C. Nonino

AN EQUAL-ORDER VELOCITY-PRESSURE ALGORITHM FOR INCOMPRESSIBLE THERMAL FLOWS, PART 1: FORMULATION

Abstract A finite-element algorithm is presented for the solution of two- and three-dimensional incompressible laminar thermal flows. The algorithm is cast in a time-dependent form and can be classified as a projection finite-element method. However, the procedure utilized for handling Ike velocity-pressure coupling shares many features with the SIMPLER finite-difference method. In fact, given an initial or guessed velocity field, the pseudo-velocities, i.e., the velocities that would prevail in the absence of the pressure field, are found first. Then, by enforcing continuity on the pseudo-velocity field, the tentative pressure is estimated and the momentum equations are solved in sequence for the velocity components. Afterward, continuity is enforced again to find corrections that are used to modify the velocity field and the estimated pressure field. Finally, if required, the energy equation is solved before moving to the next step.

Finite-element analysis of convection problems in spatially periodic domains

The finite-element method is used to solve fully developed convection problems in spatially periodic domains. Symmetric and antisymmetric periodicity in temperature is imposed in an original way that allows for different thermal boundary conditions at the walls. The formulation is first validated by comparing the numerical results with the analytical solutions for fully developed velocity and temperature distributions in a parallel-plate channel. Afterward, the accuracy and the capabilities of the procedure are demonstrated by two examples involving laminar flow and heat transfer in a periodic corrugated channel and in a parallel-plate channel with staggered fins.

A SIMPLE PRESSURE STABILIZATION FOR A SIMPLE-LIKE EQUAL-ORDER FEM ALGORITHM

A simple pressure stabilization technique is presented, consisting of filtering spurious pressure oscillations by a partial smoothing performed at the beginning of each time step. Using the method of approximate factorization to interpret the fractional step scheme, it is also shown that the proposed technique entails the implicit introduction of a stabilization term into the pressure equation and of another term into the momentum equation, which produces a moderately diffusive effect.

EFFECT OF ASPECT RATIO ON CONVECTION ENHANCEMENT IN WAVY CHANNELS

Pressure drop and heat transfer characteristics are investigated in the fully developed region of three-dimensional wavy channels whose aspect ratios (width over height) range from one to infinity. Numerical simulations show that Nusselt numbers and friction factors increase with decreasing aspect ratios, in such a way that global performances improve. In all the channels considered, friction factors always increase with the Reynolds number, while Nusselt numbers significantly increase only above the critical value of the Reynolds number at which self-sustained flow oscillations begin. In turn, the critical value of the Reynolds number decreases with the aspect ratio, down to a minimum that is reached asymptotically.

Convective heat and mass transfer in wavy finned‐tube exchangers

The paper adopts a simplified two‐dimensional approach to deal with convective heat and mass transfer in laminar flows of humid air through wavy finned‐tube exchangers. The computational domain is spatially periodic, with fully developed conditions prevailing at a certain distance from the inlet section. Both the entrance and the fully developed flow region are investigated. In the fully developed region, periodicities in the flow, temperature and mass concentration fields are taken into account. The approach is completely general, even if the finite element method is used for the discretizations. In the application section, velocity, temperature, and mass concentration fields are computed first. Then apparent friction factors, Nusselt numbers, Colburn factors for heat and mass transfer, and goodness factors are evaluated both in the entrance and in the fully developed region.

LAMINAR FORCED CONVECTION IN THREE-DIMENSIONAL DUCT FLOWS

A finite-element procedure for the prediction of laminar forced convection in three-dimensional parabolic flows is presented. The procedure, based on the parabolized simplification of the complete Navier-Stokes equations, is first validated by comparing computed results with the available literature data for thermally and hydrodynamically developing flows in flat channels. Then, new results are presented for simultaneously developing flows in square duels, with

Convective heat transfer in ribbed square channels

, and

Finite element analysis of laminar mixed convection in the entrance region of horizontal annular ducts

boundary conditions and Prandtl number ranging from 0.1 to 10.

Effect of space ratio and corrugation angle on convection enhancement in wavy channels

Three‐dimensional laminar forced convective heat transfer in ribbed square channels is investigated. In these channels, transverse and angled ribs are placed on one or two of the walls to form a repetitive geometry. After a short distance from the entrance, also the flow and the dimensionless thermal fields repeat themselves from module to module allowing the assumption of periodic, or anti‐periodic, conditions at the inlet/outlet sections of the calculation cell. Prescribed temperature boundary conditions are assumed at all solid walls, including the ribs. Pressure drop and heat transfer characteristics are compared for rib angles ranging from 90° (transverse ribs) to 45°, and different values of the Reynolds number. The influence of rib geometries is investigated below and above the onset of the self‐sustained flow oscillations that precede the transition to turbulence. Numerical simulations are carried out employing an equal order finite‐element procedure based on a projection algorithm.

Numerical Evaluation of Fin Performance Under Dehumidifying Conditions

The laminar mixed convection in the entrance region of horizontal straight ducts of an annular cross section is studied by means of a generally applicable finite element procedure based on the parabolized simplification of the Navier-Stokes and energy equations and on the Boussinesq approximation of the buoyancy term. The procedure is validated through comparisons of computed results with available data from the literature. New results concern annuli with radius ratios equal to 0.25, 0.5, and 0.75 subjected to the fundamental boundary condition of the second and the third kinds, for Prandtl numbers equal to 0.7 and 7, and different values of Grashof number.