Heat Exchangers

Among immediate HSP-VAT engineering applications we have been considering the heat exchange devices with volumetric heat exchange features.

At the present time, compact heat exchanger (CHE) design is based primarily on utilization of known standard heat exchanger calculation procedures (see, for example, Kays and London, 1984). Typical analysis of heat exchanger designs depends on the simple heat balance equations, which are widely used in the heat design industry. Analytically based models are composed of a properly constructed set of formulae for a given spatial design of heat transfer elements that allow most of the existing heat transfer mechanisms to be accounted for.

At present, simplified theoretical models that are tuned by data that has undergone some statistical averaging process represent heat transport in heat exchangers. The major drawback of this widely used approach is that it does not give a researcher the ability to directly relate the spatial, morphological, and geometrical features, even when known, to particular phenomena. Often the equations obtained by one researcher using this method are initially different from another without consideration of the further simplifications each might make. This is not the case when the mathematical modeling is based on a rigorous application of the HSP-VAT mathematical approach.

It is the acceptance of the two scales existence in the heat exchange device that is making possible the HSP-VAT approach. The upper scale space is the space where the whole device or most of it volume is being considered as embedded into the next (upper) scale space with all of it's characteristics and space related properties.

Typical tubular morphology of cross-flow heat exchangers

2-D tube heat exchanger unconsolidated morphology to investigate

Compact heat exchanger (CHE) with contracted-tubelayer morphology for one of the fluids

Three-phase unconsolidated - (a), and consolidated - (b), schematic morphology of finned tube heat exchanger

CHE morphology with separated subchannels for each of fluids

PCHE core zone of heat exchanger

CHE flow arrangements - a) two-pass cross flow, b) co-current flow, and c) counter-current flow

Plain fins geometry

Offset (strip) fin geometry for CHE

The convincing results of our previous work (and to some extent the studies by workers involved into the two scale research), make possible to apply the HSP-VAT, which is capable to addressing multiscaled as long as the hierarchical heat transport acceleration phenomena that happens to be is the volume with a scaled medium and process.

Some CHE structures have the real appearance and characteristics of a porous medium and can be studied by application of the developments for HSP-VAT porous media modeling. One particular microfoam SiC structure

was used in our previous study to advance the understanding of the scaled approach in application for design the regenerative HE intended for usage in a special automotive application.

A theoretical basis for heat and momentum transport equations obtained with volume averaging theory was developed for modeling and design of heat exchangers. Using different regime transport models, equation sets obtained for momentum transport and two-temperature or three-temperature heat transfer in non-isotropic heterogeneous CHE media that account for interphase exchange and micro-roughness are developed.

This leads to correct mathematical equations for heat exchanger modeling and for optimization by relying on the general field equations rather than on the balance equations. The derived general transport equations for a single-phase fluid in a CHE medium have many more integral and differential terms than the homogenized or classical continuum mechanics equations. Various descriptions of the porous media structural morphology determine the importance of these terms and the range of application of closure schemes. These model equations highlight the various morphological contributors to friction loss and heat transfer lending themselves to optimization of a CHE.

A few outstanding features of the closure models needed to treat the additional integral terms in the equations of flow and heat transfer were described for non-uniformly and randomly structured highly porous media. One-temperature and two-temperature, effective thermal diffusivity models were developed while emphasizing the solid phase micro-scale morphology using different techniques. Additionally, few models were mathematically outlined for various coefficients of drag resistance by implementing a VAT multiple-term superposition approach. Special attention was also given to the evaluation of the heat transfer coefficient dependence upon medium structure in a two-temperature energy models (Gratton et al., 1994, 1995, Travkin and Catton, 1994, 1995, 1998).

Our estimations allowed us to draw the clear line distinguishing the ways to state and approach the hierarchical and consecutive multiscaled heat removal in the high power devices, particularly using a heat sinks for a known or unknown base heat flux. Few main ideas regarding estimation of heterogeneous coefficients and effective coefficients in heterogeneous media as well as the Upper scale HSP-VAT heterogeneous models for heat exchangers were surfaced in few publications, for example, in
Heat Transfer-pgs41-60 (1020k)
Heat Transfer-pgs61-75 ( 991k)

Some of modeling for design of Compact Heat Exchangers and Semiconductor Heat Sinks (SHS) were done when using the simplified HSP-VAT models with the only one (Upper) scale simulation. These models' closure greatly depends on the availability of experimental data. When the closure models are selected, then the models can be used applying the rather robust numerical simulation schemes developed for the similar kind of HSP-VAT statements as for conjugated heat transport in porous channels -
Numerical Simulation of Conjugate Porous Channels .... ( 202k)

In some of our works were shown the extension to which the two methodology - Homogeneous One Scale and Heterogeneous Two- and more Scales HSP-VAT, and simplified HSP-VAT can be unified, compared and integrated.

As an example, and one of the most applicable areas we have been considering and studying during many years is a special area of HE - the interesting and urgent topics related to Semiconductor Heat Sinks (SHS) -
Semiconductors Coolers .