Abstract Optimum design of an upper-stage with bipropellant propulsion system consists of optimization of three major subsystems including thruster, feeding subsystem, and propellant tanks. Optimization of such a complex system involved in optimization of many disciplines including structure, heat transfer, aerothermodynamics, guidance and control, trajectory and propulsion. Hard coupling of the disciplines increase the optimization processing times. Multidisciplinary design optimization algorithm can derive the optimum configuration but more elapsed time is needed for single-level methods such as all at once (AAO) and lower feasibility occurred in multi-level methods such as collaborative optimization (CO). In this paper, a new multidisciplinary design optimization framework is proposed for such coupled disciplines with concentrating on the propulsion system. The proposed framework uses Combined Single-level and Bi-level Optimizations (CSBO) frameworks to minimize numbers of design variables and system constraints when feasibility is increased. For this goal, modeling of every discipline is introduced and the design algorithm validated by redesigning of two real bipropellant thrusters. Three MDO frameworks are applied for our problem including AAO, CO and CSBO. Comparisons between the results show that CSBO can find the optimum solution in shorter elapsed time with lower F-count. Therefore, CSBO is more efficient for complex systems with coupled disciplines.

    Highlights The new MDO framework is proposed for a complex system with coupled disciplines. CSBO minimizes the numbers of design variables and the system constrains. The optimum design of an upper-stage is selected as a case study. Three MDO frameworks are applied for our problem including AAO, CO and CSBO. As results, CSBO can find the optimum solution in shorter elapsed.


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    Title :

    A new approach in multidisciplinary design optimization of upper-stages using combined framework


    Contributors:

    Published in:

    Acta Astronautica ; 114 ; 174-183


    Publication date :

    2015-04-15


    Size :

    10 pages




    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English


    Keywords :

    AAO , all at once , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>V</mi></mrow> <mrow><mi>T</mi> <mi>a</mi> <mi>n</mi> <mi>k</mi></mrow></msub> <mspace></mspace></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>R</mi></mrow> <mrow><mi>T</mi> <mi>a</mi> <mi>n</mi> <mi>k</mi></mrow></msub></math> , volume, radius of tanks , CO , collaborative optimization , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>L</mi></mrow> <mrow><mi>c</mi> <mi>y</mi> <mi>l</mi></mrow></msub></math> , cylindrical length of tanks , CSBO , Combined Single-level and Bi-level Optimizations , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>R</mi></mrow> <mrow><mi>max</mi></mrow></msub> <mspace></mspace></math> , maximum permitted radius , MDO , multidisciplinary design optimization , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>Z</mi></mrow> <mrow><mi>f</mi> <mi>i</mi> <mi>l</mi> <mi>l</mi></mrow></msub> <mspace></mspace></math> , filling factor of tanks , MDF , multidisciplinary feasible , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>V</mi></mrow> <mrow><mi>f</mi> <mi>u</mi> <mi>e</mi> <mi>l</mi></mrow></msub> <mspace></mspace></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>V</mi></mrow> <mrow><mi>T</mi> <mi>a</mi> <mi>n</mi> <mi>k</mi> <mo>−</mo> <mi>f</mi> <mi>u</mi> <mi>e</mi> <mi>l</mi></mrow></msub> <mspace></mspace></math> , fuel volume, fuel tank volume , BLISS , bi-level integrated system synthesis , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>V</mi></mrow> <mrow><mi>o</mi> <mi>x</mi></mrow></msub> <mspace></mspace></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>V</mi></mrow> <mrow><mi>T</mi> <mi>a</mi> <mi>n</mi> <mi>k</mi> <mo>−</mo> <mi>o</mi> <mi>x</mi></mrow></msub> <mspace></mspace></math> , oxidant volume, oxidant tank volume , CSSO , concurrent subspace optimization , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>V</mi></mrow> <mrow><mi>e</mi> <mi>m</mi> <mi>p</mi> <mi>t</mi> <mi>y</mi></mrow></msub> <mspace></mspace></math> , Empty volume of tanks , <italic>O</italic>/<italic>F</italic>, , oxidant mass by fuel mass ratio , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>V</mi></mrow> <mrow><mi>T</mi> <mi>o</mi> <mi>t</mi> <mi>a</mi> <mi>l</mi></mrow></msub> <mspace></mspace></math> , total volume of tanks , SQP , sequential quadratic optimization , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>V</mi></mrow> <mrow><mi>P</mi> <mi>r</mi> <mi>e</mi> <mi>s</mi> <mi>s</mi> <mo>.</mo> <mspace></mspace> <mspace></mspace> <mi>T</mi> <mi>a</mi> <mi>n</mi> <mi>k</mi></mrow></msub> <mspace></mspace></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>R</mi></mrow> <mrow><mi>P</mi> <mi>r</mi> <mi>e</mi> <mi>s</mi> <mi>s</mi> <mo>.</mo> <mspace></mspace> <mspace></mspace> <mi>T</mi> <mi>a</mi> <mi>n</mi> <mi>k</mi></mrow></msub> <mspace></mspace></math> , volume, radius of pressurized gas tank , GA , genetic algorithm , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>R</mi></mrow> <mrow><mi>g</mi> <mi>a</mi> <mi>s</mi></mrow></msub> <mspace></mspace></math> , constant parameter of pressurizer gas , <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mrow><mi>A</mi></mrow> <mo>⁎</mo></msup> <mspace></mspace></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>R</mi></mrow> <mrow><mi>t</mi></mrow></msub> <mspace></mspace></math> , throat area, radius of throat , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>T</mi></mrow> <mrow><mi>∞</mi></mrow></msub></math> , initial temperature , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>P</mi></mrow> <mrow><mi>e</mi></mrow></msub> <mspace></mspace></math> , pressure at exit of the nozzle , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>M</mi></mrow> <mrow><mi>P</mi> <mi>r</mi> <mi>e</mi> <mi>s</mi> <mi>s</mi> <mo>.</mo> <mspace></mspace> <mspace></mspace> <mi>G</mi> <mi>a</mi> <mi>s</mi></mrow></msub></math> , required mass of pressurizer gas , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>M</mi></mrow> <mrow><mi>e</mi></mrow></msub> <mspace></mspace> <mspace></mspace></math> , Mach number of exit nozzle , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>P</mi></mrow> <mrow><mi>max</mi></mrow></msub> <mspace></mspace></math> , maximum pressure of pressurized gas tank , <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>γ</mi></math> , isentropic exponent , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>L</mi></mrow> <mrow><mi>f</mi> <mi>i</mi> <mi>l</mi> <mi>m</mi></mrow></msub> <mspace></mspace></math> , length of film cooling , <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>m</mi> <mo>̇</mo></mover></math> , Mass flow of nozzle (thruster) , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mover><mi>m</mi> <mo>̇</mo></mover></mrow> <mrow><mi>f</mi> <mi>i</mi> <mi>l</mi> <mi>m</mi></mrow></msub> <mspace></mspace></math> , mass flow of film cooling , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>g</mi></mrow> <mrow><mn>0</mn></mrow></msub> <mspace></mspace></math> , gravitational acc , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>T</mi></mrow> <mrow><mi>v</mi> <mi>a</mi> <mi>p</mi></mrow></msub> <mspace></mspace></math> , vaporization temperature of coolant , <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi> <mi>h</mi> <mi>r</mi> <mi>u</mi> <mi>s</mi> <msub><mrow><mi>t</mi></mrow> <mrow><mi>v</mi> <mi>a</mi> <mi>c</mi></mrow></msub> <mspace></mspace></math> , vacuum thrust , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mover><mi>m</mi> <mo>̇</mo></mover></mrow> <mrow><mi>v</mi> <mi>a</mi> <mi>p</mi></mrow></msub> <mspace></mspace></math> , mass flow of vaporization , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>A</mi></mrow> <mrow><mi>e</mi></mrow></msub> <mspace></mspace></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>R</mi></mrow> <mrow><mi>e</mi></mrow></msub> <mspace></mspace></math> , exit area, radius of exit section , <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mrow><mover><mi>q</mi> <mo>̇</mo></mover></mrow> <mrow><mi>h</mi></mrow> <mrow><mi>γ</mi></mrow></msubsup> <mspace></mspace></math> , convective heat flux , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>P</mi></mrow> <mrow><mi>c</mi> <mi>o</mi> <mi>m</mi> <mi>b</mi></mrow></msub> <mspace></mspace></math> , pressure of combustion chamber , <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mrow><mover><mi>q</mi> <mo>̇</mo></mover></mrow> <mrow><mi>r</mi></mrow> <mrow><mi>γ</mi></mrow></msubsup> <mspace></mspace></math> , radiative heat flux , <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mrow><mi>P</mi></mrow> <mo>⁎</mo></msup></math> , pressure of throat , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>h</mi></mrow> <mrow><mi>γ</mi></mrow></msub> <mspace></mspace></math> , convective heat coefficient , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>T</mi></mrow> <mrow><mi>c</mi> <mi>o</mi> <mi>m</mi> <mi>b</mi></mrow></msub></math> , temperature of combustion chamber , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>T</mi></mrow> <mrow><mi>s</mi></mrow></msub></math> , wall temperature , <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mrow><mi>T</mi></mrow> <mo>⁎</mo></msup></math> , Temperature at throat , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>ε</mi></mrow> <mrow><mi>γ</mi></mrow></msub> <mspace></mspace></math> , radiative coefficient of hot gas , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>T</mi></mrow> <mrow><mi>e</mi></mrow></msub></math> , temperature at exit section , <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>T</mi> <mo>˜</mo></mover></math> , mean temperature , <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math> , constant parameter of gas (combustion product ) , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>Z</mi></mrow> <mrow><mi>c</mi></mrow></msub> <mspace></mspace></math> , correction factor , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>V</mi></mrow> <mrow><mi>c</mi> <mi>o</mi> <mi>m</mi> <mi>b</mi></mrow></msub> <mspace></mspace></math> , volume of combustion chamber , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>C</mi></mrow> <mrow><mi>P</mi></mrow></msub> <mspace></mspace></math> , specific heat at constant pressure , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>L</mi></mrow> <mrow><mi>c</mi> <mi>o</mi> <mi>m</mi> <mi>b</mi></mrow></msub> <mspace></mspace></math> , Length of combustion chamber , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>n</mi></mrow> <mrow><mi>S</mi> <mo>.</mo> <mi>F</mi></mrow></msub> <mspace></mspace></math> , safety factor , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>V</mi></mrow> <mrow><mi>i</mi> <mi>n</mi> <mi>j</mi></mrow></msub> <mspace></mspace></math> , injection velocity of propellant , <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mrow><mover><mi>q</mi> <mo>̇</mo></mover></mrow> <mrow><mi>s</mi> <mi>t</mi> <mi>r</mi></mrow> <mrow><mi>r</mi></mrow></msubsup> <mspace></mspace></math> , radiative heat flux from structure , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>P</mi></mrow> <mrow><mi>Tank</mi></mrow></msub> <mspace></mspace></math> , tanks pressure , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>δ</mi></mrow> <mrow><mi>c</mi> <mi>o</mi> <mi>m</mi> <mi>b</mi></mrow></msub></math> , required thickness of combustion chamber , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>D</mi></mrow> <mrow><mi>c</mi> <mi>o</mi> <mi>m</mi> <mi>b</mi></mrow></msub> <mspace></mspace></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>R</mi></mrow> <mrow><mi>c</mi> <mi>o</mi> <mi>m</mi> <mi>b</mi></mrow></msub> <mspace></mspace></math> , diameter, radius of combustion chamber , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>δ</mi></mrow> <mrow><mi>p</mi> <mi>r</mi> <mi>e</mi> <mi>s</mi> <mo>.</mo> <mspace></mspace> <mi>G</mi> <mi>a</mi> <mi>s</mi></mrow></msub> <mspace></mspace></math> , required thickness of , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>θ</mi></mrow> <mrow><mn>1</mn></mrow></msub> <mspace></mspace></math> , convergent angle , <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mrow><mi>δ</mi></mrow> <mrow><mi>T</mi> <mi>a</mi> <mi>n</mi> <mi>k</mi></mrow> <mrow><mi>s</mi> <mi>p</mi> <mi>h</mi></mrow></msubsup> <mspace></mspace></math> , required thickness of spherical tank , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>θ</mi></mrow> <mrow><mn>2</mn></mrow></msub> <mspace></mspace></math> , divergent angle , <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mrow><mi>δ</mi></mrow> <mrow><mi>T</mi> <mi>a</mi> <mi>n</mi> <mi>k</mi></mrow> <mrow><mi>c</mi> <mi>y</mi> <mi>l</mi></mrow></msubsup> <mspace></mspace></math> , required thickness of cylindrical tank , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>Z</mi></mrow> <mrow><mi>e</mi> <mi>x</mi> <mi>p</mi> <mi>a</mi> <mi>n</mi> <mi>t</mi> <mi>i</mi> <mi>o</mi> <mi>n</mi></mrow></msub> <mspace></mspace></math> , expansion ratio of nozzle (area) , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>δ</mi></mrow> <mrow><mi>n</mi> <mi>o</mi> <mi>z</mi> <mi>z</mi> <mi>l</mi> <mi>e</mi></mrow></msub> <mspace></mspace></math> , required thickness of nozzle , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>L</mi></mrow> <mrow><mi>c</mi> <mi>o</mi> <mi>n</mi></mrow></msub> <mspace></mspace></math> , convergent length of nozzle , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>n</mi></mrow> <mrow><mi>σ</mi></mrow></msub> <mspace></mspace></math> , mass correction factor , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>L</mi></mrow> <mrow><mi>d</mi> <mi>i</mi> <mi>v</mi></mrow></msub> <mspace></mspace></math> , divergent length of nozzle , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>λ</mi></mrow> <mrow><mn>2</mn></mrow></msub> <mspace></mspace></math> , temperature correction factor , Multidisciplinary design , Optimization , Bipropellant thruster , Upper-stage



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