Simulation of laminar flow in a three-dimensional lid-driven cavity by lattice Boltzmann method

Purpose - The purpose of this paper is to apply lattice Boltzmann equation method (LBM) with multiple relaxation time (MRT) model, to investigate lid-driven flow in a three-dimensional (3D), rectangular cavity, and compare the results with flow in an equivalent two-dimensional (2D) cavity. Design/methodology/approach - The second-order MRT model is implemented in a 3D LBM code. The flow structure in cavities of different aspect ratios (0.25-4) and Reynolds numbers (0.01-1000) is investigated. The LBM simulation results are compared with those from numerical solution of Navier-Stokes (NS) equations and with available experimental data. Findings - The 3D simulations demonstrate that 2D models may predict the flow structure reasonably well at low Reynolds numbers, but significant differences with experimental data appear at high Reynolds numbers. Such discrepancy between 2D and 3D results are attributed to the effect of boundary layers near the side-walls in transverse direction (in 3D), due to which the vorticity in the core-region is weakened in general. Secondly, owing to the vortex stretching effect present in 3D flow, the vorticity in the transverse plane intensifies whereas that in the lateral plane decays, with increase in Reynolds number. However, on the symmetry-plane, the flow structure variation with respect to cavity aspect ratio is found to be qualitatively consistent with results of 2D simulations. Secondary flow vortices whose axis is in the direction of the lid-motion are observed; these are weak at low. Reynolds numbers, but become quite strong at high Reynolds numbers. Originality/value - The findings will be useful in the study of variety of enclosed fluid flows.

Upwind compact method and direct numerical-simulation of driven flow in a square cavity

A high-order accurate finite-difference scheme, the upwind compact method, is proposed. The 2-D unsteady incompressible Navier-Stokes equations are solved in primitive variables. The nonlinear convection terms in the governing equations are approximated by using upwind biased compact difference, and other spatial derivative terms are discretized by using the fourth-order compact difference. The upwind compact method is used to solve the driven flow in a square cavity. Solutions are obtained for Reynolds numbers as high as 10000. When Re less than or equal to 5000, the results agree well with those in literature. When Re = 7500 and Re = 10000, there is no convergence to a steady laminar solution, and the flow becomes unsteady and periodic.

Method for generating maximally entangled states of multiple three-level atoms in cavity QED

We propose a scheme to generate maximally entangled states (MESs) of multiple three-level atoms in microwave cavity QED based on the resonant atom-cavity interaction. In the scheme, multiple three-level atoms initially in their ground states are sequently sent through two suitably prepared cavities. After a process of appropriate atom-cavity interaction, a subsequent measurement on the second cavity field projects the atoms onto the MESs. The practical feasibility of this method is also discussed.

Design Method for Circularly Polarized Fabry-Perot Cavity Antennas

A new class of circularly polarized (CP) Fabry-Perot cavity antennas is introduced that maintain the simplicity of a linearly polarized primary feed and a single cavity structure. The proposed antennas employ a double-sided partially reflective surface (PRS), which allows independent control of the magnitude and phase responses for the reflection and transmission coefficients. In conjunction with an anisotropic high-impedance surface (HIS) ground plane, this arrangement allows for the first time a single cavity antenna to produce a specified gain in CP from a linearly polarized primary source. A design procedure for this class of antennas is introduced. The method exploits a simple ray optics model to calculate the magnitude and phase of the electric field in the cavity upon plane wave excitation. Based on this model, analytical expressions are derived, which enforce the resonance condition for both polarizations at a predetermined PRS reflectivity (and hence predetermined antenna gain) together with a 90 degrees differential phase between them. The validity of the concept is confirmed by means of an example entailing an antenna with gain of approximately 21 dB at 15 GHz. Full-wave simulation results and experimental testing on a fabricated prototype are presented and agree well with the theoretical predictions.

Influence of sample type and collection method on Streptococcus mutans and Lactobacillus spp. counts in the oral cavity

Objectives: This study compared three methods of Streptococcus mutans and Lactobacillus spp. detection in the oral cavity: saliva swab (SS)-sample of stimulated saliva collected with swab; whole saliva (WS)-sample of 2 ml of stimulated saliva; and the dental plaque method (DP)-plaque sample of all dental surfaces.Methods: Thirty children were included in this study. In the first 15 children, the SS and WS methods were carried out before the dental plaque collection, and in the following 15, the sequence was inverted to evaluate possible interference of the methods sequence. The samples were diluted and inoculated in SB20 and Rogosa agar, respectively for S. mutans and Lactobacillus spp., at 37 degrees C for 48 h.Results: the results (cfu/mL) of S. mutans were analysed by the statistical Friedman's test. The levels of Lactobacillus spp. were analysed by descriptive statistics due to the high proportion of zero counts in the culture. In the first sequence of methods, the number of S. mutans counted for the SS method was inferior to DP and WS (P < 0.05), and the results for the WS and DP methods were similar. The detection of Lactobacillus spp. was observed just by the WS (100 %) and SS (14.3 %) methods. However, in the second experimental set the number of S. mutans detected by the DP method was similar to those of the SS and WS, however, the WS method showed higher values than SS (P < 0.05). A greater number of Lactobacillus spp. was detected by the WS method (100 %), followed by SS (55.5 %) and DP (33.3 %).Conclusions: the dental plaque collection and the sample of stimulated whole saliva presented similar results in the S. mutans count. The most suitable method to detect the Lactobacillus spp. level in the oral cavity is the stimulated whole saliva method. (c) 2004 Elsevier Ltd. All rights reserved.

Influence of cavity preparation and curing method on the marginal seal of resin composite restorations: an in vitro evaluation.

OBJECTIVE: To evaluate the influence of cavity design and photocuring method on the marginal seal of resin composite restorations. METHOD AND MATERIALS: Seventy-two bovine teeth were divided into 2 groups: group 1 received box-type cavity preparations, and group 2 received plate-type preparations. Each group was divided into 3 subgroups. After etching and bonding, Z250 resin composite (3M Espe) was applied in 2 equal increments and cured with 1 of 3 techniques: (1) conventional curing for 30 seconds at 650 mW/cm2; (2) 2-step photocuring, in which the first step was performed 14 mm from the restoration for 10 seconds at 180 mW/cm2 and the second step was performed in direct contact for 20 seconds at 650 mW/cm2; or (3) progressive curing using Jetlite 4000 (J. Morita) for 8 seconds at 125 mW/cm2 and then 22 seconds at 125 mW/cm2 up to 500 mW/cm2. The specimens were thermocycled for 500 cycles and then submitted to dye penetration with a 50% silver nitrate solution. Microleakage was assessed using a stereomicroscope. Data were analyzed using analysis of variance and Tukey test (5% level of significance). RESULTS: A statistically significant difference was found between groups when a double interaction between photocuring and cavity preparation was considered (P = .029). CONCLUSIONS: No one type of cavity preparation or photocuring method prevented micro-leakage. The plate-type preparation showed the worst dye penetration when conventional and progressive photocuring methods were used. The best results were found using the 2-step photocuring with the plate-type preparation.

Mixed convection flow of micropolar fluid in an open ended arc-shape cavity

Numerical simulations for mixed convection of micropolar fluid in an open ended arc-shape cavity have been carried out in this study. Computation is performed using the Alternate Direct Implicit (ADI) method together with the Successive Over Relaxation (SOR) technique for the solution of governing partial differential equations. The flow phenomenon is examined for a range of values of Rayleigh number, 102 ≤ Ra ≤ 106, Prandtl number, 7 ≤ Pr ≤ 50, and Reynolds number, 10 ≤ Re ≤ 100. The study is mainly focused on how the micropolar fluid parameters affect the fluid properties in the flow domain. It was found that despite the reduction of flow in the core region, the heat transfer rate increases, whereas the skin friction and microrotation decrease with the increase in the vortex viscosity parameter, Δ.

Numerical study of lid-driven square cavity with heat generation using LBM

In this study, the mixed convection heat transfer and fluid flow behaviors in a lid-driven square cavity filled with high Prandtl number fluid (Pr = 5400, ν = 1.2×10-4 m2/s) at low Reynolds number is studied using thermal Lattice Boltzmann method (TLBM) where ν is the viscosity of the fluid. The LBM has built up on the D2Q9 model and the single relaxation time method called the Lattice-BGK (Bhatnagar-Gross-Krook) model. The effects of the variations of non dimensional mixed convection parameter called Richardson number(Ri) with and without heat generating source on the thermal and flow behavior of the fluid inside the cavity are investigated. The results are presented as velocity and temperature profiles as well as stream function and temperature contours for Ri ranging from 0.1 to 5.0 with other controlling parameters that present in this study. It is found that LBM has good potential to simulate mixed convection heat transfer and fluid flow problem. Finally the simulation results have been compared with the previous numerical and experimental results and it is found to be in good agreement.

Heat transfer analysis of viscous incompressible fluid by combined natural convection and radiation in an open cavity

The effect of radiation on natural convection of Newtonian fluid contained in an open cavity is investigated in this study. The governing partial differential equations are solved numerically using the Alternate Direct Implicit method together with the Successive Over Relaxation method. The study is focused on studying the flow pattern and the convective and radiative heat transfer rates are studied for different values of radiation parameters namely, the optical thickness of the fluid, scattering albedo, and the Planck number. It was found that in the optically thin limit, an increase in the optical thickness of the fluid raises the temperature and radiation heat transfer of the fluid. However, a further increase in the optical thickness decreases the radiative heat transfer rate due to increase in the energy level of the fluid, which ultimately reduces the total heat transfer rate within the fluid.

Double diffusive Marangoni convection flow of electrically conducting fluid in a square cavity with chemical reaction

Double diffusive Marangoni convection flow of viscous incompressible electrically conducting fluid in a square cavity is studied in this paper by taking into consideration of the effect of applied magnetic field in arbitrary direction and the chemical reaction. The governing equations are solved numerically by using alternate direct implicit (ADI) method together with the successive over relaxation (SOR) technique. The flow pattern with the effect of governing parameters, namely the buoyancy ratio W, diffusocapillary ratio w, and the Hartmann number Ha, is investigated. It is revealed from the numerical simulations that the average Nusselt number decreases; whereas the average Sherwood number increases as the orientation of magnetic field is shifted from horizontal to vertical. Moreover, the effect of buoyancy due to species concentration on the flow is stronger than the one due to thermal buoyancy. The increase in diffusocapillary parameter, w caus

Unsteady Natural Convection Flow in a Square Cavity Filled with a Porous Medium Due to Impulsive Change in Wall Temperature

Unsteady natural convection flow in a two- dimensional square cavity filled with a porous material has been studied. The flow is initially steady where the left- hand vertical wall has temperature T-h and the right- hand vertical wall is maintained at temperature T-c ( T-h > T-c) and the horizontal walls are insulated. At time t > 0, the left- hand vertical wall temperature is suddenly raised to (T-h) over bar ((T-h) over bar > T-h) which introduces unsteadiness in the flow field. The partial differential equations governing the unsteady natural convection flow have been solved numerically using a finite control volume method. The computation has been carried out until the final steady state is reached. It is found that the average Nusselt number attains a minimum during the transient period and that the time required to reach the final steady state is longer for low Rayleigh number and shorter for high Rayleigh number.

A numerical study of thermocapillary flow in a rectangular cavity during laser melting

The surface tension gradient driven flow that occurs during laser melting has been studied. The vorticity-streamfunction form of the Navier-Stokes equations and the energy equation has been solved by the ‘Alternative Direction Implicit’ method. It has been shown that the inertia forces in the melt strongly influence the flow pattern in the melt. The convection in the melt modifies the isotherms in the melt at high surface tension Reynolds number and high Prandtl number. The buoyancy driven flow has been shown to be negligible compared to the surface tension gradient driven flow in laser melting.