Experimental investigation of pressure d

There are several studies, experimental or theoretical, on the heat transfer and the pressure drop for laminar and turbulent liquid or gasﬂow in microchannels.. Recently, Ghajar et al.[1

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Experimental investigation of pressure drop and friction factor

S Barlaka, S Yap ıcıa, O.N Sarab,*

a Department of Chemical Engineering, Faculty of Engineering, Atatürk University, 25240 Erzurum, Turkey

b Department of Chemical Engineering, Faculty of Engineering, Çankırı Karatekin University, 18200 Çankırı, Turkey

a r t i c l e i n f o

Article history:

Received 7 May 2010

Received in revised form

16 August 2010

Accepted 17 August 2010

Available online 8 October 2010

Keywords:

Microchannel

Microtube

Pressure drop

Friction factor

Laminar ﬂow

a b s t r a c t

The pressure drop and friction factor for theﬂow distilled water in microtubes with the diameters ranging from 0.20 mm to 0.589 mm were investigated experimentally The experiments were carried out

in the Reynolds number range of approximately 100e10000 and the length-to-diameter ratios (L/d) in the range of 16e265 It was observed that two different mechanisms of transition from laminar to turbulentﬂow occurred as smooth and abrupt The pressure drop and friction factor values agreed with the values of classical channelﬂow theory The L/d ratio had an important effect on the apparent friction factor in case of L/d< 100 It was found that the critical Reynolds number for the transition was between

2000 and 2500

1 Introduction

With development of the microsystem technology, the

investi-gation of theﬂow phenomena in microtube and channels has been

one of the most important subjects There are several studies,

experimental or theoretical, on the heat transfer and the pressure

drop for laminar and turbulent liquid or gasﬂow in microchannels

The reviews of these studies are given by several researchers[1e5]

The effects of the surface roughness, geometry of channel, type of

fluid (gas or liquid, single or two phase), flow rate, surface fluid

interaction, have been the major parameters, which were

consid-ered in the studies on theﬂuid ﬂow in the microchannel In general,

the experimental data have been compared with the conventional

theories, and in many cases contradictory results have been

reported Theﬁrst diversity between studies is that the fact that

there are three different results of the friction factor values; that is,

the results smaller than, higher than and similar to the friction

factor values predicted by classical theory These results have been

reviewed by several researchers[1e4,6] The second is related to

the critical value of Reynolds number at which theﬂow regime

changes from laminar-to-turbulent For the transition from the

laminar to turbulentflow, different Reynolds numbers have been reported for very similar conditions It was also reported very early transition Reynolds numbers such as, in the range of 200e700 for water flowing through rectangular channels having hydraulic diameters of 0.133e0.367 mm [7], and of 300e900 for water flowing in microtubes with the diameters ranging from 0.050 to 0.245 mm [8], and 240 for waterflowing through a rectangular channel with the hydraulic diameter of 0.146 mm[9]

Vijayalakshmi et al [10] investigated the effect of compress-ibility, and the transition to turbulenceﬂow through microchannels

of hydraulic diameter ranging from 0.0605 mm to 0.211 mm, employing nitrogen as the working ﬂuid They reported that the transition to turbulent occurred in the Reynolds number range of

1600e2300 They claimed that the slight decrease in the transition range may be due to the relative roughness or the edge effects of the trapezoidal channel geometry Morini et al [11]studied the laminar to turbulent transition in the fused silica and stainless steel microtubes having the diameters ranging from 0.125 to 0.180 mm, using nitrogen as workingﬂuid They reported that the transitional regime started at the Reynolds numbers around 1800e2000, and the surface roughness had no effect on the hydraulic resistance in the laminar region for a relative roughness lower than 4.4%, taking compressibility into account Lorenzini et al.[12]investigated the ﬂow of nitrogen inside circular microchannels having the diame-ters ranging from 26mm to 508mm with different surface roughness values and L/d ratios in the range of 591e1689

* Corresponding author.

E-mail addresses: onuri@rocketmail.com , onurisara@karatekin.edu.tr (O.N Sara).

Contents lists available atScienceDirect International Journal of Thermal Sciences

j o u rn a l h o m e p a g e : w w w e l s e v i e r c o m / l o c a t e / i j t s

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In macro channelﬂow, the effect of inlet conﬁguration, namely

squared-edged, re-entrant and bell-mouth, of the circular straight

horizontal tube on the transition to turbulence was investigated by

Ghajar and Madon[13]under isothermalﬂow conditions, by Tam

and Ghajar[14]for non-isothermalﬂow conditions They used 316

stainless steel tubes with an inside diameter of 1.58 cm and

length-to-diameter ratio (L/d) of 386 to provide fully developed ﬂow

condition It is reported that the transition occurred in the Reynolds

number range of 1980e2600 for the re-entrant inlet, 2070e2800

for the square-edged inlet and 2125e3200 for the bell-mouth inlet

for isothermal conditions, and it changed depending on heatﬂux in

the case of non-isothermal ﬂow On the other hand, several

investigators remarked the dependence of critical Reynolds

number on the surface roughness and geometry[11,15,16]

In microchannel ﬂow, the ﬂow regime is often in laminar or

transition region, especially, in the case of liquidﬂow Therefore,

the pressure drop and friction factor characteristic of ﬂuid ﬂow

under transition condition is important Recently, Ghajar et al.[17]

performed an experimental investigation for friction factor in the

transition region for waterﬂow in stainless steel minitubes and

microtubes with the diameters in the range of 337mme2083mm They reported that the decrease in the tube diameter and increase

in the relative roughness affected friction factor, even in the laminar ﬂow, and that the Reynolds number range for the transition ﬂow became narrower with decreasing tube diameter It was also reported that when the diameter of the tube changed from

2083 mm to 667 mm, the onset of transition region delayed at Reynolds number from 1500 to 2200

Although there are several studies on pressure drop and friction factor characteristics of the microchannel, because of the diversities between results, it can be said that further investigation is required

in order to verify if the classical correlations can predict friction factor in laminar, transition and turbulent regimes Moreover, in many of the studies, the length-to-diameter ratio of the channel has been selected higher than 100 to provide fully developed condition [11,12] However, in some practical applications such as micro-exchangers, micro-reactors etc, it can be difficult to establish a flow length for hydrodynamically fully developedflow Therefore, the entrance effect, L/d ratio should be taken into account for pressure drop and friction factor characteristics of thefluid flow in micro-tubes In this study, it was aimed to investigate the pressure drop and friction factor of water flowing through microtubes with different diameters and L/d ratios for the cases of laminar, transition and turbulentflow conditions

2 Experimental set up and data reduction Experimental set up adapted from our previous study[18,19]is shown schematically inFig 1 It consists of mainly a high-pressure nitrogen gas tube, a microfilter, a digital balance, a circulated water bath and the test section including micro-tube Theflow to the test section was provided by high-pressure nitrogen gas and theflow rates were adjusted by a two-stage gas regulator Thefluid passed through a microfilter before entering test section and was collected after the test section to be weighed Distilled water was used as working fluid and its temperature was kept at 25 0.2 C by circulated bath Five stainless steal tubes, produced for the purpose

of the medical treatment, with diameter in range of 0.200

mme0.589 mm were used as test channel The geometrical dimensions of the channels used in the experiments are given in Table 1 The dimension of the tubes was measured by N_IKON MM

400 L video measuring microscope The pressure difference in the test section was measured by pressure transmitter (KELLER) in range 0e6 bar 0.5% FS

Nomenclature

d tube diameter (m)

f friction factor ()

K loss coefﬁcient

L tube length (m)

DP pressure drop (Pa)

Re Reynolds number ()

u mean velocity (m s1)

r density (kg m3)

m viscosity (kg m1s1)

Subscripts

app apparent

d developing

m miscellaneous

P

3

1 2

6 7

2 Pressure vessel 7 Fluid collection tank

3 Thermostat 8 Flowmeter

4 G as regulator 9 pressure drop measurement

5 Test tube 10 Pressure measurement

8

1

5 4

10

9

S Barlak et al / International Journal of Thermal Sciences 50 (2011) 361e368 362

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Table 2

Uncertainties of major parameters.

Friction factor 12.92%e19.76% depending on the measured

pressure value

50 100 150 200 250 300

0 300 600 900 1200 1500 1800 2100 2400 2700

Re

A1 A2 A3 A4

50 100 150 200 250

0 1000 2000 3000 4000 5000 6000 7000

Re

C1 C2 C3 C4

a

b

Fig 3 Pressure drop versus Reynolds number.

Table 1

Geometrical and ﬂow characteristic of tested tubes.

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The measured pressure drop,DPt, includes minor loss

contri-butions, DPm, and the net pressure drop in the test tube can be

calculated by:

The minor losses consist of the contributions of the inlet, the

exit and the developingﬂow pressure drops, and can be calculated

by the following equation

where Kiand Keare the loss coefﬁcients for inlet and exit, respec-tively, and can be calculated by using the procedure given in clas-sical textbooks [20,21] In this study, Ki is taken equal to 0.2 calculated by the equation given by[20]while Keis equal 0 because the outlet of the tube is open to the atmosphere K(x) is the incremental pressure drop number due to the entrance region effect, and for the L> Lhyit is called K(N) and is given as 1.20 þ 38/

Re by Chen (1972) for laminarﬂow[21] In the turbulent region, the effect of the entrance region on the pressure drop is relatively lower than that of laminarﬂow and the entrance length is shorter The L/

d ratio required for a fully turbulentﬂow changes in the range of

10e60 [22] For turbulent ﬂow in the hydrodynamic entrance

0.01

0.10

1.00

10.00

Re

A1 A2 A3 A4 64/Re

0.01 0.10 1.00

Re

B1 B2 64/Re Blasius

0.01

0.10

1.00

Re

C1 C2 C3 C4 64/Re Blasius

e

0.01 0.10 1.00

Re

D1 D2 D3 D4 64/Re Blasius

0.01 0.10 1.00

Re

E1 E2 E3 E4 64/Re Blasius

Fig 4 Fully developed friction factor as function of Reynolds number.

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region of a smooth circular duct, the K(x) values are given as

function of (L/d)/Re1/4 by Bhatti and Shah [23] For (L/d)/Re1/

4> 1.067, it reaches a constant value of 0.070

The friction factor is expressed as follow:

f ¼ 2DPnet

The friction factor f, calculated from Eq.(3), refers to fully

devel-oped friction factor The friction factor calculated from Eq.(3)with

usingDPmwithout K(x), called apparent friction factor and denoted

by fapp, which reﬂects pressure drop arising from both momentum

ﬂux during the velocity proﬁle development and the shear stress at

the wall[13] The experimental uncertainties of the parameters were

determined using the method described by Holman[24], and the

uncertainties of the major parameters are given inTable 2

3 Results and discussion Pressure drop measurements were conducted with the tubes having different diameter and length at various ﬂow rates The Reynolds numbers employed in the experiments are given inTable

1 For each tube, the pressure measurement was performed by beginning with the longest tube and then the length of the same tube was shortened mechanically to obtain the other length Therefore, for a tube of any length, the inlet geometry and surface condition remained the same As an example, Fig 2 shows the pictures of the cross-sections of the tubes before and after short-ening for the two different lengths of the tubes A and C InFig 3, the net pressure drop (DPnet), which is determined by Eq.(1), is plotted

as a function of Reynolds number for the tubes A and C As can be seen from thisﬁgure,DPeRe relation is linear for Re < 2000 This behaviour can be clearly seen for tubes having the diameter of

20

40

60

80

100

120

140

160

180

200

0 400 800 1200 1600 2000 2400 2800

Re

A1 A2 A3 A4 64

0 50 100 150 200 250

Re

B1 B2 64 Blasius

0

100

200

300

400

500

0 1000 2000 3000 4000 5000 6000 7000

Re

C1 C2 C3 C4 64 Blasius

0 100 200 300 400 500 600

Re

D1 D2 D3 D4 Blasius 64

0 100 200 300 400 500 600 700

0 2000 4000 6000 8000 10000 12000 14000

Re

E1 E2 E3 E4 64 Blasius

c

e

d

Fig 5 fRe as function of Reynolds number.

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0.20 mm inFig 3(a) This relation shows a non-linear behaviour for

Re> 2000 The power of the Re changes in the range of 1e1.13 for

Re < 2000 (Fig 3(a)), which is close to 1, showing that the

HagenePoiseuille type ﬂow prevails, and for Re > 2000 in the range

of 1.56e2.18 for the other tubes of CeE

The measured pressure values were converted to the fully

developed friction factor values (f) by using Eq.(3) The friction

factor data for all channel conﬁgurations are plotted inFig 4as

a function of Reynolds number, known as Moody diagram To

compare with the experimental data, the friction factor values were

calculated from classical theory of macro channels, by using the

equations of f ¼ 64/Re for fully developed laminar ﬂow, and

f¼ 0.316Re0.25, known as Blasius equation, for fully developed

turbulentflow, which were presented graphically inFig 4.Fig 4(a) shows the experimental data for the tube having 0.20 mm diam-eter As seen from thisfigure, the experimental friction factor values agree with HagenePoiseuille flow The values for Re < 200 are lower than those predicted from 64/Re; however, the deviation is in the range of experimental uncertainty For this tube no distin-guished transition form laminar to turbulentflow was observed at the Reynolds numbers in the range of 100e2300 In the case of the other tubes, namely, BeE, the Reynolds numbers are in the range of

500e10000, as shown fromFig 4(b)e(e) At the Reynolds number greater than about 2000, the deviation from the laminarﬂow was observed, which means the transition from laminar to turbulent ﬂow started To determine the critical Reynolds number at which

0

0.1

0.2

0.3

0.4

0.5

100 600 1100 1600 2100 2600

Re

64/Re Blasius

0.00 0.04 0.08 0.12 0.16 0.20

Re

0.00

0.04

0.08

0.12

0.16

0.20

1000 2000 3000 4000 5000 6000 7000

Re

Blasius

0.00 0.04 0.08 0.12 0.16 0.20 0.24

Re

Blasius

0.00 0.04 0.08 0.12 0.16 0.20 0.24

1000 3000 5000 7000 9000 11000 13000

Re

Blasius

e

Fig 6 Apparent friction factor as function of Reynolds number.

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the transitionﬂow starts, fRe product was plotted as function of the

Reynolds number for all the tested tubes in Fig 5 For the

comparison purpose, the values of fRe predicted from 64/Re for fully

developed laminarﬂow and from Blasius equation for turbulent

ﬂow are also given in this ﬁgure.Fig 5(a) shows the results of the

tube-A As seen from this ﬁgure, fRe products agree with the

theoretical value within the range of the experimental uncertainty

for the investigated Reynolds number in the range of 75e2390 It is

also shown that even at the maximum Reynolds number of 2390

for this tube, theﬂow maintained its laminar ﬂow character; no

transition was observed The experimental results of the tube-B are

shown in Fig 5(b) For the Reynolds numbers in the range of

2000e2500, the fRe value deviated from the behaviour of the

laminarﬂow, and a transition from laminar to turbulent ﬂow was

observed for this tube.Fig 5(c)e(e) shows the fRe relation versus

Re for the other test tubes used in this study, namely C, D and E

From theseﬁgure, at a Reynolds number around 2000, the

occur-rence of the transition can be clearly seen An imported result

pointed out from Figs 4 and 5, the transition from laminar to

turbulentﬂow occurs with two different mechanisms as abrupt

transition for the tube-B and smooth transition for the tubes-CeE

Similar results have been observed by Lorenzi et al.[12]forﬂow

through circular microtubes The fact that for the tube-B the critical

Reynolds number is higher than that for the tubes of C, D and E can

be attributed to the geometry and condition Ghajar and Madon

[13]investigated the effect of the channel inlet geometry on the

transition Reynolds number for three different inlet geometries,

namely re-entrant, square-edged and bell-mouth It was reported

that the critical Reynolds number for bell-mouth was higher than

the other inlet geometries in the range of 2125< Re < 3200 The

inlet geometry of the tubes A and B is closer to the bell-mouth

geometry than that for other tubes This can be the reason that no

transition occurs at Re¼ 2390 for the tube-A Although, for the

circular macro channels, the upper limit of the critical Reynolds

number is undeﬁned; however, for practical applications, the ﬂow

in range of 2300 Re 104is accepted as transitionﬂow[23]

In general, in the studies of the pressure drop and friction factor

in microchannels, higher L/d ratio was selected as emphasized

before The L/d ratio used in this study changes in range of 16e265

To see the entrance length effect on the friction factor, the apparent

friction factor for all tested tubes were plotted as function of the

Reynolds number inFig 6, which reﬂects both the surface friction

and the developingﬂow effects.Fig 6(a) shows the results of the

tube-A having the L/d ratio in the range 105e265 Although the

apparent friction factor values for L/d¼ 105 are slightly higher, no

important effect of the L/d ratio was observed in the investigated range For hydrodynamically developing laminar flow in circular duct, the relation for the hydrodynamic entrance length, Lhy, was given by Bhatti and Shah [23] as Lhy/d ¼ 0.056 Re When this equation is used for the tube-A of the present work, the Lhy/d ratio was found to be in the range of 4e133 depending upon Re, which constitutes as much as % 4e127 of the minimum L/d ratio (¼105) used for the tube-A It is claimed that the effect of the entrance length can be ignored for the L/d value above 300 for laminarflow [25] The results of this study show that the L/d has no important affect on the friction factor fort the L/d ratios in range of 105e265 However, for the other test tubes of BeE, the L/d ratio affects seri-ously the values of the friction factor, as seen fromFig 6(b)e(e) Decreasing L/d increases the friction factor For theflow through macro circular pipes, the fully developed length for turbulentflow was given by the equation of Lhy/d¼1.3590Re1/4[23] For the Rey-nolds number range of 2000e10000, Lhy/d values lay in the range of 8.4e12 fappRe products were plotted versus (L/d)/Re values for

Re> 2000 inFig 7 Since the Reynolds number for theflow in the tube-A remains below this value, thisfigure does not include the results for the tube-A The results calculated from the Blasius equation were also included in this figure for L/d ¼ 80, for comparison

4 Conclusion

An experimental investigation of the water ﬂow through the microtubes made of stainless steel with the diameters ranging from 0.200 to 0.589 mm and the values of the length-to-diameter ratio from 16 to 265 was performed The majorﬁndings obtained from the experimental results can be summarized as follows: It was observed that two different mechanisms of transition from laminar

to turbulentﬂow occurred; smooth and abrupt The pressure drop and friction factor values agreed with the values of classical channel ﬂow theory within the experimental uncertainty The L/d ratio had

an important effect on the apparent friction factor in the case of L/

d< 100 It was found that the critical Reynolds number for the transition was between 2000 and 2500

Acknowledgements This study was funded by (TÜB_ITAK-MAG) under the grant number of 106M304, and their support is gratefully acknowledged References

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Fig 7 f app Re as function (L/d)/Re.

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