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NASA NTRS2009

Use of Raman Spectroscopy and Delta Volume Growth from Void Collapse to Assess Overwrap Stress Gradients Compromising the Reliability of Large Kevlar/Epoxy COPVs

Composite Overwrapped Pressure Vessels (COPVs) are frequently used for storing pressurized gases aboard spacecraft and aircraft when weight saving is desirable compared to all-metal versions. Failure mechanisms in fibrous COPVs and variability in lifetime can be very different from their metallic counterparts; in the former, catastrophic stress-rupture can occur with virtually no warning, whereas in latter, a leak before burst design philosophy can be implemented. Qualification and certification typically requires only one burst test on a production sample (possibly after several pressure cycles) and the vessel need only meet a design burst strength (the maximum operating pressure divided by a knockdown factor). Typically there is no requirement to assess variability in burst strength or lifetime, much less determine production and materials processing parameters important to control of such variability. Characterizing such variability and its source is crucial to models for calculating required reliability over a given lifetime (e.g. R = 0.9999 for 15 years). In this paper we present a case study of how lack of control of certain process parameters in COPV manufacturing can result in variations among vessels and between production runs that can greatly increase uncertainty and reduce reliability. The vessels considered are 40-inch ( NASA Glenn Research center, Cleveland, OH, 44135 29,500 in3 ) spherical COPVs with a 0.74 in. thick Kevlar49/epoxy overwrap and with a titanium liner of which 34 were originally produced. Two burst tests were eventually performed that unexpectedly differed by almost 5%, and were 10% lower than anticipated from burst tests on 26-inch sister vessels similar in every detail. A major observation from measurements made during proof testing (autofrettage) of the 40-inch vessels was that permanent volume growth from liner yielding varied by a factor of more than two (150 in3 to 360 in3 ), which suggests large differences in the residual stress gradient through their overwraps. This resulted in large uncertainty in true fiber stress ratio (fiber stress at operating pressure divided by fiber stress at burst) which governs lifetime. The vessels were originally designed with tight safety margins, so it became crucial to develop a non-destructive evaluation (NDE) technique to directly measure the overwrap residual stress state of each vessel, and to identify those vessels at highest risk of having poor reliability. This paper describes a Raman Spectroscopy technique for measuring certain patterns of fluctuation in fiber elastic strains over the outside vessel surface (where all but one wrap is exposed at certain locations) that are shown to directly correlate to increased fiber stress ratios and reduced reliability.

Kezirian, Michael T.↗

NASA NTRS2018

Conductivity of a Copper-Carbon Covetic Composite

NASA is currently engaged in the development of highly electrically conductive wire for space and aviation power and propulsion applications. Higher levels of electrical conductivity and lower densities compared to copper and aluminum are needed to improve the efficiency of commercial aviation and space flight. Carbon, in various forms, is being considered as a component in composites to increase conductivity and decrease density in Cu and Al. One form of carbon that is currently receiving much interest is known as covectic. The technology currently known as covetics was first introduced by Shugart and Scherer whose patents claimed "Carbon can be incorporated into any of these metals by melting the metal, mixing the carbon into the molten metal and, while mixing, applying a current of sufficient amperage to the molten mixture such that the carbon becomes incorporated into the metal, thereby forming a single phase metal-carbon material." It is reported that in this process a conversion reaction occurs with the carbon forming covalent bonds with the host metal, and that covetic processing enables higher carbon solubility and improvements in properties. Although there is a growing body of work supporting covetic materials, it is still a very new and somewhat controversial field. Composition, density, and electrical conductivity measurements of a covetically processed alloy ingot of Cu and C, with a nominal composition of Cu-0.4wt.% C, were made. A pure Cu ingot was similarly processed for comparison. Sections of these ingots were worked into wire and tested. Only small amounts of C could be detected in the Cu-0.4wt.% C ingot, and trace amounts (0.006 wt.%) in the wire. All wires had densities very close to the full density of pure Cu, indicating a high level of Cu purity and low void fraction. Finally, the electrical conductivity of the Cu-0.4wt.% C wires were 9% lower than the samples similarly processed but without C additions. The wires made without C additions had conductivities approximately equal to pure Cu. The low conductivity of the Cu-0.4wt.% C material is believed to be due to: (1) a structure of interfaces in the wire created by collapsed voids lined with elemental C, (2) impurities, such as Fe in the Cu, which came from the added C, and (3) a small volume fraction of voids.

Degroh, Henry C.↗

NASA NTRS2017

An Efficient Modelling Approach for Prediction of Porosity Severity in Composite Structures

Porosity, as a manufacturing process-induced defect, highly affects the mechanical properties of cured composites. Multiple phenomena affect the formation of porosity during the cure process. Porosity sources include entrapped air, volatiles and off-gassing as well as bag and tool leaks. Porosity sinks are the mechanisms that contribute to reducing porosity, including gas transport, void shrinkage and collapse as well as resin flow into void space. Despite the significant progress in porosity research, the fundamentals of porosity in composites are not yet fully understood. The highly coupled multi-physics and multi-scale nature of porosity make it a complicated problem to predict. Experimental evidence shows that resin pressure history throughout the cure cycle plays an important role in the porosity of the cured part. Maintaining high resin pressure results in void shrinkage and collapse keeps volatiles in solution thus preventing off-gassing and bubble formation. This study summarizes the latest development of an efficient FE modeling framework to simulate the gas and resin transport mechanisms that are among the major phenomena contributing to porosity.

Bedayat, Houman↗

NASA NTRS1972

Numerical calculation of the lunar wake in a magnetohydrodynamic model.

Following previous interpretation, a model is developed which has the solar wind flowing directly into the lunar surface and the magnetic field passing unimpeded through the moon. The collapse of the plasma void behind the moon is calculated numerically using the equations of magnetohydrodynamics. The model is three-dimensional, allowing complete calculations to be made without special restrictions on the magnetic field direction. A cursory quantitative comparison with data shows agreement to be satisfactory. The calculations indicate that the rate of collapse of the void does not depend strongly on the solar wind-magnetic field angle. The penumbral decrease depends very strongly on both the solar wind-magnetic field angle and the angle of passage through the wake.

Beers, B. L.↗

NASA NTRS2019

The Mutual Orbit, Mass, and Density of Transneptunian Binary Gǃkúnǁ’hòmdímà (229762 2007 UK126)

We present high spatial resolution images of the binary transneptunian object Gǃkúnǁ'hòmdímà (229762 2007 UK126) obtained with the Hubble Space Telescope and with the Keck observatory on Mauna Kea to determine the orbit of Gǃò'é ǃhúGǃò'é ǃhú, the much smaller and redder satellite. Gǃò'é ǃhú orbits in a prograde sense, on a circular or near-circular orbit with a period of 11.3 days and a semimajor axis of 6000 km. Tidal evolution is expected to be slow, so it is likely that the system formed already in a low-eccentricity configuration, and possibly also with the orbit plane of the satellite in or close to the plane of Gǃkúnǁ'hòmdímà's equator. From the orbital parameters we can compute the system mass to be 1.4 × 10(exp 20) kg. Combined with estimates of the size of Gǃkúnǁ'hòmdímà from thermal observations and stellar occultations, we can estimate the bulk density as about 1 g cm(exp −3). This low density is indicative of an ice-rich composition, unless there is substantial internal porosity. We consider the hypothesis that the composition is not unusually ice-rich compared with larger TNOs and comet nuclei, and instead the porosity is high, suggesting that mid-sized objects in the 400 to 1000 km diameter range mark the transition between small, porous objects and larger objects that have collapsed their internal void space as a result of their much higher internal pressures and temperatures.

W. M. Grundy↗

NASA NTRS2019

The Mutual Orbit, Mass, and Density of Transneptunian Binary Gǃkúnǁ'hòmdímà (229762 2007 UK126)

We present high spatial resolution images of the binary transneptunian object Gǃkúnǁ'hòmdímà (229762 2007 UK126) obtained with the Hubble Space Telescope and with the Keck observatory on Mauna Kea to determine the orbit of Gǃò'é ǃhúGǃò'é ǃhú, the much smaller and redder satellite. Gǃò'é ǃhú orbits in a prograde sense, on a circular or near-circular orbit with a period of 11.3 days and a semimajor axis of 6000 km. Tidal evolution is expected to be slow, so it is likely that the system formed already in a low-eccentricity configuration, and possibly also with the orbit plane of the satellite in or close to the plane of Gǃkúnǁ'hòmdímà's equator. From the orbital parameters we can compute the system mass to be 1.4 × 1020 kg. Combined with estimates of the size of Gǃkúnǁ'hòmdímà from thermal observations and stellar occultations, we can estimate the bulk density as about 1 g cm−3. This low density is indicative of an ice-rich composition, unless there is substantial internal porosity. We consider the hypothesis that the composition is not unusually ice-rich compared with larger TNOs and comet nuclei, and instead the porosity is high, suggesting that mid-sized objects in the 400 to 1000 km diameter range mark the transition between small, porous objects and larger objects that have collapsed their internal void space as a result of their much higher internal pressures and temperatures.

W M Grundy↗

NASA NTRS1999

MRI Measurements and Granular Dynamics Simulation of Segregation of Granular Mixture

A counter intuitive axial segregation phenomenon in a rotating horizontal cylinder has recently captured attention of many researchers in different disciplines. There is a growing consensus that the interplay between the particle dynamics and the evolution of the internal structure during the segregation process must be carefully investigated. Magnetic resonance imaging (MRI) has been used to non-invasively obtain much needed dynamic/static information such as velocity and concentration profiles, and it has proven to be capable of depicting the evolution of segregation processes. Segregation in a rotating cylinder involves two processes: the first is to transport small particles in the radial direction to form a radial core, and the second is to transform the radial core into axially segregated bands. Percolation and/or "stopping" have been proposed as mechanisms for the radial segregation. As to mechanisms for axial band formation, much less is known. The difference in the dynamic angle of repose has been proposed to segregate different components in the axial direction. Recently, Hill and Kakalios have reported that particles mix or demix depending upon the competition between diffusion and preferential drift whose order can be determined by the dynamic angle of repose through the adjustment of the rotation rate. We claim that the dynamic angle of repose could be one of the causes, however, it fails to offer reasonable explanations for certain aspects of the axial migration. For example, we always observe that the radial segregation precedes the axial segregation and small particles migrate in the radial direction to form an axially extended radial core. It then transforms into axially segregated bands. By definition, the effects of the dynamic angle of repose are restricted near the free surface where the flowing layer is present. However, during the process of transforming from the radially segregated core to axially segregated bands, small particles located in the deep core region, which is untouched by the flowing layer, also completely disappear. Usually, the dynamics angle of repose are uniquely defined for individual species to characterize particle properties, and the dynamic angle of repose thus defined provides little information for the dynamic angle of repose of the mixture since the concentration ratio and the internal packing structure do not remain the same during the segregation processes. Under microgravity environment, the dynamics angle of repose argument does not hold since there is simply no flowing layer to influence/determine the preferred directions of segregation. We have thus designed an experiment so that the effects of the dynamic angle of repose can be minimized by filling the cylinder almost completely full. Small particles still formed a radial core and also migrated to form axial bands. As ground based experiments we have designed and conducted both 2D and 3D segregation experiments. The 2D experiments are performed using a thin cylinder (the gap between two end caps is about 5 mm) filled with different combinations of particles. The 3D experiments are conducted with a long cylinder of its length and diameter of 27cm and 7cm, respectively. Results of 2D experiments indicate that different mechanisms govern particle motion in regions near and far from the axis of rotation. Results of 3D experiments indicate that a series of collapses of microstructures of particle packing (micro-collapses) may be responsible for the creation of voids for small particles to migrate through in the axial direction. We have successfully eliminated the dynamic angle of repose as a cause for segregation, however, by almost completely filling the cylinder with the particles, we have lost an opportunity to investigate a possibility of particle "mobility" being a cause for segregation which requires a flowing surface but not the difference in the angle of repose. This is currently being investigated.

Nakagawa, M.↗

NASA NTRS1993

A cosmological hydrodynamic code based on the total variation diminishing scheme

An explicitly second-order finite difference code based on a total variation diminishing scheme for self-gravitating cosmological hydrodynamic systems is described. The code was developed to follow correctly the adiabatic changes of extremely supersonic preshock flows with a Mach number larger than 100 as well as very strong shocks. In calculations of the formation of a 1D Zel'dovich pancake, an energy accuracy of 1 percent is obtained for 32 cells per unit wavelength, and the accuracy reaches 0.01 percent as the number of cells approach 1024. It is shown that shocks are well resolved and separate cleanly the hot, dense, collapsed peaks from the cold, low-density, expanding voids.

Ryu, Dongsu↗

NASA NTRS1990

Hierarchical fragmentation model for the evolution of self-gravitating clouds

A hierarchical model for the fragmentation of cold, self-gravitating gas clouds is developed, and the model is applied to the collapse of matter accumulated at the boundaries of large-scale voids in the universe. In this model, the mass function for fragment sizes and the correlation function for fragment positions are naturally related. Using this relationship, the mass function for galaxies is derived from the observed galaxy-galaxy two-point correlation function. Assuming that galaxy masses and luminosities are proportional to one another, the derived luminosity function agrees with the empirical Schecter function at low luminosity. It is argued that the correlation function itself may be a natural outcome of large-scale gravitational instability at each stage of the hierarchy.

Newman, William I.↗

NASA NTRS1986

Evolution of the intergalactic medium - What happened during the epoch z = 3-10?

An attempt is made to model consistently the thermal and dynamic history of the intergalactic medium (IGM) from the era of reheating (z = 10-5) to the present, and to provide a unified explanation for the origin of ordinary galaxies, blue compact objects, and Lyman-alpha clouds. The evolution of the intergalactic gas is analyzed, treating the IGM as perfectly homogeneous at every epoch and taking into account radiative and Compton cooling, adiabatic cooling, shock heating, and heating produced by the diffuse UV flux. It is suggested that the IGM must have been heated to higher than a 10 to the 6th K by shock heasting caused either by explosions of pregalactic objects or expanding voids. The formation of intergalactic clouds by fragmentation of the resulting shells and the subsequent collapse of the shells to form galaxies are studied. An attempt is made to determine model parameters on the basis of an analysis of Lyman-alpha absorption lines.

Ikeuchi, S.↗

NASA NTRS1949

Report on Investigation of Developed Turbulence

The recent experiments by Jakob and Erk, on the resistance of flowing water in smooth pipes, which are in good agreement with earlier measurements by Stenton and Pannell, have caused me to change my opinion that the empirical Blasius law (resistance proportional to the 7/4 power of the mean velocity) was applicable up to arbitrarily high Reynolds numbers. According to the new tests the exponent approaches 2 with increasing Reynolds number, where it remains an open question whether or not a specific finite limiting value of the resistance factor lambda is obtained at R = infinity. With the collapse of Blasius' law the requirements which produced the relation that the velocity in the proximity of the wall varied in proportion to the 7th root of the wall distance must also become void. However, it is found that the fundamental assumption that led to this relationship can be generalized so as to furnish a velocity distribution for any empirical resistance law. These fundamental assumptions can be so expressed that for the law of velocity distribution in proximity of the wall as well as for that of friction at the wall, a form can be found in which the pipe diameter no longer occurs, or in other words, that the processes in proximity of a wall are not dependent upon the distance of the opposite wall.

Prandtl, L.↗

NASA NTRS1973

The Computerized Anatomical Man (CAM) model

A computerized anatomical man (CAM) model, representing the most detailed and anatomically correct geometrical model of the human body yet prepared, has been developed for use in analyzing radiation dose distribution in man. This model of a 50-percentile standing USAF man comprises some 1100 unique geometric surfaces and some 2450 solid regions. Internal body geometry such as organs, voids, bones, and bone marrow are explicitly modeled. A computer program called CAMERA has also been developed for performing analyses with the model. Such analyses include tracing rays through the CAM geometry, placing results on magnetic tape in various forms, collapsing areal density data from ray tracing information to areal density distributions, preparing cross section views, etc. Numerous computer drawn cross sections through the CAM model are presented.

Billings, M. P.↗

NASA NTRS1998

Deep Basalt Aquifers in Orcus Patera, Elysium Basin Mars: Perspectives for Exobiology Exploration

Direct indicators of shorelines, spillways, and terraces allowed to determine the extent of the Elysium Paleolake between the contour-lines 1000 and 500 m below the Martian datum. The Elysium Paleolake is bordered north by Orcus Patera (14N/181W), which lies west of the Tartarus Montes and Tartarus Colles. The Orcus Patera displays an ellipse-shaped collapsed caldera of 360-km long and 100-km wide. Viking topographic data show that the bottom of the caldera is located at 2500 below the Martian datum, and surrounded by a steep-walled ram art which crest is located at about 0 m elevation. Considering the localization of Orcus Patera in the Elysium paleolake, its altimetry, and the magmatic origin of this caldera, we propose the existence of a paleolake in Orcus Patera generated (a) by juvenile water from magma during the Noachian period, and (b) by intermittent influx of the Elysium Basin from Hesperian to Amazonian. Results are encouraging to consider this site as a potential high-energy source environment for microbial communities. are circumscribed by a 50-km wide lava field mapped as Noachian material. The structure of Orcus Patera represents the record of material erupted from a magmatic reservoir. The caldera is enclosed by steep inner walls (25% measured from topographic data), values which could be in agreement with the presence of a deep magmatic reservoir, as suggested by the typology of Crumpler et.al. The depth of the caldera might be due to the collapse of the magma reservoir, and the release of gases accompanying the magma thermal evolution. Origins of water for the paleolake(s): The water that generated a paleolake in Orcus Patera may have come from two origins: (1) Juvenile water: Plescia and Crips estimated a magma H20 content by weight between 0.5% and 1.5% using for the first value a comparison with terrestrial basalt, and for the second values from a Martian meteorite. The amount of H20 can be estimated by the volume of erupted lava, and the lava content of the caldera. In this study, we adopt a water content of 1%. The total volume of magma that has been contained in the caldera, and the volume of lava contained in the observed lava field is about 110 x 10(exp 6) cubic km, that gives a total volume of 1.10 x 10(exp 6) cubic km of water. The juvenile water expelled by the overpressure within the magma chamber charged with desolved water-vapor may have moved into the crust. The decrease in overburden pressure led to bubble formation. The ascent of these bubbles generated a pressurization of the magma, which was sufficient to fracture the overlaying magma layer, (2) Water from Elysium paleolake. During the Amazonian, the rise of the Elysium paleolake level generated an overspilling that supplied the caldera with water. The southern portion of the crest shows a deep gap 12-km wide at -1500 m elevation, locating the gap between 500 to 1000 in below the assumed water of Elysium paleolake, thus facilitating the influx of Elysium paleolake water into Orcus Patera. Bathymetric calculations give a floor area of 25,500 sq km at -2000 m elevation, and a water volume of 42,000 cubic km, with a lake-level at -1500 m. A substantial amount of water may have percolated through the fractured lava, and part of the volume may have overspilled the northern crest of Orcus Patera to debouch in the Tartarus Montes region. We envision the formation of a subsurface aqueous environment in basaltic rocks at the contact of the two water-source origins, possibly the percolating surface lake water, and more likely the juvenile water. Similarly to terrestrial calderas, Orcus Patera might be surrounded by ring-fractures caused by the collapse of the magma chamber that followed the release of gases. These ring-fractures may have been covered later by sedimentation in the caldera (lacustrine, aeolian, and volcanic), and by mass wasting. The detumescence of the magma in the caldera, and the vesiculation of the juvenile water may have operated simultaneously. Comparatively to terrestrial melts, Martian iron-rich melts are denser. This greater density implies greater effusion rates (eight-times terrestrial values), and larger fissuration widths (two-times terrestrial ones). With increasing vesiculation of magma, the bubbles interact with one-another because there are of similar pressure. They make a magma froth at the contact with the caldera surface, and on the walls of the fractures. In the saturated magma, froth, where the volume ratio of gases-to-liquid is about 4:1, the bubbles form a huge surface area of interconnected spaces. Bubbles near the caldera surface disrupt the magma, and fragmentation takes place, which moves downward through the magma column. On Earth, the bubbles are likely to grow between 1 and 50 mm in diameter due to the difference between the magma surface tension, and the bubble supersaturation pressure. The Martian low-pressure at surface level is likely to accelerate the expansion of the bubbles, and increase their final diameter and number, creating more voids in the magma. The strong magma froth with enclosed juvenile water bubbles interconnected with exsolved gas bubbles constitute a potential geothermal environment for geochemical energy production from basalt and water that does not require excessive temperatures. This process can start at +20C. Similar types of environments have been shown on Earth as potential energy sources for microbial metabolism, and could have provided deep aqueous basaltic niches for possible Martian microorganisms, even geologically recently. During the Amazonian, combination of volcanism and water activity still existed on Mars. Moreover, this type of potential niches open ways for investigation of possible oases of extinct or extant life, not only on paleolakes, and surface hydrothermalism spring areas, but also all large systems of fossae, which combine hydrologic and volcanic activities, and which provide an energy source, and an underground shelter to prevent surface UV bombardment. Additional information contained in the original.

Grin, E. A.↗

NASA NTRS1999

A Study of Nucleate Boiling with Forced Convection in Microgravity

The ultimate objective of basic studies of flow boiling in microgravity is to improve the understanding of the processes involved, as manifested by the ability to predict its behavior. This is not yet the case for boiling heat transfer even in earth gravity, despite the considerable research activity over the past 30 years. The elements that constitute the nucleate boiling process - nucleation, growth, motion, and collapse of the vapor bubbles (if the bulk liquid is subcooled) - are common to both pool and flow boiling. It is well known that the imposition of bulk liquid motion affects the vapor bubble behavior relative to pool boiling, but does not appear to significantly influence the heat transfer. Indeed, it has been recommended in the past that empirical correlations or experimental data of pool boiling be used for design purposes with forced convection nucleate boiling. It is anticipated that such will most certainly not be possible for boiling in microgravity, based on observations made with pool boiling in microgravity. In earth gravity buoyancy will act to remove the vapor bubbles from the vicinity of the heater surface regardless of how much the imposed bulk velocity is reduced, depending, of course, on the geometry of the system. Vapor bubbles have been observed to dramatically increase in size in pool boiling in microgravity, and the heat flux at which dryout took place was reduced considerably below what is generally termed the critical heat flux (CHF) in earth gravity, depending on the bulk liquid subcooling. However, at heat flux levels below dryout, the nucleate pool boiling process was enhanced considerably over that in earth gravity, in spite of the large vapor bubbles formed in microgravity and perhaps as a consequence. These large vapor bubbles tended to remain in the vicinity of the heater surface, and the enhanced heat transfer appeared to be associated with the presence of what variously has been referred to as a liquid microlayer between the bubble and the heater surface. The enhancement of the boiling process with low velocities in earth gravity for those orientations producing the formation of a liquid macrolayer described above, accompanied by "sliding" vapor bubbles, has been demonstrated. The enhancement was presented as a function of orientation, subcooling, and heated length, while a criterion for the heat transfer for mixed natural/forced convection nucleate boiling was given previously. A major unknown in the prediction and application of flow boiling heat transfer in microgravity is the upper limit of the heat flux for the onset of dryout (or critical heat flux - CHF), for given conditions of fluid-heater surfaces, including geometry, system pressure and bulk liquid subcooling. It is clearly understood that the behavior in microgravity will be no different than on earth with sufficiently high flow velocities, and would require no space experimentation. However, the boundary at which this takes place is still an unknown. Previous results of CHF measurements were presented for low velocity flow boiling at various orientations in earth gravity as a function of flow velocity and bulk liquid subcooling, along with preliminary measurements of bubble residence times on a flat heater surface. This showed promise as a parameter to be used in modeling the CHF, both in earth gravity and in microgravity. The objective of the work here is to draw attention to and show results of current modeling efforts for the CHF, with low velocities in earth gravity at different orientations and subcoolings. Many geometrical possibilities for a heater surface exist in flowing boiling, with boiling on the inner and outer surfaces of tubes perhaps being the most common. If the vapor bubble residence time on and departure size from the heater surface bear a relationship to the CHF, as results to be given indicate, it is important that visualization of and access to vapor bubble growth be conveniently available for research purposes. In addition, it is desirable to reduce the number of variables as much as possible in a fundamental study. These considerations dictated the use of a flat heater surface, which is rectangular in shape, 1.91 cm by 3.81 cm (0.75 x 1.5 inches), consisting either of a 400 Angstrom thick semi-transparent gold film sputtered on a quartz substrate which serves simultaneously as a heater and a resistance thermometer, or a copper substrate of the same size. The heater substrate is a disc which can be rotated so that the heated length in the flow direction can be changed from 1.91 to 3.81 cm (0.75 to 1.5 inches). The fluid is R-113, and the velocities can be varied between 0.5 cm/s and 60 cm/s. For a sufficiently low velocity the CHF can be modeled reasonably well at various orientations by the correlation for pool boiling corrected for the influence of bulk liquid subcooling, multiplied by the square root of q, the angle relative to horizontal. This arises from equating buoyancy and drag forces in the inverted positions where the vapor bubbles are held against the heater surface as they slide. A distortion of the measurements relative to pool boiling occurs as the flow velocity increases. In modeling this effect at different levels of subcooling it appeared appropriate to estimate the volumetric rate of vapor generation, using measurements of bubble frequency (or residence time), void fraction and average bubble boundary layer thickness. These were determined with the use of a platinum hot wire probe 0.025 mm in diameter by 1.3 mm long, applying a constant current to distinguish between contact with liquid or vapor. Two-dimensional spatial variations are obtained with a special mechanism to resolve displacements in increments of 0.025 mm. From such measurements it was determined that the fraction of the surface heat transfer resulting in evaporation varies inversely with the subcooling correction factor for the CHF. The measured inverse bubble residence time is normalized relative to that predicted for an infinite horizontal flat plate at the CHF, and is correlated well with the CHF normalized relative to that for pool boiling, for various orientation angles and subcooling levels. This correspondence is then combined with a normalizing factor for the energy flux leaving the heater surface at the CHF and the computed bubble radius at departure, determined from the balance between the outward velocity of the interface due to evaporation and the buoyance induced velocity of the center of mass of the bubble. The product of the CHF and the corresponding residence time was determined to be a constant for all orientations at a given bulk flow velocity and liquid subcooling, and must be determined empirically for each velocity and subcooling at present. It then becomes possible to predict the CHF for the different orientations, velocities, and subcoolings. These are compared with normalized measurements of the CHF for velocities ranging from 4 cm/s to 55 cm/s, subcoolings from 2.8 to 22.2 K, over orientations angles of 360 degrees.

Merte, Herman, Jr.↗