durst forced 4101

J. Fluid Mech. (2006), vol. 560, pp. 449464. c 2006 Cambridge University Pressdoi:10.1017/S0022112006000528 Printed in the United Kingdom

449

Forced laminar-to-turbulent transitionof pipe ows

By FRANZ DURST AND BULENT UNSALInstitute of Fluid Mechanics, FriedrichAlexander Universitat Erlangen-Nurnberg,

Cauerstrasse 4, D-91058 Erlangen, Germany

[email protected]

(Received 25 October 2005 and in revised form 14 March 2006)

This paper presents the results of investigations into particular features of laminar-to-turbulent transition of pipe ows. The rst part considers transitional ows thatoccur naturally, i.e. without any forcing, when a critical Reynolds number is reached.Measurements are reported that were carried out to study the intermittent natureof pipe ows before they become fully turbulent. The second part of the paperconcentrates on forced laminar-to-turbulent transition where the forcing was achievedby ring-type obstacles introduced into the ow close to the pipe inlet. The inuenceof the ring height was investigated and the results showed a dependence of thecritical Reynolds number on the normalized height of the disturbances. The laminar-to-turbulent transition was also investigated when caused by partially closing aniris diaphragm that permitted the ow to be forced to turbulence over short timeintervals. Investigations of controlled intermittency became possible in this way andcorresponding results are presented.

1. Introduction, literature and aim of the workAt least since the famous dye experiment of Reynolds (1883), there has been

an overall understanding that uids can ow through pipes in two distinct states,depending on the Reynolds number, Re, of the ow. Below a critical Reynolds number,the ow has the properties of a HagenPoiseuille ow and accidental disturbancesthat enter the ow are rapidly obliterated. The ow is referred to as being laminarand is said to be stable with respect to the introduced disturbances. As the Reynoldsnumber is increased, the ow becomes increasingly sensitive to disturbances and it isobserved that the uid motion becomes irregular in time and space. This state of theow is referred to as turbulent and its irregular motion at every location in the pipeis accompanied by an increase in friction factor, cf (Re). All this is well known andthe overall properties of laminar and turbulent pipe ows can be considered as beingavailable in the uid mechanics literature.

In spite of the good knowledge of laminar and turbulent pipe ows, there arestill a number of open questions regarding details of the two ow states. Most ofthese questions relate to the regime where the ow changes from the laminar tothe turbulent state. Available studies suggest that the ow becomes turbulent at acritical Reynolds number in the range 2000100 000 (e.g. see Schiller 1934; Ekman1883; Pfenniger 1861), depending on the smoothness of the inlet to the pipe ow.However, this general explanation is insucient to explain the wide range of criticalReynolds numbers found in the literature for the occurrence of transitions. No clear

450 F. Durst and B. Unsal

picture exists of what smoothness of the inlet means and how it relates to the criticalReynolds number at which transition occurs, i.e. there is no clear picture of whatcauses the ow to go from the laminar to the turbulent state in pipe ows.

One of the most detailed studies of the laminar-to-turbulent transition of pipeows was carried out by Rotta (1956). He performed hot-wire velocity measurementsthrough a pipe with length-to-diameter ratio L/D = 333 and he was able to keep theair ow rate constant with a specially designed air supply valve, to prevent the ow rateoscillations usually induced by pressure drop changes, at the transitional Reynoldsnumbers. With three dierent inlet congurations, he obtained similar transitionalReynolds numbers. In Rottas case, the ow was intermittent in the range 2000Re3000. Mean velocity proles and intermittency were measured at dierent locationsover the entire pipe length and, in this way, various details of the ow behaviouremerged.

Even more extensive work was carried out by Wygnanski & Champagne (1973),Wygnanski, Sokolov & Friedman (1975) and Rubin, Wygnanski & Haritonidis (1980).They showed the existence of two dierent ow structures during the laminar-to-turbulent transition of the ow, and referred to them as pus and slugs, dependingon their occurrence and dependence on the Reynolds number of the ow. Pus weregenerated in their experiments by large disturbances at the inlet of the pipe and existedfor the range 2000 Re 2700 and slugs were generated by small disturbances forRe 3200. These authors carried out detailed hot-wire velocity measurements in anL/D = 500 pipe test rig, and it was claimed that a constant pressure drop for the airow through the pipe was established for the investigations. The transitional Reynoldsnumber measured in the investigations of Wygnanski and co-workers varied whenthe inlet nozzlepipe conguration was changed or when mechanical disturbanceswere applied at the inlet. They measured mean velocities and turbulence intensitiesby using conditional sampling methods and ensemble averaging techniques to yieldmean ow data. From these measurements, it was concluded that in their interiorow structure slugs had similar characteristics to the corresponding fully developedturbulent ow. The ow structures of the observed pus diered from these typicalcharacteristics of the fully developed state of the turbulent ow. Slugs also showeddenite interfaces at their heads and tails. The length of a slug was of the same orderas the pipe length and in some cases its duration corresponded to a time longer thanthe passage through the pipe length. Pus, on the other hand, did not show a clearinterface at their head, their mean velocities were roughly the same as the mean owvelocity of the pipe ow, the length of pus stayed, on average, constant at a givenReynolds number and their duration was in general shorter than the passage timecorresponding to the pipe length.

In investigations by Darbyshire & Mullin (1995), a constant-mass-ow-rate test rigwas used similar to that of Rotta (1956), but using water as the uid medium.Disturbances were created by water injections with one and with six injectorcongurations at L/D = 70 downstream from the pipe inlet. They observed similarow structures as Wygnanski & Champagne (1973). However, the main aim of theirstudy was not the distinction of dierent ow structures but nding the thresholddisturbance amplitude to initiate transition. They did not observe any turbulentmotion below Re 1760. From their investigations, Darbyshire & Mullin (1995)concluded that the turbulent structures that they observed were independent of thekind of macroscopic disturbances that they applied to the ow.

In more recent studies by Draad, Kuiken & Nieuwstadt (1998) and Hof, Juel& Mullin (2003), investigated the amplitudes of the threshold disturbances yielding

Forced laminar-to-turbulent transition of pipe ows 451

Air at 5 bar

Mass flow ratecontroller

Flow conditioner

Pressure sensors

Pr1

0.03 m 2 m 1 m 2 m10 m 15 mm

brass pipe

2 m 1 m 1 m 0.97 m

Pr2 Pr3 Pr4 Pr5 Pr6 Pr7

Hot-wire probe

Hot-wireanemometer

Oscilloscope

Amplifier

DAQ interface

Figure 1. Schematic representation of the experimental test-rig.

laminar-to-turbulent transition of pipe ows and their dependence on the Reynoldsnumber. In these studies, very similar to those of Darbyshire & Mullin (1995), periodicblowing and sucking through holes in the wall were used to disturb the ow. Thethreshold amplitudes were dened based on the injected mean ow rate. Owing todierences in the experimental details, quantitative agreement with the results ofDarbyshire & Mullin (1995) was not obtained, as discussed by Trefethen et al. (2000).

The present investigations are based on the above-mentioned results of previousinvestigations and can be considered as an extension of the studies by Rotta (1956)and Wygnanski & Champagne (1973). The investigations were preformed with a testrig including a 15 mm diameter brass pipe, with L/D = 667. A mass ow control unitwas applied to generate constant ow rates corresponding to predetermined Reynoldsnumber. Along the pipe and over its entire length, seven pressure transducers wereinstalled, which allowed one to observe the growth and decay of the transitional owstructures. At the exit of the pipe, hot-wire velocity measurements were conducted torecord the state of the ow. In 2, the experimental test rig and the measurementsconducted are described. Section 3 summarizes the measurements conducted undernatural transition conditions. In 4, the results are given for ring-type obstacles atthe pipe inlet. The results for the iris-diaphragm-triggered turbulence are summarizedin 5, and in 6 conclusions and an outlook for future research in this eld arepresented.

2. Test rig and measuring equipmentTo carry out investigations of various aspects of laminar-to-turbulent transitions

of pipe ows, a test rig was set up with the major components shown in gure 1.Its main part consisted of a brass pipe of 15mm diameter and total length 10m,corresponding to L/D =666.7. The ow of air was provided by a high-pressure supplyline connected to a mass ow rate control unit of the type described by Durst et al.(2003). This unit is shown in gure 2, providing information about the theoreticalbackground of the operation of the control valve and of its control electronics. Thisgure provides information on all the essential parts that control the mass ow ratesupplied to the brass pipe test rig to within 1% of the required ow. The entiresystem operates in such a way that pressure changes in the transitional ow regimedo not inuence the mass ow through the pipe.

The ow rate control unit was driven by a pressure supply of 5 bar imposed in itspre-chamber. This generated a ow through a critical nozzle, providing a constant


(a)

(b)

Digital input(parallel port)

Analogue in(0...10v)

Vent off

Calibration

A/D

PH PLTL

PHReTH

U1(x1), T(x1)P(x1), (x1)

THH L

High-pressurechamber

Low-pressurechamber

Valve closed Valve open

D

xRx

R

R2

AB

R

c b

ax

drR sin

sin 2 1 + 2 cos

x2

x1

1 1

+ 1 + 122

m =m = F (PH, TH, , R2, x, )..

Status

Flow rate display

Electronic controllerfor flow ratesupply valve

Flow ratesupplyvalve

Air out0180 1min1

Controlunit

Figure 2. (a) Basic uid ow considerations and relationship for m(x); (b) control circuit,actual mass ow rate controller.

2.0Re = 16980

150201003050002030

(a) (b)

1.6

1.2

0.8

0.4

01.0 0.5 0

r/R Re

U/U

mea

n

u/U

0.5 1.0 0103

102

101

3000 6000 9000 12000 15000 18000

Figure 3. (a) Selected mean velocity proles across the pipe and (b) centreline turbulenceintensity variation with Reynolds number at the pipe exit.

mass ow rate proportional to the nozzle area, as shown in gure 2. Pressure variationsin the pre-chamber of the mass ow rate control unit were recorded and used bythe electronics sketched in gure 2 to ensure that mass ow rate m = constant wasachieved for each set ow rate. Hence the nozzle ow area was set to achieve aconstant Reynolds number by a linear drive, as explained by Durst et al. (2003). Inthis way, the test rig, sketched in gure 1, permitted pipe ow investigations understeady ow conditions.

To provide a well-controlled inlet ow to the pipe, various ow conditioners wereapplied and the nal one chosen was installed. As shown in gure 3, it permitted


the laminar ow regime of the pipe ow to be monitored up to Re 13000. Byrepeating experiments it was shown that the Reynolds number range at which thelaminar-to-turbulent transition occurred was highly repeatable within 2% of theappropriate Reynolds number setting. Typical velocity proles, measured at the exitof the pipe for dierent Reynolds number, are also given in gure 3. For the highestReynolds number, still lying in the laminar regime, the turbulence level of the ow isindicated in gure 3, showing a turbulence level of u/U 0.2%. This turned out tobe suciently small to carry out the investigations described in this paper.

To carry out instantaneous pressure measurements along the pipe, seven pressuretransducers were installed, each with an operating range of 20mbar and 1 kHz timeresolution. The locations of the pressure transducers along the pipe are shown ingure 1 registering the occurrence of laminar or turbulent ow, at that particularlocation along the pipe, of course only with the local resolution given by theselocations. This turned out to be sucient for the laminar-to-turbulent ow transitionalinvestigations described in this paper.

As already mentioned, a hot-wire anemometer set-up was employed at the exit ofthe pipe to carry out local velocity measurements. It included a traversing systemand a single wire probe connected to a DISA 55 M01 constant-temperature hot-wireanemometer. To obtain velocity prole measurements, the vertical motion of thetraversing system was activated and controlled through a PC. All pressure transducerand hot-wire anemometer output was connected to a 16-channel 16-bit 333 kHz dataacquisition card for simultaneous measurements of velocity and corresponding wallpressures. The output ow rate of the mass ow rate controller was also set bythe PC and a special software program ensured that the entire measurements couldbe carried out in a well-controlled manner. Various sub-programs within the dataacquisition system were written to carry out the processing of all data to yield theow and pressure information provided in this paper.

The above-described properties of the ow control unit and the test-rig make itclear that this ow facility is ideally suited to studying transitional ows. Whenturbulent transition occurs in a pipe, the pressure drop changes and the unit, whichthe authors have built for this purpose, automatically adjusts immediately to take thisincreased pressure drop into account to yield a pipe ow with a constant mass owrate. Wygnanski and co-workers had to achieve this by running their test-rig at highpressures so that the pressure changes due to laminar-to-turbulent transition did nothave a big eect on their results.

3. Studies of natural transitionThe test rig (gure 1) represented an ideal test section for studying the naturally

occurring laminar-to-turbulent transition. As mentioned in the previous section, initialexperiments showed that for the nally chosen inlet ow conditioner the laminar-to-turbulent transition took place at a Reynolds number of around 13000. Below thiscritical value, the turbulence intensity, at the centreline of the ow, remained below0.2%, representing the background turbulence of the test facility. With increasingReynolds numbers, the ow became intermittently turbulent, yielding instantaneousvelocity records at the end of the pipe, as indicated in gure 4. The instantaneouscentreline velocity is shown in gure 4 for various Reynolds numbers, Re 12990,indicating the onset of intermittency for Re 13080. The ow was fully turbulent, i.e.intermittency free, for Re 13300. The intermittency of the ow resulted in slug-likedisturbances, as observed by Wygnanski & Champagne (1973) and Wygnanski et al.


28

24

20

U (

m s

1)

U (

m s

1)

16

0 10 20 30

Re = 12990

Re = 13265

40 50 60

28

24

20

16

0 10 20 30Time (s) Time (s) Time (s)

40 50 60

(a)

(d) Re = 13355 (e) Re = 13450 ( f )

28

24

20

16

0 10 20 30

Re = 13080

Return tolaminar state Return to

laminar state

40 50 60

28

24

20

16

0 10 20 30 40 50 60

(b)

28

24

20

16

0 10 20 30

Re = 13170

40 50 60

28

24

20

16

0 10 20 30 40 50 60

(c)

Figure 4. Instantaneous centreline velocity plots around the transitional Reynolds numbersfor natural transition to turbulence.

1.0

0.8

0.6

0.4

Inte

rmit

tenc

y

0.2

011000 12000 13000

Re Re14000

Start of intermittent flow

Re-range ofintermittent flow

15000 16000 11000 12000 13000 14000 15000 16000

101 Velocityovershoot Turbulence intensity

above Recr

Turbulence intensity

below Recr

102u/U

103

Figure 5. Intermittency at the pipe exit and corresponding turbulence intensity as a functionof Reynolds number.

(1975), consisting of time-varying ow periods with jumps from the laminar to theturbulent ow state and vice versa.

From the intermittency function (ratio of total turbulent state duration to overallmeasurement time) of gure 5 and the corresponding turbulent intensities, as a fuctionof Reynolds number, one can see that high turbulent intensity values are measuredowing to high velocity jumps between laminar and turbulent velocity proles asindicated in gure 4(b) and 4(c). The turbulent intensity overshoots shown for theaxial velocity uctuation in gure 5 are due to this jump-like ow behaviour.

These velocity and intermittency measurements permit a good insight into theoverall ow structures that occurred in the Reynolds number range of laminar-to-turbulent transition, although all information was deduced from the velocitymeasurements at the outlet of the pipe. The corresponding pressure measurementsin gure 6(a) show the pressure variation with time in the Reynolds number rangewhen slugs were formed. Figure 6(b) shows the corresponding velocity signal at the


1600

1400

1200

1000

Pre

ssur

e (P

a)

800

600

400

200

042.0

t1 t3

x/D

t2

x/D = 2135

28

24

20

18

42.0 42.5 43.0 43.5 44.0

U (

m s

1)

203336470536603

42.5 43.0Time (s) Time (s)

43.5 44.0

t1

t2

t3

Figure 6. Measured pressure and velocity waveforms of a single slug structure. The pressurewaveforms indicate the travel of a slug structure through the pipe length and the velocitywaveform shows the slug structure at the pipe exit.

end of the pipe. Looking at both time traces permits the following information to bededuced:

(i) The slug ow starts to develop from the inlet of the pipe. It is swept downstreamand lls the pipe as time proceeds. This development occurs within the time periodt1 to t2.

(ii) At time instant t2, the slug front reaches the pipe exit and at this time the sluglength in the pipe is a maximum.

(iii) In the time period from t2 to t3, the slug tail moves through pipe and leavesthe pipe at time instant t3.The combined velocity and pressure information is shown in gure 7. Figure 7(a)shows the r.m.s. values of longitudinal velocity uctuations at the axis of the pipeas a function of Reynolds number. The corresponding local turbulence intensity ispresented in gure 7(b), showing the increase at Re 13000, when the laminar-to-turbulent transition occurs. The overshoot in the r.m.s. velocity uctuations is clearlyvisible, caused by the laminar-to-turbulent and turbulent-to-laminar velocity jumpsthat occur at the beginning and end of the slug-like ows. Thereafter, i.e. for Re 13500, the region of fully developed turbulent pipe ow exists at all times with itswell-known turbulent ow properties.

This ow behaviour is also reected by the friction factor f =2w/( U2) that

corresponds for Re 13000 to the theoretically predicted relationship flam =64/Re,as indicated in gure 7(c). For Re 13500, the experimentally obtained friction factoris described well by the relationship fturb =0.3614/Re

1/4. It is interesting that the peakin the r.m.s. value of the longitudinal velocity uctuation on the axis of the pipe owdoes not result in a corresponding overshoot of the friction factor.

Overall, the experimental results described in this section clearly reveal that theexperimental test facility permitted laminar-to-turbulent pipe ows of air to beinvestigated in a well-controlled manner yielding highly repeatable results. Theseresults showed that the investigated laminar-to-turbulent ow transition apparentlyoccurred as a result of disturbances at the pipe inlet, i.e. transition always started at thepipe inlet. This phenomenon will require further experimental and theoretical studies.However, the results obtained so far are sucient to permit the study of the forcedlaminar-to-turbulent ow transition described in the next two sections. They wereused in the investigations to distinguish between pu-like and slug-like transition


(a)

(c)

(b)101

101

102

103

100

101u

f

u/U

102

1030 3000 6000 9000

Re

Re

Re

fturb

flam

120001500018000 0 3000 6000 9000 1200015000 18000

0 3000 6000 9000 12000 15000 18000103

102

101

100

Figure 7. (a) RMS velocity, (b) turbulence intensity and (c) friction factor change with Refor natural laminar-to-turbulent transition. Velocities were measured at the centreline of thepipe exit. Pressures were measured by the last two transducers.

D d h

t

% Blockage d (mm) h/t

7.5 14.427

14.23013.829

13.416

12.990

12.550

11.619

2.87

3.855.85

7.92

10.05

12.25

16.91

10

15

20

2530

40

Flow direction

D = 15 mm, t = 0.1 mm

Figure 8. Sketch showing the application the ring-type obstacles of diameter d which wereplaced at the exit of the ow conditioner and a table showing the dimensions of the rings withdierent blockage ratios.

to turbulence. The ow structures are so distinctly dierent that a dierentiationbetween pus and slugs represented no problem in all phases of the investigations.

4. Transition forced by ring obstaclesIt is common practice in turbulent pipe ow research to utilize triggering devices up-

stream of the investigated ow to force the ow to become turbulent in a more denedmanner. For turbulent pipe ow, ring-type obstacles of the kind shown in gure 8 arecommonly employed. This encouraged the authors to look at such triggering devicesand to investigate their inuence on the laminar-to-turbulent ow transition in pipes.Various rings were used and were mounted between the ow control unit shown ingure 1 and the inlet of the pipe. To ensure high concentricity of the inner and outerdiameters d and D of the rings, laser cutting and special machining were employed


Turbulent flow regime

Puffs

Slugs

Laminar flow regime

Reup

Relow

Re

14

12

10

8

6

4

2

02000 4000 6000 8000 10000 12000

h* =

hUw

/

Figure 9. The variation of lower (Relow) and upper critical (Reup) Reynolds number withdimensionless ring-height h. The dashed areas correspond to the transitional regime the withslugs and pus were indicated separately with dierent shadings.

to ensure that both diameters to had common centre and also to be accurate within 10 m. Dierent blockage ratios were employed, as indicated in gure 8. For eachblockage ratio, a separate set of investigations was carried out utilizing the velocityand pressure measurement facilities employed for the transition studies described in 3. Hence, the state of the ow in the pipe was deduced from pressure gradientmeasurements and turbulence intensity records at the end of the pipe.

The investigations carried out with dierent obstacles revealed that the criticalReynolds number for the laminar-to-turbulent ow transition decreased withincreasing obstacle height. This is shown in gure 9, providing a summary of thetransitional ow results.

For the ows triggered by obstacles at the pipe inlet, investigations were performedon the critical Reynolds number occurring for each obstacle. The results clearlyshowed, for both the pressure and velocity measurements, that the laminar-to-turbulent transition occurred over a small nite Reynolds number range, indicated byRelow and Reup. Figure 10 shows how extrapolated values of the turbulence intensitymeasurements to the laminar state of the ow, Relow, and to the turbulent state of theow, Reup, were employed to dene the Reynolds number range within which owtransition occurs.

These investigations permit the critical ring obstacle height that is needed to turnthe ow from the laminar to turbulent state to be dened. Dimensional analysissuggests that the normalized height h can be introduced as

h =hU

(4.1)

to characterize the critical height, where h is the obstacle height, U =

w/ the wallfriction velocity of the laminar ow, the kinematic viscosity, Umean the mean velocityof the pipe ow and D the pipe diameter. Utilizing h = f (Re) in gure 9 yields aclear separation between the laminar and turbulent ow regimes of the pipe ow whentriggered by ring-type obstacles. The decrease in the normalized obstacle height with


101

100

101

102

100

101

102

103

103

101

102

103

0 3000 6000 9000 12000 15000 18000

Relow

Relow

Reup

Reup= 4 104 Re

0.772

= 0.2 Re0.154

0%7.5%10%15%20%25%30%40%

0%7.5%10%15%20%25%30%40%

0%7.5%10%15%20%25%30%40%

u

0 3000 6000 9000 12000 15000 18000

0 3000 6000 9000 12000 15000 18000

fturb

flam

f

Re

u/U

Figure 10. Measured r.m.s. velocity, turbulent intensity and friction factor for ring-obstaclesat the pipe exit.

Reynolds number of the ow (abscissa) is clearly seen in gure 9. Furthermore theturbulent structures observed during the intermittent ow Reynolds number dier asthe Reynolds number increases. For intermittent ow Reynolds number below 3000pu-type turbulent structures were observed and for higher Reynolds number slug-type structures. This nding is also indicated in gure 9. Figure 11 shows examplesof centreline time records of pu and slug structures with velocitytime records verysimilar to those observed during the experiments of Wygnanski & Champagne (1973)and Wygnanski et al. (1975). The ow characteristics of these pu and slug structureswill be considered further in the next section.


Uc

(t)

Time

(a) (b)

Time

Figure 11. Centreline velocity time records as examples of (a) pu and (b) slug-typeturbulent structures.

Figure 12. Picture of the electronically controlled iris diaphragm placed at the inlet of thepipe section.

5. Forced transition by the iris-diaphragmThe results presented in 2 made it clear that naturally occurring laminar-to-

turbulent transition occurs in an intermittent way and in these experiments thishappened at a critical Reynolds number of Rec 13000. At this Reynolds numberthe ow in the pipe starts to exist as a sequence of slugs that are produced in anuncontrolled way. Over a small Reynolds number range (see gure 4), the numberof slugs and their individual duration are increased until the fully developed stage ofturbulent pipe ow is reached.

In order to force the ow to show similar intermittent laminar-to-turbulent transi-tion at lower Reynolds number, ring-type obstacles were employed in a sequence ofexperiments as described in 3. Depending on the height of the ring-type obstacles,the critical Reynolds number could be adjusted to be anywhere in the range 2000 Rec 13000. At any adjusted Reynolds number for Rec 3500, the transition againtook place in the form of slugs that occurred in a random manner with uncontrolleddurations. Figure 10 indicates that, in principle, at a length of L/D =666.7, thenaturally occurring and the triggered laminar-to-turbulent transitions show the samecharacteristic ow properties. Hence, ring-type obstacles are eective in controllingow transition in pipe ows, i.e. to x the critical Reynolds number for the laminar-to-turbulent transition of the ow.

To provide even better control of the ow that permits the time of occurrenceof turbulent slugs to be controlled, in addition to their duration, an iris diaphragmwas installed at the inlet of the pipe test section as indicated in gure 12. Using


16 10

8

6

4

2

0

14

12

10

8

250

200

150

100

50

0

0 4 8 12 16 20

Vel

ocit

y (m

s1

)Time neededto pass pipe

length

Time lengthof individual

slug Con

trol

sig

nal (

V)

VelocityControl signal

tL tS

4 8 12 16 20Time (s)

Pre

ssur

e (P

a)

x/D

x/D = 1.93135.27202.6335.93469.27535.93602.6

Figure 13. Centreline velocity and pressure records of periodically generated slug structuresby the application of the iris-diaphragm triggering device.

the results in gure 9 the iris diaphragm could be used to provide conditions forthe laminar-to-turbulent ow transition to occur in the form of slugs and pus atany Reynolds number in the range 2650 Rec 13000. Initial experiments carriedout by opening and closing the iris diaphragm conrmed this. The actual time tobring the iris diaphragm into position to represent a ring-type obstacle, i.e. to providethe required ow triggering, was adjusted to be 10ms. This time turned out to beshort enough to produce intermittently and in a controlled manner pus and slugsin the pipe ow, depending on the setting of the Reynolds number of the ow inaccordance with the results in gure 9. Preliminary studies conrmed that the irisdiaphragm triggering device produced turbulent slugs very similar to those obtainedin the studies described in 3. Figure 13 shows examples of slugs produced in thisway, i.e. it shows corresponding velocity records at the end of the pipe test rig andpressuretime records along the pipe, measured for Re=5176.

The extended test rig, sketched in gure 12, enabled sequences of pus and slugsto be generated at dierent frequencies and with dierent durations. To trigger theseow structures, characteristic for the laminar-to-turbulent ow transition in pipes, the


2.0

1.6

1.2

0.8

0.4

0 1 2 3 4 5103

102

101

100

1.0 1.5 2.0 2.5 3.0 3.5

0.5 1.0 1.5 2.0

4.0

r/R = 0.95r/R = 00.12

(a)

(b)

0.220.320.490.620.750.850.900.950.99

r/R = 00.280.380.480.580.680.780.850.900.950.98

0.750.450

r/R = 0.950.850.680

U/U

mea

n

2.0

1.6

1.2

0.8

0.4

0 0.5 1.0 1.5 2.00

U/U

mea

n

u/U

103

102

101

100

u/U

Time (s)Time (s)

Figure 14. Time-averaged velocity and turbulence intensity proles of (a) a slug structure atRe=5000 and (b) a pu structure at Re=2850.

results in gure 9 were used to provide the appropriate size of the iris diaphragmfor each set of Reynolds number. In this way, the individual ow properties ofpus and slugs could be studied. The same time sequences of pus and slugs couldbe employed to study their phase-averaged mean velocity and turbulence intensityproperties. Quantities of this kind are shown in gure 14, providing the phase-averaged mean velocity as functions of the relative time for both pus and slugs. Thecorresponding turbulence intensity is also shown in gure 14. Information is providedfor various radial locations indicating that both pus and slugs occupy the wholecross-section of the pipe.

The results in gure 14 are examples chosen from a large number of time records ofinstantaneous velocities for pus and slugs. The pu structure presented in gure 14(b)corresponds to Re=2850 and the slug structure in gure 14(a) to Re=5000. One ofthe main dierences between the ow structures of pus and slugs is in the meanvelocity variations of the heads. Pus show a decaying velocity prole in their headwithout the more abrupt velocity variation of the head that is typical for slugs. At thecentre of the pipe, in general pus show higher values of the local, phase-averagedturbulent intensity.

The experimental set-up also permitted the transitional cross-sectional velocityproles to be constructed. These proles are shown in gure 15 for the pu and slugow structures analysed in gure 14.


1.0

0.5

0.5

1.00 0.4 0.8 1.2 1.6 2.0

0

1.0

0.5

0.5

(a) (b)

(c) (d)

1.00 0.5 1.0 1.5 2.0

0.5 1.0 1.5 2.00.5 1.0 1.5 2.0

0

1.0

0.5

0.5

1.00

0

1.0

0.5

0.5

1.00

0

U/Umean U/Umean

rR

rR

t = 1.4 to 1.575 s t = 3.15 to 3.3 s

t = 0.3 to 1 s t = 1 to 2 s

Figure 15. Cross-sectional velocity proles with times corresponding to gure 14: (a) slugat Re=5000, laminar-to-turbulent transition, t=1.41.575 s of gure 14(a); (b) slug at Re =5000, turbulent-to-laminar transition, t=3.153.3 s of gure 14(a); (c) pu at Re=2850,laminar-to-turbulent transition, t=0.31 s of gure 14(b); (d) pu at Re=2850, turbulent-to-laminar transition, t=12 s of gure 14(b).

Further information about the motion of pus and slugs through the pipe couldbe deduced from the pressure records along the pipe. Especially for the slug-likeow structures, it was possible to track their motion because of the high-pressuregradients that they produced. From the pressure records, it was possible to deducetheir ensemble-averaged head and tail velocities, showing that the head velocity of aslug increases during its motion through a pipe. Between the last two pressure sensorsof the test section, the head and tail velocities given in gure 16 were measured andcompared with results obtained by Wygnanski & Champagne (1973) and Lindgren(1969, 1957). This readily suggests that the iris-diaphragm triggering device can beemployed to provide pu- and slug-like ow in a well-controlled manner and so areeasily accessible to detailed experimental investigations.

These investigations make it clear that the iris-diaphragm extension of the test-riglet to a ow facility that permits detailed studies of pus and slugs because theirnatural appearance becomes deterministic, permitting transitional ow studies withhigh repeatability and reliability. Its employment is recommended for future studiesof laminar-to-turbulent transition of pipe ows forced by wall-bounded obstacles.

6. Conclusion, nal remarks and outlookThe laminar-to-turbulent transition in pipe ows occurs in form of slugs that

occurred naturally in the test rig for Rec 13000. To cause slugs to occur at lowerReynolds number, ring-type obstacles were introduced into the pipe wall and at


2.0

1.8

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

2000 4000 6000 8000 10000 12000 14000Re

UHead/Umean

UT

ail/U

mea

n, U

Hea

d/U

mea

n

UTail/Umean

Lindgren (1957)Lindgren (1969)

Wygnanski & Champagne (1975)

Figure 16. Normalized head and tail velocities of slug and pu structures with Reynoldsnumber.

the pipe inlet. Changing the height of the obstacle permitted varying the criticalReynolds number at which the laminar-to-turbulent ow transition occurred throughintermittently appearing slugs. Any Reynolds number in the range 3500 Re 13000could in this way be selected as the critical Reynolds number. The laminar-to-turbulent transition through pus could also be selected in the Reynolds numberrange 2000 Re 3500.

To provide pu- and slug-like ow structures in a more controlled way, the test-rigwas modied with an iris diaphragm. Its closing and opening were controlled bya servo-driver to produce pus and slugs at pre-determined times for pre-selecteddurations. In this way, ensemble-averaged ow properties of pus and slugs could bemeasured and are presented.

The iris diaphragm also permits controlled intermittency experiments where theintermittency factor can be adjusted to have any pre-chosen value between zero andone. In this way, intermittently occurring laminar and turbulent ows can be producedthat are expected to show advantages when applied to heat transfer in pipe ows.

The present work received support from the DFG (Deutsche Forchunggemeinsch-aft), through contract number DU 101/61-1 to produce the mass ow rate controlunit employed in this study. Further support was obtained through internal fundingfrom LSTM-Erlangen. These fundings are gratefully acknowledged.

REFERENCES

Darbyshire, A. G. & Mullin, T. 1995 Transition to turbulence in constant-mass-ux pipe ow.J. Fluid Mech. 289, 83114.

Draad, A. A., Kuiken, G. & Nieuwstadt, F. T. M. 1998 Laminar-turbulent transition in pipe owfor Newtonian and non-Newtonian uids. J. Fluid Mech. 377, 267312.

Durst, F., Heim, U., Unsal, B. & Kullik, G. 2003 Mass ow rate control system for time-dependentlaminar and turbulent ow investigations. Meas. Sci. Technol. 14, 893902.

Ekman, V. W. 1883 On the change from steady to turbulent motion of liquids. Ark. f. Math A 174,112.


Hof, B., Juel, A. A. & Mullin, T. 2003 Scaling of the turbulence transition threshold in a pipe.Phys. Rev. Lett. 91, 244502.

Lindgren, E. R. 1957 Arkiv Fys. 12, 18.

Lindgren, E. R. 1969 Propagation velocity of turbulent slugs and streaks in transition pipe ow.Phys. Fluids 12, 418425.

Pfenniger, W. 1861 Transition in the inlet length of tubes at high Reynolds numbers. In BoundaryLayer and Flow Control (ed. G. V. Lachman), pp. 970980. Pergamon.

Reynolds, O. 1883 An experimental investigation of the circumstances which determine whetherthe motion of water shall be direct of sinuous, and the law of resistance in parallel channels.Phil. Trans. R. Soc. Lond. A 174, 935982.

Rotta, J. 1956 Experimenteller Beitrag zur Entstehung Turbulenter Stromung im Rohr. Ing-Arch.24, 258281.

Rubin, Y., Wygnanski, I. J. & Haritonidis, J. H. 1980 Further observations on transition in pipe.Proc. IUTAM Symp. Stuttgart, FRG, 1979 , pp. 1926. Springer.

Schiller, L. 1934 Neu Berichte zur Turbulenzentwicklung. Z. Angew. Math. Mech. 14, 3642.

Trefethen, L., Chapman, S., Henningson, D., Meseguer, A., Mullin, T. & Nieuwstadt, F. 2000Threshold amplitudes for transition to turbulence in a pipe. http://arXiv.org/abs/physics/0007092.

Wygnanski, I. J. & Champagne, F. H. 1973 On transition in pipe. Part 1. The origin of pus andslugs and the ow in a turbulent slug. J. Fluid Mech. 59, 281351.

Wygnanski, I. J., Sokolov, M. & Friedman, D. 1975 On transition in pipe. Part 2. The equilibriumpu. J. Fluid Mech. 69, 283304.

durst forced 4101

Documents

turbulent pipe ows

laminar tothe turbulent

pipe inlet

acritical reynolds number

intermittent natureof

number of open questions

good knowledge of laminar

particular features