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NASA NTRS1988

Gravity-driven deformation of the crust on Venus

Intense horizontal deformation features are observed on the surface of Venus despite the apparent absence of terrestrial-style plate tectonics. High surface temperature, low erosion rate, and regions of elevated terrain suggest that gravity spreading may be responsible for some of these features. Gravity spreading on the Earth is known to cause extensive deformation in certain thin-skinned tectonic regions, where the uppermost layers become detached along a decollement. While the high pore pressures and soft sedimentary rocks frequently observed along decollements on the Earth are not plausible for Venus, temperature induced regions of ductile deformation may exist. Simple viscous models of gravity spreading above a ductile region of the crust are developed to examine the effects of rheology, thermal gradient, surface slope and crustal thickness on deformation. For a reasonable range of parameters, the models show that surface-slope-driven ductile deformation at relatively shallow depths in the crust is possible and may be capable of detaching the uppermost rigid portion of the crust, resulting in horizontal translation.

Smrekar, Suzanne↗

NASA NTRS1989

Euler solvers for transonic applications

The 1980s may well be called the Euler era of applied aerodynamics. Computer codes based on discrete approximations of the Euler equations are now routinely used to obtain solutions of transonic flow problems in which the effects of entropy and vorticity production are significant. Such codes can even predict separation from a sharp edge, owing to the inclusion of artificial dissipation, intended to lend numerical stability to the calculation but at the same time enforcing the Kutta condition. One effect not correctly predictable by Euler codes is the separation from a smooth surface, and neither is viscous drag; for these some form of the Navier-Stokes equation is needed. It, therefore, comes as no surprise to observe that the Navier-Stokes has already begun before Euler solutions were fully exploited. Moreover, most numerical developments for the Euler equations are now constrained by the requirement that the techniques introduced, notably artificial dissipation, must not interfere with the new physics added when going from an Euler to a full Navier-Stokes approximation. In order to appreciate the contributions of Euler solvers to the understanding of transonic aerodynamics, it is useful to review the components of these computational tools. Space discretization, time- or pseudo-time marching and boundary procedures, the essential constituents are discussed. The subject of grid generation and grid adaptation to the solution are touched upon only where relevant. A list of unanswered questions and an outlook for the future are covered.

Vanleer, Bram↗

NASA NTRS1988

Head-on collision of viscous vortex rings

The head-on collision of two identical axisymmetric viscous vortex rings is studied through direct simulations of the incompressible Navier-Stokes equations. The initial vorticity distributions considered are those of Hill's spherical vortex and of rings with circular Gaussian cores, each at Reynolds numbers of about 350 and 1000. The Reynolds number is defined by Gamma/Nu, the ratio of circulation to viscosity. As the vortices approach each other by self-induction, the radii increase by mutual induction, and vorticy cancels through viscous cross-diffusion across the collision plane. Following contact, the vorticity distribution in the core forms a head-tail structure (for the cases considered). The characteristic time of vorticity annihilation is compared with that of a 3D collision experiment and 3D numerical simulations. It is found that the annihilation time is somewhat longer in the axisymmetric case than it is in the symmetry plane of the experiment and 3D numerical simulation. By comparing the annihilatiom time with a viscous timescale and a circulation timescale, it is deduced that both the strain rate due to local effects and to 3D vorticity realignment are important.

Stanaway, S.↗

NASA NTRS1993

Transition prediction and control in subsonic flow over a hump

The influence of a surface roughness element in the form of a two-dimensional hump on the transition location in a two-dimensional subsonic flow with a free-stream Mach number up to 0.8 is evaluated. Linear stability theory, coupled with the N-factor transition criterion, is used in the evaluation. The mean flow over the hump is calculated by solving the interacting boundary-layer equations; the viscous-inviscid coupling is taken into consideration, and the flow is solved within the separation bubble. The effects of hump height, length, location, and shape; unit Reynolds number; free-stream Mach number, continuous suction level; location of a suction strip; continuous cooling level; and location of a heating strip on the transition location are evaluated. The N-factor criterion predictions agree well with the experimental correlation of Fage; in addition, the N-factor criterion is more general and powerful than experimental correlations. The theoretically predicted effects of the hump's parameters and flow conditions on transition location are consistent and in agreement with both wind-tunnel and flight observations.

Masad, Jamal A.↗

NASA NTRS2004

Condensation Front Migration in a Protoplanetary Nebula

Condensation front dynamics are investigated in the mid-solar nebula region. A quasi-steady model of the evolving nebula is combined with equilibrium vapor pressure curves to determine evolutionary condensation fronts for selected species. These fronts are found to migrate inwards from the far-nebula to final positions during a period of 10(exp 7) years. The physical process governing this movement is a combination of local viscous heating and luminescent heating from the central star. Two luminescent heating models are used and their effects on the ultimate radial position of the condensation front are discussed. At first the fronts move much faster than the nebular accretion velocity, but after a time the accreting gas and dust overtakes the slowing condensation front.

Davis, Sanford S.↗

NASA NTRS2020

Simulation-Based Analysis and Prediction of Thrust Vector Servoelastic Coupling

A method of analysis and prediction of servoelastic coupling in launch vehicles is presented, surveying the discovery and subsequent resolution of a predicted servoelastic resonance phenomenon affecting the NASA Space Launch System launch vehicle at specific flight conditions. A physics-based linearized multibody mechanization of the governing equations is combined with first principles analysis to demonstrate that antisymmetric bending of the solid rocket motors leads to a reduction of equivalent viscous modal damping through coupling with the thrust vector control actuators. The sensitivity to parameters and the effects of the resonance phenomenon on flight control performance and stability are confirmed through extensive simulation verification in the time and frequency domain. A novel enhancement in model fidelity that accounts for Coriolis effects of fluid flow on bending within the solid rocket motor case and nozzle is shown to add sufficient damping to reduce the risk of adverse control-structure interaction.

Jeb S Orr↗

NASA NTRS1989

Transonic airfoil design for helicopter rotor applications

Despite the fact that the flow over a rotor blade is strongly influenced by locally three-dimensional and unsteady effects, practical experience has always demonstrated that substantial improvements in the aerodynamic performance can be gained by improving the steady two-dimensional charateristics of the airfoil(s) employed. The two phenomena known to have great impact on the overall rotor performance are: (1) retreating blade stall with the associated large pressure drag, and (2) compressibility effects on the advancing blade leading to shock formation and the associated wave drag and boundary-layer separation losses. It was concluded that: optimization routines are a powerful tool for finding solutions to multiple design point problems; the optimization process must be guided by the judicious choice of geometric and aerodynamic constraints; optimization routines should be appropriately coupled to viscous, not inviscid, transonic flow solvers; hybrid design procedures in conjunction with optimization routines represent the most efficient approach for rotor airfroil design; unsteady effects resulting in the delay of lift and moment stall should be modeled using simple empirical relations; and inflight optimization of aerodynamic loads (e.g., use of variable rate blowing, flaps, etc.) can satisfy any number of requirements at design and off-design conditions.

Hassan, Ahmed A.↗

DOE OSTI2021

Mass accommodation and gas–particle partitioning in secondary organic aerosols: dependence on diffusivity, volatility, particle-phase reactions, and penetration depth

Abstract. Mass accommodation is an essential process for gas–particle partitioning of organic compounds in secondary organic aerosols (SOA). The mass accommodation coefficient is commonly described as the probability of a gas molecule colliding with the surface to enter the particle phase. It is often applied, however, without specifying if and how deep a molecule has to penetrate beneath the surface to be regarded as being incorporated into the condensed phase (adsorption vs. absorption). While this aspect is usually not critical for liquid particles with rapid surface–bulk exchange, it can be important for viscous semi-solid or glassy solid particles to distinguish and resolve the kinetics of accommodation at the surface, transfer across the gas–particle interface, and further transport into the particle bulk. For this purpose, we introduce a novel parameter: an effective mass accommodation coefficient αeff that depends on penetration depth and is a function of surface accommodation coefficient, volatility, bulk diffusivity, and particle-phase reaction rate coefficient. Application of αeff in the traditional Fuchs–Sutugin approximation of mass-transport kinetics at the gas–particle interface yields SOA partitioning results that are consistent with a detailed kinetic multilayer model (kinetic multilayer model of gas–particle interactions in aerosols and clouds, KM-GAP; Shiraiwa et al., 2012) and two-film model solutions (Model for Simulating Aerosol Interactions and Chemistry, MOSAIC; Zaveri et al., 2014) but deviate substantially from earlier modeling approaches not considering the influence of penetration depth and related parameters. For highly viscous or semi-solid particles, we show that the effective mass accommodation coefficient remains similar to the surface accommodation coefficient in the case of low-volatility compounds, whereas it can decrease by several orders of magnitude in the case of semi-volatile compounds. Such effects can explain apparent inconsistencies between earlier studies deriving mass accommodation coefficients from experimental data or from molecular dynamics simulations. Our findings challenge the approach of traditional SOA models using the Fuchs–Sutugin approximation of mass transfer kinetics with a fixed mass accommodation coefficient, regardless of particle phase state and penetration depth. The effective mass accommodation coefficient introduced in this study provides an efficient new way of accounting for the influence of volatility, diffusivity, and particle-phase reactions on SOA partitioning in process models as well as in regional and global air quality models. While kinetic limitations may not be critical for partitioning into liquid SOA particles in the planetary boundary layer (PBL), the effects are likely important for amorphous semi-solid or glassy SOA in the free and upper troposphere (FT–UT) as well as in the PBL at low relative humidity and low temperature.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1994

Gravity gradient or gravity jitter induced viscous stress and moment fluctuations in microgravity

The dynamical behavior of fluids affected by the asymmetric gravity gradient and gravity jitter accelerations, in particular the effect of surface tension on partially-filled rotating fluids with a special example applicable to a full-scale Gravity Probe-B Spacecraft dewar tank, has been investigated. Results of slosh wave excitation along the liquid-vapor interface induced by gravity gradient acceleration indicated one-up one-down and one-down and one-up oscillations of two bubbles in the cross-section of doughnut profiles in the vertical r-z plane of a rotating dewar, and an eccentric contour of a bubble rotating around the axis of the dewar in the horizontal r-theta plane. Results of slosh wave excitation along the liquid-vapor interface induced by gravity jitter acceleration showed an equivalent to the time-dependent oscillatory force which pushes a bubble in the combined bubble motion of down-and-up and leftward-and-rightward as the bubble is rotating with respect to a rotating dewar axis. Fluctuations of fluid stress forces, fluid stress moments, and moment arm of fluid moment exerted on the dewar wall of the container due to slosh wave excitations driven by gravity gradient acceleration or gravity jitter acceleration are also investigated.

Hung, R. J.↗

NASA NTRS1985

The collisional dynamics of particulate disks

It is shown that the use of the Krook equation greatly simplifies the discussion of the collisional dynamics of particulate disks. Collisions are assumed to be inelastic from the outset. A simple heuristic argument is used to compute the effective collision rate in a disk of spherical particles with a power-law distribution of sizes. For Saturn's rings, the effective collision rate for momentum transport is substantially lower than that conventionally estimated on the basis of an observed optical depth at visual wavelengths. The closure of the vertically integrated set of moment equations without discarding the third-order moments at the outset is discussed, allowing for the possibility of a bent disk. In the limit that the collision frequency is much larger than the orbit frequency, the usual Navier-Stokes equations of viscous hydrodynamics for a thin disk are recovered with an explicit expression for the shear viscosity. The method is generalized to include the effects of gravitational scattering.

Shu, F. H.↗

NASA NTRS1991

The effects of X-ray illumination on accretion disk interiors

The structure of accretion disks illuminated by X-ray from a central compact object. At radii larger than a certain value, X-ray heating can dominate the viscous heating and determine the disk structure in a standard alpha-disk model. The disk structure resulting from X-ray illumination is calculated both analytically and numerically for low-mass X-ray binaries as well as for active galactic nuclei. X-ray illumination does have important effects on the disk structures, under a variety of circumstances; instabilities may arise under significant X-ray heating.

Ko, Yuan-Kuen↗

NASA NTRS1977

Liquid jet impingement normal to a disk in zero gravity

The free surface shapes of circular liquid jets impinging normal to sharp-edged disks in zero gravity are determined. Zero gravity drop tower experiments yielded three distinct flow patterns that were classified in terms of the relative effects of surface tension and inertial forces. An order of magnitude analysis was conducted that indicated regions where viscous forces were not significant in the computation of free surface shapes. The free surface analysis was simplified by transforming the governing potential flow equations and boundary conditions into the inverse plane, where the stream function and velocity potential became the coordinates. The resulting nonlinear equations were solved by standard finite difference methods, and comparisons were made with the experimental data for the inertia dominated regime.

Labus, T. L.↗

NASA NTRS1979

Fundamental mechanisms that influence the estimate of heat transfer to gas turbine blades

Estimates of the heat transfer from the gas to stationary (vanes) or rotating blades poses a major uncertainty due to the complexity of the heat transfer processes. The gas flow through these blade rows is three dimensional with complex secondary viscous flow patterns that interact with the endwalls and blade surfaces. In addition, upstream disturbances, stagnation flow, curvature effects, and flow acceleration complicate the thermal transport mechanisms in the boundary layers. Some of these fundamental heat transfer effects are discussed. The chief purpose of the discussion is to acquaint those in the heat transfer community, not directly involved in gas turbines, of the seriousness of the problem and to recommend some basic research that would improve the capability for predicting gas-side heat transfer on turbine blades and vanes.

Graham, R. W.↗

NASA NTRS1979

Fundamental mechanisms that influence the estimate of heat transfer to gas turbine blades

Heat tranfer problems in aircraft gas turbines required for improved prediction of turbine blade or vane gas-side heat transfer are examined. Estimates of the heat transfer from the gas to vanes or rotating blades are uncertain due to the complexity of the heat transfer processes, since the gas flow is three dimensional with complex secondary viscous flow patterns that interact with the endwalls and blade surfaces. In addition, upstream disturbances, stagnation flow, curvature effects, and flow acceleration complicate the thermal transport mechanisms in the boundary layers. The thermal state and flow characteristics of the hot gases that enter the turbine blade row, analytical methods for calculating the gas-side heat transfer to turbine blades, and flow phenomena such as stagnation, curvature effects, acceleration, secondary flows, and transition that influences local heat transfer rates are discussed.

Graham, R. W.↗

NASA NTRS1982

Numerical solution of three-dimensional unsteady transonic flow over wings including inviscid/viscous interactions

A method is presented for computing the unsteady three-dimensional transonic flowfield about twin wings of arbitrary planform and section geometry including the effects of inviscid/viscous interaction. Dominant effects of the shock-boundary-layer interaction are accounted for by a simple empirically defined model, while viscous regions adjacent to the wing surface and along the trailing wake are described by a set of integral equations appropriate for two-dimensional turbulent flows. The validity of the proposed method is verified by comparison with steady three-dimensional experimental data and a solution of more exact equations for a typical transport wing configuration.

Rizzetta, D. P.↗

NASA NTRS1985

Dynamic fission instability of dissipative protoplanets

Analytical and numerical approaches are taken to consider if a rapidly rotating, viscous protoearth would have lost mass by a fission process and thereby given birth to the moon. The fast rotation is assumed as the source of the instability in the dissipative liquid protoearth. Governing hydrodynamic equations are defined for the evolution of the protoearth. Account is taken of viscous dissipation, the pressure equation of state for the atmospheric material sent on a ballistic trajectory, and the effective viscosity. The results indicate that dynamic fission was probably not the process by which the protomoon came into existence.

Boss, A. P.↗

NASA NTRS1985

Constraints on the rheological structure of the mantle

Rheological models of the mantle are at present limited to radial symmetry, usually with homogeneous linearly viscous or viscoelastic incompressible layers. While such models are probably overly simple, they readily allow calculation of geophysical effects, such as post glacial rebound and related changes in the Earth's shape. They are also directly applicable to problems of global mantle flow and plate motions.

Oconnell, R. J.↗

NASA NTRS1988

Effects of a temperature-dependent rheology on large scale continental extension

The effects of a temperature-dependent rheology on large-scale continental extension are investigated using a thin viscous sheet model. A vertically-averaged rheology is used that is consistent with laboratory experiments on power-law creep of olivine and that depends exponentially on temperature. Results of the calculations depend principally on two parameters: the Peclet number, which describes the relative rates of advection and diffusion of heat, and a dimensionless activation energy, which controls the temperature dependence of the rheology. At short times following the beginning of extension, deformation occurs with negligible change in temperature, so that only small changes in lithospheric strength occur due to attenuation of the lithosphere. However, after a certain critical time interval, thermal diffusion lowers temperatures in the lithosphere, strongly increasing lithospheric strength and slowing the rate of extension. This critical time depends principally on the Peclet number and is short compared with the thermal time constant of the lithosphere. The strength changes cause the locus of high extensional strain rates to shift with time from regions of high strain to regions of low strain. Results of the calculations are compared with observations from the Aegean, where maximum extensional strains are found in the south, near Crete, but maximum present-day strain rates are largest about 300 km further north.

Sonder, Leslie J.↗