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NASA NTRS2006

Fuel Cells Utilizing Oxygen From Air at Low Pressures

A fuel cell stack has been developed to supply power for a high-altitude aircraft with a minimum of air handling. The fuel cell is capable of utilizing oxygen from ambient air at low pressure with no need for compression. For such an application, it is advantageous to take oxygen from the air (in contradistinction to carrying a supply of oxygen onboard), but it is a challenging problem to design a fuel-cell stack of reasonable weight that can generate sufficient power while operating at reduced pressures. The present fuel-cell design is a response to this challenge. The design features a novel bipolar plate structure in combination with a gas-diffusion structure based on a conductive metal core and a carbon gas-diffusion matrix. This combination makes it possible for the flow fields in the stack to have a large open fraction (ratio between open volume and total volume) to permit large volumes of air to flow through with exceptionally low backpressure. Operations at reduced pressure require a corresponding increase in the volume of air that must be handled to deliver the same number of moles of oxygen to the anodes. Moreover, the increase in the open fraction, relative to that of a comparable prior fuel-cell design, reduces the mass of the stack. The fuel cell has been demonstrated to operate at a power density as high as 105 W/cm2 at an air pressure as low as 2 psia (absolute pressure 14 kPa), which is the atmospheric pressure at an altitude of about 50,000 ft ( 15.2 km). The improvements in the design of this fuel cell could be incorporated into designs of other fuel cells to make them lighter in weight and effective at altitudes higher than those of prior designs. Potential commercial applications for these improvements include most applications now under consideration for fuel cells.

Cisar, Alan↗
NASA NTRS2005

Improved Cathode Structure for a Direct Methanol Fuel Cell

An improved cathode structure on a membrane/electrode assembly has been developed for a direct methanol fuel cell, in a continuing effort to realize practical power systems containing such fuel cells. This cathode structure is intended particularly to afford better cell performance at a low airflow rate. A membrane/electrode assembly of the type for which the improved cathode structure was developed (see Figure 1) is fabricated in a process that includes brush painting and spray coating of catalyst layers onto a polymer-electrolyte membrane and onto gas-diffusion backings that also act as current collectors. The aforementioned layers are then dried and hot-pressed together. When completed, the membrane/electrode assembly contains (1) an anode containing a fine metal black of Pt/Ru alloy, (2) a membrane made of Nafion 117 or equivalent (a perfluorosulfonic acid-based hydrophilic, proton-conducting ion-exchange polymer), (3) a cathode structure (in the present case, the improved cathode structure described below), and (4) the electrically conductive gas-diffusion backing layers, which are made of Toray 060(TradeMark)(or equivalent) carbon paper containing between 5 and 6 weight percent of poly(tetrafluoroethylene). The need for an improved cathode structure arises for the following reasons: In the design and operation of a fuel-cell power system, the airflow rate is a critical parameter that determines the overall efficiency, cell voltage, and power density. It is desirable to operate at a low airflow rate in order to obtain thermal and water balance and to minimize the size and mass of the system. The performances of membrane/electrode assemblies of prior design are limited at low airflow rates. Methanol crossover increases the required airflow rate. Hence, one way to reduce the required airflow rate is to reduce the effect of methanol crossover. Improvement of the cathode structure - in particular, addition of hydrophobic particles to the cathode - has been demonstrated to mitigate the effects of crossover and decrease the airflow required.

Valdez, Thomas↗
NASA NTRS1975

Operational performance of a low cost, air mass 2 solar simulator

Modifications and improvements on a low cost air mass 2 solar simulator are discussed. The performance characteristics of total irradiance, uniformity of irradiance, spectral distribution, and beam subtense angle are presented. The simulator consists of an array of tungsten halogen lamps hexagonally spaced in a plane. A corresponding array of plastic Fresnel lenses shapes the output beam such that the simulator irradiates a 1.2 m by 1.2 m area with uniform collimated irradiance. Details are given concerning individual lamp output measurements and placement of the lamps. Originally, only the direct component of solar irradiance was simulated. Since the diffuse component may affect the performance of some collectors, the capability to simulate it is being added. An approach to this diffuse addition is discussed.

Yass, K.↗
NASA NTRS1990

The interstellar medium in galaxies; Proceedings of the 2nd Teton Conference, Grand Teton National Park, WY, July 3-7, 1989

The present conference on the interstellar medium in galaxies discusses the cool phase of the interstellar medium, molecular clouds in spiral galaxies, interstellar dust in galaxies, and the diffuse interstellar medium. Attention is given to cooling flows and X-ray emission in early-type galaxies, the interstellar medium in active galaxies, abundances in extragalactic H II regions, and thermal phases of the interstellar medium in galaxies. Topics considered include large-scale interstellar gasdynamics in disk galaxies, gas during mergers, magnetic fields in galaxies, and large-scale star formation in the interstellar medium. Also discussed are gaseous halos and disks of galaxies at large redshift, the star-gas cycle in galaxies, measuring atomic hydrogen masses using the 21-cm line, and mass determinations from far-infrared and from CO observations.

Thronson, Harley A., Jr.↗
NASA NTRS1993

PDF approach for compressible turbulent reacting flows

The objective of the present work is to develop a probability density function (pdf) turbulence model for compressible reacting flows for use with a CFD flow solver. The probability density function of the species mass fraction and enthalpy are obtained by solving a pdf evolution equation using a Monte Carlo scheme. The pdf solution procedure is coupled with a compressible CFD flow solver which provides the velocity and pressure fields. A modeled pdf equation for compressible flows, capable of capturing shock waves and suitable to the present coupling scheme, is proposed and tested. Convergence of the combined finite-volume Monte Carlo solution procedure is discussed, and an averaging procedure is developed to provide smooth Monte-Carlo solutions to ensure convergence. Two supersonic diffusion flames are studied using the proposed pdf model and the results are compared with experimental data; marked improvements over CFD solutions without pdf are observed. Preliminary applications of pdf to 3D flows are also reported.

Hsu, A. T.↗
NASA NTRS1994

Nonaxisymmetric evolution in protostellar disks

We present a two-dimensional, multigridded hydrodynamical simulation of the collapse of an axisymmetric, rotating, 1 solar mass protostellar cloud, which forms a resolved, hydrotastic disk. The code includes the effects of physical viscosity, radiative transfer and radiative acceleration but not magnetic fields. We examine how the disk is affected by the inclusion of turbulent viscosity by comparing a viscous simulation with an inviscid model evolved from the same initial conditions, and we derive a disk evolutionary timescale on the order of 300,000 years if alpha = 0.01. Effects arising from non-axisymmetric gravitational instabilities in the protostellar disk are followed with a three-dimensional SPH code, starting from the two-dimensional structure. We find that the disk is prone to a series of spiral instabilities with primary azimulthal mode number m = 1 and m = 2. The torques induced by these nonaxisymmetric structures elicit material transport of angular momentum and mass through the disk, readjusting the surface density profile toward more stable configurations. We present a series of analyses which characterize both the development and the likely source of the instabilities. We speculate that an evolving disk which maintains a minimum Toomre Q-value approximately 1.4 will have a total evolutionary span of several times 10(exp 5) years, comparable to, but somewhat shorter than the evolutionary timescale resulting from viscous turbulence alone. We compare the evolution resulting from nonaxisymmetric instabilities with solutions of a one-dimensional viscous diffusion equation applied to the initial surface density and temperature profile. We find that an effective alpha-value of 0.03 is a good fit to the results of the simulation. However, the effective alpha will depend on the minimum Q in the disk at the time the instability is activated. We argue that the major fraction of the transport characterized by the value of alpha is due to the action of gravitational torques, and does not arise from inherent viscosity within the smoothed particle hydrodynamics method.

Laughlin, Gregory↗
NASA NTRS2005

Numerical Analysis of Flow Evolution in a Helium Jet Injected into Ambient Air

A computational model to study the stability characteristics of an evolving buoyant helium gas jet in ambient air environment is presented. Numerical formulation incorporates a segregated approach to solve for the transport equations of helium mass fraction coupled with the conservation equations of mixture mass and momentum using a staggered grid method. The operating parameters correspond to the Reynolds number varying from 30 to 300 to demarcate the flow dynamics in oscillating and non-oscillating regimes. Computed velocity and concentration fields were used to analyze the flow structure in the evolving jet. For Re=300 case, results showed that an instability mode that sets in during the evolution process in Earth gravity is absent in zero gravity, signifying the importance of buoyancy. Though buoyancy initiates the instability, below a certain jet exit velocity, diffusion dominates the entrainment process to make the jet non-oscillatory as observed for the Re=30 case. Initiation of the instability was found to be dependent on the interaction of buoyancy and momentum forces along the jet shear layer.

Satti, Rajani P.↗
NASA NTRS2004

Direct Electrolytic Deposition of Mats of Mn(x)O(y) Nanowires

Mats of free-standing manganese oxide (MnxOy) nanowires have been fabricated as experimental electrode materials for rechargeable electrochemical power cells and capacitors. Because they are free-standing, the wires in these mats are electrochemically accessible. The advantage of the mat-of-nanowires configuration, relative to other configurations of electrode materials, arises from the combination of narrowness and high areal number density of the wires. This combination offers both high surface areas for contact with electrolytes and short paths for diffusion of ions into and out of the electrodes, thereby making it possible to charge and discharge at rates higher than would otherwise be possible and, consequently, to achieve greater power densities. The nanowires are fabricated in an electrolytic process in which there is no need for an electrode binder material. Moreover, there is no need to incorporate an electrically conductive additive into the electrode material; the only electrically conductive material that must be added is a thin substrate contact film at the anchored ends of the nanowires. Hence, the mass fraction of active electrode material is close to 100 percent, as compared with about 85 percent in conventional electrodes made from a slurry of active electrode material, binder, and conductive additive pressed onto a metal foil. The locations and sizes of the nanowires are defined by holes in templates in the form of commercially available porous alumina membranes. In experiments to demonstrate the present process, alumina membranes of various pore sizes and degrees of porosity were used. First, a film of Au was sputtered onto one side of each membrane. The membranes were then attached, variously, to carbon tape or a gold substrate by use of silver or carbon paste. Once thus attached, the membranes were immersed in a plating solution comprising 0.01 M MnSO4 + 0.03 M (NH4)2SO4. The pH of the solution was kept constant at 8 by addition of H2SO4 or NH4OH as needed. Mn(x)O(y) nanowires were potentiostatically electrodeposited in the pores in the alumina templates. Depending on the anodic deposition potentials, Mn(x)O(y) was deposited in various oxidation states [divalent (Mn3O4), trivalent (Mn2O3), or tetravalent (MnO2)]. The Mn(x)O(y) wires were made free-standing (see figure) by dissolving the alumina templates, variously, in KOH or NaOH at a concentration of 20 volume percent.

Myung, Nosang↗
NASA NTRS1990

Direct numerical simulations of stably-stratified sheared turbulence: Implications for oceanic mixing

Direct numerical simulations of the time evolution of homogeneous stably stratified turbulent shear flows have been performed for several Richardson numbers Ri and Reynolds numbers R(sub lambda) in earlier works. The results show excellent agreement with length scale models developed from laboratory experiments to characterize oceanic turbulence. When the Richardson number Ri is less than the stationary value Ri(sub s), the turbulence intensity grows at all scales, and the growth rate appears to be a function of Ri. The size of the vertical density inversions also increases. On the other hand, when Ri is greater than or equal to Ri(sub s) the largest turbulent eddies become vertically constrained by buoyancy when the Ellison (turbulence) scale L(sub E) and the Ozmidov (buoyancy) scale L(sub O) are equal. At this point, the mixing efficiency is maximal and corresponds to a flux Richardson number R(sub f) = 0.20. The vertical mass flux becomes counter-gradient when epsilon = 19(nu)N(exp 2) and vertical density overturns are suppressed in less than half a Brunt-Vaisala period. The results of the simulations were also recast in terms of the Hydrodynamic Phase Diagram introduced in fossil turbulence models. The so-called point of fossilization occurs when epsilon = 4DCN(exp 2); Gibson proposed 13DCN(exp 2). This value is in agreement with indirect laboratory observations and field observations. Finally, the validity of the steady-state models to estimate vertical eddy diffusivities in the oceanic thermocline is discussed.

Itsweire, E. C.↗
NASA NTRS2004

An Evolving Trio of Hybrid Stars: C 111

Our goal is to understand the behavior of the outer atmosphere in this intermediate stage to create a comprehensive picture of atmospheric evolution. In the hybrid phase, the large-scale magnetic dynamo activity decays and hydrodynamic processes assume importance. Some hot plasma is still confined close to the star by magnetic loops, yet the confining field is breaking open, the atmosphere can escape through these open field lines, and the diffuse corona may be warm. There may well be a more extended and variable transition process. It remains for FUSE to identify the controlling parameters of the hybrid stars. It shows the positions of our 3 targets in the color-magnitude diagram where it is seen that they are at the extreme end of the hybrid region. Originally we had been awarded the hybrid star Iota Aur, but due to newly imposed pointing constraints of FUSE, that target was not accessible. And so we substituted Iota Dra, a giant of mass similar to our other targets but less evolved. In addition, Iota Dra was recently found to harbor a sub-stellar objects, possibly a planet, and so it could reveal the stellar environment of the planet. This substitution was accepted.

Oliversen, Ronald↗
NASA NTRS2007

High Temperature Stability of Dissimilar Metal Joints in Fission Surface Power Systems

Future generations of power systems for spacecraft and lunar surface systems will likely require a strong dependence on nuclear power. The design of a space nuclear power plant involves integrating together major subsystems with varying materia1 requirements. Refractory alloys are repeatedly considered for major structural components in space power reactor designs because refractory alloys retain their strength at higher temperatures than other classes of metals. The relatively higher mass and lower ductility of the refractory alloys make them less attractive for lower temperature subsystems in the power plant such as the power conversion system. The power conversion system would consist more likely of intermediate temperature Ni-based superalloys. One of many unanswered questions about the use of refractory alloys in a space power plant is how to transition from the use of the structural refractory alloy to more traditional structural alloys. Because deleterious phases can form when complex alloys are joined and operated at elevated temperatures, dissimilar material diffusion analyses of refractory alloys and superalloys are needed to inform designers about options of joint temperature and operational lifetime. Combinations of four superalloys and six refractory alloys were bonded and annealed at 1150 K and 1300 K to examine diffusional interactions in this study. Joints formed through hot pressing and hot isostatic pressing were compared. Results on newer alloys compared favorably to historical data. Diffusional stability is promising for some combinations of Mo-Re alloys and superalloys at 1150 K, but it appears that lower joint temperatures would be required for other refractory alloy couples.

Locci, Ivan E.↗
NASA NTRS1972

The EOLE experiment: Early results and current objectives

The EOLE experiment with 480 constant level balloons released in the Southern Hemisphere is described. Each balloon floating freely at approximately the 200 mb level, is a precise tracer of the horizontal motion of air masses, the accuracy of which is limited only by the laminated structure of the stratospheric flow, within an RMS uncertainty of 1.5 m/sec. The balloons were found after 2 months to distribute at random over the whole hemisphere outside the tropics, irrespective of their original launching site. Early results of Eulerian and Lagrangian averages of the EOLE wind data are given for describing the mean 200 mb zonal and meridional circulations. The effect of the small scale eddies of two-dimensional turbulence has been studied with respect to the relative eddy diffusion of pairs of balloons and the relative dispersion of triangular clusters. New estimates of the RMS divergence of the 200 mb flow are given, together with their scale dependence which was found to be a logarithmic law.

Morel, P.↗
NASA NTRS1992

A coupled Eulerian/Lagrangian method for the solution of three-dimensional vortical flows

A coupled Eulerian/Lagrangian method is presented for the reduction of numerical diffusion observed in solutions of three-dimensional rotational flows using standard Eulerian finite-volume time-marching procedures. A Lagrangian particle tracking method using particle markers is added to the Eulerian time-marching procedure and provides a correction of the Eulerian solution. In turn, the Eulerian solutions is used to integrate the Lagrangian state-vector along the particles trajectories. The Lagrangian correction technique does not require any a-priori information on the structure or position of the vortical regions. While the Eulerian solution ensures the conservation of mass and sets the pressure field, the particle markers, used as 'accuracy boosters,' take advantage of the accurate convection description of the Lagrangian solution and enhance the vorticity and entropy capturing capabilities of standard Eulerian finite-volume methods. The combined solution procedures is tested in several applications. The convection of a Lamb vortex in a straight channel is used as an unsteady compressible flow preservation test case. The other test cases concern steady incompressible flow calculations and include the preservation of turbulent inlet velocity profile, the swirling flow in a pipe, and the constant stagnation pressure flow and secondary flow calculations in bends. The last application deals with the external flow past a wing with emphasis on the trailing vortex solution. The improvement due to the addition of the Lagrangian correction technique is measured by comparison with analytical solutions when available or with Eulerian solutions on finer grids. The use of the combined Eulerian/Lagrangian scheme results in substantially lower grid resolution requirements than the standard Eulerian scheme for a given solution accuracy.

Felici, Helene Marie↗
NASA NTRS2000

Inertial Effects in Suspension Dynamics

The present work analyses the dynamics of a suspension of heavy particles in shear flow. The magnitude of the particle inertia is given by the Stokes number St = m(gamma/6(pi)a, which is the ratio of the viscous relaxation time of a particle tau(sub p) = m=6pi(eta)a to the flow time gamma(sup -1). Here, m is the mass of the particle, a is its size, eta is the viscosity of the suspending fluid and gamma is the shear rate. The ratio of the Stokes number to the Reynolds number, Re = (rho)f(gamma)a(exp 2)/eta, is the density ratio rho(sub p)/rho(sub f). Of interest is to understand the separate roles of particle (St) and fluid (Re) inertia in the dynamics of suspensions. In this study we focus on heavy particles, rho(sub p)/rho(sub f) much greater than 1, for which the Stokes number is finite, but the Reynolds number is sufficiently small for inertial forces in the fluid to be neglected; thus, the fluid motion is governed by the Stokes equations. On the other hand, the probability density governing the statistics of the suspended particles satisfies a Fokker-Planck equation that accounts for both configuration and momentum coordinates, the latter being essential for finite St. The solution of the Fokker-Planck equation is obtained to O(St) via a Chapman-Enskog type-procedure, and the conditional velocity distribution so obtained is used to derive a configuration-space Smoluchowski equation with inertial corrections. The inertial effects are responsible for asymmetry in the relative trajectories of two spheres in shear flow, in contrast to the well known symmetric structure in the absence of inertia. Finite St open trajectories in the plane of shear suffer a downward lateral displacement resulting from the inability of a particle of finite mass to follow the curvature of the zero-Stokes-number pathlines. In addition to the induced asymmetry, the O(St) inertial perturbation dramatically alters the nature of the near-field trajectories. The stable closed orbits (for St = 0) in the plane of shear now spiral in, approaching particle-particle contact in the limit. All trajectories starting from an initial offset of O(St(sup 1/2) or less (which remain open for St = 0) also spiral in. The asymmetry of the trajectories leads to a non-Newtonian rheology and diffusive behavior. The latter because a given particle (moving along a finite St open trajectory) suffers a net displacement in the transverse direction after a single interaction. A sequence of such uncorrelated displacements leads to the particle executing a random walk. The inertial diffusivity tensor is anisotropic on account of differing strengths of interaction in the gradient and vorticity directions. Since the entire region (constituting an in finite area) of closed orbits in the plane of shear spirals onto contact for #finite St, the latter represents a singular surface for the pair-distribution function. The exact form of the pair-distribution function at contact is still, however, indeterminate in the absence of non-hydrodynamic effects. It should also be noted that finite St non-rectilinear flows do not support a spatially uniform number density owing to the cross-streamline inertial migration of particles.

J. F. Brady↗
NASA NTRS1999

EGRET Observations of the Diffuse Gamma-Ray Emission in Orion: Analysis Through Cycle 6

We present a study of the high-energy diffuse emission observed toward Orion by the Energetic Gamma-Ray Experiment Telescope (EGRET) on the Compton Gamma-Ray Observatory. The total exposure by EGRET in this region has increased by more than a factor of two since a previous study. A simple model for the diffuse emission adequately fits the data; no significant point sources are detected in the region studied (1 = 195 deg to 220 deg and b = -25 deg to -10 deg) in either the composite dataset or in two separate groups of EGRET viewing periods considered. The gamma-ray emissivity in Orion is found to be (1.65 +/- 0.11) x 10(exp -26)/s.sr for E > 100 MeV, and the differential emissivity is well-described as a combination of contributions from cosmic-ray electrons and protons with approximately the local density. The molecular mass calibrating ratio is N(H2)/W(sub CO) = (1.35 +/- 0.15) x 10(exp 20)/sq cm.(K.km/s).

Digel, S. W.↗
NASA NTRS2007

Runtime and Pressurization Analyses of Propellant Tanks

Multi-element unstructured CFD has been utilized at NASA SSC to carry out analyses of propellant tank systems in different modes of operation. The three regimes of interest at SSC include (a) tank chill down (b) tank pressurization and (c) runtime propellant draw-down and purge. While tank chill down is an important event that is best addressed with long time-scale heat transfer calculations, CFD can play a critical role in the tank pressurization and runtime modes of operation. In these situations, problems with contamination of the propellant by inclusion of the pressurant gas from the ullage causes a deterioration of the quality of the propellant delivered to the test article. CFD can be used to help quantify the mixing and propellant degradation. During tank pressurization under some circumstances, rapid mixing of relatively warm pressurant gas with cryogenic propellant can lead to rapid densification of the gas and loss of pressure in the tank. This phenomenon can cause serious problems during testing because of the resulting decrease in propellant flow rate. With proper physical models implemented, CFD can model the coupling between the propellant and pressurant including heat transfer and phase change effects and accurately capture the complex physics in the evolving flowfields. This holds the promise of allowing the specification of operational conditions and procedures that could minimize the undesirable mixing and heat transfer inherent in propellant tank operation. It should be noted that traditional CFD modeling is inadequate for such simulations because the fluids in the tank are in a range of different sub-critical and supercritical states and elaborate phase change and mixing rules have to be developed to accurately model the interaction between the ullage gas and the propellant. We show a typical run-time simulation of a spherical propellant tank, containing RP-1 in this case, being pressurized with room-temperature nitrogen at 540 R. Nitrogen, shown in blue on the right-hand side of the figures, enters the tank from the diffuser at the top of the figures and impinges on the RP-1, shown in red, while the propellant is being continuously drained at the rate of 1050 lbs/sec through a pipe at the bottom of the tank. The sequence of frames in Figure 1 shows the resultant velocity fields and mixing between nitrogen and RP-1 in a cross-section of the tank at different times. A vortex is seen to form in the incoming nitrogen stream that tends to entrain propellant, mixing it with the pressurant gas. The RP-1 mass fraction contours in Figure 1 are also indicative of the level of mixing and contamination of the propellant. The simulation is used to track the propagation of the pure propellant front as it is drawn toward the exit with the evolution of the mixing processes in the tank. The CFD simulation modeled a total of 10 seconds of run time. As is seen from Figure 1d, after 5.65 seconds the propellant front is nearing the drain pipe, especially near the center of the tank. Behind this pure propellant front is a mixed fluid of compromised quality that would require the test to end when it reaches the exit pipe. Such unsteady simulations provide an estimate of the time that a high-quality propellant supply to the test article can be guaranteed at the modeled mass flow rate. In the final paper, we will discuss simulations of the LOX and propellant tanks at NASA SSC being pressurized by an inert ullage. Detailed comparisons will be made between the CFD simulations and lower order models as well as with test data. Conditions leading to cryo collapse in the tank will also be identified.

Field, Robert E.↗
NASA NTRS1989

Molecular and mass spectroscopic analysis of isotopically labeled organic residues

Experimental studies aimed at understanding the evolution of complex organic molecules on interstellar grains were performed. The photolysis of frozen gas mixtures of various compositions containing H2O, CO, NH3, and CH4 was studied. These species were chosen because of their astrophysical importance as deducted from observational as well as theoretical studies of ice mantles on interstellar grains. These ultraviolet photolyzed ices were warmed up in order to produce refractory organic molecules like the ones formed in molecular clouds when the icy mantles are being irradiated and warmed up either by a nearby stellar source or impulsive heating. The laboratory studies give estimates of the efficiency of production of such organic material under interstellar conditions. It is shown that the gradual carbonization of organic mantles in the diffuse cloud phase leads to higher and higher visual absorptivity - yellow residues become brown in the laboratory. The obtained results can be applied to explaining the organic components of comets and their relevance to the origin of life.

Mendoza-Gomez, Celia X.↗
NASA NTRS1989

Theory of droplet. Part 1: Renormalized laws of droplet vaporization in non-dilute sprays

The vaporization of a droplet, interacting with its neighbors in a non-dilute spray environment is examined as well as a vaporization scaling law established on the basis of a recently developed theory of renormalized droplet. The interacting droplet consists of a centrally located droplet and its vapor bubble which is surrounded by a cloud of droplets. The distribution of the droplets and the size of the cloud are characterized by a pair-distribution function. The vaporization of a droplet is retarded by the collective thermal quenching, the vapor concentration accumulated in the outer sphere, and by the limited percolative passages for mass, momentum and energy fluxes. The retardation is scaled by the local collective interaction parameters (group combustion number of renormalized droplet, droplet spacing, renormalization number and local ambient conditions). The numerical results of a selected case study reveal that the vaporization correction factor falls from unity monotonically as the group combustion number increases, and saturation is likely to occur when the group combustion number reaches 35 to 40 with interdroplet spacing of 7.5 diameters and an environment temperature of 500 K. The scaling law suggests that dense sprays can be classified into: (1) a diffusively dense cloud characterized by uniform thermal quenching in the cloud; (2) a stratified dense cloud characterized by a radial stratification in temperature by the differential thermal quenching of the cloud; or (3) a sharply dense cloud marked by fine structure in the quasi-droplet cloud and the corresponding variation in the correction factor due to the variation in the topological structure of the cloud characterized by a pair-distribution function of quasi-droplets.

Chiu, H. H.↗