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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

An improved method of Nusselt number calculation

A novel method for calculating the Nusselt number, Nu, in a steady-state Rayleigh-Benard convection problem is presented, in which calculations are done for a square box with constant temperature, free-slip boundary conditions at the top and bottom, and a reflection symmetry along the side walls. The element heat flux is obtained by averaging over the entire element; element heat fluxes are then projected to the adjacent nodes. Compared with previous methods, the approach reduces the calculated depth variation in horizontally averaged flux by more than a factor of 10 and shows more rapid convergence of Nu as a function of grid size.

Ho-Liu, Phyllis↗
NASA NTRS1996

Studies of Two-Phase Flow Dynamics and Heat Transfer at Reduced Gravity Conditions

The ability to predict gas-liquid flow patterns is crucial to the design and operation of two-phase flow systems in the microgravity environment. Flow pattern maps have been developed in this study which show the occurrence of flow patterns as a function of gas and liquid superficial velocities as well as tube diameter, liquid viscosity and surface tension. The results have demonstrated that the location of the bubble-slug transition is affected by the tube diameter for air-water systems and by surface tension, suggesting that turbulence-induced bubble fluctuations and coalescence mechanisms play a role in this transition. The location of the slug-annular transition on the flow pattern maps is largely unaffected by tube diameter, liquid viscosity or surface tension in the ranges tested. Void fraction-based transition criteria were developed which separate the flow patterns on the flow pattern maps with reasonable accuracy. Weber number transition criteria also show promise but further work is needed to improve these models. For annular gas-liquid flows of air-water and air- 50 percent glycerine under reduced gravity conditions, the pressure gradient agrees fairly well with a version of the Lockhart-Martinelli correlation but the measured film thickness deviates from published correlations at lower Reynolds numbers. Nusselt numbers, based on a film thickness obtained from standard normal-gravity correlations, follow the relation, Nu = A Re(sup n) Pr(exp l/3), but more experimental data in a reduced gravity environment are needed to increase the confidence in the estimated constants, A and n. In the slug flow regime, experimental pressure gradient does not correlate well with either the Lockhart-Martinelli or a homogeneous formulation, but does correlate nicely with a formulation based on a two-phase Reynolds number. Comparison with ground-based correlations implies that the heat transfer coefficients are lower at reduced gravity than at normal gravity under the same flow conditions. Nusselt numbers can be correlated in a fashion similar to Chu and Jones.

Witte, Larry C.↗
NASA NTRS1992

Geoid anomalies and dynamic topography from convection in cylindrical geometry - Applications to mantle plumes on earth and Venus

A variety of evidence suggests that at least some hotspots are formed by quasi-cylindrical mantle plumes upwelling from deep in the mantle. Such plumes are modeled in cylindrical, axisymmetric geometry with depth-dependent, Newtonian viscosity. Cylindrical and sheet-like, Cartesian upwellings have significantly different geoid and topography signatures. However, Rayleigh number-Nusselt number systematics in the two geometries are quite similar. The geoid anomaly and topographic uplift over a plume are insensitive to the viscosity of the surface layer, provided that it is at least 1000 times the interior viscosity. Increasing the Rayleigh number or including a low-viscosity asthenosphere decreases the geoid anomaly and the topographic uplift associated with an upwelling plume.

Kiefer, Walter S.↗
NASA NTRS1978

Heat transfer characteristics for inline and staggered arrays of circular jets with crossflow of spent air

Heat transfer characteristics were measured for two dimensional arrays of jets impinging on a surface parallel to the jet orifice plate. The impinging flow was constrained to exit in a single direction along the channel formed by the jet plate and the heat transfer surface. Both mean Nusselt numbers and streamwise Nusselt number profiles are presented as a function of Reynolds number and geometric parameters. These are the streamwise and transverse hole spacings ranging from 5 to 10 and 4 to 8 jet orifice diameters, respectively; the channel height ranging from 1 to 6 diameters; and the hole pattern which includes both inline and staggered arrays. The results show that significant periodic variations occur in the streamwise Nusselt number profiles, persisting downstream for at least ten rows of jet holes. Channel height can have a significant effect on the chordwise profiles, smoothed across the periodic variations. For the smaller channel heights, Nusselt numbers first decrease and then increase downstream. Where significant differences exist, inline hole patterns provide better heat transfer than staggered ones. These and other effects of the geometric parameters are presented and discussed.

Metzger, D. E.↗
NASA NTRS2005

Analysis of Hydrodynamics and Heat Transfer in a Thin Liquid Film Flowing over a Rotating Disk by Integral Method

An integral analysis of hydrodynamics and heat transfer in a thin liquid film flowing over a rotating disk surface is presented for both constant temperature and constant heat flux boundary conditions. The model is found to capture the correct trends of the liquid film thickness variation over the disk surface and compare reasonably well with experimental results over the range of Reynolds and Rossby numbers covering both inertia and rotation dominated regimes. Nusselt number variation over the disk surface shows two types of behavior. At low rotation rates, the Nusselt number exhibits a radial decay with Nusselt number magnitudes increasing with higher inlet Reynolds number for both constant wall temperature and heat flux cases. At high rotation rates, the Nusselt number profiles exhibit a peak whose location advances radially outward with increasing film Reynolds number or inertia. The results also compare favorably with the full numerical simulation results from an earlier study as well as with the reported experimental results.

Basu, S.↗
NASA NTRS2017

Viscous Three-Dimensional Simulation of Flow in an Axial Low Pressure Compressor at Engine Icing Operating Points

Viscous three-dimensional simulations of the Honeywell ALF502R-5 low pressure compressor (sometimes called a booster) using the NASA Glenn code GlennHT have been carried out. A total of ten simulations were produced. Five operating points are investigated, with each point run with two different wall thermal conditions. These operating points are at, or near, points where engine icing has been determined to be likely. In the future, the results of this study will be used for further analysis such as predicting collection efficiency of ice particles and ice growth rates at various locations in the compressor. A mixing plane boundary condition is used between each blade row, resulting in convergence to steady state within each blade row. The k-omega turbulence model of Wilcox, combined with viscous grid spacing near the wall on the order of one, is used to resolve the turbulent boundary layers. For each of the operating points, heat transfer coefficients are generated on the blades and walls. The heat transfer coefficients are produced by running the operating point with two different wall thermal conditions and then solving simultaneously for the heat transfer coefficient and adiabatic wall temperature at each point. Average Nusselt numbers are calculated for the most relevant surfaces. The values are seen to scale with Reynolds number to approximately a power of 0.7. Additionally, images of surface distribution of Nusselt number are presented. Qualitative comparison between the five operating points show that there is relatively little change in the character of the distribution. The dominant observed effect is that of an overall scaling, which is expected due to Reynolds number differences. One interesting aspect about the Nusselt number distribution is observed on the casing (outer diameter) downstream of the exit guide vanes (EGVs). The Nusselt number is relatively high between the pairs of EGVs, with two lower troughs downstream of each EGV trailing edge. This is of particular interest since rather complex ice shapes have been observed in that region.

compressor↗
NASA NTRS1992

Heat transfer in thin, compact heat exchangers with circular, rectangular, or pin-fin flow passages

Heat transfer and pressure drop have been measured of three thin, compact heat exchangers in helium gas at 3.5 MPa and higher, with Reynolds numbers of 450 to 36,000. The flow geometries for the three heat exchanger specimens were: circular tube, rectangular channel, and staggered pin fin with tapered pins. The specimens were heated radiatively at heat fluxes up to 77 W/sq cm. Correlations were developed for the isothermal friction factor as a function of Reynolds number, and for the Nusselt number as a function of Reynolds number and the ratio of wall temperature to fluid temperature. The specimen with the pin fin internal geometry had significantly better heat transfer than the other specimens, but it also had higher pressure drop. For certain conditions of helium flow and heating, the temperature more than doubled from the inlet to the outlet of the specimens, producing large changes in gas velocity, density, viscosity, and thermal conductivity. These changes in properties did not affect the correlations for friction factor and Nusselt number in turbulent flow.

Olson, D. A.↗
NASA NTRS1951

Analytical investigation of fully developed laminar flow in tubes with heat transfer with fluid properties variable along the radius

Relations were analytically obtained for the prediction of radial distributions of velocity and temperature for fully developed laminar flow of gases and of liquid metals in tubes with fluid properties variable along the radius. The relations are applicable to both heating and cooling of the fluid. By use of the relations for velocity and temperature distributions, relations were obtained among Nusselt number, friction parameter, and ratio of wall to bulk temperature. The Nusselt number and friction parameter were found to be independent of Reynolds number and Prandtl number. The effects of ratio of wall to bulk temperature on Nusselt number and friction parameter could be eliminated by evaluating the fluid properties at specified temperatures in the fluid.

Deissler, Robert G↗
NASA NTRS1980

A numerical investigation of thermal convection in a heat-generating fluid layer

Finite difference solutions of the equations governing thermal convection driven by uniform volumetric energy sources are presented for two-dimensional flows in a rectangular domain. The boundary conditions are a rigid (i.e, zero slip), zero heat-flux lower surface, rigid adiabatic sides, and either a rigid or free (i.e., zero shear) isothermal upper surface. Computations are carried out for Prandtl numbers from 0.05 to 20 and Rayleigh numbers from 5 x 10 to the 4th to 5 x 10 to the 8th. Nusselt numbers and average temperature profiles within the layer are in good agreement with experimental data for rigid-rigid boundaries. For rigid-free boundaries, Nusselt numbers are larger than in the former case. The structure of the flow and temperature fields in both cases is dominated by rolls, except at larger Rayleigh numbers where large-scale eddy transport occurs. Generally, low velocity upflows over broad regions of the layer are balanced by higher velocity downflows when the flow exhibits a cellular structure. The hydrodynamic constraint at the upper surface and the Prandtl number are found to influence only the detailed nature of flow and temperature fields. No truly steady velocity and temperature fields are found despite the fact that average Nusselt numbers reach steady values.

Emara, A. A.↗
NASA NTRS1977

Studies of heat-source driven natural convection: A numerical investigation

Thermal convection driven by uniform volumetric energy sources was studied in a horizontal fluid layer bounded from above by a rigid, isothermal surface and from below by a rigid, zero heat-flux surface. The side walls of the fluid domain were assumed to be rigid and perfectly insulating. The computations were formally restricted to two-dimensional laminar convection but were carried out for a range of Rayleigh numbers which spans the regimes of laminar and turbulent flow. The results of the computations consists of streamline and isotherm patterns, horizontally averaged temperature distributions, and horizontally averaged Nusselt numbers at the upper surface. Flow and temperature fields do not exhibit a steady state, but horizontally averaged Nusselt numbers reach limiting, quasi-steady values for all Rayleigh numbers considered. Correlations of the Nusselt number in terms of the Rayleigh and Prandtl numbers were determined.

Emara, A. A.↗
NASA NTRS1975

Modal equations for cellular convection

We expand the fluctuating flow variables of Boussinesq convection in the planform functions of linear theory. Our proposal is to consider a drastic truncation of this expansion as a possible useful approximation scheme for studying cellular convection. With just one term included, we obtain a fairly simple set of equations which reproduces some of the qualitative properties of cellular convection and whose steady-state form has already been derived by Roberts (1966). This set of 'modal equations' is analyzed at slightly supercritical and at very high Rayleigh numbers. In the latter regime the Nusselt number varies with Rayleigh number just as in the mean-field approximation with one horizontal scale when the boundaries are rigid. However, the Nusselt number now depends also on the Prandtl number in a way that seems compatible with experiment. The chief difficulty with the approach is the absence of a deductive scheme for deciding which planforms should be retained in the truncated expansion.

Gough, D. O.↗
NASA NTRSDate not supplied

Comparison of Convective Heat Transfer Correlations and Their Application to NTP Reactors

This study analyzes various Nusselt number and friction factor correlations and applies them to a Small Nuclear Rocket Engine model with a Sinusoidal power distribution profile to understand their effects on the temperatures and pressures inside the reactor. A nodal thermal hydraulic solver was used to determine the fluid and channel surface temperatures while also incorporating variable fluid properties and channel roughness. The results showed that the considered friction factors could essentially be used interchangeably given that their difference affected the pressure by less than 1%. However, large variations in the tube surface temperature were obtained for the different Nusselt numbers while the fluid temperature distribution was forced to remain the same. Supersonic flow conditions presented by Maynard Taylor are investigated to serve as a baseline for how experimental errors can lead to uncertainties in the reported empirical correlations. Detailed experimental investigation is necessary to determine the Nusselt number correlation that will provide the best prediction of the thermal hydraulic performance inside the reactor fluid flow channels.

Nuclear Thermal Propulsion↗
NASA NTRS2000

Unsteady High Turbulence Effects on Turbine Blade Film Cooling Heat Transfer Performance Using a Transient Liquid Crystal Technique

Unsteady wake effect, with and without trailing edge ejection, on detailed heat transfer coefficient and film cooling effectiveness distributions is presented for a downstream film-cooled gas turbine blade. Tests were performed on a five-blade linear cascade at an exit Reynolds number of 5.3 x 10(exp 5). Upstream unsteady wakes were simulated using a spoke-wheel type wake generator. Coolant blowing ratio was varied from 0.4 to 1.2; air and CO2 were used as coolants to simulate different density ratios. Surface heat transfer and film effectiveness distributions were obtained using a transient liquid crystal technique; coolant temperature profiles were determined with a cold wire technique. Results show that Nusselt numbers for a film cooled blade are much higher compared to a blade without film injection. Unsteady wake slightly enhances Nusselt numbers but significantly reduces film effectiveness versus no wake cases. Nusselt numbers increase only slic,htly but film cooling, effectiveness increases significantly with increasing, blowing ratio. Higher density coolant (CO2) provides higher effectiveness at higher blowing ratios (M = 1.2) whereas lower density coolant (Air) provides higher 0 effectiveness at lower blowing ratios (M = 0.8). Trailing edge ejection generally has more effect on film effectiveness than on the heat transfer, typically reducing film effectiveness and enhancing heat transfer. Similar data is also presented for a film cooled cylindrical leading edge model.

Han, J. C.↗
NASA NTRS1984

Channel flow modeling of impingement cooling of a rotating turbine blade

Local heat transfer distributions in impingement cooling have been measured by Kreatsoulas and Prieser for a range of conditions which model those in actual turbine blades, including the effects of rotation. These data were reported as local Nusselt numbers, but referred to coolant supply conditions. By means of a channel flow modeling of the flow in the supply and impingement passages, the same data are here presented in terms of local Nusselt number distributions such as are used in design. The results in this form are compared to the nonrotating impingement results of Chupp and to the rotating but nonimpingement results of Morris. Rotation reduces the mean Nusselt numbers from these found by Chupp by about 30 percent, and introduces important radial variations which are sensitive to rotation and to leading edge stagger angle.

Koo, J. J.↗
NASA NTRS1991

Heat transfer and pressure drop in a compact pin-fin heat exchanger with pin orientation at 18 deg to the flow direction

The heat transfer and pressure drop characteristics of a novel, compact heat exchanger in helium gas were measured at 3.5 MPa and Reynolds numbers of 450 to 12,000. The pin-fin specimen consisted of pins, 0.51 mm high and spaced 2.03 mm on centers, spanning a channel through which the helium flows; the angle of the row of pins to the flow direction was 18 deg. The specimen was radiatively heated on the top side at heat fluxes up to 74 W/sq cm and insulated on the back side. Correlations were developed for the friction factor and Nusselt number. The Nusselt number compares favorably to those of past studies of staggered pin-fins, when the measured temperatures are extrapolated to the temperature of the wall-fluid interface.

Olson, D. A.↗