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NASA NTRS1997

Modeling of Water Injection into a Vacuum

A loosely coupled two-phase vacuum water plume model has been developed. This model consists of a source flow model to describe the expansion of water vapor, and the Lagrangian equations of motion for particle trajectories. Gas/Particle interaction is modeled through the drag force induced by the relative velocities. Particles are assumed traveling along streamlines. The equations of motion are integrated to obtain particle velocity along the streamline. This model has been used to predict the mass flux in a 5 meter radius hemispherical domain resulting from the burst of a water jet of 1.5 mm in diameter, mass flow rate of 24.2 g/s, and stagnation pressure of 21.0 psia, which is the nominal Orbiter water dump condition. The result is compared with an empirical water plume model deduced from a video image of the STS-29 water dump. To further improve the model, work has begun to numerically simulate the bubble formation and bursting present in a liquid stream injected into a vacuum. The technique of smoothed particle hydrodynamics was used to formulate this simulation. A status and results of the on-going effort are presented and compared to results from the literature.

Alred, John W.↗

NASA NTRS1988

Continuum theories for fluid-particle flows: Some aspects of lift forces and turbulence

A general framework is outlined for the modeling of fluid particle flows. The momentum exchange between the constituents embodies both lift and drag forces, constitutive equations for which can be made explicit with reference to known single particle analysis. Relevant results for lift are reviewed, and invariant representations are posed. The fluid and particle velocities and the particle volume fraction are then decomposed into mean and fluctuating parts to characterize turbulent motions, and the equations of motion are averaged. In addition to the Reynolds stresses, further correlations between concentration and velocity fluctuations appear. These can be identified with turbulent transport processes such as eddy diffusion of the particles. When the drag force is dominant, the classical convection dispersion model for turbulent transport of particles is recovered. When other interaction forces enter, particle segregation effects can arise. This is illustrated qualitatively by consideration of turbulent channel flow with lift effects included.

Mctigue, David F.↗

NASA NTRS1983

Evaluation of a stochastic model of particle dispersion in a turbulent round jet

A stochastic model of particle dispersion by turbulence, proposed by Gosman and Ioannides (1981), is evaluated. The method employs a k-epsilon model to estimate turbulence properties. Dispersion is determined by computing particle motion, with random sampling to obtain instantaneous flow properties for a statistically significant number of particle trajectories. The stochastic model yields good results particularly when eddy lifetimes are evaluated. The method allows the effects of large relative velocities between the particles and the flow, drag properties at Reynolds numbers greater than the Stokes flow regime, and the variations of local turbulence properties to be readily handled, at least for boundary layer flows.

Shuen, J.-S.↗

NASA NTRS1992

Microgravity monitoring instrument development and application to vernier guidance, navigation, and vehicle control

The fact that a spacecraft traveling through the 'vacuum' of space conforms to the classical Keplerian ellipse has recently been disproven. It is now well known that such a vehicle is acted on by many external forces such as drag in the rarefied particle atmosphere, solar wind and particle impact. This paper discusses the development of sensors and sensor systems to measure these minute forces of acceleration/deceleration. Four systems will be discussed: a 10 exp -4 g system, a 10 exp -6 g system, a 10 exp -(6-8) g system and a 10 exp -9 g system. The design of each system will be explained along with the advantages/disadvantages of each. Various applications unique to each system will be discussed. Configurations, design schemes, test plans and calibration procedures, both in the ground laboratory and inflight, will be presented. The current design/development/operational status of each system will be examined and future plans discussed. Application to aerodynamic studies and vernier guidance, navigation, and vehicle control will also be examined.

Howell, Joseph J.↗

NASA NTRS2000

Effect of Melt Convection at Various Gravity Levels and Orientations on the Forces Acting on a Large Spherical Particle in the Vicinity of a Solidification Interface

Numerical modeling was Undertaken to analyze the influence of both radial and axial thermal gradients on convection patterns and velocities claiming solidification of pure Al and an Al-4 wt% Cu alloy. The objective of the numerical task was to predict the influence of convective velocity on an insoluble particle near a solid/liquid (s/l) interface. These predictions were then be used to define the minimum gravity level (q) required to investigate the fundamental physics of interactions between a particle and a s/l interface. This is an ongoing NASA founded flight experiment entitled "particle engulfment and pushing by solidifying interfaces (PEP)". Steady-state calculations were performed for different gravity levels and orientations with respect to the gravity vector The furnace configuration used in this analysis is the quench module insert (QMI-1) proposed for the Material Science Research Facility (MSRF) on board the International Space Station (ISS). The general model of binary alloy solidification was based on the finite element code FIDAP. At a low g level of 10(exp -4) g(sub o) (g(sub o) = 9.8 m/square s) maximum melt convection was obtained for an orientation of 90 deg. Calculations showed that even for this worst case orientation the dominant forces acting on the particle are the fundamental drag and interfacial forces.

Bune, Andris V.↗

NASA NTRS2010

Grid-Sphere Electrodes for Contact with Ionospheric Plasma

Grid-sphere electrodes have been proposed for use on the positively biased end of electrodynamic space tethers. A grid-sphere electrode is fabricated by embedding a wire mesh in a thin film from which a spherical balloon is formed. The grid-sphere electrode would be deployed from compact stowage by inflating the balloon in space. The thin-film material used to inflate the balloon is formulated to vaporize when exposed to the space environment. This would leave the bare metallic spherical grid electrode attached to the tether, which would present a small cross-sectional area (essentially, the geometric wire shadow area only) to incident neutral atoms and molecules. Most of the neutral particles, which produce dynamic drag when they impact a surface, would pass unimpeded through the open grid spaces. However, partly as a result of buildup of a space charge inside the grid-sphere, and partially, the result of magnetic field effects, the electrode would act almost like a solid surface with respect to the flux of electrons. The net result would be that grid-sphere electrodes would introduce minimal aerodynamic drag, yet have effective electrical-contact surface areas large enough to collect multiampere currents from the ionospheric plasma that are needed for operation of electrodynamic tethers. The vaporizable-balloon concept could also be applied to the deployment of large radio antennas in outer space.

Stone, Nobie H.↗

NASA NTRS2015

Terrestrial Planet Formation Constrained By Mars and the Structure of the Asteroid Belt

Reproducing the large Earth/Mars mass ratio requires a strong mass depletion in solids within the protoplanetary disc between 1 and 3 au. The Grand Tack model invokes a specific migration history of the giant planets to remove most of the mass initially beyond 1 au and to dynamically excite the asteroid belt. However, one could also invoke a steep density gradient created by inward drift and pile-up of small particles induced by gas drag, as has been proposed to explain the formation of close-in super-Earths. Here we show that the asteroid belt’s orbital excitation provides a crucial constraint against this scenario for the Solar system. We performed a series of simulations of terrestrial planet formation and asteroid belt evolution starting from discs of planetesimals and planetary embryos with various radial density gradients and including Jupiter and Saturn on nearly circular and coplanar orbits. Discs with shallow density gradients reproduce the dynamical excitation of the asteroid belt by gravitational self-stirring but form Mars analogues significantly more massive than the real planet. In contrast, a disc with a surface density gradient proportional to r(exp −5.5) reproduces the Earth/Mars mass ratio but leaves the asteroid belt in a dynamical state that is far colder than the real belt. We conclude that no disc profile can simultaneously explain the structure of the terrestrial planets and asteroid belt. The asteroid belt must have been depleted and dynamically excited by a different mechanism such as, for instance, in the Grand Tack scenario.

Numerical methods↗

NASA NTRS1975

Shock wave relations in lunar ash flow

A detailed analysis of steady normal shock waves in a layer of lunar ash by the theory of two phase flow of a mixture of a gas and small solid particles is presented. New terms of pressure gradient and virtual mass forces in the particle momentum equation and the particle kinetic energy and work done in the particle energy equation are included in the fundamental equations and their influences are investigated. The flow variables as functions of the free stream Mach number, initial particle volume fraction and the density ratio G are presented. The thickness of the relaxation zone is found to increase with decreasing initial particle volume fraction and almost independent of G for any given values of free stream Mach number. A new empirical relation of the drag coefficient for the spherical particles in the mixture is proposed to fit experimental data.

Pai, S. I.↗

NASA NTRS1996

Numerical Investigation of Slag Behavior for RSRM

It is known that the flow field of the redesigned solid rocket motor (RSRM) is very complicated due to the complex characteristics of turbulent multi-phase flow, chemical reaction, particle combustion, evaporation, breakup and agglomeration etc. It requires multi-phase calculations, chemical reaction simulation, and particle combustion, evaporation, and breakup models to obtain a better understanding of thermophysics for the RSRM design using numerical methods. Also, the slag buildup due to the molten particles is another factor affecting the performance of the RSRM. To achieve this goal, the volume of fluid (VOF) method is used to capture the free surface motion so as to simulate the accumulation of the molten particles (slag) of the RSRM. A finite rate chemistry model is used to simulate the chemical reaction effects. For multi-phase calculations, the Hermsen combustion model is used for the aluminum particle combustion analysis and the Taylor Analogy Breakup (TAB) model is used for the particle breakup analysis. An interphase mas-exchange model introduced by Spalding is used for the evaporation calculation. The particle trajectories are calculated using a one-step implicit method for several groups of particle sizes by which the drag forces and heat fluxes are then coupled with the gas phase equations. The preliminary results predicted a reasonable physical simulation of the particle effects using a simple two dimensional solid rocket motor configuration. It shows that the AL/AL2O3 particle sizes are reduced due to the combustion, evaporation, and breakup. The flow field is disturbed by the particles. Mach number distributions in the nozzle are deformed due to the effect of particle concentrations away from the center line.

Liaw, P.↗

NASA NTRS1957

A study of liquid boric oxide particle growth rates in a gas stream from a simulated jet engine combustor

It was experimentally determined that the liquid boric oxide particles leaving a jet engine combustor, burning a boron-containing fuel, will have diameters of 1.0 x 10(exp -5) to 2.0 x 10(exp -5) centimeter. For this size range the particle heat-transfer and drag coefficients are essentially infinite. The results may be applied to any boron-containing fuel. Equations are developed that enable the calculation of the particle size-time history. A study of boric oxide deposition mechanisms is included, and suggestions for decreading deposition rates given.

Setze, Paul C↗

NASA NTRS1994

The fragmentation of dust in the innermost comae of comets: Possible evidence from ground-based images

Dust particles when released from the nucleus of a comet are entrained in the expanding gas flow created by the vaporization of ices (mainly water ice). Traditional approaches to dusty-gas dynamics in the inner comae of comets consider there to be an initial distribution of dust particle sizes which do not fragment or evaporate. The standard Finson-Probstein model (and subsequent variations) yields a one-to-one-to-one correspondence between the size of a dust particle, its terminal velocity owing to gas drag, and its radiation pressure acceleration which creates the notable cometary dust tail. The comparison of a newly developed dust coma model shows that the typical elongated shapes of isophotes in the dust comae of comets on the scale of greater than 10(exp 4) km from the nucleus requires that the one-to-one-to-one relationship between particle size, terminal velocity and radiation pressure acceleration cannot in general be correct. There must be a broad range of particles including those having a small velocity but large radiation pressure acceleration in order to explain the elongated shape. A straightforward way to create such a distribution is if particle fragmentation, or some combination of fragmentation with vaporization, routinely occurs within and/or just outside of the dusty-gas dynamic acceleration region (i.e., up to several hundred km). In this way initially large particles, which are accelerated to fairly slow velocities by gas-drag, fragment to form small particles which still move slowly but are subject to a relatively large radiation pressure acceleration. Fragmentation has already been suggested as one possible interpretation for the flattened gradient in the spatial profiles of dust extracted from Giotto images of Comet Halley. Grain vaporization has been suggested as a possible spatially extended source of coma gases. The general elongated isophote shapes seen in ground-based images for many years represents another possible signature of fragmentation.

Combi, Michael R.↗

NASA NTRS1983

Use of a generalized Stokes number to determine the aerodynamic capture efficiency of non-Stokesian particles from a compressible gas flow

The aerodynamic capture efficiency of small but nondiffusing particles suspended in a high-speed stream flowing past a target is known to be influenced by parameters governing small particle inertia, departures from the Stokes drag law, and carrier fluid compressibility. By defining an effective Stokes number in terms of the actual (prevailing) particle stopping distance, local fluid viscosity, and inviscid fluid velocity gradient at the target nose, it is shown that these effects are well correlated in terms of a 'standard' (cylindrical collector, Stokes drag, incompressible flow, sq rt Re much greater than 1) capture efficiency curve. Thus, a correlation follows that simplifies aerosol capture calculations in the parameter range already included in previous numerical solutions, allows rational engineering predictions of deposition in situations not previously specifically calculated, and should facilitate the presentation of performance data for gas cleaning equipment and aerosol instruments.

Israel, R.↗

NASA NTRS1974

Dynamics and column densities of small particles ejected from spacecraft

Trajectories and relative motions of small particles ejected from a spacecraft were analyzed, and modifications to the clearing times and column densities because of orbital dynamics were assessed. It was found that despite the fact that such particles are confined by orbital dynamics to move along similar trajectories with the spacecraft rather than to continue their free expansion, the effect is negligible for viewing angles away from the orbital path. Small particles are rapidly swept away by drag and will not contribute significantly to the column density when viewing along the velocity vector in 420-km earth orbit. However, substantial increases in column density can results when viewing in a direction opposite to the velocity vector because of drag effects. In the absence of drag, significant column densities can build up both in front of and behind the spacecraft in earth orbit for particles released at a few meters per second. This effect is much less pronounced in lunar orbit because the same release velocity produces a larger orbital perturbation for the particle.

Naumann, R. J.↗

NASA NTRS1986

Shear stress cleaning for surface departiculation

A cleaning technique widely used by the nuclear utility industry for removal of radioactive surface contamination has proven effective at removing non-hazardous contaminant particles as small as 0.1 micrometer. The process employs a controlled high velocity liquid spray inside a vapor containment enclosure to remove particles from a surface. The viscous drag force generated by the cleaning fluid applies a shear stress greater than the adhesion force that holds small particles to a substrate. Fluid mechanics and field tests indicate general cleaning parameters.

Musselman, R. P.↗

NASA NTRS1990

Mathematical modeling of the flow field and particle motion in a rotating bioreactor at unit gravity and microgravity

The biotechnology group at NASA Johnson Space Center is developing systems for culturing mammalian cells that stimulate some aspect of microgravity and provide a low shear environment for microgravity-based studies on suspension and anchorage dependent cells. The design of these vessels for culturing cells is based on the need to suspend cells and aggregates of cells and microcarrier beads continually in the culturing medium. The design must also provide sufficient circulation for adequate mass transfer of nutrients to the cells and minimize the total force on the cells. Forces, resulting from sources such as hydrodynamic fluid shear and collisions of cells and walls of the vessels, may damage delicate cells and degrade the formation of three dimensional structures. This study examines one particular design in both unit gravity and microgravity based on two concentric cylinders rotating in the same direction at different speeds to create a Couette flow between them. A numerical simulation for the flow field and the trajectories of particles in the vessel. The flow field for the circulation of the culturing medium is modeled by the Navier-Stokes equations. The forces on a particle are assumed to be drag from the fluid's circulation, buoyancy from the gravitational force and centrifugal force from the rotation of the vessel. The problem requires first solving the system of partial differential equations for the fluid flow by a finite difference method and then solving the system of ordinary differential equations for the trajectories by Gear's stiff method. Results of the study indicate that the trajectories in unit gravity and microgravity are very similar except for small spatial deviations on the fast time scale in unit gravity. The total force per unit cross sectional area on a particle in microgravity, however, is significantly smaller than the corresponding value in unit gravity, which is also smaller than anticipated. Hence, this study indicates that this design for a bioreactor with optimal rates of rotation can provide a good environment for culturing cells in microgravity with adequate circulation and minimal force on the cells.

Boyd, Ernest J.↗

NASA NTRS1998

Turbulence, Chondrules, and Planetesimals

It has been shown both numerically and experimentally that 3-D turbulence concentrates aerodynamically size-selected particles by orders of magnitude. In a previous review chapter, in "Chondrules and the protoplanetary disk" we illustrated the initial predictions of Turbulent Concentration (TC) as applied to the solar nebula. We predicted the particle size which will be most effectively concentrated by turbulence; it is the particle which has a gas drag stopping time equal to the overturn time of the smallest (Kolmogorov scale) eddy. The primary uncertainty is the level of nebula turbulence, or Reynolds number Re, which can be expressed in terms of the standard nebula eddy viscosity parameter alpha = Re(nu)(sub m)/cH, where nu(sub m) is molecular viscosity, c is sound speed, and H is vertical scale height. Several studies, and observed lifetimes of circumstellar disks, have suggested that the level of nebula turbulence can be described by alpha = 10(exp -2) - 10(exp -4). There is some recent concern about how energy is provided to maintain this turbulence, but the issue remains open. We adopt a canonical minimum mass nebula with a range of alpha > 0. We originally showed that chondrule-sized particles are selected for concentration in the terrestrial planet region if alpha = 10(exp -3) - 10(exp -4). In addition, Paque and Cuzzi found that the size distribution of chondrules is an excellent match for theoretical predictions. One then asks by what concentration factor C these particles can be concentrated; our early numerical results indicated an increase of C with alpha, and were supported by simple scaling arguments, but the extrapolation range was quite large and the predictions (C ~ 10(exp 5) - 10(exp 6) not unlikely) uncertain. The work presented here, which makes use of our recent demonstration that the particle density field is a multifractal with flow-independent properties provides a far more secure ground for such predictions. We also indicate how fine-grained dust rims on chondrules might enter into constraining the situation.

Cuzzi, Jeffrey↗

NASA NTRS1998

Planetesimal Formation in the Protoplanetary Nebula

In this talk we will address two distinct phases of planetesimal formation, each of which is fundamentally dependent upon the coupled interactions of particles and turbulent nebula gas. It has been shown both numerically and experimentally that 3-D (three dimensional) turbulence concentrates aerodynamically size-selected particles by orders of magnitude. In a previous review chapter we illustrated the initial predictions of Turbulent Concentration (TC) as applied to the solar nebula. We predicted the particle size which will be most effectively concentrated by turbulence; it is the particle which has a gas drag stopping time equal to the overturn time of the smallest (Kolmogorov scale) eddy. The primary uncertainty is the level of nebula turbulence, or Reynolds number Re, which can be expressed in terms of the standard nebula eddy viscosity parameter alpha = Rev(sub m)/cH, where v(sub m) is molecular viscosity, c is sound speed, and H is vertical scale height. Several studies, and observed lifetimes of circumstellar disks, have suggested that the level of nebula turbulence can be described by alpha = 10(exp -2) - 10(exp -4). There is some recent concern about how energy is provided to maintain this turbulence, but the issue remains open. We adopt a canonical minimum mass nebula with a range of alpha is greater than 0. We originally showed that chondrule-sized particles are selected for concentration in the terrestrial planet region if alpha = 10(exp -3) - 10(exp -4). In addition, Paque and Cuzzi found that the size distribution of chondrules is an excellent match for theoretical predictions. One then asks by what concentration factor C these particles can be concentrated; our early numerical results indicated an increase of C with alpha, and were supported by simple scaling arguments, but the extrapolation range was quite large and the predictions (C is approximately equal to 10(exp 5) - 10(exp 6) not unlikely) uncertain. The work presented here, which makes use of our recent demonstration that the particle density field is a multifractal with flow-independent properties provides a far more secure ground for such predictions. We also indicate how fine-grained dust rims on chondrules might enter into constraining the situation. Once large particles (meter-size mass equivalent) reach the midplane, perhaps in the form of dense aggregates of the sort formed in 3D turbulence, they remain stable against gravitational instability but might grow rapidly by accretion of their drifting neighbors, depending on the level of global turbulence.

Cuzzi, Jeffrey N.↗

NASA NTRS2020

Modeling Heatshield Erosion due to Dust Particle Impacts for Martian Entries

Heatshield design for spacecraft entering the atmosphere of Mars may be affected by the presence of atmospheric dust. Particle impacts with sufficient kinetic energy can cause spallation damage to the heatshield that must be estimated. The dust environment in terms of particle size distribution and number density can be inferred from ground-based or atmospheric observations at Mars. Using a Lagrangian approach, the particle trajectories through the shock layer can be computed using a set of coupled ordinary differential equations. The dust particles are small enough that non-continuum effects must be accounted for when computing the drag coefficient and heat transfer to the particle surface. Surface damage correlations for impact crater diameter and penetration depth are presented for fused-silica, AVCOAT, Shuttle tiles, cork, and Norcoat Liège. The cork and Norcoat Liège correlations are new and were developed in this study. The modeling equations presented in this paper are applied to compute the heatshield erosion due to dust particle impacts on the ExoMars Schiaparelli entry capsule during dust storm conditions.

Palmer, Grant↗