Keywords: CFD, heat exchangers, numerical methods, verification, validation, corrugated plates, automobile radiators.

In most of the gas-liquid heat exchanger applications fin-and-tube exchangers are used. Even though these heat exchangers are widely used in industry for decades, optimum designs are very difficult to obtain due to the extremely complex physical phenomena involved. In spite of that, designs are very often based on simple mathematical models restricted by a large number of hypothesis. To go beyond these limitations, different computational simulations based on global conservation balances of mass, momentum and energy over macro-volumes have been proposed in the technical literature [1]. Some empirical inputs are needed in order to describe fluid-solid interaction and some fluid flow three-dimensional effects. These models are more rigorous, general and accurate for rating and design purposes than the analytical ones, representing an important step to get more reliable thermal and fluid dynamic predictions within a modest computing budget.

The highest level of simulation is represented by general-purpose CFD codes, which are based on the numerical resolution of the multi-dimensional Navier-Stokes equations. A very large number of control volumes is needed to discretize the whole heat exchanger domain considering all the detail flow structure and solid elements. These codes are not still suitable as a rating and design tool for the complete heat exchanger due to the huge amount of computational resources needed to run a single test. However, this kind of high level simulation is essential to get deeper insight into the physical phenomena of the flow in characteristic parts of the heat exchanger (specific zones of the equipment). Furthermore, the simulation allows the calculation of local values of heat transfer coefficients and friction factors which are necessary to characterise the heat transfer surfaces and to feed the above mentioned codes for rating and design purposes.

To assist in obtaining optimum heat exchanger designs, a judicious combination of a hierarchy of mathematical models (analytical models, advanced rating and design codes, CFD computations) is necessary. Experimental studies are also needed to validate the mathematical models and to generate basic information to be used in the rating codes. Comparison between the different possibilities for a given specification should be performed by means of appropriate performance evaluation criteria.

This paper is focussed on the detail analysis of some specific parts of this type of heat exchangers using CFD methodologies. Specifically, the study deals with the external airflow through parallel corrugated plates and the single-phase flow through the internal circuitry (headers and tubes).

The multidimensional simulation developed in both cases is based on fully implicit finite volume techniques. The coupled time averaged governing equations are solved in a segregated manner using pressure-based algorithms. Some topics about the numerical procedure are commented, such as the numerical implementation of (inflow and/or outflow) pressure boundary conditions or the strategy of the parallel implementation of the code based on the (approximately) spatial parabolic flow structure [2]. An important issue addressed in this work has been the analysis of the quality of the obtained numerical solutions. A post-processing procedure based on the generalised Richardson extrapolation for h-refinement studies and on the grid convergence index (GCI) has been used [3]. In this way, criteria about the sensitivity of the simulation to the computational model parameters that account for the discretization errors are presented. This tool estimates the order of accuracy of the numerical solution (observed order of accuracy) and an error band where the grid independent solution is expected to be contained (uncertainty due to discretization), also giving criteria about credibility of these estimations. With this methodology, both global estimators and local estimators are calculated.

The two kind of flows mentioned above, airflow through parallel corrugated plates and the single-phase flow inside headers and tubes, are studied. Different aspects related to the quality of the numerical solution (grid properties, numerical schemes) are highlighted. After that, different parameters (geometry and boundary conditions) which have an influence on the thermal and fluid dynamic behaviour of these flows are analysed.

1

C. Oliet, C. D. P�rez-Segarra, O. Garc�a-Valladares, A. Oliva. "Advanced Numerical Simulation of Compact Heat Exchangers. Application to Automotive, Refrigeration and Air-Conditioning Industries". In Proceedings of the European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS), Barcelona, 2000.

2

M. Soria, J. Cadafalch, K. Claramunt, A. Oliva. "A parallel algorithm for the detailed numerical simulation of reactive flows". In Parallel CFD 99, pages 389-396, Virginia, USA, 2000.

3

J. Cadafalch, C. D. P�rez-Segarra, R. C�nsul, and A. Oliva. "Verification of finite volume computations on steady state fluid flow and heat transfer". Journal of Fluids Engineering, 124:11-21, 2002. doi:10.1115/1.1436092

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