SELF PRESERVATION OF MIXINGLAYERANDJET

characteristics at different X/D locations. The location of peaks are found Lo be at about 112

=

(Y - Yo.50l/Bo.IO

=

0.9, whereas the peak of Hussain and Clark's [21] data are found at 112 = 0.7. The Reynolds stresses in the range 5 ~ X/D ~ 12.5 are presented in the Fig. 5.4.9. The peak values are found to increase in the range 5 ~ X/D ~ 8 and then decreases from X/D = 10.0. Wygnanski and Fiedler's [51] data for range 50 ~ ^{X/D ~} 75 shows similar characteristics but significant shift near the jet centerline. The data in the range 12.5 ~ X/D ~ 20.0 shows decreasing peak values. with increasing X/D location. Wygnanski's data are found to be more or less same when a transformation of Y

IX

= Y

IX

+ 0.017 is made. It can be said that as the present. measurement. is done upto X/D = 20, and Wygnanski's data are in t.he range 50 ~ X/D ~ 75, the transformation is meaningful.

49 TABLE 5.5.1

Table of Acceptance: Shear Layer Mode.

Self Preserving Variable Acceptance Remarks

Unexcited Excited U/Uo u'/U U/U u'/U

MA MA MA MA MA

'lJ -

l--X

y-y ••

A A A A A

'lJ3- y-Yo.so

6

^0•10

A A MA A A

'lJ3= Y-Yo.so X

NA NA NA NA NA

'lJ4=-- Y Yo.so

A A MA A A

'lJs= Y-Yo .• s

Yo.so-Yo .• s ^.

NA NA NA NA NA

'lJ6= Y-Yo.so bn

The above table shows that tl2' tl3 and tis can be accepted as self preserving variable for the present flow analysis while ^TIl can be moderately accepted in the shear layer zone.

The self preservation profiles ,of jet column mode of unexcited jet are presented in the Figs. 5.5.25 to 5.536. The acceptancei table for jet column mode is given below (Table 5.5.2).

TABLE 5.5.2

Table of Acceptance: Jet Column Mode.

Self Preserving Variable Acceptance Remarks

Unexcited

U/Uo u'/U

NA Outer region NA

Y-Y: sensitive

111=--"

X

NA Inner region NA

y- ^YO.50 sensitive

112=

6

^0•10

A Inner region A

Y-YO•50 sensitive

113= X

A Inner region A

y sensitive

11 =--

• YO•50

MA MA MA

115= ^{Y- YO•95}

YO.50-YO.95

MA MA MA

116=y- ^YO.50 bn

From the above table and nature of the profiles in the related figures it is found that downstream measurements beyond X/D = 20.0 are necessary to confirm the self preservation. The above table indicates ''13 and 11. as accepted variable for flow analysis- in the developed zone.,

I

From the tables of acceptance of self preserving variables of shear layer mode and jet column mode it can be decided that the variable '113may be accepted for

both the modes.

51 5.6 EFFECT OF EXCITATION ON AXISYMMETRIC JET

The effect of upstream excitation on centerline mean velocity at Red= 8.56 x 106

is presented in Fig. 5.6.1. The centerline mean velocity decreases considerably at Strouhal number, Std

=

0.046, which corresponds the excitation frequency of 10 Hz. The increase in centerline mean velocity is found to occur at, Std = 0.923 and f = 200 Hz. An increase in centerline mean velocity is due to suppression of centerline turbulence intensity and a decrease corresponds to turbulence enhancement as because turbulence is generated by taking. energy from the mean flow field.

The effect of upstream excitation on centerline longitudinal turbulence intensity at Red= 8.56 x 10⁴ is presented in the Fig. 5.6.2. Turbulence enhancement is found maximumat Std

=

^{0.046 (f}

=

10 Hz) and suppression is found in the range 0.346 < Std < 0.923 (75 Hz <f < 200 Hz). The pattern found by Hossain [14] upon excitation shows significant difference from the present study. The reason behind this may be due to the different jet exit condition.

Fig. 5.6.3 shows the variation of mean velocity on a Y/D = 0.50 line at Red= 8.56 x 10⁴ for different excitation conditions. For all excitations the mean velocity increases very near to jet leap but remains less than unexcited value for the downstream location. Maximumreduction is observed in Std = 0.115.

The effect of excitation on turbulence intensity of a Y/D = 0.50 line at Red= 8.56 x 104 is presented in Figs. 5.6.4 and 5.6.5 in normal and logarithmic scales respectively. The effect of excitation is felt strong in the near field of the jet leap. After X/D= 2.0 the effect is much less. Upto X/D = 0.25, excitation at any strouhal number suppress turbulence. Turbulence enhancement is observed in the range 0.5 < X/D < 1.5 at Stdi= 0.461 and 0.692, but suppression is otherwise observed for all other Std in the measurement range of 0.115 < Std <0.692.

Streamwise evolution of peak longitudinal turbulence intensity of unexcited and excited jet at Red= 8.56 x 104 is presented in Fig. 5.6.6. The peak intensities of unexcited jet is found to increase upto X/D

=

1.0, decrease a bit at X/D

=

^{2.0 and}

then to sharply increase to a maximum value at X/D

=

^{3.0. After reaching}

maximum,the peak intensities drop down for further downstream locations. The

peak intensities when excited at Std= 0.046 shows always higher value upto X/D

=

7.0 except at X/D

=

1.0; the peaks are found below unexcited value after X/D

= 7.0 Hossain [14) found maximumpeak intensity of unexcited jet at X/D= 1.5 and at X/D = 0.5 when unexcited but found peak to be less than unexcited value at X/D = 3.0.

The location of peak turbulence intensity is found to shift the position towards centerline in the range 3.5

<

X/D

<

7.5 when excited at preferred mode and is presented in the Fig. 5.6.7.

The effect of excitation on longitudinal turbulence intensity profile at X/D = 0.50, Red

=

3.49 x 104 is shown in Fig. 5.6.8. Turbulence enhancement at Std

=

0.034 is always higher in all Y/D locations. The suppression of turbulence is observed except in the range 0.45

<

Y/D

<

0.55, when excited at Std = 0.453. The reason is found when the fluctuation vs time traces are analyzed. It is found that the frequency of turbulence fluctuation are different in different Y/D location. Similar results are also found at X/D= 5.0 and is presented in Fig.5.6.9. Both turbulence enhancement and suppression is observed in the inner and outer region except around the half width of jet.

Starting from the jet exit at X/D

=

0.025, the longitudinal turbulence intensity profiles of excited and unexcited condition at different downstream locations are shown in figures Figs. 5.6.10 to 5.6.20 for Red= 8.56 x 10^4• From these graphs it can be said that the region around the jet half width is not sensitive to excitation, the effect of excitation become weaker in the downstream locations and suppression and enhancement may occur in different location when excited with a particular frequency or Strouhal number.

To visualize the effect' of excitation on the total turbulent flow field, it is wise to plot the turbulence intensity of several single points with varying excitation on a Y= constant line. Two lines are chosen in this study namely Y/D = 0.0 line

(centerline) and Y/D = 0.50 line (wall line). Several single points are chosen on centerline at X/D= 2.5, 50., 7.5 and 10.0 and on wall line at X/D = 0.25, 0.50 and 0.75. The reason for choosing these locations can be explained by the turbulence intensity plots of these lines in Figs. 5.6.2 and 5.6.4. Study with two Reynolds number viz. Red = 3.49 x 104 and 8.56 x 104 are presented with different

53 excitation condition namely upstream excitation, surface excitation and combined excitation.

The effect of upstream excitation at four different X/D locations on centerline at Red= 3.49 x 10⁴ is presented in Fig. 5.6.21 and is analyses in the following table (Table 5.6.1).

TABLE5.6.1

Analysis Table Centerline (Upstream Excitation): Red= 3.49 X 10⁴

Location 1st peak Suppression

X/D

=

^{2.5 10 Hz (Std}

=

0.113) 40 - 100 Hz

0.453 < St. < 1.132

X/D

=

^{5.0 7 Hz (Std}

=

^{0.079) 25 - 90 Hz}

0.283 < St. < 1.019

X/D

=

^{7.5 6 Hz (St.}

=

0.068)

---

X/D

=

^{10.0 3 Hz (Std}

=

^0.034)

^---

The above table shows that the excitation frequency which produces maximum turbulence enhancement decreases in the downstream which indicates that shear interaction is prominent in the near field. Turbulence enhancement in the centerline (2.5 < X/D <10.0) occurs when excited at, 3 Hz < f < 10Hz (0.034 <Std

< 0.113). Turbulence suppression is observed prominent at X/D

=

2.5 and 5.0, the ranges are shown in the table. The suppression of turbulence in the further downstream locations are insignificant.

The effect of surface excitation on centerline at Red= 3.49 x 10⁴ is presented in Fig. 5.6.22 and the characteristics of the curves are shown in the following table (Table 5.6.2).

TABLE 5.6.2

Analysis Table: Centerline (Surface Excitation): Red = 3.49 x 104

Location 1st Peak Other Peaks Suppression

X/D = 2.5 3 Hz (Std

=

^0.034) 7Hz (std = 0.079) 40 - 90 Hz 0.453 <St" <1.019 X/D

=

^5.0 0.9 Hz (Std = 0.010) 15Hz (Std =0.169) 20 - 90 Hz

0.226<St.•<1.019

X/D

=

^7.5 0.2 Hz (St.• = 0.002)

--- ^---

X/D

=

^10.0 0.1 Hz (St.• = 0.001)

--- ^---

The above table shows similar trend as upstream excitation but the maximum amplification now occurs at much lower frequencies, 0.1 Hz < f < 3 Hz (0.001

<

std

< 0.034). The suppression of turbulence are more or less similar as upstream excitation.

The effect of upstream excitation on a Y

ID

= 0.50 line at Red = 3.49 x 104 is presented in Fig. 5.6.23. Turbulence enhancement occurs at any frequency less than 100 Hz near the wall at X/D = 0.25. Beyond f = 100 Hz suppression is insignificant. The other two locations, .X/D = 0.50 and 0.75 shows both enhancement and suppression of turbulence intensity. Similar but more organized turbulence enhancement and suppression is observed in the case of surface excitation, which is presented in Fig. 5.6.24.

,

Stl'ouhal number.

The amount of location wise turbulence enhancement and understood jf the excited turbulence intensity,

the unexciled, value, u'ux and plotted against

u'ex is made

suppression is well non-dimensional with

i

The ratio of upstream excited. and unexcited turbulence intensities on centerline at Red = 3.49 x 10⁴ is presented in Fig. 5.6.25. At ^X/D = 2.5, 41% turbulence suppression is found at Std = 0.096. Immediately after that, 48% turbulence enhancement is found at St.d = 0.128 followed by a continuous suppression. The maximum suppression at X/D

=

2.5 is found to be 76% at Std = 0.891. Similar pattern is fOllnd at X/D = 0.50. About 20% turbulence suppression at Std = 0.06 followed by a 44% enhancement at St .•

=

0.118. From this maximum turbulence

{

55 amplification, excitation causes suppression in the range 0.40<Std<1.1O having maximum suppression of 51% at Std = 0.667. The other two X/D locations shows much less effects than the preceding two. The effect of excitation is negligible after Std = 2.0 for X/D ~ 5.0.

The variation of u' e/u' ux upon upstream excitation at Red = 8.56 x 10⁴ is presented in the Fig. 5.6.26. AtX/D = 2.50, 16%turbulence enhancement is found at Std = 0.044 followed by first suppression of 38% at Std = 0.444 and second suppression of 34% at Std = 0.90. At X/D = 5.0, 27% turbulence enhancement is found at Std = 0.223 and 23% suppression at Std = 0.884. The behavior of the other two locations (X/D = 7.5 and 10.0) are found to be like X/D = 2.5 but their relative value of turbulence suppression and enhancement is less.

The effect of upstream excitation on a Y

ID

= 0.50 line is not stable over a band of excitation frequency but sensitive to individual frequencies as shown in Figs.

5.6.27 and 5.6.28. A very zigzag pattern upto Std = 2.0 is observed but after that the effect of excitation is negligible. The following table (Table 5.6.3) summarizes the maximum amplification and suppression for two different Reynolds number.

TABLE 5.6.3

Analysis Table Wall (Upstream Excitation): YID = 0.50.

Reynolds number Location MaximumTurbulence MaximumTurbulence Amplification Suppression

3.49 x 10⁴ X/D

=

^0.50 53% (St. = 0.091) 26% (St.

=

0.727) X/D _{= 0.75} 38% (St" = 0.103) 22% (St.

=

^0.151)

8.56 x 10⁴ X/D _{= 0.50} 35% (St" = 0.132) 42% (St. = 0.323) X/D _{= 0.75} 22% (St. = 0.543) 19% (St"

=

^0.247)

I

The effect of surface excitation on centerline at Red= 3.49 x 10⁴ is presented in Fig. 5.6.29. At X/D = 5.0, maximum turbulence amplification of 58% occurs at Std

=0.013 and maximumsuppression of 46% occurs at Std

=

^{0.847. At X/D}

=

^{7.50 and}

10.0, the excitation has less effect than X/D = 5.0.

The effect of surface excitation on wall at Red = 3.49 x 104 is presented in Fig.

5.6.30. At X/D = 0.50, turbulence amplification of 65% occurs at Std = 0.046 and

first suppression of 25%is found at Std = 0.154 followed by a second suppression of 30%at Std

=

0.616. For location X/D

=

0.75, maximum turbulence amplification of 65%occurs at Std

=

0.078. First suppression of 10%occurs at Red

=

^{0.065 and}

second suppression of 28% occurs at Std = 0.477. These two locations are sufficiently close compared to centerline points, but the turbulence characteristics on excitation are different. So, it can be concluded that, though the pattern of excitation characteristics are similar but they are function of geometric locations.

Fig. 5.6.31 shows the effect of the location of excitation source on centerline turbulence intensity at X/D

=

^{2.50, Red}

=

^{3.49 x 104•} The comparison shows that turbulence amplification occurs at much earlier frequencies in case of surface excitation and the relative amplification is much higher (maximum450%)than the upstream excitation (maximum 48%). However the suppression characteristics is more stable in case of upstream excitation though there location is almost the

same.

AtX/D = 5.0, surface excitation shows earlier and greater turbulence amplification but similar and unstable suppression and is presented in Fig. 5.6.32.

So, surface excitation can cause much more turbulence amplification in the near field of a jet but have similar hut unstable suppression characteristics. Hence for stable turbulence suppression upstream excitation can be recommended.

The effect of the location of excitation source at X/D

=

0.25 on a YID

=

0.50 line is presented in Fig. 5.6.33. With negligible suppression characteristics surface excitation can amplify turbulence about twice the upstream excitation. As presented in Fig. 5.6.34, downstream traverse reduces the effect of surface excitation but still remain iIi prestigious position than upstream excitation.

However, the combined excitation i.e. upstrp.am and surface excitation together, plays a mediocre role.