• 한국전산유체공학회:학술대회논문집
• /
• 한국전산유체공학회 2003년도 The Fifth Asian Computational Fluid Dynamics Conference
• /
• pp.15-16
• /
• 2003

An implicit pressure correction method on unstructured Cartesian grid is developed for the incompressible Navier-Stokes equations. An immersed boundary method is also incorporated to treat the body geometry. Tests show that with an appropriate amount of dissipation, the method is second order accurate both in time and space. The driven cavity flows with and without immersed bodies are computed to demonstrate the capability of the present scheme.

• 대한수학회지
• /
• 제35권4호
• /
• pp.869-880
• /
• 1998

In this paper, we show that the weak solutions of the time-dependent Magnetohydrodynamics equations in 3 dimensional periodic domain belong to L(equation omitted)(0, T; V$_{r}$) following the method of Foias-Guillope-Temam for Navier-Stokes equations.s.

• 대한기계학회논문집B
• /
• 제27권10호
• /
• pp.1457-1463
• /
• 2003

In this paper, the response surface method using three-dimensional Navier-Stokes analysis to optimize the shape of a multi-blade centrifugal fan, is described. For numerical analysis, Reynolds-averaged Navier-Stokes equations with standard k - c 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. Linear Upwind Differencing Scheme(LUDS) is used to approximate the convection terms in the governing equations. SIMPLEC algorithm is used as a velocity-pressure correction procedure. 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. It was found that the optimization process provides reliable design of this kind of fans with reasonable computing time.

• 대한기계학회:학술대회논문집
• /
• 대한기계학회 2003년도 춘계학술대회
• /
• pp.2157-2161
• /
• 2003

In this paper, the response surface method using three-dimensional Navier-Stokes analysis to optimize the shape of a forward-curved blades centrifugal fan, is described. For numerical analysis, Reynolds-averaged Navier-Stokes equations with standard k-e 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 forward-curved blades centrifugal fan, the flow inside of the fan is regarded as steady flow by introducing the impeller force models for economic calculations. Linear Upwind Differencing Scheme(LUDS) is used to approximate the convection terms in the governing equations. SIMPLEC algorithm is used as a velocity-pressure correction procedure. 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. It was found that the optimization process provides reliable design of this kind of fans with reasonable computing time

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제3권2호
• /
• pp.161-171
• /
• 1999

Aerodynamic sensitivity analysis codes are developed via the hand-differentiation using a direct differentiation method and an adjoint method respectively from discrete two-dimensional compressible Navier-Stokes equations. Unlike previous other researches, Baldwin-Lomax algebraic turbulence model is also differentiated by hand to obtain design sensitivities with respect to design variables of interest in turbulent flows. Discrete direct sensitivity equations and adjoint equations are efficiently solved by the same time integration scheme adopted in the flow solver routine. The required memory for the adjoint sensitivity code is greatly reduced at the cost of the computational time by allowing the large banded flux jacobian matrix unassembled. Direct sensitivity code results are found to be exactly coincident with sensitivity derivatives obtained by the finite difference. Adjoint code results of a turbulent flow case show slight deviations from the exact results due to the limitation of the algebraic turbulence model in implementing the adjoint formulation. However, current adjoint sensitivity code yields much more accurate sensitivity derivatives than the adjoint code with the turbulence eddy viscosity being kept constant, which is a usual assumption for the prior researches.

• 대한기계학회:학술대회논문집
• /
• 대한기계학회 2002년도 학술대회지
• /
• pp.31-34
• /
• 2002

An efficient implicit multigrid method is presented for the Navier-Stokes and $k-{\omega}$ turbulence equations. Freezing and limiting strategies are applied to improve the robustness and convergence of the multigrid method. The eddy viscosity and strongly nonlinear production terms of turbulence are frozen in the coarser grids by passing down the values without update of them. The turbulence equations together with the Navier-Stokes equations, however, are consecutively solved on the coarser grids in a loosely coupled fashion. A simple limit for k is also introduced to circumvent slow-down of convergence. Numerical results for the unseparated and separated transonic airfoil flows show that all computations converge well without any robustness problem and the computing time is reduced to a factor of about 3 by the present multigrid method.

• 대한기계학회논문집
• /
• 제17권9호
• /
• pp.2329-2338
• /
• 1993

An accurate analysis procedure to solve the flow about a flat plate at various incidences has been developed. The Navier-Stokes equations of stream function and vorticity form are solved in a sufficiently large computational domain, in which the grid lines are mutually orthogonal. The details of the flow near the singularity at the tip of the plate is well captured by the analytic solution which is asymptotically matched to the numerically generated outer solution. The solution for each region is obtained iteratively : the solution of one (inner or outer) region uses that of the other as the boundary condition after each cycle. The resulting procedure is accurate everywhere and also computationally efficient as the singularity has been removed. It is applied to the flat plate for a wide range of Re : the results agree very well with the existing computation and experiment.

• Journal of Mechanical Science and Technology
• /
• 제14권9호
• /
• pp.1005-1012
• /
• 2000

Numerical optimization techniques combined with a three-dimensional thin-layer Navier-Stokes solver are presented to find an optimum shape of a stator blade in an axial compressor through calculations of single stage rotor-stator flow. Governing differential equations are discretized using an explicit finite difference method and solved by a multi-stage Runge-Kutta scheme. Baldwin-Lomax model is chosen to describe turbulence. A spatially-varying time-step and an implicit residual smoothing are used to accelerate convergence. A steady mixing approach is used to pass information between stator and rotor blades. For numerical optimization, searching direction is found by the steepest decent and conjugate direction methods, and the golden section method is used to determine optimum moving distance along the searching direction. The object of present optimization is to maximize efficiency. An optimum stacking line is found to design a custom-tailored 3-dimensional blade for maximum efficiency with the other parameters fixed.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제14권1호
• /
• pp.43-56
• /
• 2010

The representative numerical algorithms to solve the time dependent Navier-Stokes equations are projection type methods. Lots of projection schemes have been developed to find more accurate solutions. But most of projection methods [4, 11] suffer from inconsistency and requesting unknown datum. E and Liu in [5] constructed the gauge method which splits the velocity $u=a+{\nabla}{\phi}$ to make consistent and to replace requesting of the unknown values to known datum of non-physical variables a and ${\phi}$. The errors are evaluated in [9]. But gauge method is not still obvious to find out suitable combination of discrete finite element spaces and to compute boundary derivative of the gauge variable ${\phi}$. In this paper, we define 4 gauge algorithms via combining both 2 decomposition operators and 2 boundary conditions. And we derive variational derivative on boundary and analyze numerical results of 4 gauge algorithms in various discrete spaces combinations to search right discrete space relation.

• 대한수학회지
• /
• 제48권6호
• /
• pp.1153-1170
• /
• 2011

In this paper, spatial decay estimates for the time dependent compressible viscous isentropic flow in a semi-infinite three dimensional pipe are derived. An upper bound for the total energy in terms of the initial boundary data is obtained as well. The results established in this paper may be viewed as a version of Saint-Venant's principle in transient compressible Navier-Stokes flow.