T. S. Lee

Computational and experimental studies of convective fluid motion and heat transfer in inclined non-rectangular enclosures

Computational and experimental studies of the fluid motion and heat transfer characteristics of an incompressible fluid contained in a non-rectangular inclined enclosure are described in this paper. The enclosure has two 45° inclined side walls one of which was heated and the other cooled. The remaining two sides of the enclosure are parallel and insulated. The enclosure was rotated about the long axis in steps of 30° through 360°. Experiments were performed to study the effects of Rayleigh number, aspect ratios and orientation of the enclosure. The computational method uses a mesh transformation technique coupled with the introduction of ‘false transient’ parameters for the steady state solution of the problem. The experimental method uses smoke for flow visualization studies. With aspect ratios of 3 and 6, the results indicate that the heat transfer and fluid motion within the enclosure is a strong function of both the Rayleigh number and the cavity orientation angle. A minimum and a maximum mean Nusselt number occurred as the angle of inclination was increased from 0 to 360°. A transition in the mode of circulation occurred at the angle corresponding to the minimum or maximum rate of heat transfer. Stream lines and isotherms are presented for the most representative cases

A numerical method for flows in porous and homogenous fluid domains coupled at the interface by stress jump

A numerical method was developed for flows involving an interface between a homogenous fluid and a porous medium. The numerical method is based on the finite volume method with body-fitted and multi-block grids. A generalized model, which includes Brinkman term, Forcheimmer term and non-linear convective term, was used to govern the flow in the porous medium region. At its interface, a shear stress jump that includes the inertial effect was imposed, together with a continuity of normal stress. Furthermore, the effect of the jump condition on the diffusive flux was considered, additional to that on the convective part which has been usually considered. Numerical results of three flow configurations are presented. The method is suitable for coupled problems with regions of homogeneous fluid and porous medium, which have complex geometries. Copyright

Numerical experiments with fluid convection in tilted nonrectangular enclosures

Numerical experiments were performed on an incompressible fluid contained in a tilted nonrectangular enclosure. Rayleigh numbers of l02-l05 and Prandtl numbers of 0.001-100 are considered. The wall angles are 22.5°, 45°, and 77.5° with aspect ratios of 3 and 6. Results indicate that the heat transfer and fluid motion within the enclosure are strong functions of Rayleigh number, Prandtl number, and orientation angle of the enclosure. For Rayleigh numbers greater than 1& and Prandtl numbers greater than 0.1, a minimum and a maximum mean Nusselt number occurred as the angle of orientation was increased from 0° to 360°. A transition in the mode of circulation occurred at the angles corresponding to the minimum or maximum rate of heat transfer.

APPLICATION OF GDQ METHOD FOR THE STUDY OF NATURAL CONVECTION IN HORIZONTAL ECCENTRIC ANNULI

A generalized differential-integral quadrature (GDQ) discretization technique developed by one of the authors was used to solve a natural convection problem in a body-fit coordinate system in their primitive variables form. A special treatment of the boundary conditions to satisfy the continuity and momentum equations along the boundaries with the implementation of the GDQ method was investigated. Comparisons with the experimental and numerical results of other investigators are presented and discussed. In contrast with the existing published results, this highly accurate method was able to reveal extremely weak net circulation around the inner eccentric cylinder that was not found previously by other investigators. This net circulation has its maximum value when the inclination angle of eccentricity is in the horizontal position.

AN AXISYMMETRIC INCOMPRESSIBLE LATTICE BOLTZMANN MODEL FOR PIPE FLOW

In this paper an accurate axisymmetric lattice Boltzmann D2Q9 model is proposed to simulate the steady and pulsatile flows in circular pipes. Present model is derived from an incompressible D2Q9 model and some errors in a previous model [Halliday et al., Phys. Rev. E 64, 011208 (2001)] are revised. In the previous model, some terms relative to the radial velocity are missing and would lead to large error for constricted or expanded pipe flows. Present model is validated by cases of laminar steady flow through constricted tubes and 3D Womersley flow. Comparing with the previous model, our model is much more accurate for steady flow in constricted circular pipes. For 3D Womersley flow, it is also observed that the present model can reduce the compressibility effect in previous model.

Mass Transport and Shear Stress in a Microchannel Bioreactor: Numerical Simulation and Dynamic Similarity

Microchannel bioreactors have been used in many studies to manipulate and investigate the fluid microenvironment around cells. In this study, substrate concentrations and shear stresses at the base were computed from a three-dimensional numerical flow-model incorporating mass transport. Combined dimensionless parameters were developed from a simplified analysis. The numerical results of substrate concentration were well correlated by the combined parameters. The generalized results may find applications in design analysis of microchannel bioreactors. The mass transport and shear stress were related in a generalized result. Based on the generalized results and the condition of dynamic similarity, various means to isolate their respective effects on cells were considered.

THERMAL CURVED BOUNDARY TREATMENT FOR THE THERMAL LATTICE BOLTZMANN EQUATION

In this paper, a recent curved non-slip wall boundary treatment for isothermal Lattice Boltzmann equation (LBE) [Z. Guo, C. Zheng and B. Shi, Phys. Fluids 14(6) (2002)] is extended to handle the thermal curved wall boundary for a double-population thermal lattice Boltzmann equation (TLBE). The unknown distribution population at a wall node which is necessary to fulfill streaming step is decomposed into its equilibrium and non-equilibrium parts. The equilibrium part is evaluated according to Dirichlet and Neumann boundary constraints, and the non-equilibrium part is obtained using a first-order extrapolation from fluid lattices. To validate the thermal boundary condition treatment, we carry out numerical simulations of Couette flow between two circular cylinders, the natural convection in a square cavity, and the natural convection in a concentric annulus between an outer square cylinder and an inner circular cylinder. The results agree very well with analytical solution or available data in the literature. Our numerical results also demonstrate that the TLBE together with the present boundary scheme is of second-order accuracy.

Numerical computation of fluid convection with air enclosed between the annuli of eccentric heated horizontal rotating cylinders

Abstract In this paper, numerical experiments are performed to study the effects of the convective fluid motion of air enclosed between the annuli of eccentric horizontal cylinders. The inner cylinder is assumed heated and rotating. The rotational Reynolds number (Re) considered is in the range 0–1120; the Rayleigh number (Ra) considered is in the range 10 3 –10 6 . When the inner cylinder is made to rotate, numerical experiments show that the multicellular flow patterns observed in stationary cylindrical annuli subside in a manner dependent on the eccentricity and the rotational Re of the inner cylinder. At higher rotational Re, the flow tends toward a uniform flow. With a fixed Ra, when the inner cylinder is made to rotate, the mean Nusselt number decreases throughout the flow.

The Influence of Strip Location on the Pressure Drop and Heat Transfer Performance of a Slotted Fin

In this article, a numerical study is conducted to predict the air-side heat transfer and pressure drop characteristics of slit fin-and-tube heat transfer surfaces. A three-dimensional steady laminar model is applied, and the heat conduction in the fins is also considered. Five types of slit fins, named slit 1, slit 2, slit 3, slit 4, and slit 5, are investigated, which have the same global geometry dimensions and the same numbers of strips on the fin surfaces. The only difference among the five slit fins lies in the strip arrangement. Slit 1 has all the strips located in the front part of the fin surface, then, following the order from slit 1 to slit 5, the strip number in the front part decreases and, correspondingly, the strip number in the rear part increases, so that all the strips of slit 5 are located in the rear part. Furthermore, slit 1 and slit 5, slit 2 and slit 4, have a symmetrical strip arrangement along the flow direction. The numerical results show that, following the order from slit 1 and slit 5, the heat transfer rate increases at first, reaching a maximum value at slit 3, which has the strip arrangement of “front coarse and rear dense”; after that, it begins to decrease, as does the fin efficiency. Although they have the symmetrical strip arrangement along the flow direction, slit 5 has 7% more Nusselt number than slit 1, and slit 4 also has 7% more Nusselt number than slit 2, which shows that strip arrangement in the rear part is more effective than that in the front part. Then the difference of heat transfer performance among five slit fins is analyzed from the viewpoint of thermal resistance, which shows that when the thermal resistances in the front and rear parts are nearly identical, the optimum enhanced heat transfer fin can be obtained. This quantitative rule, in conjunction with the previously published qualitative principle of “front sparse and rear dense,” can give both quantitative and qualitative guides to the design of efficient slotted fin surfaces. Finally, the influence of fin material on the performance of enhanced-heat-transfer fins is discussed.

NUMERICAL EXPERIMENTS WITH LAMINAR FLUID CONVECTION BETWEEN CONCENTRIC AND ECCENTRIC HEATED ROTATING CYLINDERS

A numerical investigation is carried out to determine the temperature and flow pat-terra of a fluid bounded by two horizontal isothermal concentric and eccentric cylinders. The inner cylinder is assumed to be at a higher temperature and rotating. The numerical method involves a mesh transformation technique coupled with the introduction of “false transient“ parameters for the steady-state solution of the problem. The parameters studied were for a Prandtl number of 0.7 and a radius ratio of 2.6 at different Rayleigh numbers, Reynolds numbers, and eccentricities. The results show that the mean Nusselt number increases with Rayleigh number. For a fixed Rayleigh number, when the inner cylinder is made to rotate, the mean Nusselt number decreases throughout the flow.