This paper proposes an approach for the multidisciplinary design & optimization of space launch vehicle, wherein the structure/mass, aerodynamics, propulsion and the trajectory system design are performed simultaneously using non-dominated sorting based genetic algorithm. The design problem is posed as an optimization problem in which all the discipline parameters constitute the design variables, which are used to optimize the multi-objective function, thereby resulting in an optimal overall design. The approach is demonstrated by application to the integrated design of a four stage solid launch vehicle. The mission is to deliver predefined payload to the low earth (circular) orbit. An existing, real world system has been used to validate the multistage launch vehicle system model. Nomenclature E a = ratio of thrust in vacuum to thrust in ground D = solid rocket motor diameter, m cr d = throat diameter, m ex d = exit diameter, m o G = vehicle liftoff mass, kg I G = mass of guidance system, steering system and instrument section, kg prop G = mass of propulsion system, kg noz G = mass of nozzle, kg case G = mass of motor case, kg shell G = mass of combustion chamber shell, kg coating G = mass of coating inside, kg silver G = mass of grain silver, kg red G = mass of redundancy of grain, kg aux G = mass of auxiliary parts, kg E spo I = ground effective specific impulse, sec c p = combustion chamber pressure, N/m 2 m p = ratio of total mass to x-sectional area, kg/m 2 k t = running time of ith stage solid rocket motor, sec ε = expansion ratio 1 Doctoral student, School of Astronautics, Student member AIAA, zafar6909@yahoo.com 2 Professor, School of Astronautics, helinshu@sina.com 3 Associate Professor, School of Astronautics, xdj@buaa.edu.cn Downloaded by ROKETSAN MISSLES INC. on February 4, 2015 | http://arc.aiaa.org | 2 gn λ = fineness of grain k µ = ratio of dry mass to total mass o ν = mass to thrust ratio
A new approach is proposed incorporating heuristic optimization algorithm with a switch to a local search algorithm for the multidisciplinary design of solid launch vehicle at conceptual level. Heuristic optimization algorithms such as Genetic Algorithm often may locate near optimum solutions at the expense of large function evaluations. Local search algorithms including both gradient and non gradient based optimization methods are only efficient in finding the optimal solutions within convex areas of the design space but fail to determine the global optimal in multimodal design space. The hybrid optimization approach presented in this paper switches between the global and local search methods to minimize the gross liftoff weight to deliver the predetermine payload to the low earth orbit. The computational efficiency of the devised hybrid method is compared with the computational efficiency of conventional hybrid method applied to the same problem. Comparison of the developed scheme with the conventional optimization approach shows that developed approach requires less computation time. Nomenclature e A = area of nozzle exit, m 2 t A = throat area of nozzle, m 2 c * = characteristic velocity, m/sec T c = coefficient of thrust 0 g = acceleration due to gravity, m/sec sp I = specific Impulse . m = nozzle mass flow rate, kg/sec a p = pressure of atmosphere, N/m 2 c p = gas pressure combustion chamber, N/m 2 e p = pressure at the exit of the nozzle, N/m 2 R = gas constant, J/kg.mol.K c T = temperature in combustion chamber, K T = solid rocket motor thrust, KN e V = exhaust velocity at nozzle exit, m/sec γ = specific heat ratio of gas ρ = density of exhaust gasses, kg/m 3
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