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NASA NTRS1983

The minimum mantle viscosity of an accreting earth

The minimum mantle viscosity in an earth accreting from planetesimals is estimated. A plausible distribution of planetesimal sizes deposits enough energy to melt the outer nine-tenths of earth's mass; however, vigorous convection keeps temperatures near the solidus. Viscosity is significantly lower than prevails now. The temperature-dependent viscosity provides self-regulation so there is a continuing balance between accretional energy input and heat transfer out. This allows calculation of the minimum viscosity necessary to transfer out heat by a Nu/Ra-number relation. Typical viscosities are 0.1 to a million sq m/sec, lowest at mid-accretion when the mass growth rate is largest. Terrestrial planets are compared, and minimum iron descent times to central lithospheres are calculated.

Cooperman, S. A.↗

NASA NTRS1985

Measurement and correlation of jet fuel viscosities at low temperatures

Apparatus and procedures were developed to measure jet fuel viscosity for eight current and future jet fuels at temperatures from ambient to near -60 C by shear viscometry. Viscosity data showed good reproducibility even at temperatures a few degrees below the measured freezing point. The viscosity-temperature relationship could be correlated by two linear segments when plotted as a standard log-log type representation (ASTM D 341). At high temperatures, the viscosity-temperature slope is low. At low temperatures, where wax precipitation is significant, the slope is higher. The breakpoint between temperature regions is the filter flow temperature, a fuel characteristic approximated by the freezing point. A generalization of the representation for the eight experimental fuels provided a predictive correlation for low-temperature viscosity, considered sufficiently accurate for many design or performance calculations.

Schruben, D. L.↗

NASA NTRS1986

Plasma viscosity elevations with simulated weightlessness

A hypothesis correlating an increase in blood viscosity during bed rest to a decrease in aerobic capacity during simulated weightlessness is tested. Eight human subjects were studied on the sixth day of bed rest during two consecutive 10-d bed rest periods separated by a 14-d recovery interval designed to simulate the flight-layover schedule of Shuttle astronauts. Plasma viscosity and volume were measured, together with maximal aerobic capacity (VO2max). An increase in hematocrit, plasma protein, and fibrinogen concentrations was found, contributing to an elevation in plasma viscosity. VO2max decreased significantly in the first, but not the second bed rest cycle, and though many individuals exhibited a decrease in plasma volume and aerobic capacity coupled with elevated plasma viscosity, correlations between these variables were lacking. It is concluded that the decrease in VO2max observed following simulated weightlessness cannot be attributed to alterations in muscle blood flow resulting from increased blood viscosity.

Martin, D. G.↗

NASA NTRS1987

Calculated viscosity-distance dependence for some actively flowing lavas

The importance of viscosity as a gauge of the various energy and momentum dissipation regimes of lava flows has been realized for a long time. Nevertheless, despite its central role in lava dynamics and kinematics, it remains among the most difficult of flow physical properties to measure in situ during an eruption. Attempts at reconstructing the actual emplacement viscosities of lava flows from their solidified topographic form are difficult. Where data are available on the position of an advancing flow front as a function of time, it is possible to calculate the effective viscosity of the front as a function of distance from the vent, under the assumptions of a steady state regime. As an application and test of an equation given, relevant parameters from five recent flows on Mauna Loa and Kilauea were utilized to infer the dynamic structure of their aggregate flow front viscosity as they advanced, up to cessation. The observed form of the viscosity-distance relation for the five active Hawaiian flows examined appears to be exponential, with a rapid increase just before the flows stopped as one would expect.

Pieri, David↗

NASA NTRS1987

The effect of a shallow low viscosity zone on the apparent compensation of midplate swells

A model for midplate swells is assumed where the swell topography is dynamically maintained by convection beneath a conducting lid. Using an idealized viscosity structure consisting of a low viscosity layer underneath the lid and overlying a constant viscosity region, the effect of the low viscosities, the layer thickness, and the Rayleigh number on the flow and on the inference of a compensation mechanism from the associated gravity, geoid, and topography anomalies is investigated. The calculations show that a simple plume model with stratified viscosity variations of less than two orders of magnitude near the surface can produce the range of depths of compensation seen at midplate swells. Shallow depths of compensation, therefore, cannot be used to argue against dynamic models for the formation of hot spot swells.

Robinson, Elizabeth M.↗

NASA NTRS1987

Quantitative characterization of the viscosity of a microemulsion

The viscosity of the three-component microemulsion water/decane/AOT has been measured as a function of temperature and droplet volume fraction. At temperatures well below the phase-separation temperature the viscosity is described by treating the droplets as hard spheres suspended in decane. Upon approaching the two-phase region from low temperature, there is a large (as much as a factor of four) smooth increase of the viscosity which may be related to the percolation-like transition observed in the electrical conductivity. This increase in viscosity is not completely consistent with either a naive electroviscous model or a simple clustering model. The divergence of the viscosity near the critical point (39 C) is superimposed upon the smooth increase. The magnitude and temperature dependence of the critical divergence are similar to that seen near the critical points of binary liquid mixtures.

Berg, Robert F.↗

NASA NTRS1988

The effect of a shallow low-viscosity zone on the mantle flow, the geoid anomalies and the geoid and depth-age relationships at fracture zones

A two-dimensional FEM is used to investigate the flow driven by the horizontal temperature gradient at a fracture zone and to calculate the resulting geoid and topography anomalies. Using a three-layered viscosity structure for the upper mantle, results are presented for the effects of varying: (1) the viscosity contrast between the fluid layers: (2) the Rayleigh number based on the viscosity of the bottom layer; and (3) the thickness of the low-viscosity channel. Good agreement is obtained with the results of geoid anomalies over the Udintsev fracture zone when the viscosity of the top layer is greater than one order of magnitude less than post-glacial rebound values.

Robinson, Elizabeth M.↗

NASA NTRS1990

Effect of artificial viscosity on three-dimensional flow solutions

Artificial viscosity is added either implicitly or explicitly in practically every numerical scheme for suppressing spurious oscillations in the solution of fluid dynamics equations. In the present central-difference scheme, artificial viscosity is added explicitly for suppressing high frequency oscillations and achieving good convergence properties. The amount of artificial viscosity added is controlled through the use of pre-selected coefficients. In the standard scheme, scalar coefficients based on the spectral radii of the Jacobian of convective fluxes are used. However, this can add too much viscosity to the slower waves. Hence, use the matrix-valued coefficients, which give appropriate viscosity for each wave component is suggested. With the matrix-valued coefficients, the central-difference scheme produces more accurate solutions on a given grid, particularly in the vicinity of shocks, while still maintaining good convergence properties.

Turkel, Eli↗

NASA NTRS1991

Lower-mantle viscosity constrained by seismicity around deglaciated regions

It is shown here that seismicity around the margins of deglaciated areas provides a constraint on the viscosity of the lower mantle. Calculations using a spherical, viscoelastic earth model show that the present-day magnitude of the stress fields induced in the lithosphere beneath the Laurentide and Fennoscandian ice sheets is very sensitive to the value of the lower-mantle viscosity. Stress of about 100 bar, sufficient to cause seismicity, can still remain in the lithosphere for lower-mantle viscosities greater than about 10 to the 22nd Pa-s; for lower-mantle viscosities of about 10 to the 21st Pa-s, only a few tens of bars of stress persist in the lithosphere today. This influence of lower-mantle viscosity on the state of stress in the lithosphere also has implications for the migration of stress from earthquakes, and hence for earthquake recurrence times.

Spada, G.↗

NASA NTRS1992

Estimation of the viscosities of silicate liquids at high pressure from measurements of oxygen diffusivity

The dynamics and evolution of a magma ocean depend significantly on the structure and physical properties of silicate liquids at high pressure. Viscosity is particularly important because of its effect on the dynamics of convection and crystal setting. Traditionally, the viscosities of silicate liquids have been measured at high pressure by falling sphere viscometry but, due to some limitations of this technique, few measurements have been made at pressures exceeding 2.5 GPa. An alternative approach, which has previously been proven up to 2 GPa, is to use high pressure measurements of oxygen self-diffusivity (D) to estimate viscosity (eta) from the Eyring relationship eta = kT/D lambda (where k is the Boltzmann constant, T is absolute temperature, and lambda is the diffusive jump distance). We have performed preliminary experiments on Na2Si4O9 liquid in order to explore the feasibility of this method up to pressures in excess of 10 GPa. Diffusion couples were prepared from glass starting materials with one half of the sample enriched in O-18 and the other half containing the natural abundance (0.2 wt percent). Diffusion experiments were performed at 1600 to 1800 C at pressures in the range of 2.5 to 10 GPa for times up to 6 minutes using a 1200 ton multianvil apparatus. Oxygen diffusivities were derived from the resulting O-18 concentration profiles, which were analyzed using an ion microprobe. At 1800 C, oxygen diffusivities increase continuously from 1 x 10(exp -10) m(exp -2) s(exp -1) at 2.5 Gpa to 5 x 10(exp -10) m(exp -2) s(exp -1) at 10 GPa. From the Eyring relationship, the viscosity of Na2SiO9 liquid is predicted to decrease by approx. 0.7 log units over this pressure range at 1800 C. These trends, which can be related to changes in the structure of the liquid at high pressure, are in agreement with results of molecular dynamics calculations. These results suggest that it should be possible to estimate the viscosities of silicate liquids up to at least 15 GPa and 2200 C by this method.

Rubie, D. C.↗

NASA NTRS1992

Constraints on mantle viscosity from relative sea level variations in Hudson Bay

Frechet kernels for the RSL data in Hunson Bay are computed to determine the detailed depth-dependent sensitivity of the data to variations in a viscosity profile which is consistent with the past inferences. The RSL data provide a robust constraint on the average viscosity in the top half of the lower mantle only (the average must be near 10 exp 21 Pa s). The data admit models whose average viscosity in the deep mantle (below 1800 km depth) and in the upper mantle can differ significantly from the value (near 10 exp 21 Pa s) estimated for the top half of the lower mantle. The total variation in the viscosity from the surface to the CMB can exceed an order of magnitude or more and still satisfy the constraint provided by the Hudson Bay RSL data set. The necessity of invoking an isoviscous mantle model in previous studies is a consequence of the limited class of viscosity model solutions employed in those studies.

Mitrovica, J. X.↗

NASA NTRS1994

A New K-epsilon Eddy Viscosity Model for High Reynolds Number Turbulent Flows: Model Development and Validation

A new k-epsilon eddy viscosity model, which consists of a new model dissipation rate equation and a new realizable eddy viscosity formulation, is proposed. The new model dissipation rate equation is based on the dynamic equation of the mean-square vorticity fluctuation at large turbulent Reynolds number. The new eddy viscosity formulation is based on the realizability constraints: the positivity of normal Reynolds stresses and Schwarz' inequality for turbulent shear stresses. We find that the present model with a set of unified model coefficients can perform well for a variety of flows. The flows that are examined include: (1) rotating homogeneous shear flows; (2) boundary-free shear flows including a mixing layer, planar and round jets; (3) a channel flow, and flat plate boundary layers with and without a pressure gradient; and (4) backward facing step separated flows. The model predictions are compared with available experimental data. The results from the standard k-epsilon eddy viscosity model are also included for comparison. It is shown that the present model is a significant improvement over the standard k-epsilon eddy viscosity model.

Shih, T.-H.↗

NASA NTRS1994

Viscosity estimates for the crust and upper mantle from patterns of lacustrine shoreline deformation in the Eastern Great Basin

The deformed shorelines of Lake Bonneville constitute a classic source of information on lithospheric elastic thickness and upper mantle viscosity. We describe and apply a new model to a recently augmented data set. New data better constrain both the complex spatio-temporal pattern of the lake load and the crustal deformation response to that load. The history of lake level fluctuations has been significantly refined and somewhat modified. This is due to both more radiocarbon dates from within the Bonneville basin and to an improved calibration of the radiocarbon timescale itself. The data which constrain the crustal deformation pattern consist of ages and shoreline elevations from several hundred points which sample three major levels of Lake Bonneville and corresponding elevations from the high stands of three smaller lakes situated to the west of Lake Bonneville. The geometry of the Earth model incorporates an arbitrary number of layers overlying a half-space, and the rheology of each level can accommodate an arbitrary number of Maxwell viscoelastic elements in parallel. The inverse modeling comprises three complementary approaches: for the simplest configurations, we performed a direct search of the parameter space and delineated the irregular boundary of the subspace of acceptable models. For more complex configurations, we constrained the elastic parameters to their seismically determined values and then solved for viscosity versus depth profiles by either expressing the log(viscosity) versus log(depth) profile as a series of specially constructed orhtogonal polynomials, or by allowing each of 8-10 layers (plus the half-space) to have an independently determined viscosity. We found that the data do not strongly support (nor can they conclusively exclude) a more complex rheology than simple Maxwell viscoelasticity. The orthogonal polynomial solution exhibits an essentially monotonic decrease in viscosity with depth.

Bills, Bruce G.↗

NASA NTRS1995

Localization of toroidal motion and shear heating in 3-D high Rayleigh number convection with temperature-dependent viscosity

We have applied spectral-transform methods to study three-dimensional thermal convection with temperature-dependent viscosity. The viscosity varies exponentially with the form exp(-BT), where B controls the viscosity contrast and T is temperature. Solutions for high Rayleigh numbers, up to an effective Ra of 6.25 x 10(exp 6), have been obtained for an aspect-ratio of 5x5x1 and a viscosity contrast of 25. Solutions show the localization of toroidal velocity fields with increasing vigor of convection to a coherent network of shear-zones. Viscous dissipation increases with Rayleigh number and is particularly strong in regions of convergent flows and shear deformation. A time-varying depth-dependent mean-flow is generated because of the correlation between laterally varying viscosity and velocity gradients.

Balachandar, S.↗

NASA NTRS1994

Effect of artificial viscosity on three-dimensional flow solutions

Artificial viscosity is added either implicity or explicitly in practically every numerical scheme for suppressing spurious oscillations in the solution of fluid-dynamics equations. In the present central-difference scheme, artificial viscosity is added explicitly for suppressing high-frequency oscillations and achieving good convergence properties. The amount of artificial viscosity added is controlled through the use of preselected coefficients. In the standard scheme, scalar coefficients based on the spectral radii of the Jacobian of the convective fluxes are used. However, this can add too much viscosity to the slower waves. Hence, the use of matrix-valued coefficients, which give appropriate viscosity for each wave component, is suggested. With the matrix-valued coefficients, the central-difference scheme produces more accurate solutions on a given grid, particularly in the vicinity of shocks and boundary layers, while still maintaining good convergence properties.

Turkel, Eli↗

NASA NTRS1995

A new non-eddy viscosity subgrid-scale model and its application to channel flow

To date, most large-eddy simulations (LES) have been carried out with eddy viscosity subgrid scale (SGS) models, with only a few exceptions that used the mixed model. Even though the assumptions behind Smagorinsky's model are rather stringent, it has been applied successfully to a variety of turbulent flows. This success is attributed to the ability of eddy viscosity models to drain energy from large scales, thus simulating the dissipative nature of turbulence. Most SGS models are absolutely dissipative, i.e. they remove energy from the large scales at every instant. However, SGS stresses may transfer energy back to the large scales intermittently; this reverse transfer or backscatter is especially important in geophysical flows and in transition. In a fully developed channel flow, there is reverse flow of energy from small to large scales near the walls, but eddy viscosity models are unable to account for this important feature. The dynamic localization eddy viscosity model of Ghosal et al. (1995) allows backscatter by co-evolving an auxiliary equation for the SGS energy; however, the computational cost is considerably larger than for conventional SGS models (Cabot 1994). In this report, a new non-eddy viscosity model based on local approximation of total quantities in terms of filtered ones is introduced; the scale similarity model of Bardina (1983) is a special case of this model. This procedure does not require the assumption of homogeneity, permits backscatter of energy from small to large scales, and is readily implemented in finite difference codes. The results of applying the proposed model to second order finite volume simulation of plane channel flow at high Reynolds numbers (Re(sub b) = 38,000) is described in this report. Greater emphasis is placed on the high Reynolds number flow since it provides a more rigorous test of the SGS model and its potential application. The results are compared to ones produced by the conventional and dynamic Smagorinsky models and the spectral LES of Piomelli (1993).

Shah, K. B.↗

NASA NTRS1995

The Spreading of Variable-Viscosity Axisymmetric Radial Gravity Currents: Applications to the Emplacement of Venusian 'Pancake' Domes

The Magellan images of Venus have revealed a number of intriguing volcanic features, including the steep-sided or 'pancake' domes. These volcanic domes or flows have morphologies that suggest formation by a single continuous emplacement of lava with a higher viscosity than that of the surrounding basaltic plains. Numerous investigators have suggested that such high viscosity is due to high silica content, leading to the conclusion that the domes are evidence of evolved magmatic products on Venus. However, viscosity depends on crystallinity as well as on silica content: high viscosity could therefore also be due to a cooler (and therefore higher crystal content) lava. Models of dome emplacement which include both cooling and composition factors are thus necessary in order to determine the ranges of crystallinity and silica content which might lead to the observed gross dome morphologies. Accordingly, in this study domes are modelled as radial viscous gravity currents with an assumed cooling-induced viscosity increase to include both effects. Analytical and numerical results indicate that pancake dome formation is feasible with compositions ranging from basaltic to rhyolitic. Therefore, observations of gross dome morphology alone are insufficient for determining composition and the domes do not necessarily represent strong evidence for evolved magmatism on Venus.

Sakimoto, S. E. H.↗

NASA NTRS2002

Viscosity Measurement Using Drop Coalescence in Microgravity

We present in here validation studies of a new method for application in microgravity environment which measures the viscosity of highly viscous undercooled liquids using drop coalescence. The method has the advantage of avoiding heterogeneous nucleation at container walls caused by crystallization of undercooled liquids during processing. Homogeneous nucleation can also be avoided due to the rapidity of the measurement using this method. The technique relies on measurements from experiments conducted in near zero gravity environment as well as highly accurate analytical formulation for the coalescence process. The viscosity of the liquid is determined by allowing the computed free surface shape relaxation time to be adjusted in response to the measured free surface velocity for two coalescing drops. Results are presented from two sets of validation experiments for the method which were conducted on board aircraft flying parabolic trajectories. In these tests the viscosity of a highly viscous liquid, namely glycerin, was determined at different temperatures using the drop coalescence method described in here. The experiments measured the free surface velocity of two glycerin drops coalescing under the action of surface tension alone in low gravity environment using high speed photography. The liquid viscosity was determined by adjusting the computed free surface velocity values to the measured experimental data. The results of these experiments were found to agree reasonably well with the known viscosity for the test liquid used.

Antar, Basil N.↗