• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.1 s.173
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• pp.16-28
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• 2000

The steady rotating flows in eccentric annulus has been studied by a numerical method based on the spectral collocation method. The inner cylinder has a constant angular velocity while the outer on e is stationary. Flow between eccentric cylinders is of considerable technical importance as it occurs in journal bearings. In the present work, the governing equations for laminar flow are expressed as Navier-Stokes equations, including the non-linear convection terms. The solutions were utilized i, estimate the effects of the nonlinear terms on the load acting on the rotating cylinder. Based on the half and the full Sommerfeld methods, the load on the rotating cylinder is evaluated with eccentricity, by integrating the pressure and skin friction around the cylinder. The attitude angle and Sommerfeld reciprocal are calculated from the load. Also, the torque on the rotating inner cylinder was calculated. considering the skin friction. The attitude angle and Sommerfeld reciprocal are decreased with eccentricity. Viscous damping coefficient due to the skin friction becomes larger with decreasing the annular space. It is found the non-linear effects of the convection terms on the flow and the load are important. especially on the attitude angle, for relatively wide annular configurations however, the effects on those are minor for very narrow annular ones.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.6 no.3
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• pp.9-16
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• 1997

A numerical method based on the spectral collocation method is developed for the steady rotating flows in eccentric annulus. Steady flows between rotating cylinders are of interest on lubrication in large rotating machinery. Steady rotating flow is generated by the rotating inner cylinder with constant angular velocity. The governing equations for laminar flow are simplified from Navier-Stokes equations by neglecting the non-linear convection terms. Integrating the pressure round the rotating cylinder based on the half Sommerfeld method, the load on the cylinder is evaluated with eccentricity. The attitude angle and Sommerfeld variable are calculated from the load. It is found that those values are influenced by the eccentricity. The attitude and Sommerfeld reciprocal are decreased with eccentricity. As expected, the effect of the annular gap ratio on them is negligible.

• 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

• 유체기계공업학회:학술대회논문집
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• 1998.12a
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• pp.42-48
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• 1998

Numerical study is presented for the analysis of three-dimensional incompressible turbulent flows in multiblade centrifugal fan. Reynolds-averaged Navier-Stokes equations with standard k - $\epsilon$ turbulence model are transformed to non-orthogonal curvilinear coordinates, and are discretized with finite volume approximations. 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. The computational area is divided into three blocks; core, impeller and scroll, which are linked by multi-block method. The flow inside of the fan is regarded as steady flow, and mathematical formula established from the cascade theory and empirical coefficient are employed to simulate tile flow through the impeller. From comparisons between the computational results and the experimental data, the validity of the mathematical formula for the blade forces was examined and good results were obtained qualitatively. Hence, we can get the flow characteristics of multi-blade centrifugal fan and it will be a corner stone of the development of the multiblade centrifugal fan.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.8 no.2
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• pp.123-136
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• 1996

A three-dimensional Galerkin-FEM model which can handle the temporal and spatial variation of density is presented. The hydrostatic approximation is used and density effects are included by means of conservation equation of heat and the equation of state. The finite difference grids are used in the horizontal plane and a set of linear-shape functions is used for the vertical expansion. The similarity transform is introduced to solve resultant matrix equations. The proposed model was first applied to the density-driven circulation in an idealized basin in the presence of the heat exchange between the air and the sea. The advection terms in the momentum equation were ignored, while the convection terms were retained in the heat equation. Coefficients of the vertical eddy viscosity and diffusivity were fixed to be constant. Calculation in a non-rotating idealized basin shows that the difference in heat capacity with depth gives rise to the horizontal gradient of temperature. Consequently, there is a steady new in the upper layer in the direction of increasing depth with compensatory counter flow .in the lower layer. With Coriolis force, geostrophic flow was predominant due to the balance between the pressure gradient and the Coriolis force. As a test in region of irregular topography, the model is applied to the Yellow Sea. Although the resultant flow was very complex, the character of the flow Showed to be geostrophic on the whole.