• Korea-Australia Rheology Journal
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• v.15 no.4
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• pp.197-208
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• 2003

Two measures of distributive mixing are examined: the standard deviation $\sigma$ and the maximum error E, among average concentrations of finite-sized samples. Curves of E versus sample size L are easily interpreted in terms of the size and intensity of the worst flaw in the mixture. E(L) is sensitive to the size of this flaw, regardless of the overall size of the mixture. The measures are used to study distributive mixing for time-periodic flows in a rectangular cavity, using the mapping method. Globally chaotic flows display a well-defined asymptotic behavior: E and $\sigma$ decrease exponentially with time, and the curves of E(L) and $\sigma$ (L) achieve a self-similar shape. This behavior is independent of the initial configuration of the fluids. Flows with large islands do not show self-similarity, and the final mixing result is strongly dependent on the initial fluid configuration.

• 한국전산유체공학회:학술대회논문집
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• 2006.05a
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• pp.83-84
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• 2006

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.6
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• pp.1179-1194
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• 1992

QUICKER scheme has several attractive properties. However, under highly convective conditions, it produces overshoots and possibly some oscillations on each side of steps in the dependent variable when the flow is convected at an angle oblique to the grid line. Fortunately, it is possible to modify the QUICKER scheme using non-linear and linear functional relationship. Details of the development of polynomial upwinding scheme are given in this paper, where it is seen that this non-linear scheme has also third order accuracy. This polynomial upwinding scheme is used as the basis for the SHARPER and SMARTER schemes. Another revised scheme was developed by partial modification of QUICKER scheme using CDS and UPWIND schemes(QUICKUP). These revised schemes are tested at the well known bench mark flows, Two-Dimensional Pure Convection Flows in Oblique-Step, Lid Driven Cavity Flows and Buoyancy Driven Cavity Flows. For pure convection oblique step flow test problem, QUICKUP, SMARTER and SHARPER schemes remain absolutely monotonic without overshoot and oscillation. QUICKUP scheme is more accurate than any other scheme in their relative accuracy. In high Reynolds number Lid Driven Cavity Flow, SMARTER and SHARPER schemes retain lower computational cost than QUICKER and QUICKUP schemes, but computed velocity values in the revised schemes produced less predicted values than QUICKER scheme which is strongly effected by overshoot and undershoot values. Also, in Buoyancy Driven Cavity Flow, SMARTER, SHARPER and QUICKUP schemes give acceptable results.

• 한국전산유체공학회:학술대회논문집
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• 2006.05a
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• pp.311-314
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• 2006

The supersonic flow around tandem cavities was investigated by three- dimensional numerical simulations using the Reynolds-Averaged Navier-Stokes(RANS) equation with the $\kappa-\omega$ thrbulence model. The flow around a cavity is characterized as unsteady flow because of the formation and dissipation of vortices due to the interaction between the freestream shear layer and cavity internal flow, the generation of shock and expansion waves, and the acoustic effect transmitted from wake flow to upstream. The upwind TVD scheme based on the flux vector split using van Leer's limiter was used as the numerical method. Numerical calculations were performed by the parallel processing with time discretizations carried out by the 4th-order Runge-Kutta method. The aspect ratio of cavities are 3 for the first cavity and 1 for the second cavity. The ratio of cavity interval to depth is 1. The ratio of cavity width to depth is 1 in the case of three dimensional flow. The Mach number and the Reynolds number were 1.5 and $4.5{\times}10^5$, respectively. The characteristics of the dominant frequency between two-dimensional and three-dimensional flows were compared, and the characteristics of the second cavity flow due to the fire cavity flow cavity flow was analyzed. Both two dimensional and three dimensional flow oscillations were in the 'shear layer mode', which is based on the feedback mechanism of Rossiter's formula. However, three dimensional flow was much less turbulent than two dimensional flow, depending on whether it could inflow and outflow laterally. The dominant frequencies of the two dimensional flow and three dimensional flows coincided with Rossiter's 2nd mode frequency. The another dominant frequency of the three dimensional flow corresponded to Rossiter's 1st mode frequency.

• 한국전산유체공학회:학술대회논문집
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• 2005.10a
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• pp.235-238
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• 2005

The unsteady supersonic flow over two- and three-Dimensional cavities has been analyzed by the integration of unsteady Reynolds-Averaged Navier-Stokes(RANS) with the k - w turbulence model. The unsteady flow is characterized by the periodicity due to the mutual relation between the shear layer and the internal flow in cavities. Numerical method is upwind TVD scheme based on the flux vector split with the Van Leer limiters, and time accuracy is used explicit 4th stage Runge-Kutta scheme. Cavity flows are Comparison of two- and three-dimensional. The cavity has a L/D ratio of 3 for two-dimensional case. and same L/D and W/D ratio is 1 for three-dimensional case. The Mach and Reynolds numbers are held constant at 1.5 and 450000 respectively. For the three-dimensional case, the flow field is observed to oscillate in the 'shear layer mode' with a feedback mechanism that follow Rossiter's formula. On the other hand, the self-sustained oscillating flow transitions to a 'wake mode' for the two-dimensional simulation, with more violent fluctuations inside the cavity.

• Journal of Mechanical Science and Technology
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• v.19 no.11
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• pp.2077-2081
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• 2005

A symmetry breaking nonlinear fluid flow in a two-dimensional wall-driven square cavity taking symmetric boundary condition after some transients has been investigated numerically. It has been shown that the symmetry breaking critical Reynolds number is dependent on the time history of the boundary condition. The cavity has at least three stable steady state solutions for Re=300-375, and two stable solutions if Re>400. Also, it has also been showed that a particular solution among several possible solutions can be obtained by a controlled boundary condition.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.33 no.6
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• pp.435-442
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• 2009

Three-dimensional heat transfer characteristics for natural convection flows are numerically investigated in the doubly-inclined cubical-cavity according to the variation of a newly defined orientation angle �� of the hot wall surface from horizontal plane at moderate Rayleigh numbers. Numerical simulations of laminar flows are conducted in the range of Rayleigh numbers($10^4{\leq}Ra{\leq}10^5$) and $0^{\circ}{\leq}{\alpha}90^{circ}$ with a solution code(PowerCFD) employing unstructured cell-centered method. Comparisons of the average Nusselt number at the cold face are made with benchmark solutions and experimental results found in the literature. It is found that the average Nusselt number at the cold wall has a maximum value around the specified orientation ${\alpha}$ at each Rayleigh number. Special attention is also paid to three-dimensional thermal characteristics in natural convection according to new orientation angles at Ra��= $1{\times}10^5$, in order to investigate a new additional heat transfer characteristic found in the range of above Ra = $6{\times}10^4$.

• Journal of Ocean Engineering and Technology
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• v.10 no.3
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• pp.105-116
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• 1996

In this paper, we report the experimental results for the flow pattern and the material transport around a cavity subject to a sinusoidal external flow at the far region to ward the open side of the cavity. A tilting mechanism is used to generate a oscillatory flow inside a shallow rectangular container having a cavity at one side. The surface flow visualization is performed to obtain the unsteady behavior of vortices generated at two edges situated at the entrance of the cavity. It was found that at the period 4.5 sec., the behavior of the vortices is asymmetric, and there exists a steady residual flow in the cavity. The bottom flow patterns are also visualized. There are two regions outside of the cavity where the bottom fluid particles concentrate. The material transport in this flow model is very peculiar; fluid particles in the cavity flows outward through the passage along the walls starting from the edges, and particles in the outer region approach the cavity from the central region.

• 한국전산유체공학회:학술대회논문집
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• 2003.08a
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• pp.126-131
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• 2003

A series of computational simulations have been carried out for supersonic flows in a scram jet engine with and without a cavity. Transverse injection of hydrogen, a simplest form of fuel supply, is considered in the present study with the injection pressure varying from 0.5 to 1.5 MPa. The corresponding equivalence ratios are 0.167 - 0.50. The work features detailed resolution of the flow dynamics in the combustor, which was not typically available in most of the Previous studies. In particular, oscillatory flow characteristics are captured at a scale sufficient to identify the underlying physical mechanisms. Much of the flow unsteadiness is related not only to the cavity, but also to the intrinsic unsteadiness in the flowfield. The interactions between shock waves and shear layer may cause a large excursion of flow oscillation. The role of the cavity and injection pressure are examined systematically.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.39 no.6
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• pp.477-483
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• 2015

Investigations into cavity flows have been conducted for noise and vibration problems that arise in cavity systems. Cavity systems have been applied in engineering devices and have undergone rapid development in the aerospace industry. Meanwhile, to the author's best knowledge, the cavity on a curved wall has been seldom studied. The present work is conducted to study the flow physics of a cavity mounted on a curved wall. Numerical analysis is performed to investigate the cavity flow. Two variables of sub- and supersonic cavity flows were considered: the radius of curvature of the curved wall (L/R) and the inlet Mach number. The results show that the uniform vortex generated by the cavity flow on the curved wall stabilize the pressure fluctuation as time passes. As the inlet Mach number increases, the pressure fluctuation amplitude increases. The results obtained from the curved wall are compared with those from a straight wall using Rossiter's formula. The Strouhal number of the curved wall is lower than that of the straight wall. Lower Strouhal numbers have been obtained in the present computational fluid dynamics (CFD) results than in the theoretical results using Rossiter's formula.