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Regenerative heat exchangers with significant entrained fluid heat capacity
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Abstract
Entrained fluid heat capacity is shown to have a significant and positive effect on the performance of a passive regenerator.
The ineffectiveness of the regenerator is presented as a function of three dimensionless parameters: the number
of transfer units, the utilization, and the entrained fluid to matrix heat capacity ratio. Three different behaviors are
observed for a regenerator with entrained fluid heat capacity. The effect of the entrained fluid can be accounted for over
a large range of conditions using the concept of an augmented-NTU which can be substituted for the actual NTU in
analyses that neglect entrained fluid capacity.
2005 Elsevier Ltd. All rights reserved.
Keywords: Regenerator; Entrained fluid; Modeling; Heat exchanger; Augmented NTU
1. Introduction
Regenerative heat exchangers are used in many applications
including cryogenic refrigeration systems, for
building energy recovery, and in gas turbine systems.
The heat capacity of the fluid, often a gas that is entrained
in the void volume of the regenerator matrix, is
typically very small relative to the heat capacity associated
with the regenerator matrix itself. Therefore, the effect
of this entrained fluid heat capacity is almost always
neglected in regenerator analyses. A large number of
analytical and numerical solutions to the regenerator
governing equations have been presented. These include
papers by Nusselt [1], Hill and Wilmott [2], and Atthey
[3] in which axial conduction is neglected, as well as
works by Bahnke and Howard [4], Shen and Worek [5],
and Klein and Eigenberger [6] which account for axial
conduction. None of these analyses consider the effect
of the entrained heat capacity in the regenerator.
Recently there has been considerable interest in
active magnetic regenerative refrigeration (AMRR) systems
for near room temperature applications [7–9]. In an
AMRR system, a heat transfer fluid (e.g., water) is cyclically
passed through a regenerator matrix that exhibits a
magnetocaloric effect; the entropy of the matrix is
affected by magnetic field as well as by temperature.
The heat capacity of the fluid entrained in the matrix
is non-negligible in this application and can be nearly
equal to the matrix heat capacity in a practical design.
As a result, the entrained fluid heat capacity should
not be neglected when modeling an AMRR system.
Also, regenerative heat exchangers are being used at
increasingly lower temperatures in cryogenic refrigeration
devices. At very low temperature, the volumetric
0017-9310/$ - see front matter 2005 Elsevier Ltd. All rights reserved.
doi:10.1016/j.ijheatmasstransfer.2005.06.021
* Corresponding author. Tel.: +1 608 265 6266.
E-mail address: gfnellis[at]engr.wisc.edu (G.F. Nellis).
International Journal of Heat and Mass Transfer 49 (2006) 329–340
www.elsevierlocate/ijhmt
heat capacity of the entrained fluid increases due to its
increasing density whereas the heat capacity of most solids
rapidly decrease; therefore, the heat capacity of the
entrained fluid may become non-negligible in this
application.
There has been relatively little work that is aimed
specifically at understanding the effect of entrained fluid
heat capacity on regenerator performance. Willmott and
Hinchcliffe [10] develop an approximate model that is
used to estimate the effect of the entrained fluid heat
capacity on the regenerator performance. They report
results over a limited range of operating conditions
and show that entrained gas has a generally positive effect
on the performance of the regenerator, particularly
when the number of transfer units is low. Daney and
Radebaugh [11] numerically solve the governing equations
for a matrix with entrained heat capacity and present
a numerical experiment which demonstrates that, for
low thermal loads, the effectiveness of the regenerator
will actually decrease as the matrix heat capacity increases.
They attribute this counter-intuitive behavior
to the situation where a thermal wave is contained within
the heat exchanger, a result that is consistent with the
conclusions described here. Neither of these studies resulted
in a complete understanding of how entrained
heat capacity affects the performance of a passive regenerator,
when the effect of entrained heat capacity is
important, or how a designer might estimate the magnitude
of this effect during a regenerator analysis.
This paper describes a numerical model in which the
entrained heat capacity in a regenerator is included in
the governing equations. The model is verified against
solutions found in the literature in the limit of no entrained
heat capacity and subsequently used to specifically
investigate the behavior of a regenerator as the
entrained heat capacity becomes significant. Three fundamental
behaviors are identified: the ‘‘NTU-limited’’
and ‘‘capacity-limited’’ behaviors are found even in the
absence of entrained fluid heat capacity; however, a
third, ‘‘stratified’’ behavior is also observed. The behavior
of the regenerator in this region is non-intuitive; performance
may decrease with increasing NTU or
increasing matrix heat capacity. The regimes associated
with these behaviors are delineated on a map that is presented
in terms of the fundamental dimensionless parameters
that define the operating condition for the
regenerator. The concept of an augmented-NTU is introduced
to account for entrained fluid heat capacity in the
‘‘NTU-limited’’ region, which is the region of greatest
practical interest to a regenerator designer. Using the
augmented-NTU in place of the actual NTU allows
computationally simpler models that neglect the effect
of entrained fluid to provide estimates of regenerator performance
that account for this effect. The augmented-
NTU approach can be used in conjunction with other
correction factors such as those proposed by Jeffreson
to account for temperature gradients that are internal
to the regenerator matrix and axial dispersion [12].