• 한국해양공학회지
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• 제25권5호
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• pp.9-14
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• 2011

The divergence-free finite elements introduced in this paper are derived from Hermite functions, which interpolate stream functions. Velocity bases are derived from the curl of the Hermite functions. These velocity basis functions constitute a solenoidal function space, and the gradient of the Hermite functions constitute an irrotational function space. The incompressible Navier-Stokes equation is orthogonally decomposed into its solenoidal and irrotational parts, and the decoupled Navier-Stokes equations are then projected onto their corresponding spaces to form appropriate variational formulations. The degrees of the Hermite functions we introduce in this paper are bi-cubis, quartic, and quintic. To verify the accuracy and convergence of the present method, three well-known benchmark problems are chosen. These are lid-driven cavity flow, flow over a backward facing step, and buoyancy-driven flow within a square enclosure. The numerical results show good agreement with the previously published results in all cases.

• 한국전산유체공학회지
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• 제20권1호
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• pp.77-83
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• 2015

Flow characteristics of synthetic jet based flow supplying devices have been computationally investigated for different device shapes. Jet momentum was produced by the volume change of a cavity by two piezoelectric-driven diaphragms. The devices have additional flow path compared with the original synthetic jet actuator, and these flow path changes the flow characteristics of synthetic jet actuator. Four non-dimensional parameters, which were functions of the shapes of the additional flow path, were considered as the most critical parameters in jet performance. Comparative studies were conducted to compare volume flow rate and jet velocity. Computed results were solved by 2-D incompressible Navier-Stokes solver with k-w SST turbulence model. Detailed computations revealed that the additional flow path diminishes suction strength of the synthetic jet actuator. In addition, the cross section area of the flow path has more influence over the jet performances than the length of the flow path. Based on the computational results, the synthetic jet based flow supplying devices could be improved by applying suitable shape of the flow path.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2006년도 PARALLEL CFD 2006
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• pp.163-166
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• 2006

We have introduced a new version of the 3-D lid-driven cavity problem that leads to more complicated fluid parcel trajectories and thus, enhanced mixing, but at the same time weakens corner singularities. We employed an advanced form of LES to solve this problem and presented preliminary results that show very complicated streamline structures on both large and small scales, despite a relatively low Reynolds number. Finally, we demonstrated moderate speedups via parallelization. Ongoing tests are expected to resolve the questions raised regarding possible sources of the rather poor parallel performance compared with that seen in earlier studies with the same code. Because it is expected that findings may be significant for parallel performance in general, we plan to emphasize this aspect in the oral presentation the Parrel (CFD 2006 Conference.

• 대한기계학회논문집B
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• 제24권7호
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• pp.907-915
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• 2000

The preconditioned Krylov subspace methods were applied to the incompressible Navier-Stoke's equations for convergence acceleration. Three of the Krylov subspace methods combined with the five of the preconditioners were tested to solve the lid-driven cavity flow problem. The MILU preconditioned CG method showed very fast and stable convergency. The combination of GMRES/MILU-CG solver for momentum and pressure correction equations was found less dependency on the number of the grid points among them. A guide line for stopping inner iterations for each equation is offered.

• Journal of Advanced Marine Engineering and Technology
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• 제23권6호
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• pp.770-777
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• 1999

In this study a phase diagram has been used to investigate the unsteadiness of two-dimensional lid-driven closed flows within a square cavity for twelve Reynolds numbers; $7.5{\times}10^3,\; 8{\times}10^3,\; 8.5{\times}10^3,\; 9{\times}10^3,\; 9.5{\times}10^3,\; 10^4,\;1.5{\times}10^4,\;2{\times}10^4,\; 3{\times}10^4,\; 7.5{\times}10^4$ and $10^5$. The results indicate that the first critical Reynolds number at which the flow unsteadiness of sinusoidal fluctuation appears from the temporal variation of total kinetic energy curves is assumed of sinusoidal fluctuation appears form the temporal variation of total kinetic energy curves is assumed to be in the neigh-bourhood of $Re=8.5{\times}10^3$ The second critical Reynolds number where the periodic amplitude and frequency collapse to random disturbance being existed around $Re=1.5{\times}10^4$ The exponentially decreasing vortices formed at the lower two corners are found commonly at the time-mean flow pattern of $Re=3{\times}10^4$.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2000년도 추계 학술대회논문집
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• pp.115-122
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• 2000

본 연구에서는 2 차원 벽구동 캐비티 유동에 의하여 나타나는 이력효과에 의한 분기(Bifurcation)현상을 전산유체기법을 사용하여 연구하였다. 캐비티는 북쪽과 동쪽벽이 움직일 수 있고, 다른 두 벽은 고정되어있는 구조이다. 실험은 Reynolds 수 100 에서 1000까지 증가시켜가면서 북쪽벽과 동쪽벽을 동시에 가속 시켜 정상상태에 이르게 한 경우와 북쪽벽이 먼저 가속되어 정상해에 이른 후 동쪽벽을 나중에 가속하여 재차 정상상태에 이르게 한 경우를 비교하였다. 그 결과 Reynolds수가 약 200이상부터 벽에 작용하는 항력, 유량함수의 값, 재부착점등이 분기현상을 나타냄을 확인하였다.

• 대한기계학회논문집B
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• 제21권2호
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• pp.202-212
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• 1997

In this study, performance of the multi-stage explicit methods for numerical computation of the unsteady Navier-Stokes equations is investigated. Three methods under consideration are 1 st-, 2 nd-, and 4 th-order Runge-Kutta (R-K) methods. Compared in this estimation is stability, accuracy, and CPU time of each method. The computational codes developed are applied to the two-dimensional flow in a square cavity driven by an oscillating lid. It turned out that at Reynolds number 400, the 1 st-order R-K method is the best, while at 3200 the 2 nd-order R-K is recommended. At higher Reynolds numbers, it is conjectured that the 4 th-order R-K method will be the best algorithm among three due to its highest stability.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 1999년도 춘계 학술대회논문집
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• pp.106-112
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• 1999

In this article, combination of the FAS-FMG multi-grid method and the Krylov subspace method was presented in solving two dimensional driven-cavity flows. Three algorithms of the Krylov subspace method, CG, CGSTAB(Bi-CG Stabilized) and GMRES method were tested with MILU preconditioner. As a smoother of the pressure correction equation, the MILU-CG is recommended rather than MILU-GMRES(k) or MILU-CGSTAB, since the MILU-GMRES(k) preconditioner has too much computation on the coarse grid compared to the MILU-CG one. As for the momentum equation, relatively cheap smoother like SIP solver may be sufficient.

• Journal of Magnetics
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• 제18권3호
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• pp.321-325
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• 2013

The problem of mixed convection in a differentially heated lid-driven square cavity filled with Cu-water nanofluid under effect of a magnetic field is investigated numerically. The left and right walls of the cavity are kept at temperatures of $T_h$ and $T_c$ respectively while the horizontal walls are adiabatic. The top wall of the cavity moves in own plane from left to right. The effects of some pertinent parameters such as Richardson number (ranging from 0.1 to 10), the volume fraction of the nanoparticles (ranging 0 to 0.1) and the Hartmann number (ranging from 0 to 60) on the fluid flow and temperature fields and the rate of heat transfer in the cavity are investigated. It must be noted that in all calculations the Prandtl number of water as the pure fluid is kept at 6.8, while the Grashof number is considered fixed at 104. The obtained results show that the rate of heat transfer increases with an increase of the Reynolds number, while but it decreases with increase in the Hartmann number. Moreover it is found that based the Richardson and Hartmann numbers by increase in volume fraction of the nanoparticles the rate of heat transfer can be enhanced or deteriorated compared to the based fluid.

• Journal of Advanced Marine Engineering and Technology
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• 제25권2호
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• pp.304-310
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• 2001

This paper describes the analysis of flow field using a projection finite element method. The projection scheme with a pressure correction is presented for the analysis of an incompressible Navier-Stokes flow. The projection scheme is analyzed numerically and applied to the well-known bench marking problems such as lid driven cavity. Finally, the projection scheme is applied to a flow through the automobiles front. In the automobiles cooling system, the flow through its front is very important to a cooling performance. The results show that the flow quantity increases by locating the position of bumper to the further front position of a car. And, the improvement on the suction part below a bumper achieves the more passing flow quantity. The attachment of an air dam increases passing flow quantity causing the pressure rise to the front part and the pressure drop beneath a car.