• 유체기계공업학회:학술대회논문집
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• 2001.11a
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• pp.293-299
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• 2001

Since the previous cut-and-try design algorithm require much cost and time, it has recently been concerned the automatic design technique using the CFD and optimum design algorithm. In this study, the Navier-Stokes equations is solved to consider the more detail viscous flow informations of cascade interaction and O-H multiblock grid system is generated to impose an accurate boundary condition. The cubic-spline interpolation is applied to handle a relative motion of a rotor to the stator. To validate present procedure, the time averaged aerodynamic loads are compared with experiment and good agreement obtained. Once the N-S equations have been solved, the computed aerodynamic loads may be used to computed the sensitivities of the aerodynamic objective function. The Modified Method of feasible Direction(MMFD) is usef to compute the

• 한국전산유체공학회:학술대회논문집
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• 2003.10a
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• pp.33-34
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• 2003

• Journal of the Korean Mathematical Society
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• v.53 no.1
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• pp.127-146
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• 2016

We consider a coupled system of Keller-Segel type equations and the incompressible Navier-Stokes equations in spatial dimension two. We show temporal decay estimates of solutions with small initial data and obtain their asymptotic profiles as time tends to infinity.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.383-405
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• 2004

We study the incomprssible Navier Stokes equations for the flow inside contraction geometry. The governing equations are expressed in the vorticity-stream function formulations. A rectangular computational domain is arised by elliptic grid generation technique. The numerical solution is based on a technique of automatic numerical generation of acurvilinear coordinate system by transforming the governing equation into computational plane. The transformed equations are approximated using central differences and solved simultaneously by successive over relaxation iteration. The time dependent of the vorticity equation solved by using explicit marching procedure. We will apply the technique on several irregular-shapes.

• Journal of the Korean Institute of Navigation
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• v.9 no.2
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• pp.43-63
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• 1985

As a circular cylinder has a comparatively simple shape and becomes a basic problem for flows around other various shapes of bodies, the problem of two-dimensional viscous flow around the circular cylinder has been investigated, both theoretically and experimentally. But not a few problems are left unsolved. It is well known that the calculations are successfully made with the approximations of Stokes or Oseen for very low Reynolds numbers, but as Reynolds number is increased, Oseen's approximations as well as Stokes's ones become more and more remote from the exact solution of the Navier-Stokes equations. Therefore, in this paper, the authors transform the Navier-Stokes equations into the finite difference equations in the steady two-dimensional viscous flow at Reynolds number up to 45, and then solve the solution of the Navier-Stokes equations numerically. Also, the authors examine the accuracy of the solution by means of flow visualization with aluminum powder. The main results are as follows; (1) The critical Reynolds number at which twin vortices begin to form in the rear of the circular cylinder is found to be 6 in the experiment and 4 in the numerical solution. (2) As Reynolds number is increased, it is proved that the ratio of the length of the twin vortices to the diameter is grown almost linearly, both experimentally and numerically. (3) Separation angle is also increased according to reynolds number. But it is found that it would converge into 101.3 degrees, both experimentally and numerically.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.10
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• pp.1457-1463
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• 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.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.2157-2161
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• 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 Mathematical Society
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• v.50 no.5
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• pp.1129-1163
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• 2013

Based on finite element discretization, two linearization approaches to the defect-correction method for the steady incompressible Navier-Stokes equations are discussed and investigated. By applying $m$ times of Newton and Picard iterations to solve an artificial viscosity stabilized nonlinear Navier-Stokes problem, respectively, and then correcting the solution by solving a linear problem, two linearized defect-correction algorithms are proposed and analyzed. Error estimates with respect to the mesh size $h$, the kinematic viscosity ${\nu}$, the stability factor ${\alpha}$ and the number of nonlinear iterations $m$ for the discrete solution are derived for the linearized one-step defect-correction algorithms. Efficient stopping criteria for the nonlinear iterations are derived. The influence of the linearizations on the accuracy of the approximate solutions are also investigated. Finally, numerical experiments on a problem with known analytical solution, the lid-driven cavity flow, and the flow over a backward-facing step are performed to verify the theoretical results and demonstrate the effectiveness of the proposed defect-correction algorithms.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.21 no.3
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• pp.392-404
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• 1997

The flow induced by the oscillatory motion of a solid body is important in a number of practical problems. As the solid boundary oscillates harmonically, there is steady streaming motion invoked by the Reynolds stresses, which could cause extensive migration of the fluid during a period of fluid motion. We here analyzed the flow in a square cavity with an oscillating top wall for the parameters which make the time derivatives and the convective terms equally important in the entire cavity flow. The full Navier-Stokes equations are solved by the second-order time accurate Momentum Coupling Method which is devised by the authors. The particular numerical scheme does not need subiteration at each time step which is usually a required process to calculate the incompressible Navier-Stokes equations. The effect of two parameters, the Reynolds number and the frequency parameter, on the oscillatory flow has been investigated.

• Smart Media Journal
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• v.4 no.2
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• pp.9-16
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• 2015

Fluids appear in innumerable phenomena; therefore, it is interesting to reproduce those phenomena by computer graphics techniques. However, this process is not trivial. We work with a fluid simulation that uses Navier-Stokes equations to model the fluid, a semi-Lagrangian approach to solve it and the level set method to track the surface of the fluid. Modified versions of the Navier-Stokes equations for computer graphics allow us to create a wide diversity of effects. In this paper, we propose a technique that allows us to integrate a force inspired by surface tension into the model. We describe which information we need and how to modify the model with this new approach. We end up with a modified simulation that has additional effects that might be suitable for computer graphics purposes. The effects that we are able to recreate are small waves and droplet-like formations close to the surface of the fluid. This model preserves the overall behavior governed by the Navier-Stokes equations.