GENERAL JET RESPONSES

Figs. 5.2.1 to 5.2.4 show respectively the variation of mean velocity and turbulence intensities in shear layer and jet column mode. Mean profiles show that the wedge shape exit profile becomes parabolic at about X/D = 5.0.

Turbulence intensity curves show the gradual development of profile peaks along the downstream direction.

Fig. 5.2.5 and Fig. 5.2.6 shows the development and decay of turbulence intensities in different downstream locations. After exit the turbulence intensities gradually increases in the downstream direction and reaches its peak at X/D = 3.0 which is about 36%of centerline velocity. This peak then decreases in further downstream locations to about 20% of centerline velocity at X/D = 20.0.

Centerline mean velocity profiles are presented in Figs. 5.2.7 and 5.2.8 with two different parameter, Uc/U.c and (U.c/Uc)2. This two parameter are used by different researchers e.g. Moore [35]. Hossain and Husain [27]. Rajaratnam [38]

etc. The present results are co~pared with the results of C.J. Moore [35], Azim and Islam [3] and Sforza [47]. Present results are comparable with the data of Moore and Sforza but shows significant shifts from Azim and Islam. This is because the potential core of Azim and Islam is about X/D = 4.0, whereas the potential core of the present study is found at about X/D = 5.3; the corresponding value of Moore and Sfroza is about X/D = 6.0.

In Fig. 5.2.9 the centerline mean velocities at two different Reynolds number is compared. At Reynolds number 3.49 x 104 the centerline velocity decay is given by the following equation beyond the potential core at X/D = 5.3.

( Ue,,)2

_{Uc = 0.2483}

[ X

_{D - 1.263}

]

From the above equation, the rate of decay of the centerline mean velocity is found to be Kc

=

0.2483 and the location of kinematic virtual origin is Ck

=

^1.263.

The variation of (Uec/Ucl2 with X/D is found linear in two steps for Reynolds number 8.56 x 10^4• The first linear variation in the range 5.3 ~ X/D ~ 12.3 is similar to that of Reynolds number 8.56 x 10^4• The equation is given by

( Ue,,)2

_{Uc = 0.2412}

[ X

_{D - 1. 073}

]

which 1.073.

gives the decay rate Kc = 0.2412 and the The second linear variation is found in

kinematic virtual origin the range X/D ~ 12.3.

C_k -_- The corresponding equation is given by

(~:r

^{= 0.4837 [~ - 6.591]}

from which decay rate Kc

=

0.4837 and kinematic virtual origin Ck

=

^{6.591 are}

found.

From the above discussion it can be concluded that the initial or developing region of jet is upto X/D= 5, the range of transition region is 5

<

X/D

<

12 and

,

the fully developed region st!arts after X/D = 12. It can also be said that the average rate of decay of centerline mean velocity is higher for initial turbulent exit condition than the laminar condition. The kinematic virtual origin move down stream with increasing Reynolds number. Similar results were also found by Hossain and Clark [16].

41 The variation of centerline turbulence intensities of unexcited jet is presented in the Fig. 5.2.10. At both Reynolds numbers in the potential core (X/D

<

5.0) the growth pattern of turbulence intensities are nearly the same. After X/D = 5.0 the increasing rate is higher for higher Reynolds number and reaches its maximum value at about X/D = 9.0. The corresponding values of centerline intensity are 20.5% for Red

=

8.56 x 104 and 14.5% for Red

=

3.49 x 104, The centerline intensity then starts decreasing. The decreasing rate is higher for lower Reynolds number.

It may be decided that the peak centerline intensity is located in the transition region. This location of peak centerline longitudinal turbulence intensity is similar to Hossain and Husain [27] who found that the fluctuation u' c/V ec gradually increases upto X/D = 10, reaching the maximumthere then gradually decreases at a slower rate. They also decided that irrespective of jet geometry the maximum centerline turbulence fluctuation is in the range 24.5% :!: 0.5%. In the present study the peak value at Red= 8.56 x 104 is 20.5% which is comparable to Hussain and Husain data. The centerline turbulence intensity data of e,,1. Moore [35] is also compared with the present data. The data of Moore shows peak intensity of 12.5% at X/D

=

9, which is similar to the present study for Red

=

3.49 x 104.

The variation of mean velocities of unexcited jet, measured on a YID = 0.50 line, is presented in Fig. 5.2.11. Reynolds number, Re^w' based on exit velocity at wall (at X/D = 0.025 and YID = 0.50) is also shown along with the Reynolds number Red (at X/D = 0.025 and YID = 0.0). The velocity variation is found to be more sensitive to downstream location for lower Reynolds number. For Reynolds number 3.49 x 104 the wall velocity monotonically increases near the jet exit and reaches its maximumvalue which is 2.37 times the exit wall velocity at about X/D = 0.75 and then falls to a lower value at a slower rate which remains more or less constant in the range 2.5

<

X/D

<

5.00 having a value of about 2.0 times the exit wall velocity and then gradually decreases. However for Reynolds number 8.56 x 10⁴ the velocity increases 1.12 times the exit wall velocity at about X/D = 0.5 and then remain more or less constant upto X/D = 3.0 and then fall at a slower rate than lower reynolds number. This insensitivity of mean velocity variation is due to the stronger flow field at higher Reynolds number.

Fig. 5.2.12 shows the variation of turbulence fluctuations measured on a YID = 0.50 line. For lower Reynolds number the fluctuation gradually increases and reaches its maximum value of 14.2% at. about. X/D = 1.89. The turbulence

fluctuation then gradually decreases at a slower rate. On the other hand the turbulence fluctuation for higher Reynolds number sharply increases and forms a valley at X/D = 1.0. It then increases slowly to reach asymptotic value at about X/D

=

8.0. After X/D

=

2.0 the turbulence intensity in the lower Reynolds number decreases while that in the higher Reynolds number increases.

Isovels (V/Vcl of unexcited jet at Reynolds number 8.56 x 104 are presented in Fig. 5.2.13. The decrease of YO.95 upto X/D = 5.0 indicates the presence of potential core upto X/D =5.0.

The variations of inner edge, half width and outer edge of unexcited jet at Red

= 8.56 x 10⁴ are presented in the Fig. 5.2.14. Their corresponding equations are

YO.95 _ 0.481 _ 0.044 X

D D

Y^O•50 =

D 0.036 [~ - ( - 1.374)

1

Yo.~o

D =

0.529 + 0.206 ^X D

The corresponding equations given by Rajaratnam and Pani [39] for inner and outer edge are

YO.95 =

D

YO.~O

D =

0.475 - 0.097

0.535 + 0.158

X

D

XI D

One of the reason of much variation in the co-efficient is that they used Vec as the non-dimensional parameter and Vc is used for the present study. The angle of inner edge, a1

=

2.52° and the angle of outer edge, az

=

11.97° is found;

whereas the values from Rajaratnam and Pani's equations are a1

=

5.7° and az

=

9.0°.

43 From the equation of jet half width it is found that the jet spreading rate, Ks

=

0.036 and the location of geometric virtual origin, C^g

=

^-1.374.

The variations of inner edge, half width and outer edge of excited jet at Red= 8.56 x 104 are given in Fig. 5.2.15. Their corresponding equations are

YO.95 ~ 0.467 - 0.054 X

D D

YO.50

D

=

0.031 [~ - (- 1.648)]

YO•10

=

0.503 + 0.302 X

D D

It is found that the jet spreading rate Ks= 0.031 and the location of geometric virtual origin. Cg

= -

1.648. The angle of inner edge, a¹

=

3.1⁰ and the angle of outer edge, az = 17.85° is found. The prediction of Squire et al. [46] is found much lower than the present value of outer edge of jet.

As compared with the unexcited value it is found that preferred mode excitation decreases the jet spread rate and shifts the location of geometric virtual origin more upstream from nozzle leap. The inner edge angle a1 and the outer edge angle az increases in preferred mode excitation.

The variation of shear layer length scale, bm = (Yo.so - YO•9S) is presented in Fig.

5.2.16 for Red= 8.56 x 10^4• The empirical equation by Rajaratnam and Pani [39]

is given by

YO•50 - YO.95

-~~~~~- =

D 0.05 + 0.111 X

D

In the present study no such linear relationship is found. However the excited values are always found higher than unexcited values. In the range 1 < X/D <2 the excited values of bm shows consistency with Rajaratnam and Pani's measurement.

i,

I