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NASA NTRS1994

Second-order closure PBL model with new third-order moments: Comparison with LES data

This paper contains two parts. In the first part, a new set of diagnostic equations is derived for the third-order moments for a buoyancy-driven flow, by exact inversion of the prognostic equations for the third-order moment equations in the stationary case. The third-order moments exhibit a universal structure: they all are a linear combination of the derivatives of all the second-order moments, bar-w(exp 2), bar-w theta, bar-theta(exp 2), and bar-q(exp 2). Each term of the sum contains a turbulent diffusivity D(sub t), which also exhibits a universal structure of the form D(sub t) = a nu(sub t) + b bar-w theta. Since the sign of the convective flux changes depending on stable or unstable stratification, D(sub t) varies according to the type of stratification. Here nu(sub t) approximately equal to wl (l is a mixing length and w is an rms velocity) represents the 'mechanical' part, while the 'buoyancy' part is represented by the convective flux bar-w theta. The quantities a and b are functions of the variable N(sub tau)(exp 2), where N(exp 2) = g alpha derivative of Theta with respect to z and tau is the turbulence time scale. The new expressions for the third-order moments generalize those of Zeman and Lumley, which were subsequently adopted by Sun and Ogura, Chen and Cotton, and Finger and Schmidt in their treatments of the convective boundary layer. In the second part, the new expressions for the third-order moments are used to solve the ensemble average equations describing a purely convective boundary laye r heated from below at a constant rate. The computed second- and third-order moments are then compared with the corresponding Large Eddy Simulation (LES) results, most of which are obtained by running a new LES code, and part of which are taken from published results. The ensemble average results compare favorably with the LES data.

Canuto, V. M.↗

NASA NTRS2016

Evaluation of Methods for Molecular Dynamics Simulation of Ionic Liquid Electric Double Layers

We investigate how systematically increasing the accuracy of various molecular dynamics modeling techniques influences the structure and capacitance of ionic liquid electric double layers (EDLs). The techniques probed concern long-range electrostatic interactions, electrode charging (constant charge versus constant potential conditions), and electrolyte polarizability. Our simulations are performed on a quasi-two-dimensional, or slab-like, model capacitor, which is composed of a polarizable ionic liquid electrolyte, [EMIM][BF4], interfaced between two graphite electrodes. To ensure an accurate representation of EDL differential capacitance, we derive new fluctuation formulas that resolve the differential capacitance as a function of electrode charge or electrode potential. The magnitude of differential capacitance shows sensitivity to different long-range electrostatic summation techniques, while the shape of differential capacitance is affected by charging technique and the polarizability of the electrolyte. For long-range summation techniques, errors in magnitude can be mitigated by employing two-dimensional or corrected three dimensional electrostatic summations, which lead to electric fields that conform to those of a classical electrostatic parallel plate capacitor. With respect to charging, the changes in shape are a result of ions in the Stern layer (i.e. ions at the electrode surface) having a higher electrostatic affinity to constant potential electrodes than to constant charge electrodes. For electrolyte polarizability, shape changes originate from induced dipoles that soften the interaction of Stern layer ions with the electrode. The softening is traced to ion correlations vertical to the electrode surface that induce dipoles that oppose double layer formation. In general, our analysis indicates an accuracy dependent differential capacitance profile that transitions from the characteristic camel shape with coarser representations to a more diffuse profile with finer representations.

Haskins, Justin B.↗

NASA NTRS1995

Time-dependent simulation of oblique MHD cosmic-ray shocks using the two-fluid model

Using a new, second-order accurate numerical method we present dynamical simulations of oblique MHD cosmic-ray (CR)-modified plane shock evolution. Most of the calculations are done with a two-fluid model for diffusive shock acceleration, but we provide also comparisons between a typical shock computed that way against calculations carried out using the more complete, momentum-dependent, diffusion-advection equation. We also illustrate a test showing that these simulations evolve to dynamical equilibria consistent with previously published steady state analytic calculations for such shocks. In order to improve understanding of the dynamical role of magnetic fields in shocks modified by CR pressure we have explored for time asymptotic states the parameter space of upstream fast mode Mach number, M(sub f), and plasma beta. We compile the results into maps of dynamical steady state CR acceleration efficiency, epsilon(sub c). We have run simulations using constant, and nonisotropic, obliquity (and hence spatially) dependent forms of the diffusion coefficient kappa. Comparison of the results shows that while the final steady states achieved are the same in each case, the history of CR-MHD shocks can be strongly modified by variations in kappa and, therefore, in the acceleration timescale. Also, the coupling of CR and MHD in low beta, oblique shocks substantially influences the transient density spike that forms in strongly CR-modified shocks. We find that inside the density spike a MHD slow mode wave can be generated that eventually steepens into a shock. A strong layer develops within the density spike, driven by MHD stresses. We conjecture that currents in the shear layer could, in nonplanar flows, results in enhanced particle accretion through drift acceleration.

Frank, Adam↗

NASA NTRS2012

Large Eddy Simulation (LES) of Particle-Laden Temporal Mixing Layers

High-fidelity models of plume-regolith interaction are difficult to develop because of the widely disparate flow conditions that exist in this process. The gas in the core of a rocket plume can often be modeled as a time-dependent, high-temperature, turbulent, reacting continuum flow. However, due to the vacuum conditions on the lunar surface, the mean molecular path in the outer parts of the plume is too long for the continuum assumption to remain valid. Molecular methods are better suited to model this region of the flow. Finally, granular and multiphase flow models must be employed to describe the dust and debris that are displaced from the surface, as well as how a crater is formed in the regolith. At present, standard commercial CFD (computational fluid dynamics) software is not capable of coupling each of these flow regimes to provide an accurate representation of this flow process, necessitating the development of custom software. This software solves the fluid-flow-governing equations in an Eulerian framework, coupled with the particle transport equations that are solved in a Lagrangian framework. It uses a fourth-order explicit Runge-Kutta scheme for temporal integration, an eighth-order central finite differencing scheme for spatial discretization. The non-linear terms in the governing equations are recast in cubic skew symmetric form to reduce aliasing error. The second derivative viscous terms are computed using eighth-order narrow stencils that provide better diffusion for the highest resolved wave numbers. A fourth-order Lagrange interpolation procedure is used to obtain gas-phase variable values at the particle locations.

Bellan, Josette↗

NASA NTRS1995

Magnetic reconnection in the presence of sheared flow and density asymmetry: Applications to the Earth's magnetopause

Classical models of magnetic reconnection consist of a small diffusion region bounded by two symmetric slow shocks, across which the plasma is accelerated. Asymmetries often present in space plasmas are sheared plasma flow and dissimilar plasma densities on the two sides of current sheets. In this paper, we investigate magnetic reconnection in the presence of a shear flow and an asymmetric density across the current sheet using two-dimensional magnetohydrodynamic (MHD) simulations. The results demonstrate that magnetic reconnection can occur only for a plasma flow velocity (in the frame of the X line) which is below the Alfven speed in each inflow region. This limits the velocity of the X line to a certain range for a given flow shear and provides an upper limit to the total velocity shear at which reconnection ceases to operate. Depending on the direction of the flow in the adjacent inflow region, the effects from the sheared flow and from the density asymmetry will compete with or enhance each other in respect to the magnitude and location of the currents which bound the outflow regions. The results are applied to the dayside and flank regions of the magnetosphere. For the dayside region where the magnetosheath flow is slow, the magnetic field transition region is thin and the accelerated flow is earthward of the sharp current layer (magnetopause). At the flanks tailward of the X line, shear flow and density asymmetry effects compete making the magnetic field transition layer broad with the high-speed flow contained within the transition region which explains corresponding observations. At the flanks sunward of the X line, shear flow and density asymmetry effects enhance each other and lead to a strong current sheet on the magnetosheath side of the accelerated flow. The total volume affected by magnetic reconnection is much larger than the steady state region. A large bulge region precedes the steady state region. Qualitatively, the bulge and the steady state region have similar signatures and both can explain observations. We provide criteria in order to distinguish between the bulge and the steady state region in observations.

La Belle-Hamer, A. L.↗

NASA NTRS2006

Radar Probing of Planetary Regoliths: An Example from the Northern Rim of Imbrium Basin

Imaging radar measurements at long wavelengths (e.g., >30 cm) allow deep (up to tens of meters) probing of the physical structure and dielectric properties of planetary regoliths. We illustrate a potential application for a Mars orbital synthetic aperture radar (SAR) using new Earth-based 70-cm wavelength radar data for the Moon. The terrae on the northern margin of Mare Imbrium, the Montes Jura region, have diffuse radar backscatter echoes that are 2-4 times weaker at 3.8-cm, 70-cm, and 7.5-m wavelengths than most other lunar nearside terrae. Possible geologic explanations are (1) a pyroclastic deposit associated with sinuous rilles in this region, (2) buried mare basalt or a zone of mixed highland/basaltic debris (cryptomaria), or (3) layers of ejecta associated with the Iridum and Plato impacts that have fewer meter-sized rocks than typical highlands regolith. While radar data at 3.8-cm to 7.5-m wavelengths suggest significant differences between the Montes Jura region and typical highlands, the surface geochemistry and rock abundance inferred from Clementine UV-VIS data and eclipse thermal images are consistent with other lunar terrae. There is no evidence for enhanced iron abundance, expected for basaltic pyroclastic deposits, near the source vents of the sinuous rilles radial to Plato. The regions of low 70-cm radar return are consistent with overlapping concentric ''haloes'' about Iridum and Plato and do not occur referentially in topographically low areas, as is observed for radar-mapped cryptomaria. Thus we suggest that the extensive radar-dark area associated with the Montes Jura region is due to overlapping, rock-poor ejecta deposits from Iridum and Plato craters. Comparison of the radial extent of low-radar-return crater haloes with a model for ejecta thickness shows that these rock-poor layers are detected by 70-cm radar where they are on the order of 10 m and thicker. A SAR in orbit about Mars could use similar deep probing to reveal the nature of crater - and basin-related deposits.

Iridum crater↗

NASA NTRS2005

Scanning Backscatter Lidar Observations for Characterizing 4-D Cloud and Aerosol Fields to Improve Radiative Transfer Parameterizations

Clouds have a powerful influence on atmospheric radiative transfer and hence are crucial to understanding and interpreting the exchange of radiation between the Earth's surface, the atmosphere, and space. Because clouds are highly variable in space, time and physical makeup, it is important to be able to observe them in three dimensions (3-D) with sufficient resolution that the data can be used to generate and validate parameterizations of cloud fields at the resolution scale of global climate models (GCMs). Simulation of photon transport in three dimensionally inhomogeneous cloud fields show that spatial inhomogeneities tend to decrease cloud reflection and absorption and increase direct and diffuse transmission, Therefore it is an important task to characterize cloud spatial structures in three dimensions on the scale of GCM grid elements. In order to validate cloud parameterizations that represent the ensemble, or mean and variance of cloud properties within a GCM grid element, measurements of the parameters must be obtained on a much finer scale so that the statistics on those measurements are truly representative. High spatial sampling resolution is required, on the order of 1 km or less. Since the radiation fields respond almost instantaneously to changes in the cloud field, and clouds changes occur on scales of seconds and less when viewed on scales of approximately 100m, the temporal resolution of cloud properties should be measured and characterized on second time scales. GCM time steps are typically on the order of an hour, but in order to obtain sufficient statistical representations of cloud properties in the parameterizations that are used as model inputs, averaged values of cloud properties should be calculated on time scales on the order of 10-100 s. The Holographic Airborne Rotating Lidar Instrument Experiment (HARLIE) provides exceptional temporal (100 ms) and spatial (30 m) resolution measurements of aerosol and cloud backscatter in three dimensions. HARLIE was used in a ground-based configuration in several recent field campaigns. Principal data products include aerosol backscatter profiles, boundary layer heights, entrainment zone thickness, cloud fraction as a function of altitude and horizontal wind vector profiles based on correlating the motions of clouds and aerosol structures across portions of the scan. Comparisons will be made between various cloud detecting instruments to develop a baseline performance metric.

Schwemmer, Geary K.↗

NASA NTRS2002

Development of a New Membrane Casting Apparatus for Studying Macrovoid Defects in Low-G

A new membrane-casting apparatus is developed for studying macrovoid defects in polymeric membranes made by the wet- and dry-casting process in low-gravity. Macrovoids are large (10-50 micron), open cavities interspersed among the smaller pores in the substructure under the gelled skin surface layer of the cast membrane. Although their occurrence is considered endemic to the wet- and dry-casting process since they can lead to compaction or skin rupture in the membrane process, recent studies suggest several useful applications such as transdermal and osmotic drug delivery systems, miniature bioreactors, etc. However, lack of knowledge about the macrovoid formation mechanism is an obstacle to further development of applications using them. An on-going debate is the role of the surface-tension-driven solutocapillary convection during macrovoid formation. The rapid growth of macrovoids within 1-5 seconds and the high polymer concentration in and near macrovoids make it difficult to explain the mechanism of macrovoid growth by diffusion alone, which is the widely accepted hypothesis proposed by Reuvers et al. The hypothesis advanced by our research group can explain this rapid growth via a mechanism that involves diffusion from the casting solution in the meta-stable region to the macrovoid enhanced by solutocapillary convection induced by the steep nonsolvent concentration gradient in the vicinity of the macrovoid. Since macrovoid growth is hypothesized to be the interplay of a solutocapillary-induced driving force counteracted by viscous drag and buoyancy, eliminate the latter provides a means for testing this hypothesis. Moreover, free convection mass transfer in the nonsolvent immersion bath used to cause phase-separation in membrane casting complicates developing a model for both the wet-casting process and macrovoid growth. The low-g environment minimizes gravitationally induced free convection thereby permitting a tractable solution to the ternary diffusion equations that characterize membrane formation. NASA's Parabolic Flight Research Aircraft provides a small window of low-g (approximately 25 s) that can be used to study macrovoid development in both wet- and dry-cast membranes if an appropriate casting apparatus is used. This casting apparatus should be able to cast the membrane in both low- and high-g in a manner so that essential one-dimensional mass transfer conditions are achieved to insure lateral uniformity in the membrane. The apparatus used in previous research on membrane casting in low-gravity was operated with the plunger driven mechanism. The spring-loaded plunger pushes the bottom block containing the polymer casting solution well directly under the absorbent chamber located in the upper stationary block. However, membranes made via this casting apparatus often displayed lateral nonuniformities that precluded obtaining quantitative information on the macrovoid growth process. Thus, it was necessary to determine the reason for these structural irregularities observed in the low-g casting apparatus. Both experimental as well as computer simulation studies of the low-g casting apparatus established that the impulsive action of the plunger caused the undesired structural nonuniformities. The simulation results showed that the width-to-depth aspect ratio of the shallow well that contains the casting solution in this apparatus was not an important factor in minimizing this problem. Even for a 40:1 (width : depth) aspect ratio, any convection induced by the horizontal motion of the interface of the casting solution will be damped out within 6.25x10(exp 4) seconds. However, the experimental studies revealed that the impulsive motion of the plunger caused a 'sloshing' of the casting solution that had to be eliminated. Therefore, the plungerdriven mechanism was changed to a cam-driven mechanism that did not cause any impulsive motion of the casting solution. Other refinements to this new membrane-casting apparatus include provision for removing the membranes from the casting wells in a less destructive manner. This was accomplished by using a slit geometry for the casting well that permitted disassembly for removal of the cast membrane. The materials used in the construction of this casting apparatus were chosen to insure wetting at the side walls and to maintain precise control of the thickness of the polymer solution in the casting well. An additional provision in this new casting apparatus is the ability to carry out both wet- as well as dry-casting. As such, this apparatus permitted the first studies of the wet-casting of polymeric membranes in low-g. Both wet- and dry-casting experiments on NASA's KC-135 research aircraft employing this new membrane-casting apparatus are scheduled in July 2002. The morphology of the resulting membranes will be characterized using an environmental scanning electron microscope (ESEM). The results of these low-g studies will be reported later.

Lee, Hanyong↗

NASA NTRS1990

The diffuse ionized interstellar medium perpendicular to the plane of NGC 891

In an attempt to study the structure and the properties of the diffuse ionized interstellar medium perpendicular to the plane of disk galaxies researchers obtained H alpha images and spectra of NGC 891. Perhaps the most remarkable property of the H alpha emission line in NGC 891 is its extension out of the plane of the galaxy: researchers are able to measure the H alpha line out to more than 30 seconds (1.4 kpc) from the midplane. This means that the ionized hydrogen extends at least four times higher than the neutral hydrogen layer. An anomalously large scale-height for the ionized gas of approx. equals 1 kpc is also found in the Milky Way. The echelle spectra show a changing ratio of NII to H alpha. This excludes the possibility that the large scaleheight of the emission is due to scattering of disk emission by dust high above the plane. The z-extent of the H alpha emission is confirmed by the imaging result. The large z-extent of the ionized gas is confined to the inner half of the visible disk. In this inner region the H alpha distribution also shows a filamentary structure of the diffuse ionized medium. These filaments, sticking out of the plane, originate in HII regions in the plane. The H alpha image also shows a large scale asymmetry if the NE and SW parts of the disk are compared. The NE part is more prominent and extended in H alpha. The same asymmetry is also seen in the radio continuum distribution. This correlation between the diffuse ionized medium and the distribution of relativistic electrons is one example of a relation between star formation processes in the disk and the various components of the halo. Thermal filaments or spurs which are related to HII regions are also known in the Galaxy. These filamentary structures perpendicular to the galactic planes may represent the chimneys which result in the supernova dominated model of the Interstellar Medium by Norman and Ikeuchi (1989).

Dettmar, Ralf-Juergen↗

NASA NTRS2003

An Alternative Hypothesis for How Microgravity Improves Macromolecular Crystal Quality

There is a substantial body of experimental evidence, from this and other laboratories, that strongly suggests that for many proteins crystal nucleation and growth is by addition of associated species that are preformed by reversible concentration-driven self association processes in the bulk solution. We have developed a self-association model for the crystal nucleation and growth of the protein chicken egg lysozyme. The model accounts for the obtained crystal symmetry, explains the observed surface structures, and shows the importance of the symmetry obtained by self-association in solution to the process as a whole. This model also offers a possible mechanism for fluid flow effects on the growth process and how microgravity may affect it. While a single lysozyme molecule is relatively small an octamer in the 43 helix configuration (the proposed average sized growth unit) would have a M.W. approx. 115,000 and dimensions of 5.6 x 5.6 x 7.6 nm. Direct AFM measurements of growth unit incorporation indicate that units as wide as 11.2 nm and as long as 11.4 nm (a 24-mer) commonly attach to the crystal. AFM results from Weichmann et al. (Ultramicroscopy 86, 159-166, 2001) suggest that associated species of up to 40-mers in size add to the (101) faces. These measurements reflect the sizes of units that both added and desorbed from the crystal surface. The larger and less isotropic the associated species the more likely that it will be oriented to some degree in a flowing boundary layer, even at the low flow velocities measured about macromolecule crystals. On Earth, concentration gradient driven flow will maintain a high interfacial concentration, i.e., a high level (essentially that of the bulk solution) of solute association at the interface and higher growth rate. Higher growth rates mean an increased probability that misaligned growth units are trapped by subsequent growth layers before they can be desorbed and try again, or that the desorbing species is more likely to be smaller than the adsorbing species. In microgravity the extended diffusive boundary layer will lower the interfacial concentration. This results in a net dissociation of aggregated species that diffuse in from the bulk solution, i.e., smaller associated species, which are more likely able to make multiple attempts to correctly bind, yielding higher quality crystals.

Pusey, Marc↗

NASA NTRS1993

Dynamics and control of coherent structures in the turbulent wall layer: An overview

We expand the velocity field in the vicinity of the wall in empirical eigenfunctions obtained from experiment. Truncating our system and using Galerkin projection, we obtain a closed set of non-linear ordinary differential equations with ten degrees of freedom. We find a rich dynamical behavior, including in particular a heteroclinic attracting orbit giving rise to intermittency. The intermittent jump from one attracting point to the other resembles in many respects the bursts observed in experiments. Specifically, the time between jumps and the duration of the jumps, is approximately that observed in a burst; the jump begins with the formation of a narrowed and intensified updraft, like the ejection phase of a burst, and is followed by a gentle, diffuse downdraft like the sweep phase of a burst. The magnitude of the Reynolds stress spike produced during a burst is limited by our truncation. The behavior is quite robust, much of it being due to the symmetries present (Aubry's group has examined dimensions up to 128 with persistence of the global behavior). We have examined eigenvalues and coefficients obtained from experiment, and from exact simulation, which differ in magnitude. Similar behavior is obtained in both cases; in the latter case, the heteroclinic orbits connect limit cycles instead of fixed points, corresponding to cross-stream waving of the streamwise rolls. The bifurcation diagram remains structurally similar, but somewhat distorted. The role of the pressure term is made clear - it triggers the intermittent jumps, which otherwise would occur at longer and longer intervals, as the system trajectory is attracted closer and closer to the heteroclinic cycle. The pressure term results in the jumps occurring at essentially random times, and the magnitude of the signal determines the average timing. Stretching of the wall region shows that the model is consistent with observations of polymer drag reduction. Change of the third order coefficients, corresponding to acceleration or deceleration of the mean flow, changes the heteroclinic cycles from attracting to repelling, increasing or decreasing the stability, in agreement with observations. The existence of fixed points is an artifact introduced by the projection; however, a decoupled model still displays the rich dynamics. Numerous assumptions made in Aubry et al. (1988) can now be proved exactly. Feeding back eigenfuncitons with the proper phase can delay the bursting, (the heteroclinic jump to the other fixed point), decreasing the drag. It is also possible to speed up the bursting, increasing mixing to control separation. Our approach is optimal for short time tracking in control.

Berkooz, Gal↗

NASA NTRS1995

Forced Convection and Sedimentation Past a Flat Plate

The steady laminar flow of a well-mixed suspension of monodisperse solid spheres, convected steadily past a horizontal flat plate and sedimenting under the action of gravity, is examined. It is shown that, in the limit as Re approaches infinity and epsilon approaches 0, where Re is the bulk Reynolds number and epsilon is the ratio of the particle radius a to the characteristic length scale L, the analysis for determining the particle concentration profile has several aspects in common with that of obtaining the temperature profile in forced-convection heat transfer from a wall to a fluid stream moving at high Reynolds and Prandtl numbers. Specifically, it is found that the particle concentration remains uniform throughout the O(Re(exp -1/2)) thick Blasius boundary layer except for two O(epsilon(exp 2/3)) thin regions on either side of the plate, where the concentration profile becomes non-uniform owing to the presence of shear-induced particle diffusion which balances the particle flux due to convection and sedimentation. The system of equations within this concentration boundary layer admits a similarity solution near the leading edge of the plate, according to which the particle concentration along the top surface of the plate increases from its value in the free stream by an amount proportional to X(exp 5/6), with X measuring the distance along the plate, and decreases in a similar fashion along the underside. But, unlike the case of gravity settling on an inclined plate in the absence of a bulk flow at infinity considered earlier, here the concentration profile remains continuous everywhere. For values of X beyond the region near the leading edge, the particle concentration profile is obtained through the numerical solution of the relevant equations. It is found that, as predicted from the similarity solution, there exists a value of X at which the particle concentration along the top side of the plate attains its maximum value phi(sub m) and that, beyond this point, a stagnant sediment layer will form that grows steadily in time. This critical value of X is computed as a function of phi(sub s), the particle volume fraction in the free stream. In contrast, but again in conformity with the similarity solution, for values of X sufficiently far removed from the leading edge along the underside of the plate, a particle-free region is predicted to form adjacent to the plate. This model, with minor modifications, can be used to describe particle migration in other shear flows, as, for example, in the case of crossflow microfiltration.

Pelekasis, Nikolaos A.↗

NASA NTRS2008

Computational Analyses in Support of Sub-scale Diffuser Testing for the A-3 Facility: Steady Predictions - Part 1

Simulation technology can play an important role in rocket engine test facility design and development by assessing risks, providing analysis of dynamic pressure and thermal loads, identifying failure modes and predicting anomalous behavior of critical systems. Advanced numerical tools assume greater significance in supporting testing and design of high altitude testing facilities and plume induced testing environments of high thrust engines because of the greater inter-dependence and synergy in the functioning of the different sub-systems. This is especially true for facilities such as the proposed A-3 facility at NASA SSC because of a challenging operating envelope linked to variable throttle conditions at relatively low chamber pressures. Facility designs in this case will require a complex network of diffuser ducts, steam ejector trains, fast operating valves, cooling water systems and flow diverters that need to be characterized for steady state performance. In this paper, we will demonstrate with the use of CFD analyses s advanced capability to evaluate supersonic diffuser and steam ejector performance in a sub-scale A-3 facility at NASA Stennis Space Center (SSC) where extensive testing was performed. Furthermore, the focus in this paper relates to modeling of critical sub-systems and components used in facilities such as the A-3 facility. The work here will address deficiencies in empirical models and current CFD analyses that are used for design of supersonic diffusers/turning vanes/ejectors as well as analyses for confined plumes and venting processes. The primary areas that will be addressed are: (1) supersonic diffuser performance including analyses of thermal loads (2) accurate shock capturing in the diffuser duct; (3) effect of turning duct on the performance of the facility (4) prediction of mass flow rates and performance classification for steam ejectors (5) comparisons with test data from sub-scale diffuser testing and assessment of confidence levels in CFD based flowpath modeling of the facility. The analyses tools used here expand on the multi-element unstructured CFD which has been tailored and validated for impingement dynamics of dry plumes, complex valve/feed systems, and high pressure propellant delivery systems used in engine and component test stands at NASA SSC. The analyses performed in the evaluation of the sub-scale diffuser facility explored several important factors that influence modeling and understanding of facility operation such as (a) importance of modeling the facility with Real Gas approximation, (b) approximating the cluster of steam ejector nozzles as a single annular nozzle, (c) existence of mixed subsonic/supersonic flow downstream of the turning duct, and (d) inadequacy of two-equation turbulence models in predicting the correct pressurization in the turning duct and expansion of the second stage steam ejectors. The procedure used for modeling the facility was as follows: (i) The engine, test cell and first stage ejectors were simulated with an axisymmetric approximation (ii) the turning duct, second stage ejectors and the piping downstream of the second stage ejectors were analyzed with a three-dimensional simulation utilizing a half-plane symmetry approximation. The solution i.e. primitive variables such as pressure, velocity components, temperature and turbulence quantities were passed from the first computational domain and specified as a supersonic boundary condition for the second simulation. (iii) The third domain comprised of the exit diffuser and the region in the vicinity of the facility (primary included to get the correct shock structure at the exit of the facility and entrainment characteristics). The first set of simulations comprising the engine, test cell and first stage ejectors was carried out both as a turbulent real gas calculation as well as a turbulent perfect gas calculation. A comparison for the two cases (Real Turbulent and Perfect gas turbulent) of the Ma Number distribution and temperature distributions are shown in Figures 1 and 2 respectively. The Mach Number distribution shows small yet distinct differences between the two cases such as locations of shocks/shock reflections and a slightly different impingement point on the wall of the diffuser from the expansion at the exit of the nozzle. Similarly the temperature distribution indicates different flow recirculation patterns in the test cell. Both cases capture all the essential flow phenomena such as the shock-boundary layer interaction, plume expansion, expansion of the first stage ejectors, mixing between the engine plume and the first stage ejector flow and pressurization due to the first stage ejectors. The final paper will discuss thermal loads on the walls of the diffuser and cooling mechanisms investigated.

Allgood, Daniel C.↗

NASA NTRS2002

Tetragonal Lysozyme Nucleation and Crystal Growth: The Role of the Solution Phase

Lysozyme, and most particularly the tetragonal form of the protein, has become the default standard protein for use in macromolecule crystal nucleation and growth studies. There is a substantial body of experimental evidence, from this and other laboratories, that strongly suggests this proteins crystal nucleation and growth is by addition of associated species that are preformed by standard reversible concentration-driven self association processes in the bulk solution. The evidence includes high resolution AFM studies of the surface packing and of growth unit size at incorporation, fluorescence resonance energy transfer measurements of intermolecular distances in dilute solution, dialysis kinetics, and modeling of the growth rate data. We have developed a selfassociation model for the proteins crystal nucleation and growth. The model accounts for the obtained crystal symmetry, explains the observed surface structures, and shows the importance of the symmetry obtained by self-association in solution to the process as a whole. Further, it indicates that nucleation and crystal growth are not distinct mechanistically, but identical, with the primary difference being the probability that the particle will continue to grow or dissolve. This model also offers a possible mechanism for fluid flow effects on the growth process and how microgravity may affect it. While a single lysozyme molecule is relatively small (M.W. = 14,400), a structured octamer in the 4(sub 3) helix configuration (the proposed average sized growth unit) would have a M.W. = 115,000 and dimensions of 5.6 x 5.6 x 7.6 nm. Direct AFM measurements of growth unit incorporation indicate that units as wide as 11.2 nm and as long as 11.4 nm commonly attach to the crystal. These measurements were made at approximately saturation conditions, and they reflect the sizes of species that both added or desorbed from the crystal surface. The larger and less isotropic the associated species the more likely that it will be oriented to some degree in a flowing boundary layer, even at the low flow velocities measured about macromolecule crystals. Flow-driven effects resulting in misorientation upon addition to and incorporation into the crystal need only be a small fraction of a percentage to significantly affect the resulting crystal. One Earth, concentration gradient driven flow will maintain a high interfacial concentration, i.e., a high level (essentially that of the bulk solution) of solute association at the interface and higher growth rate. Higher growth rates mean an increased probability that misaligned growth units are trapped by subsequent growth layers before they can be desorbed and try again, or that the desorbing species will be smaller than the adsorbing species. In microgravity the extended diffusive boundary layer will lower the interfacial concentration. This results in a net dissociation of aggregated species that diffuse in from the bulk solution, i.e., smaller associated species, which are more likely able to make multiple attempts to correctly bind, yielding higher quality crystals.

Pusey, Marc L.↗

NASA NTRS1993

Obliquity variation in a Mars climate evolution model

The existence of layered terrain in both polar regions of Mars is strong evidence supporting a cyclic variation in climate. It has been suggested that periods of net deposition have alternated with periods of net erosion in creating the layered structure that is seen today. The cause for this cyclic climatic behavior is variation in the annually averaged latitudinal distribution of solar insolation in response to obliquity cycles. For Mars, obliquity variation leads to major climatological excursion due to the condensation and sublimation of the major atmospheric constituent, CO2. The atmosphere will collapse into the polar caps, or existing caps will rapidly sublimate into the atmosphere, dependent upon the polar surface heat balance and the direction of the change in obliquity. It has been argued that variations in the obliquity of Mars cause substantial departures from the current climatological values of the surface pressure and the amount of CO2 stored in both the planetary regolith and polar caps. In this new work we have modified the Haberle et al. model to incorporate variable obliquity by allowing the polar and equatorial insolation to become functions of obliquity, which we assume to vary sinusoidally in time. As obliquity varies in the model, there can be discontinuities in the time evolution of the model equilibrium values for surface pressure, regolith, and polar cap storage. The time constant, tau r, for the regolith to find equilibrium with the climate is estimated--depending on the depth, thermal conductivity, and porosity of the regolith--between 10(exp 4) and 10(exp 6) yr. Thus, using 2000-yr timesteps to move smoothly through the 0.1250 m.y. obliquity cycles, we have an atmosphere/regolith system that cannot be assumed in equilibrium. We have dealt with this problem by limiting the rate at which CO2, can move between the atmosphere and regolith, mimicking the diffusive nature and effects of the temperature and pressure waves, by setting the time rate of change of regolith storage proportional to the difference between equilibrium storage and current storage.

Tyler, D.↗

NASA NTRS2010

An Attempt to Derive the epsilon Equation from a Two-Point Closure

The goal of this paper is to derive the equation for the turbulence dissipation rate epsilon for a shear-driven flow. In 1961, Davydov used a one-point closure model to derive the epsilon equation from first principles but the final result contained undetermined terms and thus lacked predictive power. Both in 1987 and in 2001, attempts were made to derive the epsilon equation from first principles using a two-point closure, but their methods relied on a phenomenological assumption. The standard practice has thus been to employ a heuristic form of the equation that contains three empirical ingredients: two constants, c(sub 1 epsilon), and c(sub 2 epsilon), and a diffusion term D(sub epsilon) In this work, a two-point closure is employed, yielding the following results: 1) the empirical constants get replaced by c(sub 1), c(sub 2), which are now functions of Kappa and epsilon; 2) c(sub 1) and c(sub 2) are not independent because a general relation between the two that are valid for any Kappa and epsilon are derived; 3) c(sub 1), c(sub 2) become constant with values close to the empirical values c(sub 1 epsilon), c(sub epsilon 2), (i.e., homogenous flows); and 4) the empirical form of the diffusion term D(sub epsilon) is no longer needed because it gets substituted by the Kappa-epsilon dependence of c(sub 1), c(sub 2), which plays the role of the diffusion, together with the diffusion of the turbulent kinetic energy D(sub Kappa), which now enters the new equation (i.e., inhomogeneous flows). Thus, the three empirical ingredients c(sub 1 epsilon), c(sub epsilon 2), D (sub epsilon)are replaced by a single function c(sub 1)(Kappa, epsilon ) or c(sub 2)(Kappa, epsilon ), plus a D(sub Kappa)term. Three tests of the new equation for epsilon are presented: one concerning channel flow and two concerning the shear-driven planetary boundary layer (PBL).

Canuto, V. M.↗

NASA NTRS2003

Modeling Candle Flame Behavior In Variable Gravity

The burning of a candle, as typical non-propagating diffusion flame, has been used by a number of researchers to study the effects of electric fields on flame, spontaneous flame oscillation and flickering phenomena, and flame extinction. In normal gravity, the heat released from combustion creates buoyant convection that draws oxygen into the flame. The strength of the buoyant flow depends on the gravitational level and it is expected that the flame shape, size and candle burning rate will vary with gravity. Experimentally, there exist studies of candle burning in enhanced gravity (i.e. higher than normal earth gravity, g(sub e)), and in microgravity in drop towers and space-based facilities. There are, however, no reported experimental data on candle burning in partial gravity (g < g(sub e)). In a previous numerical model of the candle flame, buoyant forces were neglected. The treatment of momentum equation was simplified using a potential flow approximation. Although the predicted flame characteristics agreed well with the experimental results, the model cannot be extended to cases with buoyant flows. In addition, because of the use of potential flow, no-slip boundary condition is not satisfied on the wick surface. So there is some uncertainty on the accuracy of the predicted flow field. In the present modeling effort, the full Navier-Stokes momentum equations with body force term is included. This enables us to study the effect of gravity on candle flames (with zero gravity as the limiting case). In addition, we consider radiation effects in more detail by solving the radiation transfer equation. In the previous study, flame radiation is treated as a simple loss term in the energy equation. Emphasis of the present model is on the gas-phase processes. Therefore, the detailed heat and mass transfer phenomena inside the porous wick are not treated. Instead, it is assumed that a thin layer of liquid fuel coated the entire wick surface during the burning process. This is the limiting case that the mass transfer process in the wick is much faster than the evaporation process at the wick surface.

Alsairafi, A.↗

NASA NTRS2000

A Collaborative Analysis Tool for Integrated Hypersonic Aerodynamics, Thermal Protection Systems, and RBCC Engine Performance for Single Stage to Orbit Vehicles

Presented is a computer-based tool that connects several disciplines that are needed in the complex and integrated design of high performance reusable single stage to orbit (SSTO) vehicles. Every system is linked to every other system, as is the case of SSTO vehicles with air breathing propulsion, which is currently being studied by NASA. An RBCC propulsion system integrates airbreathing and rocket propulsion into a single engine assembly enclosed within a cowl or duct. A typical RBCC propulsion system operates as a ducted rocket up to approximately Mach 3. Then there is a transition to a ramjet mode for supersonic-to-hypersonic acceleration. Around Mach 8 the engine transitions to a scramjet mode. During the ramjet and scramjet modes, the integral rockets operate as fuel injectors. Around Mach 10-12 (the actual value depends on vehicle and mission requirements), the inlet is physically closed and the engine transitions to an integral rocket mode for orbit insertion. A common feature of RBCC propelled vehicles is the high degree of integration between the propulsion system and airframe. At high speeds the vehicle forebody is fundamentally part of the engine inlet, providing a compression surface for air flowing into the engine. The compressed air is mixed with fuel and burned. The combusted mixture must be expanded to an area larger than the incoming stream to provide thrust. Since a conventional nozzle would be too large, the entire lower after body of the vehicle is used as an expansion surface. Because of the high external temperatures seen during atmospheric flight, the design of an airbreathing SSTO vehicle requires delicate tradeoffs between engine design, vehicle shape, and thermal protection system (TPS) sizing in order to produce an optimum system in terms of weight (and cost) and maximum performance. To adequately determine the performance of the engine/vehicle, the Hypersonic Flight Inlet Model (HYFIM) module was designed to interface with the RBCC engine model. HYFIM performs the aerodynamic analysis of forebodies and inlet characteristics of RBCC powered SSTO launch vehicles. HYFIM is applicable to the analysis of the ramjet/scramjet engine operations modes (Mach 3-12), and provides estimates of parameters such as air capture area, shock-on-lip Mach number, design Mach number, compression ratio, etc., based on a basic geometry routine for modeling axisymmetric cones, 2-D wedge geometries. HYFIM also estimates the variation of shock layer properties normal to the forebody surface. The thermal protection system (TPS) is directly linked to determination of the vehicle moldline and the shaping of the trajectory. Thermal protection systems to maintain the structural integrity of the vehicle must be able to mitigate the heat transfer to the structure and be lightweight. Herein lies the interdependency, in that as the vehicle's speed increases, the TPS requirements are increased. And as TPS masses increase the effect on the propulsion system and all other systems is compounded. The need to analyze vehicle forebody and engine inlet is critical to be able to design the RBCC vehicle. To adequately determine insulation masses for an RBCC vehicle, the hypersonic aerodynamic environment and aeroheating loads must be calculated and the TPS thicknesses must be calculated for the entire vehicle. To accomplish this an ascent or reentry trajectory is obtained using the computer code Program to Optimize Simulated Trajectories (POST). The trajectory is then used to calculate the convective heat rates on several locations on the vehicles using the Miniature Version of the JA70 Aerodynamic Heating Computer Program (MINIVER). Once the heat rates are defined for each body point on the vehicle, then insulation thicknesses that are required to maintain the vehicle within structural limits are calculated using Systems Improved Numerical Differencing Analyzer (SINDA) models. If the TPS masses are too heavy for the performance of the vehicle the process may be repeated altering the trajectory or some other input to reduce the TPS mass. E-PSURBCC is an "engine performance" model and requires the specification of inlet air static temperature and pressure as well as Mach number (which it pulls from the HYFIM and POST trajectory files), and calculates the corresponding stagnation properties. The engine air flow path geometry includes inlet, a constant area section where the rocket is positioned, a subsonic diffuser, a constant area afterburner, and either a converging nozzle or a converging-diverging nozzle. The current capabilities of E-PSURBCC ejector and ramjet mode treatment indicated that various complex flow phenomena including multiple choking and internal shocks can occur for combinations of geometry/flow conditions. For a given input deck defining geometry/flow conditions, the program first goes through a series of checks to establish whether the input parameters are sound in terms of a solution path. If the vehicle/engine performance fails mission goals, the engineer is able to collaboratively alter the vehicle moldline to change aerodynamics, or trajectory, or some other input to achieve orbit. The problem described is an example of the need for collaborative design and analysis. RECIPE is a cross-platform application capable of hosting a number of engineers and designers across the Internet for distributed and collaborative engineering environments. Such integrated system design environments allow for collaborative team design analysis for performing individual or reduced team studies. To facilitate the larger number of potential runs that may need to be made, RECIPE connects the computer codes that calculate the trajectory data, aerodynamic data based on vehicle geometry, heat rate data, TPS masses, and vehicle and engine performance, so that the output from each tool is easily transferred to the model input files that need it.

Stanley, Thomas Troy↗