• The KSFM Journal of Fluid Machinery
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• v.7 no.3 s.24
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• pp.32-38
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• 2004

Shape of a multi-blades centrifugal fan is optimized by response surface method based on three-dimensional Navier-Stokes analysis. For numerical analysis, Reynolds-averaged Navier-Stokes equations with standard $k-{epsilon}$ turbulence model are transformed into non-orthogonal curvilinear coordinate system, and are discretized with finite volume approximations. Due to the large number of blades in this centrifugal fan, the flow inside of the fan is regarded as steady flow by introducing the impeller force models for economic calculations. Optimizations with and without constraints are carried out. Design variables, location of cur off, radius of cut off, expansion angle of scroll and width of impeller were selected to optimize the shapes of scroll and blades. Data points for response evaluations were selected by D-optimal design, and linear programming method was used for the optimization on the response surface. As a main result of the optimization, the efficiency was successfully improved. The correlation of efficiency with relative size of inactive zone at the exit of impeller is discussed as well as with average momentum fluxes in the scroll.

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.1726-1731
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• 2004

This paper presents the response surface optimization method using three-dimensional Navier-Stokes analysis to optimize the shape of a forward-curved blades centrifugal fan. For numerical analysis, Reynolds-averaged Navier-Stokes equations with $k-{\varepsilon}$ turbulence model are discretized with finite volume approximations. In order to reduce huge computing time due to a large number of blades in forward-curved blades centrifugal fan, the flow inside of the fan is regarded as steady flow by introducing the impeller force models. Three geometric variables, i.e., location of cut off, radius of cut off, and width of impeller, and one operating variable, i.e., flow rate, were selected as design variables. As a main result of the optimization, the efficiency was successfully improved. And, optimum design flow rate was found by using flow rate as one of design variables. It was found that the optimization process provides reliable design of this kind of fans with reasonable computing time.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.28 no.11
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• pp.1332-1338
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• 2004

This paper presents the response surface optimization method using three-dimensional Navier-Stokes analysis to optimize the shape of a forward-curved blades centrifugal fan. For numerical analysis, Reynolds-averaged Navier-Stokes equations with k-$\varepsilon$ turbulence model are discretized with finite volume approximations. In order to reduce huge computing time due to a large number of blades in forward-curved blades centrifugal fan, the flow inside of the fan is regarded as steady flow by introducing the impeller force models. Three geometric variables, i.e., location of cut off, radius of cut off, and width of impeller, and one operating variable, i.e., flow rate, were selected as design variables. As a main result of the optimization, the efficiency was successfully improved. And, optimum design flow rate was found by using flow rate as one of design variables. It was found that the optimization process provides reliable design of this kind of fans with reasonable computing time.

• Journal of the Korean Mathematical Society
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• v.36 no.1
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• pp.159-171
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• 1999

We formulate and study a finite element method for a linearized steady state, compressible, viscous Navier-Stokes equations in 2D, based on the discontinuous Galerkin method. Dislike the standard discontinuous galerkin method, we do not assume that the triangle sides be bounded away from the characteristic direction. the unique stability follows from the inf-sup condition established on the finite dimensional spaces for the (incompressible) Stokes problem. An error analysis having a jump discontinuity for pressure is shown.

• Journal of the Korean Mathematical Society
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• v.46 no.5
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• pp.1041-1069
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• 2009

We study the periodic homogenization of the non-stationary Stokes equations. The fundamental homogenization theorem and corrector theorem are proved under a very general assumption on the viscosity coefficients and data. The proofs are based on a weak formulation suitable for an application of classical Tartar's method of oscillating test functions. Such a weak formulation is derived by adapting an argument in Teman's book [Navier-Stokes Equations: Theory and Numerical Analysis, North-Holland, Amsterdam, 1984].

• Journal of the Korean Society of Propulsion Engineers
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• v.12 no.4
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• pp.56-62
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• 2008

This study presents the aerodynamic design and numerical analysis results on a transonic centrifugal compressor which is used for gas turbine systems. Mean-line analysis and quasi-3D analysis are used for the aerodynamic design, and Reynolds-averaged Navier-Stokes analysis is applied to flow analysis of the compressor. The aerodynamic parameters for a transonic compressor, such as pressure coefficient, swirl parameter, blade loading, are discussed, and flow characteristics in the impeller and diffuser are discussed.

• Journal of computational fluids engineering
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• v.11 no.3 s.34
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• pp.1-7
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• 2006

Euler and Navier-Stokes flow analyses for helicopter rotor in hover were performed as low and high fidelity analysis models respectively for the future multidisciplinary design optimization(MDO). These design-oriented analyses possess several attributes such as variable complexity, sensitivity-computation capability and modularity which analysis models involved in MDO are recommended to provide with. To realize PC-based analyses for both fidelity models, reduction of flow domain was made by appling farfield boundary condition based on 3-dimensional point sink with simple momentum theory and also periodic boundary condition in the azimuthal direction. Correlations of thrust, torque and their sensitivities between low and high complexity models were tried to evaluate the applicability of these analysis models in MDO process. It was found that the low-fidelity Euler analysis model predicted inaccurate sensitivity derivatives at relatively high angle of attack.

• Journal of computational fluids engineering
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• v.7 no.2
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• pp.25-32
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• 2002

The velocity and temperature profiles in the cabin of the automobile affect greatly the comfortableness of passengers. In this paper, the three dimensional flow and temperature analysis in the cabin of real automobile have been peformed. The three dimensional Navier-Stokes equation solver was validated by comparing with the other numerical data of a 1/5 scale model. The temperature field of cavity was also analyzed for the validation of energy equation solver. After the code validation, the numerical analysis of real field of flow and temperature of an automobile was peformed and the present result provides the insight of flow and temperature field of the inside of cabin.

• 한국전산유체공학회:학술대회논문집
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• 2001.05a
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• pp.1-8
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• 2001

A CFD-based design method for transonic axial compressor blades was developed based on three-dimensional Navier-Stokes flow physics. The method employs a sectional three-dimensional (S3D) analysis concept where the three-dimensional flow analysis is performed on the grid plane of a span station with spanwise flux components held fixed. The S3D analysis produced flow solutions nearly identical to those of three-dimensional analysis, regardless of the initialization of the flow field. The sectional design based on the S3D analysis can include three-dimensional effects of compressor flows and thus overcome the deficiencies associated with the use of quasi-three-dimensional flow physics in conventional sectional design. The S3D design was first used in the inverse triode to find the geometry that produces a specified target pressure distribution. The method was also applied to optimize the adiabatic efficiency of the blade sections of Rotor 37. A new blade was constructed with the optimized sectional geometries at several span stations and its aerodynamic performance was evaluated with three-dimensional analyses.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.10
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• pp.1335-1342
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• 2000

Three-dimensional flow analysis and numerical optimization methods are presented for the design of an axial-flow fan. Steady, incompressible, three-dimensional Reynolds-averaged Navier-Stokes equations are used as governing equations, and standard k- ${\varepsilon}$ turbulence model is chosen as a turbulence model. Governing equations are discretized using finite volume method. Steepest descent method, conjugate gradient method and BFGS method are compared to determine the searching directions. Golden section method and quadratic fit-sectioning method are tested for one dimensional search. Objective function is defined as a ratio of generation rate of the turbulent kinetic energy to pressure head. Two variables concerning sweep angle distribution are selected as the design variables. Performance of the final fan designed by the optimization was tested experimentally.