## RADIATION HEAT TRANSFER IN A SOLID-PROPELLANT ROCKET ENGINE

The engineering problem referred in the title of this article is important not for the definite application only. This complex problem is also a good example of a great variation of the physical conditions of thermal radiation for combustion products containing solid or liquid micron-size alumina particles.

In the combustion chamber, the optical thickness of the two-phase combustion products is so high that the major processes take place near the chamber walls near the solid propellant surface. As a rule, the appropriate models are usually 1D, but one should take into account the coupled radiation-convection effects in the thermal boundary layers. In the supersonic nozzle, the density, temperature, and optical thickness of combustion products decrease sharply with the expansion degree (along the nozzle axis). As a result, a contribution of the local thermal radiation to the heat flux to the nozzle wall is not significant. But the net radiative flux at the wall is not negligible. It can be determined on the basis of the 2D solution for the spectral radiative transfer problem, and the radiation scattering by alumina particles appears to be very important. Contrary, the radiation from the exhaust jet as a whole is weakly sensitive to the scattering effects (excluding some near-field problems), but it is important to know the real temperature and absorption-emission properties of polydisperse alumina particles. The dynamic and thermal nonequilibrium of particles suspended in the gas flow and the real temperature behavior of the infrared absorption index of alumina determine the thermal radiation of the rocket plume. The above-mentioned special features of the radiation heat transfer in solid-propellant rocket engine are considered in several subsequent articles specified under the title of the present article.

For the convenience of a reader, the major references on the problem under consideration are presented below in chronological order, starting from the early paper by Nelson published in 1984. Some more detailed (and sometimes earlier) references and their discussion are included in the particular articles on thermal radiation in the combustion chamber, the supersonic rocket nozzle, and in the exhaust jet.

#### REFERENCES

Brewster, M. Q., Radiation-stagnation flow model aluminized solid rocket motor internal insulator heat transfer, J. Thermophys. Heat Transfer, vol. 3, no. 2, pp. 132–139, 1989.

Burt, J. M. and Boyd, I. D., Monte Carlo simulation of particle radiation in high altitude solid rocket plumes, 43th AIAA/ASME/SAE/ASEE Joint Propulsion Conf. and Exibit, AIAA Paper No. 5703, Cincinati, OH, July 8-11, 2007.

Cai, G., Zhu, D., and Zhang, X., Numerical simulation of the infrared radiative signatures of liquid and solid rocket plumes, Aerospace Sci. Tech., vol. 11, no. 6, pp. 473–480, 2007.

Cohen, D. L. (1988) Simple model for particle radiative transfer in vacuum particle plumes, J. Thermophys. Heat Transfer, vol. 2, no. 4, pp. 365–367.

Dombrovsky, L. A. and Baillis, D., Thermal Radiation in Disperse Systems: An Engineering Approach, Begell House, New York and Redding, CT, 2010.

Dombrovsky, L. A., A theoretical investigation of heat transfer by radiation under conditions of two-phase flow in a supersonic nozzle, High Temp., vol. 34, no. 2, pp. 255–262, 1996a.

Dombrovsky, L. A., Radiation Heat Transfer in Disperse Systems, Begell House New York and Redding, CT, 1996b.

Dombrovsky, L. A., Approximate methods for calculating radiation heat transfer in dispersed systems, Thermal Eng., vol. 43, no. 3, pp. 235–243, 1996c.

Laredo, D. and Netzer, D. W., The dominant effect of alumina on nearfield plume radiation, J. Quant. Spectr. Radiat. Transfer, vol. 50, no. 5, pp. 511–530, 1993.

Nelson, H. F., Backward Monte Carlo modeling for rocket plume base heating, J. Thermophys. Heat Transfer, vol. 6, no. 3, pp. 556–558, 1992.

Nelson, H. F. and Fields, J. C., Particle drag coefficient in solid rocket plumes, J. Thermophys. Heat Transfer, vol. 9, no. 3, pp. 567–569, 1995.

Nelson, H. F. and Tucker, E. O., Boron slurry-fueled jet engine exhaust plume infrared signatures, J. Spacecraft Rockets, vol. 23, no. 5, pp. 527–533, 1986.

Nelson, H. F., Influence of particulates on infrared emission from tactical rocket exhausts, J. Spacecraft Rockets, vol. 21, no. 5, pp. 425–432, 1984.

Nelson, H. F., Evaluation of rocket plume signature uncertainties, J. Spacecraft Rockets, 24, no. 6, pp. 546–551, 1987.

Plastinin, Yu. A., Anfimov, N. A., Baula, G. G., Karabadzhak, G. F., Khmelinin, B. A., and Rodionov, A. V., Modeling of aluminum oxide particle radiation in a solid propellant rocket exhaust, 31st Thermophys. Conf., AIAA Paper No. 1879, New Orleans, LA, June 17-20, 1996.

Plastinin, Yu. A., Karabadzhak, G., Khmelinin, B. A., Baula, G., and Rodionov, A., Ultraviolet, visible and infrared spectra modeling for solid and liquid-fuel rocket exhausts, 39th Aerospace Sci. Meeting and Exibit, AIAA Paper No. 0660, Reno, NV, Jan. 8-11, 2001.

Reardon, J. E. and Nelson, H. F., Rocket plume base heating methodology, J. Thermophys. Heat Transfer, vol. 8, no. 2, pp. 216–222, 1994.

Shuai, Y., Dong, S. K., and Tan, H. P., Simulation of the infrared radiation characteristics of high-altitude exhaust plume including particles using the backward Monte Carlo method, J. Quant. Spectrosc. Radiat. Transfer, vol. 95, no. 2, pp. 231–240, 2005.

Surzhikov, S. T., Direct simulation Monte Carlo algorithms for the rocket exhaust plumes emissivity prediction, 40th AIAA Aerospace Sci. Meeting and Exibit, AIAA Paper No. 0795, Reno, NV, Jan. 14-17, 2002.

Surzhikov, S. T., Monte Carlo simulation of plumes spectral emission, 36th AIAA Thermophys. Conf., AIAA Paper No. 3895, Orlando, Florida, June 23-26, 2003.

Surzhikov, S. T., Three-dimensional model of the spectral emissivity of light-scattering exhaust plumes, High Temp., vol. 42, no. 5, pp. 763–775, 2004.

Victor, A. C., Effects of Multiple Scattering on Rocket Exhaust Plume Smoke Visibility, J. Spacecraft Rockets, vol. 26, no. 4, pp. 274–278, 1989.

#### Использованная литература

- Brewster, M. Q., Radiation-stagnation flow model aluminized solid rocket motor internal insulator heat transfer, J. Thermophys. Heat Transfer, vol. 3, no. 2, pp. 132â€“139, 1989.
- Burt, J. M. and Boyd, I. D., Monte Carlo simulation of particle radiation in high altitude solid rocket plumes, 43th AIAA/ASME/SAE/ASEE Joint Propulsion Conf. and Exibit, AIAA Paper No. 5703, Cincinati, OH, July 8-11, 2007.
- Cai, G., Zhu, D., and Zhang, X., Numerical simulation of the infrared radiative signatures of liquid and solid rocket plumes, Aerospace Sci. Tech., vol. 11, no. 6, pp. 473â€“480, 2007.
- Cohen, D. L. (1988) Simple model for particle radiative transfer in vacuum particle plumes, J. Thermophys. Heat Transfer, vol. 2, no. 4, pp. 365â€“367.
- Dombrovsky, L. A. and Baillis, D., Thermal Radiation in Disperse Systems: An Engineering Approach, Begell House, New York and Redding, CT, 2010.
- Dombrovsky, L. A., A theoretical investigation of heat transfer by radiation under conditions of two-phase flow in a supersonic nozzle, High Temp., vol. 34, no. 2, pp. 255â€“262, 1996a.
- Dombrovsky, L. A., Radiation Heat Transfer in Disperse Systems, Begell House New York and Redding, CT, 1996b.
- Dombrovsky, L. A., Approximate methods for calculating radiation heat transfer in dispersed systems, Thermal Eng., vol. 43, no. 3, pp. 235â€“243, 1996c.
- Laredo, D. and Netzer, D. W., The dominant effect of alumina on nearfield plume radiation, J. Quant. Spectr. Radiat. Transfer, vol. 50, no. 5, pp. 511â€“530, 1993.
- Nelson, H. F., Backward Monte Carlo modeling for rocket plume base heating, J. Thermophys. Heat Transfer, vol. 6, no. 3, pp. 556â€“558, 1992.
- Nelson, H. F. and Fields, J. C., Particle drag coefficient in solid rocket plumes, J. Thermophys. Heat Transfer, vol. 9, no. 3, pp. 567â€“569, 1995.
- Nelson, H. F. and Tucker, E. O., Boron slurry-fueled jet engine exhaust plume infrared signatures, J. Spacecraft Rockets, vol. 23, no. 5, pp. 527â€“533, 1986.
- Nelson, H. F., Influence of particulates on infrared emission from tactical rocket exhausts, J. Spacecraft Rockets, vol. 21, no. 5, pp. 425â€“432, 1984.
- Nelson, H. F., Evaluation of rocket plume signature uncertainties, J. Spacecraft Rockets, 24, no. 6, pp. 546â€“551, 1987.
- Plastinin, Yu. A., Anfimov, N. A., Baula, G. G., Karabadzhak, G. F., Khmelinin, B. A., and Rodionov, A. V., Modeling of aluminum oxide particle radiation in a solid propellant rocket exhaust, 31st Thermophys. Conf., AIAA Paper No. 1879, New Orleans, LA, June 17-20, 1996.
- Plastinin, Yu. A., Karabadzhak, G., Khmelinin, B. A., Baula, G., and Rodionov, A., Ultraviolet, visible and infrared spectra modeling for solid and liquid-fuel rocket exhausts, 39th Aerospace Sci. Meeting and Exibit, AIAA Paper No. 0660, Reno, NV, Jan. 8-11, 2001.
- Reardon, J. E. and Nelson, H. F., Rocket plume base heating methodology, J. Thermophys. Heat Transfer, vol. 8, no. 2, pp. 216â€“222, 1994.
- Shuai, Y., Dong, S. K., and Tan, H. P., Simulation of the infrared radiation characteristics of high-altitude exhaust plume including particles using the backward Monte Carlo method, J. Quant. Spectrosc. Radiat. Transfer, vol. 95, no. 2, pp. 231â€“240, 2005.
- Surzhikov, S. T., Direct simulation Monte Carlo algorithms for the rocket exhaust plumes emissivity prediction, 40th AIAA Aerospace Sci. Meeting and Exibit, AIAA Paper No. 0795, Reno, NV, Jan. 14-17, 2002.
- Surzhikov, S. T., Monte Carlo simulation of plumes spectral emission, 36th AIAA Thermophys. Conf., AIAA Paper No. 3895, Orlando, Florida, June 23-26, 2003.
- Surzhikov, S. T., Three-dimensional model of the spectral emissivity of light-scattering exhaust plumes, High Temp., vol. 42, no. 5, pp. 763â€“775, 2004.
- Victor, A. C., Effects of Multiple Scattering on Rocket Exhaust Plume Smoke Visibility, J. Spacecraft Rockets, vol. 26, no. 4, pp. 274â€“278, 1989.