• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.26 no.4
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• pp.224-243
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• 2022

In this paper, we prove the global existence of classical solutions to the 2D incompressible Boussinesq equations for the micropolar fluid. Furthermore, applying the Fourier splitting methods, we obtain the lager time decay properties.

• 한국전산유체공학회:학술대회논문집
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• 2005.04a
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• pp.75-78
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• 2005

A numerical investigation has been performed to discuss the radiation-affected steady-laminar natural convection in an enclosure under a large temperature difference. Due to inherent nature of this study, the Boussinesq approximation is no longer valid. Therefore the radiating fluid in an enclosure is treated as a ideal gas. To examine the effects of thermal radiation on thermo-fluid dynamic behaviors in complex geometries, two incomplete partitions are introduced. Based on the results of this study, the dispositions of incomplete partitions with radiatively participating medium are found to incur a distinct difference in fluid-dynamic as well as thermal behavior.

• Ocean Systems Engineering
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• v.6 no.1
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• pp.117-128
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• 2016

A theoretical study of Boussinesq equations (BEs) for internal waves propagating in a two-fluid system is presented in this paper. The two-fluid system is assumed to be bounded by two rigid plates. A set of three equations is firstly derived which has three main unknowns, the interfacial displacement and two velocity potentials at arbitrary elevations for upper and lower fluids, respectively. The determination of the optimal BEs requires a solution of depth parameters which can be uniquely solved by applying the $Pad{\acute{e}}$ approximation to dispersion relation. Some wave properties predicted by the optimal BEs are examined. The optimal model not only increases the applicable range of traditional BEs but also provides a novel aspect of internal wave studies.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.19 no.2
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• pp.136-145
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• 2007

When waves propagating over an underwater shoal break at the top of the shoal, wave heights are drastically decreased in the downstream breaking zone, but a secondary current shooting downstream with strong velocity can be induced by the breaking waves themselves. In the case that an offshore structure is placed in the breaking zone, the estimation of wave farce purely based on the visible wave height may cause an under-design of the structure. Thus, for the safe design of the structure, the breaking wave induced current should be necessarily considered in the comprehensive estimation of design load. In the present study, Boussinesq equation model to calculate the wave height distribution and breaking wave induced current was set up and applied to the scheme of a hydraulic model test previously undertaken. Based on the results of the Boussinesq model, fluid forces acting on the model structure were calculated and compared with the experimental results. The importance of the breaking wave induced current was quantitatively assessed by comparing fluid forces with or without current.

• Nuclear Engineering and Technology
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• v.54 no.9
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• pp.3540-3550
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• 2022

The supercritical carbon dioxide (S-CO₂) Brayton cycle is an important energy conversion technology for the fourth generation of nuclear energy. Since the printed circuit heat exchanger (PCHE) used in the S-CO₂ Brayton cycle has narrow channels, Rayleigh-Bénard (RB) convection is likely to exist in the tiny channels. However, there are very few studies on RB convection in supercritical fluids. Current research on RB convection mainly focuses on conventional fluids such as water and air that meet the Boussinesq assumption. It is necessary to study non-Boussinesq fluids. PRB convection refers to RB convection that is affected by horizontal incoming flow. In this paper, the computational fluid dynamics simulation method is used to study the PRB convection phenomenon of non-Boussinesq fluid-supercritical carbon dioxide. The result shows that the inlet Reynolds number (Re) of the horizontal incoming flow significantly affects the PRB convection. When the inlet Re remains unchanged, with the increase of Rayleigh number (Ra), the steady-state convective pattern of the fluid layer is shown in order: horizontal flow, local traveling wave, traveling wave convection. If Ra remains unchanged, as the inlet Re increases, three convection patterns of traveling wave convection, local traveling wave, and horizontal flow will appear in sequence. To characterize the relationship between traveling wave convection and horizontal incoming flow, this paper proposes the relationship between critical Reynolds number and relative Rayleigh number (r).

• Journal of Ocean Engineering and Technology
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• v.16 no.5
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• pp.15-20
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• 2002

In this research, the finite difference lattice Boltzmann method(FDLBM) is used to analyze gravity currents in the lock exchange configuration that occur in many natural and man-made situations. At a lock those are seen when a gate is suddenly opened, and, in the atmosphere, when the thunderstorm outflows make a cold front. At estuaries in the ocean, the phenomenon is found between fresh water from a river and salt water in the sea. Since such interesting phenomena were recognized, pioneers have challenged to make them clear by conducing both experiments and analysis. Most of them were about the currents of liquid or Boussinesq fluids, which are assumed as incompressible. Otherwise, the difference in density of two fluids is small. The finite difference lattice Boltzmann method has been a powerful tool to simulate the flow of compressible fluids. Also, numerical predictions using FDLBM to clarify the gravity currents of compressible fluids exhibit all features, but typically observed in experimental flows near the gravity current head, including the lobe-and-cleft structure at the leading edge.

• Journal of Ocean Engineering and Technology
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• v.20 no.6 s.73
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• pp.35-40
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• 2006

In recent years, there's been strong demand for seawalls that havea gentle slope and permeability that serveswater affinity and disaster prevention from wave attack. The aim of this study is to examine wave transformation, including wave run-up that propagates on the coastal structures. A numerical model based on the weak nonlinear dispersive Boussinesq equation, together with the unsteady nonlinear Darcy law for fluid motion in permeable layer, is developed. The applicability of this numerical model is examined through Deguchi and Moriwaki's hydraulic model test on the permeable slopes. From this study, it is found that the proposed numerical model can predict wave transformation and run-up on the gentle slope with a permeable layer, but can't show accurate results for slopes steeper than about 1:10.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.31 no.3 s.258
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• pp.273-282
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• 2007

Numerical calculations are carried out for the natural convection induced by temperature difference between a cold outer square cylinder and a hot inner circular cylinder. A two-dimensional solution for unsteady natural convection is obtained, using the immersed boundary method (IBM) to model an inner circular cylinder based on finite volume method, for different Rayleigh numbers varying over the range of $10^4\;to\;10^6$. The study goes further to investigate the effect of an inner cylinder location on the heat transfer and fluid flow. The location of inner circular cylinder is changed vertically along the center-line of square enclosure. The number, size and formation of cell strongly depend on Rayleigh number and the position of inner circular cylinder. The changes in heat transfer quantities have been presented.

• Journal of computational fluids engineering
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• v.7 no.1
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• pp.36-43
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• 2002

A numerical investigation is made of unsteady double-diffusive convection of a Boussinesq fluid in a rectangular cavity subject to time-periodic thermal excitations. The fluid is initially stratified between the top endwall of low solute concentration and the bottom endwall of high solute concentration. A time-dependent heat flux varying in a square wave fashion, is applied on one sidewall to induce buoyant convection. The influences of the imposed periodicity on double-diffusive convection are examined. A special concern is on the occurrence of resonance that the fluctuations of flow and attendant heat and mass transfers are mostly amplified at certain eigenmodes of the fluid system. Numerical solutions illustrate that resonant convection results in a conspicuous enhancement of time-mean mass transfer rate.

• Solar Energy
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• v.2 no.1
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• pp.9-16
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• 1982

The problem of transient laminar natural convection in compressible fluid in a rectangular enclosure is considered. The upper and lower boundaries of the enclosure are thermally insulating and the side boundaries are maintained at fixed temperatures. The fluid is considered to be a perfect gas with constant viscosity and thermal conductivity and the formulation differs from the boussinesq simplification in that the effects of variable density are completely retained. The motions are restricted to two dimensions. For incompressible fluid, the natural convection is driven mainly by buoyancy force. But the solutions show that for compressible fluid, the natural convection is driven by pressure and buoyancy forces and the thermally induced motion is acoustic in nature.