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Louvered fin design
has been extensively studied experimentally and, more
recently, numerically with CFD codes using finite element
geometry or finite volume methods such as STAR-CD.
Investigations on louvered heat exchangers are mainly
divided into three categories;
(1) Full-scale experiments for
overall airside heat transfer coefficient and pressure
drop deter-mination have been performed. Recent generalized
correlations are available in the open literature
[1], [2], [3]. These studies give global results
and no local information is provided.
(2) Scaled-up experiments (scale
factor 10 or 20) were used both for qualitative flow
pattern visualization and local heat transfer coefficient
measurement with several techniques. Smoke trace
or dye injection techniques revealed that the flow
pattern could be characterized in terms of duct-directed
or louver-directed flows, depending on the Reynolds
number (based on louver pitch, i.e. distance between
2 consecutive louvers). Laminar boundary layer growth
and renewal govern the flow within the louver array.
At low Reynolds number the boundary layers are so
thick that the gaps between adjacent louvers are
blocked and flow is duct-directed in the direction
of the fin (Fig. 4). At higher Reynolds number, the
boundary layers are thinner and the flow is almost
aligned with the louvers. The intermediate Reynolds
numbers at which the flow becomes louver-directed
is still a challenging question and CFD helps t0
understand this phenomenon.
(3) More recently, numerical investigations
of the louvered fin array have been performed, but
it is noticeable that major parts of CFD models presented
in the literature make questionable assumptions,
e.g. 2-dimensional and steady flow.
In the present study, two types
of model are handled with STAR-CD. For all models,
the flow is assumed to be laminar and this is confirmed
by experimental observations over the considered
range of Reynolds number (< 1300). The first type
is a 3D model shown in Fig. 2. This model, a complete
element of the actual airside condenser geometry
and includes the tube and the fin with the unlouvered
zone. To reduce the computational domain size, only
half of the fin and half of the tube were represented
and symmetry conditions were assumed on both sides
of the domain.
The height of the computational
domain is equal to the fin pitch and cyclic boundary
conditions were applied at the top and bottom of
the domain. The ability of STAR-CD to manage both
fluid and solid cells permits both the tube and fin
to be meshed and to take into account the material’s
thermal resistance. A constant wall temperature condition
was applied on the inner surface of the microchannel
tube. The average cell size is roughly equal to the
fin thickness in all directions.3D computations were
performed in steady state. Fig. 4 presents the velocity
and temperature profiles at a low Reynolds number
when the flow reaches steady state. Fig. 3 shows
the temperature distribution within the fin. Large
temperature variations were observed particularly
in the louvered zones. CFD analysis permits calculation
of the actual fin efficiency corresponding to the
proposed fin design, taking into account the heat
transfer coefficient variations over the fin surface.
The second type of model is a
2D model of the louvered zone under laminar unsteady
flow conditions. In order to observe the flow instabilities,
the average cell size is only one fourth of the fin
thickness and the total number of cells in the model
is 100,000. When the Reynolds number was increased,
several types of flow instability appeared and vortex
shedding occured. This appears early outside the
louver bank for a Reynolds number of around 600.
This instability is a Von Karman vortex street generated
by the unstable wake of the last flat part of the
fin where the boundary layer is swept downstream
and rolls up into a pair of periodically shed vortices
as shown in Fig.5 (temperature contours reveal the
air flow). The instability progresses upstream in
the louver bank as the Reynolds number is increased.
At Reynolds numbers near 900, instabilities are seen
in the second part of the fin. If the Reynolds number
is increased up to 1,300, all the louvers exhibit
instability (for Reynolds numbers over 1,300, the
flow becomes turbulent). As shown in Fig. 6, instabilities
within the louver bank are generated by the mixed
effects of vortex shedding from louver trailing edges
and instabilities similar to a Kelvin-Helmholtz instability.
These are characterized by waves and vortices that
appear between the boundary layer of the louver and
the secondary wake passing over the louver, which
are two fluid streams of different velocities and
densities.
All these phenomena have a profound
effect on the heat transfer characteristics and heat
transfer coefficient enhancement is observed where
waves and vortices impact on the heat transfer surface
as shown in Fig. 7. The 2D unsteady CFD approach
with STAR-CD allows one to study in detail the three
main phenomena involved in a louvered fin array:
the flow configuration (ducted or flat plate), the
thermal wake effects of the upstream louvers and
the flow instability that occurs at higher Reynolds
numbers.
For further information, please
contact: thomas.perrotin@ensmp.fr
References
1) Y.J. Chang, C.C. Wang – A generalized heat transfer correlation
for louver fin geometry – Int. J. Heat Mass Transfer Vol.40 No.3
pp533-544, 1997.
2) Y.J. Chang, K.C. Hsu, Y.T. Lin, C.C. Wang – A generalized friction
correlation for louver fin geometry – Int. J. Heat Mass Transfer
Vol.43 pp2237-2243, 2000.
3) M.H. Kim, C.W. Bullard – Air-side thermal hydraulic performance
of multi-louvered fin aluminum heat exchangers – International
Journal of Refrigeration, Volume 25, Issue 3, May 2002, Pages 390-400
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Fig. 1: Cut
of a refrigerant-to-air heat exchanger
with louvered fins and microchannels
Fig. 2: Computational domain of
the 3D model
Fig. 3: Temperature distribution
within the fin
Fig. 4: Velocity
magnitude distribution (left scale)
Fig. 5: Temperature
contours of an unstable
laminar flow at Re=648.0 Von Karman vortex street
Fig. 6: Instantaneous
temperature contours of an unstable laminar flow
at Re=864.0
Fig. 7: Instantaneous
Nusselt number for the
3 last
louvers of the fin at Re=864.0
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