• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.21 no.2
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• pp.89-107
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• 2017

In this paper, we have proposed a modified Marker-And-Cell (MAC) method to investigate the problem of an unsteady 2-D incompressible flow with heat and mass transfer at low, moderate, and high Reynolds numbers with no-slip and slip boundary conditions. We have used this method to solve the governing equations along with the boundary conditions and thereby to compute the flow variables, viz. u-velocity, v-velocity, P, T, and C. We have used the staggered grid approach of this method to discretize the governing equations of the problem. A modified MAC algorithm was proposed and used to compute the numerical solutions of the flow variables for Reynolds numbers Re = 10, 500, and 50000 in consonance with low, moderate, and high Reynolds numbers. We have also used appropriate Prandtl (Pr) and Schmidt (Sc) numbers in consistence with relevancy of the physical problem considered. We have executed this modified MAC algorithm with the aid of a computer program developed and run in C compiler. We have also computed numerical solutions of local Nusselt (Nu) and Sherwood (Sh) numbers along the horizontal line through the geometric center at low, moderate, and high Reynolds numbers for fixed Pr = 6.62 and Sc = 340 for two grid systems at time t = 0.0001s. Our numerical solutions for u and v velocities along the vertical and horizontal line through the geometric center of the square cavity for Re = 100 has been compared with benchmark solutions available in the literature and it has been found that they are in good agreement. The present numerical results indicate that, as we move along the horizontal line through the geometric center of the domain, we observed that, the heat and mass transfer decreases up to the geometric center. It, then, increases symmetrically.

• Journal of Power System Engineering
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• v.13 no.5
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• pp.11-17
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• 2009

A numerical study of unsteady mixed convection in a cavity with high viscous fluid is presented. Finite volume method was employed for the discretization and PISO algorithm was used for calculating pressure term. The parameters governing the problem are the Rayleigh number ($10^3\;{\leq}\;Ra\;{\leq}\;10^5$), the Reynolds number (0 < Re $\leq$ 1), and the aspect ratio (0.5 $\leq$ AR $\leq$ 2). The fluid used is silicon oil, a high prandtl number fluid, Pr = 909.1. The results show velocity vectors and temperature distributions. It is found that the periodic flows in a cavity are observed at very low Reynolds numbers, and the period of periodic flow decreases with increasing Reynolds and Rayleigh numbers, and increases with increasing aspect ratio. Also, the Reynolds number range of periodic flow increases with increasing Rayleigh numbers and aspect ratio.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.1
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• pp.1-8
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• 2000

A modified low-Reynolds-number Reynolds stress model is developed for the calculation of drag-reducing turbulent flows induced by polymer injection. The results without polymer injection are compared with the results of direct numerical simulation to ensure the validity of the basic model. In case of drag reduction, profiles of mean velocity and Reynolds stress components, in two-dimensional channel flow, obtained with a proper value of viscosity ratio are presented and discussed. Computed mean velocity profile is in very good agreement with experimental data. And, the qualitative behavior of Reynolds stress components with the viscosity ratio is also reasonable.

• Transactions of the Korean Society of Automotive Engineers
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• v.2 no.1
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• pp.38-50
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• 1994

To improve the efficiency of internal combustion engines, it is necessary to understand mixed air-fuel in-cylinder flow processes accurately at intake and compression strokes. There is experimental and numerical methods to analyse in-cylinder flow process. In numerical method, standard $k-{\varepsilon}$ model with wall function was mostly adopted in in-cylinder flow process. But this type model was not efficiently predicted in the near wall region. Therefore in the present study, low Reynolds number $k-{\varepsilon}$ model was adopted near the cylinder wall and standard $k-{\varepsilon}$ model in other region. Also QUICK scheme was used for convective difference scheme. This study takes axisymmetric reciprocating model engine motored at 200rpm with a centrally located valve, incorporated 60 degree seat angie, and flat piston surface excluding inlet port. Because in-cylinder flow processes are undergoing unsteady and compressible, averaged cylinder pressure and inlet velocity at arbitrary crank angle are determined from thermodynamic analytic method and incylinder states at that crank angle are iteratively determined from the numerical analytic method.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.8
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• pp.2039-2050
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• 1995

The nonlinear low-Reynolds-number k..epsilon. model of park and Sung is extended to predict the turbulent heat transports in separated and reattaching flows. The equations of the temperature variance( $k_{\theta}$ and its dissipation rate(.epsilon.$_{\theta}$ are solved, in concert with the equations of the turbulent kinetic energy(k) and its dissiation rate(.epsilon). In the present model, the near-wall effect and the non-equilibrium effect are fully taken into consideration. The validation of the model is then applied to the turbulent flow behind a backward-facing step and the flow over a blunt body. The predicted results of the present model are compared and evaluated with the relevant experiments.

• Journal of KSNVE
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• v.7 no.5
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• pp.861-869
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• 1997

An approximate analytical method has been developed for estimating hydrodynamic forces acting on oscillating inner cylinder in concentric annulus. When the rigid inner cylinder executes translational oscillation, fluid inertia and damping forces on the oscillating cylinder are generated by unsteady pressure and viscous skin friction. Considering the dynamic-characteristics of unsteady viscous flow and the added mass coefficient of inviscid fluid, these hydrodynamic forces including viscous effect are dramatically simplified and expressed in terms of oscillatory Reynolds number and the geometry of annular configuration. Thus, the viscous effect on the forces can be estimated very easily compared to an existing theory. The forces are calculated by two models developed for relatively high and low oscillatory Reynolds numbers. The model for low oscillatory Reynolds number is suitable for relatively high ratio of the penetration depth to annular space while the model for high oscillatory Reynolds number is applicable to the case of relatively low ratio. It is found that the transient ratio between two models is approximately 0.2~0.25 and the forcea are expressed in terms of oscillatory Reynolds number, explicity. The present results show good agreements with an existing numerical results, especially for high and low penetration ratios to annular gap.

• Proceedings of the KSME Conference
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• 2001.06e
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• pp.766-771
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• 2001

An experimental study was undertaken to investigate the effect of coriolis force for the turbulent flow at low Reynolds numbers in a rotating straight square duct. The study was carried out using a hot-wire anemometer. The flow Reynolds number based on the hydraulic diameter ranged from 4,000 to 18,000 and Rotation number ranged from 0 to 0.196. At Re=9000, developing turbulent flow was calculated for mean velocity and Reynolds stress. Pressure coefficient and energy dissipation spectrum were also calculated.

• Korea-Australia Rheology Journal
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• v.16 no.2
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• pp.63-73
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• 2004

Flow in a channel with an obstruction at the entry can be reverse, stagnant or forward depending on the position of the obstruction. These flow phenomena have potential applications in the control of energy and various flows in process engineering. Parameters that affect this flow inside and around the test channel are the gap (g) between the obstruction geometry and the test channel, the Reynolds number (Re) and the length (L) of the test channel. The influence of these parameters on the flow behavior was investigated using a flat plate obstruction at the entry of the channel. A low concentration polyacrylamide solution (0.018% by weight) showing a powerlaw fluid behavior was used as the fluid in this investigation. The flow phenomena were investigated by the velocity measurement and the flow visualization and their results were compared with numerical simulation. These results of low concentration polyacrylamide solution are also compared with the results of water published elsewhere (Kabir et al., 2003). The maximum reverse flow inside the test channel observed was 20% - 30% of the outside test channel velocity at a g/w (gap to width) ratio of 1 for Reynolds numbers of 1000 to 3500. The influence of the test channel length (L) and the Reynolds number (Re) on the velocity ratio ($V_i$/$V_o$: inside velocity/outside velocity in the test channel) are also presented and discussed here.

• Particle and aerosol research
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• v.17 no.4
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• pp.81-89
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• 2021

Understanding particle-laden flow around cylindrical bodies is essential for the better design of various applications such as filters. In this study, laminar flows around two tandem cylinders and the motions of particles in the flow are numerically investigated at low Reynolds numbers. We aim to reveal the effects of the spacing between cylinders, Reynolds number and particle Stokes number on the characteristics of particle trajectories. When the cylinders are placed close, the unsteady flow inside the inter-cylinder gap at Re = 100 shows a considerable modification. However, the steady recirculation flow in the wake at Re = 10 and 40 shows an insignificant change. The change in the flow structure leads to the variation of particle dispersion pattern, particularly of small Stokes number particles. However, the dispersion of particles with a large Stokes number is hardly affected by the flow structure. As a result, few particles are observed in the cylinder gap regardless of the cylinder spacing and the Reynolds number. The deposition efficiency of the upstream cylinder shows no difference from that of a single cylinder, increasing as the Stokes number increases. However, the deposition on the downstream cylinder is found only at Re = 100 with large spacing. At this time, the deposition efficiency is generally small compared to that of an upstream cylinder, and the deposition location is also changed with no deposited particles near the stagnation point.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.10
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• pp.1971-1978
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• 1992

A turbulent flow in a conical diffuser with total divergence angle of 8.deg. was numerically studied. The low Reynolds number k-.epsilon. model(Launder-Sharma model) was adopted to simulate the turbulence. The continuity and time averaged Navier-Stokes equations in a nonorthogonal coordinate system were solved by a finite volume method based on the fully elliptic formulation. The low Reynolds number k-.epsilon. model reasonably simulates the pressure recovery and the mean velocity components. However, there are also considerable discrepancies between predicted and measured shear stress distribution on the wall and turbulent kinetic energy distributions. It is necessary to investigate the flow structure at the entry of the diffuser, numerically as well as experimentally.