Summary
Steady two-dimensional and axisymmetric compressible nonsimilar laminar boundary-layer flows with non-uniform slot injection (or suction) and non-uniform wall enthalpy have been studied from the starting point of the streamwise co-ordinate to the exact point of separation. The effect of different free stream Mach number has also been considered. The finite discontinuities arising at the leading and trailing edges of the slot for the uniform slot injection (suction) or wall enthalpy are removed by choosing appropriate non-uniform slot injection (suction) or wall enthalpy. The difficulties arising at the starting point of the streamwise co-ordinate, at the edges of the slot and at the point of separation are overcome by applying the method of quasilinear implicit finite difference scheme with an appropriate selection of finer step size along the streamwise direction. It is observed that the non-uniform slot injection moves the point of separation downstream but the non-uniform slot suction has the reverse effect. The increase of Mach number shifts the point of separation upstream due to the adverse pressure gradient. The increase of total enthalpy at the wall causes the separation to occur earlier while cooling delays it. The non-uniform total enthalpy at the wall (i.e., the cooling or heating of the wall in a slot) along the streamwise co-ordinate has very little effect on the skin friction and thus on the point of separation.
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References
Dewey, C. F., Gross, J. F.: Exact solutions of the laminar boundary-layer equations. Advances in heat transfer, vol. 4, p. 317. New York: Academic Press 1967.
Sparrow, E. M., Quack, H., Boerner, E. J.: Local nonsimilar boundary-layer solutions. A.I.A.A.J.8, 1936–1942 (1970).
Kao, T., Elrod, H. G.: Laminar shear stress pattern in nonsimilar incompressible boundary layers. A.I.A.A. J.12, 1401–1408 (1974).
Kao, T., Elrod, H. G.: Rapid calculation of heat transfer in nonsimilar laminar incompressible boundary layers, A.I.A.A. J.14, 1746–1751 (1976).
Smith, A. M. O., Clutter, D. W.: Solutions of incompressible laminar boundary-layer equations. A.I.A.A. J.1, 2062–2071 (1963).
Smith, A. M. O., Clutter, D. W.: Machine calculations of compressible laminar boundary layers. A.I.A.A. J.3, 639–647 (1965).
Schlichting, H.: Boundary layer theory. New York: McGraw-Hill 1979.
Davis, T., Walker, G.: On solution of the compressible laminar boundary layer equations and their behaviour near separation. J. Fluid Mech.80, 279–292 (1977).
Venkatachala, B. J., Nath, G.: Nonsimilar laminar incompressible boundary layers with vectored mass transfer. Proc. Indian Acad. Sci. (Eng. Sci.)3, 129–142 (1980).
Krishnaswamy, R.: A numerical study of laminar compressible boundary layer problems. Ph. D. Thesis, Dept. of Applied Mathematics, Indian Institute of Sci., 1980.
Inger, G. R., Swean, T. F.: Vectored injection into laminar boundary layers with heat transfer. A.I.A.A. J.13, 616–622 (1975).
Kumar, P., Narayanan, P. S., Sarbeswar, R.: Laminar boundary layers with vectored mass transfer. Int. J. Eng. Sci.25, 1503–1509 (1987).
Chen, T. S., Sparrow, E. M.: Flow and heat transfer over a flat plate with uniformly distributed vectored surface mass transfer. Trans. A.S.M.E., J. Heat Transfer98, 674–676 (1976).
Smith, F. T., Sewartson, K.: On slot injection into a supersonic laminar boundary layer. Proc. Roy. Soc. London Ser.A332, 1–22 (1973).
Smith, F. T., Stewartson, K.: Plate injection into a separated supersonic boundary layer. J. Fluid Mech.38, 143–159 (1973).
Werle, M. J.: Supersonic laminar boundary-layer separation by slot injection. A.I.A.A. J.17, 160–167 (1979).
Napolitano, M.: Numerical study of strong slot injection into a supersonic laminar boundary layer. A.I.A.A. J.18, 72–77 (1980).
Napolitano, M., Messick, R. E.: On strong slot injection into a subsonic laminar boundary layer. Comput. Fluids8, 199–212 (1980).
Riley, N.: Non-uniform slot injection into a laminar boundary layer. J. Eng. Math.15, 299–314 (1981).
Kenworthy, M., Schetz, J. A.: Experimental study of slot injection into a supersonic stream. A.I.A.A. J.11, 585–586 (1973).
Schetz, J. A., Van Overeem, J.: Skin friction reduction by injection through combinations of slots and porous sections. A.I.A.A. J.13, 971–972 (1975).
Kwok, F. T., Andrew, P. L., Ng, W. F., Schetz, J. A.: Experimental investigation of a supersonic shear layer with slot injection of Helium. A.I.A.A. J.29, 1426–1435 (1991).
Minkowycz, W. J., Sparrow, E. M., Schneider, G. E., Pletcher, R. H.: Handbook of numerical heat transfer, p. 140. New York: Wiley 1988.
Wortman, A., Ziegler, H., Soo-Hoo, G.: Convective heat transfer at general three-dimensional stagnation point. Int. J. Heat Mass Transfer14, 149–152 (1971).
Shih-I, P.: Introduction to the theory of compressible flow. New York: Van Nostrand 1958.
Carrier, C. F., Pearson, C. E.: Partial differential equations theory and technique, p. 136, New York: Academic Press 1976.
Inouye, K., Tate, A.: Finite difference version of quasilinearization applied to boundary-layer equations. A.I.A.A. J.12, 558–560 (1974).
Varga, R. S.: Matrix iterative analysis, p. 194. New Jersey: Prentice-Hall 1962.
Schmidt, E., Wenner, L.: Wärmeabgabe über den Umfang eines angeblasenen geheizten Zylinders. NACA TM 1050, 1943.
Vasantha, R., Nath, G.: Unsteady nonsimilar laminar compressible boundary-layer flows over two-dimensional and axisymmetric bodies. Acta Mech.57, 215–231 (1985).
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Roy, S., Nath, G. Non-uniform slot injection (suction) or wall enthalpy into a steady nonsimilar compressible laminar boundary layer. Acta Mechanica 103, 45–61 (1994). https://doi.org/10.1007/BF01180217
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DOI: https://doi.org/10.1007/BF01180217