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Hypersonic Gas Dynamics of Slender Bodies

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Abstract

This article is devoted to a study of current work on theoretical gas dynamics associated with hypersonic flow past slender bodies. From the viewpoint of nonlinear fluid mechanics, the problems are attractive in that they yield to asymptotic analysis. The many flow regimes and distinct layers, on the other hand, make challenging studies of singular perturbations. The relevance of the present study to the engineering problems of hypersonic flight may be found in the discussions in (1–5).

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References

  1. G. G. Chernyi, Introduction to Hypersonic Flow, Fizmatgiz, Moscow ( 1959 ); English translation by R. F. Probstein, Academic Press, New York (1961).

    Google Scholar 

  2. C. Gazley, Jr., “Atmospheric Entry,” in: P-2052 Handbook of Astronautical Engineering, McGraw-Hill Book Co., New York (1961).

    Google Scholar 

  3. W. H. T. Loh, Dynamics and Thermodynamics of Re-Entry, Prentice-Hall, Englewood Cliffs, New Jersey (1962).

    Google Scholar 

  4. F. S. Nyland, “Hypersonic Turning with Constant Bank Angle Control,” The RAND Corporation, RM-4483-PR (March 1965).

    Google Scholar 

  5. H. Hidalgo, R. Vaglio-Laurin, and R. G. Finke, “High Altitude on Lifting Re-Entry Performance,” paper presented at the 18th International Astronautical Congress, Belgrade, Yugoslavia, September 24–30, 1967.

    Google Scholar 

  6. H. K. Cheng, “Notes on Hypersonic Flow Past Slender Bodies,” Univ. Southern California Dept. Aerospace Eng. Report USCAE 108 (1969).

    Google Scholar 

  7. W. D. Hayes and R. F. Probstein, Hypersonic Flow Theory, Academic Press, New York, 1st ed. (1959), 2nd ed. (1966).

    MATH  Google Scholar 

  8. H. K. Cheng, G. J. Hall, T. C. Golian, and A. Hertzberg, “Boundary Layer Displacement and Leading-Edge Bluntness Effects in High Temperature Hypersonic Flow,” Aerospace Sci. 28, 353–381 (1961).

    MATH  Google Scholar 

  9. V. V. Sychev, “On the Theory of Hypersonic Gas Flow with a Power-Law Shock Wave,” I Meckhan. Prikl. Matem. 24, 756–764 (1960).

    MATH  Google Scholar 

  10. J. K. Yakura, “Theory of Entropy Layers and Nose Bluntness in Hypersonic Flow,” in: Hypersonic Flow Research, F. R. Riddell, ed., Academic Press, New York (1962), pp. 421–470.

    Google Scholar 

  11. N. C. Freeman, “Newtonian Theory of Hypersonic Flow at Large Distances from Bluff Axially Symmetric Bodies,” in: Hypersonic Flow Research, F. R. Riddel, ed., Academic Press, New York (1962), pp. 345–377.

    Google Scholar 

  12. H. K. Cheng, “Hypersonic Flow with Combined Leading-Edge Bluntness and Boundary-Layer Displacement Effect,” Cornell Aero. Lab. Report AF-1285-A-4 (1960).

    Google Scholar 

  13. R. Vaglio-Laurin, “Asymptotic Flow Pattern of a Hypersonic Body,” Dept. Aero. Eng. and Appl. Mech., Poly. Inst. Brooklyn, PIBAL Report 805 (1964).

    Google Scholar 

  14. J. P. Giraud, D. Vallee, and R. Zolver, “Bluntness Effects in Hypersonic Small Disturbance Theory,” in: Basic Developments in Fluid Dynamics, Vol. 1, M. Holt, ed., Academic Press, New York (1965), pp. 127–247.

    Google Scholar 

  15. J. P. Guiraud, “Asymptotic Theory in Hypersonic Flow,” in: Fundamental Phenomena in Hypersonic Flow, G. J. Hall, ed., Cornell University Press, Ithaca, New York (1965), pp. 70–84.

    Google Scholar 

  16. M. D. Van Dyke, Perturbation Methods in Fluid Mechanics, Academic Press, New York (1964).

    MATH  Google Scholar 

  17. A. F. Messiter, “Asymptotic Theory of Inviscid Hypersonic Flow at Large Distance from a Blunt-Nosed Body,” Univ. Mich. Inst. Sci. and Tech. BOMIRAC Report 463-81-1 (1964).

    Google Scholar 

  18. H. Mirels, “Hypersonic Flow over Slender Bodies Associated with Power-Law Shocks,” in: Advances in Applied Mechanics, Vol. 7, Academic Press, New York (1962), pp. 1–54, 317–319.

    Google Scholar 

  19. N. C. Freeman, “Asymptotic Solutions in Hypersonic Flow, An Approach to Second Order Solutions of Hypersonic Small-Disturbance Theory,” in: Research Frontier in Fluid Dynamics, R. J. Seeger and G. Temple, eds., Interscience Publishers, New York (1965), pp. 284–307.

    Google Scholar 

  20. K. Stewartson and B. W. Thompson, “On One-dimensional Unsteady Flow at Infinite Mach Number,” Proc. Roy. Soc. London, Ser. A. 304, 255–273 (1968).

    Article  MATH  Google Scholar 

  21. H. K. Cheng and J. Kirsch, “Nonsimilar Structure of Blast Wave with an Expanding Interface, and Application to Hypersonic Flow,” paper read at the 18th International Astronautical Congress, Belgrade, Yugoslavia, September 25–29, 1967.

    Google Scholar 

  22. J. D. Cole, “Newtonian Flow Theory for Slender Bodies,” J. Aeron. Sci. 24, 448–455 (1957).

    MATH  Google Scholar 

  23. A. Henderson, R. D. Watson, and R. D. Wagner, “Fluid Dynamic Studies to M = 41 in Helium,” AIAA J. 4 (12) 2117–2124 (1966).

    Article  Google Scholar 

  24. M. D. Ladyzhenskii, “The Hypersonic Area Rule,” Inzh. Zh. 1 (1) 159–196 (1961); AIAA J. 1, 2696–2698 (1963).

    Google Scholar 

  25. V. M. Krasovskii, “Experimental Study of Hypersonic Helium Flow over Blunt-Nosed Bodies,” Inzh. Zh. 5 (2), 249–253 (1965).

    MathSciNet  Google Scholar 

  26. J. D. Cole, and J. Aroesty, “The Blowhard Problem—Inviscid Flows with Surface Injection,” The RAND Corporation, RM-5196-ARPA (1967); to be published in the International Journal of Heat and Mass Transfer.

    Google Scholar 

  27. M. Holt and T. D. Taylor, “High Speed Flow Past a Cone with Large Wall Injection Velocities,” paper presented at the 18th International Astronautical Congress, Belgrade, Yugoslavia, September 24–30, 1967.

    Google Scholar 

  28. R. A. Hartunian and D. J. Spencer, “Experimental Results for Massive Blowing Studies,” AIAA J. 5, 1397 (1967).

    Article  Google Scholar 

  29. K. Stewartson, “Some Recent Developments in Boundary Layer Theory,” paper presented at the 7th Symposium on Advanced Problems and Methods in Fluid Mechanics, Gdansk, Poland, September 1965.

    Google Scholar 

  30. A. Miele, ed., Theory of Optimum Aerodynamic Shapes, Academic Press, New York (1965).

    MATH  Google Scholar 

  31. A. L. Gonor, “On the Form of Three-Dimensional Bodies of Minimum Drag at Hypersonic Speeds,” Prikl. Matern, i Mekhan. 27 (1) (1963).

    Google Scholar 

  32. G. L. Maikapar, “On the Wave Drag of Non-Axisymmetric Bodies in Supersonic Flow,” Prikl. Matern, i Mekhan. 23 (2) (1959).

    Google Scholar 

  33. G. L. Maikapar, “On the Form of a Supersonic Airplane,” Tr. Tsent. Aero-Gidrodin. Inst. Mosk. (TsAGI), No. 841 (1961).

    Google Scholar 

  34. G. G. Chernyi, “On the Analysis of Bodies of Minimum Drag at Hypersonic Speed,” Prikl. Matern, i Mekhan. 28 (2), 387–389 (1964).

    MathSciNet  Google Scholar 

  35. A. Miele, “Optimum Transversal Contour of a Lifting Body at Hypersonic Speeds,” paper presented at the 18th International Astronautical Congress, Belgrade, Yygoslavia, September 24–30, 1967.

    Google Scholar 

  36. J. D. Cole and T. F. Zien, “A Class of Three-Dimensional Optimum Hypersonic Wings,” AIAA paper 68 - 158 (1968).

    Google Scholar 

  37. K. Stewartson, The Theory of Laminar Boundary Layers in Compressible Fluids, Oxford University Press (Clarendon) (1964), pp. 161–183.

    Google Scholar 

  38. F. K. Moore, “Hypersonic Boundary Layer,” in: Theory of Laminar Flows, F. K. Moore, ed., Princeton University Press, Princeton, New Jersey (1963).

    Google Scholar 

  39. N. C. Feeman and S. H. Lam, Princeton University, Dept. Aero. Eng. Reports 468 and 471 (1959).

    Google Scholar 

  40. L. Lees, “Influence of the Leading-Edge Shock Wave on the Laminar Boundary Layer at Hypersonic Speeds,” J. Aeron. Sci. 23(6), 594–600, 612 (1956).

    Google Scholar 

  41. H. Oguchi, “First-Order Approach to a Strong Interaction Problem in Hypersonic Flow over an Insulated Flat Plate,” Univ. Tokyo, Aero. Res. Inst. Report 330 (1958).

    Google Scholar 

  42. N. S. Matveeva and V. V. Sychev, “On the Theory of Strong Interaction of the Boundary Layer with an Inviscid Hypersonic Flow,” Prikl. Matern, i Mekhan. 29 (4), 644–657 (1965).

    MathSciNet  Google Scholar 

  43. W. B. Bush, “Hypersonic Strong-Interaction Similarity Solutions for Flow Past a Flat Plate,” J. Fluid Mech. 25 (1), 51–64 (1966).

    Article  MathSciNet  MATH  Google Scholar 

  44. J. D. Cole, Perturbation Methods in Applied Mathematics, Random House ( Blaisdell ), New York (1968).

    Google Scholar 

  45. R. S. Lee and H. K. Cheng, “On the Higher-Order Asymptotic Theory of Hypersonic Boundary Layers on Slender Bodies in the Strong-Interaction Regime,” paper read at the AGARD Seminar on Numerical Methods for Viscous Flows, Teddington, England, September 18–21, 1967; to be submitted for publication.

    Google Scholar 

  46. W. B. Bush and A. K. Cross, “Hypersonic Weak-Interaction Similarity Solutions for Flow Past a Flat Plate,” J. Fluid Mech. 29 (2), 349–359 (1967).

    Article  MATH  Google Scholar 

  47. Y. H. Kuo, J. Aero. Sci. 23, 125 (1956).

    MathSciNet  MATH  Google Scholar 

  48. T. Kubota and D. R. S. Ko, “A Second-Order Weak Interaction Expansion for Moderately Hypersonic Flow Past a Flat Plate,” AIAA J. 5 (10) (1967).

    Google Scholar 

  49. R. S. Lee and H. K. Cheng, “On the Outer-Edge Problem of a Hypersonic Boundary Layer” (accepted for publication in the J. Fluid Mech.).

    Google Scholar 

  50. M. Yasuhara, “Axisymmetric Viscous Flow Past a Very Slender Body of Revolution,” J. Aerospace Sci., 29, 667–679 (1962).

    MATH  Google Scholar 

  51. K. Stewartson, “Viscous Hypersonic Flow Past a Slender Cone,” Phys. Fluids 7 (5), 667–675 (1964).

    Article  MathSciNet  MATH  Google Scholar 

  52. J. W. Ellinwood and H. Mirels, “Axisymmetric Hypersonic Flow with Strong Viscous Interaction,” Aerospace Corp. Report TR 0 158(3240-10)-1 (1967).

    Google Scholar 

  53. H. Mirels and J. W. Ellinwood, “Hypersonic Viscous Interaction Theory for Slender Axisymmetric Bodies,” AIAA paper 68 - 1 (1968).

    Google Scholar 

  54. J. T. Shen and T. F. Sun, “Effect of Transverse Curvature on Axisymmetric Compressible Laminar Boundary Layer, ” (in Chinese) ACTA Mechanica Sinica 9 (2), 150–171 (1966).

    MathSciNet  Google Scholar 

  55. A. K. Cross, private communication.

    Google Scholar 

  56. M. D. Ladyzhenskii, “Hypersonic Viscous Flow over Slender Bodies,” Prikl. i Matem. Mekhan. 27 (5), 667–675 (1963).

    Google Scholar 

  57. H. K. Cheng, “The Shock-Layer Concept and Three-Dimensional Hypersonic Boundary Layer,” Cornell Aero. Lab. Report AF-1285-A-3 (1960).

    Google Scholar 

  58. M. B. Glauert, and M. J. Lighthill, Proc. Roy. Soc. A230, 188 (1950).

    MathSciNet  Google Scholar 

  59. K. Stewartson, “The Asymptotic Boundary Layer on a Circular Cylinder in Axial Incompressible Flow,” Quart. Appl. Math. 13, 113–122 (1955).

    MathSciNet  MATH  Google Scholar 

  60. J. M. Solomon, U. S. Navy Ord. Lab., White Oak, Maryland NOLTR 66 - 225 (1967).

    Google Scholar 

  61. C. C. Horstman, and M. I. Kussoy, “Hypersonic Viscous Interaction on Slender Cones,” AIAA paper 68 - 2 (1968).

    Google Scholar 

  62. W. B. Bush, “Hypersonic Strong-Interaction Similarity Solutions for Flow Past a Very Slender Axisymmetric Body,” RAND Corp. Report RM-5699 (1968).

    Google Scholar 

  63. C. F. Dewey, Jr., AIAA J. 1, 20–33 (1963).

    Article  MATH  Google Scholar 

  64. M. Kussoy, “Hypersonic Viscous Drag on Cones in Rarefied Flow,” NASA TND 4036 (1967).

    Google Scholar 

  65. J. D. Whitfield and B. J. Griffith, AIAA J. 3, 1165 (1965).

    Article  Google Scholar 

  66. H. T. Iida, “On the Three-Dimensional Hypersonic Needle Problem in the Viscous Strong-Interaction Regime,” Univ. Southern California Dept. Aerospace Eng. Thesis (1969).

    Google Scholar 

  67. G. B. Whitham, “The Flow Pattern of Supersonic Projectile,” Comm. Pure Appl. Math 5, 301–348 (1952).

    Article  MathSciNet  MATH  Google Scholar 

  68. M. J. Lighthill, “A Technique for Rendering Approximate Solutions to Physical Problems Uniformly Valid,” Phil. Mag. 40 (7), 1179–1201 (1949).

    MathSciNet  MATH  Google Scholar 

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© 1969 Plenum Press, New York

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Cheng, H.K. (1969). Hypersonic Gas Dynamics of Slender Bodies. In: Loh, W.H.T. (eds) Modern Developments in Gas Dynamics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-8624-1_4

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  • DOI: https://doi.org/10.1007/978-1-4615-8624-1_4

  • Publisher Name: Springer, Boston, MA

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