Skip to main content
SpringerLink
Log in

On the ‘computation of two- and three-dimensional steady transonic flows by relaxation methods

  • Conference paper
  • First Online:
Progress in Numerical Fluid Dynamics

Part of the book series: Lecture Notes in Physics ((LNP,volume 41))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Nieuwland, G. Y., “Transonic Potential Flow Around a Family of Quasi-Elliptical Aerofoil Sections,” National Lucht-en-Ruimteraartlaboratorium (NLR) Technical Report T. 172 (Netherlands), 1967.

    Google Scholar 

  2. Korn, D. G., “Computation of Shock-Free Transonic Flows for Airfoil Design,” Courant Institute of Math. Sci., NYO-1480-125, Oct. 1969.

    Google Scholar 

  3. Richtmyer, R. D., and Morton, K. W., Difference Methods for Initial-Value Problems, Interscience Publishers, Second ed., 1967.

    Google Scholar 

  4. Magnus, R., Gallaher, W., and Yoshihara, H., “Inviscid Supercritical Airfoil Theory,” Transonic Aerodynamics, AGARD Conference Proceedings No. 35, Sept. 1968, pp. 3–1, 3–3.

    Google Scholar 

  5. Magnus, R., and Yoshihara, H., “Inviscid Transonic Flow Over Airfoils,” AIAA Paper 70-47, Jan. 1970.

    Google Scholar 

  6. Murman, E. M., “Computational Methods for Inviscid Transonic Flows With Embedded Shock Waves,” Numerical Methods in Fluid Dynamics, AGARD Lecture Series No. 48, 1972, pp. 13-1, 13–34.

    Google Scholar 

  7. Yoshihara, H., “A Survey of Computational Methods for 2D and 3D Transonic Flows With Shocks,” Advances in Numerical Fluid Dynamics, AGARD Lecture Series No. 64, 1973, pp. 6-1, 6–35

    Google Scholar 

  8. Nieuwland, G. Y., and Spee, B. M., “Transonic Airfoils: Recent Developments in Theory, Experiment, and Design,” Annual Review of Fluid Mechanics, Annual Reviews, Inc., Vol. 5, 1973, pp. 119–150.

    Google Scholar 

  9. Emmons, H. W., “The Numerical Solution of Compressible Fluid Flow Problems,” NAGA TN 932, 1944.

    Google Scholar 

  10. Emmons, H. W., “The Theoretical Flow of a Frictionless, Adiabatic, Perfect Gas Inside of a Two-Dimensional Hypersonic Nozzle,” NAGA TN 1003, 1946.

    Google Scholar 

  11. Emmons, H. W., “Flow of a Compressible Fluid Past a Symmetrical Airfoil in a Wind Tunnel and in Free Air,” NAGA IN 1746, 1948.

    Google Scholar 

  12. Murman, E. M., and Cole, J. D., “Calculation of Plane Steady Transonic Flows,” AIAA Journal, Vol. 9, No. 1, 1971, pp. 114–121.

    Google Scholar 

  13. Steger, J. L., and Lomax, H., “Transonic Flow About Two-Dimensional Airfoils by Relaxation Procedures,” AIAA Journal, Vol. 10, No. 1, 1972, pp. 49–54.

    Google Scholar 

  14. Garabedian, P. R., and Korn, D. G., “Analysis of Transonic Airfoils,” Comm. Pure Appl. Math., Vol. XXIV, 1971, pp. 841–851.

    Google Scholar 

  15. Jameson, A., “Transonic Flow Calculations for Airfoils and Bodies of Revolution,” Grumman Aerospace Corp. Report 390-71-1, 1971.

    Google Scholar 

  16. Murman, E. M., “Analysis of Embedded Shock Waves Calculated by Relaxation Methods,” Proceedings of AIAA Computational Fluid Dynamics Conference, Palm Springs, Ca., July 1973, pp. 27–40.

    Google Scholar 

  17. Jameson, A., “Iterative Solution of Transonic Flows Over Airfoils and Wings, Including Flows at Mach 1,” to appear in Comm. Pure Appl. Math.

    Google Scholar 

  18. Cole, J. D., and Messiter, A. F., “Expansion Procedures and Similarity Laws for Transonic Flow,” Zeit. ang. Math. u. Physik., Vol. 8, No. 1, 1957, pp. 1–25.

    Google Scholar 

  19. Cole, J. D., “Twenty Years, of Transonic Flow,” Boeing Scientific Research Laboratories Document D1-82-0878, July 1969.

    Google Scholar 

  20. Ashley, Holt, and Landahl, Martin, Aerodynamics of Wings and Bodies, Addison-Wesley Publishing Co., Inc., 1965.

    Google Scholar 

  21. Lax, Peter D., “Weak Solutions of Nonlinear Hyperbolic Equations and Their Numerical Computation,” Comm. Pure Appl. Math., Vol. VII, No. 1, 1954, pp. 159–193.

    Google Scholar 

  22. Oswatitsch, K., Gas Dynamics, Academic Press, 1956.

    Google Scholar 

  23. Nonweiler, T. R. F., “The Sonic Flow About Some Symmetric Half-Bodies,” J. Fluid Mech., Vol. 4, Pt. 2, 1958, pp. 140–148.

    Google Scholar 

  24. Oswatitsch, K., and Zierep, J., “Das Problem des senkrechten Stosses an einer gekrummten wand,” Zeit. ang. Math. u. Mech., Vol. 40, Supplement, T143–144, 1960.

    Google Scholar 

  25. Krupp, J. A., “The Numerical Calculation of Plane Steady Transonic Flows Past Thin Lifting Airfoils," Boeing Scientific Research Laboratories Report D180-12958-1, June 1971.

    Google Scholar 

  26. Krupp, J. A., and Murman, E. M., “The Numerical Calculation of Steady Transonic Flows Past Thin Lifting Airfoils and Slender Bodies,” AIAA Paper 71-566, June 1971.

    Google Scholar 

  27. Murman, E. M., and Krupp, J. A., “Solution of the Transonic Potential Equation Using a Mixed Finite Difference System,” Lecture Notes in Physics, Vol. 8, Springer-Verlag, 1971, pp. 199–206.

    Google Scholar 

  28. Yoshihara, Y., “A Survey of Computational Methods for 2D and 3D Transonic Flows With Shocks,” GDCA-ERR-1726, Convair Aerosp ce Div., General Dynamics, Dec. 1972.

    Google Scholar 

  29. Magnus, R. M., “The Direct Comparison of the Relaxation Method and the Pseudo-Unsteady Finite Difference Method for Calculating Steady Planar Transonic Flow,“ TN-73-SP03, General Dynamics-Convair Aerospace Div., 1973.

    Google Scholar 

  30. Klunker, E. B., “Contributions to Methods for Calculating the Flow About Thin Lifting Wings at Transonic Speeds — Analytical Expression for the Far Field,” NASA TN D-6530, 1971.

    Google Scholar 

  31. Ballhaus, W. F., and Bailey, F. R., “Numerical Calculation of Transonic Flow About Swept Wings,” AIAA Paper 72-677, June 1972.

    Google Scholar 

  32. Bailey, F. R., and Ballhaus, W. F., “Relaxation Methods for Transonic Flow About Wing-Cylinder Combinations and Lifting Swept Wings,” Lecture Notes in Physics, Vol. 19, Springer-Verlag, 1972, pp. 2–9.

    Google Scholar 

  33. Steger, J. L., and Baldwin, B. S., “Shock Waves and Drag in the Numerical Calculation of Isentropic Transonic Flow,” NASA TN D-6997, 1972.

    Google Scholar 

  34. Bauer, E., Garabedian, P., and Korn, D., “Supercritical Wing Sections,” Lecture Notes in Economics and Mathematical Systems, Vol. 66, Springer-Verlag, 1972.

    Google Scholar 

  35. Sells, C., “Plane Subcritical Flow Past a Lifting Airfoil,” Proc. Roy. Soc. (London), Vol. 308A, 1968, pp. 377–401.

    Google Scholar 

  36. Thwaites, B., Incompressible Aerodynamics, Oxford Press, 1960.

    Google Scholar 

  37. South, J. C., and Jameson, A., “Relaxation Solutions for Inviscid Axisymmetric Transonic Flow Over Blunt or Pointed Bodies,” Proceedings AIAA Computational Fluid Dynamics Conference, Palm Springs, Ca., 1973, pp. 8–17.

    Google Scholar 

  38. Jameson, A., “Numerical Calculation of the Three Dimensional Transonic Flow Over a Yawed Wing,” Proceedings AIAA Computational Fluid Dynamics Conference, Palm Springs, Ca., 1973, pp. 18–26.

    Google Scholar 

  39. Garabedian, P. R., “Estimation of the Relaxations Factor for Small Mesh Size,” Math. Tables Aids Comp., Vol. 10, 1956, pp. 183–185.

    Google Scholar 

  40. Kacpryzynski, J., Ohman, L., Garabedian, P., and Korn, D., “Analysis of Flow Past a Shockless Airfoil in Design and Off-Design Conditions,” Paper presented at AIAA 4th Fluid and Plasma Dynamics Conference, June 21–23, 1971, Palo Alto, Ca. (see NRC Aeronautical Report LR-54 (Canada)), June 1972.

    Google Scholar 

  41. Lock, R. C., “Test Cases for Numerical Methods in Two-Dimensional Transonic Flows,” AGARD Report No. 575, Nov. 1970.

    Google Scholar 

  42. Bailey, F. R., “Numerical Calculation of Transonic Flow About Slender Bodies of Revolution,” NASA IN D-6582, 1971.

    Google Scholar 

  43. Kacprzynski, J. J., “Wind Tunnel Tests of a Boerstoel Shockless Symmetrical Airfoil-0.11-0.75-1.375," National Aircraft Establishment (NAE) Project Report 5x5/0061 (Canada), July 1972.

    Google Scholar 

  44. Boerstoel, J. W., “A Survey of Symmetrical Transonic Potential Flows About Quasi-Elliptical Airfoil Sections," National Lucht-en-Ruimtevaartlaboratorium (NLR) Technical Report T.136 (Netherlands), Jan. 1967.

    Google Scholar 

  45. Osborne, J., “A Selection of Measured Transonic Flow Pressure Distributions for the NACA 0012 Aerofoil: Provisional Data From an NPL Tunnel,” Aerodynamics Dept., Royal Aircraft Establishment, June 1971.

    Google Scholar 

  46. Melnik, R. E., and Ives, D. C., “On Viscous and Wind-Tunnel Wall Effects in Transonic Flows Over Airfoils,” AIAA Paper 73-660, July 1973.

    Google Scholar 

  47. Kacpryzynski, J., “A Second Series of Wind Tunnel Tests of the Shockless Lifting Airfoil No. 1,” Report 5x5/0062 NRC (Canada), June 1972.

    Google Scholar 

  48. Garner, H. C. et al., “Subsonic Wind Tunnel Corrections," AGARDograph 109, Oct. 1966.

    Google Scholar 

  49. Baldwin, B., Turner, J., and Knechtel, E., “Wall Interference in Wind Tunnels With Slotted and Porous Boundaries at Subsonic Speeds,” NACA TN 3176, 1954.

    Google Scholar 

  50. Taylor, R. A., and McDevitt, J. B., “Pressure Distributions at Transonic Speeds for Parabolic-Arc Bodies of Revolution Having Fineness Ratios of 10, 12, and 14,” NACA TN 4234, 1958.

    Google Scholar 

  51. Murman, E. M., “Computation of Wall Effects in Ventilated Transonic Wind Tunnels,” AIAA Paper 72-1007, Sept. 1972.

    Google Scholar 

  52. Isom, M. P., and Caradonna, F. X., “Subsonic and Transonic Potential Flow Over Helicopter Rotor Blades,” AIAA Paper 72-39, Jan. 1972.

    Google Scholar 

  53. Ballhaus, W. F., and Caradonna, F. X., “The Effect of Planform Shape on the Transonic Flow Past Rotor Tips,” Aerodynamics of Rotary Wings, AGARD Conference Proceedings No. 111, Paper 17, Sept. 1972.

    Google Scholar 

  54. Bailey, F. R., and Steger, J. L., “Relaxation Techniques for Three Dimensional Transonic Flow About Wings,” AIAA Paper 72-189, Jan. 1972.

    Google Scholar 

  55. Newman, P. A., and Kunker, E. B., “Computation of Transonic Flow About Finite Lifting Wings,” AIAA Journal, Vol. 10, No. 7, July 1972, pp. 971–973.

    Google Scholar 

  56. Cahill, J. F., and Stanewsky, E., “Wind Tunnel Tests of a Large-Chord, Swept-Panel Model to Investigate Shock-Induced Separation Phenomena,” Air Force Flight Dynamics Lab. Report AFFDL-TR-69-78, Oct. 1969.

    Google Scholar 

  57. Saaris, G. R., and Rubbert, P. E., “Review and Evaluation of a Three Dimensional Lifting Potential Flow Computational Method for Arbitrary Configurations,” AIAA Paper 72-188, Jan. 1972.

    Google Scholar 

  58. Lomax, H., Bailey, F. R., and Ballhaus, W. F., “On the Numerical Simulation of Three-Dimensional Transonic Flow With Application to the C-141 Wing,” NASA TN D-6933, 1973.

    Google Scholar 

  59. Cahill, J. F., Teron, S. L., and Hofstetter, W. R., “Feasibility of Testing a Large-Chord, Swept-Panel Model to Determine Wing Shock Location at Flight Reynolds Number,” AGARD Proc. 83, Paper 17, April 1971.

    Google Scholar 

  60. Liepmann, H. W., and Roshko, A., Elements of Gas Dynamics, John Wiley and Sons, New York, 1967.

    Google Scholar 

  61. Jones, R. T., “Reduction of Wave Drag by Antisymmetric Arrangement of Wings and Bodies,” AIAA Journal, Vol. 9, 1971, pp. 114–121.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Ames Research Center NASA, Moffett Field, 94035, Calif., USA

    F. R. Bailey

Authors
  1. F. R. Bailey
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

H. J. Wirz

Rights and permissions

Reprints and permissions

Copyright information

© 1975 Springer Verlag

About this paper

Cite this paper

Bailey, F.R. (1975). On the ‘computation of two- and three-dimensional steady transonic flows by relaxation methods. In: Wirz, H.J. (eds) Progress in Numerical Fluid Dynamics. Lecture Notes in Physics, vol 41. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-07408-2_1

Download citation

  • DOI: https://doi.org/10.1007/3-540-07408-2_1

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07408-3

  • Online ISBN: 978-3-540-37926-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation