Journal of the Korean Society of Propulsion Engineers (한국추진공학회지)

The Korean Society of Propulsion Engineers (한국추진공학회)
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Comparative Evaluation on the Deriving Method of the Heat Transfer Coefficient of the C-D Nozzle

축소 확대 노즐의 열전달 해석을 위한 열전달 계수 계산 및 검증

  • Received : 2021.12.02
  • Accepted : 2022.02.10
  • Published : 2022.04.30
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Abstract

The heat transfer coefficient on the wall, which is used as a boundary condition in the thermal analysis of general contract-divergent supersonic nozzles, affects the thermal analysis accuracy of the entire nozzle. Accordingly, many methods of deriving a heat transfer coefficient have been proposed. In this study, the accuracy of each method was compared. For this purpose, the heat transfer coefficients were calculated through theoretical-based analogy methods, semi-empirical equations, and CFD simulations for the previously performed heat transfer experiment with an isothermal wall and compared with the experimental results. The results show that the Prandtl-Taylor analogy methods and the CFD results with the k-ω SST turbulence model were in good agreement with the experimental results. Furthermore, the Modified Bartz empirical formula showed an overall over-prediction tendency.

일반적인 축소 확대형 초음속 노즐에 대한 열해석에서 경계조건으로 사용되는 벽면의 열전달 계수는 노즐 전체의 열해석 정확도에 영향을 미친다. 이에 많은 열전달계수 도출 방법이 제안되어 왔으며, 본 연구에서는 각각의 기법들을 실제 실험 조건에서 열전달 계수를 계산하고 비교하고자 하였다. 이를 위해 기 수행된 벽면 등온 노즐의 열전달실험에 대해 이론 기반의 analogy 기법과 반경험식, 유체전산해석을 통해 열전달 계수를 도출하고 실험결과와 비교하였다. 해석 결과는 반경험식들은 전반적으로 다른 방법에 비해 대류 열전달 계수를 과도하게 예측하고, Prandtl-Taylor analogy 기법과 k-ω SST 모델을 적용한 전산해석 결과가 실험결과와 비교적 잘 일치하는 경향성을 보였다.

Keywords

Acknowledgement

본 연구는 (주)LIG넥스원(63985-01)의 지원으로 수행되었으며, 지원에 감사드립니다.

References

  1. Bennett, C.O. and Myers, J.E., "Momentum, Heat, and Mass Transfer," 3rd edition, McGRAW-HILL, New York, N.Y., U.S.A, 1983.
  2. Colburn, A.P., "A method of correlating forced convection heat-transfer data and a comparison with fluid friction," International Journal of Heat and Mass Transfer, Vol. 7, No. 12, pp. 1359-1384, 1964. https://doi.org/10.1016/0017-9310(64)90125-5
  3. Bartz, D.R., "A simple equation for rapid estimation of rocket nozzle convective heat transfer coefficients," Jet Propulsion, Vol. 27, No. 1, pp. 49-51, 1957. https://doi.org/10.2514/8.12572
  4. Bartz, D.R., "Turbulent Boundary-Layer Heat Transfer from Rapidly Acceleration Flow of Rocket Combustion Gases and of Heated Air," Advances in Heat Transfer, Vol. 2, pp. 2-108, 1965.
  5. Betti, "Flow Field and Heat Transfer Analysis of Oxygen/Methane Liquid Rocket Engine Thrust Chambers," Ph.D. Thesis, Department of Mechanical and Aerospace Engineering, Sapienza University of Rome, Rome, Italy, 2012.
  6. Schuff, R., Maier, M., Sindiy, O., Ulrich, C. and Fugger, S., "Integrated Modeling and Analysis for a LOX/Methane Expander Cycle Engine: Focusing on Regenerative Cooling Jacket Design," 42nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Sacramento, C.A., U.S.A., AIAA 2006-4534, Jul. 1957.
  7. Nichols, R.H. and Nelson, C.C., "Wall Function Boundary Conditions Including Heat Transfer and Compressibility," AIAA Journal, Vol. 42, No. 6, pp. 1107-1114, June 2004. https://doi.org/10.2514/1.3539
  8. Bensayah, K., Hadjadj, A. and Bounif, A., "Heat Transfer in Turbulent Boundary Layers of Conical and Bell Shaped Rocket Nozzles with Complex Wall Temperature, Numerical Heat Transfer," Part A: Applications: An International Journal of Computation and Methodology, Vol. 66, No. 3, pp. 289-314, May 2014. https://doi.org/10.1080/10407782.2013.873283
  9. Hahm, H.C. and Kang, Y.G., "Comparative Studies of Heat Transfer Coefficients for Rocket Nozzle," Journal of the Korean Society of Propulsion Engineers, Vol. 16, No. 2, pp. 42-50, Apr. 2012. https://doi.org/10.6108/KSPE.2012.16.2.042
  10. Back, L.H., Massier, P.F. and Gier, H.L, "Convective heat transfer in a convergent-divergent nozzle," International Journal of Heat and Mass Transfer, Vol. 7, No. 5, pp. 549-568, May 1964. https://doi.org/10.1016/0017-9310(64)90052-3
  11. Kim, Y.G., Bae, J.C. and Kim, J.O., "Parametric comparative study of Rocket Nozzle Convective Heat Transfer Coefficient Application of Combustion gas characteristic and Method of Analysis," 48th KSPE Spring Conference, Jeju, Korea, pp. 651-663, May 2017.
  12. Huzel, D.K. and Huang, D.H., Modern engineering for design of liquid-propellant rocket engines, 1st ed, American Institute of Aeronautics and Astronautics, U.S.A., 1992.
  13. Pavli, A.J., Curley, J.K., Masters, P.A. and Schwartz, R.M., "Design and Cooling Performance of A Dump-Cooled Rocket Engine," NASA TN-D-3532, 1966.
  14. Simcenter STAR-CCM+ 2019.1,"Simcenter STAR-CCM+® Documentation Version 2019.1," Siemens, Wittelsbacherpl. 1, 80333 Munchen, Germany, 2019.
  15. Kader, B.A, "Temperature and concentration profiles in fully turbulent boundary layers," International Journal of Heat and Mass Transfer, Vol. 24, No. 9, pp. 1541-1544, 1981. https://doi.org/10.1016/0017-9310(81)90220-9
  16. Kam, H.D, Kim, J.S., "Assessment and Validation of Turbulence Models for the Optimal Computation of Supersonic Nozzle Flow," Journal of the Korean Society of Propulsion Engineers, Vol. 17, No. 1, pp. 18-25, 2013. https://doi.org/10.6108/KSPE.2013.17.1.018