S.J. Ormiston

Analysis of laminar forced convection of air for crossflow in banks of staggered tubes

Numerical analysis is made of forced-convection heat transfer in laminar, two-dimensional, steady crossflow in banks of plain tubes in staggered arrangements. A finite-volume method with a nonorthogonal, boundary-fitted grid and co-located variable storage is used to solve the Navier-Stokes equations and energy conservation equation for a tube bundle with 10 longitudinal rows, including inlet and outlet sections. Local and overall heat transfer and fluid flow results are presented at nominal pitch-to-diameter ratios of 1.25, 1.5, and 2.0 for equilateral triangle and rotated square tube arrangements with Reynolds numbers of 100 and 300 and a Prandtl number of 0.71. Sensitivity of the local Nusselt number and friction coefficient distributions to the computational grid distribution is noted. A comparison of the present study results with well-established experiments and empirical correlations showed good overall agreement.Numerical analysis is made of forced-convection heat transfer in laminar, two-dimensional, steady crossflow in banks of plain tubes in staggered arrangements. A finite-volume method with a nonorthogonal, boundary-fitted grid and co-located variable storage is used to solve the Navier-Stokes equations and energy conservation equation for a tube bundle with 10 longitudinal rows, including inlet and outlet sections. Local and overall heat transfer and fluid flow results are presented at nominal pitch-to-diameter ratios of 1.25, 1.5, and 2.0 for equilateral triangle and rotated square tube arrangements with Reynolds numbers of 100 and 300 and a Prandtl number of 0.71. Sensitivity of the local Nusselt number and friction coefficient distributions to the computational grid distribution is noted. A comparison of the present study results with well-established experiments and empirical correlations showed good overall agreement.

Analysis of Laminar Forced Convection of Air Crossflow in In-Line Tube Banks with NonSquare Arrangements

ABSTRACT Numerical analysis is made of forced-convection heat transfer in laminar two-dimensional steady crossflow in banks of plain tubes in square and nonsquare in-line arrangements. A finite-volume method with a nonorthogonal, boundary-fitted grid and co-located variable storage is used to solve the Navier–Stokes equations and energy conservation equation for a tube bundle with five longitudinal rows, including inlet and outlet sections. Local and overall heat transfer and fluid flow results are presented at combinations of transverse and longitudinal pitch-to-diameter ratios of 1.25, 1.5, and 2.0 at Reynolds numbers of 100 and 300 for a Prandtl number of 0.71. A comparison of the present study results with well-established experiments and empirical correlations showed good overall agreement. New equations are proposed for a correction factor for the effects of nonsquare arrangements on average friction factor.

Fully coupled solution of a two-phase model for laminar film condensation of vapor–gas mixtures in horizontal channels

Abstract Detailed results are presented for laminar film condensation of vapor–gas mixtures in horizontal flat-plate channels using a fully coupled implicit numerical approach that achieves excellent convergence behavior. These results correspond to steam–air and R134a–air mixtures over wide ranges of the independent parameters, and they include velocity, temperature, and gas concentration profiles, as well as axial variations of film thickness, pressure gradient and Nusselt number. Effects of the four independent variables (inlet values of gas concentration, Reynolds number and pressure, and the inlet-to-wall temperature difference) on the film thickness, pressure gradient, and the local and average Nusselt numbers are carefully examined. It was found that the condensation of R134a–air corresponds to thicker liquid films, lower heat transfer rates, and lower algebraic values of the pressure gradient when compared with steam–air at the same operating conditions.

Numerical predictions of natural convection in a trombe wall system

Abstract In a Trombe wall passive heating system, air from a room is circulated by natural convection through a narrow channel formed by a window on one side and a wall on the other. The circulating flow delivers the solar energy collected by the wall and window to the room. The present paper analyses an idealized Trombe wall system in which the flow is laminar and two-dimensional and the window and wall are isothermal. A dimensional analysis shows that, for a given geometry, the flow and heat transfer are characterized by two Rayleigh numbers. Flow and heat transfer predictions over a wide range of operating conditions were performed using a finite-volume method. These predictions are believed to be the first that fully account for the interaction between the room and channel, and which include the important case where the window temperature is lower than the room temperature.

Analysis of laminar mixed-convection condensation on isothermal plates using the full boundary-layer equations : mixtures of a vapor and a lighter gas

Abstract Laminar film condensation from mixtures of a vapor and a lighter noncondensable gas flowing downward along inclined isothermal plates is investigated numerically using the full boundary-layer equations for the liquid film and the mixture. The adverse net body force due to high concentration of the lighter gas near the liquid–mixture interface gives rise to the possibility of boundary-layer separation. A numerical solution was developed based on a finite-control-volume method and it was marched along the plate up to the separation location. Results were obtained for three vapor–gas mixtures covering a wide range of liquid Prandtl numbers, high gas concentration and high liquid subcooling. Comparisons with previous models (which included various simplifying assumptions) showed that agreement is possible only for conditions of low gas concentration and liquid subcooling. Results of the separation distance exhibited interesting trends, which are discussed and explained. It is also demonstrated that lighter gases can have a more inhibiting effect on heat transfer than heavier gases.

NUMERICAL MODELING OF POWER STATION STEAM CONDENSERS—PART 1: CONVERGENCE BEHAVIOR OF A FINITE-VOLUME MODEL

Abstract Computer simulation models of the flow and heat transfer in power station steam condensers have the potential for becoming important design tools. These computer models may be used to improve existing designs by identifying ways to improve condenser vacuum and to minimize flow-induced tube vibration. To date, such models seem to have experienced convergence problems, or require information to be specified that would not normally be known a priori. This article describes components of a finite-volume model that is thought to be typical of those used by several investigators. The convergence characteristics of this model are described when it is applied to two problems. This model, and its convergence characteristics, provide a baseline against which improvements can be measured. The impact of various improvements to this model are reported in a companion article.

THEORETICAL DETERMINATION OF ANISOTROPIC EFFECTIVE THERMAL CONDUCTIVITY IN TRANSFORMER WINDINGS

A two-dimensional region representing a typical transformer winding cross-section is studied analytically and numerically. The winding region is characterized by layers of round or flattened conductors separated in one direction by insulating paper. The voids within the windings are filled with transformer oil. The theoretical limits of the effective thermal conductivity in two directions are determined using both the parallel isotherms and the parallel adiabats approaches. A steady state conduction analysis in the composite region is performed using standard commercial finite element analysis software. The conductor curvature radius and contact widths were varied relative to the paper thickness for a typical value of oil thermal conductivity and for aluminum and copper conductors. It was found that the effective thermal conductivity was strongly affected by the paper and that there was negligible difference between results for aluminum and copper conductors. It was observed that the ratio of the effective thermal conductivities in the two directions could be 300 in some cases.

NUMERICAL MODELING OF POWER STATION STEAM CONDENSERS—PART 2: IMPROVEMENT OF SOLUTION BEHAVIOR

Abstract The numerical simulation of condenser flows could provide a more powerful tool for improving design if the numerical problems causing poor solution behavior could be isolated and removed. This article isolates four algorithms used in a “standard” model that cause poor solution behavior, and qualitatively establishes the importance of each. With the new algorithms, steady-state solutions can be obtained in few time steps. Attention still needs to be directed at optimizing the implementation of the algorithmic improvements.

A Coupled Pressure-Based Co-Located Finite-Volume Solution Method for Natural-Convection Flows

A pressure-based coupled solution method based on a finite-volume discretization is presented. The method uses a cell-centered co-located variable arrangement on a nonorthogonal two-dimensional structured grid. The coupled algebraic analogs of the mass, momentum, and energy conservation equations for incompressible flow are solved. In addition to coupling the mass and momentum equations, the energy equation is coupled to the velocities via a Newton-Raphson linearization of the energy advection terms. The momentum equations are coupled to the energy equation via an implicit temperature in the Boussinesq approximation. The convergence behavior of the new method is demonstrated on the solution of steady, laminar natural convection in an annulus for Prandtl numbers of 0.707 and 13,050 at a Rayleigh number of 1 × 106. A significant reduction in the number of iterations to convergence is obtained with the new method compared to a method with only velocity-to-temperature coupling and a method with energy and momentum decoupled. An improvement to the new method was obtained by using an approach that uses a delayed time-step increase and a modified face temperature value estimation.

Numerical Analysis of Laminar Forced Convection in Corrugated-Plate Channels with Sinusoidal, Ellipse, and Rounded-vee Wall Shapes

Steady, two-dimensional, developing laminar forced convection is computed in channels of ten modules of three out-of-phase (symmetric) wall corrugations: sinusoidal-wavy-shaped (SWS), rounded-ellipse-shaped (RES), and rounded-vee-shaped (RVS). Different geometric configurations of the three shapes are studied. Fluid flow and heat transfer are examined in a typical module in the fully-developed region for Reynolds numbers in the range of 25 to 300 for a Prandtl number of 2.29. Over the ranges of the geometric parameters studied, the SWS corrugation has, in general, the lowest friction factor and highest average Nusselt number values. The RES corrugation has the highest heat transfer per unit pumping power at an inlet Reynolds number of 300.