HTD-4 TOC
Proceedings
IMECE’02:
Proceedings
ofof
IMECE2002
International
Mechanical
Engineering
Congress
and
Exposition
ASME International Mechanical Engineering Congress & Exposition
November 17-22, 2002 New Orleans, LA
November 17–22, 2002, New Orleans, Louisiana
IMECE2002-39573
IMECE2002-34573
EFFECT OF ENTRANCE CONDITION ON FRICTIONAL LOSSES AND TRANSITION TO
TURBULENCE
Levi A. Campbell
Satish G. Kandlikar
[email protected]
Mechanical Engineering Department
Rochester Institute of Technology
Rochester, NY 14623
ABSTRACT
In studying the fluid flow and heat transfer in
microchannels, various claims have been made regarding
transition at Reynolds numbers significantly below 2300. As a
first step in identifying the reasons for such early transition, the
effect of entrance geometry on the pressure drop and transition
to turbulence is studied experimentally in a conventional
channel of 1.9 cm inner diameter. Four types of entrance
conditions have been studied with flow of oil in a closed loop.
The experimental results show the effect of entrance conditions
on local friction factor, hydrodynamic developing length, and
transition Reynolds number. The study will be extended to
microchannels in the future.
Keywords: entrance length, pipe flow, transition, laminar,
turbulent.
INTRODUCTION
The effect of four different entrance conditions on laminar
to turbulent transition and entrance length is the main focus of
the present work. In determining the hydrodynamic entry
region length, the following form of equation is widely used.
x fd ,h
Dh
= C fd Re
(1)
where xfd,h is the hydrodynamic entry region length, Dh is the
hydraulic diameter, and Re is the Reynolds number based on
the channel diameter. Cfd is the constant, which is determined
through experiments. Langhaar [1] recommends a value of
0.05, while Schiller [2] found it to be 0.0288.
Similar studies conducted with the rectangular channels
showed a substantial dependence of the entrance region on the
aspect ratio, but little effect on the type of entrance condition,
smooth or abrupt inlet. Hartnett et al. [3] found that in the
laminar region, the constant Cfd varied with aspect ratio as
follows:
Table 1. Effect of Aspect Ratio on the Entrance Length
Aspect ratio
Entrance
Csf
Rec
10:1
Smooth
0.033
4400
10:1
Abrupt
2500
5:1
Smooth
0.046
7000
5:1
Abrupt
2500
1:1
Smooth
0.057
4300
1:1
Abrupt
2200
Another fact noted by Hartnett et al. [3] was the notable scatter
in the pressure gradient data in the Reynolds number range
between 2000 and 4000.
NOMENCLATURE
Cfd : Constant related to hydrodynamic entrance length
Dh: Hydraulic diameter, m
fapp: apparent friction factor
ffd: fully developed fanning friction factor (ffd=16/Re)
K(x): incremental pressure drop defect
K (∞ ) : Hagenbach’s factor
p0: entrance pressure, Pa
p: pressure at any point x, Pa
Re: Reynolds number
Rec: Critical Reynolds number
rh: hydraulic radius (Dh/4), m
um: mean velocity, m/s
1
Copyright © 2002 by ASME
OBJECTIVES OF THE PRESENT WORK
The present work is aimed at obtaining experimental data
showing the effect of the entrance condition on the entrance
length, pressure gradient variation in the entry region, and the
laminar to turbulent transition for flow in a circular pipe. Two
inlet configurations are incorporated – an abrupt entry, and a
smooth conical section attached to the pipe at the inlet. In
addition, the effect of a turbulator placed at the throat in the
inlet section is also investigated. The turbulator introduces
severe flow disturbance at the inlet.
EXPERIMENTAL SETUP
Entrance cone
Turbulator
Pressure Gages
recording the static pressure at each of the 19 pressure taps
along the length of the pipe.
RESULTS
The data were reduced by first plotting static gage pressure
drop along the pipe for each inlet condition and the theoretical
pressure drop based on the fully developed fanning friction
factor against the distance traveled along the pipe normalized
by the pipe diameter. One plot was constructed for each of the
Reynolds number considered. Figure 2 is an example
representative of these plots. It is evident from Figure 2 that the
entrance conditions have a significant effect on the static
pressure at each location.
Next, the data were plotted as apparent friction factor
quantities multiplied by Reynolds number plotted against a
non-dimensional distance from the inlet, x+. The following
relationships were used, as described in Kakac et al. [4].
∆p* =
Tank
x+ =
Pump Reservoir Scale
Figure 1 Schematic of the Test Setup
The pipe flow facility consisted of a pump, stagnation
chamber, test section, reservoir and scale. The stagnation
chamber could be removed to install different entrance cones.
For the experiments described here, a flow smoothing cone and
a re-entrant bare pipe were used. Just downstream of the
stagnation chamber there was a bar-type turbulator that could
be engaged or disengaged. The length of the test section was
instrumented with 19 pressure gages. Mass flow rates were
measured by use of the scale. The momentum of the flow
exiting the pipe was absorbed by placing a splashing plate (not
shown) to eliminate its effect on the scale measurements.
The relevant test section parameters are listed below:
Table 2. Test Section Details
D
Overall Length
0.01905 m
5.7912 m
The fluid used in the experiments was a Mobil Velocite™
oil with the following properties corresponding to the test
temperature of 24°C:
Table 3. Fluid Properties
µ
ρ
9.4x10-6 m2/s
855 kg/m3
EXPERIMENTAL PROCEDURE
First, a suitable pump power setting was chosen depending
on the desired flow rate. Once the oil had begun to flow
steadily through the entire system, the scale was zeroed and set
for a high weight. A valve between the tank and reservoir was
closed so that the tank would begin to fill with oil. The time
required for the tank to fill to the chosen weight and the chosen
weight were recorded to determine the mass flow rate of oil.
Experiments then proceeded by noting the inlet condition and
p0 − p
x
= f app
2
ρum 2
rh
(
)
x Dh
Re
(2)
(3)
C fd = x +fd
(4)
Figure 3 shows a plot of the apparent friction factor (which
includes the entrance effect) multiplied by Reynolds number
plotted against the non-dimensional entrance length. It shows
that the product fRe approaches a constant value as x+ increases
for the smooth conical entrance flow with no turbulator for
different values of Reynolds numbers as expected. The actual
value of the last few points on this curve was approximately
fRe =19. The steep slope of friction factor times Reynolds
number at small values of x+ indicates the strong influence of
entrance effects up to a x+ of nearly 0.05 which was predicted
by previous work. Similar plots were constructed for each
entrance condition with the following results: for smooth
conical entrance flow with the turbulator, fRe =19, for abrupt
entrance without turbulator, fRe =19, and for the abrupt
entrance with the turbulator, fRe =19.5. The apparent friction
factor times Reynolds number, then, approached the theoretical
laminar and fully developed value in each case, offset by an
amount attributable to the entrance effect.
To study the effect of the entrance condition only, rather
than the cumulative effects of the entrance and shear in the
fully developed flow, an incremental pressure drop defect,
K(x), was studied.
K ( x ) = ( f app − f fd ) x
rh
(5)
For developing laminar flow, K(x) would approach a
constant value, K (∞ ) , or Hagenbach’s factor. For fully
turbulent flows, however, the incremental pressure drop defect
would be expected to increase throughout the length of the
pipe. Since the incremental pressure drop defect for developing
laminar flows is caused by the entrance condition only, it could
2
Copyright © 2002 by ASME
Re=1603 Pressure Drop Along Pipe Axis
20
Static Gage pressure (kPa)
18
16
14
12
10
8
6
4
2
0
0
50
100
150
200
250
300
X/D distance from inlet (m/m)
No Disturbance
Turbulator
f=64/Re
Re-entrant
Reentrant & Turbulator
Figure 2: Pressure drop along the pipe length versus non-dimensional distance from the inlet at a Reynolds number of 1603
f_app*Re vs x+ , Flow Straightener and no Turbulator
200
180
160
f_app*Re
140
120
100
80
60
40
20
0
0.00
0.05
Re 3353
Re 1443
Re 2435
Re 1215
Re 2272
0.10
x+
Re 2098
0.15
Re 2005
Re 1874
0.20
Re 1739
Re 1603
Figure 3: Apparent friction factor multiplied by Reynolds number versus non-dimensional distance from the inlet for smooth
conical entrance flow with no turbulator
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Copyright © 2002 by ASME
be expected that different entrance conditions would produce
different values for Hagenbach’s factor.
Figure 4 shows that the incremental pressure drop defect
does not approach a constant value for any but the smooth
conical entry flow with no turbulator, indicating fully turbulent
flow for all but this condition. It is interesting to note that for a
Reynolds number of 3353, the laminar flow was reestablished
for the smooth conical entry flow with no turbulator. This
behavior is in agreement with the well-established flow
behavior in the transition region. Note that the incremental
pressure drop defect for the smooth conical entrance with no
turbulator case was nearly constant by a non-dimensional
distance from the inlet of 0.05.
K(x) vs x+ for Re=2272
12
11
10
K(x)
9
8
7
6
5
4
3
2
1
0
0.00
0.01
0.02
0.03
0.04
0.05
K(x) vs x+ for Re=3353
Straightened and Smooth
11
10
9
8
K(x)
0.07
0.08
0.09
0.10
Straightened and Turbulator
Reentrant and Smooth
Reentrant and Turbulator
Figure 6: Incremental pressure drop defect versus nondimensional distance from the inlet for all entrance
conditions and a Reynolds number of 2272
12
7
6
5
4
3
2
1
0
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
x+
Straightened and Smooth
Straightened and Turbulator
Reentrant and Smooth
Figure 6 shows that for a Reynolds number less than 2300,
both inlet conditions without the turbulator show laminar
tendencies by approaching a constant pressure drop defect
value. Although the flows disturbed by the turbulator appear to
continue to accumulate pressure drop defect, the Reynolds
number is very near 2300, indicating a transitional flow. The
flows without the turbulator become fully developed by a nondimensional distance of 0.05.
Reentrant and Turbulator
K(x) vs x+ for Re=2098
Figure 4: Incremental pressure drop defect versus nondimensional distance from the inlet for all entrance
conditions and a Reynolds number of 3353
12
11
10
K(x) vs x+ for Re=2435
9
8
11
7
K(x)
12
10
K(x)
0.06
x+
6
9
5
8
4
7
3
6
2
5
1
4
0
3
0.00
2
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.11
x+
1
0
Straightened and Smooth
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
x+
Straightened and Smooth
Straightened and Turbulator
Reentrant and Smooth
Reentrant and Turbulator
Figure 5: Incremental pressure drop defect versus nondimensional distance from the inlet for all entrance
conditions and a Reynolds number of 2435
Figure 5 shows the incremental pressure drop defect plotted
against the entrance length for four different conditions at a
Reynolds number of 2435. Again it is clear that the smooth
conical entry with no turbulator entrance conditions yielded a
laminar flow while every other condition yielded turbulent flow
as seen by the increase in K(x) along the length. The smooth
conical entrance with no turbulator case still yields a fully
developed laminar flow near the non-dimensional distance of
0.05.
Straightened and Turbulator
Reentrant and Smooth
Reentrant and Turbulator
Figure 7: Incremental pressure drop defect versus nondimensional distance from the inlet for all entrance
conditions and a Reynolds number of 2098
Figure 7 shows that for each entrance condition without a
turbulator, the incremental pressure drop defect approaches a
constant value. The entrances involving the turbulator show a
small accumulation of pressure drop defect throughout the
length of the pipe, indicating transitional flow. Notice also a
nearly constant incremental pressure drop defect for the flows
with no turbulator past a non-dimensional distance from the
inlet of 0.05.
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Table 4. Effect of Entrance Condition on Flow
Re
Smooth
ReSmooth
Conical
entrant
Conical
Entrance
and
Turbulator
3353
L
T
T
2435
L
T
T
2272
L
T
I
2098
L
L
I
2008
L
L
I
1874
L
L
L
K(x) vs x+ for Re=2005
12
11
10
9
8
K(x)
7
6
5
4
3
2
1
0
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.11
0.12
x+
Straightened and Smooth
Straightened and Turbulator
Reentrant and Smooth
Reentrant and Turbulator
Figure 8: Incremental pressure drop defect versus nondimensional distance from the inlet for all entrance
conditions and a Reynolds number of 2005
T
T
I
I
I
L
CONCLUSIONS
An experimental study is conducted to study the entrance
region effect and the laminar-turbulent transition in a 1.9 cm
inner diameter with the flow of oil. The study is aimed at
developing a baseline validating the established transition
criteria before undertaking the similar studies for
microchannels.
The following conclusions are drawn from the present work:
Figure 8 shows fully developed laminar flow for all entrance
conditions without a turbulator reached by an x+ of 0.05 and
very small pressure drop defect accumulations for the flows
with the turbulator. For any Reynolds number lower than 2005,
it is expected that fully developed laminar flow would result for
each of these entrance conditions.
1. For a Reynolds number of 3300, a smooth conical
entrance yields laminar flow although all other entrance
conditions result in turbulent flow.
2. Laminar flow is re-established after a flow disturbance
for flows with Reynolds numbers below about 2300 for
entrances that did not include a turbulator.
K(x) vs x+ for Re=1874
12
3. Entrance conditions that included a turbulator exhibited
transition behavior at Reynolds numbers between 1874 and
2272.
11
10
9
8
K(x)
Re-entrant
and
Turbulator
7
4. The pressure drop defect and its variation with entrance
length depend on the type of the flow disturbance and the
entrance condition.
6
5
4
3
2
5. Below a Reynolds number of 1874, no effect on the
transition to turbulence by the entrance condition was seen.
1
0
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.11
0.12
x+
Straightened and Smooth
Straightened and Turbulator
Reentrant and Smooth
6. The established hydrodynamic entrance length of
x+=0.05 given by Langhaar [1] was valid for this range of
experiments.
Reentrant and Turbulator
Figure 9: Incremental pressure drop defect versus nondimensional distance from the inlet for all entrance
conditions and a Reynolds number of 1874
Figure 9 shows the results for a Reynolds number of 1874.
For this case, it is clearly seen that a laminar condition is
established for all entry conditions. Each final value of
Hagenbach’s factor is different, as would be expected for
different entrance conditions.
In Table 4, a summary of the entrance conditions and the
associated observed behavior is presented. The following
symbols are used: L; laminar flow, T; turbulent flow, and I; an
intermediate behavior.
7. There is evidence that for severely disturbed entrance
conditions a transitional flow may exist in the entire
channel for Reynolds numbers from 2008-2272.
In extending the study to microchannels, the effect of
different inlet conditions and their effect on pressure drop
defect and laminar-turbulent transition should be carefully
evaluated.
REFERENCES
1. Langhaar, H. L., Journal of Applied Mechanics, Vol. 64, A55, 1942.
2. Schiller, L., “Investigation on Laminar and Turbulent Flow,”
(German), Zeitschrift Angewandte Mathematik und Mechanik,
Vol. 2, 1922, p. 96.
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Copyright © 2002 by ASME
3. Hartnett, J.P., Koh, J.C.Y., and McComas, S.T., 1962, “A
Comparison of Predicted and Measured Friction Factors for
Turbulent Flow Through Rectangular Ducts,” Journal of Heat
Transfer, Vol. 84, pp. 82-88.
4. Kakac, S., Shah, R.K., and Aung, W., 1987, Handbook of
Single-Phase Convective Heat Transfer, John Wiley and Sons,
New York.
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