The near-field characteristics of circular jets at low Reynolds numbers

Pergamon

Mechanics Research Conununicatious, Vol. 23, No. 3, pp. 313-324, 1996 Copyright O 1996 Elsevier Science Ltd Printed in the USA. All fights reserved 0093-6413/96 $12.00 + .00

Pn s e ~ 3 - c , 4 1 3 ( 9 ~ . s - 6 THE NEAR-FIELD CHARACTERISTICS OF CIRCULAR JETS AT LOW REYNOLDS NUMBERS

A. A. Abdel-Rahman, S. F. AI-Fahed and W. Chakroun Center of Research for Experimental Thermal Sciences (CRETS), Mechanical & Industrial Engineering Department, Kuwait University, KU-WAIT (Received 11 August 1995; acceptedfor print 22 February 1996)

Abstract

An experimental study has been undertaken to investigate the effect of Reynolds number on the near-field region of circular turbulent air jets. Measurements were made using a twocomponent Laser Doppler Anemometer, and included mean velocity, turbulence intensity, skewness factor, flatness factors and power spectrum. Measurements were taken up to 10 nozzle exit diameter in the downstream direction for different exit Reynolds numbers in the range of 1400 to 20000. The Reynolds number was found to have a strong effect on the jet flow behavior in the near-field region; the centerline velocity decays faster (decay constant = 6.11 for Re = 19400, = 1.35 for Re = 1430) and the potential core gets shorter with decreasing Reynolds number. Profile measurements of the skewness and flatness factors indicate that the jet flow becomes more intermittent with decreasing Reynolds number. Power spectrum measurements of the streamwise fluctuating velocities reflects the high energy content of the high Reynolds number jet. It also reveals that there is greater energy at the higher frequencies with increasing Reynolds number.

Introduction

A review of the numerous published work on turbulent jets reveals that the discharge Reynolds number, in most of the cases, has been relatively high, usually above 10000 [1-7]. However, there appears to be a few studies available on low Reynolds number jet. The documented publications on jet flows seem to agree that if the Reynolds number at the jet exit is greater than a few thousand, the radial spread of the mean velocity field and the decay of the mean centerline velocity in the downstream direction are independent of Reynolds number, Re. Further, if Re is less than 30, the jet is laminar, normally called "dissipated laminar jet" [8] and [9]. According to the work of [8] and [9], for Re greater than 500, the jet has a laminar length after which it becomes turbulent. This laminar length decreases with increasing Re. For Re greater than about 2000, the jet becomes turbulent very close to the exit, with the spread of the jet becoming constant; having a value of 0.08 [7]. This value, tuned to 0.086, was recommended later by Chen and Rodi [10]. The mean flow in the near-field (up to 10 nozzle exit diameters) of round jets at two moderate Reynolds numbers; 13000 and 22000 have been studied by Obot et al. [3], where the main 313

314

A.A. ABDEL-RAHMAN,S.F. AL-FAHEDand W. CHAKROUN

objective was to investigate the effect of the nozzle geometry, rather than exit Reynolds number, on the jet behavior. However, it was reported that entrainment for each nozzle studied was found independent of the exit Reynolds number. This is in agreement with Ricou and Spalding [I 1] where it was shown that the entrainment coefficient decreases with Reynolds number up to a Reynolds number of 10,000 beyond which the entrainment coefficient takes a constant value. It is to be noted here that the same conclusion on the entrainment by the jet flow, but for the plane (slot) jet was made by Subramanian and Makhijani [12]. Oosthuizen [ 13] has undertaken an experimental study on isothermal jets, having a wide range of exit Reynolds numbers (Re = 1500 to 15000). Significant variations of all measured quantities at Reynolds number of 5000 and lower have been reported. The decay ofcenterline velocity and radial spread of velocity field were shown to increase as Reynolds number decreases. Rajaratnam and Flint - Petersen [14] investigated the variation of the spread rate of circular jets with Reynolds number. They found that the spread rate decreases continuously with Reynolds number, reaching an asymptotic value of 0.16 at Re = 10,000. Apparently, the asymptotic spread rate value of 0.16 obtained by the authors is higher than that for a high Reynolds number jet (= 0.09). The reason for this difference is not clear, as already pointed out by the authors. Sami et al. [6] have investigated experimentally the turbulent structure in the developing region, up to 10 nozzle exit diameters, of an air jet issuing from a short nozzle, but for a relatively high Reynolds number of 22 x 104. They measured all turbulent and mean flow quantities. They have found that the maximum turbulent intensity occur for the station of x/d=6; approximately at the end of the potential core. Albertson et al. [7] have derived analytical expressions for the mean flow characteristics of slot and round jets. They have also presented experimental data which justified their analytical work. The Reynolds number in their study was high (ranged between 2.2 x 104 and 5.3 x 104 ). They have reported a velocity decay constant of 6.2 along the jet axis for the jet developing region. This pioneer value is still the most reliable and recommended value [10]. Lemieux and Oosthuizen [15] and Outgan and Namer [16] have carried out two similar experimental studies on the low Reynolds number jet, but for the plane case. Both studies have reported variations in all measured jet quantities, albeit not monotonic, with Reynolds number. The asymptotic behavior of the jet flow was reached at Reynolds number of~ 6000. Due to the very little studies reported on the low Reynolds number range, particularly for round jets, it is felt that more understanding of low Reynolds number circular jets are still needed. This could lead to a greater understanding of turbulent shear flows in general and expand the data base on low Reynolds number circular jets in particular. For this reason, the present experimental work is undertaken to study the mean flow and some turbulent characteristics of circular turbulent air jets in the near-field region, having discharge Reynolds number between 1400 and 19400. Test Facility and Procedure The air flow system is designed carefully to deliver a flow of uniform velocity and low turbulence intensity at the nozzle exit. The discharge air velocity through the nozzle ranges

LOW REYNOLDSNUMBERCIRCULARJETS

315

from 1 m/s to 40 m/s. These velocities correspond to a Reynolds number (Re), based on the nozzle exit diameter (Uod/v), of 1300 to about 51000. A centrifugal fan with 3000 rev/min. is the prime mover of the air.

The belt driven fan operates by a 0.75 kW dc. thryristor

controlled motor and is provided by a forward curved impeller. The discharge air velocity at the nozzle exit is set using a manually adjusted potentiometer.

Air exiting the fan enters a 20 cm long duct with a nominal diameter of 10 cm The duct is connected by a flange to the fan housing. After the 20 cm long duct, the air passes though a linen cloth filter and then through an aluminum flow straighteners.

After the flow

straighteners, the air passes through three screen meshes that have three different open-area ratios of 0.6, 0.5 and 0.4 respectively.

Following the screens, the air enters the jet-flow nozzle. The nozzle is machined out of a cylindrical block of aluminum using the CNC machine, and was designed, according to a cosine curve, to have a contraction ratio of 5:1, an exit diameter of 2 cm and a straight neck of 4 cm long. The design of the nozzle insures that the exit turbulence intensity is low (nominally 1% for all exit velocities) and that the wall boundary layer at the exit is laminar. The nature of the wall boundary layer was indicated by profile measurements of the mean velocity and turbulence intensity at the nozzle exit. The geometric axis of the jet was carefully aligned to the vertical and the axisymmetry of the jet was checked by making preliminary measurements of the mean velocity profiles with a Pitot tube connected to an electronic micromanometer. Care was taken to avoid any possible influence of the laboratory draughts on the jet. A sketch of the test facility is shown in Figure 1. A 300 mW Argon-Ion 2-component LDA (Dantec) system was used in backward scatter mode and generated green (514.5 nm wavelength) and blue (488 nm wavelength) colors. Each color is used to measure one component of the velocity. Two-component optics with COLORBURST fiber optics capabilities is used to transmit and receive the light beams. The receiving optics are used to separate the scattered light by wavelength using color filters and color separators, it converts the light energy to electrical signals using photo multipliers, and finally to provide frequency mixing capabilities for flow reversal measurements using electronic down mixers. The third component of the system is the 400.7 mm focal length fiber optic probe to couple the laser beam from the transmitter to the optical fibers and to ensure an optimum beam intersection in the receiving focus (measuring volume). The measuring volume

316

A.A. ABDEL-RAHMAN, S.F. AL-FAHED and W. CHAKRO[~N

formed by the vertical and horizontal pairs of laser beams is an ellipsoid of minor axes of about 116 ~tm and major axis of about 2.44 mm. In the experiment arrangement, the minor axes were parallel to the vertical streamwise (x) and horizontal radial (r) measurement directions and, consequently, the major axis was perpendicular to the measurement plane. Finally is the signal processor and the data analysis software.

The 58N40 flow velocity

analyzer signal processor is used to extract velocity information after the signal exits the receiving optics.

FLOware, a graphics-oriented software, is used to control the experiment,

acquire and process the data and calculate the required statistical quantities of the flow. FVA PROCESSOR COMPUTER WITH

POWER SUPPLY

FIBER MANIPULATOR COLOUR-SEPARATOR

PHOTOMULTIPLIERS

rPROBE LASER

BEAMS JET F L O W

BENCH

AROON ION LASER EMITTER

TRANSMITTER BOX

~

~ TRAVERSING MECHANISM -

3D CONTROLLER

FAN

FIG. 1 Test facility

The fiber-optic probe is mounted on a 3-D traversing mechanism of 10 ~tm traverse resolution and maximum travels of 590, 590 and 680 mm in the x, y and z directions respectively. The connection to the computer is via an RS232 serial line, where the movements are controlled by the keyboard of the PC, or by the application software program.

The source for the signal of the LDA system are the seeding particles. Smoke generator using Shell Onida Oil is used to seed the room. In order to provide uniform spatial seeding for the measurements, the room was seeded and filled with smoke prior to the test and the blower

LOW REYNOLDS NUMBER CIRCULAR JETS

317

was used to distribute the particles uniformly. The smoke generator was then turned off before collecting the data. While the concentration of the particles diminished slowly during the measurements, their distribution remained nearly spatially uniform. Further, to avoid the problem of bias due to the fact that the sampling rate of the LDA system fluctuates in time, the residence time weighting technique was used to process the data [17]. However, The overall uncertainty of the measurement was estimated to lie in the range of 1% to 2 % depending on the local flow conditions.

In the present study, three groups of measurements have been made. In the first group, axial measurements of the mean streamwise velocity, turbulence intensity, skewness factor and flatness factor were made up to 10 nozzle-exit diameters (10d) in the streamwise direction, x. The measurements were repeated for four exit Reynolds numbers of 1430, 2790, 5190 and 19400.

In the second group, radial-profile measurements of the same quantities were made at

two downstream stations of x/d = 6 and 8, and for two exit Reynolds numbers of 3000 and 4800.

The third group included spectral measurements of the streamwise fluctuating velocity

at the jet centerline for x/d = 2, 4 and 6.

These measurements were performed for four

different exit Reynolds numbers of 3000, 5305, 8000 and 26700. In all experiments, the jet exit velocity was monitored with a micromanometer and was found to be constant at its set value within _ 1%.

The sampling time during measurements was in the range of 100 to 150 seconds, depending on the flow velocity at the measurement point. The mean data rate varied from 25 Hz to 60 Hz, except for the data acquired for the spectral calculations. During spectrum measurements, the mean data rate was in the range of 6 to 7.5 kHz, depending on the local flow velocity and the measurement location inside the jet flow. A direct Fast Fourier Transform (FFT) was used to obtain the power spectrum from the LDA signal. About 30000 data points were used in calculating the spectrum.

The FFT was applied to 50 successive blocks, thus resulting in an

average power spectrum for the velocity.

Results and Discussion The decay of centerline mean velocity (Um) for all exit Reynolds number cases are shown in dimensionless form (Um/Uo) in Figure 2 as a function of the dimensionless axial distance x/d. In the linearly growing jet flow [ 18], the centerline velocity is given by:

A.A. ABDEL-RAHMAN, S.F. AL-FAHED ,'rod W. CHAKROUN

318

in which A is the centedine velocity decay constant and xo is the location of the kinematic virtual origin of the jet. Using equation (1), the values of A's and Xo'Shave been determined from the data of Figure 2 for x/d _> 8 and given in table (1). In so doing, it is implicitly assumed that the mean jet data follow the self-preserving decay law given by equation (1) by x/d _> 8.

Therefore, the calculated values of A and x o

may be considered, at least

qualitatively, representations of the self-preserving regions of the jets. As can be seen from Figure 2 and table (1), the fastest decay is exhibited by the lowest Reynolds number jet where

TABLE 1 Re

A (95% conf.)

xo/d (95% conf.)

1430 2790 5190 19400

1.35 + 0.54 2.96 + 0.6 4.27 5:0.43 6.11 5:0.31

4.4 5::2.2 2.8 + 1.04 1.1 5:0.39 -1.4 5:0.42

8 6A

•

4Re=1430

o

0 0

2-

Re=2790 v

Re=5190

•

Re=19400

0

. . . .

I

0

UJU~ 2 0

. . . .

]

10

. . . .

15

20

8

O

~VO

0

I

. . . .

5

0

V

6

o

xo/d 4

~VO

2 0 -2

I

I

[

a

~

2

4

6

8

10

x/d

-4 12

.

.

.

.

I

.

.

.

.

I

5

.

.

10

.

.

I

15

.

.

.

.

20

Re x 10 -3

FIG. 2

FIG. 3

Decay of centerline mean velocity

Variation of A and xo/d with Re

A = 1.35, while the slowest decay is displayed by the highest Reynolds number jet where A = 6.11.

The value of6.11 compares well with 6.2 for the high Reynolds number jet as reported

LOW REYNOLDSNUMBERCIRC7OLARJETS

319

by Albenson et al. [7] and many others. It is apparent that the decay of the centerline velocity slows down with Reynolds number.

Same trend was reported by Oosthuizen [13] from his

hot-wire measur~aents. The virtual origin is also seen to continuously move in the upstream direction with Reynolds number. It is worth mentioning here that Flora and Goldschmidt [19] have found, but for the plane jet, that the virtual origin is independent of Reynolds number. This is likely due to the limited range of the Re~olds number in their study; 1.7 x 104 to 2.9 x 104 . To provide a better visualization of the variation trend of both A and x o, table (1) is presented graphically in Figure 3 where a gradual increase in A and a gradual decrease in xo/d with Reynolds number is seen. Monkewitz et al. [20], from their pitot tube measurements in the first 10d stations in two round jets of Re -- 7500 and 47000, have shown that the low Reynolds number jet exhibits faster centerline velocity decay and shorter potential core than the high Reynolds number jet.

At this point, one may conclude that lowering the Reynolds

number results in a less uniformity of the jet flow and consequently more mixing with the surroundings takes place. Accordingly, the entrainment process gets enhanced.

Figure 4 shows the streamwise mean velocity profiles for exit Reynolds numbers of 3000 and 4800.

The profiles are given for two downstream stations ofx/d = 6 and 8 to show their

evolution.

The evolution of the two Reynolds number profiles appear similar, except for

observed higher velocities in the outer region for the higher Reynolds number jet. The variation of streamwise turbulence intensity along the jet centerline is shown in Figure 5 where u' is the rms streamwise velocity. It can be seen from this Figure that the turbulence intensity level increases as the Reynolds number decreases, particularly for the region downstream from the potential core (x/d > 6). This is in agreement with the faster decay of the mean velocity as the Reynolds number decreases (refer to figure 2).

The turbulence intensity level in the

potential core region (up to rdd _-- 6), on the contrary, is seen to decrease as the Reynolds number decreases.

This is expected, anyhow, since the mean velocity in the potential core

region is constant and the turbulence level, therefore, represents the initial turbulence level of the jet flow.

Figures 6 and 7 show profiles of turbulence intensity at x/d = 6 and 8,

respectively, for both Reynolds numbers jets.

At x/d = 6, the turbulence level of the high

Reynolds number jet displays higher values in the central part. While for x/d = 8, the lower Reynolds number jet displays a higher level of turbulence intensity compared to the higher Reynolds number jet. A clear explanation of this non-monotonic behavior is not available.

320

A.A. ABDEL-RAHMAN, S.F. AL-FAHED ,'rod W. CHAKROUN

1.0 x/d = 8 0.8 o •

0.6

•

Re = 4 8 0 0

o

Re = 3 0 0 0

0.4

o

0.4

•

0.2

o°

Re=1430 Re=2790 Re=5190 Re=19400

o a

o • Q

•

• 0,3

0.0

U/U o

O°o

u'/U o

1.0 x/d=6 0.8

° o.

0.6 0.4

•

Re = 4800

o

Re = 3 0 0 0

'~' ~. ~,

o °

v

0 0

0.2

0.1

o •

~z~

•

~o~o

0.2

o

~m

c 0000

U

0

,~o 00

0.0

0

1

2

4

6

8

10

12

x/d

dd

FIG. 4

FIG. 5

Radial profiles of streamwise velocity

Turbulence intensity along the jet axis

25

30 • o

25

• o

Re = 4 8 0 0 Re = 3000

•

20

llo • ~°°

20

o 0o

•

15

~OOOoo••

• o o@ o o~oOoo

Re = 4 8 0 0 Re = 3000

o O0

u'/Uo(%)

o o

00000

0 10

@ o•

• •@

10

•

o

. . . .

0

1

2

3

F

Profiles of turbulence intensity at x/d=6

I

2 rid

r/d

FIG. 6

. . . .

1

FIG. 7 Profiles of turbulence intensity at x/d=8

LOW REYNOLDS NUMBER CIRCULAR JETS

321

The skewness factor (defined as u-~/u '3 , u being the fluctuating streamwise vdocity) profiles at x/d = 6 and 8 are shown in Figure 8 for both Reynolds number jets. It is seen that the skewness factor is very close to zero around the axis for all profiles, thus indicating that the turbulence approximates a G-aussian probability density distribution near the jet axis. In the meantime, the figure reveals that the skewness factor deviates from the zero level in the radial direction, i.e. the turbulence velocity distribution deviates from the Gaussian distribution (typical for a jet flow). This is has be~n attributed to the intermittent character of the jet flow that increases in the radial direction. For the low Reynolds number jet, the skewness factor is seen to display a more scattering deviation from the Gaussian value, which is likely due to the more intermittent behavior of the jet flow with decreasing Reynolds number.

This is in

agreement with the statement made by Albertson et al. [7]; that at low Reynolds numbers it is expected that viscous influences will prevent the full development of turbulence in the region of diffusion. This intermittent behavior is more noticeable at xJd=8 compared to that at x/d=6, thus indicating that the intermittency increases in the downstream direction. 100 o x/d = 8

R e = 3000 Re = 4800

•

o

0

•

•

..

•

o •

Re = 3 0 0 0 Re = 4800 O

•

60

O

4O

0

0

x/d = 8

80

0

0

20

.

.

.

.

0

0

0

0

I

1

0

0 0

I

0

0

1

2

2

100 o •

x/d=6

Re = 3 0 0 0 Re = 4 8 0 0

x/d = 6 8O

o •

Re = 3000 Re = 4 8 0 0

60

O O

...

0

... "

40 0

o

0

,

r

'

o

'~

~eo~o~oo~eo

0

J

1

00~

2O

2

Radial variation of skewness factor

I

o

Ooo °

1

0

dd

rid

FIG. 8

O0

FIG. 9 Radial variation of flatness factor

Figure 9 shows the profiles of flatness factor (defined as u-i/u '4 ) for both Reynolds numbers at x/d = 6 and 8.

It is seen that the flatness factors approach the values 3 (Gaussian value)

close to tbejet axis, then start to deviate from this value in the radial direction. In general the

322

A.A. ABDEL-RAHMAN,

S.F. A L - F A H E D a n d W. C H A K R O ! IN

flatness factor profiles emphasize the observations made from the skewness factor profiles (Figure 8).

That is, the jet flow tends to have a more intermittent character with decreasing

Reynolds number.

This intermittent character gets more pronounced in the downstream

direction.

Figure 10 is a 120s time history of the streamwise velocity for four different Reynolds number cases, taken at the same downstream location (x/d = 10) at the centerline of the jet flow. It is seen that the peaks of the velocity fluctuations become larger and intensified with increasing Reynolds number.

This time record reveals the increased intermittency of the jet flow, at the

jet centerline, with decreasing Reynolds number.

It is seen from the Figure that the lowest

Reynolds number jet (Re = 1430) displays the highest intermittent behavior where the velocity fluctuations appear weak, and even damped over some time intervals.

This is a typical

velocity record for an intermittent flow. 12 10 8

6 ]

4-

,...,,,, ....... ,.,.,,,,I

642oE

-2

o

4

6

10 .2 Re=5190 '

'

'

i

,

,

,

i

,

,

i

,

,

,

i

,

,

,

i

'

,

"1-

..................... . . \

"6

2

10-3

.

0

/ \

\

-2 "'.~,

-4 t3

4

10-4

2

~o

0

o.

-2

- -

Re = 26700

----

Re = 8000

---.......

Re = 5305 Re = 3000

-4 10-s 20

40

60

80

100

T i m e (s)

FIG. 10

Time record at jet axis for x/d=10

120

10

100 Frequency

(Hz)

FIG. 11 Spectrum of streamwise velocity at x/d=6

LOW REYNOLDSNUMBERCIRCULARJETS Power spectrum density taken at x/d Figure 11.

=

323

6 for the four Reynolds number cases appears in

Each spectrum, as mentioned before, is an average of at least 50 individual 512

point realizations of signal traces, reproduced at even time intervals to reduce the bias error in the velocity estimates [21 ].

In order to determine accurately the contributions to the power

spectrum of a random signal from a digital sample of the signal, the data rate must be at least twice as great as the highest frequency component which contains significant power (Nyquist criterion).

If the data rate is less than this data rate the power spectrum will be "aliased".

Further, Tropea [22] has shown that the spectrum is subject to positive bias in the low frequency range and to negative bias in the high frequency range when the average data rate is less than 2.5 times that determined from the Nyquist criterion. Therefore, the traces for the power spectrum were generated from the raw data traces at 40% of the mean arrival time of the panicles (equivalent to data rate of 2.5 times that determined from Nyquist criterion) to avoid the bias in the spectrum estimates as described by Tropea.

A direct Fast Fourier

Transform was then applied to successive blocks, thus resulting in an average power spectrum for the velocity.

As can be seen from the Figure, there is greater energy at the high

frequencies with increasing Reynolds number. Because these high frequencies correspond to smaller eddies, thus demonstrates that smaller eddies appear at higher Reynolds number which is consistent with the notion of increased vortex stretching at higher Reynolds number.

Summary and Conclusions An experimental investigation has been undertaken to study the effect of Reynolds number at the jet exit on the near-field region (up to 10d) of a round turbulent air jet. Using a LDA system, measurements were performed for a number of jet-flow cases, having exit Reynolds numbers in the range of 1400 to 20000. • The decay of centerline mean velocity of the jet was found to slow down as exit Reynolds number increases: for Re = 1430, A = 1.35 and for Re = 19400, A = 6.11. Therefore, one may conclude that lowering the Reynolds number results in a less uniformity of the jet flow, thus making the jet

experiences more mixing and interaction with the surrounding

environment relative to the high Reynolds number jet. It is worth mentioning that the value 6.11 for the high Reynolds number jet compares well with the documented value of 6, thus providing confidence in the measurements. • The virtual origin of the jet flow (xo/d) has been found to move continuously in the upstream direction as Re increases:

xo/d = 4.4 for Re = 1430 and xo/d = -1.4 for Re =

324

A.A. ABDEL-RAHMAN,S.F. AL-FAHED,'uld W. CHAKRO[rN 19400.

This is, most likely, a direct result of the decreased spread of the jet flow with

Reynolds number. • The turbulence intensity level was found to increase as Re decreases. This is consistent with the faster decay of the mean centerline velocity with decreased Re, and an indication of the more mixing of the jet flow with the surrounding with decreased Re. • In the outer region of the jet flow, the flatness factor of the jet is seen to deviate much from the Gaussian value as Re decreases.

Using the flatness factor as a measure of

intermittency, the jet flow can be said to display a more intermittent character with decreasing Reynolds number.

The distribution of the skewness factor across the jet flow

complements the same conclusion. • Spectrum measurements at the jet centerline for x/d = 6 showed that the energy content

at

the high frequencies increases as Re increases; i.e. smaller eddies appear at higher Reynolds number which is consistent with the notion of increased vortex stretching at higher Reynolds number.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.

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