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NASA NTRS1995

Modeling the heliolatitudinal gradient of the solar wind parameters with exact MHD solutions

The heliolatitudinal dependence of observations of the solar wind macroscopic quantities such as the averaged proton speed, density and the mass and momentum flux are modeled. The published observations covering the last two and a half solar cycles, are obtained either via the technique of interplanetary scintillations for the last 2 solar cycles (1970-1990), or, from the plasma experiment aboard the ULYSSES spacecraft for the recent period 1990-1994. Exact, two dimensional solutions of the full set of the steady MHD equations are used which are obtained through a nonlinear separation of the variables in the MHD equations. The three parameters emerging from the solutions are fixed from these observations, as well as from observations of the solar rotation. It is found that near solar maximum the solar wind speed is uniformly low, around the 400 km/s over a wide range of latitudes. On the other hand, during solar minimum and the declining phase of the solar activity cycle, there is a strong heliolatitudinal gradient in proton speed between 400-800 from equator to pole. This modeling also agrees with previous findings that the gradient in wind speed with the latitude is offset by a gradient in density such that the mass and momentum flux vary relatively little.

Lima, J. J. G.↗

NASA NTRS1995

Radial gradients of ion densities and temperatures observed by SWICS/Ulysses

Mean density and temperature gradients of solar wind protons and alpha-particles between 1 and 5.4 AU are established from SWICS/Ulysses observations. All parameters are classified in speed intervals. au order scheme giving us a natural extension of the Helios observations. which were usually classified according to speed of the wind. The radial gradients show a similar behaviour of both particle species, while the particles radially propagate and thereby cool off in the heliosphere. The slow solar wind is found, for protons as well as a particles. to expand adiabatically all the way out to 5.4 AU, while the fast wind evolves non-adiabatically and is heated by interplanetary sources. It, seems that the heating rate of the a-particles is larger than the heating rate of the protons. The ion temperature ratio and density ratio are determined. They do not indicate any radial dependence. The temperature ratio T(sub alpha)/T(sub p) is on average about 4. It has a maximum of 4.5 in the velocity interval where 400 km/s is less than v(sub p) is less than 500 km/s, while in slow wind with v(sub p) is less than 400 km/s it has a minimum value of 37. and for fast wind with v(sub p) is greater than 500 km/s it is 3.9. The density gradients shows compression effects resulting from fast wind overtaking the slow wind.

Liu, S.↗

NASA NTRS1996

Study of the velocity gradient tensor in turbulent flow

The behavior of the velocity gradient tensor, A(ij)=delta u(i)/delta x(j), was studied using three turbulent flows obtained from direct numerical simulation The flows studies were: an inviscid calculation of the interaction between two vortex tubes, a homogeneous isotropic flow, and a temporally evolving planar wake. Self-similar behavior for each flow was obtained when A(ij) was normalized with the mean strain rate. The case of the interaction between two vortex tubes revealed a finite sized coherent structure with topological characteristics predictable by a restricted Euler model. This structure was found to evolve with the peak vorticity as the flow approached singularity. Invariants of A(ij) within this structure followed a straight line relationship of the form: gamma(sup 3)+gammaQ+R=0, where Q and R are the second and third invariants of A(ij), and the eigenvalue gamma is nearly constant over the volume of this structure. Data within this structure have local strain topology of unstable-node/saddle/saddle. The characteristics of the velocity gradient tensor and the anisotropic part of a related acceleration gradient tensor H(ij) were also studied for a homogeneous isotropic flow and a temporally evolving planar wake. It was found that the intermediate principal eigenvalue of the rate-of-strain tensor of H(ij) tended to be negative, with local strain topology of the type stable-node/saddle/saddle. There was also a preferential eigenvalue direction. The magnitude of H(ij) in the wake flow was found to be very small when data were conditioned at high local dissipation regions. This result was not observed in the relatively low Reynolds number simulation of homogeneous isotropic flow. A restricted Euler model of the evolution of A(ij) was found to reproduce many of the topological features identified in the simulations.

Cheng, Wei-Ping↗

NASA NTRS1994

Fluid System Angular Momentum and Moment Fluctuations Driven by Gravity Gradient or Gravity Jitter in Microgravity

The dynamical behaviour of fluids affected by the asymmetric gravity gradient acceleration and gravity jitter acceleration, in particular the effect of surface tension on partially-filled rotating fluids with special example applicable to a full-scale Gravity Probe-B Spacecraft dewar tank have been investigated. Results of slosh wave excitation along liquid-vapor interface induced by gravity gradient acceleration indicated that one-up one-down and one-down one-up oscillations of two bubbles in the cross-section of doughnut profiles in the vertical r-z plane of rotating dewar, and an eccentric contour of bubble rotating around the axis of dewar in horizontal r-Theta plane. Results of slosh wave excitation along liquid-vapor interface induced by gravity jitter acceleration indicated equivalent to time-dependent oscillatory forces which push bubble in the combined bubble motion of down-and-up and leftward-and-rightward as the bubble is rotating with respect to rotating dewar axis. Fluctuations of angular momentum, fluid moment and bubble mass center caused by slosh wave excitations driven by gravity gradient acceleration or gravity jitter acceleration are also investigated.

Hung, R. J.↗

NASA NTRS1997

Response of Composite Panels with Stiffness Gradients Due to Stiffener Terminations and Cutouts

The results of an analytical and experimental study of stiffened graphite-epoxy compression panels with terminated stiffeners are presented. The local stress gradients at the stiffener termination location are determined by finite element analysis. Three stiffener termination concepts are evaluated by analysis to determine the stiffener and skin laminate parameters that affect the panel response and failure. The effects of changing local skin laminate definitions, skin reinforcement details, and stiffener termination details on local stress gradients and load-path eccentricities are discussed. Analytical and test results are presented for panels with one terminated stiffener and for panels with one terminated stiffener and two unterminated stiffeners. The effects of a cutout in the skin of a panel with a terminated stiffener is also evaluated to determine the interaction between the stress gradients in the panel due to the cutout and those due to the terminated stiffener. The results of the study indicate that the critical failure modes of the panels initiate at the skin-stiffener interface near the end of the terminated stiffener.

Ambur, Damodar R.↗

NASA NTRS1997

Gradient-Based Aerodynamic Shape Optimization Using ADI Method for Large-Scale Problems

A gradient-based shape optimization methodology, that is intended for practical three-dimensional aerodynamic applications, has been developed. It is based on the quasi-analytical sensitivities. The flow analysis is rendered by a fully implicit, finite volume formulation of the Euler equations.The aerodynamic sensitivity equation is solved using the alternating-direction-implicit (ADI) algorithm for memory efficiency. A flexible wing geometry model, that is based on surface parameterization and platform schedules, is utilized. The present methodology and its components have been tested via several comparisons. Initially, the flow analysis for for a wing is compared with those obtained using an unfactored, preconditioned conjugate gradient approach (PCG), and an extensively validated CFD code. Then, the sensitivities computed with the present method have been compared with those obtained using the finite-difference and the PCG approaches. Effects of grid refinement and convergence tolerance on the analysis and shape optimization have been explored. Finally the new procedure has been demonstrated in the design of a cranked arrow wing at Mach 2.4. Despite the expected increase in the computational time, the results indicate that shape optimization, which require large numbers of grid points can be resolved with a gradient-based approach.

Pandya, Mohagna J.↗

NASA NTRS1959

Charts and Tables for Estimating the Stability of the Compressible Laminar Boundary Layer with Heat Transfer and Arbitrary Pressure Gradient

The minimum critical Reynolds numbers for the similar solutions of the compressible laminar boundary layer computed by Cohen and Reshotko and also for the Falkner and Skan solutions as recomputed by Smith have been calculated by Lin's rapid approximate method for two-dimensional disturbances. These results enable the stability of the compressible laminar boundary layer with heat transfer and pressure gradient to be easily estimated after the behavior of the boundary layer has been computed by the approximate method of Cohen and Reshotko. The previously reported unusual result (NACA Technical Note 4037) that a highly cooled stagnation point flow is more unstable than a highly cooled flat-plate flow is again encountered. Moreover, this result is found to be part of the more general result that a favorable pressure gradient is destabilizing for very cool walls when the Mach number is less than that for complete stability. The minimum critical Reynolds numbers for these wall temperature ratios are, however, all larger than any value of the laminar-boundary-layer Reynolds number likely to be encountered. For Mach numbers greater than those for which complete stability occurs a favorable pressure gradient is stabilizing, even for very cool walls.

Tetervin, Neal↗

NASA NTRS1999

Morning Martian Atmospheric Temperature Gradients and Fluctuations Observed by Mars Pathfinder

We have studied the most prominent atmospheric temperature fluctuations observed during Martian mornings by Mars Pathfinder and have concluded, based on comparisons with wind directions, that they appear to be a result of atmospheric heating associated with the Lander spacecraft. Also, we have examined the morning surface layer temperature lapse rates, which are found to decrease as autumn approaches at the Pathfinder location, and which have mean (and median) values as large as 7.3 K/m in the earlier portions of the Pathfinder landed mission. It is plausible that brief isolated periods with gradients twice as steep are associated with atmospheric heating adjacent to Lander air bag material. In addition, we have calculated the gradient with height of the structure function obtained with Mars Pathfinder, for Mars' atmospheric temperatures measured within about 1.3 m from the surface, assuming a power law dependence, and have found that these gradients superficially resemble those reported for the upper region of the terrestrial stable boundary layer.

Mihalov, John D.↗

NASA NTRS2001

Experimental and Computational Studies of the Control of Convection of Non-Conducting Liquids During solidification by Means of a Magnetic Field Gradient

The elimination of convection is essential in experimental investigations of diffusive transport (of heat and matter) during solidification. One classical approach to damping convection in a conducting liquid is the application of a magnetic field. The damping phenomenon is the induction, by the motion of a conductor in a magnetic field, of currents which interact with the field to produce Lorentz forces that oppose the flow. However, there are many liquids which are not sufficiently conducting to exploit this phenomenon; examples include the transparent liquids (such as succinonitrile-acetone) that are used as "model alloys" in fundamental solidification studies. There have been several investigations of the solidification of these liquids that have been carried out in orbiting laboratories to eliminate natural convection. The paper describes an investigation of an alternative approach whereby a magnetic field gradient is applied to the liquid. A magnetic body force then arises which is dependent on the susceptibility of the liquid and thereby on the temperature and or concentration. With the field gradient aligned vertically and of correct magnitude, the variation of gravitational body force due to temperature/concentration dependent density can be counterbalanced by a variation in magnetic body force. Experiments have been carried out in a super-conducting magnet at Marshall Space Flight Center to measure velocities in an aqueous manganese chloride solution. The solution was contained in a chamber with temperature controlled end walls and glass side walls. Velocities were measured by particle image velocimetry. Starting from zero current in the magnet (zero field gradient) flow driven by the temperature difference between the end walls was measured. At a critical current the flow was halted. At higher currents the normal convection was reversed. The experiments included ones where the solution was solidified and were accompanied by solution of the flow/transport equations using the software package FLUENT.

Seybert, C. D.↗

NASA NTRS2004

The Distribution of Cosmic-Ray Sources in the Galaxy, Gamma-Rays and the Gradient in the CO-to-H2 Relation

We present a solution to the apparent discrepancy between the radial gradient in the diffuse Galactic gamma-ray emissivity and the distribution of supernova remnants, believed to be the sources of cosmic rays. Recent determinations of the pulsar distribution have made the discrepancy even more apparent. The problem is shown to be plausibly solved by a variation in the Wco-to-N(H2) scaling factor. If this factor increases by a factor of 5-10 from the inner to the outer Galaxy, as expected from the Galactic metallicity gradient and supported by other evidence, we show that the source distribution required to match the radial gradient of gamma-rays can be reconciled with the distribution of supernova remnants as traced by current studies of pulsars. The resulting model fits the EGRET gamma-ray profiles extremely well in longitude, and reproduces the mid-latitude inner Galaxy intensities better than previous models.

Strong, A. W.↗

NASA NTRS2003

Improvement in diastolic intraventricular pressure gradients in patients with HOCM after ethanol septal reduction

We sought to validate measurement of intraventricular pressure gradients (IVPG) and analyze their change in patients with hypertrophic obstructive cardiomyopathy (HOCM) after ethanol septal reduction (ESR). Quantitative analysis of color M-mode Doppler (CMM) images may be used to estimate diastolic IVPG noninvasively. Noninvasive IVPG measurement was validated in 10 patients undergoing surgical myectomy. Echocardiograms were then analyzed in 19 patients at baseline and after ESR. Pulsed Doppler data through the mitral valve and pulmonary venous flow were obtained. CMM was used to obtain the flow propagation velocity (Vp) and to calculate IVPG off-line. Left atrial pressure was estimated with the use of previously validated Doppler equations. Data were compared before and after ESR. CMM-derived IVPG correlated well with invasive measurements obtained before and after surgical myectomy [r = 0.8, P < 0.01, Delta(CMM - invasive IVPG) = 0.09 +/- 0.45 mmHg]. ESR resulted in a decrease of resting LVOT systolic gradient from 62 +/- 10 to 29 +/- 5 mmHg (P < 0.001). There was a significant increase in the Vp and IVPG (from 48 +/- 5to 74 +/- 7 cm/s and from 1.5 +/- 0.2 to 2.6 +/- 0.3 mmHg, respectively, P < 0.001 for both). Estimated left atrial pressure decreased from 16.2 +/- 1.1 to 11.5 +/- 0.9 mmHg (P < 0.001). The increase in IVPG correlated with the reduction in the LVOT gradient (r = 0.6, P < 0.01). Reduction of LVOT obstruction after ESR is associated with an improvement in diastolic suction force. Noninvasive measurements of IVPG may be used as an indicator of diastolic function improvement in HOCM.

NASA Program Biomedical Research and Countermeasur↗

NASA NTRS2002

Temporal gradients in shear stimulate osteoblastic proliferation via ERK1/2 and retinoblastoma protein

Bone cells are subject to interstitial fluid flow (IFF) driven by venous pressure and mechanical loading. Rapid dynamic changes in mechanical loading cause transient gradients in IFF. The effects of pulsatile flow (temporal gradients in fluid shear) on rat UMR106 cells and rat primary osteoblastic cells were studied. Pulsatile flow induced a 95% increase in S-phase UMR106 cells compared with static controls. In contrast, ramped steady flow stimulated only a 3% increase. Similar patterns of S-phase induction were also observed in rat primary osteoblastic cells. Pulsatile flow significantly increased relative UMR106 cell number by 37 and 62% at 1.5 and 24 h, respectively. Pulsatile flow also significantly increased extracellular signal-regulated kinase (ERK1/2) phosphorylation by 418%, whereas ramped steady flow reduced ERK1/2 activation to 17% of control. Correspondingly, retinoblastoma protein was significantly phosphorylated by pulsatile fluid flow. Inhibition of mitogen-activated protein (MAP)/ERK kinase (MEK)1/2 by U0126 (a specific MEK1/2 inhibitor) reduced shear-induced ERK1/2 phosphorylation and cell proliferation. These findings suggest that temporal gradients in fluid shear stress are potent stimuli of bone cell proliferation.

NASA Discipline Cell Biology↗

NASA NTRS1988

A gradient of endogenous calcium forms in mucilage of graviresponding roots of Zea mays

Agar blocks that contacted the upper sides of tips of horizontally-oriented roots of Zea mays contain significantly less calcium (Ca) than blocks that contacted the lower sides of such roots. This gravity-induced gradient of Ca forms prior to the onset of gravicurvature, and does not form across tips of vertically-oriented roots or roots of agravitropic mutants. These results indicate that (1) Ca can be collected from mucilage of graviresponding roots, (2) gravity induces a downward movement of endogenous Ca in mucilage overlying the root tip, (3) this gravity-induced gradient of Ca does not form across tips of agravitropic roots, and (4) formation of a Ca gradient is not a consequence of gravicurvature. These results are consistent with gravity-induced movement of Ca being a trigger for subsequent redistribution of growth effectors (e.g. auxin) that induce differential growth and gravicurvature.

NASA Discipline Number 40-10↗

NASA NTRS1999

Impact of Thermal Gradients on Wind Tunnel Force Measurements

In a wind tunnel facility, the direct measurement of forces and moments induced on the model are performed by a force measurement balance. The measurement balance is a precision-machined device that has strain gages at strategic locations to measure the strain (i.e., deformations) due to applied forces and moments. The strain gages convert the strain (and hence the applied force) to an electrical voltage that is measured by external meters. Thermal gradients can complicate the process, however. Thermal gradients on the balance cause differential expansion (or contraction) of various parts of the balance that induce a strain that is detected by the strain gages and is indistinguishable from an external applied force. The thermal gradients can result when testing is done at elevated temperatures or at cryogenic temperatures such as at the National Transonic Facility (NTF) at NASA Langley Research Center (LaRC).

Hereford, James↗

NASA NTRS2000

Doppler echo evaluation of pulmonary venous-left atrial pressure gradients: human and numerical model studies

The simplified Bernoulli equation relates fluid convective energy derived from flow velocities to a pressure gradient and is commonly used in clinical echocardiography to determine pressure differences across stenotic orifices. Its application to pulmonary venous flow has not been described in humans. Twelve patients undergoing cardiac surgery had simultaneous high-fidelity pulmonary venous and left atrial pressure measurements and pulmonary venous pulsed Doppler echocardiography performed. Convective gradients for the systolic (S), diastolic (D), and atrial reversal (AR) phases of pulmonary venous flow were determined using the simplified Bernoulli equation and correlated with measured actual pressure differences. A linear relationship was observed between the convective (y) and actual (x) pressure differences for the S (y = 0.23x + 0.0074, r = 0.82) and D (y = 0.22x + 0.092, r = 0.81) waves, but not for the AR wave (y = 0. 030x + 0.13, r = 0.10). Numerical modeling resulted in similar slopes for the S (y = 0.200x - 0.127, r = 0.97), D (y = 0.247x - 0. 354, r = 0.99), and AR (y = 0.087x - 0.083, r = 0.96) waves. Consistent with numerical modeling, the convective term strongly correlates with but significantly underestimates actual gradient because of large inertial forces.

Non-NASA Center↗

NASA NTRS1995

The development of concentration gradients in a suspension of chemotactic bacteria

When a suspension of bacterial cells of the species Bacillus subtilis is placed in a chamber with its upper surface open to the atmosphere complex bioconvection patterns are observed. These arise because the cells: (1) are denser than water; and (2) usually swim upwards, so that the density of an initially uniform suspension becomes greater at the top than the bottom. When the vertical density gradient becomes large enough, an overturning instability occurs which ultimately evolves into the observed patterns. The reason that the cells swim upwards is that they are aerotactic, i.e., they swim up gradients of oxygen, and they consume oxygen. These properties are incorporated in conservation equations for the cell (N) and oxygen (C) concentrations, and these are solved in the pre-instability phase of development when N and C depend only on the vertical coordinate and time. Numerical results are obtained for both shallow- and deep-layer chambers, which are intrinsically different and require different mathematical and numerical treatments. It is found that, for both shallow and deep chambers, a thin boundary layer, densely packed with cells, forms near the surface. Beneath this layer the suspension becomes severely depleted of cells. Furthermore, in the deep chamber cases, a discontinuity in the cell concentration arises between this cell-depleted region and a cell-rich region further below, where no significant oxygen concentration gradients develop before the oxygen is fully consumed. The results obtained from the model are in good qualitative agreement with the experimental observations.

NASA Discipline Cell Biology↗

NASA NTRS2006

Minimum mass design of large-scale space trusses subjected to thermal gradients

Lightweight, deployable trusses are commonly used to support space-borne instruments including RF reflectors, radar panels, and telescope optics. While in orbit, these support structures are subjected to thermal gradients that vary with altitude, location in orbit, and self-shadowing. Since these instruments have tight dimensional-stability requirements, their truss members are often covered with multi-layer insulation (MLI) blankets to minimize thermal distortions. This paper develops a radiation heat transfer model to predict the thermal gradient experienced by a triangular truss supporting a long, linear radar panel in Medium Earth Orbit (MEO). The influence of self-shadowing effects of the radar panel are included in the analysis, and the influence of both MLI thickness and outer covers/coatings on the magnitude of the thermal gradient are formed into a simple, two-dimensional analysis. This thermal model is then used to size and estimate the structural mass of a triangular truss that meets a given set of structural requirements.

thermal truss analysis↗

NASA NTRS2010

Custom Gradient Compression Stockings May Prevent Orthostatic Intolerance in Astronauts After Space Flight

Orthostatic intolerance after space flight is still an issue for astronauts as no in-flight countermeasure has been 100% effective. NASA astronauts currently wear an inflatable anti-gravity suit (AGS) during re-entry, but this device is uncomfortable and loses effectiveness upon egress from the Shuttle. We recently determined that thigh-high, gradient compression stockings were comfortable and effective after space flight, though to a lesser degree than the AGS. We also recently showed that addition of splanchnic compression to this thigh-high compression stocking paradigm improved orthostatic tolerance to a level similar to the AGS, in a ground based model. Purpose: The purpose of this study was to evaluate a new, three-piece breast-high gradient compression garment as a countermeasure to post-space flight orthostatic intolerance. Methods: Eight U.S. astronauts have volunteered for this experiment and were individually fitted for a three-piece, breast-high compression garment to provide 55 mmHg compression at the ankle which decreased to approximately 20 mmHg at the top of the leg and provides ~15 mmHg over the abdomen. Orthostatic testing occurred 30 days pre-flight (w/o garment) and ~2 hours after flight (w/ garment) on landing day. Blood pressure (BP), Heart Rate (HR) and Stroke Volume (SV) were acquired for 2 minutes while the subject lay prone and then for 3.5 minutes after the subject stands up. To date, two astronauts have completed pre- and post-space flight testing. Data are mean SD. Results: BP [pre (prone to stand): 137+/-1.6 to 129+/-2.5; post: 130+/-2.4 to 122+/-1.6 mmHg] and SV [pre (prone to stand): 61+/-1.6 to 38+/-0.2; post: 58+/-6.4 to 37+/-6.0 ml] decreased with standing, but no differences were seen post-flight w/ compression garments compared to pre-flight w/o garments. HR [pre (prone to stand): 66+/-1.6 to 74+/-3.0, post: 67+/-5.6 to 78+/-6.8 bpm] increased with standing, but no differences were seen pre- to post-flight. Conclusion: After space flight, blood pressure and stroke volume are normally decreased and heart rate is usually elevated to compensate. In this small group of subjects, breast-high gradient compression stockings seem to have prevented these negative effects of spaceflight.

Stenger, Michael B.↗