• 대한수학회지
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• 제34권4호
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• pp.841-857
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• 1997

We present analysis and some computational methods for boundary optimal and feedback control problems for Navier-Stokes equations. We use one example to illustrate our methodology and ideas which are applicable to general control problems for Navier-Stokes equations. First, we discuss the existence of optimal solutions and derive an optimality system of equations from which an optimal solution may be computed. Then we present a gradient type iterative method. Finally, we present some numerical results.

• 한국항공우주학회지
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• 제32권8호
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• pp.1-11
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• 2004

본 연구에서는 비정렬 격자계에서 가장 많이 쓰이는 근사 해법 중에 하나인 LU 기법의 Navier-Stokse 방정식에 대한 수렴성 및 안정성에 관한 연구를 수행하였다. 적절한 스칼라 모델 방정식을 사용하여 LU 기법이 갖는 고유한 특성에 관한 해석적 논의를 수행하였으며, 이를 Navier-Stokes 방정식으로 확장하여 해석하였다. 그 결과 LU 기법의 강성도는 격자 종횡비가 높아짐에 띠라, 그리고 격자 레이놀즈 수 감소함에 따라 증가하게 된다. 또한 내부반복계산을 통해서 이러한 강성도가 부분적으로 극복될 수 있음을 보였으며, 평판 난류 유동 해석을 통해서 해석 결과를 검증하였다.

• 대한기계학회논문집
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• 제16권2호
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• pp.313-324
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• 1992

Two-dimensional Navier-Stokes code has been developed for analysis of turbomachinery blade rows and other internal flows. The Navier-Stokes equations are written in a Cartesian coordinate system, then mapped into a generalized body-fitted coordinate system. All direction of viscous terms are incorporated and turbulent effects are modeled using the Baldwin-Lomax algebraic model. Equation are discretized using finite difference method on the C-type grids and solved using implicit LU-ADI decomposition scheme. Calculations are made at a VKI turbine cascade flow in a transonic wind-tunnel and compared to experimental data. Present numerical scheme is shown to be in good agreement with the previous experimental results and simulates the two-dimensional viscous flow phenomena.

• 터널과지하공간
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• 제13권5호
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• pp.389-396
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• 2003

본 연구는 정상류 Navier-Stokes 방정식에 섭동(perturbation) 이론을 적용하여 주기함수 간극에 대한 삼승법칙의 수정에 대해 논하였다. 이를 위해, 주기함수를 진폭과 파장에 대한 무차원 함수로 전환한 뒤 미소 계수에 대한 무차원 유동함수와 연속 방정식을 적용하였다. 이러한 과정을 통해 정상류 Navier-Stokes 방정식의 섭동 근사해를 구하였으며 이를 유한 차분법에 적용하였다. 단일 절리 모델에 대한유한 차분 수치해석을 통해, 수정된 삼승 법칙이 주기함수 간극의 유체 유동에 대한 정상류 Navier-Stokes 방정식의 섭동 근사해와 잘 일치하는 것으로 나타났다. 이를 통해 본 연구에서 제시된 삼승 법칙이 간극 분포에 따른 유체 유동의 평가에 있어 유용하게 적용될 수 있는 것으로 나타났다.

• Korean Journal of Mathematics
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• 제25권3호
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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.

• Tribology and Lubricants
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• 제28권5호
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• pp.218-232
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• 2012

In a spool valve analysis, the Reynolds equation is commonly used to investigate the lubrication characteristics. However, the validity of the Reynolds equation is questionable in a spool valve analysis because cavitation often occurs in the groove and the depth of the groove is much higher than the clearance in most cases. Therefore, the validity of the Reynolds equation in a spool valve analysis is investigated by comparing the results obtained from the Reynolds equation and the Navier-Stokes equation. Dimensionless parameters are determined from a nondimensional form of the governing equations. The differences between the lateral force, friction force, and volume flow rate (leakage) obtained by the Reynolds equation and those obtained by the Navier-Stokes equation are discussed. It is shown that there is little difference (less than 10%), except in the case of a spool valve with many grooves where no cavitation occurs in the grooves. In most cases, the Reynolds equation is effective for a spool valve analysis under a no cavitation condition.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2003년도 The Fifth Asian Computational Fluid Dynamics Conference
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• pp.63-65
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• 2003

General classes of boundary-pressure-driven flows of incompressible Newtonian fluids in three­dimensional (3D) channels and in 3D pipes with known steady laminar realizations are investigated respectively. The characteristic physical and geometrical quantities of the flows are subsumed in the kinetic Reynolds number Re and a parameter $\psi$, which involves the energetic ratio and the directions of the boundary-driven part and the pressure-driven part of the laminar flow. The solution of non-stationary dimension-free Navier-Stokes equations is sought in the form $\underline{u}=u_{L}+U,\;where\;u_{L}$ is the scaled laminar velocity and periodical conditions are prescribed for U in the unbounded directions. The objects of our numerical investigations are autonomous systems (S) of ordinary differential equations for the time-dependent coefficients of the spatial Stokes eigenfunction, where these systems (S) were received by application of the Galerkin-method to the dimension-free Navier-Stokes equations for u.

• 동력기계공학회지
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• 제2권3호
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• pp.15-20
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• 1998

An integrated computing system has been developed for a Navier-Stokes design procedure of an axial-flow compressor blades. The process is done on the four separate steps, i.e., determination of the basic profiles, generation of computational grids, cascade flow simulation and analysis of the computed results in design sense. Applications are made to the blade design of the LP compressor. Computational results are analyzed with respect to the flow-field characteristics and are compared with the expected design requirements. The present system are coupled with the design procedure of the turbomachinery blades using the Navier-Stokes technique.

• 유체기계공업학회:학술대회논문집
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• 유체기계공업학회 2000년도 유체기계 연구개발 발표회 논문집
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• pp.169-175
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• 2000

A design method for transonic turbine blades is developed based on Navier-Stokes equations. The present computing process is done on the four separate steps, 1.e., determination of the blade profile, generation of the computational grids, cascade flow simulation and analysis of the computed results in the sense of the aerodynamic performance. The blade shapes are designed using the cubic polynomials under the control of the design parameters. Numerical methods for the flow equations are based on Van-Leer's FVS with an upwind TVD scheme on the finite volume. Applications are made to the VKI transonic rotor blades. Computed results are analyzed with respect to the aerodynamic performance and are compared with the experimental data.

• 대한설비공학회지:설비저널
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• 제13권1호
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• pp.5-13
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• 1984

This analysis of numerical procedure is prediction of laminar flow and heat transfer at two dimension and steady flow in asymmetric sudden expansion channel. At former study, to analyse the flows with separation, the full Navier-Stokes equation is used, but there are many difficulties to analyse, and although significant progress has been made in the development of efficient computational methods for the Navier-Stokes equations, very large computation times are still required. In case of reward-facing flow, boundary-layer equation is used instead of full Navier-Stokes equation to analyse velocity fields, and result of this numerical analysis is good agreement with the given experimental study. In this case, since the computer time required for the boundary-layer calculation is an order of magnitude less than required for the solution of the full Navier-Stokes equation, this boundary-layer model provides a good approximate solution.