Search NASA⌕ Search

SEARCH · Search NASA

Results for “normal distortion”

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

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

At least 199 records · Page 11

NMR evidence for a Peierls transition in the layered square-net compound LaAgSb 2

Here, we measured the central (1/2 ↔ –1/2) and first satellite (±3/2 ↔ ±1/2) lines of the 139 La NMR spectra as a function of temperature in LaAgSb 2 , in order to elucidate the origin and nature of the charge-density-wave (CDW) transitions at $T_{\text{CDW1}}$ = 207 K and $T_{\text{CDW2}}$ = 186 K. In the normal state, the Knight shift $\mathcal{K}$ reveals a fairly linear relationship with decreasing temperature, which is ascribed to a pseudogap in the spin excitation spectrum, pointing towards the material being an unconventional metal. Upon further cooling, $\mathcal{K}$ decreases more steeply below $T_{\text{CDW1}}$, indicative of the partial Fermi surface gap opening on top of the pseudogap. The most remarkable finding in our study is a clear splitting of the satellite lines at $T_{\text{CDW1}}$ observed for $H \parallel c$, whose temperature dependence behaves as the BCS order parameter in the weak-coupling limit, evidencing that the CDW transition induces the periodic lattice distortion. Our NMR findings therefore demonstrate that the CDW transition in LaAgSb 2 is of Peierls type, being driven by the electronic instability in the vicinity of the Fermi level.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Beyond the cockpit: The visual world as a flight instrument

The use of cockpit instruments to guide flight control is not always an option (e.g., low level rotorcraft flight). Under such circumstances the pilot must use out-the-window information for control and navigation. Thus it is important to determine the basis of visually guided flight for several reasons: (1) to guide the design and construction of the visual displays used in training simulators; (2) to allow modeling of visibility restrictions brought about by weather, cockpit constraints, or distortions introduced by sensor systems; and (3) to aid in the development of displays that augment the cockpit window scene and are compatible with the pilot's visual extraction of information from the visual scene. The authors are actively pursuing these questions. We have on-going studies using both low-cost, lower fidelity flight simulators, and state-of-the-art helicopter simulation research facilities. Research results will be presented on: (1) the important visual scene information used in altitude and speed control; (2) the utility of monocular, stereo, and hyperstereo cues for the control of flight; (3) perceptual effects due to the differences between normal unaided daylight vision, and that made available by various night vision devices (e.g., light intensifying goggles and infra-red sensor displays); and (4) the utility of advanced contact displays in which instrument information is made part of the visual scene, as on a 'scene linked' head-up display (e.g., displaying altimeter information on a virtual billboard located on the ground).

Johnson, W. W.↗

Supersonic jet mixing enhancement by vortex generators

Experiments were conducted to explore the effects of vortex generators, in the form of tabs projecting normally into the jet, on the mixing and the far-field noise characteristics of a jet. A converging-diverging nozzle with a design Mach number of 1.36 was used in the experiments. The flow regimes from subsonic to highly underexpanded supersonic conditions were studied. One, two, and four tabs were used and some of the findings of previous investigators were examined and confirmed. The tabs eliminated screech noise from moderately overexpanded cases to highly underexpanded cases. Detailed flow visualizations and measurements showed that two tabs bifurcated the jet at all Mach numbers. While the effect of two tabs was persistent and the jet remained bifurcated, the distortions produced by one and four tabs disappeared by a streamwise distance of approximately 16 jet diameters. Two and four tabs significantly increased the entrainment of ambient air into the jet.

Samimy, M.↗

Multispectral and Thermal Imager Onboard Aerial Platforms Instrument Handbook

The MicaSense Altum imager is an off-the-shelf, synchronized multispectral and thermal camera, combined with a Global Positioning System (GPS) unit and downwelling light sensor (DLS). The Altum takes images of the land surface within its field of view (FOV) across five visible bands and one longwave infrared thermal band. The sensor records the radiance and converts it to digital numbers. Imagery is radiometrically corrected, taking into account the sensor calibration, lens distortions, vignette effects, sun angle, and atmospheric effects (scattering and absorption). The photogrammetry software Agisoft PhotoScan v 1.4 is used to align and stitch the images into a larger composite image using the technique of structure from motion image capture to construct a dense cloud and 3D model of the surface, which is used to produce a digital elevation model of the terrain surveyed and orthomosaic imagery. Land surface leaf area index, albedo, and surface skin temperature are provided for the user. The user can perform raster calculations on the imagery to produce various other vegetative indices, which are used to indicate plant health and land surface characteristics, including Normalized Difference Vegetation Index (NDVI), Green Normalized Difference Vegetation Index (GNDVI), Normalized Difference Water Index (NDWI), surface temperature, and Enhanced_vegetation_index (EVI). This code is provided with the readme file for each data set. The images have a resolution of 20-60 cm/pixel, which are subsampled to 100 cm/pixel.

47 OTHER INSTRUMENTATION↗

Tailoring planar slip to achieve pure metal-like ductility in body-centred-cubic multi-principal element alloys

Uniform tensile ductility (UTD) is crucial for the forming/machining capabilities of structural materials. Normally, planar-slip induced narrow deformation bands localize the plastic strains and hence hamper UTD, particularly in body-centred-cubic (bcc) multi-principal element high-entropy alloys (HEAs), which generally exhibit early necking (UTD < 5%). Here we demonstrate a strategy to tailor the planar-slip bands in a Ti-Zr-V-Nb-Al bcc HEA, achieving a 25% UTD together with nearly 50% elongation-to-failure (approaching a ductile elemental metal), while offering gigapascal yield strength. The HEA composition is designed not only to enhance the B2-like local chemical order (LCO), seeding sites to disperse planar slip, but also to generate excess lattice distortion upon deformation-induced LCO destruction, which promotes elastic strains and dislocation debris to cause dynamic hardening. Further, this encourages second-generation planar-slip bands to branch out from first-generation bands, effectively spreading the plastic flow to permeate the sample volume. Moreover, the profuse bands frequently intersect to sustain adequate work-hardening rate (WHR) to large strains. Our strategy showcases the tuning of plastic flow dynamics that turns an otherwise-undesirable deformation mode to our advantage, enabling an unusual synergy of yield strength and UTD for bcc HEAs.

36 MATERIALS SCIENCE↗

Unexpected symmetry breaking in ferroelectric wurtzite thin films on silicon observed by optical second harmonic generation

Optical second harmonic generation (SHG) exists as a popular tool for probing materials with broken inversion symmetry in the physical and biological sciences. SHG polarimetry can reveal material anisotropy with high sensitivity, including point group and phase transitions. Here, we probe ferroelectric wurtzite films with a nominal 6 mm symmetry under a normal reflection geometry using SHG microscopy and discover an unexpected symmetry breaking. Symmetry considerations would normally forbid the detection of the SHG signal when light propagates along the polar 6-fold rotation axis. Yet a uniquely anisotropic SHG response is observed in this geometry in Al 1-x B x N, Al 1-x Sc x N, Zn 1-x Mg x O, and AlN/Al 1-x Sc x N heterostructures grown on silicon that can be modeled by an average monoclinic symmetry of point group m. A significant enhancement of the SHG signal corresponding to up to a 5.3× increase in the SHG intensity (hence ∼2.3 × in effective SHG tensor coefficient) is observed at antiparallel polar domain walls, suggesting local cooperative alignment of symmetry-breaking structural distortions. Namely, it is found that the monoclinic mirror plane is oriented predominantly perpendicular to the walls. Such increases in domain wall SHG thus reveal that subtle symmetry breaking can be a pathway to large property enhancements.

36 MATERIALS SCIENCE↗

The 1982 control network of Mars

Attention is given to a planet-wide control network of Mars that was computed in September 1982 using a large single-block analytical triangulation with 47,524 measurements of 6853 control points on 1054 Mariner 9 and 757 Viking pictures. In all, 19,139 normal equations were solved, with a resulting standard error of measurement of 18.06 microns. The control points identified by name and letter designation are given, as are the aerographic coordinates of the control points. In addition, the coordinates of the Viking I lander site are given: latitude, 22.480 deg; longitude, 47.962 deg (radius, 3389.32 km). This study expands and updates the previously published network (1978). It is noted that the computation differs in many respects from standard aerial mapping photogrammetric practice. In comparison with aerial mapping photography, the television formats are small and the focal lengths are long; stereo coverage is rare, the scale of the pictures varies greatly, and the residual camera distortions are large.

Davies, M. E.↗

Producing Science-Ready Radar Datasets for the Retrieval of Forest Structure Parameters from Backscatter: Correcting for Terrain Topography and Changes in Vegetation Reflectivity

Radar backscatter data contain both geometric and radiometric distortions due to underlying topography and the radar viewing geometry. Our objective is to develop a radiometric correction algorithm specific to the UAVSAR system configuration that would improve retrieval of forest structure parameters. UAVSAR is an airborne Lband radar capable of repeat?pass interferometry producing images with a spatial resolution of 5m. It is characterized by an electronically steerable antenna to compensate for aircraft attitude. Thus, the computation of viewing angles (i.e. look, incidence and projection) must include aircraft attitude angles (i.e. yaw, pitch and roll) in addition to the antenna steering angle. In this presentation, we address two components of radiometric correction: area projection and vegetation reflectivity. The first correction is applied by normalization of the radar backscatter by the local ground area illuminated by the radar beam. The second is a correction due to changes in vegetation reflectivity with viewing geometry.

polarimetry↗

Effect of shock pressure on the structure and superconducting properties of Y-Ba-Cu-O in explosively fabricated bulk metal-matrix composites

While it is now well established that copper-oxide-based powder, or virtually any other ceramic superconductor powder, can be consolidated and encapsulated within a metal matrix by explosive consolidation, the erratic superconductivity following fabrication has posed a major problem for bulk applications. The nature of this behavior was found to arise from microstructural damage created in the shock wave front, and the residual degradation in superconductivity was demonstrated to be directly related to the peak shock pressure. The explosively fabricated or shock loaded YBa2Cu3Ox examples exhibit drastically altered rho (or R) - T curves. The deterioration in superconductivity is even more noticeable in the measurement of ac magnetic susceptibility and flux exclusion or shielding fraction which is also reduced in proportion to increasing peak shock pressure. The high-frequency surface resistance (in the GHz range) is also correspondingly compromised in explosively fabricated, bulk metal-matrix composites based on YBa2Cu3O7. Transmission electron microscopy (including lattice imaging techniques) is being applied in an effort to elucidate the fundamental (microstructural) nature of the shock-induced degradation of superconductivity and normal state conductivity. One focus of TEM observations has assumed that oxygen displaced from b-chains rather than oxygen-vacancy disorder in the basal plane of oxygen deficient YBa2Cu3Ox may be a prime mechanism. Shock-wave displaced oxygen may also be locked into new positions or interstitial clusters or chemically bound to displaced metal (possibly copper) atoms to form precipitates, or such displacements may cause the equivalent of local lattice cell changes as a result of stoichiometric changes. While the shock-induced suppression of T(sub c) is not desirable in the explosive fabrication of bulk metal-matrix superconductors, it may be turned into an advantage if the atomic-scale distortion can be understood and controlled as local flux pinning sites.

Murr, L. E.↗

Effect of shock pressure on the structure and superconducting properties of Y-Ba-Cu-O in explosively fabricated bulk metal-matrix composites

While it is now well established that copper-oxide-based power, or virtually any other ceramic superconductor powder, can be consolidated and encapsulated within a metal matrix by explosive consolidation, the erratic superconductivity following fabrication has posed a major problem for bulk applications. The nature of this behavior was found to arise from microstructural damage created in the shock wave front, and the residual degradation in superconductivity was demonstrated to be directly related to the peak shock pressure. The explosively fabricated or shock loaded YBa2Cu3Ox examples exhibit drastically altered rho (or R) - T curves. The deterioration in superconductivity is even more noticeable in the measurement of ac magnetic susceptibility and flux exclusion or shielding fraction which is also reduced in proportion to increasing peak shock pressure. The high frequency surface resistance (in the GHz range) is also correspondingly compromised in explosively fabricated, bulk metal-matrix composites based on YBa2Cu3O7. Transmission electron microscopy (including lattice imaging techniques) is being applied in an effort to elucidate the fundamental (microstructural) nature of the shock-induced degradation of superconductivity and normal state conductivity. One focus of TEM observations has assumed that oxygen displaced from b-chains rather than oxygen-vacancy disorder in the basal plane of oxygen deficient YBa2Cu3Ox may be a prime mechanism. Shock-wave displaced oxygen may also be locked into new positions or interstitial clusters or chemically bound to displaced metal (possibly copper) atoms to form precipitates, or such displacements may cause the equivalent of local lattice cell changes as a result of stoichiometric changes. While the shock-induced suppression of T(sub c) is not desirable in the explosive fabrication of bulk metal-matrix superconductors, it may be turned into an advantage if the atomic-scale distortion can be understood and controlled as local flux pinning sites.

Murr, L. E.↗

Investigation of an underslung half-cone inlet with compression surface mounted outboard from fuselage at Mach numbers of 1.5, 1.8, and 2.0

An investigation was conducted to determine the performance of an underslung half-cone inlet mounted on a missile forebody model with the compression surface outboard from the fuselage. The inlet was designed for shock-on-lip operation at Mach number 2.0 with 25 degree half-angle spike. The cowling was attached to the fuselage through the boundary-layer plow and served as part of the fuselage boundary-layer diverter system. The performance of the half-cone inlet was compared with that of a scoop-type inlet and a normal-wedge inlet on a maximum-thrust-minus-drag basis. The increase in pressure recovery obtained with the half-cone inlet over that obtained with the reference inlets offset the slightly higher drags observed over the Mach number range for the half-cone so that the performance of this configuration was equal to that of the other inlets at Mach number 2.0 and was slightly superior at the lower Mach numbers. For a particular configuration, a peak pressure recovery of 0.879 was obtained at Mach number 2.0, zero angle of attack, and 4-percent throat bleed; the subcritical stability was 16 percent. Use of a fuselage-mounted boundary-layer splitter plate ahead of the inlet did not improve the stability. Subcritical distortion values were below 10 percent for all configurations. (author)

Yeager, Richard A↗

Pulsar Pair Cascades in Magnetic Fields with Offset Polar Caps

Neutron star magnetic fields may have polar caps (PC) that are offset from the dipole axis, through field-line sweepback near the light cylinder or non-symmetric currents within the star. The effects of such offsets on electron-positron pair cascades are investigated, using simple models of dipole magnetic fields with small distortions that shift the PCs by different amounts or directions. Using a Monte Carlo pair cascade simulation, we explore the changes in the pair spectrum, multiplicity and energy flux across the PC, as well as the trends in pair flux and pair energy flux with spin-down luminosity, L(sub sd). We also give an estimate of the distribution of heating flux from returning positrons on the PC for different offsets. We find that even modest offsets can produce significant increases in pair multiplicity, especially for pulsars that are near or beyond the pair death lines for centered PCs, primarily because of higher accelerating fields. Pair spectra cover several decades in energy, with the spectral range of millisecond pulsars (MSPs) two orders of magnitude higher than for normal pulsars, and PC offsets allow significant extension of all spectra to lower pair energies. We find that the total PC pair luminosity L(sub pair) is proportional to L(sub sd), with L(sub pair) approximates 10(exp -3) L(sub sd) for normal pulsars and L(sub pair) approximates 10(exp -2) L(sub sd) for MSPs. Remarkably, the total PC heating luminosity for even large offsets increases by less than a factor of two, even though the PC area increases by much larger factors, because most of the heating occurs near the magnetic axis.

Harding, Alice K.↗

Designing the Imaging and Breadboard System for FBCE-TL Project

This presentation outlines the support work done on designing the imaging and breadboard system of the Transfer Line (TL) project, which is the third module for the Flow Boiling and Condensation Experiment (FBCE) operating in the Fluids Integrated Rack on-board the International Space Station (ISS). The goal of the FBCE is to serve as a facility for flow boiling and condensation investigating two-phase flow and heat transfer data in microgravity. The TL module aims use existing FBCE hardware to study cryogenic chilldown, a large component of cryogenic propellant tank transfer research. The TL test module will perform chilldown studies with normal-perfluorohexane (nPFH), a cryogenic simulant, flowing through a super-heated line, which is heated through the process of Joule-heating. SolidWorks and Creo were used to create electrically conductive pipe junctions that connect and seal several Indium Tin Oxide (ITO) coated sapphire tube sections together to allow for low leak probability fluid flow and circumferentially uniform electrical current density. It is necessary to understand and calculate the thermal expansion of the tubing sections such that the junctions would not leak at anticipated operating temperatures and pressures, would maintain electrical contact, and not crack the crystalline tubes. Optical imaging techniques were used to build an experimentally validated image remapping process for flight-like setups of cylindrical tubes. Then MATLAB was used to create an algorithm that distorts an image based on the refraction of light passing through the mediums we were imaging through to accurately visualize the cryogenic chilldown that is of scientific interest. This research will assist NASA to move forward with long-duration spaceflight missions where knowledge of efficient heat transfer processes becomes more critical.

imaging system↗

A grid-independent approximate Riemann solver with applications to the Euler and Navier-Stokes equations

A new two-dimensional approximate Riemann solver has been developed that obtains fluxes on grid faces via wave decomposition. By utilizing information propagation in the velocity-difference directions rather than in the grid-normal directions, this flux function more appropriately interprets and hence more sharply resolves shock and shear waves when they lie oblique to the grid. The model uses five waves to describe the difference in states at a grid face. Two acoustic waves, one shear wave, and one entropy wave propagate in the direction defined by the local velocity difference vector, while the fifth wave is a shear wave that propagates at a right angle to the other four. Test cases presented include a shock reflecting off a wall, a pure shear wave, supersonic flow over an airfoil, and viscous separated airfoil flow. Results using the new model give significantly sharper shock and shear contours than a grid-aligned solver. Navier-Stokes computations over an aifoil show reduced pressure distortions in the separated region as a result of the grid-independent upwinding.

Rumsey, Christopher L.↗

Theoretical and computational study of rotating isotropic turbulence

The various flow regimes that occur in rotating isotropic turbulence and their associated turbulence structure are studied. Direct numerical simulations are conducted for moderate and rapid rotation rates and comparisons are made with the predictions of generalized Eddy Damped Quasi-Normal Markovian (EDQNM) approximations. It is shown that at high rotation rates the nonlinear transfer terms remain small and that the development of the spectrum is through pure viscous decay. This shows that the effect of rapid rotation on the turbulence kinetic energy is through the shutting off of the production term in the dissipation rate equation. At moderate and relatively rapid rates, the rotation causes a discernible anisotropy to develop in the integral length scale with a mild trend toward a two-dimensionalization of the flow. As the flow decays, the Rossby number decreases, leading again to the shutting off of the nonlinear transfer terms. For extremely rapid rotation rates, the anisotropies in the integral length scales are small and direct numerical simulation results are in good agreement with rapid distortion theory.

Mansour, N. N.↗

A Study of Nucleate Boiling with Forced Convection in Microgravity

The ultimate objective of basic studies of flow boiling in microgravity is to improve the understanding of the processes involved, as manifested by the ability to predict its behavior. This is not yet the case for boiling heat transfer even in earth gravity, despite the considerable research activity over the past 30 years. The elements that constitute the nucleate boiling process - nucleation, growth, motion, and collapse of the vapor bubbles (if the bulk liquid is subcooled) - are common to both pool and flow boiling. It is well known that the imposition of bulk liquid motion affects the vapor bubble behavior relative to pool boiling, but does not appear to significantly influence the heat transfer. Indeed, it has been recommended in the past that empirical correlations or experimental data of pool boiling be used for design purposes with forced convection nucleate boiling. It is anticipated that such will most certainly not be possible for boiling in microgravity, based on observations made with pool boiling in microgravity. In earth gravity buoyancy will act to remove the vapor bubbles from the vicinity of the heater surface regardless of how much the imposed bulk velocity is reduced, depending, of course, on the geometry of the system. Vapor bubbles have been observed to dramatically increase in size in pool boiling in microgravity, and the heat flux at which dryout took place was reduced considerably below what is generally termed the critical heat flux (CHF) in earth gravity, depending on the bulk liquid subcooling. However, at heat flux levels below dryout, the nucleate pool boiling process was enhanced considerably over that in earth gravity, in spite of the large vapor bubbles formed in microgravity and perhaps as a consequence. These large vapor bubbles tended to remain in the vicinity of the heater surface, and the enhanced heat transfer appeared to be associated with the presence of what variously has been referred to as a liquid microlayer between the bubble and the heater surface. The enhancement of the boiling process with low velocities in earth gravity for those orientations producing the formation of a liquid macrolayer described above, accompanied by "sliding" vapor bubbles, has been demonstrated. The enhancement was presented as a function of orientation, subcooling, and heated length, while a criterion for the heat transfer for mixed natural/forced convection nucleate boiling was given previously. A major unknown in the prediction and application of flow boiling heat transfer in microgravity is the upper limit of the heat flux for the onset of dryout (or critical heat flux - CHF), for given conditions of fluid-heater surfaces, including geometry, system pressure and bulk liquid subcooling. It is clearly understood that the behavior in microgravity will be no different than on earth with sufficiently high flow velocities, and would require no space experimentation. However, the boundary at which this takes place is still an unknown. Previous results of CHF measurements were presented for low velocity flow boiling at various orientations in earth gravity as a function of flow velocity and bulk liquid subcooling, along with preliminary measurements of bubble residence times on a flat heater surface. This showed promise as a parameter to be used in modeling the CHF, both in earth gravity and in microgravity. The objective of the work here is to draw attention to and show results of current modeling efforts for the CHF, with low velocities in earth gravity at different orientations and subcoolings. Many geometrical possibilities for a heater surface exist in flowing boiling, with boiling on the inner and outer surfaces of tubes perhaps being the most common. If the vapor bubble residence time on and departure size from the heater surface bear a relationship to the CHF, as results to be given indicate, it is important that visualization of and access to vapor bubble growth be conveniently available for research purposes. In addition, it is desirable to reduce the number of variables as much as possible in a fundamental study. These considerations dictated the use of a flat heater surface, which is rectangular in shape, 1.91 cm by 3.81 cm (0.75 x 1.5 inches), consisting either of a 400 Angstrom thick semi-transparent gold film sputtered on a quartz substrate which serves simultaneously as a heater and a resistance thermometer, or a copper substrate of the same size. The heater substrate is a disc which can be rotated so that the heated length in the flow direction can be changed from 1.91 to 3.81 cm (0.75 to 1.5 inches). The fluid is R-113, and the velocities can be varied between 0.5 cm/s and 60 cm/s. For a sufficiently low velocity the CHF can be modeled reasonably well at various orientations by the correlation for pool boiling corrected for the influence of bulk liquid subcooling, multiplied by the square root of q, the angle relative to horizontal. This arises from equating buoyancy and drag forces in the inverted positions where the vapor bubbles are held against the heater surface as they slide. A distortion of the measurements relative to pool boiling occurs as the flow velocity increases. In modeling this effect at different levels of subcooling it appeared appropriate to estimate the volumetric rate of vapor generation, using measurements of bubble frequency (or residence time), void fraction and average bubble boundary layer thickness. These were determined with the use of a platinum hot wire probe 0.025 mm in diameter by 1.3 mm long, applying a constant current to distinguish between contact with liquid or vapor. Two-dimensional spatial variations are obtained with a special mechanism to resolve displacements in increments of 0.025 mm. From such measurements it was determined that the fraction of the surface heat transfer resulting in evaporation varies inversely with the subcooling correction factor for the CHF. The measured inverse bubble residence time is normalized relative to that predicted for an infinite horizontal flat plate at the CHF, and is correlated well with the CHF normalized relative to that for pool boiling, for various orientation angles and subcooling levels. This correspondence is then combined with a normalizing factor for the energy flux leaving the heater surface at the CHF and the computed bubble radius at departure, determined from the balance between the outward velocity of the interface due to evaporation and the buoyance induced velocity of the center of mass of the bubble. The product of the CHF and the corresponding residence time was determined to be a constant for all orientations at a given bulk flow velocity and liquid subcooling, and must be determined empirically for each velocity and subcooling at present. It then becomes possible to predict the CHF for the different orientations, velocities, and subcoolings. These are compared with normalized measurements of the CHF for velocities ranging from 4 cm/s to 55 cm/s, subcoolings from 2.8 to 22.2 K, over orientations angles of 360 degrees.

Merte, Herman, Jr.↗

Correlation, Cost Risk, and Geometry

The geometric viewpoint identifies the choice of a correlation matrix for the simulation of cost risk with the pairwise choice of data vectors corresponding to the parameters used to obtain cost risk. The correlation coefficient is the cosine of the angle between the data vectors after translation to an origin at the mean and normalization for magnitude. Thus correlation is equivalent to expressing the data in terms of a non orthogonal basis. To understand the many resulting phenomena requires the use of the tensor concept of raising the index to transform the measured and observed covariant components into contravariant components before vector addition can be applied. The geometric viewpoint also demonstrates that correlation and covariance are geometric properties, as opposed to purely statistical properties, of the variates. Thus, variates from different distributions may be correlated, as desired, after selection from independent distributions. By determining the principal components of the correlation matrix, variates with the desired mean, magnitude, and correlation can be generated through linear transforms which include the eigenvalues and the eigenvectors of the correlation matrix. The conversion of the data to a non orthogonal basis uses a compound linear transformation which distorts or stretches the data space. Hence, the correlated data does not have the same properties as the uncorrelated data used to generate it. This phenomena is responsible for seemingly strange observations such as the fact that the marginal distributions of the correlated data can be quite different from the distributions used to generate the data. The joint effect of statistical distributions and correlation remains a fertile area for further research. In terms of application to cost estimating, the geometric approach demonstrates that the estimator must have data and must understand that data in order to properly choose the correlation matrix appropriate for a given estimate. There is a general feeling by employers and managers that the field of cost requires little technical or mathematical background. Contrary to that opinion, this paper demonstrates that a background in mathematics equivalent to that needed for typical engineering and scientific disciplines at the masters or doctorate level is appropriate within the field of cost risk.

Dean, Edwin B.↗

Inertial collapse of a gas bubble in a shear flow near a rigid wall

Despite the extensive research on bubble collapse near rigid walls, the bubble collapse dynamics in the presence of shear flow near a rigid wall is poorly understood. We conduct direct simulations of the Navier–Stokes equations to explore the bubble dynamics and pressures during bubble collapse near a rigid, flat wall under linear shear flow conditions. We examine the dependence of the bubble collapse morphology and wall pressures on the initial bubble location and shear rate. We find that shear distorts the bubble, generating two re-entrant jets – one developing from the side opposite to the mean flow and the other from the far end toward the wall. Upon impact of the jet on the opposite side of the bubble, water-hammer shocks are produced, which propagate outward and interact with the convoluted bubble shape. The shock stretches the bubble towards the wall, resulting in a closer impact location for the jet originating from the far end compared with the case with no shear flow. The water-hammer pressure location can be approximated as the theoretical distance travelled by a particle initialised at the bubble centre with the corresponding constant shear flow velocity. The maximum wall pressures can thus be predicted by considering the distance between the far jet impingement location and the wall along the wall-normal direction. As the shear rate is increased, the maximum wall pressure increases, although only marginally. We determine the critical initial stand-off distance from the wall at which the bubble morphology is shear dominated, i.e. characterised by converging re-entrant jets.

Bhola, Sahil (ORCID:0000000236766302)↗