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Experimental and numerical study on heat transfer, flow resistance, and compactness of alternating flattened tubes
Accepted Manuscript Experimental and Numerical Study on Heat Transfer, Flow Resistance, and Compactness of Alternating Flattened Tubes Ahmad Reza Sajadi, Farshad Kowsary, Mohamad Ali Bijarchi, Sami Yamani Douzi Sorkhabi PII: DOI: Reference:
S1359-4311(16)31162-0 http://dx.doi.org/10.1016/j.applthermaleng.2016.07.033 ATE 8631
To appear in:
Applied Thermal Engineering
Please cite this article as: A.R. Sajadi, F. Kowsary, M.A. Bijarchi, S.Y. Douzi Sorkhabi, Experimental and Numerical Study on Heat Transfer, Flow Resistance, and Compactness of Alternating Flattened Tubes, Applied Thermal Engineering (2016), doi: http://dx.doi.org/10.1016/j.applthermaleng.2016.07.033
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Experimental and Numerical Study on Heat Transfer, Flow Resistance, and Compactness of Alternating Flattened Tubes Ahmad Reza Sajadia,∗, Farshad Kowsarya , Mohamad Ali Bijarchia , Sami Yamani Douzi Sorkhabib a
School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran b Department of Mechanical & Industrial Engineering, University of Toronto, Toronto, ON, Canada M5S 3G8
Abstract Recently, increasing heat transfer rate of heat exchangers and reducing their size without experiencing a significant increase in flow resistance has been the main focus of several studies. Through the course of these studies, a wide range of active and passive methods have been implemented. Among these methods, changing the geometry of the heat exchanger tubes has received an increasing attention due to its simplicity and cost-effectiveness. In this study, a new geometry called the alternating flattened tube is introduced and its performance against other widely used tubes is evaluated. To compare the heat transfer, pressure drop, and compactness of the tubes simultaneously, a parameter called tube performance enhancement ratio is introduced. Both experimental and numerical results show that the alternating flattened ∗
Corresponding author Email address: [email protected] (Ahmad Reza Sajadi)
Preprint submitted to Applied Thermal Engineering
July 4, 2016
tube has a better performance enhancement ratio compared to the previously studied tubes and can be an advantageous alternative for the conventional circular tubes. Keywords: Alternating flattened tube, Heat transfer, Flow resistance, Occupied space, Tube performance enhancement ratio.
2
1
Nomenclature
2
m ˙
Mass flow rate, kg/s
3
˙ W
Pumping power, W
4
A
Outer major axis, mm
5
a
Inner major axis, mm
6
Ac
Cross-sectional area, m2
7
As
Surface area, m2
8
AEA Alternating elliptical axis tube
9
AF
Alternating flattened tube
10
B
Outer minor axis, mm
11
b
Inner minor axis, mm
12
C
Circular tube
13
Cp
Isobaric specific heat capacity, kJ/kg · K
14
Dh
Hydraulic diameter, mm
15
E
Deformation rate matrix
16
e
Internal energy, J
17
F
Flattened tube
18
f
Friction factor
19
Gz
Graetz number 3
Convective heat transfer coefficient, W/m2 · K
20
h
21
HCW Helically coiled with corrugated wall tube
22
HSW Helically coiled with straight wall tube
23
I
Turbulence intensity
24
k
Kinetic energy, J
25
L
Tube length, m
26
n
Number of segments
27
Nu
Nusselt number
28
OS
Occupied space, mm2
29
P
Pressure, P a
30
p
Cross-sectional perimeter, m
31
P ER Tube performance enhancement ratio
32
Pr
Prandtl number
33
q
Heat, J
34
Re
Reynolds number
35
S
Segment length, mm
36
T
Temperature, K
37
t
Time, s
38
TR
Transition section length, mm
4
39
U
Flow mean velocity, m/s
40
u, v, w Physical velocity component, m/s
41
u∗
Friction velocity, m/s
42
V
Velocity, m/s
43
x, y, z x, y, and axial direction coordinates
44
Y
Distance of the closest computational node from the wall, m
45
y+
Dimensionless wall distance
46
Z
Axial position within the tube, m
47
Greek Symbols
48
∆P
Pressure drop, P a
49
∆T
Temperature difference, K
50
∆Tm Logarithmic mean temperature difference, K
51
Dissipation rate, J
52
κ
Thermal conductivity, W/m · K
53
µ
Dynamic viscosity, P a · s
54
ν
Kinematic viscosity, m2 /s
55
φ
Flattening
56
ρ
density, kg/m3
57
τw
Wall shear stress, P a
5
58
ε
Effectiveness
59
Subscripts
60
C
Circular tube
61
c
Cross-sectional
62
D
Hydraulic diameter
63
h
Hydraulic
64
i
Inlet
65
max Maximum
66
o
Outlet
67
s
Surface
68
t
Turbulent
69
w
Wall
6
70
1. Introduction
71
In recent decades, thermo-hydraulic performance enhancement of heat
72
exchangers has received increasing concerns from heat exchanger designers.
73
The main goal is to improve heat transfer efficiency of heat exchangers, while
74
reducing their size and operating cost. To this end, several methods have
75
been proposed to enhance the heat transfer rate of the heat exchangers while
76
controlling their size and pressure drop. In what follows, these enhancement
77
methods are briefly discussed and the main focus of this study is delineated.
78
The heat transfer enhancement in heat exchangers is achieved via two cat-
79
egories, namely (i) active and (ii) passive methods. Active methods are those
80
in which an external power source is utilized to enhance the heat transfer rate
81
of the heat exchangers. The well-studied active methods include system vi-
82
bration, using electrostatic fields, and flow injection in porous media [1–4].
83
Results of these studies show that active methods increase heat transfer rate
84
within a relatively constant pressure drop and space occupied by the tubes
85
at the expense of using external power sources.
86
Passive methods, on the other hand, do not use any external power source
87
and the increase in heat transfer rate is achieved by changing the working
88
fluid or manipulating the tube structure. Passive methods can be catego-
89
rized in two different groups. The first category includes improving the fluid
90
heat transfer properties. One of the most common ways to achieve this im-
91
provement is adding nanoparticles to the working fluid [5–8]. The addition
92
of nanoparticles not only increases the thermal conductivity of the fluid, 7
93
but also facilitates convective heat transfer as the particles move during the
94
heat transfer process. Moreover, the space occupied by the tubes does not
95
change as the tube geometry is not modified. However, the cost of adding
96
nanoparticles to the working fluid acts as the main hindrance against wide
97
implementation of this method [9].
98
The second category is changing the structure of the heat exchanger tubes.
99
This category is the main focus of this study and can be achieved by either
100
adding extra parts to heat exchanger tubes or changing their geometries.
101
The goal here is to facilitate generation of secondary flows and increasing
102
flow turbulence. These two factors result in an increase in both heat trans-
103
fer rate and flow resistance. In addition, the space occupied by the tubes
104
may change due to changing their structure. Thus, studying this category
105
requires the consideration of the heat transfer, flow resistance, and occupied
106
space of the tubes simultaneously. In the following paragraphs, some the
107
studies related to this category are discussed.
108
Eiamsa-ard et al. [10] showed that inserting uniform or non-uniform
109
twisted-tapes with alternate axes increases the heat transfer rate and flow
110
resistance. They investigated the twisted-tape geometry for which the highest
111
heat transfer rate and the maximum Webb’s performance evaluation criterion
112
[11] can be achieved. In a more recent study by Rivier et al. [12], the heat
113
transfer enhancement caused by fitting elliptic shaped turbulator was inves-
114
tigated experimentally. They showed that fitting these turbulators increases
115
heat transfer and flow resistance simultaneously. However, generating sur8
116
face dispersions, which is easy to manufacture, can be used as a mechanism
117
to avoid significant pressure drop increase. In these two studies, the occupied
118
space of the tubes did not change because their external geometry was not
119
modified.
120
Among the studies considering tube geometry modification, corrugated
121
and oval tubes have been widely explored. In a review study by Kareem et
122
al. [13], it was concluded that helically coiled corrugated tubes can further
123
increase the heat transfer rate due to the compound effects of curvature and
124
corrugation. Kathait et al. [14] showed that the tubes with discrete cor-
125
rugations can not only improve the thermo-hydraulic performance of heat
126
exchanger by a factor of two, but they also reduce the overall heat exchanger
127
size. Tan et al. [15] evaluated the performance of twisted oval tubes in heat
128
exchangers experimentally. It was concluded that twisted oval tube outper-
129
form circular tube in low tube side and high shell side flow rates.
130
In addition to the above mentioned studies, some studies investigated the
131
effect of tube geometry modification of flow regime. Wang et al. [16] and
132
Nascimento et al. [17] showed that changing the tube geometry can result in
133
a transient or turbulent flow in lower Reynolds numbers. They studied heat
134
transfer and flow resistance of circular tubes with ellipsoidal dimples and flat
135
tubes with shallow square dimples respectively. The change of flow regime
136
to turbulent in lower Reynolds numbers compared to circular tube caused an
137
increase in both heat transfer rate and friction factor. However, they both
138
showed that optimization of the dimpled tubes can result in a better heat 9
139
transfer performance within the same friction penalty as the smooth tubes.
140
Furthermore, both studies mentioned that generating dimples on the surface
141
of the tubes can result in obtaining more compact heat exchangers. Similar
142
to the aforementioned studies, Karami et al. [18] experimented heat transfer
143
and pressure drop of nanofluid flows in corrugated tubes. They also showed
144
that the flow becomes turbulent in lower Reynolds numbers compared to the
145
circular tube as result of the wall corrugation of the tube.
146
In other recent studies that consider tube geometry modification, Sajadi
147
et al. [19] and Zambaux et al. [20] investigated heat transfer and flow resis-
148
tance in tubes with alternating elliptical axis (AEA). Both geometries were
149
similar to the geometry investigated by Chen et al. [21]. In the study by
150
Zambaux et al., the Reynolds number was set to 388 for their whole study;
151
thus, the flow was considered to be laminar. Sajadi et al.; however, con-
152
ducted their experiments for the Reynolds number range of 500 to 2000. In a
153
similar fashion to Wang et al. [16] and Nascimento et al. [17], they concluded
154
that the flow regime is turbulent for this Reynolds number range as a result
155
of multiple expansions and contractions of the AEA tube. Both Sajadi et
156
al. and Zambaux et al. showed that there are certain geometries of their
157
investigated tubes that perform better than the circular tube. However, the
158
occupied space of these tubes and its effect on the size of the heat exchangers
159
was not investigated in any of these studies.
160
In this study, a novel tube shape called alternating flattened (AF) tube
161
[22] is introduced. This tube consists of flattened segments that are alterna10
162
tively connected to circular segments. Heat transfer oil is used as the working
163
fluid and the experiments are carried out for a Reynolds number range of 500
164
to 2000. First, the heat transfer and hydrodynamics of the AF tube are in-
165
vestigated both experimentally and numerically. Then, the effect of using
166
this tube on the heat exchanger compactness is studied. The results show
167
that the AF tube with a simpler geometry to manufacture and a smaller oc-
168
cupied space compared to the AEA tube, is able to further enhance the heat
169
transfer rate for the same pressure drop and occupied space as the circular
170
and the AEA tubes.
171
172
2. Alternating Flattened Tube
173
In this section, alternating flattened (AF) tube is introduced and its geo-
174
metric properties are discussed. Before introducing AF tube, it is interesting
175
to note how the geometries of the previously studied tubes were modified to
176
reach this new geometry. As the first step towards increasing heat transfer
177
rate, circular tube was flattened while the perimeter of the tube was kept
178
constant. The idea behind this modification was to increase presence of fluid
179
molecules in proximity to the tube wall; thus, increasing heat transfer rate
180
[23]. However, it is shown that flattening the tube is only effective when
181
increasing heat transfer rate is important and the pressure drop increase is
182
not a matter of concern [19]. The flattened tube was then modified to AEA
183
tube [21] in such a way that a higher heat transfer rate was achieved within 11
(a)
(b)
Figure 1: (a) Alternating Elliptical Axis (AEA) and (b) Alternating Flattened (AF) tubes.
184
the same pressure drop as circular tube. As shown in Fig. 1(a), an AEA tube
185
is a flattened tube with 90◦ rotation of its cross-section in each segment. It
186
was shown that transitions between horizontal and vertical cross-sections are
187
more important than the flattening of the tube [19]. To further explore this
188
finding and as shown in Fig. 1(b), the AEA tube is modified to AF tube by
189
replacing every other flattened segments with circular segments. As a result,
190
there is no rotation in the cross-section of the flattened segments.
191
Figure 2 shows the geometry of a sample AF tube. In this figure, A and
192
a are outer and inner major axes of the cross-section respectively. Similarly,
193
B and b are outer and inner minor axes of the cross-section respectively. The
194
parts of the tube in which the cross-section is changing are called transition
195
parts and their corresponding length is defined by T R. Each segment of the
196
tube is defined as a part of the tube, which is located between two transition
197
sections and the length of each segment is shown as S. The number of seg12
Figure 2: The geometry of the Alternating Flattened (AF) tube.
198
ments for a tube is shown as n. To specify the flatness of a tube, a parameter
199
called flattening is defined as
φ=
a−b . a
(1)
200
Flattening can have a value between 0 and 1. The corresponding values
201
of flattening for a circle and a line are 0 and 1, respectively. Since the
202
cross-section of the AF tube is non-circular, hydraulic diameter needs to be
203
calculated. The hydraulic diameter is calculated as
Dh =
4Ac , p
13
(2)
204
where p is the perimeter of the tube and Ac is the average area of the cross-
205
section of the tube. As mentioned before, the perimeter of the tube is kept
206
constant, however, the area of the cross-section of the tube changes due to
207
flattening. Thus, the average cross-section area over the length of the tube
208
(L) is calculated as RL Ac =
0
Ac dx . L
(3)
209
As mentioned earlier, it is important to calculate the occupied space of
210
a tube to investigate its effect on the compactness of the heat exchanger.
211
The space occupied by a tube is the volume of the rectangular prism that
212
circumscribes the tube. However, to make this parameter independent of the
213
tube length, occupied space is defined as the area of the rectangle that cir-
214
cumscribes the cross-section of the tube and is shown as OS. Figure 3 shows
215
the occupied space for circular, AEA, and AF tubes. The occupied space of
216
AF and flattened tubes are the same, as they have identical cross-sections.
217
Based on the aforementioned paragraphs, the geometric properties of
218
the investigated tubes are shown in Table 1. In this table, C and F represent
219
circular and flattened tubes, respectively. For the AF tube, the performance
220
of three different geometries called AF1, AF2, and AF3 are investigated. In
221
Sec. 4, the performance of the AF tube is compared to that of AEA tube.
222
To this end, two different geometries of AEA tube are introduced and called
223
AEA1 and AEA2. All the above mentioned tubes are made of circular copper
224
tubes with an outer diameter of
5 00 , 8
i.e., 15.875 mm, and a thickness of 0.63
14
Figure 3: Occupied space of Circular, AEA, AF tubes.
225
mm.
226
Table 1: Geometric properties of the investigated tubes.
Name C F AEA1 AEA2 AF1 AF2 AF3
B(mm) b(mm) A(mm) a(mm) 15.88 10.00 10.00 12.00 10.00 12.00 10.00
14.62 8.74 8.74 10.74 8.74 10.74 8.74
15.88 19.23 19.23 18.09 19.23 18.09 19.23
227
3. Methodology
228
3.1. Experimental method
14.62 17.97 17.97 16.83 17.97 16.83 17.97
S(mm)
T R(mm)
φ
n
1200.00 940.00 115.00 115.00 115.00 115.00 67.86
0.00 50.00 50.00 50.00 50.00 50.00 50.00
0.00 0.52 0.52 0.36 0.52 0.36 0.52
0 1 5 5 5 5 7
Dh (mm) OS(mm2 ) 14.62 12.67 12.91 11.82 13.63 13.02 13.69
229
Figure 4 shows the experimental setup for this study. In this setup, a
230
gear pump pumps the working fluid to a 4 litre reservoir for precooling. 15
252.17 305.37 369.79 327.24 305.37 287.27 305.37
Figure 4: Experimental setup.
231
Then, the working fluid passes through a shell and tube heat exchanger
232
for cooling and enters the 120 cm test section. The temperature of the
233
working fluid is measured at the inlet and the outlet of the test section using
234
two K-type thermocouples with a range and accuracy of −100 ◦ C to 1370 ◦ C
235
and 0.1 ◦ C respectively. The pressure drop of the working fluid is measured
236
using an Endress Hauser differential pressure transducer with a range and
237
accuracy of 25 Pa to 4 × 106 Pa and 1 Pa respectively. Constant temperature
238
boundary condition is imposed on the wall of the test section using saturated
239
water vapor. To monitor and ensure this boundary condition, 6 K-type
240
thermocouples are mounted on the wall of the tube with equal distances.
241
The saturated water vapor is produced in a 50 litre tank, which is equipped
16
242
with an 8 kW heater. From the heat balance point of view, the heat produced
243
by the 8 kW heater is Qhot and the heat absorbed by the working fluid is
244
Qcold . To maintain the pressure of the 50 litre tank constant and avoid having
245
superheated vapor, holes are made on the wall of the tank. The execs vapor
246
exiting the tank from these holes can be assumed as Qloss . The flow rate is
247
calculated using a 1 litre glass vessel, a drain valve, and a stop watch with an
248
accuracy of 0.01 second. The flow rate is controlled using two adjustable flow
249
control valves that are placed at the exit of the test section and the bypass
250
line.
251
The working fluid used in the mentioned experimental apparatus is the
252
heat transfer oil, whose thermophysical properties in the temperature range of 30◦ to 90◦ are shown in Table 2. Table 2: Thermophysical properties of the heat transfer oil. ◦
T ( C) ρ 30 50 70 90
kg m3
860.23 847.25 834.27 821.29
Cp
kJ kg·K
1.99 2.07 2.15 2.23
κ
W m·K
0.133 0.131 0.131 0.128
ν
m2 s
26.18 27.95 27.95 26.87
253
254
After data acquisition from the experimental apparatus, heat transfer
255
and flow resistance of investigated tubes are calculated using the inlet and
256
outlet temperature of the working fluid. The mean convective heat transfer
17
257
coefficient can be calculated as ˙ p (To − Ti ) ¯ = mC h , As ∆Tm
(4)
258
where m ˙ is the mass flow rate, Cp is the average isobaric specific heat ca-
259
pacity of the working fluid at the inlet and outlet of the test section, As is
260
the heat transfer surface area, Ti and To are the bulk temperatures of the
261
working fluid at the inlet and outlet of the test section respectively, and ∆Tm
262
is the logarithmic mean temperature difference (LMTD).
263
It is common to non-dimensionalize the convective heat transfer coeffi-
264
cient and measured pressure drop in the form of Nusselt number and friction
265
factor respectively. However, both Nusselt number and friction factor are
266
dependent on the hydraulic diameter of the tube. As shown in Table 1, the
267
hydraulic diameters of the investigated tubes are different. Thus, compari-
268
son of Nusselt number and friction factor without consideration of convective
269
heat transfer coefficient and pressure drop is not conclusive.
270
The experimental uncertainties of the studied heat transfer and flow re-
271
sistance parameters are calculated based on Kline et al’s [24] method and
272
presented in Table 3.
273
Results attained by the experimental apparatus of the present study
274
are validated using the analytical convective heat transfer and friction factor
275
correlations for circular tube. The mean Nusselt number is calculated using
276
Hausen correlation for convective heat transfer of laminar flow in circular
18
Table 3: Experimental uncertainties of the calculated parameters.
Parameter
Uncertainty
Re h Nu f
±3.0% ±3.1% ±4.1% ±4.3%
277
tube [25]. The friction factor is calculated using Darcy friction factor corre-
278
lation for laminar flow in circular tube [26].
279
Figures 5 and 6 show comparison of the experimental results for laminar
280
flow in circular tube with the existing analytical correlations. The maximum
281
error observed for heat transfer and flow resistance are 9% and 13%, respec-
282
tively. These errors are similar to the reported errors by Eiamsa-ard et al.
283
[10].
284
285
3.2. Numerical method
286
In this work, a numerical model for the oil flow in the investigated tubes
287
is developed and validated with experimental results. This model is used to
288
facilitate and expedite the investigation of heat transfer and flow resistance
289
for different geometries of the investigated tubes.
290
Fully structured computational grids are generated for the geometries
291
shown in Table 1 using Gambit 2.4.6 [27]. For all investigated tubes, grids
292
with 8,640,000 hexahedral cells and 8,744,871 nodes are generated. The gird
293
independence study is carried out for all the generated grids and the result 19
Figure 5: Validation of the numerical results for Nu number with tube C.
20
Figure 6: Validation of the numerical results for friction factor with tube C.
21
Figure 7: Grid independence study for tube AF1.
294
for tube AF1 and a Reynolds number of 1000 is shown in Fig. 7.
295
Figure 8(a) shows the cross-sectional grid for a flattened segment of AF1.
296
This grid is refined in proximity to the tube wall. Figure 8(b) shows the axial
297
grid in the connection of a flattened segment to two circular segments. The
298
grid is refined in the transition parts to achieve a better accuracy.
299
In the grid generation process, the position of the closest node to the wall
300
of the tube determines the accuracy of velocity and thermal boundary layer
301
estimations. In other words, this distance specifies whether or not the grid
302
is capable of capturing the velocity and thermal boundary layers. For this
303
study, the closest computational node to the wall of the tube is generated
304
within 0.025 mm from the wall. In what follows, it is shown that this distance 22
(a)
(b)
Figure 8: (a) Sectional and (b) axial grids.
305
provides accurate estimations of velocity and thermal boundary layers.
306
To characterize the grid estimation of the velocity boundary layer, a
307
dimensionless wall distance parameter called y + is used, which is defined as
y+ =
u∗ Y , ν
(5)
308
where Y is the distance of the closest computational node from the wall of
309
the tube, ν is the kinematic viscosity of the working fluid, and u∗ is the
310
friction velocity defined as r u∗ =
τw , ρ
(6)
311
where τw is wall shear stress and ρ is the density of the working fluid. In this
312
study enhanced wall treatment estimation was used to model the boundary
313
layer motion of the flow. The value of y + should be less than 1 in order 23
314
for the enhanced wall treatment estimation to capture the velocity boundary
315
layer [28]. Based on preliminary trials, the value of y + is between 0.1 and
316
0.6 for different investigated Reynolds numbers of this study. Thus, it can
317
be claimed that the velocity boundary layer is captured.
318
In addition to the velocity boundary layer, one needs to ensure that the
319
current grid provides an accurate estimation of the thermal boundary layer.
320
To this end, the local convective heat transfer coefficient and Nusselt number
321
are calculated in the middle of each segment of the tubes. Preliminary trials
322
showed that the value of local convective heat transfer coefficient and Nusselt
323
number do not change as the grid is refined. Thus, the grid is capable of
324
capturing the thermal boundary layer as well.
325
The boundary condition at the inlet of the tube is mass flow inlet where
326
the mass flow rate and the temperature of the working fluid are constant.
327
The boundary condition for the outlet of the tube is outflow. Finally, the wall
328
of the tube is a stationary, no slip wall with a known constant temperature.
329
After defining the boundary conditions, the problem can be solved by
330
solving the continuity, momentum, and energy equations in the Cartesian
331
coordinates for an internal fully developed fluid flow. These equations can
332
be formulated as,
333
∂ρ ∂(ρuj ) + = 0, ∂t ∂xj ∂ui ∂ui ∂P ∂ ∂ui ∂uj ρ + ρuj =− +µ + , ∂t ∂xj ∂xi ∂xj ∂xj ∂xi
24
(7)
(8)
334
∂ ρ ∂t
V2 V2 ~ ∂P ui ∂ 2T 2 ∂ui e+ + ρ∇ e + V =− +κ 2 − µ (∇~u) + 2 2 ∂xi ∂xi 3 ∂xi 2 ∂ui ∂ui ∂uj ∂ui 2µ +µ + + ρq˙ ∂xi ∂xj ∂xi ∂xj (9)
335
where xi , xj and ui , uj are position and velocity vectors of the flow in the ith
336
and jth dimensions respectively, t is time, µ is the average dynamic viscosity
337
of the working fluid at the inlet and outlet of the test section, P is pressure,
338
e is internal energy,
339
rate of volumetric heat addition per unit mass [29].
V2 2
is kinematic energy, T is temperature, and q˙ is the
340
These governing equations are solved with Fluent 6.3 [28]. The pressure
341
and velocity terms are discretized with the standard deviation and second
342
order upwind [30] schemes respectively. Then, the pressure based SIMPLEC
343
algorithm [31] couples and solves continuity and momentum equations. After
344
solving the continuity and momentum equations, the energy and turbulence
345
equations, in case the flow is turbulent, are solved in each iteration. It should
346
be mentioned that all simulations are run in parallel with 4 cores on an Intel
347
Core i7 processor with 12GB of RAM. The run time of each simulation is
348
approximately 18 hours.
349
To validate the numerical method, simulation of laminar and turbulent
350
flows with different turbulence models for the proposed tubes are performed.
351
Our trials show that using standard k- turbulence model [32] with a tur-
352
bulence intensity of 0.03 for the AF tubes results in the lowest error when
353
compared to the experimental results. The readers are referred to [28, 32] 25
354
for more details about the standard k- turbulence model. On the other
355
hand, for the flattened tube (F), the lowest error is achieved by modeling
356
the flow as a laminar flow. Generation of turbulent flow in the AF tubes
357
can be justified with the expansion and contraction that occur at each tran-
358
sition section. However, these transition sections do not exist in tube F, and
359
therefore the flow remains laminar. Figures 9 and 10 show comparison of the
360
experimental and numerical Nusselt numbers and friction factors for tubes
361
AF1 and F within a Reynolds range of 500 to 2000. The maximum observed
362
error for the Nusselt number and friction factor of tube AF1 is 19% and
363
15% respectively. Similarly, the maximum error observed for tube F is 13%
364
and 10% respectively. All these errors are less than the errors reported by
365
Eiamsa-ard et al. [10] (i.e., 15% and 20% for Nusselt number and friction
366
factor, respectively) and hence it can be concluded that the numerical model
367
is valid for engineering purposes.
368
369
4. Results and Discussion
370
In this section, heat transfer mechanism of AF tubes is investigated.
371
Then, heat transfer and flow resistance of AF tubes, tube F, and relevant
372
well-studied tubes are compared. Based on this comparison, the impact of
373
changing the geometric properties such as flattening (φ) or segment length
374
(S) on the heat transfer and pressure drop is studied. Finally, performance
375
enhancement of AF tubes for a constant pressure drop and occupied space 26
Figure 9: Comparison of experimental and numerical Nu number for tubes AF1 and F.
27
Figure 10: Comparison of experimental and numerical friction factor for tubes AF1 and F.
28
376
is evaluated and the feasibility of replacing conventional circular tubes with
377
these tubes is investigated.
378
379
4.1. Heat transfer mechanism of AF tube
380
To better understand the heat transfer mechanism in AF tube the local
381
Nusselt number distribution is plotted along the tube length for tube AF1
382
and a Reynolds number of 1000. Figure 11 shows that the transition sections
383
increase the heat transfer rate locally after each circular or flattened segment.
384
The thermal boundary layer that is generated in each segment of an AF tube
385
is destroyed in the transition sections and a larger temperature gradient is
386
created in proximity to the wall of the tube. This local increase does not allow
387
the local Nusselt number to have a behavior similar to the circular tube and
388
hence increases the overall heat transfer rate. The local Nusselt number in
389
circular tube decays rapidly along the tube as the thermal boundary layer
390
develops.
391
In addition to the local Nu number, studying the vorticity magnitude of
392
the flow along the AF tube can give a better understanding about the effect
393
of this geometry on the oil flow. Figure 12 shows the vorticity magnitude of
394
the flow along tube AF1 and for a Reynolds number of 1000. It is shown
395
that the vorticity magnitude is increased in the transition sections due to
396
the effect of expansions and contractions. The increased vorticity improves
397
both local heat transfer rate at the transition sections and the overall heat
29
Figure 11: Local Nu number along tube AF1
30
Figure 12: Vorticity magnitude along the AF1 tube
398
transfer rate of the AF tubes.
399
400
4.2. Heat transfer and flow resistance comparison
401
The heat transfer and flow resistance of AF tubes are first compared to
402
those of tube F. Then, the thermo/hydraulic performance of tube AF1 is
403
compared to those of relevant well-studied geometries. Figure 13 shows the
404
Nusselt number of AF tubes and tube F for different Reynolds numbers.
405
Comparison of the Nusselt number shows that all different geometries of AF
406
tube have a significantly higher heat transfer rate compared to tube F. The
407
transition sections do not exist in tube F and the temperature gradient close
408
to the wall is smaller compared to that of the AF tubes. Thus, AF tubes
409
have higher Nusselt numbers compared to tube F. In addition, it is observed
410
that increasing the Reynolds number results in an increase in the Nusselt
411
number. This increase is significantly larger for AF tubes compared to tube 31
412
F and can be justified with the turbulent flow regime of AF tubes.
413
As mentioned in Sec. 3.1, the difference in the hydraulic diameters of
414
the investigated AF tubes makes the comparison of their Nusselt numbers
415
inconclusive. To address this problem, the convective heat transfer coeffi-
416
cient of AF tubes and tube F are compared in Fig. 14. The comparison of
417
the convective heat transfer coefficient for different geometries of AF tubes
418
shows that AF1 and AF3 have a higher heat transfer rate compared to AF2.
419
This higher value for AF1 and AF3 is a result of having larger flattening
420
(φ) parameters compared to AF2. The Larger φ helps the fluid molecules
421
with lower temperature to be closer to the wall of the tube and increases the
422
temperature gradient near the wall. On the other hand, slightly better heat
423
transfer rate of AF3 compared to AF1 shows that increasing the number of
424
segments (n) can be helpful. A larger n results in having more transition
425
sections, but it reduces the length of the circular and flattened segments.
426
The main goal of having the transition sections is to increase heat transfer
427
rate by destroying the thermal boundary layer generated in either circular or
428
flattened sections of the tube. However, when the segment length becomes
429
shorter, the thermal boundary layer does not have the opportunity to be
430
generated and developed. Thus, as long as the flow has the opportunity to
431
develop a thermal boundary layer, increasing the number of segments (n) in-
432
creases heat transfer rate. However, increasing n ultimately results in a slight
433
increase in heat transfer rate, while the pressure drop increase persists.
434
The comparison of heat transfer in tubes is not sufficient unless flow 32
Figure 13: Nu number of investigated AF tubes and tube F.
33
Figure 14: Convective heat transfer coefficient of investigated AF tubes and tube F.
34
435
resistance comparison is taken into consideration. Figure 15 shows that the
436
friction factor of all investigated AF tubes are higher than that of tube F.
437
This can be justified with the fact that tube F has a laminar flow, while
438
the flow regime in AF tubes is turbulent. In a similar fashion to the heat
439
transfer study, the friction factor comparison is also inconclusive as a result
440
of the different hydraulic diameters of the investigated AF tubes. To make
441
the comparison independent of the hydraulic diameter, the pressure drop of
442
the investigated tubes are compared to each other. Figure 16 compares the
443
pressure drop of AF tubes and tube F for different Reynolds numbers. The
444
pressure drop comparison shows that AF1 and AF3 have a higher pressure
445
drop compared to AF2 due to their larger φ. However, reducing φ in AF2
446
leads to a pressure drop which is close to that of tube F and is significantly
447
lower than the pressure drop of tubes AF1 and AF3. The pressure drop of
448
AF3 is higher than that of AF1 due to having a larger n.
449
To compare the performance of AF tube with other well-studied tubes,
450
dimpled tube with a pitch length of 13.8 mm [33], helically coiled tube with
451
straight wall (HSW) and curvature ratio of 0.031 [34], and helically coiled
452
tube with corrugated wall (HCW) and curvature ratio of 0.031 [34] are con-
453
sidered. Figure 17 and 18 show the Nusselt number and friction factor com-
454
parison of these tubes, respectively. It is shown that AF1 has a higher Nusselt
455
number compared to dimpled tube, HSW tube, and F tube. However, tube
456
HCW shows the best heat transfer rate among the investigated tubes due to
457
its corrugated wall. On the other hand, the flow resistance of tube HCW is 35
Figure 15: Friction factor of investigated AF tubes and tube F.
36
Figure 16: Pressure drop of investigated AF tubes and tube F.
37
Figure 17: Nusselt number comparison of AF1 and relevant well-studied tubes.
458
the highest, which is also a result of wall corrugation. The friction factor of
459
AF1 is close to those of tube HSW and tube F, while the friction factor of
460
the dimpled tube is the lowest.
461
462
4.3. Performance enhancement ratio
463
It was shown in previous paragraphs that changing the geometry of cir-
464
cular and flattened tubes to AF tubes increases both heat transfer rate and
465
pressure drop. The increase of the former is desirable, while the increase of
466
the latter should be minimized. Furthermore, Table 1 shows that the oc-
467
cupied space of the AF and AEA tubes are more than that of the circular 38
Figure 18: Friction factor comparison of AF1 and relevant well-studied tubes.
39
468
tube, which may result in larger heat exchangers. Thus, there is a need for
469
a parameter that takes heat transfer rate, pressure drop, and occupied space
470
into account simultaneously.
471
As shown in Eq. 4, the transferred heat between working fluid and tube
472
wall is a function of convective heat transfer coefficient and logarithmic mean
473
temperature difference (LMTD). Webb’s performance evaluation criterion
474
[11] uses Nusselt number, which is a function of convective heat transfer
475
coefficient, to evaluate heat transfer rate. Hence, this criterion does not con-
476
sider the effect of difference between wall temperature and bulk temperature
477
of working fluid at the inlet and outlet of the tube even though this difference
478
has a direct effect on the heat transfer rate. In addition, Webb’s criterion
479
does not study the occupied space of the investigated tube. In this work,
480
tube performance enhancement ratio (PER) is defined to compare the heat
481
transfer of the investigated tubes to that of circular tube (tube C) within
482
an identical pressure drop and occupied space. To calculate PER, we first
483
need to calculate the effectiveness and the pumping power of the investigated
484
tube. The effectiveness of a tube is the ratio of its actual heat transfer rate
485
to the maximum possible heat transfer, that is
ε≡
q qmax
=
mC ˙ p (To − Ti ) , mC ˙ p (Tw − Ti )
40
(10)
486
where Tw is the constant wall temperature of the tube. The pumping power
487
needed to overcome the pressure drop in a tube can be calculated as ˙ ˙ =m W ∆P. ρ
488
(11)
Thus, the tube performance enhancement ratio (PER) is defined as
P ER =
ε/εC ˙ /W ˙C W
OS/OSC
,
(12)
489
˙ , and OS are the effectiveness, pumping power, and occupied where ε, W
490
˙ C , OSC are the effectiveness, space of the investigated tube. Similarly, εC , W
491
pumping power and occupied space of the corresponding tube C. It should
492
be noted that the flow properties, i.e., mass flow rate, inlet temperature, and
493
working fluid and the boundary conditions, i.e., wall temperature, of both
494
investigated and circular tubes should be the same for calculating PER. A
495
tube is an advantageous replacement for tube C if its PER is more than 1.
496
This means that the investigated tube has a higher heat transfer rate within
497
the same pressure drop and occupied space as tube C.
498
Figure 19 shows comparison of PER for AF tubes and tube F. It is shown
499
that PER for tube F is lower than 1 for all the investigated Reynolds num-
500
bers. In spite of the better heat transfer rate of tube F compared to tube
501
C, the increased pressure drop and occupied space do not allow this tube
502
to be an advantageous replacement for tube C. On the other hand, PER is
41
503
higher than 1 in most of the investigated Reynolds numbers for the AF tubes.
504
Among different geometries of AF tube, AF2 has the best performance and
505
the PER of this tube is higher than 1 for all the studied Reynolds number
506
range. It is shown that the heat transfer rate of tube AF2 can be up to 41%
507
more than that of the conventional circular tube within the same pressure
508
drop and occupied space. Tube AF2 has a lower φ compared to AF1 and
509
AF3; however, its other geometric parameters are the same as tube AF1.
510
The lower φ of AF2 causes lower occupied space, while the heat transfer rate
511
is not reduced to the extent that the pressure drop is reduced; thus, the PER
512
of this tube is higher than those of AF1 and AF3. It is clear that decreasing
513
φ will ultimately result in having a circular tube and there exists an optimal
514
φ for which PER is maximum. The occupied space of tubes AF1 and AF3
515
are identical; however, the PER of AF3 is slightly higher than that of AF1.
516
Tube AF3 has a higher n, which increases both heat transfer and pressure
517
drop. However, in this case, the effect of increasing heat transfer rate is more
518
than that of the pressure drop.
519
To further extend the discussion in the context of tube performance
520
enhancement ratio, the PER of AF tubes are compared to those of the pre-
521
viously studied AEA tubes. As shown in Table 1 and Fig. 1, tubes AEA1
522
and AEA2 are similar to tubes AF1 and AF2 respectively with the difference
523
that their occupied space is larger than that of the AF tubes. Figure 20
524
compares the PER of tubes AEA1 and AEA2 with that of AF1 and AF2 for
525
different Reynolds numbers. The PER of AEA2 is significantly higher than 42
Figure 19: Comparison of PER for investigated AF tubes and tube F.
43
526
that of AEA1 for all the studied Reynolds numbers. The reason is that in a
527
lower occupied space compared to AEA1, AEA2 has a higher heat transfer
528
rate and lower pressure drop [19]. The PER of the AF tubes; however, are
529
higher than those of both AEA tubes. It is shown that the PER of AF1
530
and AF2 are up to 32% and 21% higher than those of AEA1 and AEA2, re-
531
spectively. Compared AEA and AF tubes have identical number of segments
532
(n), while the total flattened length for AEA tubes is longer than that of
533
AF tubes. Thus, the pressure drop caused by this longer flattened length is
534
greater than the heat transfer improvement. Moreover, the occupied space of
535
the AF tubes is lower than that of the AEA tubes. These two factors result
536
in a lower PER for AEA tubes compared to AF tubes.
537
5. Concluding Remarks
538
This work studied heat transfer, flow resistance, and occupied space of
539
a new tube geometry called alternating flattened tube. This tube consists
540
of flattened and circular, i.e., unflattened, segments that are connected to
541
each other using transition sections. Both experimental and numerical stud-
542
ies were carried out with heat transfer oil as the working fluid and for a
543
Reynolds number range of 500 to 2000. The results were evaluated against
544
heat transfer and pressure drop of other well studied tubes. Comparison of
545
experimental and numerical results showed that the expansions and contrac-
546
tions in the geometry of the alternating flattened tube causes a turbulent
547
flow regime within the investigated Reynolds number range, while the flow 44
Figure 20: Comparison of PER for AF1, AF2, AEA1, and AEA2.
45
548
regime in conventional circular and flattened tubes is still laminar.
549
Our study showed that the heat transfer rate of all different geometries of
550
alternating flattened tube is higher than that of the flattened tube. Among
551
these different geometries; however, increasing the flattening of the tube in-
552
creases the heat transfer rate. On the other hand, increasing the number
553
of segments results in having more transition sections, i.e., expansions and
554
contractions, and increases turbulence intensity by reducing the length of
555
circular or flattened segments. Thus, increasing the number of segments in-
556
creases heat transfer rate.
557
The study on the flow resistance of the alternating flattened tube showed
558
that all the different geometries of this tube have higher pressure drop com-
559
pared to the flattened tube, which was expected due to the turbulent flow
560
regime of the alternating flattened tubes. In addition, it was shown that in-
561
creasing flattening and number of segments of the alternating flattened tube
562
increases the pressure drop.
563
After comparing heat transfer and pressure drop separately, simultane-
564
ous comparison of these parameters and the occupied space of the tubes was
565
carried out using a parameter called tube performance enhancement ratio.
566
The advantage of this comparison is that heat transfer rate of alternating
567
flattened tube is evaluated against a circular tube for the same pressure drop
568
and occupied space. Results showed that all the investigated geometries of
569
the alternating flattened tube can be advantageous replacements for circular
570
tubes, as the heat transfer rate of them is up to 41% higher than that of the 46
571
circular tube for the same pressure drop and occupied space. Furthermore,
572
it was observed that there is a specific flattening and number of segments for
573
which the best tube performance enhancement ratio can be achieved.
574
575
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Highlights
A new tube geometry called Alternating Flattened tube is introduced. Heat transfer and flow resistance are studied experimentally and numerically. The compactness of the tube is studied by considering its occupied space. Alternating Flattened tube has the best performance among the studied tubes. Alternating Flattened tube can be an advantageous alternative for circular tube.
S1359-4311(16)31162-0 http://dx.doi.org/10.1016/j.applthermaleng.2016.07.033 ATE 8631
To appear in:
Applied Thermal Engineering
Please cite this article as: A.R. Sajadi, F. Kowsary, M.A. Bijarchi, S.Y. Douzi Sorkhabi, Experimental and Numerical Study on Heat Transfer, Flow Resistance, and Compactness of Alternating Flattened Tubes, Applied Thermal Engineering (2016), doi: http://dx.doi.org/10.1016/j.applthermaleng.2016.07.033
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Experimental and Numerical Study on Heat Transfer, Flow Resistance, and Compactness of Alternating Flattened Tubes Ahmad Reza Sajadia,∗, Farshad Kowsarya , Mohamad Ali Bijarchia , Sami Yamani Douzi Sorkhabib a
School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran b Department of Mechanical & Industrial Engineering, University of Toronto, Toronto, ON, Canada M5S 3G8
Abstract Recently, increasing heat transfer rate of heat exchangers and reducing their size without experiencing a significant increase in flow resistance has been the main focus of several studies. Through the course of these studies, a wide range of active and passive methods have been implemented. Among these methods, changing the geometry of the heat exchanger tubes has received an increasing attention due to its simplicity and cost-effectiveness. In this study, a new geometry called the alternating flattened tube is introduced and its performance against other widely used tubes is evaluated. To compare the heat transfer, pressure drop, and compactness of the tubes simultaneously, a parameter called tube performance enhancement ratio is introduced. Both experimental and numerical results show that the alternating flattened ∗
Corresponding author Email address: [email protected] (Ahmad Reza Sajadi)
Preprint submitted to Applied Thermal Engineering
July 4, 2016
tube has a better performance enhancement ratio compared to the previously studied tubes and can be an advantageous alternative for the conventional circular tubes. Keywords: Alternating flattened tube, Heat transfer, Flow resistance, Occupied space, Tube performance enhancement ratio.
2
1
Nomenclature
2
m ˙
Mass flow rate, kg/s
3
˙ W
Pumping power, W
4
A
Outer major axis, mm
5
a
Inner major axis, mm
6
Ac
Cross-sectional area, m2
7
As
Surface area, m2
8
AEA Alternating elliptical axis tube
9
AF
Alternating flattened tube
10
B
Outer minor axis, mm
11
b
Inner minor axis, mm
12
C
Circular tube
13
Cp
Isobaric specific heat capacity, kJ/kg · K
14
Dh
Hydraulic diameter, mm
15
E
Deformation rate matrix
16
e
Internal energy, J
17
F
Flattened tube
18
f
Friction factor
19
Gz
Graetz number 3
Convective heat transfer coefficient, W/m2 · K
20
h
21
HCW Helically coiled with corrugated wall tube
22
HSW Helically coiled with straight wall tube
23
I
Turbulence intensity
24
k
Kinetic energy, J
25
L
Tube length, m
26
n
Number of segments
27
Nu
Nusselt number
28
OS
Occupied space, mm2
29
P
Pressure, P a
30
p
Cross-sectional perimeter, m
31
P ER Tube performance enhancement ratio
32
Pr
Prandtl number
33
q
Heat, J
34
Re
Reynolds number
35
S
Segment length, mm
36
T
Temperature, K
37
t
Time, s
38
TR
Transition section length, mm
4
39
U
Flow mean velocity, m/s
40
u, v, w Physical velocity component, m/s
41
u∗
Friction velocity, m/s
42
V
Velocity, m/s
43
x, y, z x, y, and axial direction coordinates
44
Y
Distance of the closest computational node from the wall, m
45
y+
Dimensionless wall distance
46
Z
Axial position within the tube, m
47
Greek Symbols
48
∆P
Pressure drop, P a
49
∆T
Temperature difference, K
50
∆Tm Logarithmic mean temperature difference, K
51
Dissipation rate, J
52
κ
Thermal conductivity, W/m · K
53
µ
Dynamic viscosity, P a · s
54
ν
Kinematic viscosity, m2 /s
55
φ
Flattening
56
ρ
density, kg/m3
57
τw
Wall shear stress, P a
5
58
ε
Effectiveness
59
Subscripts
60
C
Circular tube
61
c
Cross-sectional
62
D
Hydraulic diameter
63
h
Hydraulic
64
i
Inlet
65
max Maximum
66
o
Outlet
67
s
Surface
68
t
Turbulent
69
w
Wall
6
70
1. Introduction
71
In recent decades, thermo-hydraulic performance enhancement of heat
72
exchangers has received increasing concerns from heat exchanger designers.
73
The main goal is to improve heat transfer efficiency of heat exchangers, while
74
reducing their size and operating cost. To this end, several methods have
75
been proposed to enhance the heat transfer rate of the heat exchangers while
76
controlling their size and pressure drop. In what follows, these enhancement
77
methods are briefly discussed and the main focus of this study is delineated.
78
The heat transfer enhancement in heat exchangers is achieved via two cat-
79
egories, namely (i) active and (ii) passive methods. Active methods are those
80
in which an external power source is utilized to enhance the heat transfer rate
81
of the heat exchangers. The well-studied active methods include system vi-
82
bration, using electrostatic fields, and flow injection in porous media [1–4].
83
Results of these studies show that active methods increase heat transfer rate
84
within a relatively constant pressure drop and space occupied by the tubes
85
at the expense of using external power sources.
86
Passive methods, on the other hand, do not use any external power source
87
and the increase in heat transfer rate is achieved by changing the working
88
fluid or manipulating the tube structure. Passive methods can be catego-
89
rized in two different groups. The first category includes improving the fluid
90
heat transfer properties. One of the most common ways to achieve this im-
91
provement is adding nanoparticles to the working fluid [5–8]. The addition
92
of nanoparticles not only increases the thermal conductivity of the fluid, 7
93
but also facilitates convective heat transfer as the particles move during the
94
heat transfer process. Moreover, the space occupied by the tubes does not
95
change as the tube geometry is not modified. However, the cost of adding
96
nanoparticles to the working fluid acts as the main hindrance against wide
97
implementation of this method [9].
98
The second category is changing the structure of the heat exchanger tubes.
99
This category is the main focus of this study and can be achieved by either
100
adding extra parts to heat exchanger tubes or changing their geometries.
101
The goal here is to facilitate generation of secondary flows and increasing
102
flow turbulence. These two factors result in an increase in both heat trans-
103
fer rate and flow resistance. In addition, the space occupied by the tubes
104
may change due to changing their structure. Thus, studying this category
105
requires the consideration of the heat transfer, flow resistance, and occupied
106
space of the tubes simultaneously. In the following paragraphs, some the
107
studies related to this category are discussed.
108
Eiamsa-ard et al. [10] showed that inserting uniform or non-uniform
109
twisted-tapes with alternate axes increases the heat transfer rate and flow
110
resistance. They investigated the twisted-tape geometry for which the highest
111
heat transfer rate and the maximum Webb’s performance evaluation criterion
112
[11] can be achieved. In a more recent study by Rivier et al. [12], the heat
113
transfer enhancement caused by fitting elliptic shaped turbulator was inves-
114
tigated experimentally. They showed that fitting these turbulators increases
115
heat transfer and flow resistance simultaneously. However, generating sur8
116
face dispersions, which is easy to manufacture, can be used as a mechanism
117
to avoid significant pressure drop increase. In these two studies, the occupied
118
space of the tubes did not change because their external geometry was not
119
modified.
120
Among the studies considering tube geometry modification, corrugated
121
and oval tubes have been widely explored. In a review study by Kareem et
122
al. [13], it was concluded that helically coiled corrugated tubes can further
123
increase the heat transfer rate due to the compound effects of curvature and
124
corrugation. Kathait et al. [14] showed that the tubes with discrete cor-
125
rugations can not only improve the thermo-hydraulic performance of heat
126
exchanger by a factor of two, but they also reduce the overall heat exchanger
127
size. Tan et al. [15] evaluated the performance of twisted oval tubes in heat
128
exchangers experimentally. It was concluded that twisted oval tube outper-
129
form circular tube in low tube side and high shell side flow rates.
130
In addition to the above mentioned studies, some studies investigated the
131
effect of tube geometry modification of flow regime. Wang et al. [16] and
132
Nascimento et al. [17] showed that changing the tube geometry can result in
133
a transient or turbulent flow in lower Reynolds numbers. They studied heat
134
transfer and flow resistance of circular tubes with ellipsoidal dimples and flat
135
tubes with shallow square dimples respectively. The change of flow regime
136
to turbulent in lower Reynolds numbers compared to circular tube caused an
137
increase in both heat transfer rate and friction factor. However, they both
138
showed that optimization of the dimpled tubes can result in a better heat 9
139
transfer performance within the same friction penalty as the smooth tubes.
140
Furthermore, both studies mentioned that generating dimples on the surface
141
of the tubes can result in obtaining more compact heat exchangers. Similar
142
to the aforementioned studies, Karami et al. [18] experimented heat transfer
143
and pressure drop of nanofluid flows in corrugated tubes. They also showed
144
that the flow becomes turbulent in lower Reynolds numbers compared to the
145
circular tube as result of the wall corrugation of the tube.
146
In other recent studies that consider tube geometry modification, Sajadi
147
et al. [19] and Zambaux et al. [20] investigated heat transfer and flow resis-
148
tance in tubes with alternating elliptical axis (AEA). Both geometries were
149
similar to the geometry investigated by Chen et al. [21]. In the study by
150
Zambaux et al., the Reynolds number was set to 388 for their whole study;
151
thus, the flow was considered to be laminar. Sajadi et al.; however, con-
152
ducted their experiments for the Reynolds number range of 500 to 2000. In a
153
similar fashion to Wang et al. [16] and Nascimento et al. [17], they concluded
154
that the flow regime is turbulent for this Reynolds number range as a result
155
of multiple expansions and contractions of the AEA tube. Both Sajadi et
156
al. and Zambaux et al. showed that there are certain geometries of their
157
investigated tubes that perform better than the circular tube. However, the
158
occupied space of these tubes and its effect on the size of the heat exchangers
159
was not investigated in any of these studies.
160
In this study, a novel tube shape called alternating flattened (AF) tube
161
[22] is introduced. This tube consists of flattened segments that are alterna10
162
tively connected to circular segments. Heat transfer oil is used as the working
163
fluid and the experiments are carried out for a Reynolds number range of 500
164
to 2000. First, the heat transfer and hydrodynamics of the AF tube are in-
165
vestigated both experimentally and numerically. Then, the effect of using
166
this tube on the heat exchanger compactness is studied. The results show
167
that the AF tube with a simpler geometry to manufacture and a smaller oc-
168
cupied space compared to the AEA tube, is able to further enhance the heat
169
transfer rate for the same pressure drop and occupied space as the circular
170
and the AEA tubes.
171
172
2. Alternating Flattened Tube
173
In this section, alternating flattened (AF) tube is introduced and its geo-
174
metric properties are discussed. Before introducing AF tube, it is interesting
175
to note how the geometries of the previously studied tubes were modified to
176
reach this new geometry. As the first step towards increasing heat transfer
177
rate, circular tube was flattened while the perimeter of the tube was kept
178
constant. The idea behind this modification was to increase presence of fluid
179
molecules in proximity to the tube wall; thus, increasing heat transfer rate
180
[23]. However, it is shown that flattening the tube is only effective when
181
increasing heat transfer rate is important and the pressure drop increase is
182
not a matter of concern [19]. The flattened tube was then modified to AEA
183
tube [21] in such a way that a higher heat transfer rate was achieved within 11
(a)
(b)
Figure 1: (a) Alternating Elliptical Axis (AEA) and (b) Alternating Flattened (AF) tubes.
184
the same pressure drop as circular tube. As shown in Fig. 1(a), an AEA tube
185
is a flattened tube with 90◦ rotation of its cross-section in each segment. It
186
was shown that transitions between horizontal and vertical cross-sections are
187
more important than the flattening of the tube [19]. To further explore this
188
finding and as shown in Fig. 1(b), the AEA tube is modified to AF tube by
189
replacing every other flattened segments with circular segments. As a result,
190
there is no rotation in the cross-section of the flattened segments.
191
Figure 2 shows the geometry of a sample AF tube. In this figure, A and
192
a are outer and inner major axes of the cross-section respectively. Similarly,
193
B and b are outer and inner minor axes of the cross-section respectively. The
194
parts of the tube in which the cross-section is changing are called transition
195
parts and their corresponding length is defined by T R. Each segment of the
196
tube is defined as a part of the tube, which is located between two transition
197
sections and the length of each segment is shown as S. The number of seg12
Figure 2: The geometry of the Alternating Flattened (AF) tube.
198
ments for a tube is shown as n. To specify the flatness of a tube, a parameter
199
called flattening is defined as
φ=
a−b . a
(1)
200
Flattening can have a value between 0 and 1. The corresponding values
201
of flattening for a circle and a line are 0 and 1, respectively. Since the
202
cross-section of the AF tube is non-circular, hydraulic diameter needs to be
203
calculated. The hydraulic diameter is calculated as
Dh =
4Ac , p
13
(2)
204
where p is the perimeter of the tube and Ac is the average area of the cross-
205
section of the tube. As mentioned before, the perimeter of the tube is kept
206
constant, however, the area of the cross-section of the tube changes due to
207
flattening. Thus, the average cross-section area over the length of the tube
208
(L) is calculated as RL Ac =
0
Ac dx . L
(3)
209
As mentioned earlier, it is important to calculate the occupied space of
210
a tube to investigate its effect on the compactness of the heat exchanger.
211
The space occupied by a tube is the volume of the rectangular prism that
212
circumscribes the tube. However, to make this parameter independent of the
213
tube length, occupied space is defined as the area of the rectangle that cir-
214
cumscribes the cross-section of the tube and is shown as OS. Figure 3 shows
215
the occupied space for circular, AEA, and AF tubes. The occupied space of
216
AF and flattened tubes are the same, as they have identical cross-sections.
217
Based on the aforementioned paragraphs, the geometric properties of
218
the investigated tubes are shown in Table 1. In this table, C and F represent
219
circular and flattened tubes, respectively. For the AF tube, the performance
220
of three different geometries called AF1, AF2, and AF3 are investigated. In
221
Sec. 4, the performance of the AF tube is compared to that of AEA tube.
222
To this end, two different geometries of AEA tube are introduced and called
223
AEA1 and AEA2. All the above mentioned tubes are made of circular copper
224
tubes with an outer diameter of
5 00 , 8
i.e., 15.875 mm, and a thickness of 0.63
14
Figure 3: Occupied space of Circular, AEA, AF tubes.
225
mm.
226
Table 1: Geometric properties of the investigated tubes.
Name C F AEA1 AEA2 AF1 AF2 AF3
B(mm) b(mm) A(mm) a(mm) 15.88 10.00 10.00 12.00 10.00 12.00 10.00
14.62 8.74 8.74 10.74 8.74 10.74 8.74
15.88 19.23 19.23 18.09 19.23 18.09 19.23
227
3. Methodology
228
3.1. Experimental method
14.62 17.97 17.97 16.83 17.97 16.83 17.97
S(mm)
T R(mm)
φ
n
1200.00 940.00 115.00 115.00 115.00 115.00 67.86
0.00 50.00 50.00 50.00 50.00 50.00 50.00
0.00 0.52 0.52 0.36 0.52 0.36 0.52
0 1 5 5 5 5 7
Dh (mm) OS(mm2 ) 14.62 12.67 12.91 11.82 13.63 13.02 13.69
229
Figure 4 shows the experimental setup for this study. In this setup, a
230
gear pump pumps the working fluid to a 4 litre reservoir for precooling. 15
252.17 305.37 369.79 327.24 305.37 287.27 305.37
Figure 4: Experimental setup.
231
Then, the working fluid passes through a shell and tube heat exchanger
232
for cooling and enters the 120 cm test section. The temperature of the
233
working fluid is measured at the inlet and the outlet of the test section using
234
two K-type thermocouples with a range and accuracy of −100 ◦ C to 1370 ◦ C
235
and 0.1 ◦ C respectively. The pressure drop of the working fluid is measured
236
using an Endress Hauser differential pressure transducer with a range and
237
accuracy of 25 Pa to 4 × 106 Pa and 1 Pa respectively. Constant temperature
238
boundary condition is imposed on the wall of the test section using saturated
239
water vapor. To monitor and ensure this boundary condition, 6 K-type
240
thermocouples are mounted on the wall of the tube with equal distances.
241
The saturated water vapor is produced in a 50 litre tank, which is equipped
16
242
with an 8 kW heater. From the heat balance point of view, the heat produced
243
by the 8 kW heater is Qhot and the heat absorbed by the working fluid is
244
Qcold . To maintain the pressure of the 50 litre tank constant and avoid having
245
superheated vapor, holes are made on the wall of the tank. The execs vapor
246
exiting the tank from these holes can be assumed as Qloss . The flow rate is
247
calculated using a 1 litre glass vessel, a drain valve, and a stop watch with an
248
accuracy of 0.01 second. The flow rate is controlled using two adjustable flow
249
control valves that are placed at the exit of the test section and the bypass
250
line.
251
The working fluid used in the mentioned experimental apparatus is the
252
heat transfer oil, whose thermophysical properties in the temperature range of 30◦ to 90◦ are shown in Table 2. Table 2: Thermophysical properties of the heat transfer oil. ◦
T ( C) ρ 30 50 70 90
kg m3
860.23 847.25 834.27 821.29
Cp
kJ kg·K
1.99 2.07 2.15 2.23
κ
W m·K
0.133 0.131 0.131 0.128
ν
m2 s
26.18 27.95 27.95 26.87
253
254
After data acquisition from the experimental apparatus, heat transfer
255
and flow resistance of investigated tubes are calculated using the inlet and
256
outlet temperature of the working fluid. The mean convective heat transfer
17
257
coefficient can be calculated as ˙ p (To − Ti ) ¯ = mC h , As ∆Tm
(4)
258
where m ˙ is the mass flow rate, Cp is the average isobaric specific heat ca-
259
pacity of the working fluid at the inlet and outlet of the test section, As is
260
the heat transfer surface area, Ti and To are the bulk temperatures of the
261
working fluid at the inlet and outlet of the test section respectively, and ∆Tm
262
is the logarithmic mean temperature difference (LMTD).
263
It is common to non-dimensionalize the convective heat transfer coeffi-
264
cient and measured pressure drop in the form of Nusselt number and friction
265
factor respectively. However, both Nusselt number and friction factor are
266
dependent on the hydraulic diameter of the tube. As shown in Table 1, the
267
hydraulic diameters of the investigated tubes are different. Thus, compari-
268
son of Nusselt number and friction factor without consideration of convective
269
heat transfer coefficient and pressure drop is not conclusive.
270
The experimental uncertainties of the studied heat transfer and flow re-
271
sistance parameters are calculated based on Kline et al’s [24] method and
272
presented in Table 3.
273
Results attained by the experimental apparatus of the present study
274
are validated using the analytical convective heat transfer and friction factor
275
correlations for circular tube. The mean Nusselt number is calculated using
276
Hausen correlation for convective heat transfer of laminar flow in circular
18
Table 3: Experimental uncertainties of the calculated parameters.
Parameter
Uncertainty
Re h Nu f
±3.0% ±3.1% ±4.1% ±4.3%
277
tube [25]. The friction factor is calculated using Darcy friction factor corre-
278
lation for laminar flow in circular tube [26].
279
Figures 5 and 6 show comparison of the experimental results for laminar
280
flow in circular tube with the existing analytical correlations. The maximum
281
error observed for heat transfer and flow resistance are 9% and 13%, respec-
282
tively. These errors are similar to the reported errors by Eiamsa-ard et al.
283
[10].
284
285
3.2. Numerical method
286
In this work, a numerical model for the oil flow in the investigated tubes
287
is developed and validated with experimental results. This model is used to
288
facilitate and expedite the investigation of heat transfer and flow resistance
289
for different geometries of the investigated tubes.
290
Fully structured computational grids are generated for the geometries
291
shown in Table 1 using Gambit 2.4.6 [27]. For all investigated tubes, grids
292
with 8,640,000 hexahedral cells and 8,744,871 nodes are generated. The gird
293
independence study is carried out for all the generated grids and the result 19
Figure 5: Validation of the numerical results for Nu number with tube C.
20
Figure 6: Validation of the numerical results for friction factor with tube C.
21
Figure 7: Grid independence study for tube AF1.
294
for tube AF1 and a Reynolds number of 1000 is shown in Fig. 7.
295
Figure 8(a) shows the cross-sectional grid for a flattened segment of AF1.
296
This grid is refined in proximity to the tube wall. Figure 8(b) shows the axial
297
grid in the connection of a flattened segment to two circular segments. The
298
grid is refined in the transition parts to achieve a better accuracy.
299
In the grid generation process, the position of the closest node to the wall
300
of the tube determines the accuracy of velocity and thermal boundary layer
301
estimations. In other words, this distance specifies whether or not the grid
302
is capable of capturing the velocity and thermal boundary layers. For this
303
study, the closest computational node to the wall of the tube is generated
304
within 0.025 mm from the wall. In what follows, it is shown that this distance 22
(a)
(b)
Figure 8: (a) Sectional and (b) axial grids.
305
provides accurate estimations of velocity and thermal boundary layers.
306
To characterize the grid estimation of the velocity boundary layer, a
307
dimensionless wall distance parameter called y + is used, which is defined as
y+ =
u∗ Y , ν
(5)
308
where Y is the distance of the closest computational node from the wall of
309
the tube, ν is the kinematic viscosity of the working fluid, and u∗ is the
310
friction velocity defined as r u∗ =
τw , ρ
(6)
311
where τw is wall shear stress and ρ is the density of the working fluid. In this
312
study enhanced wall treatment estimation was used to model the boundary
313
layer motion of the flow. The value of y + should be less than 1 in order 23
314
for the enhanced wall treatment estimation to capture the velocity boundary
315
layer [28]. Based on preliminary trials, the value of y + is between 0.1 and
316
0.6 for different investigated Reynolds numbers of this study. Thus, it can
317
be claimed that the velocity boundary layer is captured.
318
In addition to the velocity boundary layer, one needs to ensure that the
319
current grid provides an accurate estimation of the thermal boundary layer.
320
To this end, the local convective heat transfer coefficient and Nusselt number
321
are calculated in the middle of each segment of the tubes. Preliminary trials
322
showed that the value of local convective heat transfer coefficient and Nusselt
323
number do not change as the grid is refined. Thus, the grid is capable of
324
capturing the thermal boundary layer as well.
325
The boundary condition at the inlet of the tube is mass flow inlet where
326
the mass flow rate and the temperature of the working fluid are constant.
327
The boundary condition for the outlet of the tube is outflow. Finally, the wall
328
of the tube is a stationary, no slip wall with a known constant temperature.
329
After defining the boundary conditions, the problem can be solved by
330
solving the continuity, momentum, and energy equations in the Cartesian
331
coordinates for an internal fully developed fluid flow. These equations can
332
be formulated as,
333
∂ρ ∂(ρuj ) + = 0, ∂t ∂xj ∂ui ∂ui ∂P ∂ ∂ui ∂uj ρ + ρuj =− +µ + , ∂t ∂xj ∂xi ∂xj ∂xj ∂xi
24
(7)
(8)
334
∂ ρ ∂t
V2 V2 ~ ∂P ui ∂ 2T 2 ∂ui e+ + ρ∇ e + V =− +κ 2 − µ (∇~u) + 2 2 ∂xi ∂xi 3 ∂xi 2 ∂ui ∂ui ∂uj ∂ui 2µ +µ + + ρq˙ ∂xi ∂xj ∂xi ∂xj (9)
335
where xi , xj and ui , uj are position and velocity vectors of the flow in the ith
336
and jth dimensions respectively, t is time, µ is the average dynamic viscosity
337
of the working fluid at the inlet and outlet of the test section, P is pressure,
338
e is internal energy,
339
rate of volumetric heat addition per unit mass [29].
V2 2
is kinematic energy, T is temperature, and q˙ is the
340
These governing equations are solved with Fluent 6.3 [28]. The pressure
341
and velocity terms are discretized with the standard deviation and second
342
order upwind [30] schemes respectively. Then, the pressure based SIMPLEC
343
algorithm [31] couples and solves continuity and momentum equations. After
344
solving the continuity and momentum equations, the energy and turbulence
345
equations, in case the flow is turbulent, are solved in each iteration. It should
346
be mentioned that all simulations are run in parallel with 4 cores on an Intel
347
Core i7 processor with 12GB of RAM. The run time of each simulation is
348
approximately 18 hours.
349
To validate the numerical method, simulation of laminar and turbulent
350
flows with different turbulence models for the proposed tubes are performed.
351
Our trials show that using standard k- turbulence model [32] with a tur-
352
bulence intensity of 0.03 for the AF tubes results in the lowest error when
353
compared to the experimental results. The readers are referred to [28, 32] 25
354
for more details about the standard k- turbulence model. On the other
355
hand, for the flattened tube (F), the lowest error is achieved by modeling
356
the flow as a laminar flow. Generation of turbulent flow in the AF tubes
357
can be justified with the expansion and contraction that occur at each tran-
358
sition section. However, these transition sections do not exist in tube F, and
359
therefore the flow remains laminar. Figures 9 and 10 show comparison of the
360
experimental and numerical Nusselt numbers and friction factors for tubes
361
AF1 and F within a Reynolds range of 500 to 2000. The maximum observed
362
error for the Nusselt number and friction factor of tube AF1 is 19% and
363
15% respectively. Similarly, the maximum error observed for tube F is 13%
364
and 10% respectively. All these errors are less than the errors reported by
365
Eiamsa-ard et al. [10] (i.e., 15% and 20% for Nusselt number and friction
366
factor, respectively) and hence it can be concluded that the numerical model
367
is valid for engineering purposes.
368
369
4. Results and Discussion
370
In this section, heat transfer mechanism of AF tubes is investigated.
371
Then, heat transfer and flow resistance of AF tubes, tube F, and relevant
372
well-studied tubes are compared. Based on this comparison, the impact of
373
changing the geometric properties such as flattening (φ) or segment length
374
(S) on the heat transfer and pressure drop is studied. Finally, performance
375
enhancement of AF tubes for a constant pressure drop and occupied space 26
Figure 9: Comparison of experimental and numerical Nu number for tubes AF1 and F.
27
Figure 10: Comparison of experimental and numerical friction factor for tubes AF1 and F.
28
376
is evaluated and the feasibility of replacing conventional circular tubes with
377
these tubes is investigated.
378
379
4.1. Heat transfer mechanism of AF tube
380
To better understand the heat transfer mechanism in AF tube the local
381
Nusselt number distribution is plotted along the tube length for tube AF1
382
and a Reynolds number of 1000. Figure 11 shows that the transition sections
383
increase the heat transfer rate locally after each circular or flattened segment.
384
The thermal boundary layer that is generated in each segment of an AF tube
385
is destroyed in the transition sections and a larger temperature gradient is
386
created in proximity to the wall of the tube. This local increase does not allow
387
the local Nusselt number to have a behavior similar to the circular tube and
388
hence increases the overall heat transfer rate. The local Nusselt number in
389
circular tube decays rapidly along the tube as the thermal boundary layer
390
develops.
391
In addition to the local Nu number, studying the vorticity magnitude of
392
the flow along the AF tube can give a better understanding about the effect
393
of this geometry on the oil flow. Figure 12 shows the vorticity magnitude of
394
the flow along tube AF1 and for a Reynolds number of 1000. It is shown
395
that the vorticity magnitude is increased in the transition sections due to
396
the effect of expansions and contractions. The increased vorticity improves
397
both local heat transfer rate at the transition sections and the overall heat
29
Figure 11: Local Nu number along tube AF1
30
Figure 12: Vorticity magnitude along the AF1 tube
398
transfer rate of the AF tubes.
399
400
4.2. Heat transfer and flow resistance comparison
401
The heat transfer and flow resistance of AF tubes are first compared to
402
those of tube F. Then, the thermo/hydraulic performance of tube AF1 is
403
compared to those of relevant well-studied geometries. Figure 13 shows the
404
Nusselt number of AF tubes and tube F for different Reynolds numbers.
405
Comparison of the Nusselt number shows that all different geometries of AF
406
tube have a significantly higher heat transfer rate compared to tube F. The
407
transition sections do not exist in tube F and the temperature gradient close
408
to the wall is smaller compared to that of the AF tubes. Thus, AF tubes
409
have higher Nusselt numbers compared to tube F. In addition, it is observed
410
that increasing the Reynolds number results in an increase in the Nusselt
411
number. This increase is significantly larger for AF tubes compared to tube 31
412
F and can be justified with the turbulent flow regime of AF tubes.
413
As mentioned in Sec. 3.1, the difference in the hydraulic diameters of
414
the investigated AF tubes makes the comparison of their Nusselt numbers
415
inconclusive. To address this problem, the convective heat transfer coeffi-
416
cient of AF tubes and tube F are compared in Fig. 14. The comparison of
417
the convective heat transfer coefficient for different geometries of AF tubes
418
shows that AF1 and AF3 have a higher heat transfer rate compared to AF2.
419
This higher value for AF1 and AF3 is a result of having larger flattening
420
(φ) parameters compared to AF2. The Larger φ helps the fluid molecules
421
with lower temperature to be closer to the wall of the tube and increases the
422
temperature gradient near the wall. On the other hand, slightly better heat
423
transfer rate of AF3 compared to AF1 shows that increasing the number of
424
segments (n) can be helpful. A larger n results in having more transition
425
sections, but it reduces the length of the circular and flattened segments.
426
The main goal of having the transition sections is to increase heat transfer
427
rate by destroying the thermal boundary layer generated in either circular or
428
flattened sections of the tube. However, when the segment length becomes
429
shorter, the thermal boundary layer does not have the opportunity to be
430
generated and developed. Thus, as long as the flow has the opportunity to
431
develop a thermal boundary layer, increasing the number of segments (n) in-
432
creases heat transfer rate. However, increasing n ultimately results in a slight
433
increase in heat transfer rate, while the pressure drop increase persists.
434
The comparison of heat transfer in tubes is not sufficient unless flow 32
Figure 13: Nu number of investigated AF tubes and tube F.
33
Figure 14: Convective heat transfer coefficient of investigated AF tubes and tube F.
34
435
resistance comparison is taken into consideration. Figure 15 shows that the
436
friction factor of all investigated AF tubes are higher than that of tube F.
437
This can be justified with the fact that tube F has a laminar flow, while
438
the flow regime in AF tubes is turbulent. In a similar fashion to the heat
439
transfer study, the friction factor comparison is also inconclusive as a result
440
of the different hydraulic diameters of the investigated AF tubes. To make
441
the comparison independent of the hydraulic diameter, the pressure drop of
442
the investigated tubes are compared to each other. Figure 16 compares the
443
pressure drop of AF tubes and tube F for different Reynolds numbers. The
444
pressure drop comparison shows that AF1 and AF3 have a higher pressure
445
drop compared to AF2 due to their larger φ. However, reducing φ in AF2
446
leads to a pressure drop which is close to that of tube F and is significantly
447
lower than the pressure drop of tubes AF1 and AF3. The pressure drop of
448
AF3 is higher than that of AF1 due to having a larger n.
449
To compare the performance of AF tube with other well-studied tubes,
450
dimpled tube with a pitch length of 13.8 mm [33], helically coiled tube with
451
straight wall (HSW) and curvature ratio of 0.031 [34], and helically coiled
452
tube with corrugated wall (HCW) and curvature ratio of 0.031 [34] are con-
453
sidered. Figure 17 and 18 show the Nusselt number and friction factor com-
454
parison of these tubes, respectively. It is shown that AF1 has a higher Nusselt
455
number compared to dimpled tube, HSW tube, and F tube. However, tube
456
HCW shows the best heat transfer rate among the investigated tubes due to
457
its corrugated wall. On the other hand, the flow resistance of tube HCW is 35
Figure 15: Friction factor of investigated AF tubes and tube F.
36
Figure 16: Pressure drop of investigated AF tubes and tube F.
37
Figure 17: Nusselt number comparison of AF1 and relevant well-studied tubes.
458
the highest, which is also a result of wall corrugation. The friction factor of
459
AF1 is close to those of tube HSW and tube F, while the friction factor of
460
the dimpled tube is the lowest.
461
462
4.3. Performance enhancement ratio
463
It was shown in previous paragraphs that changing the geometry of cir-
464
cular and flattened tubes to AF tubes increases both heat transfer rate and
465
pressure drop. The increase of the former is desirable, while the increase of
466
the latter should be minimized. Furthermore, Table 1 shows that the oc-
467
cupied space of the AF and AEA tubes are more than that of the circular 38
Figure 18: Friction factor comparison of AF1 and relevant well-studied tubes.
39
468
tube, which may result in larger heat exchangers. Thus, there is a need for
469
a parameter that takes heat transfer rate, pressure drop, and occupied space
470
into account simultaneously.
471
As shown in Eq. 4, the transferred heat between working fluid and tube
472
wall is a function of convective heat transfer coefficient and logarithmic mean
473
temperature difference (LMTD). Webb’s performance evaluation criterion
474
[11] uses Nusselt number, which is a function of convective heat transfer
475
coefficient, to evaluate heat transfer rate. Hence, this criterion does not con-
476
sider the effect of difference between wall temperature and bulk temperature
477
of working fluid at the inlet and outlet of the tube even though this difference
478
has a direct effect on the heat transfer rate. In addition, Webb’s criterion
479
does not study the occupied space of the investigated tube. In this work,
480
tube performance enhancement ratio (PER) is defined to compare the heat
481
transfer of the investigated tubes to that of circular tube (tube C) within
482
an identical pressure drop and occupied space. To calculate PER, we first
483
need to calculate the effectiveness and the pumping power of the investigated
484
tube. The effectiveness of a tube is the ratio of its actual heat transfer rate
485
to the maximum possible heat transfer, that is
ε≡
q qmax
=
mC ˙ p (To − Ti ) , mC ˙ p (Tw − Ti )
40
(10)
486
where Tw is the constant wall temperature of the tube. The pumping power
487
needed to overcome the pressure drop in a tube can be calculated as ˙ ˙ =m W ∆P. ρ
488
(11)
Thus, the tube performance enhancement ratio (PER) is defined as
P ER =
ε/εC ˙ /W ˙C W
OS/OSC
,
(12)
489
˙ , and OS are the effectiveness, pumping power, and occupied where ε, W
490
˙ C , OSC are the effectiveness, space of the investigated tube. Similarly, εC , W
491
pumping power and occupied space of the corresponding tube C. It should
492
be noted that the flow properties, i.e., mass flow rate, inlet temperature, and
493
working fluid and the boundary conditions, i.e., wall temperature, of both
494
investigated and circular tubes should be the same for calculating PER. A
495
tube is an advantageous replacement for tube C if its PER is more than 1.
496
This means that the investigated tube has a higher heat transfer rate within
497
the same pressure drop and occupied space as tube C.
498
Figure 19 shows comparison of PER for AF tubes and tube F. It is shown
499
that PER for tube F is lower than 1 for all the investigated Reynolds num-
500
bers. In spite of the better heat transfer rate of tube F compared to tube
501
C, the increased pressure drop and occupied space do not allow this tube
502
to be an advantageous replacement for tube C. On the other hand, PER is
41
503
higher than 1 in most of the investigated Reynolds numbers for the AF tubes.
504
Among different geometries of AF tube, AF2 has the best performance and
505
the PER of this tube is higher than 1 for all the studied Reynolds number
506
range. It is shown that the heat transfer rate of tube AF2 can be up to 41%
507
more than that of the conventional circular tube within the same pressure
508
drop and occupied space. Tube AF2 has a lower φ compared to AF1 and
509
AF3; however, its other geometric parameters are the same as tube AF1.
510
The lower φ of AF2 causes lower occupied space, while the heat transfer rate
511
is not reduced to the extent that the pressure drop is reduced; thus, the PER
512
of this tube is higher than those of AF1 and AF3. It is clear that decreasing
513
φ will ultimately result in having a circular tube and there exists an optimal
514
φ for which PER is maximum. The occupied space of tubes AF1 and AF3
515
are identical; however, the PER of AF3 is slightly higher than that of AF1.
516
Tube AF3 has a higher n, which increases both heat transfer and pressure
517
drop. However, in this case, the effect of increasing heat transfer rate is more
518
than that of the pressure drop.
519
To further extend the discussion in the context of tube performance
520
enhancement ratio, the PER of AF tubes are compared to those of the pre-
521
viously studied AEA tubes. As shown in Table 1 and Fig. 1, tubes AEA1
522
and AEA2 are similar to tubes AF1 and AF2 respectively with the difference
523
that their occupied space is larger than that of the AF tubes. Figure 20
524
compares the PER of tubes AEA1 and AEA2 with that of AF1 and AF2 for
525
different Reynolds numbers. The PER of AEA2 is significantly higher than 42
Figure 19: Comparison of PER for investigated AF tubes and tube F.
43
526
that of AEA1 for all the studied Reynolds numbers. The reason is that in a
527
lower occupied space compared to AEA1, AEA2 has a higher heat transfer
528
rate and lower pressure drop [19]. The PER of the AF tubes; however, are
529
higher than those of both AEA tubes. It is shown that the PER of AF1
530
and AF2 are up to 32% and 21% higher than those of AEA1 and AEA2, re-
531
spectively. Compared AEA and AF tubes have identical number of segments
532
(n), while the total flattened length for AEA tubes is longer than that of
533
AF tubes. Thus, the pressure drop caused by this longer flattened length is
534
greater than the heat transfer improvement. Moreover, the occupied space of
535
the AF tubes is lower than that of the AEA tubes. These two factors result
536
in a lower PER for AEA tubes compared to AF tubes.
537
5. Concluding Remarks
538
This work studied heat transfer, flow resistance, and occupied space of
539
a new tube geometry called alternating flattened tube. This tube consists
540
of flattened and circular, i.e., unflattened, segments that are connected to
541
each other using transition sections. Both experimental and numerical stud-
542
ies were carried out with heat transfer oil as the working fluid and for a
543
Reynolds number range of 500 to 2000. The results were evaluated against
544
heat transfer and pressure drop of other well studied tubes. Comparison of
545
experimental and numerical results showed that the expansions and contrac-
546
tions in the geometry of the alternating flattened tube causes a turbulent
547
flow regime within the investigated Reynolds number range, while the flow 44
Figure 20: Comparison of PER for AF1, AF2, AEA1, and AEA2.
45
548
regime in conventional circular and flattened tubes is still laminar.
549
Our study showed that the heat transfer rate of all different geometries of
550
alternating flattened tube is higher than that of the flattened tube. Among
551
these different geometries; however, increasing the flattening of the tube in-
552
creases the heat transfer rate. On the other hand, increasing the number
553
of segments results in having more transition sections, i.e., expansions and
554
contractions, and increases turbulence intensity by reducing the length of
555
circular or flattened segments. Thus, increasing the number of segments in-
556
creases heat transfer rate.
557
The study on the flow resistance of the alternating flattened tube showed
558
that all the different geometries of this tube have higher pressure drop com-
559
pared to the flattened tube, which was expected due to the turbulent flow
560
regime of the alternating flattened tubes. In addition, it was shown that in-
561
creasing flattening and number of segments of the alternating flattened tube
562
increases the pressure drop.
563
After comparing heat transfer and pressure drop separately, simultane-
564
ous comparison of these parameters and the occupied space of the tubes was
565
carried out using a parameter called tube performance enhancement ratio.
566
The advantage of this comparison is that heat transfer rate of alternating
567
flattened tube is evaluated against a circular tube for the same pressure drop
568
and occupied space. Results showed that all the investigated geometries of
569
the alternating flattened tube can be advantageous replacements for circular
570
tubes, as the heat transfer rate of them is up to 41% higher than that of the 46
571
circular tube for the same pressure drop and occupied space. Furthermore,
572
it was observed that there is a specific flattening and number of segments for
573
which the best tube performance enhancement ratio can be achieved.
574
575
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576
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52
Highlights
A new tube geometry called Alternating Flattened tube is introduced. Heat transfer and flow resistance are studied experimentally and numerically. The compactness of the tube is studied by considering its occupied space. Alternating Flattened tube has the best performance among the studied tubes. Alternating Flattened tube can be an advantageous alternative for circular tube.