Research Papers: Flows in Complex Systems

Profile Design and Multifidelity Optimization of Solid Rocket Motor Nozzle

[+] Author and Article Information
Kuahai Yu

Department of Engineering Mechanics,
Henan University of Science and Technology,
Luoyang 471023, China;
Luoyang Opt-Electro Development Center,
Luoyang 471009, China
e-mail: yukuahai@hotmail.com

Xi Yang

Department of Engineering Mechanics,
Henan University of Science and Technology,
Luoyang 471023, China
e-mail: yanglxz@qq.com

Zhan Mo

Luoyang Opt-Electro Development Center,
Luoyang 471009, China
e-mail: nihao010-313@163.com

1Corresponding author.

2Current address: Department of Engineering Mechanics, Henan University of Science and Technology, Luoyang, 471023, China.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received February 5, 2013; final manuscript received December 9, 2013; published online February 10, 2014. Assoc. Editor: Elias Balaras.

J. Fluids Eng 136(3), 031104 (Feb 10, 2014) (6 pages) Paper No: FE-13-1090; doi: 10.1115/1.4026248 History: Received February 05, 2013; Revised December 09, 2013

This paper presents a new profile modeling method and multifidelity optimization procedure for the solid rocket motor contoured nozzle design. Two quartic splines are proposed to construct the nozzle divergent section profile, and the coefficients of the splines' functions are calculated by a fortran program. Two-dimensional axisymmetric and three-dimensional compressible Navier–Stokes equations with Re-Normalisation Group (RNG) k-ε turbulent models solve the flow field as low- and high-fidelity models, respectively. An optimal Latin hypercube sampling method produces the sampling points, and Kriging functions establish the surrogate model combining with the low- and high-fidelity models. Finally, the adaptive simulated annealing algorithm is selected to complete the profile optimization, with the objectives of maximizing the thrust and the total pressure recovery coefficient. The optimization improves the thrust by 4.27%, and enhances the recovery coefficient by 4.63%. The result shows the proposed profile modeling method is feasible and effective to enhance the nozzle performance. The multifidelity optimization strategy is valid for improving the computational efficiency.

Copyright © 2014 by ASME
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Sutton, G. P., and Biblarz, O., 2001, Rocket Propulsion Elements, John Wiley & Sons Inc., New York, Ch. 3.
Flamm, J. D., Deere, K. A., Berrier, B. L., and Johnson, S. K., 2005, “An Experimental Study of a Dual Throat Fluidic Thrust Vectoring Nozzle Concept,” AIAA Paper No. 2005-3503.
Zebbiche, T., and Youbi, Z. E., 2007, “Supersonic Two-Dimensional Minimum Length Nozzle Design at High Temperature Application for Air,” Chinese J. Aeronaut., 20, pp. 29–39. [CrossRef]
Dittakavi, N., Chunekar, A., and Frankel, S., 2010, “Large Eddy Simulation of Turbulent-Cavitation Interactions in a Venturi Nozzle,” ASME J. Fluids Eng., 132(12), p. 121311. [CrossRef]
Deere, K. A., Flamm, J. D., Berrier, B. L., and Johnson, S. K., 2007, “Computational Study of an Axisymmetric Dual Throat Fluidic Thrust Vectoring Nozzle Concept for Supersonic Aircraft Application,” AIAA Paper No. 2007-5085.
Hussaini, M. M., and Korte, J. J., 1996, “Investigation of Low-Reynolds-Number Rocket Nozzle Design Using PNS-based Optimization Procedure,” NASA Technical Memorandum 1996-110295.
Vlassov, D., Vargas, J. V. C., and Ordonez, J. C., 2007, “The Optimization of Rough Surface Supersonic Nozzles,” Acta Astronaut., 61, pp. 866–872. [CrossRef]
Lijo, V., Heuy, D. K., Toshiaki, S., and Matsuo, S., 2010, “Numerical Simulation of Transient Flows in a Rocket Propulsion Nozzle,” Int. J. Heat Fluid FL., 31, pp. 409–417. [CrossRef]
Yumusak, M., 2013, “Analysis and Design Optimization of Solid Rocket Motors in Viscous Flows,” Comput. Fluids, 75, pp. 22–34. [CrossRef]
Ali, K., and LiangG., 2012, “An Integrated Approach for Optimization of Solid Rocket Motor,” Aerosp. Sci. Technol., 17, pp. 50–64. [CrossRef]
Alexeenko, A. A., and Levin, D. A., 2002, “Numerical Modelling of Axisymmetric and Three-dimensional Flows in Microelectro Mechanical Systems Nozzles,” AIAA J., 40(5), pp. 897–904. [CrossRef]
Louisos, W. F., and Hitt, D. L., 2007, “Heat Transfer & Viscous Effects in 2D & 3D Supersonic Micro-Nozzle Flows,” AIAA Paper No. 2007-3987.
Mack, Y., Goell, T., Shyy, W., and Haftka, R., 2007, “Surrogate Model-Based Optimization Framework: A Case Study in Aerospace Design,” Stud. Comp. Intel., 51, pp. 323–342. [CrossRef]
Bucher, C., and Most, T., 2008, “A Comparison of Approximate Response Functions in Structural Reliability Analysis,” Probabilist. Eng. Mech., 23, pp. 154–163. [CrossRef]
Yu, K., Yang, X., and Yue, Z., 2011, “Aerodynamic and Heat Transfer Design Optimization of Internally Cooling Turbine Blade Based Different Surrogate Models,” Struct. Multidiscip. O., 44(1), pp. 75–83. [CrossRef]
Jin, R., Chen, W., and Sudjianto, A., 2003, “An Efficient Algorithm for Constructing Optimal Design of Computer Experiments,” 2003 ASME Design Automation Conference, Chicago, IL, Paper No. ETC-DAC48760.
Basudhar, A., and Missoum, S., 2009, “A Sampling-Based Approach for Probabilistic Design With Random Fields,” Comput. Method Appl. M., 198, pp. 3647–3655. [CrossRef]
Bandler, J. W., Koziel, S., and Madsen, K., 2008, “Editorial-Surrogate Modelling and Space Mapping for Engineering Optimization,” Optim. Eng., 9, pp. 307–310. [CrossRef]
Leifsson, L., and Koziel, S., 2010, “Multi-Fidelity Design Optimization of Transonic Airfoils Using Physics-Based Surrogate Modelling and Shape-Preserving Response Prediction,” J. Comput. Sci., 1, pp. 98–106. [CrossRef]
Forrester, A. I. J., and Keane, A. J., 2009, “Recent Advances in Surrogate-Based Optimization,” Prog. Aerosp. Sci., 45, pp. 50–79. [CrossRef]
Collins, K. B., 2008, “A Multi-Fidelity Framework for Physics Based Rotor Blade Simulation and Optimization,” Ph.D. thesis, Georgia Institute of Technology, Atlanta, GA.
Zhang, M., and Shen, Y., 2008,“Three-Dimensional Simulation of Meandering River Based on 3-D RNG k Turbulence Model,” J. Hydrodyn., 20(4), pp. 448–455. [CrossRef]
Sasena, M. J., 2002, “Flexibility and Efficiency Enhancements for Constrained Global Design Optimization With Kriging Approximations,” Ph.D. thesis, University of Michigan, Ann Arbor, MI.
Yin, H., 2005, “Kriging Model Approach to Modeling Study on Relationship Between Molecular Quantitative Structures and Chemical Properties,” Ph.D. thesis, Hong Kong Baptist University, Hong Kong.


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Fig. 1

Parametric design of contoured nozzle

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Fig. 2

Profile curves with different variables and negative gradient near throat

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Fig. 3

Grid of 3D nozzle model

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Fig. 4

Grid independence study for axial Mach number

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Fig. 5

Space response surface of design variables and objective variable

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Fig. 6

Solid rocket motor nozzle multifidelity optimization procedure

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Fig. 7

Comparison of outlet Mach number

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Fig. 8

Comparison of nozzle divergent section profile



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