Search results

Numerical simulation of a fluid flow involves the specification of boundary conditions along all or part of the boundary. Designs a means of handling outflow boundary conditions for the incompressible Navier‐Stokes equations. Addresses through‐flow problems involving the specification of outflow conditions at the synthetic boundary. This outflow boundary condition is applicable to a developing flow problem. The underlying objectives behind designing the boundary condition at the truncated boundary are three‐fold, namely: matching with Navier‐Stokes equations inside the domain; taking both non‐linear and diffusive contributions into account; and ensuring the discrete divergence‐free condition. In order to meet these requirements, follows the concept of a free boundary condition by taking the outflow nodal values of u, v and p as unknowns, which are coupled with the interior unknowns through the surface integrals in the momentum equations. The computed solutions can be legitimately regarded as solutions to conservation equations under consideration when both components of the surface traction vector approach zero. With the convergent property accommodated in the present mixed finite element analysis, the task remains to simply improve the accuracy. Demonstrates the capability of the proposed non‐linear outflow boundary conditions through several benchmark tests.

A mathematical analysis of the time‐dependent multi‐dimensional Hydrodynamic model is performed to determine the well‐posed boundary conditions for semiconductor device simulation. The number of independent boundary conditions that need to be specified at electrical contacts of a semi‐conductor device are derived. Using the classical energy method, a mathematical relation among the physical parameters is established to define the well‐posed boundary conditions for the problem. Several possible sets of boundary conditions are given to illustrate the proper boundary conditions. Natural boundary conditions that can be specified are obtained from the boundary integrals of the weak‐form finite element formulations. An example is included to illustrate the importance of well‐posedness of the boundary conditions for device simulation.

A finite element method dealing with an open boundary condition for the analysis of long wave problem is presented. The key feature of the method is that spurious reflective waves which occurred for the initial transient state on the open boundary can be eliminated by introducing a subdomain technique. For the numerical outflow boundary condition, the progressive wave condition, based on the shallow water long wave theory, is successfully employed. This method is quite suitable for practical analysis because of its adaptability for the arbitrary configuration of the open boundary and shape of elements adjacent to the open boundary. This method is numerically verified for flow in a one dimensional channel and the two dimensional tidal current in Tokyo Bay. The numerical results are compared with analytical solutions and observed data obtained by field measurements. These results are all in close agreement.

External natural convection is rarely studied by numerical simulation in the literature due to the fact that flow of interest takes place in an unbounded domain and that if a limited computational domain is used the corresponding outer boundary conditions are unknown. In this study, we propose outer boundary conditions for a limited computational domain and make the corresponding numerical implementation in the scope of a projection method combining spectral methods and domain decomposition techniques. Numerical simulations are performed for both steady natural convection about an isothermal cylinder and transient natural convection around a line‐source. An experiment is also realized in water using particle image velocimetry and thermocouples to make a comparison during transients of external natural convection around a platinum wire heated by Joule effect. Good agreement, observed between numerical simulations and experiments, validated the outer boundary conditions proposed and their numerical implementation. It is also shown that, if one tolerates prediction error, numerical results obtained remain at least reasonable in a region near the line‐source during the entire transients. We thus paved the way for numerical simulation of external natural convection although further studies remain to be done for higher heating power (higher Rayleigh number).

Some results concerning the well‐posedness of the hydrodynamic model of semiconductor devices in two dimensions are given. We show the non‐ellipticity of the stationary model; give representations which exhibit its elliptic and hyperbolic components, and obtain some appropriate boundary conditions from an examination of the time‐dependent problem.

The purpose of this paper is to examine the modeling of simultaneous heat and mass transfer under dehumidifying conditions. Moist air cooling in tube‐fin exchangers is investigated using a finite element technique.

The model requires the solution of a conjugate problem, since interface temperatures must be calculated at the same time as temperature distributions in adjacent fluid and solid regions. The energy equation is solved in the whole domain, including the solid region, and the latent heat flux on the surfaces where condensation takes place is taken into account by means of an additional internal boundary condition.

Thermal performances for different Reynolds numbers of a typical two‐row tube‐fin exchanger are numerically analysed, for both in‐line and staggered arrangements of tubes. The results justify the great importance that the ratio between latent and overall rates of heat transfer has in the design of compact heat exchangers.

In this work, the capabilities of the proposed methodology to deal with industrial applications in the field of compact exchangers are outlined.

The paper presents an effective approach to the solution of conjugate conduction and convection problems with simultaneous heat and mass transfer. The formulation is completely general, even if the finite element method is used in the calculations.

The purpose of this paper is to extend the penalty concept to treat partial slip, free surface, contact and related boundary conditions in viscous flow simulation.

The penalty partial‐slip formulation is analysed and related to the classical Navier slip condition. The same penalty scheme also allows partial penetration through a boundary, hence the implementation of porous wall boundaries. The finite element method is used for investigating and interpreting penalty approaches to boundary conditions.

The generalised penalty approach is verified by means of a novel variant of the circular‐Couette flow problem, having partial slip on one of the cylindrical boundaries, for which an analytic solution is derived. Further verificationis provided by consideration of viscous flow over a sphere with partial slip on the surface, and comparison of numerical and classical solutions. Numerical studies illustrate the versatility of the approach.

The penalty approach is applied to some different boundaries: partial slip and partial penetration with no/full slip/penetration as limiting cases; free surface; space‐ and time‐varying boundary conditions which allow progressive contact over time. Application is made to curved and inclined boundaries. Sensitivity of flow to penalty parameters is an avenue for continued research, as is application of the penalty approach for non‐Newtonian flows.

This is the first work to show the relation between penalty formulation of boundary conditions and physical boundary conditions. It provides a method that overcomes past difficulties in implementing partial slip on boundaries of general shape, and which handles progressive contact. It also provides useful benchmark problems for future studies.

The purpose of this paper is to investigate the computational features of the Flowfield Dependent Variation (FDV) method, a numerical scheme built to simulate flows characterized by multiple speeds, multiple physical phenomena, and by large variations in flow variables.

Fundamentally, the FDV method may be regarded as a variant of the Lax-Wendroff Scheme (LWS) that is obtained by replacing the explicit time derivatives in LWS by a weighted combination of explicit and implicit time derivatives. The weighting factors – referred to as FDV parameters – may be broadly classified as convective and diffusive parameters which, for example, are determined using flow quantities such as the Mach number and Reynolds number, respectively. Hence, the reference to these parameters and the method as “flow field dependent.” A von Neumann Fourier analysis demonstrates that the increased implicitness makes FDV both more stable and less dispersive compared to LWS, a feature crucial to capturing shocks and other phenomena characterized by high gradients in variables. In the current study, the FDV scheme is implemented in a Taylor-Galerkin-based finite element method framework that supports arbitrarily high order, unstructured isoparametric elements in one-, two- and three-dimensional geometries.

At first, the spatial accuracy of the implemented FDV scheme is established using the Method of Manufactured Solutions, wherein the results show that the order of accuracy of the scheme is nearly equal to the order of the shape function polynomial plus one. The dispersion and dissipation errors of FDV, when applied to the compressible Navier-Stokes and energy equations, are investigated using a 2-D, small-amplitude acoustic pulse propagating in a quiescent medium. It is shown that FDV with third-order shape functions accurately captures both the amplitude and phase of the acoustic pulse. The method is then applied to cases ranging from low-Mach number subsonic flows (Mach number M=0.05) to high-Mach number supersonic flows (M=4) with shock-boundary layer interactions. For all cases, fair to good agreement is observed between the current results and those in the literature.

The spatial order of accuracy of the FDV method, its stability and dispersive properties, as well as its applicability to low- and high-Mach number flows are established.

A numerical study of a two‐dimensional turbulent flow in a partially open rectangular cavity such as a room is carried out. The turbulent flow is induced by the energy input due to a localized heat source positioned on the floor of the cavity. This flow is of interest in enclosure fires where the flow in the cavity interacts with the environment through the opening or vents. The focus is on the stable, thermal stratification that arises in the room and on the influence of the opening height. A finite‐difference method is employed for the solution of the problem, using a low Reynolds number k — ε turbulence model for the turbulent flow calculations. This model is particularly suitable for flows in which the possibility for relaminarization exists. It was found that, for high Grashof numbers and for relatively small opening heights, particularly for doorway openings, a strong stable thermal stratification is generated within the cavity, with a cooler, essentially uniform, layer underlying a warmer, linearly stratified, upper layer. As a consequence, turbulence is suppressed and the flow in the upper region of the cavity becomes laminar with turbulence confined to locations such as the fire plume above the source and the shear layer at the opening. The penetration distance and the height of the interface are both found to decrease with a reduction in the opening height. The Nusselt number for heat transfer from the source is seen to be affected to a small extent by the opening height. The basic trends are found to agree with those observed in typical compartment fires. Comparisons with results available in the literature on turbulent buoyancy‐driven enclosure flows indicate good agreement, lending support to this model and the numerical scheme.

The purpose of this study is to design numerical simulations of bubbly flow around a cylinder to better understand the characteristics of flow around a rigid obstacle.

The bubbly flow around a circular cylinder was numerically simulated using a semi-Lagrangian–Lagrangian method composed of a vortex-in-cell method for the liquid phase and a Lagrangian description of the gas phase. Additionally, a penalization method was applied to account for the cylinder inside the flow. The slip condition of the bubbles on the cylinder’s surface was enforced, and the outflow conditions were applied to the liquid flow at the far field.

The simulation clarified the characteristics of a bubbly flow around a circular cylinder. The bubbles were shown to move around and separate from both sides of the cylinder, because of entrainment by the liquid shear layers. Once the bubbly flow fully developed, the bubbles distributed into groups and were dispersed downstream of the cylinder. A three-dimensional vortex structure of various scales was also shown to form downstream, whereas a quasi-stable two-dimensional vortex structure was observed upstream. Overall, the proposed method captured the characteristics of a bubbly flow around a cylinder well.

A semi-Lagrangian–Lagrangian approach was applied to simulate a bubbly flow around a circular cylinder. The simulations provided the detail features of these flow phenomena.