processes
Article
Thermal Performance of T-shaped Obstacles in a Solar
Air Heater
Seung-Yong Ahn 1 and Kwang-Yong Kim 2, *
1
2
*
Department of Mechanical Engineering, Graduate School, Inha University, Incheon 22212, Korea;
ahnsy9028@inha.edu
Department of Mechanical Engineering, Inha University, Incheon 22212, Korea
Correspondence: kykim@inha.ac.kr; Tel.: +82-(32)-860-7317
Received: 18 September 2020; Accepted: 13 October 2020; Published: 17 October 2020
Abstract: This paper proposes T-shaped ribs as obstacles attached to the heat absorber plate in a
rectangular solar air heater to promote heat transfer. The thermal and aerodynamic performance of the
solar heater was numerically evaluated using three-dimensional Reynolds-averaged Navier–Stokes
equations with the shear stress transport turbulence model. A parameter study was performed using
the ratios of rib height to channel height, rib width to channel width, and rib width to rib height.
The area-averaged Nusselt number and friction factor were selected as the performance parameters
of the solar air heater to evaluate the heat transfer and friction loss, respectively. In addition,
the performance factor was defined as the ratio of the area-averaged Nusselt number to the friction
factor. The maximum area-averaged Nusselt number was found at h/e = 0.83 for a fixed rib area.
Compared with triangular ribs, the T-shaped ribs showed up to a 65 % higher area-averaged Nusselt
number and up to a 49.7% higher performance factor.
Keywords: solar air heater; ribs; Nusselt number; friction factor; Reynolds-averaged Navier–Stokes
equations
1. Introduction
Recently, as the problem of environmental pollution due to the use of fossil fuels has emerged,
interest in solar heat systems as a renewable energy source is increasing. A solar air heater (SAH) is a
device that heats air flowing over an absorber plate by using solar energy. It is used for space heating,
drying of agricultural products, and dehydration of industrial products [1].
Compared to liquid solar heaters, SAHs have a disadvantage of low heat transfer rate, because the
density of air is lower than that of a liquid. The heat transfer performance of an SAH is determined by
various factors such as the velocity of the flow, the length and depth of the heater, and the shape of
the heat absorber plate. The ratio between the area of the actual heat absorber and the absorber area
normal to the solar radiation, which is called the absorber shape factor, is an important parameter in
the design of SAHs.
Obstacles attached to the heat absorber plate are generally known to increase the heat transfer
by enlarging the heat transfer area and enhancing turbulence intensity. However, as the area of
the obstacles attached to the heat absorber plate increases, the pressure drop through the SAH also
increases. Therefore, many studies have been conducted on the shape of the obstacles to enhance
the overall heat transfer performance by increasing the heat transfer while minimizing the pressure
drop [2–14].
Kabeel and Mecarik [2] studied the effect of the shape of the heat absorber plate on the performance
of an SAH. It was confirmed that the heat transfer performance of the SAH with triangular obstacles
was higher than that with longitudinal pins. Moummi et al. [3] performed an energy analysis of an
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SAH with rectangular plate fins. The results for the heat transfer coefficient were compared with the
results obtained for the SAH without obstacles. The collector efficiency factor of the SAH with plate
pins increased by 30% compared to the case without obstacles. Essen [4] performed energy and exergy
analysis through experiments on obstacles of various shapes attached to an SAH. He concluded that
the heat and exergy efficiencies of the SAH with obstacles increased as compared to the SAH without
obstacles and the collector efficiency factor depended on the shape, area, orientation, and arrangements
of the obstacles. Saini and Saini [5] conducted an experimental study on the effect of the rib shape
on the heat transfer performance of an SAH with arc-shaped ribs. They developed correlations for
the Nusselt number and friction factor in terms of Reynolds number (Re), relative roughness height,
and arc angle of ribs.
Ozgen et al. [6] conducted an efficiency evaluation of an SAH with the flows flowing over the upper
and lower surfaces of a heat absorber plate where aluminum cans were attached. Depaiwa et al. [7]
experimentally studied the forced convective heat transfer and friction loss for the turbulent flow
in an SAH with rectangular winglet vortex generators. They tested an SAH with 20 winglet vortex
generators at Reynolds numbers ranging from 5000 to 23,000. The heat transfer rates in this SAH were
174% to 182% higher than that of the SAH with a smooth absorber plate. Bekele et al. [8] performed an
experimental and numerical analysis on the effects of the height and longitudinal pitch of triangular
obstacles on the heat transfer in an SAH. Through the analysis of the internal flow of the SAH, it was
reported that recirculating flows occurring around the triangular obstacles effectively increased the
turbulence intensity, thereby increasing the heat transfer rate by 3.6 times compared to the SAH without
obstacles. Yadav et al. [9] conducted an experimental study on the heat transfer performance and
friction factor of the turbulent flow over a heat absorber plate with circular protrusions arranged in
angular arc. The Nusselt number and friction factor were found to be 2.89 times and 2.93 times higher
than those of the unobstructed SAH, respectively.
Kulkarni and Kim [10] performed a numerical analysis to find the optimal shape of obstacles
attached to an SAH. Numerical analysis was performed for four different shapes and three different
arrangements of the obstacles. The Nusselt number and friction coefficient were greatly influenced by
the shape and arrangement of the obstacles, and pentagonal obstacles showed the highest performance
factor among the tested shapes. Alam and Kim [11] performed a numerical analysis to predict the heat
transfer performance of an SAH with conical protrusion ribs. The maximum thermal efficiency of the
collector was reported to be 69.8%. They developed correlations for the Nusselt number and friction
factor in terms of Reynolds number, relative roughness height, and relative rib pitch. Compared with
the results of numerical analysis, the correlations for the Nusselt numbers and friction factor showed
average absolute standard deviations of 2.78% and 5.25%, respectively. In addition, studies on SAHs
with various types of obstacles such as V-shaped ribs, diamond-shaped ribs, and arc-shaped ribs have
been also conducted to date [12–14].
In this study, T-shaped ribs are newly proposed to further improve the performance of an SAH by
considering both the heat transfer and pressure drop. The heat transfer and pressure drop characteristics
of the SAH with ribs were analyzed using three-dimensional Reynolds-averaged Navier–Stokes (RANS)
equations. A parametric study was conducted to confirm the effects of geometric parameters of the
T-shaped ribs on the heat transfer and pressure drop in the SAH. The performance of the SAH with the
proposed ribs was compared to SAHs with previously developed obstacles.
2. Solar Air Heater Model
Figure 1 shows the computational domain of the SAH and geometric parameters of the T-shaped
rib. Only a half of the entire SAH domain is included in the computational domain using symmetric
conditions. The computational domain consists of three sections; inlet Section (800 mm × 150 mm
× 50 mm (L1 × W/2 × H)), test Section (1200 mm × 150 mm × 50 mm (L2 × W/2 × H)), and outlet
Section (500 mm × 150 mm × 50 mm (L3 × W/2 × H)). This computational domain for evaluating
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the performance of the SAH was set according to the guidelines of the ASHRAE standard 93–97 [15],
0.5 solar
The
wall
(i.e.,
heat
absorber
plate) of
test section
absorbs
energy,0.5and
air is heated
and
theupper
lengths
of the
inlet
and
outlet sections
of the
the domain
are 5(WH)
and 2.5(WH)
, respectively.
as it flows
from
the
inlet
to
the
outlet
of
the
channel.
The
obstacles,
T-shaped
ribs,
are
attached
to the
The upper wall (i.e., heat absorber plate) of the test section absorbs solar energy, and air is heated
heat
plate.
Thirteen
are arranged
in a zigzag,
as shown
Figureto1a.
as itabsorber
flows from
the inlet
to therows
outletof
of ribs
the channel.
The obstacles,
T-shaped
ribs, arein
attached
theThe
thickness
of theplate.
rib isThirteen
0.5 mm,
andoftribs
is 8are
mm.
Each in
row
contains
one orinone
and
halfthickness
ribs in the
heat absorber
rows
arranged
a zigzag,
as shown
Figure
1a.a The
of the rib is 0.5domain.
mm, andThe
t is first
8 mm.
Each
row contains
one
or one
and
a half ribs inofthe
computational
computational
row
of ribs
is located
71.75
mm
downstream
the
inlet of the test
domain. The first row of ribs is located 71.75 mm downstream of the inlet of the test section.
section.
(a)
(b)
Figure
domainof of
solar
air heater
with T-shaped
ribs. (a) Computational
Figure1.1.Computational
Computational domain
thethe
solar
air heater
with T-shaped
ribs. (a) Computational
domain,
domain,
Test section.
(b) Test(b)
section.
3. Numerical Methods
3. Numerical
Methods
In this study, ANSYS-CFX 15.0 [16], a commercial code which employs an unstructured grid, was
In this study, ANSYS-CFX 15.0 [16], a commercial code which employs an unstructured grid,
used to analyze the flow and heat transfer using RANS equations. The shear stress transport (SST) [17]
was used to analyze the flow and heat transfer using RANS equations. The shear stress transport
model was used for the analysis of turbulence. The SST model was designed to take advantage of the
(SST) [17] model was used for the analysis of turbulence. The SST model was designed to take
k-ε and k-ω models by combining these two models using a weighting function so that the k-ω model
advantage
the the
k-εwall
andand
k-ωthe
models
by combining
these
using
weighting
function
is appliedofnear
k-ε model
is applied in
the two
othermodels
area. The
SST amodel
is known
to be so
that
the k-ω
is applied
the wall due
andto
the
k-ε model is applied in the other area. The SST
effective
in model
predicting
the flownear
recirculation
separation.
◦
model is
known
the flow
separation.
Air
at 25 to
C be
waseffective
used as in
thepredicting
working fluid,
andrecirculation
velocity and due
statictopressure
conditions were
2
Air
at
25
°C
was
used
as
the
working
fluid,
and
velocity
and
static
pressure
assigned to the inlet and outlet boundaries, respectively. A constant heat flux conditionconditions
of 815 W/mwere
assigned
to thetoinlet
and outlet
boundaries,
respectively.
A constant
heat
flux condition
of 815
was applied
the surface
of the
heat absorber
plate, and the
other solid
surfaces
were assumed
to W/m
be 2
was
appliedThe
to the
surface conditions
of the heatwere
absorber
and the other
were assumed
adiabatic.
symmetric
used atplate,
the symmetric
planesolid
of thesurfaces
computational
domain, to
a no-slip
condition
was used
at the wall
boundaries.
Ansymmetric
unstructured
tetrahedral
grid system
be and
adiabatic.
The
symmetric
conditions
were
used at the
plane
of the computational
domain, and a no-slip condition was used at the wall boundaries. An unstructured tetrahedral grid
system was constructed in most of the computational domain, but prism meshes were placed near
the wall to resolve the laminar sublayer. In order to use low-Re modeling for near-wall turbulence,
the y+ values of the first grid points from the wall were kept at less than 1.0.
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was constructed in most of the computational domain, but prism meshes were placed near the wall to
To find the grid dependency of the numerical solution, a test was performed according to the
resolve the laminar sublayer. In order to use low-Re modeling for near-wall turbulence, the y+ values
procedure proposed by Roache [18] and Celik and Karatekin [19]. This test analyzes the grid
of the first grid points from the wall were kept at less than 1.0.
convergence index (GCI), which represents numerical uncertainty through the estimation of
To find the grid dependency of the numerical solution, a test was performed according to the
discretization error based on Richardson extrapolation. Table 1 shows the results of the GCI analysis
procedure proposed by Roache [18] and Celik and Karatekin [19]. This test analyzes the grid convergence
where
gridwhich
refinement
factor
(r) was set
to 1.3 for through
three different
grid systems
(N1, N2, and
N3).
indexthe
(GCI),
represents
numerical
uncertainty
the estimation
of discretization
error
This
test
was
performed
on
the
SAH
with
the
reference
ribs
described
in
Table
2.
As
the
number
based on Richardson extrapolation. Table 1 shows the results of the GCI analysis where the gridof
grid
nodes increases,
the set
Nusselt
number
tends to grid
converge
gradually.
When
2 is used, the
refinement
factor (r) was
to 1.3 for
three different
systems
(N1 , N2 , and
N3 ).NThis
test was
extrapolated
relative
error
(𝑒
)
is
0.0015%
and
the
relative
error
is
0.0019%,
which
confirms
performed on the SAH with the reference ribs described in Table 2. As the number of grid
nodes a
relatively
numerical
uncertainty.
Therefore,
based on
thisNresult,
the optimum grid system is
increases,small
the Nusselt
number
tends to converge
gradually.
When
2 is used, the extrapolated relative
21
selected
as
N
2
,
which
is
shown
in
Figure
2.
error (e ) is 0.0015% and the relative error is 0.0019%, which confirms a relatively small numerical
ext
uncertainty. Therefore, based on this result, the optimum grid system is selected as N2 , which is shown
in FigureTable
2. 1. Results of grid convergence index (GCI) analysis using Richardson extrapolation.
Parameter
Value
Parameter
Number
of computational cells
Value
3,516,156/
Table 1. Results of grid convergence index (GCI) analysis using Richardson extrapolation.
8,071,835/
Number of computational cells
N1/N2/N3
N1 /N2 /N3
Grid refinement
factor
Grid refinement
factor
8,071,835/3,516,156/2,336,956
2,336,956
r
r
1.3 1.3
φ1
Computed
Nusselt numbers
Computed
Nusselt numbersφ
2
corresponding
to N1 , N2 to
, NN
3 1, N2, N3
corresponding
φ3
𝜙1
178.137
178.137
𝜙2
178.356
178.356
𝜙3
180.072
180.072
Apparent
order
Apparent
order
p
p
5.306
5.306
21
Extrapolated
value
Extrapolated
value φext
21
Approximate
relative error
Approximate
relative errorea
𝜙
178.134
178.134
𝑒
0.123%
0.123%
21
Extrapolated
relative error
Extrapolated
relative erroreext
Grid convergence
index
Grid convergence
indexGCI21
f ine
𝑒
𝐺𝐶𝐼
0.0015%
0.0015%
0.0019%
0.0019%
Table
values of
of geometric
geometricparameters.
parameters.
Table2.2.Ranges
Rangesand
and reference
reference values
ParameterLower
Lower
Limit
Parameter
Limit
Upper
Limit
Upper
LimitReference
Reference
h/H
h/H
0.3 0.3
0.7 0.7
0.50
0.50
e/W
e/W
0.067
0.067
0.133
0.133
0.10
0.10
h/e
h/e
0.380.38
1.751.75
0.83
0.83
Figure 2.
2. Example
Example of grid
Figure
grid system.
system.
In order to determine the convergence of the numerical solution, the root mean square residual
was reduced to 10-6 or less, and about 1200 iterations were performed. The computational time
required for a single analysis was about 14 h when a personal computer with an Intel Core i7 3.41
GHz CPU was used for the computations.
4. Geometric and Performance Parameters
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In order to determine the convergence of the numerical solution, the root mean square residual was
reduced to 10−6 or less, and about 1200 iterations were performed. The computational time required for
a single analysis was about 14 h when a personal computer with an Intel Core i7 3.41 GHz CPU was
used for the computations.
4. Geometric and Performance Parameters
In order to examine the effects of the rib shape shown in Figure 1 on the heat transfer performance
and pressure drop, three dimensionless parameters were selected; the ratios of the rib height to the
channel height (h/H), the rib width to the channel width (e/W), and the rib height to the rib width (h/e).
The ranges and reference values of these parameters are shown in Table 2.
Three performance parameters are defined to evaluate the heat transfer and pressure drop in the
SAH. The performance parameter related to the heat transfer is defined as follows:
Nuo
Nus
FNu =
(1)
Nuo is the area-averaged Nusselt number on the heat transfer surface.
Nuo =
q o Dh
ka Tp − Ts
(2)
where Tp is the average temperature at the surface of the heat absorber plate including the obstacles, Ts
is the bulk temperature of the working fluid, ka is the thermal conductivity of the fluid, qo is the heat
flux at the heat absorber plate, Dh is the hydraulic diameter of the flow channel, and Nus is the Nusselt
number for a fully developed flow in a smooth channel without obstacles, which is calculated from the
following Dittus–Boelter equation.
Nus = 0.024Re0.8 Pr0.4
(3)
where Reynolds number, Re, is defined using a hydraulic diameter, and Pr indicates the Prandtl number.
The definition of the performance parameter related to the pressure drop is as follows:
!
fo 1/3
Ff =
fs
(4)
Here, fo is the friction factor in the flow channel with obstacles.
fo =
2(∆P)Dh
4ρLU2
(5)
where ∆p is the pressure drop in the test section, ρ is the density of the working fluid, U is the average
velocity of the flow, L is the length of the flow channel (test section), and fs is the friction factor for
the fully developed flow in the smooth channel, which is calculated from the following modified
Blasius equation.
fs = 0.085Re−0.25
(6)
The performance factor, PF [20], for evaluating the performance of an SAH considering both the
heat transfer performance and pressure drop at the same time, is defined as follows:
PF =
FNu
Ff
(7)
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5. Results and Discussion
To prove the validity of the numerical analysis, the numerical results for the Nusselt number, Nuo ,
and friction factor, f o , are compared with corresponding empirical formulas for different Reynolds
numbers in the flow channel without obstacles, as shown in Figure 3. The numerical results show good
overall agreement with the empirical formulas. As Reynolds number increases, the relative error tends
to decrease in the case of Nuo . Compared with the experimental data, the average relative error of the6 of 15
Processes 2020, 8, x FOR PEER REVIEW
computed Nusselt numbers within the tested Reynolds number range is less than 3.29%, and it is less
Processesthan
2020,2.71%
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REVIEW
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for PEER
the friction
factor.
Figure 3. Validation of numerical results for smooth duct.
Figure 3. Validation of numerical results for smooth duct.
In addition, the validation
test was also
performed
for the
with
obstacles. The numerical
Figure 3. Validation
of numerical
results
for case
smooth
duct.
results are
compared
with
the
experimental
data
obtained
by
Bekele
et
al.
[8] for
SAH with
In addition, the validation test was also performed for the case with obstacles.
Thethe
numerical
Inresults
addition,
the under
validation
test boundary
was also
performed
for
theetcase
with
The numerical
triangular
obstacles
the
conditions,
shown
in[8]
Figure
4.SAH
Thewith
numerical
results
are compared
with
thesame
experimental
data
obtained byas
Bekele
al.
for theobstacles.
triangular
under thewith
same
boundary
conditions,data
as shown
in Figure
4.Bekele
The for
numerical
results
well the
agreeobstacles
wellcompared
qualitatively
with
the
experimental
data.
In
the by
results
number,
results
are
the
experimental
obtained
etthe
al.Nusselt
[8]
for agree
the
SAH
with
qualitatively
with
the
experimental
data.
In
the
results
for
the
Nusselt
number,
the
computational
computational
andunder
empirical
slopes
according
to the Reynolds
number
are 4.
exactly
the same results
but,
triangular
obstacles
the same
boundary
conditions,
as shown
in Figure
The numerical
and
empirical
slopes
according
to
the
Reynolds
number
are
exactly
the
same
but,
quantitatively,
they
quantitatively,
they
show
a
small
difference
unlike
the
case
without
obstacles.
The
average
relative
agree well qualitatively with the experimental data. In the results for the Nusselt number, the
a small
difference
unlike
the caseto
without
obstacles. The
average
relative
error for
the Nusselt
errorshow
for the
Nusselt
number
compared
the experimental
data
within
the are
tested
Reynolds
number
computational
and empirical
slopes according
to the Reynolds
number
exactly
the same
but,
number compared to the experimental data within the tested Reynolds number range is less than 4.43%,
range is less than
4.43%,
and
thatdifference
for the friction
factor
is less
than 1.94%,
whichThe
indicates
that
the
quantitatively,
they
show
a
small
unlike
the
case
without
obstacles.
average
relative
and that for the friction factor is less than 1.94%, which indicates that the accuracy of the numerical
accuracy
the numerical
analysis
results
acceptable
for further
calculations.
error
for theofNusselt
number
compared
to is
the
experimental
data within
the tested Reynolds number
analysis results is acceptable for further calculations.
range is less than 4.43%, and that for the friction factor is less than 1.94%, which indicates that the
accuracy of the numerical analysis results is acceptable for further calculations.
Figure
4. Validationof
of numerical
results
for afor
solaraair
heater
(SAH)
with(SAH)
triangular
ribstriangular
using experimental
Figure
4. Validation
numerical
results
solar
air
heater
with
ribs using
data of Bekele et al. [8].
experimental data of Bekele et al. [8].
The three
dimensionless
geometric
of heater
the SAH
with
proposed
T-shaped
ribs
Figure
4. Validation
of numerical
resultsparameters
for a solar air
(SAH)
with
triangular
ribs using
presented
in Table
used
to[8].
find the effects of the rib shape on the performance parameters,
experimental
data2ofwere
Bekele
et al.
i.e., FNu, Fƒ, and PF. The parametric study was performed at a Reynolds number of 22,600. In the case
of two variables, h/H and e/W, the reference value in Table 2 was applied to the parameter that was
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dimensionless
geometric parameters of the SAH with proposed T-shaped ribs presented
Processes The
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8, x FOR
PEER REVIEW
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in
Table
2
were
used
to
find
the
Processes 2020, 8, x FOR PEER REVIEW effects of the rib shape on the performance parameters, i.e., FNu , 7Ffof, 15
and PF. after
The parametric
was
at F
a ƒReynolds
of 22,600.
the case of
decreases
that (Figurestudy
5). On
theperformed
other hand,
continuesnumber
to increase
as h/HInincreases,
as two
shown
variables,
h/H
and
e/W,
the
reference
value
in
Table
2
was
applied
to
the
parameter
that
was
not
decreases
after
that
(Figure
5).
On
the
other
hand,
F
ƒ
continues
to
increase
as
h/H
increases,
as
shown
in Figure 6. Therefore, as the rib height increases with the fixed rib width, there exists the maximum
changed,
and
the
area
of
the
rib
was
changed
accordingly
during
the
parametric
study.
However,
in
Figure
6. Therefore,
as the
ribbut
height
fixed rib
width, there Similar
exists the
maximum
value
in the
heat transfer
rate,
the increases
pressure with
dropthe
increases
continuously.
heat
transfer
2 . Therefore, in this case,
in
the
case
of
h/e,
the
test
was
conducted
with
the
rib
area
fixed
at
375
mm
value
in the heat
pressure
drop5),
increases
continuously.
transfer
performances
are transfer
found atrate,
h/H but
= 0.5the
and
0.6 (Figure
but the pressure
drop Similar
is lowerheat
at the
lower
both the absolute
valuesatofh/H
h and
e changed
to
keep the
area
constant
according
to
the
change
of h/e.
performances
are
found
=
0.5
and
0.6
(Figure
5),
but
the
pressure
drop
is
lower
at
the
lower
rib height (h/H = 0.5), as shown in Figure 6. Therefore, in the PF distribution shown in Figure 7, the
In
all cases,
the
was kept
rib
height
(h/H
= size
0.5),of
astfactor
shown
inconstant.
Figure
6. Therefore,
in the PF distribution shown in Figure 7, the
maximum
performance
appears
at h/H
= 0.5.
The results of the parametric study for the ratio of the rib height to the channel height (h/H) are
maximum
performance
factor
appears
at
h/H
=
0.5.
Figure 8 shows the streamlines between the 5th and 7th ribs (indicated by a dark region in Figure
shown in Figures 5–9. Figures 5 and 6 show the changes in the performance parameters, FNu and
Figure
8 shows the
streamlines
anddifferent
7th ribs (indicated
a dark
region in
Figure
1b)F at
the symmetric
plane
(i.e., x-ybetween
plane atthe
z =5th
0) for
h/H. Due by
to the
geometric
shape
of
f , defined by Equations (1) and (2), respectively, in a range of 0.3 ≤ h/H ≤ 0.7. The computational
1b)
at
the
symmetric
plane
(i.e.,
x-y
plane
at
z
=
0)
for
different
h/H.
Due
to
the
geometric
shape
of
thevalues
rib, two
regions
areindicated
formed in
direction
of theand
rib the
height.
Asa h/H
increases,
arerecirculation
presented at five
points
bythe
circular
symbols,
line is
curve
fit of thethe
the
rib,
two
recirculation
regions
are
formed
in
the
direction
of
the
rib
height.
As
h/H
increases,
size
of theatrecirculation
region
wall
h/H
increases
fromitthe
0.3
values
these points. It
can benear
seenthe
thatupper
FNu has
theincreases.
maximum Additionally,
value between as
h/H
= 0.5
and 0.6 and
size
of
the
recirculation
region
near
the
upper
wall
increases.
Additionally,
as
h/H
increases
from
0.3
to 0.5,
the
reattachment
distance
rapidly
decreases.
This
rapid
reduction
in
the
reattachment
distance
gradually decreases after that (Figure 5). On the other hand, Ff continues to increase as h/H increases,
to
the
reattachment
rapidly
decreases.
This rapid
reduction
the
reattachment
distance
in 0.5,
this
h/H
enhances
heat
aswith
shown
in in
Figure
5, there
due to
early
as
shown
inrange
Figuregreatly
6. distance
Therefore,
as thethe
rib
heighttransfer,
increases
the fixed
rib
width,
exists
the rein
this
h/H
range
greatly
enhances
the
heat
transfer,
as
shown
in
Figure
5,
due
to
early
development
of
the
thermal
boundary
layer.
In
Figure
9,
the
local
Nusselt
number
distributions
on
maximum value in the heat transfer rate, but the pressure drop increases continuously. Similar heat redevelopment
of
the
thermal
boundary
layer.
In
Figure
9,
the
local
Nusselt
number
distributions
on
thetransfer
heat transfer
surface are
for found
h/H = 0.3
and=0.5
In 5),
thebut
case
ofpressure
h/H = 0.5,
theisNusselt
number
performances
at h/H
0.5are
anddifferent.
0.6 (Figure
the
drop
lower at
the
the
heat
transfer
h/H
= 0.3
and
0.5 are 6.
different.
In rib
thethe
case
h/Hto= the
0.5,case
the Nusselt
lower
rib height
=for
0.5),
as shown
in
Figure
Therefore,
in
PF of
distribution
shown
Figure
level
appears
to surface
be(h/H
higher
around
and
downstream
of each
compared
of in
h/H
=number
0.3.7,
level
to be
higher around
downstream
of each rib compared to the case of h/H = 0.3.
theappears
maximum
performance
factorand
appears
at h/H = 0.5.
Figure 5. Variation of the performance parameter related to heat transfer (FNu) with the ratio of the
Figure5.5.Variation
Variation of
of the
the performance
parameter
related to heat
transfer
(FNu(F
) with
the ratio
of theofrib
Figure
performance
parameter
heat
transfer
Nu) with
the(e/W)
ratio
the
rib height
to the channel
height (h/H) (the
ratio ofrelated
the ribto
width
to
the channel
width
= 0.1).
height to the channel height (h/H) (the ratio of the rib width to the channel width (e/W) = 0.1).
rib height to the channel height (h/H) (the ratio of the rib width to the channel width (e/W) = 0.1).
Figure
Variationof
of the
the performance
related
to the
drop drop
(Ff ) with
(e/W
= 0.1).
Figure
6. 6.Variation
performanceparameter
parameter
related
to pressure
the pressure
(Fƒ)h/H
with
h/H
(e/W =
Figure
0.1). 6. Variation of the performance parameter related to the pressure drop (Fƒ) with h/H (e/W =
0.1).
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Figure 7. Variation of performance factor (PF) with h/H (e/W = 0.1).
Figure7.7.
7.Variation
Variationof
ofperformance
performance factor
factor
(PF)
with
h/H
(e/W
Figure
Variation
of
performance
(e/W
== 0.1).
Figure
factor(PF)
(PF)with
withh/H
h/H
(e/W
=0.1).
0.1).
(a)
(a)
(a)
(b)
(b)
(b)
(c)
(c)
Figure 8. Streamlines on x-y plane (z = 0) between(c)
fifth and seventh ribs (dark region in Figure 1b) for
Figure 8.
8. Streamlines on x-y plane (z = 0) between
Figure
between fifth and seventh ribs (dark region in Figure 1b) for
different h/H. (a) h/H = 0.3, (b) h/H = 0.5, (c) h/H = 0.7.
different
h/H.(a)
(a)h/H
h/H
0.3,plane
(b) h/H
h/H
=fifth
0.7. and seventh ribs (dark region in Figure 1b) for
different
h/H.
==x-y
0.3,
(b)
(c) h/H =
Figure
8. Streamlines
on
(z===0.5,
0) between
different h/H. (a) h/H = 0.3, (b) h/H = 0.5, (c) h/H = 0.7.
(a)
(a)
(a)
(b)
(b)
(b)
Figure 9. Nusselt number distributions on the heated surface for different h/H. (a) h/H = 0.3, (b) h/H = 0.5.
Figure 9. Nusselt number distributions on the heated surface for different h/H. (a) h/H = 0.3, (b) h/H
Figure 9. Nusselt number distributions on the heated surface for different h/H. (a) h/H = 0.3, (b) h/H
= 0.5.
= 0.5.
Figure 9. Nusselt number distributions on the heated surface for different h/H. (a) h/H = 0.3, (b) h/H
= 0.5.
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Figure 8 shows the streamlines between the 5th and 7th ribs (indicated by a dark region in
Figure 1b) at the symmetric plane (i.e., x-y plane at z = 0) for different h/H. Due to the geometric shape
of the rib, two recirculation regions are formed in the direction of the rib height. As h/H increases,
the size of the recirculation region near the upper wall increases. Additionally, as h/H increases from 0.3
to 0.5, the reattachment distance rapidly decreases. This rapid reduction in the reattachment distance
in this h/H range greatly enhances the heat transfer, as shown in Figure 5, due to early re-development
of the 2020,
thermal
boundary
layer. In Figure 9, the local Nusselt number distributions on the heat transfer
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surface for h/H = 0.3 and 0.5 are different. In the case of h/H = 0.5, the Nusselt number level appears to
Figuresaround
10–14 and
show
the effectsofofeach
the rib
ratio
of the rib
be higher
downstream
compared
to width
the casetoofthe
h/Hchannel
= 0.3. width (e/W) on the
Figures 10–14 show the effects of the ratio of the rib width to the channel width (e/W) on the
Figuresof10–14
showFigures
the effects
of the
thevariations
rib width of
to the
the two
channel
width (e/W)
on the
performance
the SAH.
10 and
11ratio
showofthe
performance
parameters,
performance of the SAH. Figures 10 and 11 show the variations of the two performance parameters,
performance
of the SAH.
Figures
11 show
the variations
of theAs
two
performance
FNu
and Fƒ, respectively,
with
e/W,10
inand
a range
of 0.067
≤ e/W ≤ 0.133.
e/W
increases, parameters,
both FNu and
FNu and
Fƒ,Frespectively,
with
e/W,
inina arange
ofof0.067
≤≤e/W
≤ ≤0.133.
AsAs
e/W
increases,
both
FNu
and
and
,
respectively,
with
e/W,
range
0.067
e/W
0.133.
e/W
increases,
both
FNuthe
FƒFincrease
almost
linearly.
This
is
presumed
to
be
a
phenomenon
that
occurs
because
both
Nu
f
Fƒand
increase
almost
linearly.
This
is
presumed
to
be
a
phenomenon
that
occurs
because
both
the
Ff increase
almost
This
is increase
presumed
to be
phenomenon
both the
turbulence
intensity
andlinearly.
pressure
loss
due
to athe
increase in that
the occurs
area ofbecause
the obstacles
as e
turbulence
intensity
and
loss
due to
to the
the increase
increaseininthe
thearea
areaofofthe
the obstacles
turbulence
intensity
andpressure
loss increase
increase
due
asas
e e
increases
while
the height
hpressure
is kept constant.
In the
PF distribution
shown in
Figure 12,obstacles
the maximum
increases
while
the
height
h
is
kept
constant.
In
the
PF
distribution
shown
in
Figure
12,
the
maximum
increases
while
the height
keptbut
constant.
In thevariation
PF distribution
shown
in Figure
the maximum
value
is found
around
e/Wh=is0.08,
the overall
with e/W
is very
small12,
compared
to that
value
is
found
around
e/W
=
0.08,
but
the
overall
variation
with
e/W
is
very
small
compared
to in
that
is found
around e/W = 0.08, but the overall variation with e/W is very small compared to that
invalue
Figure
7 for h/H.
inFigure
Figure7 7for
forh/H.
h/H.
Figure 13 shows the streamlines between the 5th and 7th ribs at the symmetric plane for different
Figure 1313shows
the
between
the 5th
5thand
and7th
7thribs
ribsatatthe
thesymmetric
symmetricplane
planefor
fordifferent
different
shows
thestreamlines
streamlines
between
the
h/H. ItFigure
can be seen
that
as
e/W increases,
the
recirculation
region located
near the top
of the rib
h/H.
It
can
be
seen
that
as
e/W
increases,
the
recirculation
region
located
near
the
top
of
the rib
h/H. It can
be seen
as e/W increases,
thedoes
recirculation
region
located
the top
of the rib
increases.
increases.
Since
thethat
reattachment
distance
not change
with
e/W,near
the heat
transfer
enhancement
increases.
the reattachment
distance
does not
change
with
e/W,
the heat
transfer enhancement
Since theSince
reattachment
distance does
not change
with
e/W, the
heat
transfer
enhancement
according
according to the change in e/W does not seem to be related to the reattachment distance. Figure 14
according
to
the
change
in
e/W
does
not
seem
to
be
related
to
the
reattachment
distance.
Figure
to the change in e/W does not seem to be related to the reattachment distance. Figure 14 shows
the14
shows the distributions of the Nusselt number on the heat transfer surface between the 5th and 7th
distributions
of the Nusselt
number
on number
the heat transfer
surface
between
the 5th
and 7ththe
ribs.
e/W
shows
the distributions
of the
Nusselt
on the heat
transfer
surface
between
5thAs
and
7th
ribs. As e/W increases, the increased width of the rib increases the width of the high Nusselt number
increases,
increased
of thewidth
rib increases
theincreases
width of the
the width
high Nusselt
number
area number
in the
ribs.
As e/Wthe
increases,
thewidth
increased
of the rib
of the high
Nusselt
area in the lateral direction, thereby increasing the overall Nusselt number.
lateral
direction,
increasing
overall Nusselt
number.
area
in the
lateral thereby
direction,
thereby the
increasing
the overall
Nusselt number.
Figure 10. Variation of FNu with e/W (h/H = 0.5).
Figure 10.
Variation of
Figure
10. Variation
ofFFNu
Nu with
with e/W
e/W(h/H
(h/H==0.5).
0.5).
Figure 11.
11. Variation
Variation of
Figure
of FFfƒ with
withe/W
e/W(h/H
(h/H==0.5).
0.5).
Figure 11. Variation of Fƒ with e/W (h/H = 0.5).
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Figure 12. Variation of PF with e/W (h/H = 0.5).
Figure 12. Variation of PF with e/W (h/H = 0.5).
Figure12.
12.Variation
Variation of
= 0.5).
Figure
of PF
PFwith
withe/W
e/W(h/H
(h/H
= 0.5).
(a)
(a)
(a)
(b)
(b)
(b)
(c)
(c)
Figure 13. Streamlines on x-y plane (z = 0) between fifth and seventh ribs for different e/W. (a) e/W =
Figure 13. Streamlines on x-y plane (z = 0) between fifth and seventh ribs for different e/W. (a) e/W = 0.067,
0.067, (b) e/W = 0.10, (c) e/W = 0.133.
(c)fifth and seventh ribs for different e/W. (a) e/W =
Figure
Streamlines
x-y plane (z = 0) between
(b)
e/W 13.
= 0.10,
(c) e/W =on0.133.
0.067, (b) e/W = 0.10, (c) e/W = 0.133.
Figure 13. Streamlines on x-y plane (z = 0) between fifth and seventh ribs for different e/W. (a) e/W =
0.067, (b) e/W = 0.10, (c) e/W = 0.133.
(a)
(b)
(c)
(a)
(b)
(c)
Figure 14. Nusselt
distributions on the heated surface
different e/W.
(a)
(b) between fifth and seventh ribs for (c)
Figure
surface between fifth and seventh ribs for different e/W.
(a) e/W14.
= Nusselt
0.067; (b)distributions
e/W = 0.10; on
(c) the
e/Wheated
= 0.133.
(a) e/W = 0.067; (b) e/W = 0.10; (c) e/W = 0.133.
Figure 14. Nusselt distributions on the heated surface between fifth and seventh ribs for different e/W.
(a) e/W = 0.067; (b) e/W = 0.10; (c) e/W = 0.133.
Figure 14. Nusselt distributions on the heated surface between fifth and seventh ribs for different e/W.
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The variation of FNu with the ratio of the rib height to the rib width (h/e) keeping the rib area
The
variation
of Figure
FNu with
ratio= of
the ribheat
height
to the rib
width (h/e)
keeping
the of
ribFarea
constantThe
is
shown
in
15.the
At
transfer
This
variation
Nu is
variation
of FNu with
theh/e
ratio 0.83,
of thethe
rib height
to the is
ribmaximized.
width (h/e) keeping
the rib area
constant
shown
in Figure
At
h/e = in
0.83,
the heat
transfer is maximized.
variation curve
of FNu is
similar
toisthe
variation
with 15.
h/H
shown
Figure
5. However,
Figure
5,This
the
variation
constant
is shown
in Figure
15. At
h/e = 0.83,
the heat
transfer isunlike
maximized.
This
variation
of FNu is of
similar
to the
variation
h/H
shown
5.5.However,
Figure
5,the
thevariation
variation
curve
of
tointhe
variation
h/H
shownininFigure
Figure
However,
unlike
5,
FNu similar
shown
Figure
15with
iswith
more
symmetrical
as the
area
of theunlike
rib is Figure
kept constant
in this curve
case.
The
FNu of
shown
inFƒFigure
15 is
more
symmetrical
the
areaarea
ofcompared
the
ribrib
is to
kept
this
The
FNu of
shown
in Figure
15
is more
symmetrical
as the
of the
is kept
constantininwith
thiscase.
case.and
variation
with
h/e
shown
in
Figure
16 isasvery
small
theconstant
variations
h/H
variation
of F
in respectively.
Figure
16 is16
very
small
compared
thethe
variations
with
variation
of Ffh/e
with
h/e shown
in Figure
very
small
compared
to
variations
with
h/H
e/WThe
shown
inƒ with
Figures
6shown
and
11,
Inis the
cases
with
h/Htoand
e/W,
the area
ofh/H
theand
rib
e/W
shown
in
Figures
6
and
11,
respectively.
In
the
cases
with
h/H
and
e/W,
the
area
of
the
rib
and
e/W
shown
in
Figures
6
and
11,
respectively.
In
the
cases
with
h/H
and
e/W,
the
area
of
the
rib
changes, but in this case with h/e, the area of the rib remains constant. Accordingly, it can be seen
changes,
butbut
ininthis
case
h/e,
thearea
area
remains
constant.
Accordingly,
can
beofseen
this
case
with h/e,
the
of of
the
rib rib
remains
Accordingly,
it can
beit seen
that
thatchanges,
the pressure
drop
is with
greatly
influenced
bythe
the
area
of constant.
the rib
rather
than the
aspect
ratio
the
the
pressure
drop
is greatly
influenced
by theby
area
ofarea
the rib
rather
than
the than
aspectthe
ratio
of theratio
rib. of the
that
the
pressure
drop
is
greatly
influenced
the
of
the
rib
rather
aspect
rib.
rib.
2).
Figure 15. Variation of FNu with the ratio of the rib height to the rib width (h/e) (rib area = 375 mm
2 ). 2
Figure
VariationofofFFNu
withthe
theratio
ratio of
of the rib
width
(h/e)
(rib(rib
areaarea
= 375
mmmm
Figure
15.15.
Variation
ribheight
heighttotothe
theribrib
width
(h/e)
= 375
).
Nuwith
Figure 16. Variation of F with h/e (rib area = 375 mm2 ).
Figure 16. Variation of Ffƒ with h/e (rib area = 375 mm2).
Figure 16. Variation of Fƒ with h/e (rib area = 375 mm2).
Since the change in the pressure drop appears small over the entire range of h/e, the variation of
Since
the change
in the
pressure
drop appears
overa the
entire range
of h/e,
the variation
the
performance
factor
PF with
h/e, shown
in Figure small
17, shows
qualitatively
similar
variation
to that of
Since
the
change
in
the
pressure
drop
appears
small
over
the
entire
range
of
h/e,
the
variation
the of
performance
factor
with h/e,
shown
Figure
17, at
shows
qualitatively similar variation of
to
FNu (Figure 15).
ThePF
maximum
value
of PFinalso
appears
h/e = a0.83.
the
factor
PF maximum
with h/e, shown
inPF
Figure
17, shows
ah/e
qualitatively
similar variation to
thatperformance
of FFigure
Nu (Figure
15).
The
value
of
also
appears
at
=
0.83.
18 shows the Nusselt number distributions on the heat transfer surface between the 5th
that of FNu (Figure 15). The maximum value of PF also appears at h/e = 0.83.
and 7th rib rows. At h/e = 0.83, where the highest heat transfer occurs, the area of the high Nusselt
number region is the largest. This indicates that the heat transfer enhancement due to the production
of turbulent kinetic energy becomes most effective when h and e have similar sizes while keeping the
rib area constant.
To demonstrate the superiority of the heat transfer performance of the SAH with T-shaped ribs
proposed in this study, the performance parameters are compared with the experimental data for the
SAH with triangular ribs measured by Bekele et al. [8], as shown in Figures 19 and 20. The comparison
was performed for the same cross-sectional area of the ribs and the same spacing between the ribs.
The T-shaped rib used for the comparison is the reference rib presented in Table 2. Figure 19 shows the
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variations of the Nusselt number (Nuo ) and friction factor (f o ) with Reynolds number. In the case of
the friction factor, the T-shaped ribs show a slightly larger value than that with the triangular ribs in the
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entire Reynolds
number
range. However, the Nusselt number shows a large uniform improvement
at
all Reynolds numbers. Compared to the triangular ribs, the T-shaped ribs show Nusselt numbers that
are 65% higher at Re = 4510 and 21.5% higher at Re = 22,600. On the other hand, a 35% higher pressure
drop occurs at Re = 4510 and a 31% higher pressure drop occurs at Re = 22,600 than for the triangular
ribs. Figure 20 shows the comparison of the performance factor PF between the two different ribs.
The PF of the T-shaped ribs is 49.7% higher at Re = 4510, and 11% higher at Re = 22,600 than for the
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triangular ribs.
Figure 17. Variation of PF with h/e (rib area = 375 mm2).
Figure 18 shows the Nusselt number distributions on the heat transfer surface between the 5th
and 7th rib rows. At h/e = 0.83, where the highest heat transfer occurs, the area of the high Nusselt
number region is the largest. This indicates that the heat transfer enhancement due to the production
of turbulent kinetic energy becomes most effective when h and e have similar sizes while keeping the
rib area constant.
Figure 17. Variation of PF with h/e (rib area = 375 mm2 ).
Figure 17. Variation of PF with h/e (rib area = 375 mm2).
Figure 18 shows the Nusselt number distributions on the heat transfer surface between the 5th
and 7th rib rows. At h/e = 0.83, where the highest heat transfer occurs, the area of the high Nusselt
number region is the largest. This indicates that the heat transfer enhancement due to the production
of turbulent kinetic energy becomes most effective when h and e have similar sizes while keeping the
rib area constant.
(a)
(b)
(c)
Figure 18. Nusselt number distributions on the heated surface between fifth and seventh ribs for
Figure
18.h/e.
Nusselt
distributions
the =heated
different
(a) h/enumber
= 0.38; (b)
h/e = 0.83; on
(c) h/e
1.75. surface between fifth and seventh ribs for
different h/e. (a) h/e = 0.38; (b) h/e = 0.83; (c) h/e = 1.75.
Table 3 shows a comparison of PF ranges among various obstacle shapes developed to date.
Toobstacles
demonstrate
superiority
of the experimental
heat transfer
performance
the SAH
with
T-shaped
ribs
These
tested
by previous
or numericalofstudies
using
the
parameters
(a)werethe
(b)
(c)
proposed
in this pitch
study,(P
the
performance
parameters
compared
with
the experimental
datarelative
for the
of longitudinal
relative obstacle
heightare
(e/H),
relative
roughness
height (e/D),
l /e),
SAH
with triangular
ribsrelative
measured
by Bekele pitch
et al. [8],
as shown
Figures
19 and 20.
The and
comparison
roughness
pitch (P/e),
longitudinal
between
the in
rows
of winglets
(P/H),
number
was
performed
thewinglet
same cross-sectional
area of
theproposed
ribs and in
the
same
spacing
the ribs.
of waves
on thefor
delta
(φ). The T-shaped
ribs
this
study
causebetween
two recirculation
The
T-shaped
ribinused
for the direction,
comparison
is the reference
rib8presented
in to
Table
Figure geometric
19 shows
regions
formed
the height
as shown
in Figures
and 13, due
their2.unique
the
variations
of the Nusselt
numberzones
(Nuo)are
and
friction to
factor
(ƒo) with
Reynolds number.
In the
case
shape.
These multiple
recirculation
expected
promote
the production
of turbulent
kinetic
of
the friction
factor,
the
T-shaped
ribs
showona heat
slightly
larger
valuebetween
than
with
theseventh
triangular
ribs
Figure
18.thus
Nusselt
number
distributions
the heated
surface
and
for3.
energy
and
further
enhance
the
turbulent
transfer
compared
to that
thefifth
other
obstacles
inribs
Table
in different
the entire
number
the Nusselt number shows a large uniform
h/e.Reynolds
(a) h/e = 0.38;
(b) h/erange.
= 0.83; However,
(c) h/e = 1.75.
improvement at all Reynolds numbers. Compared to the triangular ribs, the T-shaped ribs show
Nusselt
numbers that
aresuperiority
65% higherof
at the
Re =heat
4510transfer
and 21.5%
higher at Re of
= 22,600.
On with
the other
hand, ribs
To demonstrate
the
performance
the SAH
T-shaped
a
35%
higher
pressure
drop
occurs
at
Re
=
4510
and
a
31%
higher
pressure
drop
occurs
at
Re
=
22,600
proposed in this study, the performance parameters are compared with the experimental data for the
than
for triangular
the triangular
Figure by
20 Bekele
shows the
comparison
of the
performance
factor
PF between
SAH
with
ribsribs.
measured
et al.
[8], as shown
in Figures
19 and
20. The
comparison
the
two
different
ribs.
The
PF
of
the
T-shaped
ribs
is
49.7%
higher
at
Re
=
4510,
and
11%
higher
Re ribs.
was performed for the same cross-sectional area of the ribs and the same spacing betweenatthe
= 22,600 than for the triangular ribs.
Processes
Processes 2020,
2020, 8,
8, 1305
x FOR PEER REVIEW
Processes 2020, 8, x FOR PEER REVIEW
13 of
of 15
15
13
13 of 15
Figure 19. Comparison of performance parameters between T-shaped and triangular ribs.
Figure19.
19.Comparison
Comparisonofofperformance
performanceparameters
parametersbetween
betweenT-shaped
T-shapedand
andtriangular
triangularribs.
ribs.
Figure
Figure 20.
20. Comparison
Comparison of
of PF
PF between
between T-shaped
T-shaped and
Figure
and triangular
triangular ribs.
ribs.
Figure 20. Comparison of PF between T-shaped and triangular ribs.
Table 3. Comparison of performance factor range obtained in the present study with those obtained in
Table
3 shows
a comparison
of PF studies
ranges on
among
various
the previous
experimental
or numerical
obstacle
shape. obstacle shapes developed to date.
Table 3 shows a comparison of PF ranges among various obstacle shapes developed to date.
These obstacles were tested by previous experimental or numerical studies using the parameters of
These obstaclesInvestigator
were tested by Geometrical
previous experimental
or numerical studies using PF
the parameters of
Shape
of Obstacles
longitudinal pitch (Pl/e), relative
obstacle
height
(e/H), relativeParameters
roughness heightRange
(e/D), relative
longitudinal pitch (Pl/e), relative obstacle height (e/H), relative
roughness height (e/D), relative
Re = 3400–28000
roughness pitch (P/e), relative longitudinal pitch between the rows
of winglets (P/H), and number of
roughness pitch (P/e), relative longitudinal pitch between the rows
of1.5–5.5
winglets (P/H), and number of
Pl /e this
=
waves on Bekele
the delta
(ϕDelta-shaped
). The T-shaped
study cause
two recirculation
et al.winglet
[8]
ribs ribs proposed in
1.10–2.14
e/Hthis
= 0.5–0.75
waves on the delta winglet (ϕ). The T-shaped ribs proposed in
study cause two recirculation
regions formed in the height direction, as shown in Figures 8 θand
13,
◦ due to their unique geometric
= 90
regions formed in the height direction, as shown in Figures 8 and
13, due to their unique geometric
shape. These multiple recirculation zones are expected to promote the production of turbulent kinetic
Re the
= 3800-18000
shape. These multiple recirculation
zonestriangular
are expected to promote
production of turbulent kinetic
Equilateral
energy andYadav
thusetfurther
to the other
obstacles in Table
al. [21]enhance the turbulent heat transfer compared
Pl /e = 7.14–35.71
1.36–2.11
energy and thus further enhance
the turbulent
heat transfer compared to the other obstacles in Table
sectioned
ribs
3.
e/D = 0.021–0.042
3.
Re = 4000–12000
Table 3. Comparison of performance
range
Multi-gap factor
V-down
ribs obtained
combinedin the
P/epresent
= 4–14 study with those obtained
et al. [22] of performance factor range obtained in the present study with 2.09–2.45
Table 3.Deo
Comparison
those obtained
staggered ribs
e/D =0.026–0.057
in the previous experimentalwith
or numerical
studies on obstacle shape.
◦
◦
in the previous experimental or numerical studies on obstacle shape.
θ = 40 – 80
Geometrical Shape
Re = 3800–18000
Investigator
Parameters
PF Range
Geometrical
Shape
of Obstacles
Investigator
Parameters
PF Range
Gawande et al. [23] L-shaped ribs
P/e = 7.14–17.86
1.62–1.90
of Obstacles
e/D = 0.042
Re = 3400–28000
Re
= 3400–28000
= 1.5–5.5
Pl/e
Re = 4000–17300
1.10–2.14
Bekele et al. [8]
Delta-shaped ribs
l/e = 1.5–5.5
Pe/H
= 0.5–0.75 1.10–2.14
P/H
=
3–6
Bekele et
al. [8] et al.
Delta-shaped
ribs
Sawhney
[24]
Wavy
delta winglets
1.46–2.09
e/H
=
0.5–0.75
φ = 3–7 θ = 90 °
= 90 °
θ = 60 ◦ θRe
= 3800-18000
Re
= 3800-18000
Re = 4510–22600
Yadav et al. [21]
Equilateral triangular sectioned ribs
Pl/e
= 7.14–35.71 1.36–2.11
Yadav et al. [21]
Equilateral triangular sectioned ribs
Pe/D
l/e = 7.14–35.71
1.36–2.11
h/H = 0.3–0.7
= 0.021–0.042
Present study
T-shaped ribs
2.07–2.63
e/D = 0.021–0.042
e/W = 0.067–0.133
Re = 4000–12000
h/e =0.38–1.75
= 4000–12000
Deo et al. [22]
Multi-gap V-down ribs combined with staggered ribsRe
P/e
= 4–14
2.09–2.45
Deo et al. [22]
Multi-gap V-down ribs combined with staggered ribs P/e
4–14
2.09–2.45
e/D= =0.026–0.057
e/D =0.026–0.057
Processes 2020, 8, 1305
14 of 15
6. Conclusions
In this study, T-shaped ribs with a staggered arrangement are proposed to enhance the heat transfer
in an SAH, and the effects of the geometric parameters of the ribs on the thermal and aerodynamic
performance of the SAH were analyzed using RANS equations. The numerical results for the heat
transfer rate and friction factor were validated by comparing with experimental data for the smooth
duct and the SAH with triangular obstacles. In the case of the SAH with the obstacles, the average
relative error of the average Nusselt number between the numerical and experimental results was
less than 4.43% within the tested Reynolds number range, and that of the friction factor was less
than 1.94%. In a parametric study using the ratios of the rib height to the channel height (h/H) and
the rib width to the channel width (e/W), the performance factor (PF) was far more sensitive to h/H
than to e/W, and the maximum PF was found at h/H = 0.5 for a fixed e/W. When h/e was varied by
keeping the rib area constant, the variation of the friction factor with h/e was very small due to the
fixed rib area, and thus the variation of the average Nusselt number was qualitatively similar to that
of PF and their maximum values were commonly found at h/e = 0.83. The proposed T-shaped ribs
showed superior performance to several other heat-transfer enhancement obstacles developed to date.
For example, when compared with the triangular ribs, the T-shaped ribs showed a 49.7% higher PF
at a Reynolds number of 4510, and an 11% higher PF at a Reynolds number of 22,600. To generalize
the present results for staggered T-shaped obstacles, further studies are required for the SAH using
different arrangements of T-shaped obstacles.
Author Contributions: S.-Y.A. presented the main idea of the T-shaped ribs; S.-Y.A. and K.-Y.K. contributed to
the overall composition and writing of the manuscript; S.-Y.A. performed numerical analysis and analyzed the
data; K.-Y.K. revised and finalized the manuscript. All authors have read and agreed to the published version of
the manuscript.
Funding: This work was supported by a National Research Foundation of Korea (NRF) grant funded by the
Korean government (MSIT) (No. 2019R1A2C1007657).
Conflicts of Interest: The authors declare there is no conflict of interest.
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