B. R. Baliga

A 1-D/2-D model and experimental results for a closed-loop thermosyphon with vertical heat transfer sections

Abstract In this paper, a new 1-D/2-D model is proposed for closed-loop thermosyphons with vertical heat transfer sections. This model improves the results of traditional 1-D models for cases where: (i) mixed-convection effects are important in the heated and cooled sections of the loop; and (ii) heat losses (or gains) from the insulated portions of the loop are significant. This is achieved by iteratively coupling local results of 2-D numerical simulations of mixed-convection flows, performed in the heated and cooled sections, and a 1-D analysis. The proposed 1-D/2-D model is validated by comparing its results with those of a complementary experimental study. The results include predictions and measurements of the average velocity in the loop, local wall temperatures in the heated section of the loop, and bulk temperatures of the fluid. The agreement between the model predictions and the experimental results is shown to be very good.

A control-volume finite element method for dilute gas-solid particle flows

Abstract The formulation of a co-located equal-order Control-Volume-based Finite Element Method (CVFEM) for the solution of two-fluid models of 2-D, planar or axisymmetric, incompressible, dilute gas-solid particle flows is presented. The proposed CVFEM is formulated by borrowing and extending ideas put forward in earlier CVFEMs for single-phase flows. In axisymmetric problems, the calculation domain is discretized into torus-shaped elements and control volumes: in a longitudinal cross-sectional plane, or in planar problems, these elements are three-node triangles, and the control volumes are polygons obtained by joining the centroids of the three-node triangles to the midpoints of the sides. In each element, mass-weighted skew upwind functions are used to interpolate the convected scalar dependent variables and the volume concentrations. An iterative variable adjustment algorithm is used to solve the discretized equations. The capabilities of the proposed CVFEM are illustrated by its application to two test problems and one demonstration problem, using a simple two-fluid model for dilute gas-solid particle flows. The results are quite encouraging.

Implementation of the Stress Jump Condition in a Control-Volume Finite-Element Method for the Simulation of Laminar Coupled Flows in Adjacent Open and Porous Domains

Laminar coupled flow of a Newtonian fluid in adjacent open and fluid-saturated porous domains is modeled using the continuity and the Navier-Stokes equations in the open domain, and a continuity equation and the Brinkman-Forchheimer equations in the porous domain. At the interface, a jump condition is used with two adjustable coefficients: one related to an excess viscous stress and the other to an excess inertial stress. This mathematical model is solved using a control-volume finite-element method and a novel procedure for incorporating the interfacial stress jump condition. The solutions of two illustrative example problems are also presented and discussed.

Comparison of one-dimensional models and a 1-D/2-D model for closed-loop thermosyphons with vertical heat transfer sections

The results of a comparison between traditional one-dimensional (1-D) models and a 1-D/2-D model for closed-loop thermosyphons with vertical heat transfer sections are reported in this paper. Attention is limited to problems in which the flow is laminar. For cases where heat losses from the insulated portions of the loop are negligible,Stm=o, it is shown that traditional 1-D models can significantly overpredict the average fluid velocity in the loop for high power inputs (highGrm). Local results of two-dimensional numerical simulations in the heated and cooled sections reveal that this discrepancy arises because the 1-D models do not account for mixed-convection effects which distort the velocity and temperature profiles from their fully developed forced convection shapes. Furthermore, for cases whereStm ≠ o, predictions of heat losses (or gains) produced by the 1-D models are handicapped by inaccuracies in the corresponding temperature predictions inside the loop.ZusammenfassungIn dieser Arbeit werden die Ergebnisse eines Vergleichs zwischen traditionellen eindimensionalen (1-D) Modellen und einem 1-D/2-D Modell zur Berechnung geschlossener Thermosiphonkreisläufe mit vertikalen Wärmeübergangsabschnitten mitgeteilt. Die Untersuchung beschränkt sich auf reine Laminarströmungen. In Fällen, wo die Wärmeverluste an den isolierten Abschnitten des Kreislaufs vernachlässigt werden können (Stm=o), zeigt sich, daß traditionelle 1-D Modelle die mittlere Strömungsgeschwindigkeit im Kreislauf bei hohem Leistungseintrag (Grm hoch) signifikant überbewerten. Örtliche Ergebnisse zweidimensionaler Simultationsrechnungen für die beheizten bzw. gekühlten Abschnitte zeigen, daß diese Widersprüche im Unvermögen der 1-D Modelle begründet liegen, Mischkonvektionseffekte berücksichtigen zu können. Diese deformieren die reiner Zwangskonvektion in ädaquate Form der Geschwindigkeits- und Temperaturfelder. Ferner leidet im FalleStm ≠ o die Berechnung von Wärmeverlusten oder -gewinnen nach den 1-D Modellen unter der ungenauen Kenntnis der Temperaturverteilung im Inneren des Kreislaufs.