A multidisciplinary approach in optimization of a solid rocket motor for structural strength and internal ballistic performance

Humans have always desired to explore the universe and this enthusiasm was reached to top at the beginning of the 20th Century. Honorable scientists like Konstantin Tsiolkovsky, Hermann Oberth and Robert Goddard worked intensely on projects that made it possible to travel into universe getting away from the gravitational force of the earth. Since their dreams and aims were beyond the time that they lived in, their studies did not draw much interest that they deserved and Hermann Oberth's doctoral dissertation named as "The Rocket into Planetary Space" was rejected in 1922 claiming that it was "utopian". On the other hand, determined scientists having similar ideas as Oberth, like his student Wernher Von Braun who, was the designer of Saturn V, eventually provided the system that enabled to travel to the moon in 1969. The significance of the studies related to rocket science was realized during World War II and rockets had also been designed for military purposes since those dates. In later years, rockets had also been designed for satellite launching purposes in order to meet the increasing communication demand. Rocket motors are grouped into three main categories according to their propellant type that they use: which are solid rockets, liquid rockets and hybrid rockets. Solid rocket motors are usually preferred for military duties due to their reliability, low cost and ease of storage. Design process of solid rocket motors consists of two main disciplines which are internal ballistic performance analysis and structural strength analysis of the propellant. Single discipline analyses of these disciplines lead to iterative design processes which yield increased design costs and extension of the design time. Furthermore, separate analyses of these disciplines result with bulky and heavier rocket motor designs with lower internal ballistic performance relative to an optimum design. In order to prevent this, within the content of this thesis, a coupled analysis strategy is developed and used in order to design and optimize a solid rocket motor with a certain mass. This research consists of 6 essential topics which are: characterization of the solid propellant, construction of the parametric finite element analysis model, evaluation of the finite element analysis results, burnback analysis, internal ballistic performance analysis and multidisciplinary optimization of the system. In this thesis, after introducing solid rocket motor components and summarizing literature review in Chapter 1, mechanical properties of solid rocket propellants are explained in Chapters 2 and 3. In Chapter 3, characterization of solid rocket propellants and construction of propellant master curve are presented. Within this scope, test techniques such as stress relaxation and uniaxial tension tests which are used while generating the propellant master curve are further eloborated. Additionally, information about termomechanical analyses and differential scanning calorimetry tests which are used to determine the material properties of the propellant are explained in detail. In Chapter 4, broad information about the finite element model of the solid rocket motor is presented. Geometrical properties, material properties, boundary conditions and load specification is adressed. Within the content of this work, finite element model and analysis have to be updated very frequently due to the optimization process. Therefore, a simplified finite element model was constructed using symmetry boundary conditions under plane strain assumption in order to save time during structural analysis. Two loading steps are constructed in the finite element model which are cool-down and ignition steps. In the cool-down step, solid rocket motor is cooled down from its stress-strain free temperature to its minimum operating temperature using a special refrigerator that is blowing cold air with constant speed. Then, stress and strain distribution of the propellant during the cool down process is recorded. In the ignition step, pressure peak value (corresponding to first sudden rise in the pressure vs time history plot) is derived from internal ballistic performance analysis and is applied to the burning surface of the propellant. Then, additional stress and strain distributions resulting from the ignition step in addition to the cool-down step are superposed and finally stress and strain results obtained from cool-down and ignition loads are transferred to an in house code for margin of safety calculation. Meanwhile, in order to analyze the cool-down process of viscoelastic solid propellant with high accuracy, one needs to determine the temperature distribution as a function of cool-down time. Temperature distribution of the propellant during this process is determined by performing heat transfer analysis. Then, the temperature distribution is used as an input data for the cool-down step of viscoelastic finite element analysis. On the other hand, in order to predict the cool-down time of the propellant without any iterations a surrogate analytical equation is developed and validated by using the response surface method. This step also enables parametrization of the finite element analysis models. This step also enables the parametrization of finite element analysis model. Finally, the finite element model is validated for simple tubular geometry using the analytical solutions. Evaluation of the finite element analysis results using deterministic approach is explained in Chapter 5. The methodology taken into account during the determination of knock-down factors is also explained in this section. After the parametric finite element model is generated, an efficient approach to achieve the burnback analysis is established. Considering the fact that the optimization iterations require numerious burnback analyses, an analytical burnback solution method is developed as the most efficient method for this problem. In order to obtaion burnback solutions of slotted grains, first, all of the possible design scenarios are investigated and 12 burnback patterns are determined. Analytical equations for each of the burnback patterns are formulated and then validated in Chapter 6. In Chapter 7, a zero dimensional (0D) internal ballistic performance solver is implemented and validated. This solver provides satisfactory results for solid rocket motor designs with aspect ratio (Length/Diameter) of 5 as maximum. Geometric variation of burning surface and port volume with respect to web thickness is generated and transferred to zero dimensional internal ballistic solver. The implemented internal ballistic solver is validated using analytical and experimental results found in the literature. Outputs of the internal ballistic solver are, mass of the propellant, pressure vs time and thrust vs time history plots, specific impulse and total impulse. From this output, pressure vs time history data is utilized as load data for ignition step of the viscoelastic finite element model. In Chapter 8, effects of sectional geometric parameters of slotted grain on mass of the propellant, specific impulse, pressure load corresponding to first sudden increase in the pressure vs time history and the time which corresponds to that pressure, strain margin of safety values calculated for the end of cool-down and the ignition steps are analyzed using response surface method. In Chapter 9, multidisciplinary optimization process is integrated to the above framework by employing Multi Objective Genetic Algorithm (MOGA). In the optimization iterations, first, internal ballistic performance analyses are accomplished and mass of the propellant, pressure vs time history, specific impulse and total impulse are determined. The parametric heat transfer analysis provides temperature distribution as a function of time for viscoelastic structural analysis. Both of these loads are applied to the propellant in separate steps. After receiving structural results, highest strain and stress values are fed to an in house code to calculate the structural margin of safety values with respect to time using a deterministic approach. The multi-objectives of the optimization problem are to minimize the mass of the propellant while maximizing the specific impulse. As structural constraints, the optimum design is required to satisfy a margin of safety value greater than 0.1 for both stress and strain criteria. As a further study, formulations representing the approximate maximum specific and total impulse values in terms of a certain propellant mass are derived from the pareto-optimal chart. The goal of this thesis is to develop a methodology to enable and enhance the design of optimum missile systems and launching systems with improved multidisciplinary performance and strength crtieria. This approach can contribute significantly to industrial missile development projects by providing sought-after design alternatives in an efficient and affordable way to serve the demands of defence industry.