# Analysis of the IR Signature and Radiative Base Heating from a Supersonic Solid Rocket Exhaust Plume

## Abstract

The plume flow and radiative base heating of a solid rocket have been important factors for rocket survivability in the modern battlefield, in which the standard of technology determines the dominant position. To enhance rocket survivability and reduce base heating, infrared (IR) signatures emitted from an exhaust plume should be determined. In this work, therefore, IR signatures and radiative base heating characteristics in the plumes exhausted from a solid rocket operating at Mach number of 1.6 and altitudes of 5 km and 10 km, respectively, are numerically examined to find the physics related to the plume flow and radiative characteristics. The plume flow and radiative characteristics are obtained using a pre-conditioning method and weighted sum of gray gases model (WSGGM) coupled with finite volume method for radiation, respectively, and the IR signature at each location is post-processed with the narrow band-based WSGGM after plume fields are developed. After validating models adopted in this work by comparing with other solutions, the plume flow field, IR signature, and radiative base heating characteristics are investigated by changing such various parameters as altitude and particle concentrations in the exhaust plume. As a result, it is found that the particular wavelength IR signature level has high spectral characteristics because of \( \text{CO}_{2} \) and \( \text{H}_{\text{2}} \text{O} \) behaviors in the plume, and the radiative heat flux coming into the base plane decreases with higher flight altitude and longer distance from the nozzle exit.

## Keywords

Infrared (IR) signatures Rocket plume base heating NB-based WSGGM Finite volume method## List of Symbols

- \( C \)
Specific heat, J/kg K

- \( I \)
Radiation intensity, W/m

^{2}*K*Number of total gray gases

*L*Thickness of the gas layer

- \( N_{\theta } \), \( N_{\phi } \)
Discretized number of each radiation direction

- \( q_{\text{slab}}^{\text{C}} \)
Convective heat flux, W/m

^{2}- \( q_{\text{slab}}^{\text{R}} \)
Radiative heat flux, W/m

^{2}- \( q_{\text{slab}}^{\text{T}} \)
Total heat flux, W/m

^{2}*r*,*z*Axes of cylindrical coordinate

- \( T \)
Temperature, K

## Greek Symbols

- \( \kappa_{\text{a}} \)
Absorption coefficient, m

^{−1}- \( \mu ,\,\,\,\eta ,\,\,\,\xi \)
Direction cosine

- \( \rho \)
Density of slab or scale, kg/m

^{3}- \( \sigma \)
Stefan–Boltzmann constant, \( 5.67 \times 10^{ - 8} {\text{ W/m}}^{2} \;{\text{K}}^{4} \)

- \( \phi \)
Azimuthal angle measured from radial direction

*∆A*_{i}Surface area of the control volume

*∆V*Volume of the control volume

## Subscripts

- b
Blackbody

- \( \eta \)
Each band

- g
Gas

*k**k*th gray band- p
Particle

## Superscript

*m*Radiation direction

## Notes

### Acknowledgements

This work is supported by the National Research Foundation of Korea (NRF) Grant funded by the Korean Government (MSIP) (no. NRF-2018R1D1A1B07048355).

## References

- 1.Mahulikar SP, Rao GA, Kolhe PS (2006) Infrared signatures of low flying aircraft and their rear fuselage skin’s emissivity optimisation. J Aircr 43:226–232CrossRefGoogle Scholar
- 2.Sonawane HR, Mahulikar SP (2011) Tacktical air warface: generic model for aircraft susceptibility to infrared guided missiles. J Aerosp Sci Technol 16:249–260CrossRefGoogle Scholar
- 3.Yi KJ, Baek SW, Kim MY, Lee SN, Kim WC (2014) The effects of heat shielding in jet engine exhaust systems on aircraft survivability. Numer Heat Transf Part A Appl 66:89–106CrossRefGoogle Scholar
- 4.Morizumi SJ, Carpenter HJ (1964) Thermal radiation from the exhaust plume of an aluminized composite propellant rocket. J Spacecr Rockets 1:501–507CrossRefGoogle Scholar
- 5.Stockham LW, Love TJ (1968) Radiative heat transfer from a cylindrical cloud of particles. AIAA J 6:1935–1940CrossRefGoogle Scholar
- 6.Waston GH, Love AL (1977) Thermal radiation model for solid rocket booster plumes. J Spacecr Rockets 14:641–647CrossRefGoogle Scholar
- 7.Nelson HF (1984) Influence of particulates on infrared emission from tactical rocket exhausts. J Spacecr Rockets 21:425–432CrossRefGoogle Scholar
- 8.Baek SW, Kim MY (1997) Analysis of radiative heating of a rocket plume base with the finite-volume method. Int J Heat Mass Transf 40:1501–1508CrossRefGoogle Scholar
- 9.Tan H-P, Shuai Y, Dong S-K (2005) Analysis of rocket plume base heating by using backward Monte-Carlo method”. J Thermophys Heat Transf 19:125–127CrossRefGoogle Scholar
- 10.Kim MY, Yu MJ, Cho JH, Baek SW (2008) Influence of particles on radiative base heating from the rocket exhaust plume. J Spacecr Rockets 45:454–458CrossRefGoogle Scholar
- 11.Kim OJ, Song TH (2000) Data base of WSGGM-based spectral model for radiation properties of combustion products. J Quant Spectrosc Radiat Transf 64:379–394CrossRefGoogle Scholar
- 12.Lee SN, Baek SW (2012) Analysis of radiative heat flux for nozzle flow. J Appl Mech Mater 110–116:3025–3030Google Scholar
- 13.Turkel E (1999) Preconditioning techniques in computational fluid dynamics. Annu Rev Fluid Mech 31:385–416MathSciNetCrossRefGoogle Scholar
- 14.Weiss JM, Smith WA (1995) Preconditioning applied to variable and constant density flows. AIAA J 33:2050–2057CrossRefGoogle Scholar
- 15.Smith TF, Shen ZF, Friedman JN (1982) Evaluation of coefficients for the weighted sum of gray gas model. J Heat Transf 104:602–608CrossRefGoogle Scholar
- 16.Liou MS (2006) A sequel to AUSM: AUSM+-up for all speeds. J Comput Phys 214:137–170MathSciNetCrossRefGoogle Scholar
- 17.Chai JC, Lee HS, Patankar V (1994) Finite-volume method for radiation heat transfer. J Thermophys Heat Transf 8:419–425CrossRefGoogle Scholar
- 18.Kim OJ, Song TH (1996) Implementation of the weighted sum of gray gases model to a narrow band: application and validity. Numer Heat Transf Part B 30:453–468CrossRefGoogle Scholar
- 19.Park W-H, Kim T-K (2003) Application of the weighted sum of gray gases model for nonhomogeneous gas mixtures having arbitrary compositions. In: Proceedings of the Eurotherm 73 on computational radiation in participating media, 15–17 Apr 2003, Mons, Belgium, pp 129–137Google Scholar
- 20.Park W-H, Kim T-K (2005) Development of the WSGGM using a gray gas regrouping technique for the radiative solution within a 3-D enclosure filled with nonuniform gas mixtures. JSME Int Ser B 48:310–315CrossRefGoogle Scholar
- 21.Nelson HF (1992) Backward Monte-Carlo modeling for rocket plume base heating. J Thermophys Heat Transf 6:556–558CrossRefGoogle Scholar