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Exact solutions of laminar-boundary-layer equations with constant property values for porous wall with variable temperature

Description: Exact solution of the laminar-boundary-layer equations for wedge-type flow with constant property values are presented for transpiration-cooled surfaces with variable wall temperatures. The difference between wall and stream temperature is assumed proportional to a power of the distance from the leading edge. Solutions are given for a Prandtl number of 0.7 and ranges of pressure-gradient, cooling-air-flow, and wall-temperature-gradient parameters. Boundary-layer profiles, dimensionless boundary-layer thicknesses, and convective heat-transfer coefficients are given in both tabular and graphical form. Corresponding results for constant wall temperature and for impermeable surfaces are included for comparison purposes.
Date: January 1, 1955
Creator: Donoughe, Patrick L & Livingood, John N B
Partner: UNT Libraries Government Documents Department

Solutions of laminar-boundary-equations which result in specific-weight-flow profiles locally exceeding free-stream values

Description: Revised solutions of the laminar-boundary-layer equations for cases which involved cooling at the wall combined with large pressure gradients in the main stream produced specific-weight-flow profiles which locally exceeded free-stream values. Heat-transfer and friction coefficients, boundary-layer thicknesses, and velocity, temperature, and specific-weight-flow distributions resulting from the revised solutions are presented for Euler numbers of 0.5 and 1, stream-to-wall temperature ratios of 2 and 4, and cooling-air flow rates through porous walls designated by flow parameters of 0, -0.5, and -1.
Date: September 1, 1952
Creator: Brown, W Byron & Livingood, John N B
Partner: UNT Libraries Government Documents Department

Cooling of Gas Turbines, 3, Analysis of Rotor and Blade Temperatures in Liquid-Cooled Gas Turbines

Description: A theoretical analysis of the radial temperature distribution through the rotor and constant cross sectional area blades near the coolant passages of liquid cooled gas turbines was made. The analysis was applied to obtain the rotor and blade temperatures of a specific turbine using a gas flow of 55 pounds per second, a coolant flow of 6.42 pounds per second, and an average coolant temperature of 200 degrees F. The effect of using kerosene, water, and ethylene glycol was determined. The effect of varying blade length and coolant passage lengths with water as the coolant was also determined. The effective gas temperature was varied from 2000 degrees to 5000 degrees F in each investigation.
Date: February 11, 1947
Creator: Brown, W. Byron & Livingood, John N. B.
Partner: UNT Libraries Government Documents Department

Cooling of gas turbines IX : cooling effects from use of ceramic coatings on water-cooled turbine blades

Description: The hottest part of a turbine blade is likely to be the trailing portion. When the blades are cooled and when water is used as the coolant, the cooling passages are placed as close as possible to the trailing edge in order to cool this portion. In some cases, however, the trailing portion of the blade is so narrow, for aerodynamic reasons, that water passages cannot be located very near the trailing edge. Because ceramic coatings offer the possibility of protection for the trailing part of such narrow blades, a theoretical study has been made of the cooling effect of a ceramic coating on: (1) the blade-metal temperature when the gas temperature is unchanged, and (2) the gas temperature when the metal temperature is unchanged. Comparison is also made between the changes in the blade or gas temperatures produced by ceramic coatings and the changes produced by moving the cooling passages nearer the trailing edge. This comparison was made to provide a standard for evaluating the gains obtainable with ceramic coatings as compared to those obtainable by constructing the turbine blade in such a manner that water passages could be located very near the trailing edge.
Date: October 13, 1948
Creator: Brown, W Byron & Livingood, John N B
Partner: UNT Libraries Government Documents Department

Calculations of Laminar Heat Transfer Around Cylinders of Arbitrary Cross Section and Transpiration-Cooled Walls with Application to Turbine Blade Cooling

Description: An approximate method for development of flow and thermal boundary layers in laminar regime on cylinders with arbitrary cross section and transpiration-cooled walls is obtained by use of Karman's integrated momentum equation and an analogous heat-flow equation. Incompressible flow with constant property values throughout boundary layer is assumed. Shape parameters for approximated velocity and temperature profiles and functions necessary for solution of boundary-layer equations are presented as charts, reducing calculations to a minimum. The method is applied to determine local heat-transfer coefficients and surface temperature-cooled turbine blades for a given flow rate. Coolant flow distributions necessary for maintaining uniform blade temperatures are also determined.
Date: September 24, 1951
Creator: Eckert, E.R.G. & Livingood, John N.B.
Partner: UNT Libraries Government Documents Department

Study of ram-air heat exchangers for reducing turbine cooling-air temperature of a supersonic aircraft turbojet engine

Description: The sizes and weights of the cores of heat exchangers were determined analytically for possible application for reducing turbine cooling-air temperatures of an engine designed for a Mach number of 2.5 and an altitude The sizes and weights of the cores of heat exchangers were determined analytically for possible application for reducing turbine cooling-air temperatures of an engine designed for a Mach number of 2.5 and an altitude of 70,000 feet. A compressor-bleed-air weight flow of 2.7 pounds per second was assumed for the coolant; ram air was considered as the other fluid. Pressure drops and inlet states of both fluids were prescribed, and ranges of compressor-bleed-air temperature reductions and of the ratio of compressor-bleed to ram-air weight flows were considered.
Date: August 3, 1956
Creator: Diaguila, Anthony J; Livingood, John N B & Eckert, Ernst R G
Partner: UNT Libraries Government Documents Department

Method for calculation of laminar heat transfer in air flow around cylinders of arbitrary cross section (including large temperature differences and transpiration cooling)

Description: The solution of heat-transfer problems has become vital for many aeronautical applications. The shapes of objects to be cooled can often be approximated by cylinders of various cross sections with flow normal to the axis as, for instance heat transfer on gas-turbine blades and on air foils heated for deicing purposes. A laminar region always exists near the stagnation point of such objects. A method previously presented by E. R. G. Eckert permits the calculation of local heat transfer around the periphery of cylinders of arbitrary cross section in the laminar region for flow of a fluid with constant property values with an accuracy sufficient for engineering purposes. The method is based on exact solutions of the boundary-layer equations for incompressible wedge-type flow and on the postulate that at any point on the cylinder the boundary-layer growth is the same as that on a wedge with comparable flow conditions. This method is extended herein to take into account the influence of large temperature differences between the cylinder wall and the flow as well as the influence of transpiration cooling when the same medium as the outside flow is used as coolant.
Date: January 1, 1953
Creator: Eckert, E R & Livingood, John N B
Partner: UNT Libraries Government Documents Department

Analysis of spanwise temperature distribution in three types of air-cooled turbine blade

Description: From Summary: An approximate method for determining the allowable stress-limited blade-temperature distribution is included, with brief accounts of a method for determining the maximum allowable effective gas temperatures and the cooling-air requirements. Numerical examples that illustrate the use of the various temperature-distribution equations and of the nondimensional charts are also included.
Date: 1950~
Creator: Livingood, John N B & Brown, W Byron
Partner: UNT Libraries Government Documents Department

Analysis of temperature distribution in liquid-cooled turbine blades

Description: From Summary: "This report presents analytical methods for computing temperature distributions in liquid-cooled turbine blades, or in simplified shapes used to approximate sections of the blade. The individual analyses are first presented in terms of their mathematical development. Nondimensional charts to simplify some temperature-distribution calculations are also given."
Date: October 27, 1950
Creator: Livingood, John N B & Brown, W Byron
Partner: UNT Libraries Government Documents Department

Cooling of Gas Turbines, 6, Computed Temperature Distribution Through Cross Section of Water-Cooled Turbine Blade

Description: A theoretical analysis of the cross-sectional temperature distribution of a water-cooled turbine blade was made using the relaxation method to solve the differential equation derived from the analysis. The analysis was applied to specific turbine blade and the studies icluded investigations of the accuracy of simple methods to determine the temperature distribution along the mean line of the rear part of the blade, of the possible effect of varying the perimetric distribution of the hot gas-to -metal heat transfer coefficient, and of the effect of changing the thermal conductivity of the blade metal for a constant cross sectional area blade with two quarter inch diameter coolant passages.
Date: May 1, 1947
Creator: Livingood, John N. B. & Sams, Eldon W.
Partner: UNT Libraries Government Documents Department