A shape design optimization methodology based on the method of characteristics for rocket nozzles
Tóm tắt
Even though shape optimization is a powerful tool for designing aerospace vehicles, it can be time-consuming when high-fidelity models are employed. Thus, lower-fidelity simulations covering a wider design space can be a solution for shape optimization in the early design phases. With this in mind, the present work aims to develop a low-fidelity and fast method to conduct nozzle shape optimization. This method consists in using the free-form deformation (FFD) parameterization technique to control the nozzle shape by means of an optimization algorithm to maximize the coefficient of thrust determined by a two-dimensional method of characteristics (MoC). To verify the reliability of the proposed method, a similar optimization process is carried out, recurring to high-fidelity simulations, namely using an Euler solver, in the open-source framework
$$\text {SU}^2$$
. This latter optimization process is established as a surrogate-based optimization (SBO) not only to mitigate the
$$\text {SU}^2$$
framework limitations in performing shape optimization on nozzles, but also as a way to reduce the computational power. A good agreement between the results from both methods is achieved, displaying solely a small offset concerning the optimal contour width and the coefficient of thrust. Hence, this proves the usefulness of the developed shape optimization strategy based on the MoC for the preliminary design of nozzles.
Tài liệu tham khảo
Rome, P.: Every satellite orbiting Earth and who owns them. https://dewesoft.com/daq/every-satellite-orbiting-earth-and-who-owns-them. Last accessed on: (October 2022)
Larson, W.J., Wertz, J.R.: Space mission analysis and design, 3rd edn. Microcosm Press Inc, Portland (2005)
Sutton, G.P., Biblarz, O.: Rocket propulsion elements, 8th edn. John Wiley and Sons Inc, Hoboken (2010)
Harris, F.R.: The parsons centenary-a hundred years of steam turbines. Proc. Inst. Mech. Eng. Part A: Power Process Eng. 198(3), 183–224 (1984). https://doi.org/10.1243/PIME_PROC_1984_198_024_02
Goddard, R.H.: A method of reaching extreme altitudes. Smithsonian Institution (1919). https://doi.org/10.5479/sil.918318.39088014683783
O’Leary, R.A., Bech, J.E.: Nozzle design. http://www.rocket-propulsion.info/resources/articles/NozzleDesign.pdf (1992) last accessed on: (October 2022)
Frey, M., Makowka, K., Aichner, T.: The tictop nozzle: a new nozzle contouring concept. CEAS Space J. 9(2), 175–181 (2017). https://doi.org/10.1007/s12567-016-0139-z
Rao, G.V.R.: Exhaust nozzle contour for optimum thrust. J. Jet Propuls. 28(6), 377–382 (1958). https://doi.org/10.2514/8.7324
Hagemann, G., Immich, H., Terhardt, M.: In: 34th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit (1998). https://doi.org/10.2514/6.1998-3522
Khare, S., Saha, U.: Rocket nozzles: 75 years of research and development. Sādhanā 46, 76 (2021). https://doi.org/10.1007/s12046-021-01584-6
Afridi, S., Khan, T.A.: Multi-objective nozzle design optimization for maximum thrust vectoring performance. Proc. Inst. Mech. Eng.: Part G J. Aerosp. Eng. (2022). https://doi.org/10.1177/09544100221106656
Chasman, D., Birch, M., Haight, S., Osborne, M., Oh, Y., Hink, A.: Multi-disciplinary optimization method for an innovative multi nozzle (MNG) design. 42nd AIAA Aerospace Sciences Meeting and Exhibit 10, 6032–6054 (2004). https://doi.org/10.2514/6.2004-619
Kishore, M., Velliangiri, M., Kirubakaran, A., Kamesh Adithya, S.B., Naveen Kumar, G.: Design and CFD analysis of supersonic nozzle. Int. J. Res. Appl. Sci. Eng. Technol. 8, 1539–1547 (2022). https://doi.org/10.22214/ijraset.2020.30550
Sun, D., Luo, T., Feng, Q.: New contour design method for rocket nozzle of large area ratio. Int. J. Aerosp. Eng. (2019). https://doi.org/10.1155/2019/4926413
Cai, G., Fang, J., Xu, X., Liu, M.: Performance prediction and optimization for liquid rocket engine nozzle. Aerosp. Sci. Technol. 11(2), 155–162 (2007). https://doi.org/10.1016/j.ast.2006.07.002
Colonno, M., Van der Weide, E., Alonso, J.J.: In 46th AIAA Aerospace Sciences Meeting and Exhibit (Reno, Nevada. USA (2008). https://doi.org/10.2514/6.2008-911
Asha, S., Mohana, G. Dhathri Naga., Priyanka, K. Sai., Govardhan, D.: Design of minimum length supersonic nozzle using the method of characteristics. Int. J. Innov. Technol. Explor. Eng. 9(2), 1370–1374 (2019). https://doi.org/10.35940/ijitee.b6183.129219
Khan, M.A., Sardiwal, S.K., Sharath, M., Chowdary, D.: Design of a supersonic nozzle using method of characteristics. Int. J. Eng. Res. Technol. (IJERT) 02(11), 19–24 (2013). https://doi.org/10.17577/IJERTV2IS110026
Matsunaga, M., Fujio, C., Ogawa, H., Higa, Y., Handa, T.: Nozzle design optimization for supersonic wind tunnel by using surrogate-assisted evolutionary algorithms. Aerosp. Sci. Technol. 130, 107,879 (2022). https://doi.org/10.1016/j.ast.2022.107879
Anderson, J.D.: Fundamentals of Aerodynamics, 6th edn. McGraw Hill Education, New York (2017)
Ferri, A.G.: The Method of Characteristics. Princeton University Press (2015)
Sederberg, T.W., Parry, S.R.: Free-form deformation of solid geometric models. ACM SIGGRAPH Comput Gr. 20(4), 151–160 (1986). https://doi.org/10.1145/15886.15903
Martins, J.R.R.A., Ning, A.: Engineering design optimization. Cambridge University Press, Cambridge (2021)
Kulkarni, V.D.: Lecture 34 in Gas Dynamics. https://nptel.ac.in/courses/112103021. Last accessed on: (October 2022)
Seshadri, A.: NSGA - II: A multi-objective optimization algorithm. https://www.mathworks.com/matlabcentral/fileexchange/10429-nsga-ii-a-multi-objective-optimization-algorithm (2022). Last accessed on: 23 Oct 2022
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002). https://doi.org/10.1109/4235.996017
Cummings, R.M., Mason, W.H., Morton, S.A., McDaniel, D.R.: Applied computational aerodynamics: a modern engineering approach. Cambridge University Press, Cambridge (2015)
Economon, T.D., Palacios, F., Copeland, S.R., Lukaczyk, T.W., Alonso, J.J.: SU2: an open-source suite for multiphysics simulation and design. AIAA J. 54(3), 828–846 (2016). https://doi.org/10.2514/1.J053813
Wesseling, P.: Principles of computational fluid dynamics. Springer, Berlin Heidelberg, Berlin, Heidelberg (2001)
Examining Spatial (Grid) Convergence. https://www.grc.nasa.gov/www/wind/valid/tutorial/spatconv.html (2021). Last accessed on: (October 2022)
Murnaghan, M.: Study of minimum length, supersonic nozzle design using the method of characteristics. Master’s thesis, Universitat Politècnica de Catalunya (2019)