J. Rafael Pacheco

A General Scheme for the Boundary Conditions in Convective and Diffusive Heat Transfer With Immersed Boundary Methods

We describe the implementation of an interpolation technique, which allows the accurate imposition of the Dirichlet, Neumann, and mixed (Robin) boundary conditions on complex geometries using the immersed-boundary technique on Cartesian grids, where the interface effects are transmitted through forcing functions. The scheme is general in that it does not involve any special treatment to handle either one of the three types of boundary conditions. The accuracy of the interpolation algorithm on the boundary is assessed using several two- and three-dimensional heat transfer problems: (1) forced convection over cylinders placed in an unbounded flow, (2) natural convection on a cylinder placed inside a cavity, (3) heat diffusion inside an annulus, and (4) forced convection around a stationary sphere. The results show that the scheme preserves the second-order accuracy of the equations solver and are in agreement with analytical and/or numerical data.

The solution of viscous incompressible jet flows using non-staggered boundary fitted co-ordinate methods

A new approach for the solution of the steady incompressible Navier-Stokes equations in a domain bounded in part by a free surface is presented. The procedure is based on the finite difference technique, with the non-staggered grid fractional step method used to solve the flow equations written in terms of primitive variables. The physical domain is transformed to a rectangle by means of a numerical mapping technique. In order to design an effective free solution scheme, we distinguish between flows dominated by surface tension and those dominated by inertia and viscosity. When the surface tension effect is insignificant we used the kinematic condition to update the surface; whereas, in the opposite case, we used the normal stress condition to obtain the free surface boundary

Analysis of Thin Film Flows Using a Flux Vector Splitting

We propose a flux vector splitting (FVS) for the solution of film flows radially spreading on a flat surface created by an impinging jet using the shallow-water approximation. The governing equations along with the boundary conditions are transformed from the physical to the computational domain and solved in a rectangular grid. A first-order upwind finite difference scheme is used at the point of the shock while a second-order upwind differentiation is applied elsewhere. Higher-order spatial accuracy is achieved by introducing a MUSCL approach. Three thin film flow problems (1) one-dimensional dam break problem, (2) radial flow without jump, and (3) radial flow with jump, are investigated with emphasis in the prediction of hydraulic jumps

Bifurcations with imperfect SO(2) symmetry and pinning of rotating waves

Rotating waves are periodic solutions in SO(2) equivariant dynamical systems. Their precession frequency changes with parameters and it may change sign, passing through zero. When this happens, the dynamical system is very sensitive to imperfections that break the SO(2) symmetry and the waves may become trapped by the imperfections, resulting in steady solutions that exist in a finite region in parameter space. This is the so-called pinning phenomenon. In this study, we analyse the breaking of the SO(2) symmetry in a dynamical system close to a Hopf bifurcation whose frequency changes sign along a curve in parameter space. The problem is very complex, as it involves the complete unfolding of high codimension. A detailed analysis of different types of imperfections indicates that a pinning region surrounded by infinite-period bifurcation curves appears in all cases. Complex bifurcational processes, strongly dependent on the specifics of the symmetry breaking, appear very close to the intersection of the Hopf bifurcation and the pinning region. Scaling laws of the pinning region width and partial breaking of SO(2) to Zm are also considered. Previous as well as new experimental and numerical studies of pinned rotating waves are reviewed in the light of the new theoretical results.

Numerical Analysis of a Multi-Row Multi-Column Compact Heat Exchanger

apacheco@calstatela.eduAbstract. In the present study we carry out three-dimensional fluid flow and heat transfersimulations on the external side of a compact heat exchanger to analyze the interaction betweenthe fluid and its geometry. The overall objective is to use the resulting information for thedesign of more compact devices. The type of heat exchanger considered here is the commonplain-fin and tube, with air flowing over the tubes and water as the inner-tube fluid. Two heatexchanger configurations, in which the tube arrangement is either in-line or staggered, conformthe basic geometries. The size of the heat exchanger –regardless of the type of arrangement–which serves as the baseline for the parametric analysis, is defined by fixing its length; i.e.,the number of rows in the flow direction. For the two heat exchanger configurations examinedhere, the dimensional form of the governing equations, along with the corresponding boundaryconditions, are solved under specific flow and temperature values using a finite element methodto compute the velocity, pressure and temperature fields. From these, the heat transfer rate andpressure drop are then calculated. The computations are performed for a range in the valuesof the Reynolds number within the laminar regime. For all cases considered, results from thisinvestigation indicate that the geometrical arrangement plays a major role in the amount ofheat being exchanged and that, for a given device, the length needed to exchange 99% of thecorresponding amount of energy that may be transferred by the baseline model, is confined toless than 30% of the size of the original device.

Enhancement of chaotic mixing in electroosmotic flows by random period modulation

In this paper we propose a random period-modulation strategy as a mean to enhance mixing in electroosmotic flows. This period-modulation is applied to an active mixer of an electroosmotic flow. It is shown that under such period-modulation the Kolmogorov-Arnold-Moser (KAM) curves break up and chaotic mixing is significantly enhanced. The enhancement effect increases with the strength of the modulation, and it is much reduced as diffusion is increased.Copyright

Rate of Decay of a Passive Scalar in a Micro-Mixer and the Frequency of the Advecting Velocity Fields

In the current work, the mixing of a diffusive passive-scalar, e.g., thermal energy or species concentration, driven by electro-osmotic fluid motion being induced by an applied potential across a micro-channel is studied numerically. Secondary time-dependent periodic or random electric fields, orthogonal to the main stream, are applied to generate cross-sectional mixing. This investigation focuses on the mixing dynamics and its dependence on the frequency (period) of the driving mechanism. For periodic flows, the probability density function (PDF) of the scaled passive scalar (i.e., concentration), settles into a self-similar curve showing spatially repeating patterns. In contrast, for random flows there is a lack of self-similarity in the PDF for the interval of time considered in this investigation. The present study confirms an exponential decay of the variance of the concentration for the periodic and random flows.Copyright

On the Boundary Conditions for Heat Transfer Using Immersed Boundary Methods

We describe the implementation of a general interpolation technique which allows the accurate imposition of the Dirichlet, Neumann and mixed boundary conditions on complex geometries when using the immersed boundary technique on Cartesian grids. The scheme is general in that it does not involve any special treatment to handle either one of the three types of boundary conditions. The accuracy of the interpolation algorithm on the boundary is assessed using three heat transfer problems: (1) forced convection over a cylinder placed in an unbounded flow, (2) natural convection on a cylinder placed inside a cavity, and (3) heat diffusion inside an annulus. The results show that the accuracy of the scheme is second order and are in agreement with analytical and/or numerical data.Copyright