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A general discussion of applying these formulas to the numerical solution of partial differential equations is made. An illustrative problem with function value given on a circular boundary is solved by both relaxation and matrix methods. Similar applications to compressible flow past isolated and cascade airfoils, through turbomachines, and temperature and stress distribution is cooled turbine blades is indicated.
Includes the Committee's Technical reports no. 1-1058, reprinted in v. 1-37.

Report

United States. Office of Scientific Research and Development

Published: 1963

Total Pages: 1522


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An analytical method is presented for obtaining turbulent temperature recovery factors for a thermally insulated surface in supersonic flow. The method is an extension of Squire's analysis for incompressible flow. The boundary layer velocity profile is represented by a power law and a similarity is postulated for squared-velocity the static-temperature-difference profiles.
Basic equations of Karman and Chien are solved by representing the shape of a torsion box by means of a Fourier series. Angles of twist, longitudinal stresses, and shear stresses are determined in terms of the series coefficients. The method is applied to the calculation of angles of twist and stresses in torsion boxes of rectangular, elliptical, and airfoil cross section. Results obtained for angles of twist and normal stresses are in good agreement with results of Karman and Chien except at sharp corners. Results obtained for shear stresses indicate the necessity for the use of large number of terms of the series for satisfactory accuracy.
An analysis of combined heat and mass transfer from a flat plate has been made in terms of Prandtl's simpified physical concept of the turbulent boundary layer. The results of the analysis show that tor conditioins of reasonably small heat and mass transfer, the ratio of the mass- and heat-transfer coefficients is dependent on the Reynolds number of the boundary layer, the Prandtl number of the medium of diffusion, and the Schmidt number of the diffusing fluid in the medium of diffusion. For the particular case of water evaporating into air, the ratio of mass-transfer coefficient to heat-transfer coefficient is found to be slightly greater than unity.