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

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## 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

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## References

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