• Journal of Ocean Engineering and Technology
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• v.36 no.2
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• pp.101-107
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• 2022

Dean (1965) proposed the use of the root mean square error (RMSE) in the dynamic free surface boundary condition (DFSBC) and kinematic free-surface boundary condition (KFSBC) as an error evaluation criterion for wave theories. There are well known wave theories with RMSE more than 1%, such as Airy theory, Stokes theory, Dean's stream function theory, Fenton's theory, and trochodial theory for deep-water waves. However, none of them can be applied for deep-water breaking waves. The purpose of this study is to provide a closed-form solution for deep-water waves with RMSE less than 1% even for breaking waves. This study is based on a previous study (Shin, 2016), and all flow fields were simplified for deep-water waves. For a closed-form solution, all Fourier series coefficients and all related parameters are presented with Newton's polynomials, which were determined by curve fitting data (Shin, 2016). For verification, a wave in Miche's limit was calculated, and, the profiles, velocities, and the accelerations were compared with those of 5^th-order Stokes theory. The results give greater velocities and acceleration than 5^th-order Stokes theory, and the wavelength depends on the wave height. The results satisfy the Laplace equation, bottom boundary condition (BBC), and KFSBC, while Stokes theory satisfies only the Laplace equation and BBC. RMSE in DFSBC less than 7.25×10^-2% was obtained. The series order of the proposed method is three, but the series order of 5^th-order Stokes theory is five. Nevertheless, this study provides less RMSE than 5^th-order Stokes theory. As a result, the method is suitable for offshore structural design.

• Transactions of the Korean Society of Mechanical Engineers
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• v.7 no.4
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• pp.386-391
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• 1983

Two-dimensional slow viscous flow due to a stokeslet near a slit is investigated on the basis of Stokes approximation. Velocity fields and stream function are obtained in closed forms by finding two sectionally holomorphic functions which are determined by reducing the problem to Riemann-Hilbert problems. The force exerted on a small cylinder is calculated for the arbitrary position of the cylinder translating in an arbitrary direction. The features of fluid flow are also investigated.

• 한국전산유체공학회:학술대회논문집
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• 2005.04a
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• pp.228-233
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• 2005

Two-dimensional Stokes flows through a micro channel with a couple of symmetric vertical fins are investigated. At far up- and down-stream from the fins, the plane Poiseuille flow exists in the channel. The slip boundary conditions are applied to take account of the Knudsen number effects. For the analysis, the method of eigen function expansion and collocation method are employed. By the results, the streamline patterns and pressure distributions are shown and the force exerted on the fin and the excess pressure drop due to the fins are determined as functions of the length of the fin and Knudsen number. It may be conjectured that the force and the excess pressure drop are almost independent of the Knudsen number.

• Journal of Electrical Engineering and Technology
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• v.4 no.2
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• pp.249-254
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• 2009

This article deals with the analysis of a coupling between stationary Maxwell's equations, the transient state Navier-Stokes and thermal equations. The resolution of these equations is obtained by introducing the magnetic vector potential A, the vorticity ${\xi}$, the stream function ${\psi}$ and the temperature T. The flux density, the electromagnetic thrust, the electric power density, the velocity, the pressure and the temperature are graphically visualized. Also, the influence of the frequency is presented.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.6
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• pp.1163-1170
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• 1992

A computer program was developed to analyze the two-dimensional unsteady incompressible viscous flow behind a rectangular bluff body between two parallel plates. The Peaceman-Rachford alternating direction implicit numerical method and Wachspress parameter were adopted to solve the governing equations in vorticity-transport and stream function formulation. The steady state flow and the vortex flow behind a rectangular bluff body in a chemical were investigated for Reynolds numbers of 200 and 500. The vortex shedding was generated by a physical pertubation numerically imposed at the center of the flow field for a short time. It was observed that the perturbed flow became periodic after a transient period.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.37 no.10
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• pp.895-900
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• 2013

A two-dimensional Stokes flow past a circular cylinder in a channel is analyzed. The circular cylinder is located at the center of the channel, and a plane Poiseuille flow exists upstream and downstream far from the circular cylinder. The Stokes approximation is used, and the flow is investigated analytically by using the eigenfunction expansion and the least square methods. From the analysis, the stream function and pressure distribution are obtained, and the pressure and shear stress distributions on the circular cylinder and channel wall are calculated. The additional pressure drop induced by the circular cylinder and the force exerted on it are calculated as functions of the length of the radius of the circular cylinder. For a typical length of the radius of the circular cylinder, the streamline pattern and pressure distribution are shown.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.35 no.6
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• pp.609-615
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• 2011

A two-dimensional Stokes flow past a vertical plate in a channel is analyzed. The vertical plate is located at the center of the channel, and plane Poiseuille flow exists far upstream and downstream of the vertical plate. The Stokes approximation is used, and the flow is investigated analytically using the method of eigenfunction expansion and the point collocation method. From the analysis, the stream function and pressure distribution are obtained, and the pressure and shear stress distributions on the plate and channel wall are calculated. The additional pressure drop induced by the vertical plate and the force exerted on it are calculated as functions of the length of the vertical plate. For a typical length of the vertical plate, the streamline pattern and pressure distribution are shown. In addition, numerical analysis of laminar flow with a small Reynolds number is carried out to analyze the effect of a small Reynolds number on the flow pattern.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.10
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• pp.2617-2629
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• 1995

The flow through a centrifugal compressor rotor was calculated using the quasi-3-dimensional and fully 3-dimensional Navier-Stokes solution methods. The calculated results, obtained during the development of the computer codes for both methods are discussed. In the inviscid quasi 3-dimensional analysis, stream function formulation was used for the blade to blade (B-B) plane calculations, and the streamline curvature method was used for the meridional (H-S) plane calculations. In the viscous 3-dimensional flow analysis, a control volume method based on a general rotating curvilinear coordinate system was used to solve the time-averaged Navier-Stokes equations, and a standard k-.epsilon. model was used to obtain eddy viscosity. The quasi-3-dimensional analysis reasonably predicts the pressure distributions and requires much less computation time in the region where viscous effects are not strong; however, it fails to predict velocity field and loss mechanism through the impeller passage. The viscous 3-dimensional flow analysis shows reasonable pressure distributions and typical jet-wake flow field through the impeller passage. Secondary flow and total pressure distributions on cross-sectional planes explain the loss mechanisms through the impeller.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.39 no.4
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• pp.335-341
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• 2015

In this study, we analyzed a two-dimensional Stokes flow through a microchannel containing projections with constant spacing attached to each wall. The projections on the top and bottom walls were semi-circular in shape, with in-phase locations. By considering the periodicity and symmetry of the flow, the eigenfunction expansion and least squared error method were applied to determine the stream function and pressure distribution. For some typical radius and spacing values, the streamline patterns and pressure distributions in the flow field are shown, and the shear stress distributions on the boundary walls are plotted. In addition, the average pressure gradients in the microchannel are also calculated and shown with the radius and spacing of the projections. In particular, the results for the case of extremely small gaps between the projections on the top and bottom walls are in good agreement with the lubrication results.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.5 no.2
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• pp.85-93
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• 1993

The rise of a large gas bubble or slug in a Micro Two-Phase Closed Thermosyphon with a thin wire insert has been analiged by the potential flow theory. The effect of the interfacial surface tension is explicitly accounted by application of the Kelvin-Laplace equation and solved for the bubble shape. The solution is expressed in terms of the Stokes stream function which consists of an infinite series of Bessel functions. The conditions of the bubble movement in a Micro Two-Phase Closed Thermosyphon were theoretically ascertained.