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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

High-Power Polyphase PCB-Type Inductive Coupler for Wireless Electric Vehicle Charging

The cost and manufacturing difficulty of traditionally wound coils for wireless charging of electric vehicles has led to the exploration of alternative manufacturing for scalable deployment at a range of rated powers. A rotating-field polyphase wireless coupler is developed with balanced fully pitched coils which are not possible with conventional Litz wire. The usage of printed circuit board (PCB) technology is proposed for the innovative construction at large dimensions due to reduced cost, increased ease of manufacturability, and potential geometric customization compared to would coils. Design considerations specific to PCBs are detailed for wireless power transfer coils including advantages such as the potential for many turns and transposition with planar interconnections. A design procedure is developed which may be used to investigate the frequency to power to dimension correlation and limits associated with PCB coils. Designs are simulated in 3D electromagnetic finite element analysis (FEA) for the polyphase coil to evaluate the coupling between coils with varying geometric parameters at 100mm and 500mm outer diameters. A discussion is included on methods to increase PCB power ratings through a mixture of layer stacking, connections, and material selection.

Lewis, Donovin D.↗
DOE OSTI2021

Distinct Clinical Impact and Biological Function of Angiopoietin and Angiopoietin-like Proteins in Human Breast Cancer

Secreted angiopoietin/angiopoietin-like (ANGPT/ANGPTL) proteins are involved in many biological processes. However, the role of these proteins in human breast cancers (BCs) remains largely unclear. Here, we conducted integrated omics analyses to evaluate the clinical impact of ANGPT/ANGPTL proteins and to elucidate their biological functions. In BCs, we identified rare mutations in ANGPT/ANGPTL genes, frequent gains of ANGPT1, ANGPT4, and ANGPTL1, and frequent losses of ANGPT2, ANGPTL5, and ANGPTL7, but observed that ANGPTL1, 2, and 4 were robustly downregulated in multiple datasets. The expression levels of ANGPTL1, 5, and 8 were positively correlated with overall survival (OS), while the expression levels of ANGPTL4 were negatively correlated with OS. Additionally, the expression levels of ANGPTL1 and 7 were positively correlated with distant metastasis-free survival (DMFS), while the expression levels of ANGPT2 and ANGPTL4 were negatively correlated with DMFS. The prognostic impacts of ANGPT/ANGPTL genes depended on the molecular subtypes and on clinical factors. We discovered that various ANGPT/ANGPTL genes were co-expressed with various genes involved in different pathways. Finally, with the exception of ANGPTL3, the remaining genes showed significant correlations with cancer-associated fibroblasts, endothelial cells, and microenvironment score, whereas only ANGPTL6 was significantly correlated with immune score. Our findings provide strong evidence for the distinct clinical impact and biological function of ANGPT/ANGPTL proteins, but the question of whether some of them could be potential therapeutic targets still needs further investigation in BCs.

60 APPLIED LIFE SCIENCES↗
NASA NTRS1976

Simultaneous radio and optical observations of UV Ceti-type flare stars

The UV Ceti-type stars, YZ Canis Minoris, AD Leonis, and Wolf 424 AB, were monitored for 57.8 hours from January 15 to February 22, 1974, using the 1000-foot (305-m) radio telescope at Arecibo, Puerto Rico, and the 91-cm or 76-cm reflector at McDonald Observatory. Radio observations were made at frequencies of 430, 318, and 196 MHz, and optical monitoring was done in the Johnson U or B band, the Stromgren u band, or white light. During the period of simultaneous observations, 62 optical flares were detected. A total of 13 RF flares were independently identified, of which 10 reached maximum flux within 10 min of the peak time of an optical flare. Using times of optical-flare events as reference data, an additional 15 cases of radio enhancements associated with optical flares are identified. The most probable delay interval between the optical-flare maximum and 318-MHz radio peak was found to be 0 to 5 min, with the optical flare occurring first. Aside from this statistical delay of peak occurrence and a general tendency for radio and optical flares to be associated, no systematic correlations of optical and radio amplitudes or morphology were found. The possible consequences of the radio emission's being due to a coherent process are discussed.

Spangler, S. R.↗
NASA NTRS1979

The temporal structure of the HF and VHF radiation produced by intracloud lightning discharges

Measurements of the radio frequency emissions produced by large-amplitude intracloud lightning impulses are presented in correlation with the associated electric radiation field. The RF radiation starts at almost the same time as the field, and the peak RF tends to occur during the initial half cycle of the field pulse. This temporal behavior is in marked contrast to that exhibited by the RF during the return stroke portions of cloud-to-ground flashes.

Krider, E. P.↗
NASA NTRS1981

Jet array impingement with crossflow-correlation of streamwise resolved flow and heat transfer distributions

Correlations for heat transfer coefficients for jets of circular offices and impinging on a surface parallel to the jet orifice plate are presented. The air, following impingement, is constrained to exit in a single direction along the channel formed by the jet orifice plate and the heat transfer (impingement) surface. The downstream jets are subjected to a crossflow originating from the upstream jets. Impingement surface heat transfer coefficients resolved to one streamwise jet orifice spacing, averaged across the channel span, are correlated with the associated individual spanwise orifice row jet and crossflow velocities, and with the geometric parameters.

Florschuetz, L. W.↗
NASA NTRS1986

The structure, energetics and evolution of the dominant frequency-dependent three-dimensional atmospheric modes

The three-dimensional structure of the dominant modes of wintertime variability are examined, and the mode structures are determined by an EOF analysis of the coupled vertical mean and shear streamfunction fields for a wide range of time-scale classes. The time mean energy conversions are determined from a two-layer quasigeostrophic model. Lag-cross correlations between the dominant low-frequency modes tend to be small and/or symmetric about zero, the high frequency modes are found to show highly asymmetric sinusoidal cross correlation functions similar to traveling waves, and some intermediate and short-time scale modes exhibit correlations indicating an association with the decaying phases of blocking in the Pacific. It is suggested that the mean flow barotropic (baroclinic) instabilities are an important source of variance for some of the lowest (highest) fluctuations considered.

Schubert, S. D.↗
NASA NTRS1990

Aeroservoelasticity

Accomplishments and current research projects along four main thrusts in aeroservoelasticity at the NASA Langley Research Center are described. One activity focuses on enhancing the modelling and the analysis procedures to accurately predict aeroservoelastic interactions. In the area of modelling, improvements to the minimum-state method of approximating unsteady aerodynamics are shown to provide precise, low-order models for design and simulation tasks. Recent extensions in aerodynamic correction factor methodology are also described. With respect to analysis procedures, the paper reviews novel enhancements to Matched Filter Theory and Random Process Theory for predicting the critical gust profile and the associated time-correlated gust loads for structural design considerations. In another activity, two research projects leading towards improved design capability are summarized. The first program involves the development of an integrated structure/control design capability; the second provides procedures for obtaining low-order, robust digital control laws for aeroelastic applications. Experimental validation of new theoretical developments is the third activity. As such, a short description of the Active Flexible Wing Project is presented, and recent wind-tunnel test accomplishments are summarized. Finally within the area of application, a study performed to assess the state-of-the-art of aeroelastic and aeroservoelastic analysis and design technology with respect to hot, hypersonic flight vehicles is reviewed.

Noll, Thomas E.↗
NASA NTRS1990

Acousto-ultrasonic nondestructive evaluation of materials using laser beam generation and detection

The acousto-ultrasonic method has proven to be a most interesting technique for nondestructive evaluation of the mechanical properties of a variety of materials. Use of the technique or a modification thereof, has led to correlation of the associated stress wave factor with mechanical properties of both metals and composite materials. The method is applied to the nondestructive evaluation of selected fiber reinforced structural composites. For the first time, conventional piezoelectric transducers were replaced with laser beam ultrasonic generators and detectors. This modification permitted true non-contact acousto-ultrasonic measurements to be made, which yielded new information about the basic mechanisms involved as well as proved the feasibility of making such non-contact measurements on terrestrial and space structures and heat engine components. A state-of-the-art laser based acousto-ultrasonic system, incorporating a compact pulsed laser and a fiber-optic heterodyne interferometer, was delivered to the NASA Lewis Research Center.

Huber, Robert D.↗
NASA NTRS1990

Aeroservoelasticity

The paper describes recent accomplishments and current research projects along four main thrusts in aeroservoelasticity at NASA Langley. One activity focuses on enhancing the modeling and analysis procedures to accurately predict aeroservoelastic interactions. Improvements to the minimum-state method of approximating unsteady aerodynamics are shown to provide precise low-order models for design and simulation tasks. Recent extensions in aerodynamic correction-factor methodology are also described. With respect to analysis procedures, the paper reviews novel enhancements to matched filter theory and random process theory for predicting the critical gust profile and the associated time-correlated gust loads for structural design considerations. Two research projects leading towards improved design capability are also summarized: (1) an integrated structure/control design capability and (2) procedures for obtaining low-order robust digital control laws for aeroelastic applications.

Noll, Thomas E.↗
NASA NTRS1993

Optical effects of space weathering: The role of the finest fraction

The optical properties of lunar soils are different than those of rocks which they are derived. As a consequence of lunar space weathering, soils are darker and exhibit a distinctive red-sloped continuum and weaker mineral absorption bands. The accumulation of dark glass-welded aggregates (agglutinates) has been thought to account for these optical effects of space weathering on lunar soils. Spectroscopic analyses of agglutinate separates and size fractions for a suite of lunar soils presented here indicate that the agglutinate paradigm is insufficient to fully account for lunar optical alteration. It is the finest fraction of lunar soils (less than 25 microns which constitute approximately 25% wt.) that dominates the optical properties of the bulk soil. Unlike size fractions of most silicates for which the finest fraction is the brightest, the lunar soil size fractions all have comparable albedos in the short-wavelength visible. In the near infrared, however, it is the finest fraction that exhibits the steep red continuum and weak absorption bands. The properties of the finest fraction cannot be duplicated by preparing a fine fraction by grinding larger agglutinate-rich soil particles. These results suggest space weathering on airless bodies is dominated by surface correlated processes (perhaps associated with the developement of fine-grained Fe(dot) on or near the surface of grains), and the accumulation of the large agglutinates is not necessarily required to account for lunar optical alteration.

Pieters, C. M.↗
NASA NTRS1996

Grant Proposal for the Continuation of the Voyager Interstellar Mission: LECP Investigation

This proposal documents the plans of the Low Energy Charged Particle (LECP) investigation team for participation in NASA's Voyager Interstellar Mission (VIM) as the Voyager 1 and 2 spacecraft explore the outer reaches of the heliosphere and search for the termination shock and the heliopause. The proposal covers the four year period from 1 January 1997 to 31 December 2000. The LECP instruments on Voyager 1 and 2 measure in situ intensities of charged particles with energies from about 30 keV to 100 MeV for ions, and about 20 keV to greater than 10 MeV for electrons. The instruments provide detailed spectral, angular, and compositional information about the particles. Composition is available for greater than 200 keV/nuc using multi-parameter measurements. Angular information is obtained by a mechanically scanned platform that rotates at various commanded rates. Measurements of low energy ion and electron intensities versus time and spatial location within the heliosphere contain an abundance of information regarding various transport and acceleration processes on both local (approx. 1 hr, approx. 0.01 AU) and global (approx. 11 yrs, approx. 100 AU) scales. The LECP instruments provide unique observations of such dynamical processes, and we anticipate that it will return critical information regarding the boundaries of the heliosphere. Several recent and exciting discoveries based on LECP measurements emphasize the important role that low energy charged particle distributions play in physical processes in the interplanetary medium. Yet, at the same time, these discoveries also underscore the fact that our understanding of processes in the outer heliosphere is, in most cases, incomplete, and in others, only rudimentary at best. Among the discoveries referred to above are the following: (1) Shocks: Examination of greater than 30 keV ion intensities have revealed: (a) a total absence of acceleration beyond only -100-200 keV at a strong transient shock in May 1991 at 35 AU, despite an enhanced level of seed particles; (b) a large transient shock in September 1991 of global scale, with intensities of shock-accelerated ions greater than or equal to 30 keV to approx. 30 MeV showing complex, highly energy-dependent spatial evolution, and small-scale (approx. few gyroradii), often anisotropic, micro-structures; (c) recurrent intensity increases in greater than or equal to 30 keV to -few MeV ions, with structures that, in some cases, show no correlation with the associated corotating shock. (2) Superthermal ion pressure: A global merged interaction region with a leading shock, downstream of which the superthermal ion (greater than or equal to 30 keV to approx. 4 MeV) pressure is comparable to that of the thermal plasma, and the total particle pressure yields a plasma beta of order unity. (3) Pickup ions: Measurements of the C/O ratio within transient structures at 35-45 AU showing the first clear evidence that transient shocks can pre-accelerate interstellar pickup ions from approx. 1 keV/nuc to at least 1 MeV/nuc. (4) Seed particles: Injection of ions for acceleration to high energies at the termination shock is unlikely to be a problem, since interplanetary transient and recurrent shocks are continually accelerating ions, of solar wind or interstellar origin, to highly superthermal energies. (5) Precursor electrons: Ambient solar electrons (greater than or equal to few tens of keV) that exist in the outer heliosphere ca form a broad precursor, several days wide, that is upstream of the termination shock and potentially observable a few months prior to the shock crossing. (6) Solar wind velocity at Voyager 1: We can use LECP ion data to obtain the solar wind velocity at Voyager 1, enabling us to provide critical measurement of the plasma flow as we approach and encounter the termination shock and other regions (necessary due to the partial failure of the Voyager 1 PLS experiment). The work of the LECP investigator team during the VIM will include: (1) Continuing operations with regard to the receipt, processing, verification, cataloging, display, and distribution of the data from the LECP instruments on Voyager 1 and 2, (2) Monitoring the health and performance of the LECP instruments, and evaluating and characterizing the response of the LECP instruments to various energetic particle and plasma environments, (3) Participating in, and supporting Voyager Project planning exercises and other coordinated activities relevant to exploration of the outer heliosphere, (4) Developing analysis techniques and operational procedures suitable for searching for and characterizing the boundaries and unique regions of the outher heliosphere, (5) Continuing the preparation of data sets appropriate for submission to the National Space Sciences Data Center (NSSDC) and, where appropriate, the Planetary Data System (PDS), (6) Maintaining direct Web access to online LECP data through the JHU/APL Voyager LECP home page, (7) Performing scientific evaluations of the Voyager 1 and 2 LECP data sets in conjunction with other data sets and other investigators, with particular focus on the outer regions of the heliosphere, and (8) Publishing the results of these evaluations in the scientific literature and presenting the results in scientific conferences.

Krimigis, Stamatios M.↗
NASA NTRS1998

The Three Dimensional Flow Field at the Exit of an Axial-Flow Turbine Rotor

A systematic and comprehensive investigation was performed to provide detailed data on the three dimensional viscous flow phenomena downstream of a modem turbine rotor and to understand the flow physics such as origin, nature, development of wakes, secondary flow, and leakage flow. The experiment was carried out in the Axial Flow Turbine Research Facility (AFTRF) at Penn State, with velocity measurements taken with a 3-D LDV System. Two radial traverses at 1% and 10% of chord downstream of the rotor have been performed to identify the three-dimensional flow features at the exit of the rotor blade row. Sufficient spatial resolution was maintained to resolve blade wake, secondary flow, and tip leakage flow. The wake deficit is found to be substantial, especially at 1% of chord downstream of the rotor. At this location, negative axial velocity occurs near the tip, suggesting flow separation in the tip clearance region. Turbulence intensities peak in the wake region, and cross- correlations are mainly associated with the velocity gradient of the wake deficit. The radial velocities, both in the wake and in the endwall region, are found to be substantial. Two counter-rotating secondary flows are identified in the blade passage, with one occupying the half span close to the casino and the other occupying the half span close to the hub. The tip leakage flow is well restricted to 10% immersion from the blade tip. There are strong vorticity distributions associated with these secondary flows and tip leakage flow. The passage averaged data are in good agreement with design values.

Lakshminarayana, B.↗
NASA NTRS2000

Monitoring Global Sea Level: Eustatic Variations, Local Variations, and Solid Earth Effects

Project BIFROST (Baseline Inferences for Fennoscandian Rebound Observations. Sea-level and Tectonics) combines networks of continuously operating CPS receivers in Sweden and Finland to measure ongoing crustal deformation due to glacial isostatic adjustment, (CIA). We present an analysis of data collected in the years 1993-1998. We compare the CPS determinations of three-dimensional crustal motion to predictions calculated using the high resolution Fennoscandian deglaciation model recently proposed by Lambeck et al. We find that the the maximum observed uplift rate (approx. 10 mm/ yr) and the maximum predicted uplift rate agree to better than 1 mm/ yr. The patterns of uplift also agree quite well, although differences are discernible. The chi(exp 2) difference between predicted and GPS-observed radial rates is reduced by a factor of 5-6 compared to that for the "null" (no uplift) model, depending on whether a mean difference is first removed. The north components of velocity agree at about the same relative level. whereas the agreement for the east components is worse, a problem possibly related to the lack of bias fixing. We have also compared the values for the observed radial deformation rates to those based on sea-level rates from Baltic tide gauges. The weighted RMS difference between CPS and tide-gauge rates (after removing a mean) is 0.6 mm/ yr, giving an indication of the combined accuracy of the CPS and tide-gauge measurement systems. Spectral analysis of the time series of position estimates yields spectral indices in the range -1 to -2. An EOF analysis indicates, however, that much of this power is correlated among the sites. The correlation appears to be regional and falls off only slightly with distance. Some of this correlated noise is associated with snow accumulation on the antennas or, for those antennas with radomes, on the radomes. This problem has caused us to modify the radomes used several times, leading to one of our more significant sources of uncertainty.

Davis, James L.↗
NASA NTRS2003

Sheet Flows, Avalanches, and Dune Evolution on Earth and Mars

This investigation is a collaboration between researchers at Cornell University, the University of Florida, and the University of Rennes 1, France. Flow modeling at Cornell University focused on mechanisms for the suspension and transport of wind-blown sand that are important in both terrestrial and Martian environments. These mechanisms include the saltation (or jumping) of grains, collisions between grains, and the interaction of grains with the velocity fluctuations of the turbulent wind. Of particular interest are sheet flows; these are relatively thin, highly concentrated regions of grains flowing near the ground under the influence of a strong turbulent wind. In them, the grains are suspended by interparticle collisions. Sheet flows may be relatively rare events, but they have the capacity to move great amounts of sand. In order to describe sheet flows, a turbulent mixture theory was formulated for particles in a fluid in which fluctuations in the volume fiaction of the particles take place on the scale of the turbulent eddies. Ensemble averaged equations for particle and fluid mass, momentum, and energy and fluid rate of dissipation were expressed in terms of Farve (concentration) averaged velocities and the associated velocity fluctuations. Correlations that describe the turbulent suspension of particles and dissipation of turbulent energy of both phases due to fluid particle interactions were modeled and boundary conditions at the bed and at the upper surface of the collisional flow were formulated. The boundary conditions at the upper surface were tested in a numerical simulation developed at the University of Florida. Steady and unsteady solutions for steady and unsteady fully-developed flows were obtained over a range of wind speeds fiom the lowest for which collisional between particles occurred to at which turbulent suspension is found to dominate collisional suspension. Below the value of the wind speed at which collisions between particles were unimportant, numerical solutions were obtained for the velocity distribution function and the resulting fields of concentration, particle and gas mean velocity, and particle shear stress for the steady two-dimensional saltation of spherical sand particles driven by a turbulent wind over a bed characterized by a simple relationship (the splash function) between the properties of incoming particles and those of the rebounding particles and other particles ejected fiom the bed. At the University of Rennes 1, experiments devoted to the characterization of the splash function for beds consisting of either random or ordered arrays of spheres in two- dimensions were completed. These indicated the role played by the packing geometry in the rebound and ejection of grains. Preliminary experiments on response of a three- dimensional collision bed to a collision with a single particle were performed. Data was taken with a single camera focused on the plane of collision. Here, for example, the decrease of the effective coefficient of restitution of the bed with an increase of the angle of incidence of the incoming particle has been measured. Other experiments on avalanches at Rennes studied the properties of the flows of particles that are responsible for the motion of the leeward side of a dune. In these, the dependence of the initiation of avalanches on the packing and depth of the particles was measured. Particle migration was studied in inclined flows of a binary mixture of disks and the mechanisms of diffision and segregation were isolated and characterized. The influence of side wall on dense, rapid inclined flows was measured and shown to be the reason why the angle of the free surface in such flows can exceed the static angle of repose. Future research will be devoted to a better understanding the transition between saltating (collisionless) and collisional flows as the wind speed the increases. This will involve the understanding of the evolution of the splash function as clisions with the bed become more numerous, more frequent, and more violent.

Source record↗
NASA NTRS2011

Characterizing the Joint Effect of Diverse Test-Statistic Correlation Structures and Effect Size on False Discovery Rates in a Multiple-Comparison Study of Many Outcome Measures

In their 2009 Annals of Statistics paper, Gavrilov, Benjamini, and Sarkar report the results of a simulation assessing the robustness of their adaptive step-down procedure (GBS) for controlling the false discovery rate (FDR) when normally distributed test statistics are serially correlated. In this study we extend the investigation to the case of multiple comparisons involving correlated non-central t-statistics, in particular when several treatments or time periods are being compared to a control in a repeated-measures design with many dependent outcome measures. In addition, we consider several dependence structures other than serial correlation and illustrate how the FDR depends on the interaction between effect size and the type of correlation structure as indexed by Foerstner s distance metric from an identity. The relationship between the correlation matrix R of the original dependent variables and R~, the correlation matrix of associated t-statistics is also studied. In general R~ depends not only on R, but also on sample size and the signed effect sizes for the multiple comparisons.

Feiveson, Alan H.↗
DOE OSTI2020

Linking Hydrology and Dissolved Organic Matter Characteristics in a Subtropical Wetland: A Long-Term Study of the Florida Everglades

Dissolved organic matter (DOM) acts as an important biogeochemical component of aquatic ecosystems that controls nutrient cycling, influences water quality, and links terrestrial and oceanic carbon pools, yet long-term studies of how changing environmental drivers alter its abundance and composition are rare. Using a ten-year, spatially explicit dataset from Everglades National Park (ENP), a globally significant wetland, we investigated the relationships between DOM quality/quantity and hydrologic/climatic drivers along two contrasting marsh-estuarine transects based on generalized linear modeling and a cumulative sums analysis. Analyses revealed distinct spatial, seasonal, and interannual patterns in variability of DOC and optical properties. Landscape-scale seasonal patterns showed an enrichment in microbial-like and protein-like DOM during the dry season relative to the wet season. We found that, while some compositional constituents varied with the solar calendar, responsive to temperature and photoperiod, others varied with the hydrologic calendar. Independent water level and discharge effects indicated strong hydrologic control on DOM quality that differed between the two transects, evidencing differences in their connectivity to areas of high agricultural activity. Across all sites, a significant long-term increasing trend in the fluorescence index was observed, associated with a positive correlation with precipitation and also potential changes in agricultural inputs, with other features associated with drought and hurricanes. Lastly, the cumulative sums analysis revealed differences between the two transects in the sensitivity of DOM composition to decreased water levels associated with 30-year climate scenarios, with the less hydrologically dynamic transect exhibiting greater potential sensitivity.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Characterizing initial- and final-state effects of relativistic nuclear collisions

Here, the multiphase transport model (AMPT) is used to study the final-state effects on the symmetric correlations (SC), asymmetric correlations (ASC), normalized symmetric correlations (NSC), and normalized asymmetric correlations (NASC) in Au+Au collisions at 200 GeV. The correlators' sensitivity to nonflow effects associated with long- and short-range nonflow correlations are also discussed using the HIJING model. The results indicate that SC, ASC, NSC, and NASC can give accompanying constraints for initial- and final-state effects. In addition, conducting further detailed experimental measurements spanning a broad range of collision systems and beam energies will serve as an additional constraint for the theoretical models' calculations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1968

Internal low Reynolds number turbulent heat transfer

The results of a semi-analytical and experimental study of adiabatic tube flow and an analytical and experimental investigation of the thermal entrance region for gas flowing through electrically heated circular tubes are presented. Emphasis is placed on the low Reynolds number turbulent flow regime--defined as fully turbulent flow at bulk Reynolds numbers from 3,000 to about 15,000. Adiabatic air velocity and friction data and localized heat transfer measurements for air and helium, at low heating rates, are presented for this range. The adiabatic data were obtained in a 1.61 inch 1D tube for flow at bulk Reynolds numbers from 3,000 to 15,000. A continuous, Reynolds number-dependent, profile is developed from the data by using a modification of Reichardts' wall and middle law eddy diffusivity expressions. The velocity profile satisfies continuity. It is valid for all Reynolds numbers in excess of 3,000 for which the flow is fully turbulent and the Blasius friction factor expression is valid. The thermal entrance problem for a fully developed velocity profile is solved analytically by the method of Sparrow, Hallman, and Siegel. The solution is based on the profile developed from the velocity study. Tabular values of the eigenvalues and normalized Nusselt numbers for gases are presented for it range of Reynolds numbers from 3,000 to 50,000. The axial variation of Nusselt number is found to be correlated by [Nu/Nu_(∞)] = 1 + 0.8 (1+ 70,000 Re^(-3/2)) ((x/D)^(-1)) to within ± 5 per cent for x/D ≥2. The fully developed value agrees with the Dittus - Boelter correlation, Nu_(∞) = 0.021 Re^(0.8) Pr^(0.4) For the eigenvalues, λ^(2)_(n), and the associated constants, A_(n), correlations of the form λ^(2)_(n) =A_(1,n) Re^(-b_(1,n) + C_(1,n) Re^(-d_(1,n)) A_(n) = -A_(2,n) Re^(-b_(2,n) + C_(2,n) Re^(-d_(2,n)) are obtained. The coefficients and powers are presented in tabular form. Heat transfer data are presented, primarily for helium, for the low Reynolds number turbulent range. A one-quarter inch, resistively heated, vertical, circular tube was used for the study. The data cover an axial range from 1.2 to 96 diameters; wall-to-bulk temperature ratios vary from 1 to 1.4. In the low Reynolds number turbulent regime, these data clearly support the present analytical solution rather than the prediction obtained by applying the eddy diffusivity distribution used by Sparrow, Hallman, and Siegel.

Harold C. Reynolds, Jr.↗