[Abstract]: 

The effect of Reynolds number, Re = Uo,cH/μ , where Uo,c is

the nozzle exit centreline velocity, H is the slot-opening width and n is the kinematic viscosity of air) on the velocity field of a turbulent plane jet from a radially contoured nozzle of aspect ratio 60 is investigated. Measurements are conducted using a single wire anemometer over an axial distance of 160h. The Reynolds number is varied between 1,500 and 16,500. Results show that the Re affects various flow properties such as the velocity decay rate, half-width and turbulence intensity. The significant dependence on Re of the mean flow field persists till Re = 16,500, while the Re effect on the turbulent properties

becomes weaker above Re = 10,000. The present investigation

also suggests that an increase in Re leads to a higher rate of mixing in the near field but a lower rate in the far field

Deo, Ravinesh C.

Mi, Jianchun

Nathan, Graham J.

English

The effect of Reynolds number, µ/Re HU co = , where Uo,c is the nozzle exit centreline velocity, H is the slot-opening width and n is the kinematic viscosity of air) on the velocity field of a turbulent plane jet from a radially contoured nozzle of aspect ratio 60 is investigated. Measurements are conducted using a single wire anemometer over an axial distance of 160h. The Reynolds number is varied between 1,500 and 16,500. Results show that the Re affects various flow properties such as the velocity decay rate, half-width and turbulence intensity. The significant dependence on Re of the mean flow field persists till Re = 16,500, while the Re effect on the turbulent properties becomes weaker above Re = 10,000. The present investigation also suggests that an increase in Re leads to a higher rate of mixing in the near field but a lower rate in the far field

Ravinesh C Deo

Jianchun Mi

Graham J Nathan

CiteSeerX

Experimental Investigations of the Effect of Reynolds Number on a Plane Jet

The effect of Reynolds number, Re =Uo,cH /μ , where Uo,c is the nozzle exit centreline velocity, H is the slot-opening width and n is the kinematic viscosity of air) on the velocity field of a turbulent plane jet from a radially contoured nozzle of aspect ratio 60 is investigated. Measurements are conducted using a single wire anemometer over an axial distance of 160h. The Reynolds number is varied between 1,500 and 16,500. Results show that the Re affects various flow properties such as the velocity decay rate, half-width and turbulence intensity. The significant dependence on Re of the mean flow field persists till Re = 16,500, while the Re effect on the turbulent properties becomes weaker above Re = 10,000. The present investigation also suggests that an increase in Re leads to a higher rate of mixing in the near field but a lower rate in the far field

Deo, R. C.

Mi, J.

Nathan, G. J.

University of Queensland eSpace

16th Australasian Fluid Mechanics Conference 
Crown Plaza, Gold Coast, Australia 
2-7 December 2007 
Experimental Investigations of the Effect of Reynolds Number on a Plane Jet 
 
Ravinesh C Deo1, Jianchun Mi2 and Graham J Nathan2 
 
1Center for Remote Sensing and Spatial Information Sciences 
School of Geography Planning and Architecture 
The University of Queensland 
Brisbane 4072 AUSTRALIA 
Corresponding Author: r.deo1@uq.edu.au  
            
2 Turbulence, Energy and Combustion Group, School of Mechanical Engineering 
             The University of Adelaide, Adelaide, South Australia, 5005 AUSTRALIA 
 
Abstract 
The effect of Reynolds number, µ/Re
,
HU co= , where Uo,c is 
the nozzle exit centreline velocity, H is the slot-opening width 
and n is the kinematic viscosity of air) on the velocity field of a 
turbulent plane jet from a radially contoured nozzle of aspect 
ratio 60 is investigated. Measurements are conducted using a 
single wire anemometer over an axial distance of 160h. The 
Reynolds number is varied between 1,500 and 16,500. Results 
show that the Re affects various flow properties such as the 
velocity decay rate, half-width and turbulence intensity. The 
significant dependence on Re of the mean flow field persists till 
Re = 16,500, while the Re effect on the turbulent properties 
becomes weaker above Re = 10,000. The present investigation 
also suggests that an increase in Re leads to a higher rate of 
mixing in the near field but a lower rate in the far field.  
 
Introduction  
 A true plane jet issues from a rectangular nozzle of high 
aspect ratio, w/H (where w is the short side and H is the long side 
of the rectangular nozzle). The jet is confined within two parallel 
side walls, attached to the short sides of the nozzle. This 
configuration enables the jet to spread in the lateral (y) direction 
only. Some applications of a plane jet include engineering 
environments, e.g. in propulsion units and lift-producing devices, 
Quinn [1], air curtains and some combustion applications.  
 It is well established experimentally that, at sufficiently high 
Reynolds number, the normalized mean velocity profiles and the 
spreading rates of a round jet are almost independent of Reynolds 
number (Panchapakesan and Lumley [1], Hussain et al. [3]). The 
visualizations of Mungal and Hollingsworth [4] for their jet at 
very high Reynolds number (Re ~ 2 × 108) showed that its 
spreading rates and normalized mean velocity profiles are close 
to those of a laminar jet. In contrast, at low Reynolds numbers, 
both the mean and turbulent flow fields depend significantly on 
Re. This is evident, from Oosthuizen [5] for round jet, measured 
at moderate Re. Likewise, both Lemieux and Oosthuizen [6] and 
Namar and Otugen [7], studied the effect of Reynolds number in 
a plane free jet, over the Re ranges of 700 – 4200 and 1000 – 
7000, revealed that Re influenced the entire mixing field.  
 When Lofdahl et al. [8] investigated a plane wall jet, they 
found the jet spreading rates to remain variable even up to Re = 
20,000. An investigation by Stanley et al [9] and Klein et al [10] 
at Re = 3,000 and Re ~ 6,000, respectively, was conducted only 
in the near and transition fields (x/H ≤ 15 and x/H ≤ 20) even 
though Klein et al [10] claimed they covered the far field.  
 Clearly, wide range of different conditions makes it 
impossible to isolate the effect of Reynolds number from that of 
other variables. Hence conclusive quantitative data describing the 
Re dependence of a plane jet is not available. To address this 
issue, we have carried out an experimental investigation into a 
plane jet at Re between 1,500 and Re = 16,500, using a radial 
contraction nozzle with aspect ratio of w/H = 60, bounded by side 
walls, over a wider Re-range, and flow region up to x/H = 160. 
 
Experimental Details 
 The overall jet facility, shown in Figure 1, has been 
described in detail in Deo [11].  
 
Figure 1: Schematic diagrams of the plane jet facility, showing 
the wind tunnel, plane nozzle arrangement and side-walls. 
  
 The present plane nozzle is referred to as a radial contraction 
nozzle r/H  ≈ 2.14, where r is the nozzle exit radius), to 
differentiate it from the smooth contraction nozzles used in most 
previous investigations (e.g. Gutmark and Wyngnanski [11], 
Namar and Otugen [7], Bradbury [13] and Antonia et al [14]). 
For a comprehensive description of the radially contoured nozzle, 
see Deo [11] and Deo et al [15]. A constant temperature hot-wire 
anemometer (CTA) was employed to undertake measurements. A 
copper plated tungsten single hot wire probe, length lw ~ 1 mm 
and diameter dw ~ 5 µm was mounted parallel to the z-axis of the 
traverse. Hot wire calibration was performed in the jet potential 
core (turbulence intensity ~ 0.5%. Control of the jet Reynolds 
number, µ/Re
,
HU co= , was achieved by varying the speed of 
the wind tunnel fan. The maximum achievable Reynolds number 
was 16,500, without reducing the nozzle aspect ratio. The range 
of Reynolds numbers was selected to be 1,500 ≤ Re ≤ 16,500. 
The extent of measurements along the axial direction was 0 ≤ x/H 
≤ 160, to include the near, transition and far fields.  
 
Results and Discussion 
 
262
 2 
Figure 2 shows the normalized profiles of mean velocity and 
turbulence intensity obtained at x ≈ 0.5H for Re = 3,000, 10,000 
and 16,500.  
0
0.2
0.4
0.6
0.8
1.0
1.2
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
Re = 1500
           3000
           7000
         10000
         16500
U
/U
o
,
c
0
0.02
0.04
0.06
0.08
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
(b)
y/h
u
'/U
o
,
c
 
Figure 2: Lateral profiles of (a) normalized mean velocity and (b) 
turbulence intensity obtained at x/H ≈ 0.5. 
0.6
0.7
0.8
0.9
1.0
1.1
0 2 4 6 8 10 12 14 16
Re = 3000
       10000
       16500
(xp,Re) ≅ (5H, 1500)
≅ (3H, 16500)
≅ (4H, 10000)
x/H
U
c/U
o
,
c
 
Figure 3 The near-field mean velocity variation along the 
centerline and potential core length for different Re. 
0
0.2
0.4
0.6
0.8
1.0
0 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00
Re = 3000
          7000
        16500
U
/U
c
 
Figure 4: Lateral profiles of U/Uc at x/H = 5. 
 
 A dependence of the normalized exit velocity and turbulence 
intensity profiles on Re is noticeable. However, they become 
nearly identical when Re ≈ 10,000. Dependence of exit velocity 
profiles on Re were also noted by Namar and Otugen [7] for their 
`plane' jet without side walls, however, their velocity profiles did 
not become identical even at Re = 7,000. The present turbulence 
intensities in the central region (|y/H| ≤ 0.3 - 0.4) are below 1.0% 
for all Re. The peak values of turbulence intensity occur in the 
mixing layers and their magnitudes decrease as Reynolds number 
increases. Furthermore, over the range |y/H| ≤ 0.30 - 0.4, the 
mean velocity is uniform (i.e. U/Uo,c ~ 1), indicating that the 
present radial contraction nozzle can produce a similar exit 
velocity profile to that from the conventional smooth contraction 
nozzle. 
0
10
20
30
40
0 20 40 60 80 100 120 140 160 180
Re
 
= 1500
         3000
         4300
         7000
       10000
       16500
Re
c
o
,
c
 
Figure 5: Centerline variation of the mean velocity decay. 
 
 Figure 3 presents the near-field mean velocity along the 
centerline. As demonstrated, the length (xp) of the potential core, 
where the mean velocity is approximately constant and equal to 
Uo,c is a function of Re. For example, xp/H ≈ 5 for Re = 3,000 and 
xp/H ≈ 3 for Re = 16,500. Namely, xp/H decreases with Re. 
Correspondingly, the jet spreads more rapidly for higher Re, 
which is verified by lateral profiles of U/Uc in Figure 4. These 
together imply that the relative entrainment, thus mixing, of the 
jet is enhanced by increasing the Re in the near field.  
 
Decay Spread 
Investigation Re Ku x01/H Ky x02/H 
Jenkins & Goldschmidt [17] 14000 0.160 0.40 0.093 -8.20 
Hitchman et al. [16] 7000 0.147 8.05 0.108 -1.94 
Browne et al. [18] 7700 0.147 8.05 0.112 -1.94 
Gutmark & Wyngnanski [12] 30000 0.174 -0.7 0.099 -3.21 
Table 1: A summary of plane jet decay and spreading of jets with 
side walls 
 
Figure 6: Dependence of Ku and x01 on Reh 
 
 The mean velocity decay is shown in Figure 4. The data 
conform to the well-known inverse square relationship expressed 
by 






+=





H
x
H
x
K
U
U
u
c
co 01
2
,
 
where Ku is the slope and x01 is the x-location of the virtual origin 
of the profiles.  
 Figure 5 demonstrates that the velocity decay rates for Reh = 
7,000 and 16,500 agree well with Hitchman et al. [16] for Re = 
7,000 and Jenkins and Goldschmidt [17] for Re = 14,000, 
263
 3 
 
[18] 
[12] 
[13] 
providing confidence in our measurements. Further, the velocity 
decay rate can be measured by the magnitudes of Ku. 
 
 
Figure 7: Stream wise variations of y0.5 at different Re. 
 
 
Figure 8: Dependence of Ky on the Re. 
 
Figure 9: Evolutions of the centerline turbulence intensity. 
 
 Figure 6 shows the dependence of Ku on Re. As 
demonstrated, Ku decreases monotonically with an increase in Re 
and that Ku does not approach to an asymptotic value, even at to 
Re = 16,500. This suggests that the Re continues to affect the 
mean velocity field even at Re = 16,500. In addition, it appears 
from Figure 6 that the virtual origin x01 is smaller at higher 
Reynolds number. 
  
Figure 10: Reynolds number effect on *mu  and 
*
∞
u . 
 Figure 7 shows the stream wise variations of the velocity 
half-width y0.5 at different Reynolds numbers. Note that y0.5 is the 
lateral distance from the centerline at which the local mean 
velocity is half the centerline value. The values of y0.5 were 
derived from the lateral velocity measurements (not presented 
here). 
 As expected, the data conform to the following far-field 
relation: 






+=
h
x
h
xK
h
y
y
025.0
 
where constants Ky and x02 are determined by experiments.  
 When Re changes from 1,500 to 16,500, the half-width 
spreads out at different rates. This is better illustrated in Figure 8 
by the Re-dependence of Ky, a measure of the spreading rate. 
Clearly, the spreading rate decreases with an increase in Re 
which is consistent with the trend in the decay of Uc (Fig. 5). 
This together proves that, different from the near-field case, the 
far-field entrainment rate is reduced by increasing Re. 
 Figure 9 shows the centerline turbulence intensities 
(normalized rms, u* = u’c/Uc) for the different Re values. The 
development of u* is similar to that of Browne et al. [13] for a 
plane jet (w/H = 20 and Re = 7,700). However, the near-field 
local maximum in the intensity (u*m) is slightly different. Their 
local maximum occurs at x/H = 12 and has a magnitude of 0.23 
while ours for Re = 7,000 occurs at x/H = 11 and has a magnitude 
of 0.24. This difference could be due to the big difference in the 
aspect ratio (our w/H = 60 versus w/H = 20 in Browne et al. 
[18]). Thomas and Goldschmidt [19] found yet another value of 
the maximum for Re = 6,000, which occurs at x/H = 11, with a 
magnitude of 0.27. The discrepancies observed are likely due to 
differences in jet initial conditions, consistent with Mi et al. [20], 
that the occurrence of the pronounced local maximum in scalar 
intensity of a round jet depends upon exit conditions.  
 Further, as Re increases from 1,500 to 16,500, the 
magnitudes of u*m decreases from 0.31 to 0.22 (Fig. 10). The 
values of u*m are nearly identical for Re ≥ 10,000. The 
occurrence of higher u*m for lower Re suggests that the 
underlying large-scale structures are initially more coherent and 
organized for low Reynolds numbers. In these cases, the 
intermittent incursion of induced low velocity ambient fluid 
across the jet produces higher fluctuation amplitudes and lower 
mean values of the local velocity, and thus higher relative 
turbulence intensities. When Re is increased, the underlying 
structures become more three-dimensional and less coherent, and 
consequently the magnitude of u*m is reduced. Figure 10 also 
indicates that u* converges to a single curve for Re = 10,000 and 
16,500. It appears as well that in both cases u* reaches an 
asymptotic value of u*∞ = 0.22 at x/H > 60. However, for Re < 
10,000, the intensity and its evolution trend are both strongly 
dependent on the Re. Over 100 ≤ x/H ≤ 160, u* asymptotes to 
different values of u*∞ for different Re for Re < 10,000, see Fig. 
10. Clearly, u*∞  increases with increasing Re.  
 
Conclusion 
 The measurements revealed that Re affect various flow 
properties (mean velocity decay rate, half-width and turbulence 
intensity). The dependence on Re of the mean flow field appears 
to persist at Re = 16,500, while the Re effect on the turbulent 
properties is eliminated above Re ≈ 10,000. Our measurements 
also suggest that increasing Re leads the jet to mix its 
surroundings at a higher rate in the near field but less rapidly in 
the far field. 
 Specifically, the findings from present work are as follows.  
• Our radially contoured nozzle, of r/H ≈ 2.14, generates a 
quasi-top hat mean exit velocity profile. The uniform part of 
the profile widens as the Re increases. For Re ≥ 10,000, the 
profiles become independent of Re.  
• The length of jets’ potential core decreases with Re. The jet 
decay and spread rates downstream of the potential core 
 
[17] 
[16] 
[18] 
264
 4 
decrease with increasing Re, and this trend persists even at 
Re = 16,500.  
• The centerline turbulence intensity shows a local maximum 
in the near-field. Below Re = 10,000, its magnitude and 
axial location decrease as Re is increased.  
 
Acknowledgments 
 
The authors acknowledge the support of ARC Discovery Grant, 
International Postgraduate Research Scholarship and Adelaide 
University Scholarship for supporting first author’s PhD research 
on which this paper is based.  
 
References 
 
[1] Quinn W R. Development of a large-aspect ratio rectangular 
turbulent free jet. AIAA Journal, 32(3), 547-555, 1994. 
[2] Panchapakesan N R and Lumley J L. Turbulence 
measurements in axisymmetric jets of air and helium, part 1, 
air jet. J. Fluid Mech., 246, 197-223, 1993. 
[3] Hussain H J, Capp S P , and George W K. Velocity 
measurements in a high Reynolds number momentum 
conserving axisymmetric turbulent jet. J. Fluid Mech., 258, 
31-75, 1994. 
[4] Mungal G and Hollingsworth D K. Organized motion in a 
high Reynolds number jet. Phys. Fluids, 1(10), 1615-1623, 
1989. 
[5] Oosthuizen P H. An experimental study of low Reynolds 
number turbulent circular jet flow. volume 83-FE-36 of 
ASME Applied Mechanics, Bioengineering, and Fluids 
Engineering Conference, Houston/TX USA, June 20-22 
1983. 
[6] Lemieux G P and Oosthuizen P H. Experimental study of 
behaviour of plane turbulent jets at low Reynolds numbers. 
AIAA Journal, pages 1845, 1846, 1985. 
[7] Namar I and Otugen M V. Velocity measurements in a 
plane turbulent air jet at moderate Reynolds numbers. Exp. 
Fluids, 6:387{399, 1988. 
[8] Lofdahl L, H Abrahamson, B Johansson and T 
Hadzianagnostakis. On the Reynolds number dependence of 
a plane two-dimensional wall-jet. Doktorsavhandlingar vid 
Chalmers Tekniska Hogskol, 1292, 8pp, 1997. 
[9] Stanley S A, Sarkar S, and Mellado J P. A study of the eld 
evolution and mixing in a planar turbulent jet using direct 
numerical simulations. J. Fluid Mech., 450, 377-407, 2002. 
[10] Klein M, Sadiki A, and Janicka J. Investigation of the 
influence of the Reynolds number on a plane jet using direct 
numerical simulation. Int. J. Heat and Fluid Flow, 24, 785-
794, 2003. 
[11] Deo R C. Experimental investigations of the influence of 
Reynolds number and boundary conditions on a plane air 
jet. Ph.D. thesis, School of Mechanical Engineering, The 
University of Adelaide, South Australia, ADT Program: 
http://thesis.library.adelaide.edu.au/public/adt-
UA20051025.054550/index.html, (2005). 
[12] Gutmark E and Wyngnanski I. The planar turbulent jet. J. 
Fluid Mech., 73(3), 465-495, 1976. 
[13] Bradbury L J S. The structure of self-preserving turbulent 
plane jet. J. Fluid Mech., 23, 31-64, 1965. 
[14] Antonia R A, Browne W B, Rajagopalan S , and Chambers 
A J . On organized motion of a turbulent plane jet. J. Fluids 
Mech., 134, 49-66, 1983. 
[15] Deo R C, Mi, J and Nathan, G J. The influence of nozzle-
exit geometric profile on statistical properties of a plane jet. 
Experim. Therm.  Fluid Sc, Online doi: 
10.1016/j.expthermflusci.2006.08.010, 32(2), 545-559  
[16] Hitchman G J, Strong A B, Slawson P R and Ray G . 
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Journal, 28(10), 1699-1700, 1990. 
[17] Jenkins P E and Goldschmidt V W. Mean temperature and 
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A J. Interaction region of a two-dimensional turbulent plane 
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265


University of Southern Queensland ePrints

16th Australasian Fluid Mechanics Conference Crown Plaza, Gold Coast, Australia 2-7 December 2007 Experimental Investigations of the Effect of Reynolds Number on a Plane Jet  Ravinesh C Deo1, Jianchun Mi2 and Graham J Nathan2  1Center for Remote Sensing and Spatial Information Sciences School of Geography Planning and Architecture The University of Queensland Brisbane 4072 AUSTRALIA Corresponding Author: r.deo1@uq.edu.au              2 Turbulence, Energy and Combustion Group, School of Mechanical Engineering              The University of Adelaide, Adelaide, South Australia, 5005 AUSTRALIA  Abstract The effect of Reynolds number, µ/Re,HU co= , where Uo,c is the nozzle exit centreline velocity, H is the slot-opening width and n is the kinematic viscosity of air) on the velocity field of a turbulent plane jet from a radially contoured nozzle of aspect ratio 60 is investigated. Measurements are conducted using a single wire anemometer over an axial distance of 160h. The Reynolds number is varied between 1,500 and 16,500. Results show that the Re affects various flow properties such as the velocity decay rate, half-width and turbulence intensity. The significant dependence on Re of the mean flow field persists till Re = 16,500, while the Re effect on the turbulent properties becomes weaker above Re = 10,000. The present investigation also suggests that an increase in Re leads to a higher rate of mixing in the near field but a lower rate in the far field.   Introduction   A true plane jet issues from a rectangular nozzle of high aspect ratio, w/H (where w is the short side and H is the long side of the rectangular nozzle). The jet is confined within two parallel side walls, attached to the short sides of the nozzle. This configuration enables the jet to spread in the lateral (y) direction only. Some applications of a plane jet include engineering environments, e.g. in propulsion units and lift-producing devices, Quinn [1], air curtains and some combustion applications.   It is well established experimentally that, at sufficiently high Reynolds number, the normalized mean velocity profiles and the spreading rates of a round jet are almost independent of Reynolds number (Panchapakesan and Lumley [1], Hussain et al. [3]). The visualizations of Mungal and Hollingsworth [4] for their jet at very high Reynolds number (Re ~ 2 × 108) showed that its spreading rates and normalized mean velocity profiles are close to those of a laminar jet. In contrast, at low Reynolds numbers, both the mean and turbulent flow fields depend significantly on Re. This is evident, from Oosthuizen [5] for round jet, measured at moderate Re. Likewise, both Lemieux and Oosthuizen [6] and Namar and Otugen [7], studied the effect of Reynolds number in a plane free jet, over the Re ranges of 700 – 4200 and 1000 – 7000, revealed that Re influenced the entire mixing field.   When Lofdahl et al. [8] investigated a plane wall jet, they found the jet spreading rates to remain variable even up to Re = 20,000. An investigation by Stanley et al [9] and Klein et al [10] at Re = 3,000 and Re ~ 6,000, respectively, was conducted only in the near and transition fields (x/H ≤ 15 and x/H ≤ 20) even though Klein et al [10] claimed they covered the far field.   Clearly, wide range of different conditions makes it impossible to isolate the effect of Reynolds number from that of other variables. Hence conclusive quantitative data describing the Re dependence of a plane jet is not available. To address this issue, we have carried out an experimental investigation into a plane jet at Re between 1,500 and Re = 16,500, using a radial contraction nozzle with aspect ratio of w/H = 60, bounded by side walls, over a wider Re-range, and flow region up to x/H = 160.  Experimental Details  The overall jet facility, shown in Figure 1, has been described in detail in Deo [11].   Figure 1: Schematic diagrams of the plane jet facility, showing the wind tunnel, plane nozzle arrangement and side-walls.    The present plane nozzle is referred to as a radial contraction nozzle r/H  ≈ 2.14, where r is the nozzle exit radius), to differentiate it from the smooth contraction nozzles used in most previous investigations (e.g. Gutmark and Wyngnanski [11], Namar and Otugen [7], Bradbury [13] and Antonia et al [14]). For a comprehensive description of the radially contoured nozzle, see Deo [11] and Deo et al [15]. A constant temperature hot-wire anemometer (CTA) was employed to undertake measurements. A copper plated tungsten single hot wire probe, length lw ~ 1 mm and diameter dw ~ 5 µm was mounted parallel to the z-axis of the traverse. Hot wire calibration was performed in the jet potential core (turbulence intensity ~ 0.5%. Control of the jet Reynolds number, µ/Re,HU co= , was achieved by varying the speed of the wind tunnel fan. The maximum achievable Reynolds number was 16,500, without reducing the nozzle aspect ratio. The range of Reynolds numbers was selected to be 1,500 ≤ Re ≤ 16,500. The extent of measurements along the axial direction was 0 ≤ x/H ≤ 160, to include the near, transition and far fields.   Results and Discussion  262 2 Figure 2 shows the normalized profiles of mean velocity and turbulence intensity obtained at x ≈ 0.5H for Re = 3,000, 10,000 and 16,500.  00.20.40.60.81.01.2-0.6 -0.4 -0.2 0 0.2 0.4 0.6Re = 1500           3000           7000         10000         16500U/Uo,c00.020.040.060.08-0.6 -0.4 -0.2 0 0.2 0.4 0.6(b)y/hu'/Uo,c Figure 2: Lateral profiles of (a) normalized mean velocity and (b) turbulence intensity obtained at x/H ≈ 0.5. 0.60.70.80.91.01.10 2 4 6 8 10 12 14 16Re = 3000       10000       16500(xp,Re) ≅ (5H, 1500)≅ (3H, 16500)≅ (4H, 10000)x/HUc/Uo,c Figure 3 The near-field mean velocity variation along the centerline and potential core length for different Re. 00.20.40.60.81.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00Re = 3000          7000        16500U/Uc Figure 4: Lateral profiles of U/Uc at x/H = 5.   A dependence of the normalized exit velocity and turbulence intensity profiles on Re is noticeable. However, they become nearly identical when Re ≈ 10,000. Dependence of exit velocity profiles on Re were also noted by Namar and Otugen [7] for their `plane' jet without side walls, however, their velocity profiles did not become identical even at Re = 7,000. The present turbulence intensities in the central region (|y/H| ≤ 0.3 - 0.4) are below 1.0% for all Re. The peak values of turbulence intensity occur in the mixing layers and their magnitudes decrease as Reynolds number increases. Furthermore, over the range |y/H| ≤ 0.30 - 0.4, the mean velocity is uniform (i.e. U/Uo,c ~ 1), indicating that the present radial contraction nozzle can produce a similar exit velocity profile to that from the conventional smooth contraction nozzle. 0102030400 20 40 60 80 100 120 140 160 180Re = 1500         3000         4300         7000       10000       16500Reco,c Figure 5: Centerline variation of the mean velocity decay.   Figure 3 presents the near-field mean velocity along the centerline. As demonstrated, the length (xp) of the potential core, where the mean velocity is approximately constant and equal to Uo,c is a function of Re. For example, xp/H ≈ 5 for Re = 3,000 and xp/H ≈ 3 for Re = 16,500. Namely, xp/H decreases with Re. Correspondingly, the jet spreads more rapidly for higher Re, which is verified by lateral profiles of U/Uc in Figure 4. These together imply that the relative entrainment, thus mixing, of the jet is enhanced by increasing the Re in the near field.   Decay Spread Investigation Re Ku x01/H Ky x02/H Jenkins & Goldschmidt [17] 14000 0.160 0.40 0.093 -8.20 Hitchman et al. [16] 7000 0.147 8.05 0.108 -1.94 Browne et al. [18] 7700 0.147 8.05 0.112 -1.94 Gutmark & Wyngnanski [12] 30000 0.174 -0.7 0.099 -3.21 Table 1: A summary of plane jet decay and spreading of jets with side walls  Figure 6: Dependence of Ku and x01 on Reh   The mean velocity decay is shown in Figure 4. The data conform to the well-known inverse square relationship expressed by +=HxHxKUUucco 012, where Ku is the slope and x01 is the x-location of the virtual origin of the profiles.   Figure 5 demonstrates that the velocity decay rates for Reh = 7,000 and 16,500 agree well with Hitchman et al. [16] for Re = 7,000 and Jenkins and Goldschmidt [17] for Re = 14,000, 263 3  [18] [12] [13] providing confidence in our measurements. Further, the velocity decay rate can be measured by the magnitudes of Ku.   Figure 7: Stream wise variations of y0.5 at different Re.   Figure 8: Dependence of Ky on the Re.  Figure 9: Evolutions of the centerline turbulence intensity.   Figure 6 shows the dependence of Ku on Re. As demonstrated, Ku decreases monotonically with an increase in Re and that Ku does not approach to an asymptotic value, even at to Re = 16,500. This suggests that the Re continues to affect the mean velocity field even at Re = 16,500. In addition, it appears from Figure 6 that the virtual origin x01 is smaller at higher Reynolds number.   Figure 10: Reynolds number effect on *mu  and *∞u .  Figure 7 shows the stream wise variations of the velocity half-width y0.5 at different Reynolds numbers. Note that y0.5 is the lateral distance from the centerline at which the local mean velocity is half the centerline value. The values of y0.5 were derived from the lateral velocity measurements (not presented here).  As expected, the data conform to the following far-field relation: +=hxhxKhyy025.0 where constants Ky and x02 are determined by experiments.   When Re changes from 1,500 to 16,500, the half-width spreads out at different rates. This is better illustrated in Figure 8 by the Re-dependence of Ky, a measure of the spreading rate. Clearly, the spreading rate decreases with an increase in Re which is consistent with the trend in the decay of Uc (Fig. 5). This together proves that, different from the near-field case, the far-field entrainment rate is reduced by increasing Re.  Figure 9 shows the centerline turbulence intensities (normalized rms, u* = u’c/Uc) for the different Re values. The development of u* is similar to that of Browne et al. [13] for a plane jet (w/H = 20 and Re = 7,700). However, the near-field local maximum in the intensity (u*m) is slightly different. Their local maximum occurs at x/H = 12 and has a magnitude of 0.23 while ours for Re = 7,000 occurs at x/H = 11 and has a magnitude of 0.24. This difference could be due to the big difference in the aspect ratio (our w/H = 60 versus w/H = 20 in Browne et al. [18]). Thomas and Goldschmidt [19] found yet another value of the maximum for Re = 6,000, which occurs at x/H = 11, with a magnitude of 0.27. The discrepancies observed are likely due to differences in jet initial conditions, consistent with Mi et al. [20], that the occurrence of the pronounced local maximum in scalar intensity of a round jet depends upon exit conditions.   Further, as Re increases from 1,500 to 16,500, the magnitudes of u*m decreases from 0.31 to 0.22 (Fig. 10). The values of u*m are nearly identical for Re ≥ 10,000. The occurrence of higher u*m for lower Re suggests that the underlying large-scale structures are initially more coherent and organized for low Reynolds numbers. In these cases, the intermittent incursion of induced low velocity ambient fluid across the jet produces higher fluctuation amplitudes and lower mean values of the local velocity, and thus higher relative turbulence intensities. When Re is increased, the underlying structures become more three-dimensional and less coherent, and consequently the magnitude of u*m is reduced. Figure 10 also indicates that u* converges to a single curve for Re = 10,000 and 16,500. It appears as well that in both cases u* reaches an asymptotic value of u*∞ = 0.22 at x/H > 60. However, for Re < 10,000, the intensity and its evolution trend are both strongly dependent on the Re. Over 100 ≤ x/H ≤ 160, u* asymptotes to different values of u*∞ for different Re for Re < 10,000, see Fig. 10. Clearly, u*∞  increases with increasing Re.   Conclusion  The measurements revealed that Re affect various flow properties (mean velocity decay rate, half-width and turbulence intensity). The dependence on Re of the mean flow field appears to persist at Re = 16,500, while the Re effect on the turbulent properties is eliminated above Re ≈ 10,000. Our measurements also suggest that increasing Re leads the jet to mix its surroundings at a higher rate in the near field but less rapidly in the far field.  Specifically, the findings from present work are as follows.  • Our radially contoured nozzle, of r/H ≈ 2.14, generates a quasi-top hat mean exit velocity profile. The uniform part of the profile widens as the Re increases. For Re ≥ 10,000, the profiles become independent of Re.  • The length of jets’ potential core decreases with Re. The jet decay and spread rates downstream of the potential core  [17] [16] [18] 264 4 decrease with increasing Re, and this trend persists even at Re = 16,500.  • The centerline turbulence intensity shows a local maximum in the near-field. Below Re = 10,000, its magnitude and axial location decrease as Re is increased.   Acknowledgments  The authors acknowledge the support of ARC Discovery Grant, International Postgraduate Research Scholarship and Adelaide University Scholarship for supporting first author’s PhD research on which this paper is based.   References  [1] Quinn W R. Development of a large-aspect ratio rectangular turbulent free jet. AIAA Journal, 32(3), 547-555, 1994. [2] Panchapakesan N R and Lumley J L. Turbulence measurements in axisymmetric jets of air and helium, part 1, air jet. J. Fluid Mech., 246, 197-223, 1993. [3] Hussain H J, Capp S P , and George W K. Velocity measurements in a high Reynolds number momentum conserving axisymmetric turbulent jet. J. Fluid Mech., 258, 31-75, 1994. [4] Mungal G and Hollingsworth D K. Organized motion in a high Reynolds number jet. Phys. Fluids, 1(10), 1615-1623, 1989. [5] Oosthuizen P H. An experimental study of low Reynolds number turbulent circular jet flow. volume 83-FE-36 of ASME Applied Mechanics, Bioengineering, and Fluids Engineering Conference, Houston/TX USA, June 20-22 1983. [6] Lemieux G P and Oosthuizen P H. Experimental study of behaviour of plane turbulent jets at low Reynolds numbers. AIAA Journal, pages 1845, 1846, 1985. [7] Namar I and Otugen M V. Velocity measurements in a plane turbulent air jet at moderate Reynolds numbers. Exp. Fluids, 6:387{399, 1988. [8] Lofdahl L, H Abrahamson, B Johansson and T Hadzianagnostakis. On the Reynolds number dependence of a plane two-dimensional wall-jet. Doktorsavhandlingar vid Chalmers Tekniska Hogskol, 1292, 8pp, 1997. [9] Stanley S A, Sarkar S, and Mellado J P. A study of the eld evolution and mixing in a planar turbulent jet using direct numerical simulations. J. Fluid Mech., 450, 377-407, 2002. [10] Klein M, Sadiki A, and Janicka J. Investigation of the influence of the Reynolds number on a plane jet using direct numerical simulation. Int. J. Heat and Fluid Flow, 24, 785-794, 2003. [11] Deo R C. Experimental investigations of the influence of Reynolds number and boundary conditions on a plane air jet. Ph.D. thesis, School of Mechanical Engineering, The University of Adelaide, South Australia, ADT Program: http://thesis.library.adelaide.edu.au/public/adt-UA20051025.054550/index.html, (2005). [12] Gutmark E and Wyngnanski I. The planar turbulent jet. J. Fluid Mech., 73(3), 465-495, 1976. [13] Bradbury L J S. The structure of self-preserving turbulent plane jet. J. Fluid Mech., 23, 31-64, 1965. [14] Antonia R A, Browne W B, Rajagopalan S , and Chambers A J . On organized motion of a turbulent plane jet. J. Fluids Mech., 134, 49-66, 1983. [15] Deo R C, Mi, J and Nathan, G J. The influence of nozzle-exit geometric profile on statistical properties of a plane jet. Experim. Therm.  Fluid Sc, Online doi: 10.1016/j.expthermflusci.2006.08.010, 32(2), 545-559  [16] Hitchman G J, Strong A B, Slawson P R and Ray G . Turbulent plane jet with and without confining walls. AIAA Journal, 28(10), 1699-1700, 1990. [17] Jenkins P E and Goldschmidt V W. Mean temperature and velocity measurements in a plane turbulent jet. Trans. ASME J., 95, 581-584, 1973. [18] Browne L W B, Antonia R A, Rajagopalan S and Chambers A J. Interaction region of a two-dimensional turbulent plane jet in still air. In Structure of Complex Turbulent Shear Flows, IUTAM Symposium, 411-419, 1982. [19] Thomas F O and Goldschmidt V W. Structural characteristics of a developing turbulent planar jet. J. Fluid Mech., 163, 227-256, 1986.  [20] Mi J, Nobes D and Nathan G J. Influence of exit conditions of round nozzles on the passive scalar field of a jet. J. Fluid Mech., 432, 91-125, 2001. 265

A study of the eld evolution and mixing in a planar turbulent jet using direct numerical simulations.

An experimental study of low Reynolds number turbulent circular jet flow. volume 83-FE-36

Development of a large-aspect ratio rectangular turbulent free jet.

Experimental investigations of the influence of Reynolds number and boundary conditions on a plane air jet.

Experimental study of behaviour of plane turbulent jets at low Reynolds numbers.

Influence of exit conditions of round nozzles on the passive scalar field of a jet.

Interaction region of a two-dimensional turbulent plane jet in still air.

Investigation of the influence of the Reynolds number on a plane jet using direct numerical simulation.

Mean temperature and velocity measurements in a plane turbulent jet.

On organized motion of a turbulent plane jet.

On the Reynolds number dependence of a plane two-dimensional wall-jet. Doktorsavhandlingar vid Chalmers Tekniska Hogskol,

Organized motion in a high Reynolds number jet.

Structural characteristics of a developing turbulent planar jet.

The influence of nozzleexit geometric profile on statistical properties of a plane jet.

The planar turbulent jet.

The structure of self-preserving turbulent plane jet.

Turbulence measurements in axisymmetric jets of air and helium, part 1, air jet.

Turbulent plane jet with and without confining walls.

Velocity measurements in a high Reynolds number momentum conserving axisymmetric turbulent jet.

Velocity measurements in a plane turbulent air jet at moderate Reynolds numbers.

Experimental investigations of the effect of Reynolds number on a plane jet

The effect of Reynolds number, Re =Uo,cH /μ , where Uo,c is the nozzle exit centreline velocity, H is the slot-opening width and n is the kinematic viscosity of air) on the velocity field of a turbulent plane jet from a radially contoured nozzle of aspect ratio 60 is investigated. Measurements are conducted using a single wire anemometer over an axial distance of 160h. The Reynolds number is varied between 1,500 and 16,500. Results show that the Re affects various flow properties such as the velocity decay rate, half-width and turbulence intensity. The significant dependence on Re of the mean flow field persists till Re = 16,500, while the Re effect on the turbulent properties becomes weaker above Re = 10,000. The present investigation also suggests that an increase in Re leads to a higher rate of mixing in the near field but a lower rate in the far field.Ravinesh C Deo, Jianchun Mi and Graham J Natha

Deo, R.

Nathan, G.

Adelaide Research &amp; Scholarship

http://espace.library.uq.edu.au/eserv/UQ:120788/Deo_afmc_16_07.pdf

Experimental investigations of the effect of Reynolds number on a plane jet

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Experimental investigations of the effect of Reynolds number on a plane jet

Abstract

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Full text

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University of Queensland eSpace

University of Southern Queensland ePrints

University of Southern Queensland ePrints

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Adelaide Research & Scholarship