• Proceedings of the KSME Conference
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• 2007.05b
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• pp.2797-2802
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• 2007

It has been confirmed that implementation of the no-slip boundary conditions for the lattice-Boltzmann method play an important role in the overall accuracy of the numerical solutions as well as the stability of the solution procedure. We in this paper propose a new algorithm, i.e. the method of the dynamic boundary condition for no-slip boundary condition. The distribution functions on the wall along each of the links across the physical boundary are assumed to be composed of equilibrium and nonequilibrium parts which inherit the idea of Guo's extrapolation method. In the proposed algorithm, we apply a dynamic equation to reflect the computational slip velocity error occurred on the actual wall boundary to the correction; the calculated slip velocity error dynamically corrects the fictitious velocity on the wall nodes which are subsequently employed to the computation of equilibrium distribution functions on the wall nodes. Along with the dynamic selfcorrecting process, the calculation efficiently approaches the steady state. Numerical results show that the dynamic boundary method is featured with high accuracy and simplicity.

• Proceedings of the KSME Conference
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• 2001.06e
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• pp.430-435
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• 2001

This paper introduces a pressure correction method for microflow computation. Conventional CFD methods with no slip boundary condition fail to predict the rarefaction effect of the wall when simulating gas microflows in the slip-flow regime. Pressure correction method with an appropriate slip boundary condition is an efficient tool in analyzing microscale flows. The present unstructured SIMPLE algorithm adopts both the classical Maxwell boundary condition and Langmuir boundary condition proposed by Myong. The simulation results of microchannel flows show that the proposed method has an effective predictive capability for microscale flows.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.33 no.6
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• pp.2267-2275
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• 2013

Existing conventional model for analysis of shallow water flow just assumed the internal boundary condition as free-slip, which resulted in the wrong prediction about the velocity, vorticity, water level, shear stress distribution, and time variation of drag and lift force around a structure. In this study, a finite element model that can predict flow characteristics around the structure accurately was developed and internal boundary conditions were generalized as partial slip condition using slip length concept. Laminar flow characteristics behind circular cylinder were analyzed by varying the internal boundary conditions. The simulation results of (1) time variations of longitudinal and transverse velocities, and vorticity; (2) wake length; (3) vortex shedding phenomena by slip length; (4) and mass conservation showed that the vortex shedding had never observed and laminar flow like creeping motion was occurred under free-slip condition. Assignment of partial slip condition changed the velocity distribution on the cylinder surface and influenced the magnitude of the shear stress and the occurrence of vorticity so that the period of vortex shedding was reduced compared with the case of no slip condition. The maximum mass conservation error occurred in the case of no slip condition, which had the value of 0.73%, and there was 0.21 % reduction in the maximum mass conservation error by changing the internal boundary condition from no slip to partial slip condition.

• KSTLE International Journal
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• v.7 no.2
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• pp.27-34
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• 2006

Knudsen number is the ratio of molecular mean free path versus mm thickness and the criterion to determine the flow form. When its value is lower than 0.01, the flow can be assumed to has no slip boundary condition. And in the case that the value is between 0.01 and 10, then the flow has slip boundary condition at both the adjacent walls. The condition of the air flow between the rotating journal and top foil in the air foil bearing is determined by the rotating speed and load, and the Knudsen number is also varied by those values. Because the molecular mean free path is variable to the pressure and temperature, more exact formulation is necessary to understand and analyze the flow regime. In this study, the analysis considering Knudsen number formulated with those variables (pressure, temperature and mm thickness) was executed. The approximate value was examined using the equation to confirm whether the flow has the slip or no-slip boundary condition. From the analytic investigation, it was decided to range approximately 0.01 to 1.0 and the flow can be supposed to have the slip boundary condition. Under the condition of the slip flow, the static characteristics of the air foil bearing were examined using modified Reynolds equations. The results were compared with those considering no slip condition. It shows that the slip condition makes the flow decelerates and the load carrying capacity decreases compared with no slip condition. And as the bearing number and eccentricity ratio increase, the load carrying capacity also increased at both the cases. From this result, it can be supposed that the bearing torque also increases. In the analysis of the dynamic characteristics, the perturbed Knudsen number was taken into consideration. Because the Knudsen number is expressed as the terms of each variable, the perturbed equation can be simply derived. The results of both cases considering and not considering Knudsen number were compared each other. In the case of the direct terms of the stiffness and damping coefficients, the difference between both cases was little and increased as the bearing number and eccentricity ratio increased. And the cross terms have less or more differences.

• Journal of Ocean Engineering and Technology
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• v.13 no.4 s.35
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• pp.151-158
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• 1999

A model harbour with Plan scale of $1.08{\times}1.08m$ is built on a tidal tank using a Froude relationship from a real harbour($432{\times}432m$). Velocity components are measured by a ultrasonic velocity meter and flow structure is then predicted using a 2-D depth integrated hydrodynamic model. In the finite difference model implemented in this study, various wall boundary conditions, i.e. no-slip, free-slip, partial-slip and semi-slip are used to represent turbulent diffusion terms, e.g. ${\partial}^2U_{ij}/{\partial}x^2\;or\;{\partial}^2U_{ij}/{\partial}y^2$. These conditions are focused to investigate their influence on the flow structure along the wall and basin of the harbour with aspect ratio of unity, i.e. Length/Breadth. Numerical experiments are compared with the measurements and used to analyse flow patterns in the basin during tidal cycles. It is shown from the results that no-slip closed boundary condition is the most appropriate method with respect to the location of the eddy centre, although the condition underestimates velocity components along the wall.

• Journal of computational fluids engineering
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• v.19 no.3
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• pp.77-84
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• 2014

The lattice Boltzmann (LB) method has been used to simulate rarefied gas flows in a micro-system as an alternative tool. However, previous results were mainly focused on a simple geometry with flat walls because the LB method is modeled on uniform Cartesian lattices. When previous boundary conditions for the microflows are applied to curved walls, the use of them requires approximation of the curved boundary by a series of stair steps, and introduces additional errors. For macroflows, no-slip curved wall boundary treatments have been developed remarkably in order to overcome these limits. However, the investigations for the slip curved wall boundary have rarely been performed for microflows. In this work, a curved boundary treatment of the LB method for a slip flow has been introduced. The results of the LB method for 2D microchannel and 3D microtube flows are in excellent agreement with the analytical solutions.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.21 no.4
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• pp.509-517
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• 1997

Results of flat plate compressible boundary layer calculation, based on discrete formulation of DSMC method, are presented in low Mach number and low Knudsen number range. The free stream is a uniform flow of pure nitrogen at various Mach numbers in low pressures (i.e. rarefied gas). Complete thermal accommodation and diffuse molecular reflections are used as the wall boundary condition, replacing unreal no-slip condition used in continuum calculations. In the discrete formulation of DSMC method, there is no need to use ad hoc assumptions on transport properties like viscosity and thermal conductivity, instead viscosity is calculated from values of other field variables (velocity and shear stress). Also the results are compared with existing self-similar continuum solutions. In all Mach number cases computed, velocity slip is most pronounced in regions near the leading edge where continuum formulation renders the solution singular. As the boundary layer develops further downstream, velocity slips asymptote to values that are between 10 to 20% of the magnitude of free stream velocity. When the free stream number density is reduced, so the gas more rarefied, the velocity slip increases as expected.

• Journal of computational fluids engineering
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• v.18 no.3
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• pp.34-41
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• 2013

We develop a novel immersed boundary (IB) method based on implicit direct forcing scheme for incompressible flows. The proposed IB method is based on an iterative procedure for calculating the direct forcing coupled with the momentum equations in order to satisfy no-slip boundary conditions on IB surfaces. We perform simulations of two-dimensional flows over a circular cylinder for low and moderate Reynolds numbers. The present method shows that the errors for estimated velocities on IB surfaces are significantly reduced even for low Reynolds number with a fairly large time step while the previous methods based on direct forcing failed to provide no-slip boundary conditions on IB surfaces.

• Journal of computational fluids engineering
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• v.11 no.3 s.34
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• pp.28-36
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• 2006

NSBT(No Slip Boundary Treatment) is a newly developed scheme for the treatment of a no slip condition on the solid wall of obstacle in a flow field. In our research, NSBT was used to perform LBM simulation of a flow over a circular cylinder to determine the flow feature and aerodynamics characteristic of the cylinder. To ascertain the applicability of NSBT on the complex shape of the obstacle, it was first simulated for the case of the flow over a circular and square cylinder in a channel and the results were compared against the solution of Navier-Stokes equation. The simulations were performed in a moderate range of Reynolds number at each cylinder position to identify the flow feature and aerodynamic characteristics of circular cylinder in a channel. The drag coefficients of the cylinder were calculated from the simulation results. We have numerically confirmed that the critical reynolds number for vortex shedding is in the range of 200$\sim$250. For the gap parameter $\gamma$ = 2 cases at Re > 240, the vortex shedding were symmetric and it resembled the Karmann vortex. As the cylinder approached to one wall, the vorticity significantly reduced in length while the vorticity on the other side elongated and the vorticity combined with the wall boundary-layer vorticity. The resultant $C_d$ by LBM concurred with the results of DNS simulation performed by previous researchers.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.1
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• pp.163-168
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• 1991

During Compression molding of polymeric composite materials, the flow characteristics should be obtained. Understanding the flow states may be useful for determination of optimum molding conditions, charge pattern etc. So far, for obtaining the flow analysis, no-slip boundary condition was applied on the mold surface. However, The study under consideration of the slip was conducted by Barone and Caulk. They have introduced the nondimensional parameter which is the ratio of viscous to friction resistance and governs the frictional condition. But the method for determining the parameter could not be proposed. In our work, the parameter which explains the interfacial friction is measured under a variety of molding conditions. Two-dimensional rectangular part and circular hollow disk are simulated with the measured parameter using the finite element method. Effects of the parameter on shapes of flow fronts are also presented.