the plagioclase megacrysts occur in pillowed and massive flows, sills, dikes, large inclusions in dikes, and intrusive anorthositic complexes with areas of up to a few 100 sq km and spanning a period of at least 100 m.y. in the 2.7 to 2.8 b.y. time frame; (2) as basaltic dike swarms in stable cratonic areas forming parallel to subparallel patterns over hundreds of thousands of square kilometers intruding both granitic gneisses and supracrustal belts including greenstones. These swams include the Ameralik-Saglek system at 3.1 to 3.4 b.y., the Matachewan system at 2.5 to 2.6 b.y., and the Beartooth-Bighorn system at 2.2 to 2.3 b.y.; and, (3) as anorthositic complexes associated with marbles and quartzites (Sittampundi, India and Messina, South Africa) in granulite grade terrains. Initial attempts to correlate tectonic settings of similar modern crystbearing units with their Archean counterparts were only partially successful.

Phinney, W. C.↗

Basic research for the geodynamics program

The mathematical models of space very long base interferometry (VLBI) observables suitable for least squares covariance analysis were derived and estimatability problems inherent in the space VLBI system were explored, including a detailed rank defect analysis and sensitivity analysis. An important aim is to carry out a comparative analysis of the mathematical models of the ground-based VLBI and space VLBI observables in order to describe the background in detail. Computer programs were developed in order to check the relations, assess errors, and analyze sensitivity. In order to investigate the estimatability of different geodetic and geodynamic parameters from the space VLBI observables, the mathematical models for time delay and time delay rate observables of space VLBI were analytically derived along with the partial derivatives with respect to the parameters. Rank defect analysis was carried out both by analytical and numerical testing of linear dependencies between the columns of the normal matrix thus formed. Definite conclusions were formed about the rank defects in the system.

Source record↗

Surface fitting three-dimensional bodies

The geometry of general three-dimensional bodies is generated from coordinates of points in several cross sections. Since these points may not be smooth, they are divided into segments and general conic sections are curve fit in a least-squares sense to each segment of a cross section. The conic sections are then blended in the longitudinal direction by fitting parametric cubic-spline curves through coordinate points which define the conic sections in the cross-sectional planes. Both the cross-sectional and longitudinal curves may be modified by specifying particular segments as straight lines and slopes at selected points. Slopes may be continuous or discontinuous and finite or infinite. After a satisfactory surface fit has been obtained, cards may be punched with the data necessary to form a geometry subroutine package for use in other computer programs. At any position on the body, coordinates, slopes and second partial derivatives are calculated. The method is applied to a blunted 70 deg delta wing, and it was found to generate the geometry very well.

Dejarnette, F. R.↗

Large-scale computation of incompressible viscous flow by least-squares finite element method

The least-squares finite element method (LSFEM) based on the velocity-pressure-vorticity formulation is applied to large-scale/three-dimensional steady incompressible Navier-Stokes problems. This method can accommodate equal-order interpolations and results in symmetric, positive definite algebraic system which can be solved effectively by simple iterative methods. The first-order velocity-Bernoulli function-vorticity formulation for incompressible viscous flows is also tested. For three-dimensional cases, an additional compatibility equation, i.e., the divergence of the vorticity vector should be zero, is included to make the first-order system elliptic. The simple substitution of the Newton's method is employed to linearize the partial differential equations, the LSFEM is used to obtain discretized equations, and the system of algebraic equations is solved using the Jacobi preconditioned conjugate gradient method which avoids formation of either element or global matrices (matrix-free) to achieve high efficiency. To show the validity of this scheme for large-scale computation, we give numerical results for 2D driven cavity problem at Re = 10000 with 408 x 400 bilinear elements. The flow in a 3D cavity is calculated at Re = 100, 400, and 1,000 with 50 x 50 x 50 trilinear elements. The Taylor-Goertler-like vortices are observed for Re = 1,000.

Jiang, Bo-Nan↗

A New Fitting Procedure for the Blended He I 1083 nm Multiplet

The He I 1083 nm multiplet is a powerful tool for observing the outer solar atmosphere but is difficult to analyze because the lines are weak, highly variable, and spectrally blended, both internally and with other neighboring solar and telluric lines. After separation from nearby spectral features, two components of the He I multiplet are resolved. Fitting these lines with two unconstrained Gaussian profiles always gives a ratio of major to minor component of less than half the value which would be expected for optically thin lines. One possibility for explaining the discrepancy between the weakness of the lines and the ratio of the spectral components is to assume that the line formation regions are concentrated in laterally unresolved, optically thick structures with small filling factor. However, we present here a least-squares fitting technique using cubic splines with fixed breakpoints with the constraint that the blend is the sum of three identically shaped profiles shifted in wavelength according to the atomic structure of the blend and weighted by the corresponding statistics weights, in agreement with optically thin line formation. The basis functions for the fitting procedure have no built-in spectral symmetry or shape. The resulting underlying profiles tend to be asymmetric with excess absorption to the blue, consistent with formation by "hot" and "cool" spatial elements within the observed volume, with the hotter regions having differential motion toward the observer. The results agree well with NASA/XSO Spectromagnetograph observations in quiet sun and coronal holes. Partial funding of this research was provided through the NASA Sun-Earth Connection SR&T program.

Jones, H. P.↗

Carbon Monoxide Accumulation in the Extravehicular Mobility Unit

Introduction: Life support technology in large closed systems like submarines and space stations catalyzes carbon monoxide (CO) to carbon dioxide, which is easily removed. However, in a small system like the Extravehicular Mobility Unit (EMU), spacesuit, CO from exogenous (contaminated oxygen (O (sub 2) supply) and endogenous (human metabolism) sources will accumulate in the free suit volume. The free volume becomes a sink for CO that is rebreathed by the astronaut. The accumulation through time depends on many variables: the amount absorbed by the astronaut, the amount produced by the astronaut (between 0.28 and 0.34 moles per hour per kilogram)[1], the amount that enters the suit from contaminated O (sub 2), the amount removed through suit leak, the free volume of the suit, and the O (sub 2) partial pressure[2], just to list a few. Contamination of the EMU O (sub 2) supply with no greater than 1 part per million CO was the motivation for empirical measurements from CO pulse oximetry (SpCO) as well as mathematical modeling of the EMU as a rebreather for CO. Methods: We developed a first-order differential mixing equation as well as an iterative method to compute CO accumulation in the EMU. Pre-post measurements of SpCO (Rad-57, Masimo Corporation) from EMU ground training and on-orbit extravehicular activities (EVAs) were collected. Results: Initial modeling without consideration of the astronaut as a sink but only the source of CO showed that after 8 hours breathing 100 percent O (sub 2) with a 10 milliliter per minute (760 millimeters Hg at 21 degrees Centigrade standard) suit leak, an endogenous production rate of 0.23 moles per hour per kilogram for a 70 kilogram person with 42 liters (1.5 cubic feet) free suit volume resulted in a peak CO partial pressure (pCO) of 0.047 millimeters Hg at 4.3 pounds per square inch absolute (222 millimeters Hg). Preliminary results based on a 2008 model[3] with consideration of the astronaut as a sink and source of CO suggests that most of the rebreathed CO stays bound to hemoglobin and myoglobin and; therefore, pCO only increased to 0.002 millimeters Hg in the EMU. Hemoglobin saturation after 8 hours was an insignificant 0.4 percent compared to about 4 percent for cigarette smokers in the general population. This preliminary modeling result supplements 11 pre-post index finger SpCO measurements from EMU ground training (mean 0.5 percent versus 1 percent, probability equal to 0.41 from paired t-test) and 10 on-orbit pre-post EVAs (mean 1.5 percent versus 1.1 percent, probability equal to 0.17 from paired t-test) that showed no consistent increase, at least no increase outside the accuracy of the oximeter (1 percent display resolution with plus or minus 3 percent Standard Deviation). Discussion: Simulations continue, but a preliminary conclusion is that rebreathing endogenous CO accumulating in the EMU is not a serious medical issue during EVA. The absence of CO poisoning signs or symptoms following hundreds of EVAs is also good empirical evidence that corroborates the limited SpCO measurements and preliminary modeling results.

Conkin, J.↗

The NuSTAR Extragalactic Survey: A First Sensitive Look at the High-Energy Cosmic X-Ray Background Population

We report on the first 10 identifications of sources serendipitously detected by the Nuclear Spectroscopic Telescope Array (NuSTAR) to provide the first sensitive census of the cosmic X-ray background source population at approximately greater than 10 keV. We find that these NuSTAR-detected sources are approximately 100 times fainter than those previously detected at approximately greater than 10 keV and have a broad range in redshift and luminosity (z = 0.020-2.923 and L(sub 10-40 keV) approximately equals 4 × 10(exp 41) - 5 × 10(exp 45) erg per second; the median redshift and luminosity are z approximately equal to 0.7 and L(sub 10-40 keV) approximately equal to 3 × 10(exp 44) erg per second, respectively. We characterize these sources on the basis of broad-band approximately equal to 0.5 - 32 keV spectroscopy, optical spectroscopy, and broad-band ultraviolet-to-mid-infrared spectral energy distribution analyses. We find that the dominant source population is quasars with L(sub 10-40 keV) greater than 10(exp 44) erg per second, of which approximately 50% are obscured with N(sub H) approximately greater than 10(exp 22) per square centimeters. However, none of the 10 NuSTAR sources are Compton thick (N(sub H) approximately greater than 10(exp 24) per square centimeters) and we place a 90% confidence upper limit on the fraction of Compton-thick quasars (L(sub 10-40 keV) greater than 10(exp 44) erg per second) selected at approximately greater than 10 keV of approximately less than 33% over the redshift range z = 0.5 - 1.1. We jointly fitted the rest-frame approximately equal to 10-40 keV data for all of the non-beamed sources with L(sub 10-40 keV) greater than 10(exp 43) erg per second to constrain the average strength of reflection; we find R less than 1.4 for gamma = 1.8, broadly consistent with that found for local active galactic nuclei (AGNs) observed at approximately greater than 10 keV. We also constrain the host-galaxy masses and find a median stellar mass of approximately 10(exp 11) solar mass, a factor approximately 5 times higher than the median stellar mass of nearby high-energy selected AGNs, which may be at least partially driven by the order of magnitude higher X-ray luminosities of the NuSTAR sources. Within the low source-statistic limitations of our study, our results suggest that the overall properties of the NuSTAR sources are broadly similar to those of nearby high-energy selected AGNs but scaled up in luminosity and mass.

Spectroscopic↗

Investigation of Magmatic Activities on Early Mars Using Igneous Mineral Chemistry in Gale Crater, Mars

One objective of rover missions is exploring the geological context of the surroundings. Over the years, igneous petrology and sedimentology have been disconnected, the first investigating magmatic processes and volcanic activities, and the second seeking environmental conditions in the past and assessing the habitability of the planet. Although different, one is related to the other: igneous rocks are altered and broken down, leading to the formation of sedimentary rocks, which can in turn be used to back out the nature of their magmatic source. The Curiosity rover that landed in the 3.7 Gyr old impact crater Gale is traveling through sedimentary rocks. About fifty float rocks have been observed, and several of them with ambiguous texture and composition have been classified as igneous or sedimentary depending on studies such as Jake_M. The composition of several unambiguous igneous rocks has been analyzed [4- 6] but their heterogeneity at a larger instrumental (measurement size < 2 cm) scale prevents the measurement of a bulk composition as performed on Earth. An original approach avoiding these two last issues is to consider igneous mineral chemistry analyzed within igneous and sedimentary rocks to assess magmatic processes that could have formed them. Most Curiosity data are used to explore ancient environmental conditions, and a significant number of compositional analyses are under-explored for constraining magmatic activities. We will present how we can make use of sedimentary data for investigating igneous processes in the vicinity of Gale crater. Geological Context: We focus on the first 750 martian days, corresponding to measurements in a coherent lacustrine sedimentary unit called Bradbury, because all sedimentary rocks were sourced from the same watershed and appear to have a consistent source with minimal alteration [2-3]. Igneous detrital minerals including feldspar and pyroxene, are observed in sedimentary rocks. Monte Carlo models showed that minimal cation loss is observed based on the composition of all Bradbury rocks, implying negligible weathering [3]. Although clay minerals are detected in few rocks [7], chemical compositions of rocks can be explained by a mixture of primary igneous minerals [3]. Variation of composition within Bradbury rocks can be explained by mineral sorting and one distinct source component. While a common magmatic source is suggested, Bradbury sediments likely come from several volcanic eruptions from a single magmatic chamber [9- 10]. The occurrence of alkali minerals like sanidine and K-rich rocks throughout Bradbury supports the presence of a potassic component, likely trachytic, while plagioclase and a mafic composition suggest a basaltic component [8-9]. Instruments: Mineral chemistry can be estimated by three instruments onboard Curiosity. The CheMin instrument enables detection of mineral assemblages using X-ray diffraction (XRD). Using Rietveld refinement, each mineral is identified according to their 1D XRD pattern [11]. Note that distinction between pyroxene minerals is challenging with the CheMin instrument due to overlapping peaks on XRD patterns and low angular resolution of the instrument [12]. Then, using least square regression and optimization algorithms based on unit-cell parameters, mineral chemistry has been estimated by [11]. Plagioclase composition has been estimated using the NaAlSi3O8- CaAl2Si2O8 system and alkali feldspar is based on the NaAlSi3O8-KAlSi3O8 system (stars in Fig.1). Two mudstone samples (John Klein and Cumberland) and one sandstone sample (Windjana) were analyzed by CheMin at Yellowknife Bay and Kimberley, respectively. Figure 1. Ternary diagrams of feldspars (top) and pyroxene (bottom) quadrilateral. Stars correspond to CheMin composition and the gray patches to ChemCam composition. The colored dots are the composition of feldspar and pyroxene that crystallized during fractional crystallization at FMQ+1 of a melt extracted at distinct melting degree during the adiabatic ascent of a primitive mantle composition, without any water (left panels) and with 0.5 wt.% of water (right panels) at distinct pressure. The ChemCam instrument enables the analysis of the chemical compositions of rocks at hundreds of micrometer scale (350-550 μm) using laser induced breakdown spectroscopy (LIBS), which may provide the composition of minerals when they are larger than the beam spot (>550 μm) [13]. Within >5000 LIBS points, we performed a typical stoichiometric filtering allowing us to distinguish 56 feldspar and 10 pyroxene mineral compositions (grey patches in Fig. 1). Finally, the Alpha Particle X-ray Spectrometer (APXS) analyzes the composition of rocks with a 1.6 cm diameter spot size. Monte Carlo mass balance modeling allowed [3] to decipher a feldspar range varying between An30 and An40 (Fig. 1). Discussion: Although there could be a more complex history and other ways to form the whole compositional range of igneous minerals analyzed within the Bradbury formation, we are presenting here simple magmatic pathways commonly occurring on Earth using the thermodynamical softwares pMELTS and rhyoliteMELTS [14]. The objective is to find reasonable igneous processes that produce minerals that parallel the compositions of feldspar and pyroxene analyzed by the Curiosity rover. As commonly observed for mid-ocean ridge basalts, the adiabatic ascent of a primitive mantle composition [15] partially melting at 2 GPa has been modeled, followed by the extraction of a liquid at distinct degrees of partial melting, which undergoes fractional crystallization at an oxygen fugacity +1 log unit above the fayalite-magnetite-quartz (FMQ) buffer within the crust (0.02-0.4 GPa) with H2O = 0- 0.5 wt. %. These latter conditions correspond to those recorded within igneous clasts from the Noachian martian breccia NWA 7034 and paired and within Gale igneous rocks (colored dots in Fig. 1) [16-17]. To check the reliability of these 2-step models, we also tested fractional crystallization at similar conditions (FMQ+1; P=0.02-0.4 GPa; H2O = 0-0.5 wt. %) of starting compositions corresponding to that of magmas with distinct melting degrees obtained from isobaric experiments at 2 GPa [18]. Mineral compositions obtained from both models are similar. As shown on Fig. 1, the whole range of observed feldspar compositions cannot be reproduced by fractionation of one magma only. Indeed, while alkali feldspar and Na-plagioclase likely crystallized from fractional crystallization of a low-degree melt (here <15%), plagioclase and pyroxene can only be formed by fractional crystallization of a higher degree melt (here >19%). The corresponding liquid descent lines are broadly in agreement with compositions estimated by ChemCam corresponding to float igneous rocks (Fig. 2) [4-6]. Figure 2. Silica versus alkali content. Lines show the liquid lines of descent from magmas with distinct degrees of melting. Gray patches represents the composition of Gale igneous rocks [4-6]. Trachytic to rhyolitic magmas crystallize alkali feldspar, and andesite to dacite magmas likely form plagioclase. Therefore, at least two starting magmas at distinct melting degrees, which could easily come from a single mantle source, are necessary to explain the whole compositional range of feldspar and pyroxene analyzed within Bradbury rocks. Conclusion: Because rocks from the Bradbury formation are likely originating from the same magmatic source with minimal weathering as supported by several studies using different approaches, igneous mineral chemistry analyzed by CheMin and ChemCam allows us to back out reasonable magmatic pathways that could have crystallized them. Fractional crystallization of at least two starting magmas originating from distinct melting degrees of a single mantle source can explain the whole range of feldspar and pyroxene composition. Both alkaline and sub-alkaline liquids can be produced, with compositions corresponding to those of the igneous rocks analyzed by ChemCam within the Bradbury formation, highlighting the complexity of Mars magmatism.

Payre, V.↗

Investigation of Navier-Stokes Code Verification and Design Optimization

With rapid progress made in employing computational techniques for various complex Navier-Stokes fluid flow problems, design optimization problems traditionally based on empirical formulations and experiments are now being addressed with the aid of computational fluid dynamics (CFD). To be able to carry out an effective CFD-based optimization study, it is essential that the uncertainty and appropriate confidence limits of the CFD solutions be quantified over the chosen design space. The present dissertation investigates the issues related to code verification, surrogate model-based optimization and sensitivity evaluation. For Navier-Stokes (NS) CFD code verification a least square extrapolation (LSE) method is assessed. This method projects numerically computed NS solutions from multiple, coarser base grids onto a freer grid and improves solution accuracy by minimizing the residual of the discretized NS equations over the projected grid. In this dissertation, the finite volume (FV) formulation is focused on. The interplay between the xi concepts and the outcome of LSE, and the effects of solution gradients and singularities, nonlinear physics, and coupling of flow variables on the effectiveness of LSE are investigated. A CFD-based design optimization of a single element liquid rocket injector is conducted with surrogate models developed using response surface methodology (RSM) based on CFD solutions. The computational model consists of the NS equations, finite rate chemistry, and the k-6 turbulence closure. With the aid of these surrogate models, sensitivity and trade-off analyses are carried out for the injector design whose geometry (hydrogen flow angle, hydrogen and oxygen flow areas and oxygen post tip thickness) is optimized to attain desirable goals in performance (combustion length) and life/survivability (the maximum temperatures on the oxidizer post tip and injector face and a combustion chamber wall temperature). A preliminary multi-objective optimization study is carried out using a geometric mean approach. Following this, sensitivity analyses with the aid of variance-based non-parametric approach and partial correlation coefficients are conducted using data available from surrogate models of the objectives and the multi-objective optima to identify the contribution of the design variables to the objective variability and to analyze the variability of the design variables and the objectives. In summary the present dissertation offers insight into an improved coarse to fine grid extrapolation technique for Navier-Stokes computations and also suggests tools for a designer to conduct design optimization study and related sensitivity analyses for a given design problem.

Vaidyanathan, Rajkumar↗