# Dissociation effects in hypersonic flow past a circular cone at an angle of attack

- 44 Downloads

## Abstract

The analytical solution to the steady, compressible, non-viscous, inviscid hypersonic flow past a circular cone at an angle of incidence, with an attached Shockwave, in the presence of dissociation of air in the shock layer, has been obtained here under the assumption of thermal equilibrium. Expression for the velocity, pressure, temperature, density, velocity of air, Mach number, pressure, drag and lift coefficients have been obtained both in the shocklayer outside the vortical layer and on the surface of the cone inside the vortical layer.

## Keywords

Mach Number Supersonic Flow Lift Coefficient Shock Layer Hypersonic Flow## Symbols

- R,
*θ, ϕ* spherical polar co-ordinates

*u, v, w*velocity components

*p*pressure

*ρ*density

- T
absolute temperature

*a*velocity of sound

*a*semi-vertical angle of the cone

*ψ*shock wave angle

*β*angle of attack

*q*resultant velocity

- a
_{∞} free stream velocity

- M
Mach number

- M
_{∞} free-stream Mach number

- C
maximum speed of air under adiabatic conditions

- u
_{0} value of

*u*on the surface of the cone in the case of zero angle of incidence- S
_{0} constant reference value of the specific entropy

- C
_{D} drag coefficient

- C
_{L} lift coefficient

- C
_{X} axial pressure force coefficient

- C
_{N} normal pressure force coefficient

*h*specific enthalpy

- S
specific entropy

*v*ratio of specific heats

*m*molecular weight of air

*k*density ratio in the case of zero angle of incidence (taken as 0 · 1)

- λ
_{1}...λ_{4} defined by equations (19) to (22)

- U
_{1}..., V_{1}..., R_{1},..., Q_{1}..., S_{1}..., etc functions of θ

- C
_{v} specific heat at constant volume

## Subscripts

- 1, 2
conditions ahead of the shock and behind it respectively

- Bar (-)
condition in the shock layer (in the presence of dissociation) in the case of zero angle of incidence

## Preview

Unable to display preview. Download preview PDF.

## References

- 1.Taylor, G. I. and Maccoll, J. W. “The air pressure on a cone moving at high speed,”
*Proc. Roy. Soc., London*, Series A, 1933,**139**, 278–311.CrossRefGoogle Scholar - 2.Maccoll, J. W... “The conical shock wave formed by a cone moving at high speed,”
*Ibid.*, Series A, 1937,**159**, 451–72.Google Scholar - 3.Von Kármán Th. and Moore, N. B. “Resistance of slender bodies moving with supersonic velocities with special reference to projectiles,”
*Trans. Amer. Soc. Mech. Eng.*, 1932,**54**(23), 303–10.Google Scholar - 4.Hord, R.A. .. “An approximate solution for axially symmetric flow over a cone with an attached shock wave,”
*N.A.C.A. Tech. Note No.*3485, 1955.Google Scholar - 5.Nath, G... “Hypersonic flow past unyawed circular cones,”
*J.I.M.S.*1964,**28**(1), 7–24.MathSciNetGoogle Scholar - 6.Zienkiewicz, H. K... “Flow about cones at very high speeds,”
*The Aeronautical Quarterly*, Nov. 1957,**8**, Part 4, 384–94.MathSciNetGoogle Scholar - 7.Nath, G... “Approximate solution for unyawed circular cones at hyper- sonic speeds,”
*Proc. Ind. Acad. Sci.*, 1964,**59 A**(4), 207–26.Google Scholar - 8.—.. “Effects of dissociation or ionization on hypersonic flow past a cone,”
*Ibid.*, 1965,**62 A**(2), 112–24.Google Scholar - 9.Stone, A. H... “On supersonic flow past a slightly yawing cone,”
*Journal of Math. and Phys.*, April 1948,**27**(1), 67–81.MATHGoogle Scholar - 10.—.. “On supersonic flow past a slightly yawing cone—II,”
*Ibid.*, Jan. 1952,**30**(4), 200–13.MATHGoogle Scholar - 11.Young, G. B.W. and Siska, C. P. “Supersonic flow around cones at large yaw,”
*J. Aero Sci.*, Feb. 1952,**19**(2), 111–19.MathSciNetGoogle Scholar - 12.Staff of the Computing Section, Centre of Analysis (Under the direction of Z. Kopal) “Tables of supersonic flow around cones,”
*Tech. Report No 1*M.I.T., 1947.Google Scholar - 13.- .. “Tables of supersonic flow around yawing cones,”
*Tech. Report No.*3, M.I.T., 1947.Google Scholar - 14.- ... “Tables of supersonic flow around cones of large yaw,”
*Tech. Report No. 5*, M.I.T., 1949.Google Scholar - 15.Ferri, Antonio ... “Supersonic flow around circular cones at angles of attack,”
*N.A.C.A. Report No.*1045, 1951.Google Scholar - 16.Willet, Joseph, E... “Supersonic flow at the surface of a circular cone at angle of attack,”
*J. Aero Space Sci.*, Dec. 1960,**27**(12), 907–12, 920.Google Scholar - 17.Hilsenrath, J. and Beckett, C.W. “Thermodynamic properties of Argon-free air to 15,000° K,” Arnold Engineering Development Centre, T.N.-56-12, Sept. 1956.Google Scholar
- 18.Roberts, Richard, C. and Riley, James D. “A guide to the use of the
**M.I.T.**Cone tables,”*J. Aero. Sci.*, 1954,**21**, 336–42.MATHMathSciNetGoogle Scholar - 19.Willet, Joseph E. .. “Vortical layer effects on the supersonic flow around circular cones at large angle of attack,”
*Mcdonnell Aircraft Corporation, Report No.*6765, March 1959.Google Scholar - 20.Cheng, Hsien, K. .. “Hypersonic shock layer theory of yawed cone and other, three-dimensional pointed bodies,”
*W.A.D.C, T.N.*59–335, Oct. 1959.Google Scholar - 21.Moore, Franklin K. .. “Laminar boundary layer on a circular cone in supersonic flow at a small angle of attack,”
*N.A.C.A., T.N.*2521, Oct. 1951.Google Scholar - 22.Halt, Maurice and Blackie, John “Experiments on circular cones at yaw in supersonic flow,”
*J. Aero. Sci.*, Oct., 1956,**23**(10), 931.MathSciNetGoogle Scholar - 23.Waiter, S. A. and Choudhury, P. Roy.. “Correlation equations for determining the equilibrium conditions behind a strong shock,” Readers’ Forum,
*J. Aero. Space Sci.*, May, 1962,**29**(5), 618–19.Google Scholar - 24.Hayes, W. D. and Prob-Stein, R. F....
*Hypersonic Flow Theory*, Academic Press, New York, 1959, pp. 143–50.MATHGoogle Scholar - 25.Ferri, Antonio .. “The method of characteristic for the determination of super-sonic flow over bodies of revolution at small angles of attack,”
*N.A.C.A. Report*1044, 1951.Google Scholar - 26.Sims, Joseph L. ... “Supersonic flow around right circular cones—Tables for zero angle of attack,”
*A.B.M.A, Report D.A.T.R.*, March 1 1960, 11–60.Google Scholar - 27.- .. “Supersonic flow around right circular cones—Tables for small angle of attack,”
*Ibid.*, April 27, 1960, 19–60.Google Scholar - 28.Stone, A. H. - Corrections to the paper on Supersonic flow past a slightly yawing cone—II,”
*Journal of Math. and Phys.*, Jan 1953**31**(4), 300.Google Scholar - 29.Ferri, A., Ness, N. and Kaplita, T. T. “Supersonic flow over conical bodies without axial symmetry,”
*J. Aero. Sci.*, Aug. 1953,**20**(**8**), 563–71.MATHGoogle Scholar - 30.Gonor, A. L. ... “Flow about a cone at an angle of attack at large supersonic speed in Russian,” (
*Izv. Akad. Nauk. S.S.S.R., Otd. Tekh. Nauk*, No. 7), 1958, 102–05.Google Scholar