Dynamical analysis of non-equilibrium forced convective boiling flows
Dynamical analysis of nonequilibrium, forced convective, boiling liquid metal flows
Pan, C. H. T.↗
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Direct Numerical Simulation of Wetting and Spreading Behavior on Heterogeneous and Roughened Substrates
A method of calculation is presented that allows the simulation of the time-dependent three-dimensional motion of thin liquid layers on solid substrates for systems with finite equilibrium contact angles. The contact angle is a prescribed function of position on the substrate. Similar mathematical models are constructed for substrates with a pattern of roughness. Evolution equations are given, using the lubrication approximation, that include viscous, capillary and disjoining forces. Motion to and from dry substrate regions is made possible by use of a thin energetically-stable wetting layer. We simulate motion on heterogeneous substrates with periodic arrays of high contact-angle patches. Two different problems are treated for heterogenous substrates. The first is spontaneous motion driven only by wetting forces. If the contact-angle difference is sufficiently high, the droplet can find several different stable positions, depending on the previous history of the motion. A second simulation treats a forced cyclical motion. Energy dissipation per cycle for a heterogeneous substrate is found to be larger than for a uniform substrate with the same total energy. The Landau-Levich solution for plate removal from a liquid bath is extended to account for a pattern of roughness on the plate.
Schwartz, Leonard W.↗
Mathematical and computational studies of equilibrium capillary free surfaces
The results of several independent studies are presented. The general question is considered of whether a wetting liquid always rises higher in a small capillary tube than in a larger one, when both are dipped vertically into an infinite reservoir. An analytical investigation is initiated to determine the qualitative behavior of the family of solutions of the equilibrium capillary free-surface equation that correspond to rotationally symmetric pendent liquid drops and the relationship of these solutions to the singular solution, which corresponds to an infinite spike of liquid extending downward to infinity. The block successive overrelaxation-Newton method and the generalized conjugate gradient method are investigated for solving the capillary equation on a uniform square mesh in a square domain, including the case for which the solution is unbounded at the corners. Capillary surfaces are calculated on the ellipse, on a circle with reentrant notches, and on other irregularly shaped domains using JASON, a general purpose program for solving nonlinear elliptic equations on a nonuniform quadrilaterial mesh. Analytical estimates for the nonexistence of solutions of the equilibrium capillary free-surface equation on the ellipse in zero gravity are evaluated.
Albright, N.↗
Phase equilibrium constraints on the howardite-eucrite-diogenite association
Model determinations of fractional crystallization and equilibrium partial melting in the 0-10-kbar range have been performed for a series of compositions relevant to diogenite and eucrite petrogenesis. Olivine is found to react with diogenite parent liquids along the plagioclase-absent olivine/low-Ca pyroxene liquidus boundary under conditions of both fractional and equilibrium crystallization up to about 2 kbar. Olivine also reacts with eucritic liquids saturated with plagioclase and low-Ca pyroxene to pressures in excess of 2 kbar. The ability of simple fractional crystallization at 2 kbar to account for mineralogical and chemical features of the diogenite-eucrite association is discussed.
Longhi, John↗
Simplified thermodynamic functions for vapor-liquid phase separation and fountain effect pumps
He-4 fluid handling devices near 2 K require novel components for non-Newtonian fluid transport in He II. Related sizing of devices has to be based on appropriate thermophysical property functions. The present paper presents simplified equilibrium state functions for porous media components which serve as vapor-liquid phase separators and fountain effect pumps.
Yuan, S. W. K.↗
Polar wander of an ice shell on Europa
The present consideration of a hypothesized ice shell around Europa, which is decoupled from the silicate core by a liquid water layer and possesses a spatially varying thermal equilibrium thickness profile, proceeds through the development of equations for variations in the inertia tensor of a body when second-harmonic-degree topography is added to the crustal base. Attention is given to a realistic model in which the shell and ocean are assumed to undergo reorientations as a single entity independently of the core, but subject to viscous dissipation within the shell. Shell friction is in this case noted to preclude polar wander, unless a low conductivity regolith increases the near-surface temperature by a few tens of degrees C; the ice beneath the regolith would then behave viscously on the time-scale of polar wander.
Ojakangas, Gregory W.↗
Application of Simulated Annealing and Related Algorithms to TWTA Design
Simulated Annealing (SA) is a stochastic optimization algorithm used to search for global minima in complex design surfaces where exhaustive searches are not computationally feasible. The algorithm is derived by simulating the annealing process, whereby a solid is heated to a liquid state and then cooled slowly to reach thermodynamic equilibrium at each temperature. The idea is that atoms in the solid continually bond and re-bond at various quantum energy levels, and with sufficient cooling time they will rearrange at the minimum energy state to form a perfect crystal. The distribution of energy levels is given by the Boltzmann distribution: as temperature drops, the probability of the presence of high-energy bonds decreases. In searching for an optimal design, local minima and discontinuities are often present in a design surface. SA presents a distinct advantage over other optimization algorithms in its ability to escape from these local minima. Just as high-energy atomic configurations are visited in the actual annealing process in order to eventually reach the minimum energy state, in SA highly non-optimal configurations are visited in order to find otherwise inaccessible global minima. The SA algorithm produces a Markov chain of points in the design space at each temperature, with a monotonically decreasing temperature. A random point is started upon, and the objective function is evaluated at that point. A stochastic perturbation is then made to the parameters of the point to arrive at a proposed new point in the design space, at which the objection function is evaluated as well. If the change in objective function values (Delta)E is negative, the proposed new point is accepted. If (Delta)E is positive, the proposed new point is accepted according to the Metropolis criterion: rho((Delta)f) = exp((-Delta)E/T), where T is the temperature for the current Markov chain. The process then repeats for the remainder of the Markov chain, after which the temperature is decremented and the process repeats. Eventually (and hopefully), a near-globally optimal solution is attained as T approaches zero. Several exciting variants of SA have recently emerged, including Discrete-State Simulated Annealing (DSSA) and Simulated Tempering (ST). The DSSA algorithm takes the thermodynamic analogy one step further by categorizing objective function evaluations into discrete states. In doing so, many of the case-specific problems associated with fine-tuning the SA algorithm can be avoided; for example, theoretical approximations for the initial and final temperature can be derived independently of the case. In this manner, DSSA provides a scheme that is more robust with respect to widely differing design surfaces. ST differs from SA in that the temperature T becomes an additional random variable in the optimization. The system is also kept in equilibrium as the temperature changes, as opposed to the system being driven out of equilibrium as temperature changes in SA. ST is designed to overcome obstacles in design surfaces where numerous local minima are separated by high barriers. These algorithms are incorporated into the optimal design of the traveling-wave tube amplifier (TWTA). The area under scrutiny is the collector, in which it would be ideal to use negative potential to decelerate the spent electron beam to zero kinetic energy just as it reaches the collector surface. In reality this is not plausible due to a number of physical limitations, including repulsion and differing levels of kinetic energy among individual electrons. Instead, the collector is designed with multiple stages depressed below ground potential. The design of this multiple-stage collector is the optimization problem of interest. One remaining problem in SA and DSSA is the difficulty in determining when equilibrium has been reached so that the current Markov chain can be terminated. It has been suggested in recent literature that simulating the thermodynamic properties opecific heat, entropy, and internal energy from the Boltzmann distribution can provide good indicators of having reached equilibrium at a certain temperature. These properties are tested for their efficacy and implemented in SA and DSSA code with respect to TWTA collector optimization.
Radke, Eric M.↗
Equilibrium shapes of acoustically levitated drops
The quantitative determination of the shape of liquid drops levitated in an ultrasonic standing wave has provided experimental data on the radiation pressure-induced deformations of freely suspended liquids. Within the limits of small deviations from the spherical shape and small drop diameter relative to the acoustic wavelength, an existing approximate theory yields a good agreement with experimental evidence. The data were obtained for millimeter and submillimeter drops levitated in air under 1 g, where g is the sea level gravitational acceleration.
Trinh, E. H.↗
First-order wetting transition at a liquid-vapor interface
Evidence from reflectance and contact angle measurements is presented that three-phase mixtures of i-C3H7OH-C7F14 exhibit a first-order wetting phase transition at the liquid-vapor interface at 38 C. Equilibration phenomena support this interpretation. Ellipsometry was used to measure the apparent thickness of the intruding layer in the three-phase mixture. At temperatures slightly above the wetting temperature T(w), the intruding layer's thickness is several hundred angstroms and its variation with temperature is extremely weak. Below T(w), three-phase contact can occur between the vapor and both the upper and lower liquid phases; one of the angles which characterizes this contact has a very simple temperature dependence. The thickness of the intruding layer, monitored as the solutions approached equilibrium, is found to depend quite weakly on the height spanned by the upper liquid phase in the vicinity of a first-order wetting transition.
Schmidt, J. W.↗
Structure of confined laminar spray diffusion flames: Numerical investigation
The structure of confined laminar spray diffusion flames is investigated numerically by solving the gas-phase conservation equations for mass species, continuity, momentum, and energy and the liquid-phase equations for droplet position, velocity, size, and temperature. A one-step global reaction scheme along with six equilibrium reactions are employed to model the flame chemistry. Monodisperse as well as polydisperse sprays are considered. The numerical results demonstrate that liquid spray flames substantially differ from gaseous flames in their structure, i.e., temperature, concentration, and velocity fields, shape, and dimensions under the same conditions. Spray flames are predicted to be taller and narrower than their counterpart gaseous ones and their shapes are almost cylindrical. This is in agreement with experimental observations. The numerical computations also show that the use of the equilibrium reactions with the one-step reaction scheme decreases the flame temperature compared to the one-step reaction scheme without the equilibrium reactions and more importantly increases the surface area of the flame zone due to a phenomenon termed 'equilibrium broadening.' The spray flames also possess a finite thickness with minimal overlap of the fuel and oxygen species. A case for which a fuel-mixture consisting of 20 to 80 percent gas-liquid by mass is introduced into the combustor is also investigated and compared with predictions using only gaseous or liquid fuel.
Mawid, M. A.↗
Dynamic Nucleation of Supercooled Melts and Measurement of the Surface Tension and Viscosity
We investigate the phenomenon of acoustic pressure-induced nucleation by using a novel approach involving the large amplitude resonant radial oscillations and collapse of a single bubble intentionally injected into a supercooled liquid. Using a combination of previously developed and proven techniques, the bubble is suspended in a fluid host by an ultrasonic field which supplies both the levitation capability as well as the forcing of the radial oscillations. We observe the effects of an increase in pressure (due to bubble collapse) in a region no larger than 100 microns within the supercooled melt to rigorously probe the hypothesis of pressure-induced nucleation of the solid phase. The use of single bubbles operating in narrow temporal and spatial scales will allow the direct and unambiguous correlation between the origin and location of the generation of the disturbance and the location and timing of the nucleation event. In a companion research effort, we are developing novel techniques for the non-contact measurements of the surface tension and viscosity of highly viscous supercooled liquids. Currently used non-invasive methods of surface tension measurement for the case of undercooled liquids generally rely of the quantitative determination of the resonance frequencies of drop shape oscillations, of the dynamics of surface capillary waves, or of the velocity of streaming flows. These methods become quickly ineffective when the liquid viscosity rises to a significant value. An alternate and accurate method which would be applicable to liquids of significant viscosity is therefore needed. We plan to develop such a capability by measuring the equilibrium shape of levitated undercooled melt droplets as they undergo solid-body rotation. The experimental measurement of the characteristic point of transition (bifurcation point) between axisymmetric and two-lobed shapes will be used to calculate the surface tension of the liquid. Such an approach has already been validated through the experimental verification of numerical modeling results. The experimental approach involves levitation, melting, and solidification of undercooled droplets using a hybrid ultrasonic-electrostatic technique in both a gaseous as well as a vacuum environment. A shape relaxation method will be investigated in order to derive a reliable method to measure the viscosity of undercooled melts. The analysis of the monotonic relaxation to equilibrium shape of a drastically deformed and super-critically damped free drop has been used to derive interfacial tension of immiscible liquid combinations where one of the component has high viscosity. A standard approach uses the initial elongation of a droplet through shear flows, but an equivalent method could involve the initial deformation of a drop levitated in a gas by ultrasonic radiation pressure, electric stresses, or even solid body rotation. The dynamic behavior of the free drop relaxing back to equilibrium shape will be modeled, and its characteristic time dependence should provide a quantitative means to evaluate the liquid viscosity.
Trinh, E. H.↗
On the Stability of Liquid Water on Present Day Mars
The mean annual surface pressure and temperature on present day Mars do not allow for the long term stability of liquid water on the surface. However, theoretical arguments have been advanced that suggest liquid water could form in transient events even though it would not be in equilibrium with the environment. Using a Mars General Circulation Model, we calculate where and for how long the surface pressure and surface temperature meet the minimum requirements for this metastability of liquid water. These requirements are that the pressure and temperature must be above the triple point of water, but below its boiling point. We find that there are five regions on Mars where these requirements are periodically satisfied: in the near equatorial regions of Amazonis, Arabia, and Elysium, and in the Hellas and Argyre impact basins. Whether liquid water ever forms in these regions depends on the availability of ice and heat, and on the evaporation rate. The latter is poorly understood for low pressure CO2 environments, but is likely to be so high that melting occurs rarely, if at all. However, in the relatively recent past, surface pressures may have been higher than they are today perhaps by as much as a factor of 2 or 3. Under these circumstances melting would have been easier to achieve. We plan to undertake laboratory experiments to better understand the potential for melting in low pressure environments.
Haberle, Robert M.↗
Space-charge dynamics of liquids.
The propagation and instability characteristics of small-signal electro-fluid-mechanical space-charge and polarization waves in nonhomogeneous fluids are developed. Stratified equilibrium configurations with fluid properties and space-charge density constant within planar, cylindrical, and spherical surfaces, are emphasized. Equilibrium electric fields due both to charges in the fluid and to externally imposed potentials are normal to these surfaces. The liquid is modeled as incompressible, inviscid, and perfectly insulating, with domains of sufficiently high frequency or growth rate to validate the last assumption defined in terms of electrical conductivity or mobility. A general set of relations for perturbation field and flow variables on the perturbed surfaces of fluid layers having constant properties and space charge are derived in each of the configurations.
Zahn, M.↗
Evaluation of the bray sudden-freezing criterion for predicting nonequilibrium performance in multireaction rocket nozzle expansions.
Bray sudden freezing criterion for predicting nonequilibrium performance in multireaction liquid rocket nozzle expansion
LIQUID PROPELLANT↗
The stability of a rotating liquid mass.
Stability of rotating liquid mass /e.g. earth/, following Jeans treatment of Jacobi ellipsoidal equilibrium configurations
HYDRODYNAMIC STABILITY↗
The decompression of cold neutron star matter
The ejection of cold neutron-star matter is examined, and an attempt is made to determine whether the final composition of this matter may be similar to that normally associated with the hot high-neutron-flux r-process. A semiempirical liquid-drop model is used for the nucleus, and the equilibrium composition of the matter is determined by assuming it to be in its absolute ground state at a given density. Physical mechanisms operating during the expansion are analyzed, and the composition of the ejected matter is found as a function of its density during expansion. The results indicate that it is virtually impossible for deuterium to form, that neutrons can be captured only after beta decay increases the atomic numbers of nuclei, and that no free neutrons can escape. It is concluded that neutron-star ejecta can produce heavy neutron-rich nuclei and may produce somewhat heavier nuclei than a standard r-process.
Lattimer, J. M.↗
Low cost silicon solar array project: Feasibility of low-cost, high-volume production of silane and pyrolysis of silane to semiconductor-grade silicon
Silicon epitaxy analysis of silane produced in the Process Development Unit operating in a completely integrated mode consuming only hydrogen and metallurgical silicon resulted in film resistivities of up to 120 ohms cm N type. Preliminary kinetic studies of dichlorosilane disproportionation in the liquid phase have shown that 11.59% SiH4 is formed at equilibrium after 12 minutes contact time at 56 C. The fluid-bed reactor was operated continuously for 48 hours with a mixture of one percent silane in helium as the fluidizing gas. A high silane pyrolysis efficiency was obtained without the generation of excessive fines. Gas flow conditions near the base of the reactor were unfavorable for maintaining a bubbling bed with good heat transfer characteristics. Consequently, a porous agglomerate formed in the lower portion of the reactor. Dense coherent plating was obtained on the silicon seed particles which had remained fluidizied throughout the experiment.
Breneman, W. C.↗
Determination of the Accomodation Coefficient Using Vapor/Gas Bubble Dynamics in an Acoustic Field
Non-equilibrium liquid/vapor phase transformations can occur in superheated or subcooled liquids in fast processes such as in evaporation in a vacuum, in processing of molten metals, and in vapor explosions. The rate at which such a phase transformation occurs, Xi, can be described by the Hertz-Knudsen-Langmuir formula. More than one century of the history of the accommodation coefficient measurements shows many problems with its determination. This coefficient depends on the temperature, is sensitive to the conditions at the interface, and is influenced by small amounts of impurities. Even recent measurements of the accommodation coefficient for water (Hagen et al, 1989) showed a huge variation in Beta from 1 for 1 micron droplets to 0.006 for 15 micron droplets. Moreover, existing measurement techniques for the accommodation coefficient are complex and expensive. Thus development of a relatively inexpensive and reliable technique for measurement of the accommodation coefficient for a wide range of substances and temperatures is of great practical importance.
Gumerov, Nail A.↗