Arturo Pacheco-Vega

Neural network analysis of fin-tube refrigerating heat exchanger with limited experimental data

We consider the problem of accuracy in heat rate estimations from artificial neural network (ANN) models of heat exchangers used for refrigeration applications. Limited experimental measurements from a manufacturer are used to show the capability of the neural network technique in modeling the heat transfer phenomena in these systems. A well-trained network correlates the data with errors of the same order as the uncertainty of the measurements. It is also shown that the number and distribution of the training data are linked to the performance of the network when estimating the heat rates under different operating conditions, and that networks trained from few tests may give large errors. A methodology based on the cross-validation technique is presented to find regions where not enough data are available to construct a reliable neural network. The results from three tests show that the proposed methodology gives an upper bound of the estimated error in the heat rates. The procedure outlined here can also help the manufacturer to find where new measurements are needed.

Numerical Simulations of Heat Transfer and Fluid Flow Problems Using an Immersed-Boundary Finite-Volume Method on NonStaggered Grids

ABSTRACT This article describes the application of the immersed boundary technique for simulating fluid flow and heat transfer problems over or inside complex geometries. The methodology is based on a fractional step method to integrate in time. The governing equations are discretized and solved on a regular mesh with a finite-volume nonstaggered grid technique. Implementations of Dirichlet and Neumann types of boundary conditions are developed and completely validated. Several phenomenologically different fluid flow and heat transfer problems are simulated using the technique considered in this study. The accuracy of the method is second-order, and the efficiency is verified by favorable comparison with previous results from numerical simulations and laboratory experiments.

Simultaneous determination of in- and over-tube heat transfer correlations in heat exchangers by global regression

We propose a method of data reduction that improves the predictions of correlations obtained from heat exchanger measurements. If we define an ideal heat exchanger on the basis of commonly made assumptions, the two heat transfer correlations corresponding to both sides of the heat transfer surface can be simultaneously determined. A local regression analysis, however, gives a multiplicity of possible correlations corresponding to the given data. The best correlations are obtained from this set by using a global regression procedure. Three methods are evaluated for this purpose: genetic algorithms, simulated annealing and interval analysis. All three perform well, with some differences in accuracy and CPU time. The predictions are further improved by correlating the error that is introduced by the assumptions of the ideal heat exchanger. The heat rate predictions are then improved considerably, giving a good idea of the extent to which these assumptions degrade them.

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.

Nonlinear analysis of tilted toroidal thermosyphon models

We analyze one-dimensional models for single-phase tilted toroidal thermosyphons for three different heating conditions: known heat flux, known wall temperature and mixed heating. For the first two the governing equations lend themselves to exact reduction to a set of three ordinary differential equations, while for the third the equations remain coupled as an infinite set. For all three cases, the tilt angle is stabilizing while the heat rate is a destabilizer. A nonlinear analysis is carried out using center manifold theory and normal form analysis. The known heat flux solutions lose stability through a supercritical Hopf bifurcation, while for the other two heating conditions the Hopf bifurcation is supercritical under some conditions and subcritical under others. Stable limit-cycle oscillations exist only for the supercritical cases, otherwise instability leads directly to chaos. Analysis also provides an estimate for the amplitude of oscillation for the supercritical conditions. Numerical experiments have confirmed the theoretical predictions qualitatively and quantitatively.

Heat Transfer Correlations in an Air-Water Fin-Tube Compact Heat Exchanger by Symbolic Regression

In the present study we propose the application of evolutionary algorithms to find correlations that can predict the performance of a compact heat exchanger. Genetic programming (GP) is a search technique in which computer codes, representing functions as parse trees, evolve as the search proceeds. As a symbolic regression approach, GP looks for both the functional form and the coefficients that enable the closest fit to experimental data. Two different data sets are used to test the symbolic regression capability of genetic programming, the first being artificial data from a one-dimensional function, while the second are data generated by previously determined correlations from experimental measurements of a single-phase air-water heat exchanger. The results demonstrate that the correlations found by symbolic regression are able to predict well the data from which they were determined, and that the GP technique may be suitable for modeling the nonlinear behavior of heat exchangers. It is also shown that there is not a unique answer for the best-fit correlation from this procedure. The advantage of using genetic programming as symbolic regression is that no initial assumptions on the functional forms are needed, which is contrary to the traditional approach.Copyright

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

Genetic-Programming-Based Symbolic Regression for Heat Transfer Correlations of a Compact Heat Exchanger

We describe a symbolic regression methodology based on genetic programming to find correlations that can be used to estimate the performance of compact heat exchangers. Genetic programming is an evolutionary search technique in which functions represented as parse trees evolve as the search proceeds. An advantage of this approach is that functional forms of the correlation need not be assumed. The algorithm performs symbolic regression by seeking both the functional structure of the correlation and the coefficients therein that enable the closest fit to experimental data. This search is conducted within a functional domain constructed from sets of operators and terminals that are used to build tree-structures representing functions. A penalty function is used to prevent large correlations. The methodology is tested using first artificial data from a one-dimensional function and later a set of published heat exchanger experiments. Comparison with published results from the same data show that symbolic-regression correlations are as good or better. The effect of the penalty parameters on the “best function” is also analyzed.Copyright

A Takagi-Sugeno Fuzzy Model of a Concentric-Tubes Heat Exchanger

In the present study we develop a Takagi-Sugeno (TS) fuzzy model of a concentric-tubes heat exchanger. The model is structured on fuzzy logic reasoning with sets of linguistic rules describing the dynamic characteristics of the thermal system. Using a system identification technique based on adaptive neural networks, the fuzzy rules are derived from experimental data of the flow rates and fluid temperatures in the heat exchanger. The accuracy of the resulting model is assessed by predicting the time-dependent response of the outlet hot- and cold-water temperatures under a step-change in the mass flow rate of the cold fluid. The results indicate that the TS fuzzy model is able to estimate the behavior of the physical system with very little predicting errors. Upon the basis of this empirical model, in the near future we will report on a control strategy for the regulation and tracking of the outlet temperatures in the heat exchanger.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