• Title/Summary/Keyword: Navier-Stokes analysis

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ANALYSIS AND COMPUTATIONS OF OPTIMAL AND FEEDBACK CONTROL PROBLEMS FOR NAVIER-STOKES EQUATIONS

  • Lee, Hyung-Chun
    • Journal of the Korean Mathematical Society
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    • v.34 no.4
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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.

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Convergence and Stability Analysis of LU Scheme on Unstructured Meshes: Part II - Navier-Stokes Equations (비정렬 격자계에서 LU implicit scheme의 수렴성 및 안정성 해석: Part II - Navier-Stokes 방정식)

  • Kim, Joo-Sung;Kwon, Oh-Joon
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.32 no.8
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    • pp.1-11
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    • 2004
  • A comprehensive study has been made for the investigation of the convergence and stability characteristics of the LU scheme for solving the Navier-Stokes equations on unstructured meshes. For this purpose the characteristics of the LU scheme was initially studied for a scalar model equation. Then the analysis was extended to the Navier-Stokes equations. It was shown that the LU scheme has an inherent stiffness in the streamwise direction. This stiffness increases when the grid aspect ratio becomes high and the cell Reynolds number becomes small. It was also shown that the stiffness related to the grid aspect ratio can be effectively eliminated by performing proper subiteration. The results were validated for a flat-plate turbulent flow.

Navier-Stokes Analysis of Two Dimensional Cascade Flow (2차원 익렬유동의 Navier-Stokes 해석)

  • 정희택;백제현
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.16 no.2
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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.

Modification of the Cubic law for a Sinusoidal Aperture using Perturbation Approximation of the Steady-state Navier-Stokes Equations (섭동 이론을 이용한 정상류 Navier-Stokes 방정식의 주기함수 간극에 대한 삼승 법칙의 수정)

  • 이승도
    • Tunnel and Underground Space
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    • v.13 no.5
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    • pp.389-396
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    • 2003
  • It is shown that the cubic law can be modified regarding the steady-state Navier-Stokes equations by using perturbation approximation method for a sinusoidal aperture variation. In order to adopt the perturbation theory, the sinusoidal function needs to be non-dimensionalized for the amplitude and wavelength. Then, the steady-state Navier-Stokes equations can be solved by expanding the non-dimensionalized stream function with respect to the small value of the parameter (the ratio of the mean aperture to the wavelength), together with the continuity equation. From the approximate solution of the Navier-Stokes equations, the basic cubic law is successfully modified for the steady-state condition and a sinusoidal aperture variation. A finite difference method is adopted to calculate the pressure within a fracture model, and the results of numerical experiments show the accuracy and applicability of the modified cubic law. As a result, it is noted that the modified cubic law, suggested in this study, will be used for the analysis of fluid flow through aperture geometry of sinusoidal distributions.

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.

A Comparative Study of the Navier-Stokes Equation & the Reynolds Equation in Spool Valve Analysis (스풀밸브 해석에서 Navier-Stokes 방정식과 Reynolds 방정식에 의한 비교 연구)

  • Hong, Sung-Ho;Son, Sang-Ik;Kim, Kyung-Woong
    • Tribology and Lubricants
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    • v.28 no.5
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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.

Applications of Stokes Eigenfunctions to the Numerical Solutions of the Navier-Stokes Equations in Channels and Pipes

  • Rummler B.
    • 한국전산유체공학회:학술대회논문집
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    • 2003.10a
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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.

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Application of Navier-Stokes Equations to Aerodynamic Design of Two-Dimensional Axial-Flow Compressor Blades (2차원 축류압축기 블레이드의 공력설계를 위한 Navier-Stokes방정식 적용 연구)

  • Chung, H.T.;Kim, J.S.
    • Journal of Power System Engineering
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    • v.2 no.3
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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.

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Parametric Study on the Aerodynamic Design of Axial-Flow Turbine Blades Using Two-Dimensional Navier-Stokes Equations (Navier-Stokes 방정식에 의한 축류터빈 블레이드의 공력학적 설계변수 특성 연구)

  • Chung, Ki-Seob;Chung, Hee-Taeg;Park, Jun-Young;Baek, Je-Hyun;Chang, Beom-Ik;Cho, Soo-Yong
    • 유체기계공업학회:학술대회논문집
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    • 2000.12a
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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.

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Analysis of Laminar Flow and Heat Transfer in Asymmetric, Sudden Expansion Channel (비대칭급확대채널의 층류유동 및 열전달 해석)

  • Won, Seung-Ho;Maeng, Joo-Sung;Son, Byung-Jin
    • The Magazine of the Society of Air-Conditioning and Refrigerating Engineers of Korea
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    • v.13 no.1
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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.

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