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NASA NTRS1989

Inviscid spatial stability of a compressible mixing layer. Part 3: Effect of thermodynamics

The results of a comprehensive comparative study of the inviscid spatial stability of a parallel compressible mixing layer using various models for the mean flow are reported. The models are: (1) the hyperbolic tangent profile for the mean speed and the Crocco relation for the mean temperature, with the Chapman viscosity-temperature relation and a Prandtl number of one; (2) the Lock profile for the mean speed and the Crocco relation for the mean temperature, with the Chapman viscosity-temperature relation and a Prandtl number of one; and (3) the similarity solution for the coupled velocity and temperature equations using the Sutherland viscosity temperature relation and arbitrary but constant Prandtl number. The purpose was to determine the sensitivity of the stability characteristics of the compressible mixing layer to the assumed thermodynamic properties of the fluid. It is shown that the quantative features of the stability characteristics are quite similiar for all models but that there are quantitative differences resulting from the difference in the thermodynamic models. In particular, it is shown that the stability characteristics are sensitive to the value of the Prandtl number.

Jackson, T. L.↗

NASA NTRS1988

Viscous effects on the resonance of a slotted wind tunnel using finite elements

Prompted by the fact that wind tunnel flutter and oscillatory airload measurements are affected by acoustic vibration mode coupling when the model frequency lies near a wind tunnel resonance frequency, a numerical method has been developed for design sensitivity analysis. Solid curves represent the resonant frequency for the slot, without considering the slot's viscosity. While the viscosity effect decreases with increasing slot width, the viscosity effect also decreases as the slot width approaches zero.

Lee, IN↗

NASA NTRS1989

Rift propagation

A model for rift propagation which treats the rift as a crack in an elastic plate which is filled from beneath by upwelling viscous asthenosphere as it lengthens and opens. Growth of the crack is driven by either remotely applied forces or the pressure of buoyant asthenosphere in the crack and is resisted by viscous stresses associated with filling the crack. The model predicts a time for a rift to form which depends primarily on the driving stress and asthenosphere viscosity. For a driving stress on the order of 10 MPa, as expected from the topography of rifted swells, the development of rifts over times of a few Myr requires an asthenosphere viscosity of 10 to the 16th Pa s (10 to the 17th poise). This viscosity, which is several orders of magnitude less than values determined by postglacial rebound and at least one order of magnitude less than that inferred for spreading center propagation, may reflect a high temperature or large amount of partial melting in the mantle beneath a rifted swell.

Parmentier, E. M.↗

NASA NTRS1987

Investigation of turbulent flow in highly curved ducts with application to turbomachinery components

Numerical predictions were performed using a semi-elliptic calculation procedure for the case of turbulent flow in passage through a 90 deg bend of square cross section. Two versions of the isotropic turbulent viscosity two equation k-epsilon model were used. The first, the wall function model (WFM), employs the logarithmic law-of-the-wall relation and the notion of equilibrium flow to set all the necessary boundary conditions at the first grid point adjacent to a solid wall. The second model, the Van Driest model (VDM), employs Prandtl's original mixing length formulation, in conjunction with Van Driest's semi-empirical relation for the mixing length, to calculate the turbulent viscosity in the near wall regions of the flow. In this case, boundary conditions for k and epsilon, required to calculate these quantities in the core of the flow, are obtained by matching the mixing length and Reynolds number model formulations in an overlapping region of the flow near the walls. In both cases the results obtained show an improvement over earlier calculations using an elliptic numerical procedure. This is attributed to the finer grids possible in the present work. Of the two models, the VDM formulation shows better overall conformity with the mean flow measurements. Neither model reproduces well the details of the stress distribution as a result of the implied isotropic turbulent viscosity.

Humphrey, J. A. C.↗

NASA NTRS1989

Local error estimates for discontinuous solutions of nonlinear hyperbolic equations

Let u(x,t) be the possibly discontinuous entropy solution of a nonlinear scalar conservation law with smooth initial data. Suppose u sub epsilon(x,t) is the solution of an approximate viscosity regularization, where epsilon greater than 0 is the small viscosity amplitude. It is shown that by post-processing the small viscosity approximation u sub epsilon, pointwise values of u and its derivatives can be recovered with an error as close to epsilon as desired. The analysis relies on the adjoint problem of the forward error equation, which in this case amounts to a backward linear transport with discontinuous coefficients. The novelty of this approach is to use a (generalized) E-condition of the forward problem in order to deduce a W(exp 1,infinity) energy estimate for the discontinuous backward transport equation; this, in turn, leads one to an epsilon-uniform estimate on moments of the error u(sub epsilon) - u. This approach does not follow the characteristics and, therefore, applies mutatis mutandis to other approximate solutions such as E-difference schemes.

Tadmor, Eitan↗

NASA NTRS1990

Polysiloxanes derived from the controlled hydrolysis of tetraethoxysilane as precursors to silica for use in ceramic processing

Synthesis, properties, and potential applications in ceramic processing for two polysiloxane silica precursors derived from the controlled hydrolysis of tetraethoxysilane (TEOS) are presented. The higher molecular weight TEOS-A is a thick adhesive liquid of viscosity 8000 to 12,000 c.p. having a SiO2 char yield of about 55 percent. The lower molecular weight TEOS-B is a more fluid liquid of viscosity 150 to 200 c.p. having a SiO2 char yield of about 52 percent. The acid catalyzed hydrolysis of TEOS to hydrated silica gel goes through a series of polysiloxane intermediates. The rate of this transition increases with the quantity of water added to the TEOS; thus, for ease of polymer isolation, the amount of water added must be carefully determined so as to produce the desired polymer in a reasonable time. The water to TEOS mole ratio falls in the narrow range of 1.05 for TEOS-A and 0.99 for TEOS-B. Further polymerization or gelation is prevented by storing at -5 C in a freezer. Both polysiloxanes thermoset to a glassy solid at 115 C. The liquid polymers are organic in nature in that they are miscible with toluene and ethanol, slightly souble in heptane, but immiscible with water. For both polymers, results on viscosity versus time are given at several temperatures and water additions. Based on these results, some examples of practical utilization of the precursors for ceramic fabrication are given.

Philipp, Warren H.↗

NASA NTRS1990

A turbulent two-phase flow model for nebula flows

A new and very efficient turbulent two-phase flow numericaly model is described to analyze the environment of a protoplanetary nebula at a stage prior to the formation of planets. Focus is on settling processes of dust particles in flattened gaseous nebulae. The model employs a perturbation technique to improve the accuracy of the numerical simulations of such flows where small variations of physical quantities occur over large distance ranges. The particles are allowed to be diffused by gas turbulence in addition to settling under gravity. Their diffusion coefficients is related to the gas turbulent viscosity by the non-dimensional Schmidt number. The gas turbulent viscosity is determined by the means of the eddy viscosity hypothesis that assumes the Reynolds stress tensor proportional to the mean strain rate tensor. Zero- and two-equation turbulence models are employed. Modeling assumptions are detailed and discussed. The numerical model is shown to reproduce an existing analytical solution for the settling process of particles in an inviscid nebula. Results of nebula flows are presented taking into account turbulence effects of nebula flows. Diffusion processes are found to control the settling of particles.

Champney, Joelle M.↗

NASA NTRS1989

Long-wavelength variations in earth's geoid - Physical models and dynamical implications

Seismic tomography and fluid dynamical models are extended to include a detailed and realistic parameterization of the viscosity structure of the mantle. The model also includes the effects of heterogeneity inferred from surface-wave studies of upper-mantle structure. It is found that about 90 percent of the observed geoid may be explained by density anomalies inferred from tomography, a model of subducted slabs, and an earth model with a low-viscosity asthenosphere over a moderate-viscosity lower mantle.

Hager, B. H.↗

NASA NTRS1990

Wave formation on a liquid layer for de-icing airplane wings

Wave formation on a thin liquid layer used for deicing aircraft wings is investigated by studying the stability of airflow over a liquid-coated flat plate at zero angle of incidence. The ratio of the viscosity of the liquid to that of air is very high (over 500,000), and the Reynolds number based on liquid depth and air viscosity is of the order of a few thousand. Under these circumstances the analysis gives two formulas, in closed form, for the growth rate and phase velocity of the waves in terms of the wavenumber and other relevant parameters. The expected wavenumber is that for which the growth rate is the maximum. The instability is one in which the viscosity difference between the two fluids (air and liquid) plays the dominant role, and is of the kind found by Yih (1967).

Yih, Chia-Shun↗

NASA NTRS1991

Fluid volcanism on Miranda and Ariel - Flow morphology and composition

Several types of volcanic units have been recognized on the icy Uranian satellites Miranda and Ariel. On Miranda, ridges characterized by crest grooves are up to 10 km wide and 500 m high. A continuous flat-topped flow band also 10 km wide and 500 m high forms the outer southern margin of Elsinore Corona, which appears to comprise coalesced flow bands and ridges. On Ariel, in addition to at least one ridge unit similar to those on Miranda, flood plains material has covered the floors of deep chasmata (grabens) and an irregular depression. Flows on both satellites are characterized by linear vent geometries and distinct topographic margins, which indicate extrusion of a relatively viscous material. The topography of the flows can be used to estimate flow viscosity or yield strength using a Bingham plastic model. Extrusion viscosity estimates, incorporating plausible volcanologically based emplacement time scales and a rigid crust correction, range from 10 MP to 1 GP (10 TP in the unlikely absence of a chilled crust). Viscosity estimates are dependent on the assumed emplacement time scale, however, and could be as high as 10 PP, if a solid-state-based time scale is assumed.

Schenk, Paul M.↗

NASA NTRS1991

Inviscid spatial stability of a compressible mixing layer. III - Effect of thermodynamics

The results of a comprehensive comparative study of the inviscid spatial stability of a parallel compressible mixing layer using various models for the mean flow are reported. The models are: (1) the hyperbolic tangent profile for the mean speed and the Crocco relation for the mean temperature, with the Chapman viscosity-temperature relation and a Prandtl number of one; (2) the Lock profile for the mean speed and the Crocco relation for the mean temperature, with the Chapman viscosity-temperature relation and a Prandtl number of one; and (3) the similarity solution for the coupled velocity and temperature equations using the Sutherland viscosity temperature relation and arbitrary but constant Prandtl number. The purpose was to determine the sensitivity of the stability characteristics of the compressible mixing layer to the assumed thermodynamic properties of the fluid. It is shown that the quantitative features of the stability characteristics are quite similar for all models but that there are quantitative differences resulting from the difference in the thermodynamic models. In particular, it is shown that the stability characteristics are sensitive to the value of the Prandtl number.

Jackson, T. L.↗

NASA NTRS1991

Studies on the dynamics of Venus ionosphere - Effects of varying the ionopause height and the onset of turbulence

The conservation equations of plasma dynamics in the upper ionosphere of Venus have been solved by using a spectral method in the horizontal and finite differencing in the vertical direction. The effect of varying the ionopause height on the computed nightside ion densities is investigated. These ion densities show a sharp decrease as the ionopause altitude is reduced to 300 km. The effect of viscous forces on the horizontal plasma flow is investigated for a wide range of values of the coefficient of viscosity. The Reynolds numbers characteristics of the flow are calculated and the conditions for the onset of turbulence discussed. It is found that the Reynolds number can be large (greater than 1000) in the subsolar region for a coefficient of viscosity of up to 1.6 x 10 to the -10th g/cm s. The influence of magnetic fields on viscosity is also discussed.

Singhal, R. P.↗

NASA NTRS1990

On the Subgrid-Scale Modeling of Compressible Turbulence

A new sub-grid scale model is presented for the large-eddy simulation of compressible turbulence. In the proposed model, compressibility contributions have been incorporated in the sub-grid scale eddy viscosity which, in the incompressible limit, reduce to a form originally proposed by Smagorinsky (1963). The model has been tested against a simple extension of the traditional Smagorinsky eddy viscosity model using simulations of decaying, compressible homogeneous turbulence. Simulation results show that the proposed model provides greater dissipation of the compressive modes of the resolved-scale velocity field than does the Smagorinsky eddy viscosity model. For an initial r.m.s. turbulence Mach number of 1.0, simulations performed using the Smagorinsky model become physically unrealizable (i.e., negative energies) because of the inability of the model to sufficiently dissipate fluctuations due to resolved scale velocity dilations. The proposed model is able to provide the necessary dissipation of this energy and maintain the realizability of the flow. Following Zeman (1990), turbulent shocklets are considered to dissipate energy independent of the Kolmogorov energy cascade. A possible parameterization of dissipation by turbulent shocklets for Large-Eddy Simulation is also presented.

Squires, Kyle↗

NASA NTRS1992

Effects of curvature and rotation on turbulence in the NASA low-speed centrifugal compressor impeller

The flow in the NASA Low-Speed Impeller is affected by both curvature and rotation. The flow curves due to the following: (1) geometric curvature, e.g. the curvature of the hub and shroud profiles in the meridional plane and the curvature of the backswept impeller blades; and (2) secondary flow vortices, e.g. the tip leakage vortex. Changes in the turbulence and effective turbulent viscosity in the impeller are investigated. The effects of these changes on three-dimensional flow development are discussed. Two predictions of the flow in the impeller, one with, and one without modification to the turbulent viscosity due to rotation and curvature, are compared. Some experimental and theoretical background for the modified mixing length model of turbulent viscosity will also be presented.

Moore, Joan G.↗

NASA NTRS1991

A mantle plume model for the Equatorial Highlands of Venus

The possibility that the Equatorial Highlands are the surface expressions of hot upwelling mantle plumes is considered via a series of mantle plume models developed using a cylindrical axisymmetric finite element code and depth-dependent Newtonian rheology. The results are scaled by assuming whole mantle convection and that Venus and the earth have similar mantle heat flows. The best model fits are for Beta and Atla. The common feature of the allowed viscosity models is that they lack a pronounced low-viscosity zone in the upper mantle. The shape of Venus's long-wavelength admittance spectrum and the slope of its geoid spectrum are also consistent with the lack of a low-viscosity zone. It is argued that the lack of an asthenosphere on Venus is due to the mantle of Venus being drier than the earth's mantle. Mantle plumes may also have contributed to the formation of some smaller highland swells, such as the Bell and Eistla regions and the Hathor/Innini/Ushas region.

Kiefer, Walter S.↗

NASA NTRS1992

The secondary outburst maximum of T Coronae Borealis - Implications for the physics of accretion disks

The hypothesis of Webbink (1976) that the accretion of a torus of matter onto a main-sequence star caused secondary maxima during the 1866 and 1946 eruptions of the recurrent nova T CrB is examined. Simple 1D calculations show that the accretion disk viscosity must increase with time to produce light curves resembling observations. It is inferred that the physical mechanism responsible for producing the viscous dissipation in the accretion disk has a fast growth rate and saturates to a viscosity parameter of order unity. The good agreement between parameters estimated from observations and those derived from a physical mechanism suggests that the growth rate instability identified by Balbus and Hawley (1991) is a promising source for accretion disk viscosity.

Cannizzo, John K.↗

NASA NTRS1992

Effects on post-glacial rebound from the hard rheology in the transition zone

The effect of an increase of viscosity in the earth-mantle's transition zone between 420 and 670 km on the geophysical signatures induced by postglacial rebound was analyzed using a self-gravitating model consisting of an elastic lithosphere, a three-layer viscoelastic mantle, and an inviscid core. Results show that the horizontal displacements and velocities as well as the stress pattern are extremely sensitive to the viscosity increase and to the chemical stratification of the transition zone. The findings indicate that geodetic data on intraplate deformation can be used to put constraints on the viscosity increase in the transition zone and on the amount of chemical stratification in the mantle.

Spada, Giorgio↗

NASA NTRS1992

Numerical models of mantle convection

An overview of numerical methods describing the structure and dynamics of the mantle is presented with attention given to novel 3D modeling techniques. The paper reviews 3D spherical and Cartesian models for constant viscosity emphasizing the assumptions regarding style of convection, time dependence, and implications for the mantle. Similarly treated are 3D Cartesian models with temperature-dependent viscosities, and briefly examined are models that are based on compressibility, nonlinear viscosity, or plates. Extensive illustrations are presented detailing: (1) temperature variations from models of 3D thermal convection in spherical shells; (2) thermal anomalies in equatorial cross sections; and (3) temperature variations in a spherical shell heated from within. The discussion relates the numerical results of the models with real mantle-convection events, and the simulations are shown to yield increasingly realistic representations of material behavior.

Schubert, G.↗