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NASA NTRS2021

An Investigation of the Grain Size and Adhesion Strength of High-Speed Impact Ice

Ice accumulation on aircraft from supercooled water droplets (impact icing) can increase drag and decrease lift, leading to a decrease in fuel efficiency and a potential for unsafe situations. Anti-icing materials and coatings are of high interest to prevent aircraft icing. Because no anti-icing material suitable for in-flight situations has been realized, icing models aim to predict the accumulation and shape of the ice to understand its effects. In both cases, understanding the physical mechanism behind ice adhesion and shedding is necessary. A recent literature review has shown that the apparent ice adhesion strength to any specific material varies over several orders of magnitude across studies and test methods. One of the reasons for this high variance is likely to be the varying microstructure of the ice used for different studies. Although the microstructure of impact ice has been studied in the past, those conditions were not relevant to that of in-flight aircraft icing. The microstructure of the ice formed will determine both its bulk and surface properties, yet it has been overlooked in the ice adhesion community. Here, we use optical microscopy to study the non-uniform ice crystal grain size in impact ice accreted in NASA Glenn Research Center’s Icing Research Tunnel at various icing conditions. Similar to other environmental conditions studied in the literature, we show an increase in grain size at larger distances from the growth interface; however, the data shows substantially larger grains than what was expected from the prior literature. Ice accrued at lower temperatures has a smaller grain size at all distances from the growth interface. No change in grain size was noticed when varying only the wind speed. A correlational analysis shows that smaller grain sizes at the growth interface corresponded to an increase in the apparent ice adhesion strength when the adhesive failure was interfacial, but not when the failure was cohesive. These results may explain the overall trend in the literature of increasing apparent adhesion strength with decreasing temperature. Incorporating microstructure trends for various environmental conditions in icing models may increase the certainty in predicting ice adhesion strength and shedding, and will provide a better basis for comparison between adhesive tests on ice produced in different facilities and at different storage times.

• Ice Fabric↗

NASA NTRSDate not supplied

Expanding the Capability of A Legacy Combustion Flametube to Test High Temperature Engine Materials in Relevant Environments

New materials and component designs are needed to advance gas turbine engine technology and provide the performance and efficiency needs for future applications. In order to advance these materials, testing in combustion environments is a critical step prior to engine testing. In this work, we detail the design and the fabrication of a materials test sector in a flametube combustor facility. The facility simulates a combustion environment similar to that experienced by components in gas turbine engines. The flow regime is characterized by a combination of high-temperature, high-velocity, high-heat flux, and high-velocity that components experience in gas turbine engines. Exposure of components in this facility allows for the study of combined environmental effects and the impact on both coating and substrate durability. The test facility may operate across a wide range of pressures from 275-400 psig (1,896-2,758 kPa) and an air flow rate of 5 lb/s (2.27 kg/s). While combustion gas temperature is expected in excess of 3,000°F (1,649°C), 900°F (482°C) cooling air may be supplied to the backside of components or test articles. The flametube combustor was previously used to evaluate fuel injectors and combustion products, and the new test configuration will also allow for materials exposure to complex, engine-like conditions. The interior of the Test Section was additively manufactured from GRCop-84 and cryogenically fit and brazed to a stainless steel 304 housing. The use of a copper liner minimizes welds and with active cooling, is expected to provide better durability over traditional hardware using stainless steel or Inconel with a ceramic liner. The Test Section has two opposing removable windows approximately 230 mm x 80 mm that can accommodate articles up to 85 mm tall. This modular design allows for custom platforms to hold coupons, panels, or airfoil shapes to be tested with minimal re-engineering or fabrication. The bolted joint and sealing remains consistent, so any new testing only needs to work within the existing design footprint. This paper will provide an overview of the facility capabilities, design considerations, as well as thermal and structural analysis of the hardware. Future testing of ceramic matrix composite (CMC) airfoils and advanced environmental barrier coatings (EBCs) will also be discussed.

Combustion↗

NASA NTRS1976

Wind shear and turbulence around airports

A two part study was conducted to determine the feasibility of predicting the conditions under which wind/turbulence environments hazardous to aviation operations exist. The computer model used to solve the velocity temperature, and turbulence distributions in the atmospheric boundary layer is described, and the results of a parameteric analysis to determine the expected range of wind shear and turbulence to be encountered in the vicinity of airports are given. The second part describes the delineation of an ensemble of aircraft accidents in which low level wind shear and/or turbulence appeared to be causative factors. This set of accidents, encompassing a wide range of meteorological conditions, should prove useful in developing techniques for reconstructing hazardous wind environments for aircraft safety investigation purposes.

Lewellen, W. S.↗

NASA NTRS1993

Computational Fluid Dynamic (CFD) analysis of axisymmetric plume and base flow of film/dump cooled rocket nozzle

Film/dump cooling a rocket nozzle with fuel rich gas, as in the National Launch System (NLS) Space Transportation Main Engine (STME), adds potential complexities for integrating the engine with the vehicle. The chief concern is that once the film coolant is exhausted from the nozzle, conditions may exist during flight for the fuel-rich film gases to be recirculated to the vehicle base region. The result could be significantly higher base temperatures than would be expected from a regeneratively cooled nozzle. CFD analyses were conduced to augment classical scaling techniques for vehicle base environments. The FDNS code with finite rate chemistry was used to simulate a single, axisymmetric STME plume and the NLS base area. Parallel calculations were made of the Saturn V S-1 C/F1 plume base area flows. The objective was to characterize the plume/freestream shear layer for both vehicles as inputs for scaling the S-C/F1 flight data to NLS/STME conditions. The code was validated on high speed flows with relevant physics. This paper contains the calculations for the NLS/STME plume for the baseline nozzle and a modified nozzle. The modified nozzle was intended to reduce the fuel available for recirculation to the vehicle base region. Plumes for both nozzles were calculated at 10kFT and 50kFT.

Tucker, P. K.↗

NASA NTRS2012

Evaluation of Wall Boundary Conditions for Impedance Eduction Using a Dual-Source Method

The accuracy of the Ingard-Myers boundary condition and a recently proposed modified Ingard-Myers boundary condition is evaluated for use in impedance eduction under the assumption of uniform mean flow. The evaluation is performed at three centerline Mach numbers, using data acquired in a grazing flow impedance tube, using both upstream and downstream propagating sound sources, and on a database of test liners for which the expected behavior of the impedance spectra is known. The test liners are a hard-wall insert consisting of 12.6 mm thick aluminum, a linear liner without a facesheet consisting of a number of small diameter but long cylindrical channels embedded in a ceramic material, and two conventional nonlinear liners consisting of a perforated facesheet bonded to a honeycomb core. The study is restricted to a frequency range for which only plane waves are cut on in the hard-wall sections of the flow impedance tube. The metrics used to evaluate each boundary condition are 1) how well it educes the same impedance for upstream and downstream propagating sources, and 2) how well it predicts the expected behavior of the impedance spectra over the Mach number range. The primary conclusions of the study are that the same impedance is educed for upstream and downstream propagating sources except at the highest Mach number, that an effective impedance based on both the upstream and downstream measurements is more accurate than an impedance based on the upstream or downstream data alone, and that the Ingard-Myers boundary condition with an effective impedance produces results similar to that achieved with the modified Ingard-Myers boundary condition.

Watson, W. R.↗

NASA NTRS1995

Prediction of Wind Tunnel Effects on the Installed F/A-18A Inlet Flow Field at High Angles-of-attack

NASA Lewis is currently engaged in a research effort as a team member of the High Alpha Technology Program (HATP) within NASA. This program utilizes a specially equipped F/A-18A, the High Alpha Research Vehicle (HARV), in an ambitious effort to improve the maneuverability of high performance military aircraft at low subsonic speed, high angle of attack conditions. The overall objective of the Lewis effort is to develop inlet technology that will ensure efficient airflow delivery to the engine during these maneuvers. One part of the Lewis approach utilizes computational fluid dynamics codes to predict the installed performance of inlets for these highly maneuverable aircraft. Wind tunnel tests were a major component of the Lewis program. Since the available wind tunnel was small (9 x 15 ft) as compared to the scale of the model of the F/A-18A (19.78 percent), there were questions about the capability to obtain useful inlet performance data. The blockage effects were expected to be very large. This report represents the results of an analysis to determine how the wind tunnel walls effect inlet performance at several angles of attack. The predictions for the external particle traces along the fuselage indicate the influence of the wind tunnel side wall under the model is greater at 30 deg angle of attack than at 50 deg angle of attack on the under Leading Edge Extension (LEX) vortex trajectory. The side wall above the model appears to have negligible influence on the under LEX vortex. This may be due to the LEX acting as 'shield' to the upper wall effects. As expected, the wind tunnel has a significant influence on the external forces. The lift and drag coefficients increase significantly for the wind tunnel model as compared to free stream conditions. The wind tunnel had a small effect on the inlet recovery and on inlet total pressure distortion patterns. The predicted recoveries for the wind tunnel model are within one percentage point of the model recoveries in free stream conditions.

Smith, Crawford F.↗

NASA NTRS1981

Results to be expected from light scattering dust analyzer during a rendezvous mission

The light scattering principle for particle detection is customary for the measurement of aerosols. Light scattering techniques can be applied to mixtures of particles (nephelometers) and to single particles as well. Measuring particle mixtures simplify detection because of the higher intensity level, however, information concerning the individual particle is lost. To provide well defined conditions over the whole rendezvous period, i.e., constant illumination beam and unchangeable scattering angle, the use of an artificial light source (instead of the sun) and a scattering volume located within the S/C is desirable. Considering this and the relatively low particle densities to be expected, the measurement of particle mixtures must be excluded.

Zerull, R. H.↗

NASA NTRS1995

Interplanetary magnetic field control of mantle precipitation and associated field-aligned currents

Dayside reconnection, which is particularly effective for a southward interplanetary magnetic field (IMF), allows magnetosheath particles to enter the magnetosphere where they form the plasma mantle. The motions of the reconnected flux tube produce convective flows in the ionosphere. It is known that the convection patterns in the polar cap are skewed to the dawnside for a positive IMF B(sub y) (or duskside for a negative IMF B(sub y)) in the northern polar cap. Correspondingly, one would expect to find asymmetric distributions of mantle particle precipitation, but previous results have been unclear. In this paper the correlation between B(sub y) and the distribution of mantle particle precipitation is studied for steady IMF conditions with southward IMF. Ion and electron data from the Defense Meteorological Satellite Program (DMSP) F6 and F7 satellites are used to identify the mantle region and IMP 8 is used as a solar wind monitor to characterize the IMF. We study the local time extension of mantle precipitation in the prenoon and postnoon regions. We find that, in accordance with theoretical expectations for a positive (negative) IMF B(sub y), mantle particle precipitation mainly appears in the prenoon region of the northern (southern) hemisphere. The mantle particle precipitation can extend to as early as 0600 magnetic local time (MLT) in the prenoon region but extends over a smaller local time region in the postnoon sector (we did not find mantle plasma beyond 1600 MLT in our data set although coverage is scant in this area). Magnetometer data from F7 are used to determine whether part of the region 1 current flows on open field lines. We find that at times part of the region 1 sense current extends into the region of mantle particle precipitation, and is therefore on open field lines. In other cases, region 1 currents are absent on open field lines. Most of the observed features can be readily interpreted in terms of the open magnetosphere model.

Xu, Dingan↗

NASA NTRS2012

Spacesuit Portable Life Support System Breadboard (PLSS 1.0) Development and Test Results

A multi-year effort has been carried out at the Johnson Space Center to develop an advanced EVA PLSS design intended to further the current state of the art by increasing operational flexibility, reducing consumables, and increasing robustness. This multi-year effort has culminated in the construction and operation of PLSS 1.0, a test rig that simulates full functionality of the advanced PLSS design. PLSS 1.0 integrates commercial off-the-shelf hardware with prototype technology development components, including the primary and secondary oxygen regulators, ventilation loop fan, Rapid Cycle Amine (RCA) swingbed, and Spacesuit Water Membrane Evaporator (SWME). PLSS 1.0 was tested from June 17th through September 30th, 2011. Testing accumulated 233 hours over 45 days, while executing 119 test points. An additional 164 hours of operational time were accrued during the test series, bringing the total operational time for PLSS 1.0 testing to 397 hours. Specific PLSS 1.0 test objectives assessed during this testing include: (1) Confirming prototype components perform in a system level test as they have performed during component level testing, (2) Identifying unexpected system-level interactions (3) Operating PLSS 1.0 in nominal steady-state EVA modes to baseline subsystem performance with respect to metabolic rate, ventilation loop pressure and flow rate, and environmental conditions (4) Simulating nominal transient EVA operational scenarios (5) Simulating contingency EVA operational scenarios (6) Further evaluating prototype technology development components Successful testing of the PLSS 1.0 provided a large database of test results that characterize system level and component performance. With the exception of several minor anomalies, the PLSS 1.0 test rig performed as expected. Documented anomalies and observations include: (1) Ventilation loop fan controller issues at high fan speeds (near 70,000 rpm, whereas the fan speed during nominal operations would be closer to 35,000 rpm) (2) RCA performance at boundary conditions, including carbon dioxide and water vapor saturation events, as well as reduced vacuum quality (3) SWME valve anomalies (4 documented cases where the SWME failed to respond to a control signal or physically jammed, preventing SWME control) (4) Reduction of SWME hollow fiber hydrophobicity and significant reduction of the SWME degassing capability after significant accumulated test time.

Watts, Carly A.↗

NASA NTRS1989

Reddening and extinction towards H II regions

The light emitted by the gas in H II regions is attenuated by dust. This extinction can be measured by comparing H alpha, H beta, and radio continuum fluxes, since the intrinsic ratios of the Balmer line and thermal radio continuum emissivities are nearly constant for reasonable conditions in H II regions. In the case of giant extragalactic H II regions, the extinction was found to be considerably greater than expected. The dust between the Earth and the emitting gas may have an optical thickness which varies. The dust may be close enough to the source that scattered light contributes to the flux, or the dust may be actually mixed with the emitting gas. It is difficult to decide which configuration is correct. A rediscussion of this question in light of recent observations, with the Fabry-Perot spectrophotometers, of the large Galactic H II region is presented. The color excesses are compared for stars embedded in these H II regions with those derived (assuming the standard law) from the nebular extinction and reddening.

Caplan, James↗

NASA NTRS1991

Numerical propulsion system simulation

The cost of implementing new technology in aerospace propulsion systems is becoming prohibitively expensive. One of the major contributors to the high cost is the need to perform many large scale system tests. Extensive testing is used to capture the complex interactions among the multiple disciplines and the multiple components inherent in complex systems. The objective of the Numerical Propulsion System Simulation (NPSS) is to provide insight into these complex interactions through computational simulations. This will allow for comprehensive evaluation of new concepts early in the design phase before a commitment to hardware is made. It will also allow for rapid assessment of field-related problems, particularly in cases where operational problems were encountered during conditions that would be difficult to simulate experimentally. The tremendous progress taking place in computational engineering and the rapid increase in computing power expected through parallel processing make this concept feasible within the near future. However it is critical that the framework for such simulations be put in place now to serve as a focal point for the continued developments in computational engineering and computing hardware and software. The NPSS concept which is described below will provide that framework.

R.W. Claus↗

NASA NTRS1991

Cometary apparitions - 1990-2010

Osculating orbital elements are listed (chronologically by perihelion passage time) for all periodic comets expected to arrive at perihelion during the 1990-2010 interval. Plots which make it possible to readily determine the earth-based viewing conditions of a particular cometary apparition are presented. These plots are drawn in a rotating coordinate system so that the sun-earth line is fixed for each apparition.

Yeomans, Donald K.↗

NASA NTRS1990

Numerical propulsion system simulation

Lytle, John K.↗

NASA NTRS1995

Thrust measurement in a 2-D scramjet nozzle

The two-dimensional thrust nozzle presents a challenging problem. The loading is not axisymmetric as in the case of a cone and the internal flow presents some design difficulties. A two-sting system has been chosen to accomodate the internal flow and achieve some symmetry. The situation is complicated by the fact that with the small ramp angle and the internal pressure on the nozzle walls, loading is predominantly transverse. Yet it is the axial thrust which is to be measured (i.e., the tensile waves propagating in the stings). Although bending stress waves travel at most at only 60% of the speed of the axial stress waves, the system needs to be stiffened against bending. The second sting was originally only used to preserve symmetry. However, the pressures on each thrust surface may be quite different at some conditions, so at this stage the signals from both stings are being averaged as a first order approximation of the net thrust. The expected axial thrust from this nozzle is not large so thin stings are required. In addition, the contact area between nozzle and sting needs to be maximized. The result was that it was decided to twist the stings through 90 deg, without distorting their cross-sectional shape, just aft of the nozzle. Finite element analysis showed that this would not significantly alter the propagation of the axial stress wave in the sting, while the rigidity of the system is greatly increased. A Mach 4 contoured nozzle is used in the experiments. The thrust calculated by integrating the static pressure measurements on the thrust surfaces is compared with the deconvolved strain measurement of the net thrust for the cases of air only and hydrogen fuel injected into air at approximately 9 MJ/kg nozzle supply enthalpy. The gain in thrust due to combustion is visible in this result.

Tuttle, Sean↗

NASA NTRS1994

Interplanetary magnetic field dependency of stable Sun-aligned polar cap arcs

This is the first analysis, using a statistically significant data set, of the morphological dependence of the presence, orientation, and motion of stable sun-aligned polar cap arcs upon the vector interplanetary magnetic field (IMF). For the one winter season analyzed we had 1392 all-sky 630.0-nm images of 2-min resolution containing a total of 150 polar cap arcs, all with corresponding values of the IMF as measured by International Monitoring Platform (IMP) 8 or International Sun Earth Explorer (ISEE) 2. After demonstrating an unbiased data set with smooth normal distributions of events versus the dimensions of time, space, and IMF component, we examine IMF dependencies of the properties of the optical arcs. A well-defined dependence for B(sub z) is found for the presence/absence of stable Sun-aligned polar cap arcs. Consistent with previous statistical studies, the probability of observing polar cap aurora steadily increases for larger positive values of B(sub z), and linearly decreases when B(sub z) becomes more negative. The probability of observing Sun-aligned arcs within the polar cap is determined to vary sharply as a function of the arc location; arcs were observed 40% of the time on the dawnside and only 10% on the duskside. This implies an overall probability of at least 40% for the whole polar cap. 20% of the arcs were observed during 'southward IMF conditions,' but in fact under closer inspection were found to have been formed under northward IMF conditions; these 'residual' positive B(sub z) arcs ha d a delayed residence time in the polar cap of about what would be expected after a north to south transition of B(sub z). A firm dependence on B(sub y) is also found for both the orientation and the dawn-dusk direction of motion of the arcs. All the arcs are Sun-aligned to a first approximation, but present deviations from this orientation, depending primarily upon the location of the arc in corrected geomagnetic (CG) coordinates. The arcs populating the 06-12 and the 12-18 quadrants of the CG coordinate system point toward the cusp. The B(sub y) dependency of the arc alignment is consistent with a cusp displacement in local time according to the sign of B(sub y). We found that the arc direction of motion depended both on B(sub y) and the arc location within the polar cap. For a given value of B(sub y) two well-defined regions (or cells) exist. Within each cell the arcs move in the same direction toward the boundary between the cells. The arcs located in the duskside move dawnward; those in the dawnside move duskward. The relative size of these dusk and dawn regions (or cells) are controlled by the magnitude of B(sub y). This persistent dusk-dawn motion fo the polar cap arcs is interpreted in terms of newly open flux tubes entering the polar cap and exerting a displacement of the convective cells and the polar cap arcs that are embedded within them.

Valladares, C. E.↗

NASA NTRS1994

ECMWF and SSM/I global surface wind speeds

Monthly mean 2.5 deg x 2.5 deg resolution 10-m height wind speeds from the Special Sensor Microwave/Imager (SSM/I) instrument and the European Centre for Medium-Range Weather Forecasts (ECMWF) forecast-analysis system are compared between 60 deg S and 60 deg N during 1988-91. The SSM/I data were uniformly processed while numerous changes were made to the ECMWF forecast-analysis system. The SSM/I measurements, which were compared with moored-buoy wind observations, were used as a reference dataset to evaluate the influence of the changes made to the ECMWF system upon the ECMWF surface wind speed over the ocean. A demonstrable yearly decrease of the difference between SSM/I and ECMWF wind speeds occurred in the 10 deg S-10 deg N region, including the 5 deg S-5 deg N zone of the Pacific Ocean, where nearly all of the variations occurred in the 160 deg E-160 deg W region. The apparent improvement of the ECMWF wind speed occurred at the same time as the yearly decrease of the equatorial Pacific SSM/I wind speed, which was associated with the natural transition from La Nina to El Nino conditions. In the 10 deg S-10 deg N tropical Atlantic, the ECMWF wind speed had a 4-yr trend, which was not expected nor was it duplicated with the SSM/I data. No yearly trend was found in the difference between SSM/I and ECMWF surface wind speeds in middle latitudes of the Northern and Southern Hemispheres. The magnitude of the differences between SSM/I and ECMWF was 0.4 m/s or 100% larger in the Northern than in the Southern Hemisphere extratropics. In two areas (Arabian Sea and North Atlantic Ocean) where ECMWF and SSM/I wind speeds were compared to ship measurements, the ship data had much better agreement with the ECMWF analyses compared to SSM/I data. In the 10 deg S-10 deg N area the difference between monthly standard deviations of the daily wind speeds dropped significantly from 1988 to 1989 but remained constant at about 30% for the remaining years.

Halpern, David↗

NASA NTRS1993

Does the ballooning instability trigger substorms in the near-Earth magnetotail?

The stability of the near-Earth magnetotail against ballooning (or configurational) instability is examined in the framework of the MHD approximation. It is emphasized that a change in plasma pressure induced by a meriodional electric field drift delta u(sub n) is an important factor that determines the stability. We have to consider two ways in which plasma pressure changes, that is, a convective change -delta u(sub n) grad(P(sub 0)), where P(sub 0) is background plasma pressure, and plasma expansion/compression -P(sub 0) dive (delta u(sub n)). Since delta u(sub n) is perpendicular to the magnetic field and its magnitude is inversely proportional to the magnetic field strength, delta u(sub n) diverges/converges in usual tail magnetic field configurations. For the instability, the convective change must overwhelm the effects of the plasma expansion/compression. However, near the equator in the near-Earth tail, the latter may overcompensate for the former. We describe the ballooning instability in terms of a coupling between the Alfven and slow magnetosonic waves in an inhomogeneous plasma and derive instability conditions. The result shows that the excessive curvature stabilizes, rather than destabilizes, perturbations. It is also found that the field-aligned flow stabilizes perturbations, as well as the field-aligned current. We infer that under quiet conditions, the plasma pressure gradient in the near-Earth tail is not sharp enough to trigger the instability. The plasma sheet is expected to become more stable during the substorm growth phase because of an increase in the field line curvature associated with the plasma sheet thinning. In the region closer to the Earth, including the ring current, the plasma pressure gradient may be localized in a limited range of the radial distance during the growth phase. However, recently reported plasma and magnetic field parameters before substorm onsets do not provide very convincing evidence that the ballooning instability is the triggering mechanism of substorms.

Ohtani, Shin-Ichi↗

NASA NTRS1998

Elemental Fractionation During Rapid Accretion of the Moon Triggered by a Giant Impact

Recently, Ida et al. made an N-body simulation of lunar accretion from a protolunar disk formed by a giant impact. One of their important conclusions is that the accretion time of the Moon is as short as one month. Such rapid accretion is a necessary consequence of the high surface density of a lunar mass disk accreting just beyond the Roche limit (about 3Re); the Safronov accretion time (a few days) is even shorter. The energy of accretion always exceeds the gravitational binding energy of newly arriving matter. Hence, without an energy sink, the accreting body is thermally unstable. For the Earth and other planets, radiation acts as the sink. However, in such a short accretion time, the Moon cannot radiate the accretional energy. Even radiating at a silicate cloudtop temperature of roughly 2000 K, it would take more than 100 yr to radiatively cool the Moon. The plausible alternative heat sinks are heat capacity, latent heat of vaporization, and thermal escape of the gas to space (i.e., hydrodynamic blowoff). The latter becomes plausible for the Moon because the scale height at 2000 K (about 300 km) is a significant fraction of the lunar radius. The early stages of lunar (or "lunatesimal") growth release relatively little energy and can occur simply by heating the material, especially if the accreting material is originally cold. However, the material is unlikely to be cold, because the disk itself is hot and cooling time is long, while the lunar accretion time iss very short. Therefore, the moon is likely to accrete condensed material just after it condenses. Accordingly, the newly accreted material will be on the verge of vaporization and will have very little heat capacity to spare. The immediate heat sink is the latent heat of vaporization. Most of the vapor will escape from the moon, because the thermal energy in the gas can be used to drive escape. However, vaporization is generally incomplete. the latent heat of vaporization exceeds the energy of accretion. Viewed globally, the accretional energy is about half the energy required to vaporize the entire Moon. Thus to first approximation, half of the Moon-forming material can be vaporized and lost during accretion. During this process, we would expect preferential loss of relatively volatile elements. Escape will retard the rate of accretion. To test these ideas, we computed detailed models of the thermal state of the Moon during accretion. We pay special attention to the structure of the silicate atmosphere and its loss rate by calculating the chemical species at equilibrium. We used the PHEQ program which includes 12 elements (H,O,C,Mg,Si,Fe,Ca, Al, Na,Ti, and N.) and 272 compounds (including ionic compounds). Because of the large heats of vaporization and ionization, the adiabatic atmosphere is nearly isothermal and massive escape is expected. The pressure of the atmosphere is determined by the balance between vaporization of a accreting material and escape. If the accretion time is one month, a 0.3 bar atmosphere is expected. Elemental fractionation depends strongly on the temperature of the accreting material. The initial temperature of the material can be estimated from the condition of gravitational instability in the protolunar disk. As shown by Ida et al, accretion starts when gravitational instability occurs when more than 99% of the material condenses. At this point, all of Ca, Al, Si, Mg, and Fe, and 95% of Na (probably K also), are in condensed phases. If the moon is formed from the accretion of such material, volatile elements such as Na, and K are retained by the moon only early in accretion. At later times, K and Na are lost and a fraction of the MG, Si and Fe is lost. However, refractory elements such as Ca and Al are retained and so achieve a mild degree (factor 2) of superabundance.

Abe, Y.↗