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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.↗

Effects of surface temperature and Reynolds number on heat transfer to the Shuttle Orbiter leeward fuselage

Heat-transfer data obtained at hypersonic shock tunnel conditions and three-dimensional flow field computations were used to study the influence of surface temperature and Reynolds number on the heating experienced by the leeward fuselage area of the Space Shuttle Orbiter configuration. The basic results of this study indicate that systematic variations in the average total enthalpy within a boundary layer (as obtained through controlled nonadiabatic processes) has an influence on the heat transfer to downstream areas which can be correlated; even in three-dimensional separated flow areas. Specifically, the average separated-flow Stanton number for the fuselage leeward surface is shown to be moderately dependent on the windward-wall to free-stream total temperature ratio.

Bertin, J. J.↗

Laminar friction and heat transfer at Mach numbers from 1 to 10

Velocity and temperature profiles and laminar boundary-layer characteristics have been computed for Mach numbers from 1 to 10, utilizing experimental values of the heat capacity, viscosity, and conductivity. The analysis shows that effective temperature, which is a function of the surface temperature and stream conditions, arises naturally and is the proper reference temperature to be used in heat-transfer calculations. The effective temperature and the recovery temperature become identical for the condition of zero heat transfer.

Klunker, E B↗

Analysis of fully developed turbulent heat transfer at low Peclet numbers in smooth tubes with application to liquid metals

An analysis was made of heat transfer at low Peclet numbers for fluids flowing turbulently in smooth tubes. Previous analyses for flow of gases and liquid metals at low Peclet numbers gave higher heat-transfer coefficients than were indicated experimentally. When the mixing-length theory was modified in order to account for the heat transferred by conduction to a turbulent particle as it moves transversely, the predicted results were brought into agreement with the experimental results.

PIPES↗

Sharp flat plate heat transfer in helium at Mach numbers of 22.8 to 86.8 and in corner flow with air at Mach number of 19

Surface heat transfer rates were measured on a sharp flat plate at zero angle of attack in a hypersonic shock tunnel. The density and leading edge Knudsen number were varied to span the continuum to near free molecule regimes. The strong interaction parameter varied from 11 to 16,000 with Knudsen numbers from 0.56 to 17.1 respectively. Local heat transfer rates in the corner flow region produced by the intersection of two perpendicular flat plates with sharp leading edges were determined for various flow densities. The strength of the shock wave from the vertical plate was varied by adjusting the angle of attack from 0 to 5 deg. The unit Reynolds number varied from 1,000 to 17,200 and the Knudsen numbers from 1.6 to 27. The strong interaction parameter varied from 14 to 500.

Nagamatsu, H. T.↗

Time dependent heat transfer rates in high Reynolds number hypersonic flowfields

Time dependent heat transfer rates have been calculated from time dependent temperature measurements in the vicinity of shock-wave boundary-layer interactions due to conical compression ramps on an axisymmetric body. The basic model is a cylindrical body with a 10 degree conical nose. Four conical ramps, 20, 25, 30, and 35 degrees serve as shock wave generators. Flowfield surveys have been made in the vicinity of the conical ramp vertex, the separation point, and the reattachment point. A significant effort was made to characterize the natural frequencies and relative powers of the resulting fluctuations in heat transfer rates. This research effort, sponsored jointly by NASA and the Air Force, was conducted in the Air Force Flight Dynamics Directorate High Reynolds Facility. The nominal freestream Mach number was 6, and the freestream Reynolds numbers ranged from 2.2 million/ft to 30.0 million/ft. Experimental results quantify temperature response and the resulting heat transfer rates as a function of ramp angle and Reynolds number. The temperature response within the flowfield appears to be steady-state for all compression ramp angles and all Reynolds numbers, and hence, the heat transfer rates appear to be steady-state.

Flanagan, Michael J.↗

Analysis of supersonic plug nozzle flowfield and heat transfer

A number of problems pertaining to the flowfield in a plug nozzle, designed as a supersonic thruster nozzle, with provision for cooling the plug with a coolant stream admitted parallel to the plug wall surface, were studied. First, an analysis was performed of the inviscid, nonturbulent, gas dynamic interaction between the primary hot stream and the secondary coolant stream. A numerical prediction code for establishing the resulting flowfield with a dividing surface between the two streams, for various combinations of stagnation and static properties of the two streams, was utilized for illustrating the nature of interactions. Secondly, skin friction coefficient, heat transfer coefficient and heat flux to the plug wall were analyzed under smooth flow conditions (without shocks or separation) for various coolant flow conditions. A numerical code was suitably modified and utilized for the determination of heat transfer parameters in a number of cases for which data are available. Thirdly, an analysis was initiated for modeling turbulence processes in transonic shock-boundary layer interaction without the appearance of flow separation.

Murthy, S. N. B.↗

Sharp flat plate heat transfer in helium at Mach numbers of 22.8 to 86.8

Surface heat transfer rates were measured on a sharp flat plate at zero angle of attack with helium over a Mach number range of 22.8 to 86.8 in a hypersonic shock tunnel. The density and leading edge Knudsen numbers were varied to span the continuum to near free molecule regimes. The strong interaction parameter varied from 11 to 16,000 with leading edge Knudsen numbers from 0.56 to 17.1, respectively. For high unit Reynolds number the rate of change of the heat transfer coefficient with the strong interaction parameter agreed well with the strong interaction theory of Li and Nagamatsu (1953, 1955).

Nagamatsu, H. T.↗

On-orbit cryogenic fluid transfer

A number of future NASA and DOD missions have been identified that will require, or could benefit from resupply of cryogenic liquids in orbit. The most promising approach for accomplishing cryogenic fluid transfer in the weightlessness environment of space is to use the thermodynamic filling technique. This approach involves initially reducing the receiver tank temperature by using several charge hold vent cycles followed by filling the tank without venting. Martin Marietta Denver Aerospace, under contract to the NASA Lewis Research Center, is currently developing analytical models to describe the on orbit cryogenic fluid transfer process. A detailed design of a shuttle attached experimental facility, which will provide the data necessary to verify the analytical models, is also being performed.

Aydelott, J. C.↗

On-orbit cryogenic fluid transfer

A number of future NASA and DOD missions have been identified that will require, or could benefit from resupply of cryogenic liquids in orbit. The most promising approach for accomplishing cryogenic fluid transfer in the weightlessness environment of space is to use the thermodynamic filling technique. This approach involves initially reducing the receiver tank temperature by using several charge hold vent cycles followed by filling the tank without venting. Martin Marietta Denver Aerospace, under contract to the NASA Lewis Research Center, is currently developing analytical models to describe the on orbit cryogenic fluid transfer process. A detailed design of a Shuttle attached experimental facility, which will provide the data necessary to verify the analytical models, is also being performed.

Aydelott, J. C.↗