S. F. Tsai

Flow topology in a steady three-dimensional lid-driven cavity

Abstract We present in this paper a thorough investigation of three-dimensional flow in a cubical cavity, subject to a constant velocity lid on its roof. In this steady-state analysis, we adopt the mixed formulation on tri-quadratic elements to preserve mass conservation. To resolve difficulties in the asymmetric and indefinite large-size matrix equations, we apply the BiCGSTAB solution solver. To achieve stability, weighting functions are designed in favor of variables on the upstream side. To achieve accuracy, the weighting functions are properly chosen so that false diffusion errors can be largely suppressed by the equipped streamline operator. Our aim is to gain some physical insight into the vortical flow using a theoretically rigorous topological theory. To broaden our understanding of the vortex dynamics in the cavity, we also study in detail the longitudinal spiralling motion in the flow interior.

Some physical insights into a two-row finned-tube heat transfer

A three-dimensional numerical study was conducted to broaden our knowledge of the conjugate heat transfer in a finned-tube heat exchanger element. A finite volume discretization method and a SIMPLE-based solution algorithm were applied to working differential equations and their discrete counterparts for computation of gas velocities and temperatures. Since the heat transfer between the gaseous and solid phases is determined by the complex flow structure, calculations for three-dimensional thermally and hydrodynamically developing laminar flows are performed by iteratively solving the heat conduction equation for the plate fin and conservation equations for the gas phase via the coupling boundary condition. The emphasis of this study is directed toward numerical exploration of the flow structure. To this end, the underlying topological theory shows the promise of being a powerful tool for the study of flow details. In dry conditions, some insight in the heat-transfer capability of the two-row finned-tube heat exchanger can be gained by examining the span-averaged Nusselt number and span-averaged pressure drop in the flow passage.

Heat transfer in a conjugate heat exchanger with a wavy fin surface

Abstract A three-dimensional computational study on conjugate heat exchangers was conducted. Attention was specifically directed towards studying extended surfaces used to increase heat transfer. The strategy adopted in the present investigation of forced convection in a flow passage was to use the finite volume method. Our implementation incorporated a SIMPLE-based semi-implicit solution algorithm which was applied to working equations formulated within the single-phase catalog. The analysis allowed for marked changes in thermodynamic and flow properties. To justify using the proposed numerical model to simulate this conjugate heat transfer problem, we considered first a heat exchanger with a plane fin simply because experimental data are available for comparison. This validation study was followed by a study of how a newly designed fin pattern can provide increased heat transfer. The efficiency has been judged by considering several aspects, namely the span-averaged pressure drop, Nusselt number and heat flux. To better illuminate the flow and heat transfer characteristics in a flow passage bounded by two fins having wavy geometries, we have plotted solutions in a three-dimensional format.

Topological flow structures in backward-facing step channels

Abstract The present paper is intended to solve the steady-state Navier-Stokes equations for different Reynolds numbers. Through out this paper, the incompressible fluid will be considered in three-dimensional channels with different spans. The flow field under investigation was characterized as having a backward-facing step across which a fully-developed three-dimensional channel flow expanded into the channel with an expansion ratio of 1.9432. Numerical solutions for this backward-facing step problem were obtained on the basis of the step height, 0.9423, various spans, taking on values up to 10, and Reynolds numbers as high as 800. Of the different flow conditions that were considered, we elaborate on the flow topology under the conditions of an intermediate Reynolds number, Re = 389, and the largest width of the channel, 10. Following Lighthill [Lighthill, M., Attachment and separation in three-dimensional flow. In Laminar Boundary Layers , Vol. 2(6), ed. L. Rosenhead, II. Oxford University Press, 1963, pp. 72–82.] [1], we apply topology theory, which provides a rigorous mathematical foundation for studying kinematically possible flows. The present computational results, together with the inferred flow topology, reveal details of the flow structure which suggest a mechanism for the development of strongly three-dimensional flow with increasing Reynolds numbers. The computation of ‘oil-flow’ streamlines improves the visualization of the flow field and helps sketch the complicated flow patterns by clarifying the three-dimensional flow separation just behind the step. The scope of this enhancement to improved visualization of flow structure is also extended to the flow reattachment on the floor as well as the roof recirculatory flow pattern, manifested itself by the upstream separation and downstream reattachment surfaces. Notably addressed is the separation-reattachment phenomenon emanating only from the roof near the two side walls.

Structural development of vortical flows around a square jet in cross-flow

The present computational study is devoted to unfolding the complex process of three–dimensional flow interaction around a square jet in cross–flow. The aim is to provide a clear understanding about the structural development of the entire vortical flow field, which may immensely enhance our knowledge regarding mutual interaction among various vortical structures that takes place around the jet. Careful attempts have been made to capture the detailed mechanism of formation of the near–field horseshoe–vortex system and the roll–up process of the hovering vortices. The rolled–up shear–layer hovering vortices, which wrap around the front and the lateral jet–cross–flow interface, are observed to initiate the Kelvin–Helmholtz–like instability. The present study also clearly displays the inception process of the counter–rotating vortex pair (CVP) from the shear layers that develop on the two lateral side walls of the jet pipe. In order to better understand the complete flow–interaction process and the governing flow physics, the simulation was performed for a moderate value of the Reynolds number (Re = 225), and for a jet–to–free–stream velocity ratio of 2.5. The interaction process between the streamwise wall vortices and the developed upright (or spin–off, or zipper) vortices in the downstream boundary layer is observed to contribute substantially in the structural development of the jet wake. The upright vortices were seen to originate from the tornado–like critical points on the channel floor shear layer, and subsequently the vortices lift themselves away from the channel floor to merge ultimately with the evolving CVP. Importantly, such merging processes are observed to locally enhance the CVP strength. Following the topological theory of Legendre, the depicted map of computed critical points and the separation lines helps to provide additional insight into the flow mechanism. The computed results clearly demonstrate the entire vortical flow–interaction process to its totality, including all the recent experimental predictions that are made for such flows. Notably, as it was experimentally verified for round jets in cross–flow, in the present configuration too, the flow separation on the channel floor is found to be the basic source of inception of the wall and the upright vortices. The separated flow in the vicinity of different wall vortical corelines joins to form the upright vortices.

Three-dimensional analysis for radio-frequency ablation of liver tumor with blood perfusion effect

Increase of temperature above 50 ∼ 60°C for few minutes by the emitted radio-frequency (RF) energy has been shown to be able to denaturate the intracellular proteins and destruct membranes of tumor cells. To improve the efficacy of this thermal therapy, it is important to investigate factors that may affect the RF heating characteristics for the hepatocellular carcinoma and metastatic liver tumors. In order to make sure the applied RF energy is adequate to ablate the target tumor, a 3D thermoelectric analysis for the system consisting of liver, liver arteries and 4 mm diameter tumor is conducted. The effect of blood perfusion is addressed in this study.

A monotone finite element method with test space of Legendre polynomials

This paper is concerned with the development of a multi-dimensional monotone scheme to deal with erroneous oscillations in regions where sharp gradients exist. The strategy behind the underlying finite element analysis is the accommodation of the M-matrix to the Petrov-Galerkin finite element model. An irreducible diagonal-dominated coefficient matrix is rendered through the use of exponential weighting functions. With a priori knowledge capable of leading to a Monotone matrix, the analysis model is well conditioned with the monotonicity-preserving property. In order to stress the effectiveness of test functions in resolving oscillations, we considered two classes of the convection-diffusion problem. As seen from the computed results, we can classify the proposed finite element model as legitimate for the problem free of boundary layer. Also, through the use of this model, we can capture the solution for the problem involving a high gradient. In this study, we are interested in a cost-effective method which ensures monotonicity irrespective of the value of the Peclet number throughout the entire domain. To gain access to these desired properties, it is tempting to bring in the Legendre polynomials and the characteristic information so that by virtue of the inherent orthogonal property the integral can be obtained exactly by two Gaussian integration points along each spatial direction while maintaining stability in the M-matrix satisfaction sense.

NUMERICAL STUDY OF HEAT TRANSFER IN TWO-ROW HEAT EXCHANGERS HAVING EXTENDED FIN SURFACES

This paper reports on a three-dimensional study of air through two-row cylinder tubes. The analysis is intended to present a comparison of numerical and experimental data to validate the laminar flow postulation. The current study explores the influence of four perforated fin surfaces on the pressure drop and heat transfer rate. To gain further insight into the three-dimensional vortical flow structure, we conduct a topological study of the velocity field. Examination of the surface flow topology and the flow patterns at cross-flow planes sheds some light on the complex interaction of the cylinder tube with the mainstream flow. This study clearly reveals a saddle point in front of the first row of cylinder tubes. Also clearly revealed by the computed solutions is a flow reversal found in the wake of the tube. The character of the critical-point-induced flow is also addressed. This study shows that the addition of perforated fins is not without deficiency. There is, in fact, a trade-off between the benefit...

A finite element study of the blood flow in total cavopulmonary connection

Abstract The present study is a preliminary investigation into the total cavopulmonary connection (TCPC) blood flow structure in Fontan procedures. Our aim is to gain a better understanding of flow reversal in vascular circulation. In this paper we consider a two-dimensional mathematical model of the Navier–Stokes equations. Specifically, we study the laminar flow in the blood vessel with outlets at which a free boundary condition is specified. To further simplify the analysis, the vessel walls are regarded as being rigid. In quadratic elements, we employ the streamline upwind Petrov–Galerkin finite element model as our strategy to simulate incompressible fluid flows. The adopted finite element model is featured by the presence of artificial damping terms added solely in the streamline direction. With these terms added to the formulation, the discrete system is enhanced while solution accuracy is maintained without deterioration due to false diffusion errors. In this finite element flow study, our emphasis is placed on the role of the offsets as a control parameter in order to optimize the blood flow after the surgical intervene.

Finite element analysis of particle motion in steady inspiratory airflow

Abstract To accurately model the inhaled particle motion, equations governing particle trajectories in carrier flow are solved together with the Navier–Stokes equations. Under the relatively dilute particle condition in the mixture, equations for two phases are coupled through the interface drag shown in the solid-phase momentum equations. The present study investigates bifurcation flow in the human central airway using the finite element method. In the gas phase, we employ the biquadratic streamline upwind Petrov–Galerkin finite element model to simulate the incompressible air flow. To solve the equations of motion for the inhaled particles, we apply another biquadratic streamline upwind finite element model. A feature common to two models applied to each phase of equations is that both of them provide nodally exact solutions to the convection–diffusion and the convection–reaction equations, which are prototype equations for the gas-phase and the solid-phase equations, respectively. In two dimensions, both models have ability to introduce physically meaningful artificial damping terms solely in the streamline direction. With these terms added to the formulation, the discrete system is enhanced without compromising the numerical diffusion error. Tests on inspiratory problem were conducted, and the results are presented, with an emphasis on the discussion of particle motion.