• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.479-490
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• 1997

We consider long nonlinear waves in the two-layer flow of an inviscid and incompressible fluid bounded above by a free surface and below by a rigid boundary. The flow is forced by a bump on the bottom. The derivation of the forced KdV equation fails when the density ratio h and the depth ratio $\rho$ yields a condition $1 + h\rho = (2-h)((1-h)^2 + 4\rho h)^{1/2}$. To overcome this difficulty we derive a forced modified KdV equation by a refined asymptotic method. Numerical solutions are given and hydraulic fall solution of a two layer fluid is expressed analytically in the case that derivation of the forced KdV (FKdV) equation fails.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.12
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• pp.3949-3959
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• 1996

A new interfacial instability between two vertical fluid layers of different densities is studied. The two layers are flowing between two parallel vertical plates vertically upward or downward, forming counter- or concurrent flows. In order to extend the study to highly-nonlinear regime in future studies, a nonlinear interface evolution equation is derived, and the stability analysis is performed based on the evolution equation. Among the parameters studies are the ratios of the fluid densities and layer thicknesses and the net flow rate.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.8
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• pp.605-611
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• 2003

A simply supported pipe conveying fluid and two moving masses upon it constitute this nitration system. The equation of motion is derived by using Lagrange's equation. The influence of the velocities of two moving masses, the distance between two moving masses, and the velocities of fluid flow in the pipe have been studied on the dynamic behavior of a simply supported pipe by numerical method. The velocities of fluid flow are considered with in its critical values of a simply supported pipe without moving masses upon It. Their coupling effects on the transverse vibration of a simply supported pipe are inspected too. As the velocity of two moving masses increases, the deflection of a simply supported pipe is increased and the frequency of transverse vibration of a simply supported pipe is not varied. In case of small distance between two masses, the maximum deflection of the pipe occur when the front mass arrive at midspan. Otherwise as the distance get larger, the position of the front masses where midspan deflection is maximum moves beyond the midpoint of a simply supported pipe. The deflection of a simply supported pipe is increased by coupling of the velocities of moving masses and fluid flow.

• Coupled systems mechanics
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• v.8 no.2
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• pp.147-168
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• 2019

This work aims to simulate three-dimensional heavy oil flow in a reservoir with heater-wells. Mass, momentum and energy balances, as well as correlations for rock and fluid properties, are used to obtain non-linear partial differential equations for the fluid pressure and temperature, and for the rock temperature. Heat transfer is simulated using a two-equation model that is more appropriate when fluid and rock have very different thermal properties, and we also perform comparisons between one- and two-equation models. The governing equations are discretized using the Finite Volume Method. For the numerical solution, we apply a linearization and an operator splitting. As a consequence, three algebraic subsystems of linearized equations are solved using the Conjugate Gradient Method. The results obtained show the suitability of the numerical method and the technical feasibility of heating the reservoir with static equipment.

• Journal of computational fluids engineering
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• v.12 no.4
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• pp.20-27
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• 2007

Two-dimensional stagnation flow toward a plane wall coated with magnetic fluid of uniform thickness is investigated. The flow field is represented as a similarity solution of the Navier-Stokes equation for this incompressible laminar flow. The resulting third order ordinary differential equation is solved numerically by using the shooting method and by determining two shooting parameters so as to satisfy the boundary and interface conditions. Features of the flow including streamline patterns are investigated for the varying values of density ratio, viscosity ratio, and Reynolds number. An adverse flow with double eddy pair in magnetic fluid region is found to emerge as the Reynolds number becomes higher than a threshold value. The results for the interface velocity, interface and wall shear stress, and boundary layer and displacement thickness are also presented.

• The KSFM Journal of Fluid Machinery
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• v.11 no.3
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• pp.7-13
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• 2008

The cavitating flow simulation is of practical importance for many engineering systems, such as pump, turbine, nozzle, Infector, etc. In the present work, a solver for two-phase flows has been developed and applied to simulate the cavitating flows past hydrofoils. The governing equation is the two-phase Navier-Stokes equation, comprised of the continuity equation of liquid and vapor phase. The momentum and energy equation is in the mixture phase. The solver employs an implicit, dual time, preconditioned algorithm using finite difference scheme in curvilinear coordinates. An experimental data and other numerical data were compared with the present results to validate the present solver. It is concluded that the present numerical code has successfully accounted for two-phase Navier-Stokes model of cavitation flow.

• 한국전산유체공학회:학술대회논문집
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• 2005.04a
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• pp.219-222
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• 2005

A compressible two-fluid two-phase flow computation model using the stiffened-gas equation of state is formulated. Since the conservation equation system is of mixed type, it gives complex eigenvalues. The sonic speeds obtained from the individual single phase have been simply used in the literature for the fastest wave speeds necessary in the HLL scheme. This method has worked fine but proved to be quite diffusive according to our test. To improve the accuracy, we here propose to utilize the analytic eigenvalues evaluated from an approximate Jacobian matrix lot the fastest wave speeds. The interfacial transfer terms were dropped in constituting the Jacobian matrix for this purpose. The present scheme proved efficient, robust and accurate in comparison with other existing methods. We solved the cavitating flow problem using the present scheme. The result shows more detailed wave structure in the cavitating process caused by the strong expansion waves.

• Macromolecular Research
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• v.11 no.1
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• pp.53-61
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• 2003

A molecular-thermodynamic model is developed for the salt-induced protein precipitation. The protein molecules interact through four intermolecular potentials. An equation of state is derived based on the statistical mechanical perturbation theory with the modified Chiew's equation for the fluid phase, Young's equation for the solid phase as the reference system and a perturbation based on the protein-protein effective two body potential. The equation of state provides an expression for the chemical potential of the protein. In a single protein system, the phase separation is represented by fluid-fluid equilibria. The precipitation behaviors are simulated with the partition coefficient at various salt concentrations and degree of pre-aggregation effect for the protein particles. In a binary protein system, we regard the system as a fluid-solid phase equilibrium. At equilibrium, we compute the reduced osmotic pressure-composition diagram in the diverse protein size difference and salt concentrations.

• Journal of the Korean Vacuum Society
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• v.17 no.5
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• pp.400-407
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• 2008

In this study, Two dimensional spatial profile of electromagnetic field for capacitively coupled plasma source is calculated. Based on one dimensional fluid equation, spatial profile for the axial direction of electric field and conduction current density is firstly calculated. The two dimensional spatial profile for the electromagnetic field is calculated from solution of Maxwell equation that is expanded to power series for ${\omega}r/c$ into the radial direction.

• Structural Engineering and Mechanics
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• v.81 no.4
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• pp.523-527
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• 2022

The objective of this study is to simulate the flow in pipes with various boundary conditions. Free-pressure fluid model, is used in the pipe based on Navier-Stokes equation. The models are solved by using the numerical method. A problem called "stability of pipes" is used in order to compare frequency and critical fluid velocity. When the initial conditions of problem satisfied the instability conditions, the free-pressure model could accurately predict discontinuities in the solution field. Employing nonlinear strains-displacements, stress-strain energy method the governing equations were derived using Hamilton's principal. Differential quadrature method (DQM) is used for obtaining the frequency and critical fluid velocity. The results of this paper are analyzed by hyperbolic numerical method. Results show that the level of numerical diffusion in the solution field and the range of well-posedness are two important criteria for selecting the two-fluid models. The solutions for predicting the flow variables is approximately equal to the two-pressure model 2. Therefore, the predicted pressure changes profile in the two-pressure model is more consistent with actual physics. Therefore, in numerical modeling of gas-liquid two-phase flows in the vertical pipe, the present model can be applied.