• Title, Summary, Keyword: drag minimization

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PENALIZED APPROACH AND ANALYSIS OF AN OPTIMAL SHAPE CONTROL PROBLEM FOR THE STATIONARY NAVIER-STOKES EQUATIONS

  • Kim, Hong-Chul
    • Journal of the Korean Mathematical Society
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    • v.38 no.1
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    • pp.1-23
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    • 2001
  • This paper is concerned with an optimal shape control problem for the stationary Navier-Stokes system. A two-dimensional channel flow of an incompressible, viscous fluid is examined to determine the shape of a bump on a part of the boundary that minimizes the viscous drag. by introducing an artificial compressibility term to relax the incompressibility constraints, we take the penalty method. The existence of optima solutions for the penalized problem will be shown. Next, by employing Lagrange multipliers method and the material derivatives, we derive the shape gradient for the minimization problem of the shape functional which represents the viscous drag.

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A Design Optimization Study of Blunt Nose Hypersonic Flight Vehicle Using Surface Heat-transfer and Drag Minimization (표면열전달과 항력을 고려한 극초음속 비행체 선두부 최적형상설계)

  • Lim S.;Seo J. I.;Song D. J.
    • 한국전산유체공학회:학술대회논문집
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    • pp.197-201
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    • 2004
  • A design optimization of Sphere-Cone blunt nose hypersonic flight vehicle has been studied by using upwind Navier-Stokes method and numerical optimization method. Heat transfer coefficient and drag coefficient are selected as objective function or design constraint. Control points of Bezier curve are considered as design variable.

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Reference Trajectory Design for Atmosphere Re-entry of Transportation Mechanical Structure (수송기계구조물의 대기권 재진입 기준궤도 설계)

  • Park, J.H.;Eom, W.S.
    • Journal of Power System Engineering
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    • v.7 no.4
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    • pp.67-73
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    • 2003
  • The entry guidance design involves trajectory optimization and generation of a drag acceleration profile as the satisfaction of trajectory conditions during the entry flight. The reference trajectory is parameterized and optimized as piecewise linear functions of the velocity. A regularization technique is employed to achieve desired properties of the optimal drag profile. The regularized problem has smoothness properties and the minimization of performance index then prevents the drag acceleration from varying too fast, thus eliminating discontinuities. This paper shows the trajectory control using the simple control law as well as the information of reference drag acceleration.

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Design Optimization of Transonic Airfoils Based on the Navier-Stokes Equation (Navier-Stokes 방정식을 이용한 천음속 익형의 설계최적화 연구)

  • Lee Hyeong Min;Jo Chang Yeol
    • 한국전산유체공학회:학술대회논문집
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    • pp.177-185
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    • 1999
  • The airfoil design optimization procedures based on the Navier-Stokes equations were developed, This procedure enables more realistic and practical transonic airfoil designs. The modified Hicks-Henne functions were used to generate the shape of airfoils. Five Hick-Henne functions were used to design upper surface of airfoil only. To enhance the ability of Hick-Henne function to generate various airfoil shape with limited number of functions, the positions of control points were adjusted through optimization procedure. The design procedure was applied to the single-point design for the drag minimization problem with lift and area constraints. The result shows the capability of the procedure to generate much realistic airfoils with very small drag-creep in the low transonic regime. This is mainly due to the viscosity effect of Navier-Stokes flow analysis. However, in the higher transonic range tile drag-creep appears. The multi-point design is shown to be an effective way to avoid the drag-creep and improve off-design performance which is very similar in the Euler design.

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A Multi-Point Design Optimization of a Space Launcher Nose Shapes Using Response Surface Method (반응면 기법을 이용한 발사체 선두부 다점 최적설계)

  • Kim Sang-Jin;Seon Yong-Hee;Lee Jae-Woo;Byun Yung-Hwan
    • 한국전산유체공학회:학술대회논문집
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    • pp.46-53
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    • 2000
  • To improve the performance at all design points, multi-point optimization method is implemented for the nose fairing shape design of space launcher. The response surface method is used to effectively reduce the huge computational loads during the optimization process. The drag is selected as the objective function, and the surface heat transfer characteristics, and the internal volume of the nose fairing ate considered as design constraints. Full Wavier-Stokes equations are selected as governing equations. Two points drag minimization, and two points drag / heat flux optimization were successfully performed and configurations which have good performance for the wide operation range were derived. By considering three design points, the space launcher shape which undergoes the least drag during whole flight mission was designed. For all the design cases, the constructed response surfaces show good confidence level with only 23 design points with the proper stretching of the design space.

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SENSITIVITY ANALYSIS OF A SHAPE CONTROL PROBLEM FOR THE NAVIER-STOKES EQUATIONS

  • Kim, Hongchul
    • Korean Journal of Mathematics
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    • v.25 no.3
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    • pp.405-435
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    • 2017
  • We deal with a sensitivity analysis of an optimal shape control problem for the stationary Navier-Stokes system. A two-dimensional channel flow of an incompressible, viscous fluid is examined to determine the shape of a bump on a part of the boundary that minimizes the viscous drag. By using the material derivative method and adjoint variables for a shape sensitivity analysis, we derive the shape gradient of the design functional for the model problem.

MULTI-STAGE AERODYNAMIC DESIGN OF AIRCRAFT GEOMETRIES BY KRIGING-BASED MODELS AND ADJOINT VARIABLE APPROACH (Kriging 기반 모델과 매개변수(Adjoint Variable)법을 이용한 항공기형상의 2단계 공력최적설계)

  • Yim, J.W.;Lee, B.J.;Kim, C.
    • 한국전산유체공학회:학술대회논문집
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    • pp.57-65
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    • 2009
  • An efficient and high-fidelity design approach for wing-body shape optimization is presented. Depending on the size of design space and the number of design of variable, aerodynamic shape optimization process is carried out via different optimization strategies at each design stage. In the first stage, global optimization techniques are applied to planform design with a few geometric design variables. In the second stage, local optimization techniques are used for wing surface design with a lot of design variables to maintain a sufficient design space with a high DOF (Degree of Freedom) geometric change. For global optimization, Kriging method in conjunction with Genetic Algorithm (GA) is used. Asearching algorithm of EI (Expected Improvement) points is introduced to enhance the quality of global optimization for the wing-planform design. For local optimization, a discrete adjoint method is adopted. By the successive combination of global and local optimization techniques, drag minimization is performed for a multi-body aircraft configuration while maintaining the baseline lift and the wing weight at the same time. Through the design process, performances of the test models are remarkably improved in comparison with the single stage design approach. The performance of the proposed design framework including wing planform design variables can be efficiently evaluated by the drag decomposition method, which can examine the improvement of various drag components, such as induced drag, wave drag, viscous drag and profile drag.

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Influence of Flow Solvers On Airfoil Shape Optimization (날개꼴의 형상 최적화를 위한 유동방정식 영향 연구)

  • Chung H. T.;Ryu B. S.
    • 한국전산유체공학회:학술대회논문집
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    • pp.171-176
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    • 1999
  • In the present paper, three types of the flow solvers were used to investigate the influence on the airfoil shape optimization. The adopted equations, i.e., Euler , thin layer Navier- Stokes and full Navier-Stokes ones, are solved using implicit LU-ADI decomposition scheme. The feasible direction algorithm with the sinusoidal function was used as an optimization algorithm. The present numerical method was applied to the drag minimization problems under the initial shape of NACA0012 airfoils.

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Influence of Flow Solvers On Airfoil Shape Optimization (날개꼴의 형상 최적화를 위한 유동방정식 영향 연구)

  • H. T. 경상대학교 항공기계공학부;Ryu B. S.
    • Journal of computational fluids engineering
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    • v.4 no.2
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    • pp.67-73
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    • 1999
  • In the present paper, three types of the flow solvers were used to investigate the influence on the airfoil shape optimization. The adopted equations, i.e., Euler, thin layer Navier-Stokes and full Navier-Stokes ones. are solved using implicit LU-ADI decomposition scheme. The gradient projection method with the sinusoidal function was used as an optimization algorithm. The present numerical method was applied to the drag minimization problems under the initial shape of NACA0012 airfoils.

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A BOUNDARY CONTROL PROBLEM FOR THE TIME-DEPENDENT 2D NAVIER-STOKES EQUATIONS

  • Kim, Hongchul;Kim, Seon-Gyu
    • Korean Journal of Mathematics
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    • v.16 no.1
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    • pp.57-84
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    • 2008
  • In this paper, a boundary control problem for a flow governed by the time-dependent two dimensional Navier-Stokes equations is considered. We derive a mathematical formulation and a relevant process for an appropriate control along the part of the boundary to minimize the drag due to the flow. After showing the existence of an optimal solution, the first order optimality conditions are derived. The strict differentiability of the state solution in regard to the control parameter shall be exposed rigorously, and the necessary conditions along with the system for the optimal solution shall be deduced in conjunction with the evaluation of the first order Gateaux derivative to the performance functional.

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