• 한국전산유체공학회:학술대회논문집
• /
• 2009.11a
• /
• pp.49-55
• /
• 2009

This paper evaluates performances of a recently developed divergence-free finite element method based on Hermite interpolated stream functions. Velocity bases are derived from Hermite interpolated stream functions to form divergence-free basis functions. These velocity basis functions constitute a solenoidal function space, and the simple gradient of the Hermite functions constitute an irrotational function space. The incompressible Navier-Stokes equation is orthogonally decomposed into a solenoidal and an irrotational parts, and the decoupled Navier-Stokes equations are projected onto their corresponding spaces to form proper variational formulations. To access accuracy and convergence of the present algorithm, three test problems are selected. They are lid-driven cavity flow, flow over a backward-facing step and buoyancy-driven flow within a square enclosure. Hermite interpolation functions from cubic to quintic are chosen to run the test problems. Numerical results are shown. In all cases it has shown that the present method has performed well in accuracies and convergences. Moreover, the present method does not require an upwinding or a stabilized term.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.22 no.3
• /
• pp.360-372
• /
• 1998

This study deals with the interaction between buoyancy-induced convection and externally imposed excitation in the form of harmonic rocking and the effect of the interaction upon heat transfer in low-Pr liquids. A wide array of system responses are discussed using the spectral collocation numerical technique. The superposition of buoyancy and Coriolis forces leads to complex fluid flow and heat transfer. The transition to chaotic convection is accelerated, and heat transfer rates are reduced as the enclosure is excited at the fundamental frequency of oscillation associated with the pure buoyancy-driven case. Average heat transfer rates are correlated for Pr=0.02 and 0.03. The heat transfer is affected more in the Pr=0.03 liquid than the case of Pr=0.02.

• Journal of Ocean Engineering and Technology
• /
• v.25 no.5
• /
• pp.9-14
• /
• 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.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.18 no.11
• /
• pp.2999-3007
• /
• 1994

The unsteady numerical simulations have been presented for the laminar natural convection in a partially open compartment. Computations were performed within the domain of the compartment in order to show the thermal radiation and the partially opening effects on the flow fields and heat transfer characteristics. The results were shown for different Planck numbers(0.05~5) and opening ratios(0.25~0.75) being fixed with Ra=$10^5$ and Pr=0.71. Considering the flow which is buoyancy driven from the heated wall, and the buoyancy is not much affected by the further outside region from the opening, the numerical computations have been performed without an outer region by the particular boundary treatments on the flow velocity and temperature at the different partial openings. The confined numerical domain reduced the CPU time and the memory of computer. P-1 approximation of radiative transfer equation was employed with Marshak type boundary conditions along with the pseudo-black body approximation at the partial openings. The numerical results clearly show that the natural convective flow and heat transfer are much affected by increase of thermal radiation particularly from the initial state. When thermal radiation is not much affecting the flow ($PL{\le}1$), it was found that thermal radiation effects are almost negligible.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.32 no.2
• /
• pp.158-165
• /
• 2008

The carbon dioxide properties change sharply near the critical or pseudo-critical point in the heat transfer processes. The reduction in turbulent, convective heat transfer parameters observed in some supercritical data and in experiments with common gases can be due to property variation, acceleration, buoyancy or combinations of these phenomena, depending on the conditions of the applications. In this study, the measurement for the secondary flow driven by buoyancy was carried out on the supercritical carbon dioxide turbulent flows in the different boundary condition with the constant mass flow rate. The available measuring techniques were used to clarify the behaviour of any supercritical fluid. Laser Doppler Velocimeter (LDV) and a special device was used to measure the secondary velocity and turbulent characteristics of the supercritical flows.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.21 no.1
• /
• pp.153-164
• /
• 1997

Flame oscillation phenomena in a co-flow diffusion flame was experimentally studied with periodic fuel supply using a solenoid valve. The degree of excitation was controlled by changing the volume flux of fuel passing through the valve. Flame oscillation frequencies were measured utilizing a photodiode, a spectrum analyzer, video and high speed movies. Laser planar visualization was employed to study the correlation between the flame oscillation and the toroidal vortices. Observed are three regimes of flame oscillation, where the oscillation frequencies are for the multiples of excitation, the excitation itself and the flame natural oscillation. Both periods of natural oscillation and of excitation induced oscillation exist over one cycle of the excitation in the frequency multiplied regime. It is considered as an effect of balancing the influence of buoyancy driven vortex with that of excitation induced vortex near the excitation rate of 0.2. Flame shapes are become monotonous as increasing the excitation frequency to the range of over two fold of the natural oscillation. The flame oscillation can be modulated to the frequency of either multiples of excitation or excitation itself under certain conditions. This implies that the flame oscillation could be modulated to avoid the resonance frequency of the combustor, and shows the possibility of active control of the flame oscillation.

• 한국전산유체공학회:학술대회논문집
• /
• 2007.10a
• /
• pp.220-225
• /
• 2007

This paper is a continuation of the recent development on the hermite-based divergence free basis function and deals with a non-isothermal fluid flow thru the buoyancy driven flow in a square cavity with temperature difference across the two sides. The basis functions for the velocities consist of the hermite function and its curl. However, the basis for the temperature are the hermite function and its gradienst. Hence, the number of degrees of freedom at a node becomes 6, which are the stream function, two velocities, the temperature and its x- and y-derivatives. Numerical results for the streamlines, the temperatures, the x-velocities and the y-velocities show good agreements with those of De vahl Davis[7].

• Journal of computational fluids engineering
• /
• v.4 no.1
• /
• pp.8-18
• /
• 1999

In devising a numerical approximation for the convective spatial transport of a fluid mechanical quantity, it is noted that the convective motion of a scalar quantity occurs in one-way, or from upstream to downstream. This consideration leads to a new scheme termed a pure upwind difference scheme (PUDS) in which an estimated value for a fluid mechanical quantity at a control surface is not influenced from downstream values. The formal accuracy of the proposed scheme is third order accurate. Two typical benchmark problems of a wall-driven fluid flow in a square cavity and a buoyancy-driven natural convection in a tall cavity are computed to evaluate performance of the proposed method. for comparison, the widely used simple upwind scheme, power-law scheme, and QUICK methods are also considered. Computation results are encouraging: the proposed PUDS sensitized to the convection direction produces the least numerical diffusion among tested convection schemes, and, notable improvements in representing recirculation of fluid stream and spatial change of a scalar. Although the formal accuracy of PUDS and QUICK are the same, the accuracy difference of approximately a single order is observed from the revealed results.

• 한국전산유체공학회:학술대회논문집
• /
• 1998.11a
• /
• pp.121-126
• /
• 1998

A numerical optimization procedure is developed to find the inlet velocity profile that yields the most uniform epitaxial layer in a vertical MOCVD reactor. It involves the solution of fully elliptic equations of motion, temperature, and concentration; the finite volume method based on SIMPLE algorithm has been adopted to solve the Navier-Stokes equations. The overall optimization process is highly nonlinear and has been efficiently treated by the sequential linear programming technique that breaks the non-linear problem into a series of linear ones. The optimal profile approximated by a 6th-degree Chebyshev polynomial is very successful in reducing the spatial non-uniformity of the growth rate. The optimization is particularly effective to the high Reynolds number flow. It is also found that a properly constructed inlet velocity profile can suppress the buoyancy driven secondary flow and improve the growth-rate uniformity.

• Nuclear Engineering and Technology
• /
• v.48 no.4
• /
• pp.925-931
• /
• 2016

In this study, laminar natural circulation and heat transfer in a tall rectangular enclosure with disconnected vertical partitions inside were investigated. Analytical expressions were developed to predict the circulation flow rate and the average Nusselt number in a partially partitioned enclosure with isothermal side walls at different temperatures and insulated top and bottom walls. The proposed formulas are then validated against numerical results for modified Rayleigh numbers of up to $10^6$. The impacts of the governing parameters are also examined along with a discussion of the heat transfer regimes.