Abstract
An improved constant volume cycle (CVC) model is developed to analyze the nozzle effects on the thrust and specific impulse of pulse detonation rocket engine (PDRE). Theoretically, this model shows that the thrust coefficient/specific impulse of PDRE is a function of the nozzle contraction/expansion ratio and the operating frequency. The relationship between the nozzle contraction ratio and the operation frequency is obtained by introducing the duty ratio, by which the key problem in the theoretical design can be solved. Therefore, the performance of PDRE can be accessed to guide the preliminary shape design of nozzle conveniently and quickly. The higher the operating frequency of PDRE is, the smaller the nozzle contraction ratio should be. Besides, the lower the ambient pressure is, the larger the expansion ratio of the nozzle should be. When the ambient pressure is 1.013 × 105 Pa, the optimal expansion ratio will be less than 2.26. When the ambient pressure is reduced to vacuum, the extremum of the optimal thrust coefficient is 2.236 9, and the extremum of the specific impulse is 321.01 s. The results of the improved model are verified by numerical simulation.
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Lin, T. J. and Pu, Q. An exact solution for incompressible flow through a two-dimensional laval nozzle. Applied Mathematics and Mechanics (English Edition), 7(6), 525–534 (1986) https://doi.org/10.1007/BF01899551
Maddahian, R., Farhanieh, B., and Firoozabadi, B. Turbulent flow in converging nozzles, part one: boundary layer solution. Applied Mathematics and Mechanics (English Edition), 32(5), 645–662 (2011) https://doi.org/10.1007/s10483-011-1446-6
Fan, W. and Li, J. L. Introduction to the Study of Detonation Combined Cycle Engine (in Chinese), Science Press, Beijing, 120–158 (2014)
Allgood, D., Gutmark, E., and Hoke, J. Performance measurements of multi-cycle pulse detonation engine exhaust nozzles. Journal of Propulsion and Power, 22, 770–779 (2006)
Yan, Y., Fan, W., Wang, K., Zhu, X. D., and Mu, Y. Experimental investigations on pulse detonation rocket engine with various injectors and nozzles. Acta Astronautica, 69, 39–47 (2011)
Wang, Y. Y. and Weng, C. S. Experimental investigation on nozzles of two-phase pulse detonation engine (in Chinese). Journal of Propulsion Technology, 35, 282–288 (2014)
Zhang, Q. B., Fan, W., Wang, K., Lu, W., Chi, Y. Q., and Wang, Y. J. Impact of nozzles on a valveless pulse detonation rocket engine without the purge process. Applied Thermal Engineering, 100, 1161–1168 (2016)
Yungster, S. and Perkins, H. D. Multiple cycle simulation of a pulse detonation engine ejector. 38th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Joint Propulsion Conferences & Exhibit, Indianapolis, 2002–3630 (2002)
Li, H. H., Yang, J. M., and Xu, L. G. A numerical simulation on the nozzle flow of pulse detonation engine (in Chinese). Journal of Propulsion Technology, 25, 553–556 (2004)
Qin, Y. X., Yu, J. L., and Gao, G. Computational analysis on the nozzle performance of pulse detonation engines (in Chinese). Journal of Aerospace Power, 25, 366–372 (2010)
Talley, D. G. and Coy, E. B. Constant volume limit of pulsed propulsion for a constant gamma ideal gas. Journal of Propulsion and Power, 18, 400–406 (2002)
Li, J. L., Fan, W., Wang, Y. Q., Qiu, H., and Yan, C. J. Performance analysis of the pulse detonation rocket engine based on constant volume cycle model. Applied Thermal Engineering, 30, 1496–1504 (2010)
Wintenberger, E., Austin, J. M., Cooper, M., Jackson, S., and Shepherd, J. E. Analytical model for the impulse of single-cycle pulse detonation tube. Journal of Propulsion and Power, 19, 22–38 (2003)
McBride, B. J. and Gordon, S. Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications, NASA Reference Publication, Ohio, 1996–1311 (1996)
Fan, W., Yan, C. J., Li, Q., Hu, C. Q., and Ye, B. Experimental investigation on pulse detonation engine nozzles (in Chinese). Journal of Aerospace Power, 22, 869–872 (2007)
Yan, C. J. and Fan, W. Principles and Key Technologies of Pulse Detonation Engines (in Chinese), Northwestern Polytechnical University Press, Xi’an (2005)
Aarnio, M., Hinkey, J., and Bussing, T. Multiple cycle detonation experiments during the development of a pulse detonation engine. 32nd Joint Propulsion Conference and Exhibit, Joint Propulsion Conferences, AIAA Paper 96-3263, Florida (1996)
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Li, G. Y., Li, X. W., Ding, J., Weng, P. F., and Lu, Z. B. An improved constant volume cycle model for performance analysis and shape design of PDRE’s nozzle. Applied Mathematics and Mechanics (English Edition) (2018) https://doi.org/10.1007/s10483-018-2294-6
Project supported by the National Natural Science Foundation of China (No. 11472167)
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Li, G., Li, X., Ding, J. et al. An improved constant volume cycle model for performance analysis and shape design of PDRE nozzle. Appl. Math. Mech.-Engl. Ed. 39, 193–206 (2018). https://doi.org/10.1007/s10483-018-2294-6
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DOI: https://doi.org/10.1007/s10483-018-2294-6