Laser doppler velocimetry measurements in coaxial, co- and counter-swirling, isothermal jets

•

•

May 1986

LASER DOPPLER VELOCIMETRY MEASUREMENTS

IN COAXIAL, CO- AND COUNTER-SWIRLING, ISOTHERMAL JETS

by

_•

_SEP.

'986

P. A. Robinson, R. A. Cusworth, and J. P. Sislian

TECHNISCHE HOGESCHOOL D~t

'UCHTVAART-EN RUIMTEVAARnEC1fN~

BIBLIOTHEEK KluyveJ:weg 1 -

DaFT

•

LASER OOPPLER VELOCIMETRY MEASUREMENTS

IN COAXIAL, CO- ANO COUNTER-SWIRLING, ISOTHERMAL JETS

by

P. A. Robinson, R. A. Cusworth, and J. P. Sislian

Submitted January 1986

May 1986

UTIAS report No. 308 CN ISSN 0082-5255

Acknowledgements.

The authors wish to express their appreciation to Or. I. I. Glass for his encouragement and support throughout the course of this work.

The financial support of the Natural Sciences and Engineering Research Council under Strategie grant G0691 is gratefully acknowledged.

Summary.

Measured values of the three components of mean velocity and the six components of the turbulent stress tensor are reported in free, co-axial, isothermal, co- and counter-swirling jet flows representative of combustor flows. The objectives are to investigate the effects of specific radial distributions of mean swirl velocity, and co- and counter-swirling annular flows on the flow field. A one-dimensional laser Doppler velocimeter is used to obtain the measurements. It consists of a 15mW He-Ne laser, DISA 55X modular optics with a Bragg cell and electronic frequency shifting to handle high turbulence intensities and reverse flow regions, and a TSI model 1980A counter processor. Data reduction is carried out on-line by a Motorola 6809 microcomputer system which reads and reduces the data from the processor. Measured values are presented for two tangential velocity profiles in co-and counter-swirling annular flows, in all, for four different cases. A central recirculation zone occurs in each case. Streamlines are calculated from the measured velocity distributions, and contours of turbulent kinetic energy are presented. The former show the structure of the CRZ, and the latter indicate the zones of high turbulence intensity (or intense mixing of the flows). Experimental data indicates that the flows are more affected by the direction of rotation of the annular flow than by altering the radial distribution of mean swirl velocity. Counter-swirl tends to increase the turbulent stresses with the maxima occurring near the boundary of the CRZ.

'- _1.0 2.0 3.0 4.0 Table of Contents. Acknowledgements

...

Summary

...

Notation

...

I NTRODUCTI ON

...

EXPERIMENTAL APPARATUS

...

2.1 2.2 2.3

Test Facil ity

...

Swirler Design

...

Laser Doppler Velocimeter Arrangement

...

RESULTS AND DISCUSSION

...

3.1 Effects of co- and counter-swirl cases A and C

...

3.2 _{Effects of co- and counter-swi rl cases} B and D

...

3.3 _{Effect of the radial distribution of W; cases A and} B

3.4 _{Effect of the radial di st ri buti on of W; cases C and D}

CONCLUS IONS

...

REFERENCES FIGURES

...

1 2 4 6 9 9 9 12 15 15 18 20 21 21 23

Notation.

a probe volume major axis.

b, c probe volume minor axes.

c, cl' c₂ constants used in swirler design.

c

N ro S U V W

laser Doppler velocimeter calibration factor, Eq. 2.21; swirler blade chord.

diameter at specified swirler blade station. laser beam exit diameter, dl

=

1.1 mmo

nozzle exit diameter.

beam expander magnification factor, E

=

1.938.

focal length of transmitting opties lens, f

=

600 mm; frequency.

focal length of receiving opties close-up lens, f I

=

300mm. focal length of recelvlng opties lens, f ₂

=

100mm.

focal length of combined receiving opties lenses, fc

=

75mm.

normalized turbulent kinetic energy. turbulent kinetic energy.

mean mass flow at exit.

mean mass flow up to radius r. unit sensitivity vector.

number of data points measured in a sample; number of blades in a swirler.

number of cycles counted by the processor.

radial distance to the edge of the flow at the exit. swirler hub radius; inner radius of annular swirler. nozzle exit radius; swirler outer radius.

radial distance.

radial distance to the edge of the reverse flow zone. swirl number, Eq. 2.1.

axial velocity component. radial velocity component.

tangential (swirl) velocity component. longitudinal distance.

angles formed by sensitivity vector and coordinate axes.

fringe spacing in LDV control volume, óf

=

5.7119 ~.

o

total angle formed by intersecting laser beams, 0

=

6.35080;

flow turning angle of swirler blade 0

=

tan-1

_(W/U).

Doppler frequency.

stream function, Eq. 3.1. exit mean mass flow rate. fluid density.

Superscripts.

time averaged value. fluctuating quantity.

1.0 Introduction

The combustion process, as employed in thermodynamic cycles to increase the internal energy of the working fluid, is performed, in practice, in combustion chambers or furnaces. One practical example is the gas turbine combustion chamber. Stable and efficient combustion is required over a wide range of operating conditions. Added to this are the economic and environmental demands that the combustion be complete and, as much as possible, pollutant-free. Such requirements have led to increased interest in the aerodynamics involved in combustion chamber design, including the aerodynamics involved in efficient combustion.

Stable combustion is sustained by recirculation zones in the flow. These provide a source of hot reaction products convected upstream to mix with and ignite the incoming fuel and air. These recirculation regions can be produced by several means, e.g. bluff bodies, or by imparting rotational motion (swirl) to the fluid. Such swirling flows form a fundamental part of the gas dynamics of many combustion chambers. By swirling the fluid, an adverse axial pressure gradient can be created which exceeds the

momentum of the flow. When the amount of swirl is high, vortex breakdown occurs and causes recirculation in the core region of the flow.

Much work, both experimental and analytical, has been carried out in the field of swirling flows. Sislian and Cusworth (ref. 1) used a

one-dimensional laser Ooppler velocimeter to measure mean velocities and turbulence intensities in a free isothermal swirling jet. The flows were created by single flat-vane swirlers. The existence and dimensions of the central recirculation zone (CRZ) were investigated for strongly swirling .jets. Vu and Gouldin (ref. 2) investigated an isothermal, coaxial,

confined swirling jet, for co- and counter-swirling cases using pitot

probes and hot-wire anemometry. The recirculation region size was found to diminish as annular counter-swirl was decreased. Also higher turbulence levels were found in the shear layer between the jets with counter-swirl. Gouldin and Oepsky (ref. 3) studied the existence of a CRZ for varying degrees of swirl, in reacting and non-reacting co- and counter-swirling

flows, using a one-dimensional LOV. It was found that a recirculation zone was produced in the counter-swirl case regardless of whether the flow was

reacting or isothermal. However, in the co-swir1 case, a recircu1ation zone was only formed in the reacting flow. Sommer (ref. 4) performed similar measurements using a two-dimensiona1 LOV to measure velocity and turbulence properties in a confined, co- and counter-swirling, isothermal jet and found good agreement with previous experimental and numeri cal results. Habib and Whitelaw (ref. 5) investigated a confined coaxial jet with and without swirl. Three methods of measurement were compared, namely pitot pressure probes, hot-wire, and laser Ooppler anemometry. However these measurements were carried out at weak swirl and it is mainly the comparison of pressure probe, hot-wire, and LOV techniques that is of interest here.

One other requirement of the combustion chamber is that the pressure drop across it be smalle This is especially important in aircraft gas turbines from the point of view of efficiency. These pressure losses can be

attributed to wall friction, bends, and the swirlers. Swirler losses can account for up to 25% of the total pressure losse Mathur and Maccal1um (ref. 6) used a Hiett and Powell pressure probe to investigate isothermal, free, swir1ing flows produced by various flat vane-type swirlers of varying degrees of swirl. In that work an equation for the total pressure drop through a f1at-vane swir1er was derived. Kilik (ref. 7) and Lefebvre (ref. 8) point out that flat-vane swirlers, especially those imparting large amounts of swirl (i.e. large vane angle), operate with the vanes stalled. Clearly this is inefficient as the air is not being turned to the angle of the blades, and there will be a large rise in the pressure 10ss across the blades associated with this flow breakdown. One solution to this problem is to use curved blades, which will turn the air in a gentler manner thereby reducing the risk of flow separation and the resulting losses. Ki1ik found that the angle of the vanes in a flat-vane swirler (with

respect to the axial direction), for a given swirl number, was greater than that for a curved blade swirler. Whereas Kilik's blades were simply

circular arcs of constant chord, Buckley et al (ref. 9) derived a method to design a swir1er, of a given swirl number, to produce a predetermined

tangential velocity profile over a radius at the swir1er exit. The resulting b1ades were curved to minimize pressure drop.

Buckley's work forms the basis of the swirler design for this report. Whereas Kilik compared the performance of flat-vane swirlers to the curved vane counterpart, the present work will compare not only the effect of different tangential velocity profiles on the flow field (especially the CRZ), but also the effect of co- and counter-swirling annular flows produced by curved-vane swirlers.

It should be noted, however, that although the swirlers in the present investigation use curved blades, this is done primarily for ease of manufacture (see section 2.2). No pressure drop measurements are attempted.

Much of the previous work was carried out using hot-wire anemometry and/or pressure probes. The present report uses a one-dimensional laser Doppler velocimeter to measure mean velocities and turbulence intensities in non-reacting, strongly swirling flows.

In the next section, a detailed description of the experimental apparatus and the relevant instrumentation used in this work is presented. Section 2.1 contains a description of the various components of the test facility. Section 2.2 outlines the criteria and procedure involved in the design of the swirlers. A brief outline of the analytical procedure is included. Section 2.3 is devoted to the laser Doppler velocimeter system used to perform the measurements. The function of each optical module, and the order in which they are assembled is described, and the basic parameters of the system derived. A brief statement on the estimated accuracy of the measurements performed is also given in this section. Section 3 contains the results of the measurements and discussion on their implications. Two main effects are under investigation; namely, the effect of co- and

. counter-swirling annular flows, and the effect of varying the radial

distribution of the mean tangential velocity in the inner flow. The former is examined in sections 3.1 and 3.2, and the latter in sections 3.3 and 3.4. In all four sections the behaviour of the three mean velocity

components, and six Reynolds stresses are discussed, and the areas of high turbulent kinetic energy located, and compared. Finally, in section 4,

conclusions are drawn on the basis of the experimental results. 2.0 Experimental Apparatus

2.1 Test Facility.

The experimental set-up is shown in fig. 1. A photograph of the actual facility is shown in fig. 2. A centrifugal blower (Joy B900SWS1), driven

by a 1 HP motor, passes air via flexiblepipes into two 406.4 11111 (1611)

diameter settling chambers. The air is filtered (to < 3~) by a filter at

the blower inlet. Inside the settling chambers are a series of baffles to slow the incoming flow, and reduce any asymmetry caused from the blower. Flow is metered by means of a motor tachometer to measure the rotational speed of the blower. The motor speed is calibrated to the velocity at the pipe exit plane. The two coaxial pipes have inside diameters of 101.6 mm (411

) and 50.8 l1l1l (211) . With a rotor speed of 3200 rpm, the velocity across

the exit plane is 10 mis (the velocity in the inner pipe equals that in the

annular pipe). This gives a flow Reynolds number of 6.301x104 • Within

both pipes are honeycomb flow straighteners, and turbulence generating baffles to attain a flat axial velocity profile across the exit plane. The inner and outer flows were both seeded by separate TSI model 3076 constant output atomizers. Air passed through the atomizers was at 40 psi.

This rig was placed on a three-dimensional traversing mechanisme The positioning accuracy of this mechanism is ±.125 mm in the horizontal

directions, and approximately ±1 l1l1l in the vertical direction. The range

of travel is 140 l1l1l in the horizontal plane, and 450 mm vertically. This

allows measurements to an r/D of 1.4, and an x/D of 4. The traversing mechanism was operated manually in all three directions.

2.2 Swirler Design.

The swirler design was based on work carried out by Buckley et al (refs.

9, and 11). All swirlers were designed with a swirl number of 1.5 so as to '

characterizes the intensity of the swirl imparted to the flow, is the ratio ofaxial flux of angular momentum to the axial flux of axial momentum (see

ref. 23). It is defined by;

S

=

--- (2.1)

r dr

Rayleigh (ref. 10) showed that the stability of a fluid in rotational motion depended on the behaviour of the quantity pWr with r. Instability arises when pWr decreases as r increases. In accordance with this theory the cent ral swirlers were designed with mean tangential velocity profiles W = c/r (free vortex); and

W

= c/r2; where c is a constant. Both central swirlers had vanes in the same directions. Two annular swirlers were

manufactured both with profiles W

=

c (constant angle). One annular

swirler had vanes in the opposite direction to that of the other three. The four swirler combinations can now be defined as:

case central w annular w swi rl

A W

=

l/r W

=

c co-swi rl

-B W

=

1/r 2 W

=

c co-swirl -C W

=

l/r W

=

-c counter-swi rl -0 W

=

l/r 2 W

= -c

counter-swirl

With these swirlers in four different combinations, the effect of W-profile may be studied, as well as the effect of co- and counter-swirling annular fl ows.

The design of the swirlers is now described. For more detail see refs. 9,11. Firstly the tangential velocity profile must be chosen. Secondly, the swirl number must be defined for the design. It is assumed that the mean axial velocity, U, is constant both along the blade leading edge, and across the swirler. So with U

=

constant, Eq. 2.1 becomes;

$ = _{--- (2.2)} R

2 U

( R~ - Rf )

2

The blade geometry is shown in fig. 3. It can be seen that the turning angle e

= tan-I(W/U). The radius of curvature, R, at any given radial

position is set equal to the radial distance from the the inlet centreline. This is done for ease of manufacture.

It is now possible to substitute the W profiles constant angle swirler (W = c), this gives

into equation 2.2. For the

3 3

2 (R2 - Rl)

$

=

tan

e

--- (2.3)

Similar functions are derived for different distributions of W, by

substitution in Eq. 2.2. $0 for a swirl number, S

=

1.5; Rl

=

0 m, R₂

=

0.0254 m, for the cent ral swirler; Rl

=

0.0294 m, R₂

= 0.0508 m, for the

annular swirler, the following functions of e were calculated:

W

= ±C

I: W=C ₂ Ir: W

=

C 3 I r2: o = ±61.687 deg. o

= tan- I{.0381/r)

0= tan- I{4.83387x10-4_/r2) (2.4) (2.5) (2.6) The swirl vane geometry (fig. 3) was developed using Carterls rule, based on experimental data obtained from two-dimensional cascades (ref. 11). From these considerations the following equation is derived:

e(~)

+ (2 sin- l

~R)[0.21

+ .002

sin-I(~R)

-

(~)1/2]

= 0

-- (2.7)

The values of

e

from Eqs. 2.4-2.6, are evaluated along the radius and used in Eq. 2.7 to solve for the blade chord, C, along the radius. In Eq. 2.7, d is the diameter at a specified blade station, and N is the number of blades (8 for the central swirlers, and 10 for the annular swirlers). This was solved by means of a computer program. Figure 4(a) shows the swirler

2.3 Laser Ooppler Velocimeter Arrangement.

The optical arrangement has been built up from standard OISA 55X Modular Optics components. A 15mw Spectra Physics model 124B helium-neon laser provided a monochromatic, coherent light source of wavelength À

=

632.8 nm and beam diameter

=

1.1 mmo The be am is folded with a OISA 55X45 prism bench (see fig. 5) and split into two parallel beams of equal intensity by a 55X45 splitter module. The frequency of the central laser beam is th en upshifted by 40 MHz by means of a 55X29 Bragg cell. This causes the interference fringes in the control volume to move at the velocity vf =

40 MHz x öf, where öf is the fringe spacing, and allows for the

determination of fluid direction as well as velocity. The central zero, and first order diffracted beams are then displaced by a 55X28 displacer module. The emerging unshifted and diffracted (shifted) beams pass through the 55X30 backscatter section (not used in this work) and are fed to the 55X32 beam translator, which blocks off the non-diffracted (zero-order) beam and makes it possible to vary the radial separation of the unshifted beam and the parallel first order diffracted (frequency shifted) beam. For an optimum intersection of the beams in the control volume for the present investigation, the separation of the beams was chosen to be 39 mmo The beams then pass through a 55X12 beam expander which expands the parallel incoming beams by a factor E

=

1.938 and hence decreases the dimensions of the probe volume (see equations bel ow), and approximately quadruples the light intensity within it. The resulting pair of beams leave the beam expander through a lens of focal length f = 600 mm, at a separation

distance of 70 mm, and intersect at an angle

e =

6.3508 degs. (see fig. 1). The spacing of the interference fringes is then

Ö _f

=

=

5.7119x10-6 metres

The beam waist of the focused laser beam is d

f

=

~ ~ • E d Î-À

=

2.269x10-4 metres

1

--- (2.8)

--- (2.9)

optical axis of the system) :

d_f

a

=

=

4.096x10-3 _metres

Minor (lateral) axes : d si n

(~)

-- (2.10) b = fe

=

2.272xl0-4 metres cos

(2 )

c

=

_df

=

2.269x10-4 _metres (2.11) In order to reduce the effective size of the major axis, and hence

increase the measurement resolution, the receiving optics were placed 20 degs. off-axis (see fig. 5). The new dimension of the major axis is

F₁

al

=

d

a • _F

2 sin(200)

=

8. 77xl0-4 met res (2.12)

The number of fringes in the control volume is N = _b_ '" 39

f ö

f

(2.13) The light scattered from the seed particles in the probe volume is

collected in the forward direction via the 55X34 receiving optics. The system used in this work consists of two lenses of focal lengths F 1

=

300 mm (close-up lens), and F₂

=

100 mmo The combined lens, which has a focal length 1 1 _₁ ( - + - )

=

75 mm

=

-- (2.14) F 1 F2

focuses the collected light onto apinhole aperture of 0.1 mm diameter situated at a distance of 100 mm from the combined lens arrangement. The focused light is then filtered with a 55X38 narrow bandwidth interference filter (red). The photomultiplier section 55X08 which houses the

photomutiplier tube with a quantum efficiency of ~13% and high sensitivity

(300 ~A/lumen), converts the photon flux to an elecrical signal. The

optical set-up represents a one-dimensional forward scatter system

operating in the differential Doppler mode. The laser and its associated

on the other side of the traversing mechanisme The entire LDV system is kept stationary and the swirler arrangement is moved. The transmitting optics can be rotated 360 degs.; the maximum lateral displacement of the control volume from the axis of rotation, when the system is rotated, is less than 0.1 mmo

Th~ LDV actually measures the instantaneous velocities of small seeding

particles in the flow, which act as light scattering centres. These

particles should be small enough to follow the local gas velocity. For the range of atomizer pressure settings used, the mean oil droplet diameter (previously determined from a special LDV set-up using the so-called

"visibility method"), ranged from 0.8 to 1.0 ~. This particle diameter

range is appropriate in gas flows where turbulence frequencies exceeding

1kHz are to be followed (see ref. 22). The operation of the seeder yielded

a range of particle densities in the order of 109 - 1010 _{particles/m3• The}

outer air surrounding the cold jets was not seeded.

The details of the signal and data acquisition systems, as well as the procedure for rejection of "bad" data points are given in ref. 1. The LDV signal was processed by a counter type signal processor (TSI model 1980A), and was continuously monitored on a HP 1744A oscilloscope. The data

reduction was performed on a Motorola 6809 based microcomputer. The reduced data was displayed on a CRT terminal and then transferred to an on-line printer. A constant time interval sampling method, suggested in ref. 18, was used to correct for velocity bias. No other attempts have been made, in the present experiments, to correct for other biases, for example those due to non-uniform seeding, incomplete signal, and velocity gradients within the probe volume. The last two biasing errors in the present data were considered to be small, in view of the significant amount of frequency shift used and the relatively small dimensions of the probe volume, respect i ve ly.

Measurements of the mean velocity components and turbulence intensities were performed by sparsely seeding the swirling jets, so that only one partiele was present in the probe volume at a given instant of time. The average data rates (as monitored by the TSI 1980A processor) were 12,000/s

exit diameters downstream, and about 200/s at the edges of the flow. The measurement procedure is similar to the method outlined in ref. 1.

For each data point, approximately 8000 individual realizations we re averaged. The various possible errors associated with the processing of individual Ooppler bursts have been discussed in some detail in ref. 24. It is estimated that with the optical and signal processing arrangement used here, the values of the mean velocity components may be expected to be

accurate to 3 - 4% (slightly higher for the

V -

component), the normal

intensities to ~7%, and the shear stresses to ~ 10%.

3.0 Results and Discussion.

Results of performed measurements at axial distances x/O

=

1/8, 1, 2, 3, and 4, are presented in figures 7-52. Because the air surrounding the swirling jet was not seeded, it was not possible to perform measurements near the edge of the jet. The figures show that in all cases, variations in the flow properties die out rapidly as the flow proceeds downstream, and at x/D ) 3 are negligible. The effects of co- and counter-swirl on the

flow field can be assessed by comparing results obtained for cases A and C, and Band 0, whereas the effects of radial swirl velocity distribution can be studied by comparing results obtained for cases A and B, and C and D.

3.1 Effects of co- and counter-swirl; cases A and C.

The mean streamlines of the flows considered are calculated by i nt eg rat i ng the mean axi al velocity components as fo" ows:

r R

<)I

=

21t

J

pUr dr <)10

=

21t

J

pUr dr --(3.1)

0 0

These are plotted in figs. 8{a) and 8{c). The st reaml i nes in case C show a

pronounced waist at x/O

= l.O. At this section the zero streamline passes

through r/O

= 0.305 for case A, and r/O

=

0.20 for case C. It can be seen that the CRZ in case A is longer than in case C. The reverse flow velocities

at this section are -4

mis

for C and -3

mis

for A (figs. 9 and 31). The axial variations of the normalized reverse mass flow rate, calculated using

ra

f

Ur dr mr _a

=

_R- - (3.2) ma

f

Ur dr a

where ro is the radius of the boundary of the reverse flow zone, are shown in fig. 7. The amount of the reverse flow rate is closely related to the strength of recirculation. The rate of heat transfer to the fresh fuel/air mixture by the hot combustion products is proportional to the reverse mass flow rate, and its magnitude is particularly important for combustion stability studies.

The profiles of the radial component of the mean velocity, V, differ markedly. In the co-swirling case (fig. 10) at the exit, V increases

sharply, from 1 to 7

mis

at the boundary of the reverse flow region. In the counter-swirling case (fig. 32) this change is smoother and develops to a slightly lower maximum than in the co-swirl case. The plateau of this profile, which exists in case A, and extends through the shear layer, is absent in C. The magnitude of V in the counter-swirling case does not drop off as rapidly as it does in the co-swirling case.

The profiles of the mean swirl velocity, W, in the co-swirling case (fig. 11) show, most notably at xlO = 1/8, 1, and 2, solid body rotation within

the reverse flow region. At the exit, as U becomes positive, W increases sharply and reaches its maximum value (15.75

mis)

in the shear layer

(riO

=

0.4). It then falls off sharply past this point. In the counter-swirling case (fig. 33), the profiles of W consist of narrow regions of solid body rotation. At the reverse flow boundary (U

=

0) there is a small region

(riO

=

0.275 - 0.35) where W changes direction and reaches a maximum of 1

mis.

This is followed by a sharp decrease to a negative maximum almost equal to that of case A (15.5

mis).

Further downstream the two cases exhibit similar profiles with similar magnitudes but opposite directions.

Despite the constant value of the mean axial velocity component, U, in the reverse flow zone in case A, the normal stresses ~ (fig. 12) change more

rapidly than in case C (fig. 34), although the maximum values reached by

üï2

in both cases were similar (in A

U'2

= 40.5 m2/s 2, and in C

Ui2

=

max max

34.5 m2/s2). Further downstream at x/D

=

1.0, these stresses tend to be

higher in the co-swirling case than in the counter-swirling case. At the

exit the maximum of

UT2

in the co-swirling case occurs at the boundary of

the reverse flow region, whereas in the counter-swirl case this maximum occurs outside the reverse flow region closer to the boundary of the CRI.

Also at the exit section, the radial normal stress

VT7

is higher in the

counter-swirl case (fig. 35) than in the co- swirl case (fig. 13), with corresponding maxima of 27 m2/s 2 and 22 m2/s 2, respectively. As with the

axial normal stresses ~, these maxima occur near the boundary of the

reverse flow zone in case A and near the boundary of the CRI in case C.

However, at x/D = 1.0, the ~ values are higher in the co-swirl case as

compared to the counter-swirl case. Further downstream the magnitudes of the

normal stress V'2 are of the same order, and quite smalle The behaviour of

the tangential normal stress, W'2 , in both cases A and Care very similar to

that of

V"'2

(figs. 14 and 36). However, in general , values of wl

2 are

smaller than those of Vi 2, especially at downstream sections.

The turbulent kinetic energy, k, is calculated by:

k

=

_{--- (3.3)}

2

The profile of k has a higher peak value, at the exit, in case C (fig. 40), this being located near the boundary of the CRI, than in case A (fig. 18) where the peak value of k at the exit is closer to the boundary of the reverse flow zone. Downstream of the exit, values of k are of the same order of magnitude in both cases.

Figures 16 and 38 show that in the near exit region, the shear stress

UTVT

is, in general , larger in case A than in case C. In both cases it is

negative in the CRI and gradually becomes positive outwards to the edge of

the flow. Downstream, the magnitudes of

UTV'

are of the same order and

become quite smalle The shear stresses, UIWI, at the exit, in the

case (fig. 15). In case C, they are nearly negative in the CRZ, except for a small region of positive u'w' corresponding to the change of direction of

W,

dropping off sharply to a negative peak value of -12 m2/s2. In the co-swirl case the values of u'w' are positive and the peak value at the exit is 2.8 m2/s2. In both cases, positive and negative peak values are situated near the boundary of the reverse flow region. In general, the shear stresses yaWl are larger in case C (fig. 39). They are almost zero in the reverse flow region, and negative outside it, except at the exit, where yaWl has a positive maximum at the U = 0 line, and negative maximum near the

~ = 0 line in case C (fig. 39), and a negative maximum at the

U

= 0 line, and a positive maximum at the ~ = 0 line in case A (fig.17).

3.2 Effects of co- and counter-swirl; cases Band O.

The mean streamlines for these cases are presented in figs. 8(b) and 8(d), and show a narrowing of the CRZ with counter-swirl, as well as a slight lengthening. The largest values of ~/~o calculated in the co-swirl case is greater than that in the counter-swirl case implying a greater entrainment of ambient air.

The behaviour of the axial velocity components, U, in both flows considered are similar (figs. 20 and 42). At the exit, U reaches a positive peak just af ter the U = 0 line in case B, and near the line ~ = 0, in case O. At this

section, U has a slight negative maximum near the line U

=

0, in case O. In both cases, at the exit, V is zero within the CRZ up to the boundary of the reverse flow zone (figs. 21 and 43). In both cases

V

rises sharply to a maximum of 8.8 mis at riO

=

0.35, near the boundary of the reverse flow zone in case B, and to maximum of 7 mis at riO = 0.35 near the boundary of

the CRZ in case O. At xlO

=

1, both cases show a negative V, with case B inducing a maximum of -1.8 mis, and in case 0 a maximum of 1.2 mis. Both cases exhibit solid body rotation inside the reverse flow region but in opposite directions (figs. 22 and 44). In the co-swirl case B, W attains a maximum value of 15.8 mis at r

=

0.45, near the boundary of the CRZ. For case 0, W reaches a negative maximum at the edge of the flow (r

=

0.475). Further downstream, the magnitudes of Ware similar in absolute value.

Normal turbulent intensities at the exit reach a maximum at the boundary of the reverse flow region in the co-swirl case, and near the boundary of the CRZ in the counter-swirl case (figs. 23-25 and 45-47). The magnitudes of the

normal stresses

ü'1

and ~ in both cases are of the same order at the exit

whereas ~ in the counter-swirl case is higher (27.5 m2/s2) than in the

co-swirl case (17 m2/s2). The maximum of ~ in the counter-swirl case

coincides with the region of W profile reversal. Further downstream, radial

profiles of

WT2

behave similarly in both cases (figs. 25 and 47).

Lines of normalised turbulent kinetic energy are determined by normalizing the values of k along a section, and joining points of equal values, i.e.

nomalized kinetic energy K

=

--- (3.4)

2 U2 o

where Uo is the integrated mean axial velocity over the exit section. Constant turbulent kinetic energy lines show much higher values in the counter-swirl case (see figs. 30 and 52). The decay of k is more rapid in

the counter-swirl case (see figs. 29 and 51). Oownstream, radial

distributions are comparable. In both cases, maximum values of k coincide with the shear layer and radial distributions exhibit double peak values which decay rapidly as the flow proceeds downstream.

Radial distributions of the shear stress

ü'V'

are similar in both cases

considered (figs. 27 and 49). However, the shear stresses u'w' differ

appreciably in both cases (figs. 26 and 48), being higher in the

counter-swirl case (a maximum at the exit of 6.5 m2/s 2 at r/O

=

0.3). At the

exit in case 0, the radial distribution of u'w' is similar in form to the distribution of w'2 (see fig. 47). The negative maximum of -13 m2/s 2 of

ü'W'

in this case occurs outside the shear layer (r/O

=

0.42), and is much higher than the corresponding maximum of 4 m2/s 2 for u'w' in the co-swirl case. This is primarily due to the W profile reversal. Further downstream, u'w' behaves in similar ways in both cases, but in opposite directions. The

radial distributions of the shear stress v'w' at the exit are very different (figs. 28 and 50). In the co-swirl case, v'w' attains a negative maximum near the boundary of the CRZ, whereas in the counter-swirl case, it first reaches a positive maximum near the boundary of the reverse flow zone and

then drops sharply to a negative maximum similar in magnitude to the co-swirl case. Oownstream, the magnitudes of v·w· decay rapidly and are

almost zero at the axial section xlO

= 2.0.

3.3 Effect of the radial distribution of

W;

cases A and B.

Comparison of the streamlines in both cases considered (figs. 8{a) and {b)),show that, although the lengths of the CRZ·s are similar, its width in

case B is larger than in case A. For example at xlO

= 1.0, the

U

= 0 line in

case A passes through riO = 0.3, whereas in case B it passes through riO =

0.36. The reverse mass flow rate is also higher in case B, at this section

(fig. 7). There are no noticeable differences between the radial

distributions of the mean velocity components

U

and

W

in both cases (see

figs. 9 and 11, 20 and 22). The magnitude of the radial component of the

mean velocity, V, seems to be higher in case B (figs. 10 and 21). This may

explain the reason for the expansion of the CRZ in case B (fig. 8{b)). The

magnitudes of the normal stresses,

UI2,

w· 2, and of the turbulent kinetic

energy k, at the exit, are all higher in the co-swirl cases. However, the

magnitude of the normal stress

V'2

is higher in case B. These maxima occur

at the boundary of the reverse flow region in both cases. Their radial distributions downstream are similar, their magnitude decaying rapidly with

distance from the ~xit. Turbulent kinetic energy is significantly higher in

case A near the exit section (see figs. 19 and 30).

There are no noticeable differences in the radial distributions of the shear stresses u·v· in both cases considered (figs. 16 and 27). However the

magnitude of shear stresses u·w· and v·w· at the exit are higher in case B

with W a 1/r2 , (figs. 15,17 and 26,28). Throughout the flow field, maxima of

the shear stress u·w· occur at the same radial locations in both cases. This shear stress seems to be nearly zero in the reverse flow regions (figs. 15,26). Their maxima also occur at the same radial locations, and the radial

3.4 Effect of the radial distribution of W; cases C and O.

The streamline diagrams (figs. 8(c) and(d)), indicate that the CRZ in case C

is overall, despite the waist at xlO

=

1.0, shorter and wider than in case

O. In case C, more ambient air is entrained, with the highest value of

~/~o shown as 2.3, compared to 1.7 in case O. The radial profiles of the mean axial velocity component, U, are similar in both cases, and peak at the same radial positions (figs. 31 and 42). At the exit in case C, the radial

component of the mean velocity, V, has a smoother rise to a peak value at

riO

=

0.4 than in case 0 where this rise is steeper and occurs at r/O

=

0.35 (figs. 32 and 43). However, in case 0 at x/O

=

1.0, V reaches a

negative maximum of -1 mis at riO

=

0.4, whereas in case C, V increases

gently to around +1 mis. Oownstream from the exit region, V distributions

are similar to each other, and their magnitudes decay rapidly. Radial distributions of the swirl component of the mean velocity, W, are, in

general, similar in both cases (figs. 33 and 44). In both cases the point at which W = 0 coincides with the point at which U = O. It should be noted that at the exit section in both cases, there is a point where U = W = O. At this point, V

=

3 mis in case C, and 1.8 mis in case O. This may account for the contraction of the CRZ in case C.

Radial distributions of the turbulent normal stresses and the turbulent kinetic energy are similar in both cases (see figs. 34-36 and 45-47). At the exit, the turbulent kinetic energy is higher in case C (see figs. 41 and 52), but decays more rapidly than in case O. The shear stresses are, in

general, higher in case 0 than in C, especially near the exit (figs. 37-39

and 48-50). For example, at the exit in case C, u'v' reaches a negative peak value of -3.2 m2/s2 at riO

=

0.3, while in case 0, the negative peak value

of this stress is -4.9 m2/s2. Also, at this section, v'w' reaches a negative

peak value of -7 m2/s2 in case C and of -13 m2_/s 2 _{in case D.}

4.0 Conclusions.

A one-dimensional laser Ooppler velocimeter with optical and electronic frequency shift has been used to obtain measurements of the three components

of mean velocity, and the six components of the Reynolds stress tensor under isothermal conditions in free co- and counter-swirling jet flows. A set of curved va ne swirlers were designed and manufactured to generate

predetermined distributions of the mean tangential velocity W. All swirlers were designed with a swirl number of 1.5. Curved vanes operate much more efficiently than flat vanes due to the fact that the latter always run under stal led conditions. Because of the higher momentum losses, a larger pressure drop across the swirler is associated with flat vane swirlers as opposed to those with curved vanes. Measurements were performed at axial di stances x/D

=

1/8, 1, 2, 3, and 4. These show that in all cases considered, that

variations in the measured quantities decay rapidly downstream, and that at x/D ) 3, they are negligible.

The lengths of the CRZ's are approximately the same in all cases considered, except in the counter-swirl case with W

=

c/r, where it is appreciably

shorter. The CRZ in this case has a pronounced waist at x/D

=

1.0. The jet flow is wider and the entrainment of ambiant air is higher in the co-swirl case. The effects of co- and counter-swirl are, in general, more significant than the effect of the radial distribution of the swirl velocity. In the co-swirling case, turbulence intensities at the exit attain their peak values at the boundaries of the revese flow zones i.e. U

=

0, while in the counter-swirl case, they attain their peak values at the boundary of the CRZ i.e. ~/~o= O. In general, the turbulent stresses are higher in the

..

References.

1. Sislian J. P., and Cusworth R. A., "Laser Doppler Velocimetry

Measurements of Mean Velocity and Turbulent Stress Tensor Components in Free Isothermal Swirling Jet", UTIAS Report No. 281, 1984.

2. Vu B. T. and Gouldin F. C., "Flow Measurements in a Model Swirl

Combustor", AIAA Paper No. 80-0076, 1980; see also AIAA J., Vol. 20, No. 5, pp 642-651.

3. Gouldin F. C., Depsky J. S., and Lee S. L., "Velocity Field

Characteristics of a Swirling Flow Combustor", AIAA 21st Aerospace Sciences Meeting, 1983, Paper No. 83-0314.

4. Sommer H. T., "Swirling Flow in Research Combustor", AlAA 21st Aerospace Sciences Meeting, 1983, Paper No. 83-0313.

5. Habib M. A. and Whitelaw J. H., "Velocity Characteristics of Confined Coaxial Jets with and without Swirl", ASME 1979, Paper No. 79-WAjFE-21. 6. Mathur M. L. and Maccallum N. R. L., "Swirling Air Jets Issuing from

Vane Swirlers. Part 1: Free Jets", Journalof the Institute of Fuel, 1967, pp 214-225.

7. Kilik E., "The Influence of Swirler Design Parameters on the

Aerodynamics of the Downstream Recirculation Region", Ph.D. Thesis, Cranfield Institute of Technology, 1976.

8. Lefebvre A. W., Gas Turbine Combustion, McGraw-Hill series, 1983. 9. Buckley P. L., Craig R. R., Davis D. L., and Schwartzkopf K. G., "The

Design and Combustion Performance of Practical Swirlers for Integral Rocket/Ramjets", AIAA 6th Aeroacoustics Conference, 1980, Paper No. 80-1119.

10. Lord Rayleigh, "On the Dynamics of Revolving Fluids", Proceedings of the Royal Society, London, 1916, A93 pp 148-154.

11. "Aerodynamic Design of Axial-Flow Compressors", NASA SP-36, pp 210-211. 12. Burington R. S. and May D. C., Handbook of Probability and Statistics,

McGraw-Hill Co., 1970.

13. Pfeiffer H. F., "Signal Processing by Counters and Digital Processing of LDA Signals", Lecture series 1981-3, Von Karman Institute for Fluid Dynamics, 1981, p. 498.

14. McLaughlin D. K. and Tiederman W. G., "Biasing Correction for Individual Realization Laser Anemometer Measurements in Turbulent Flows", Phys. Fluids, 1973, Vol. 16., No. 12, pp 2082-2088.

15. Durao D. and Whitelaw J. H., "The Influence of Sampling Procedures on Velocity Bias in Turbulent Flows", Proc. LDA Symposium, Copenhagen, 1975, pp 138-149.

16. George W. K., Jr., "Limitations to Measuring Accuracy Inherent in Laser

Doppler Signals", Proc. LDA Symposium, Copenhagen, 1975, pp 20-63~

17. Buchhave P. and George W. K., Jr., "Bias Corrections in Turbulence Measurements by the Laser Doppler Anemometer", Laser Velocimetry and Particle Sizing, Proc. 3rd International Workshop on Laser Velocimetry. Eds., H. D. Thompson and W. H. Stevenson, Hemisphere Publishing Corp., Washington, 1979, pp 110-119.

18. Stevenson W. H., Thompson D. H., and Roesler T., "Direct Measurements of

Laser Velocimeter Bias Errors in a Turbulent Flow", AIAA Journal, 1982, Vol. 20, No. 12, pp 1720-1723.

19. Mattingly J., "An Experimental Investigation of the Mixing of Co-Annular Swirling Flows", AIAA 23rd Aerospace Sciences Meeting, 1985, Paper No. AIAA-85-0186.

20. Syred N., Chigier N. A., and Beér J. M., "Flame Stabilization in

Recirculation Zones of Jets with Swirl", 13th Symp. on Combustion, The Combustion Institute, Pittsburgh, 1971, pp 617-624.

21. Beltagui S. A. and Maccallum N. R. L., "The Modelling of Vane-Swirled Fl ames in Furnaces ", Jou rn. Inst. of Fue 1, 1976, pp 193-200.

22. Durst F., Melling A., and Whitelaw J. h., Principles and Practice of Laser Doppler Anemometry, Academic Press, 1976, chap. 9.

23. Beér J. M. and Chigier N. A., Combustion Aerodynamics, Krieger Publishing Co.

24. Thompson H. and Flack R. Jr., "An Application of Laser Velocimetry to the Interpretation of Turbulent Structure", Proceedings of ISL/AGARD Workshop on Laser Anemometry, German-French Research Institute, Editors: H. J. Pfeifer and J. Haertig, St. Louis, France, pp 189-239, 1976.

,.. 600mm -1--300mm--e lm A t

( ' m per ure

III

70m~

6.3508°1 - - -

r-T:iJ

I

Photo~ul~i~lie

'

r

.

" " 1 ()1 f..mm - ~

I

and ReCelvlng OptlCS

for Laser and Optics

920mm I I 1 I I I I Table Top Swirlers

Perforated Cylindrical Baffles

... 406. 4mn:t h' - I

Annular Jet Atomizer

r

L-..J

2 Settl in?

Atomization Air

+

L=o 11

t

Central Jet Atomizer

1 }- l I A I A t ' I ' t

i i i , V • nnu ar omlzer n]ec orLlïïii""'" '4iiI

I

-I

10

1

\

_R

Inlet Velocity

u

s

F I G . 3 .

Resultant Outlet Velocity

N Number of Blades _{8 for Central Swirlers} 10 for Annular Swirlers

(a) case A

2 311 1

4151617181

9 17

n

15

\

-=:::,~r~~~

(

I~_

l

__

~J

_

:1_

I I

12

r=-:=l t=..=J 18

FIG_ 5_ TOP VIEW OF EXPERIMENTAL TABLE

AND SCHEMATIC OF DATA

1.

TABLE TOPS

2. 15 mW He-Ne LASER

3.

PRISM-BENCH

4. BEAM SPL ITTER

5 .

'

BRAGG CELL (40 ftiz)

6.

'

BEAM DISPLACER

7. BACKSCATTER SECTION

8. BEAM TRANSLATOR

9. BEAM EXPANDER AND 600 MM

FOCAL LENGTH FRONT LENS

10. JET NOZZLE AND SWIRLERS

11. COLLECTING OPTICS

12. PHOTOMULTIPLIER

13. FREQUENCY SHIFTER

14. COUNTER PROCESSOR

15. 6809 MICROPROCESSOR

16. 2-DISC DRIVES FOR DATA

STORAGE

17. HARDCOPY PRINTER

18. OSCILLOSCOPE

.L To Optical Allis

LDV

Optical Axis

)(

r ; I r - • r

F I G . 6 . FLOW SVSTEM GEOMETRV FOR

EVALUATION OF LASER . DOPPLER

1\ n4 A n4

x

1\ n3 W ,

-</l

n2

POINT A •

13

=

90°

x

A n3

- 1-.

r n2

POINT B. Y

=

90°

</l

A nd K ., r

POl NT C ..

a

=

90°

rn . r-1Tle:> A 0.14 L 0.12 0.10 ~ • 0.08 I-0.06

o.J

O.O2~

+ o O' 0.125 o

•

+ A 1.0

•

c a . s e A 0

..

_B A

..

C +

..

D

•

•

0 A +

•

t

A I I _:t 2.0 _{3.0 4.0} x / D

x / D 1.0 l.:) 1.7 2.0 3~~--~~~4--+---+~--+---+---+---~ 2~--~~~+-~~---+-+-+--~----~---~ 1~-++-~~~~~+-~~~~---____________ ~ - - - - U 0 S t r e a m l i n e s

~~~~~~~~---~

o

0.5 1.0 1.5 r / D c e n . t r a l : annl....llar: c c > - s ' - N i r l w w C / r C

x /D ~ 4~~~~~~ __ T-~ ____ -r ______ O~._7~1_.O_·~1_.3 ___ jï·_7 __ 2r··_O ______________ ~ 3~-+~~~~-r--~--~-+--+-~---+---~ 1 ~~~-+-+-+~~r-~~~~---~

Ya~~~~~~~---~

o

0.5 F I G . 1.0 1.5 r /D c::c:~n t :r a 1.: W <'"'l.r")r")l...l.J.a r : W C Q - s " " i r ]. STREAMLINES IN CASE B C /.r'" C

x / D 4~~~--r-r---'---~--~---r~r---~ 2~~--~-+H+~~-+-+-+--+-~~---~ 1

~~~~~~~---~

o

0.5 r / D 1.0 c e n t r a 1 : ann-u.>1 a r : 1.5 w w c c > - u . n t e r - s " - J i r 1 C / r - C

x / D 0.3 0.7 1.0 1.3 1.7 4~~-r--~--r---r---1ï--'--'---'---~ 3~~-+~+-~~-+----~~--4---4---~ 2~-+--~~-+r--r---+--~+----L---~ 1 1 1 1 1

Ya~~~l~~~~---~

o 0.5 1.0 1.5 r / D c e n t r a . l . : w a n n u l . a . r : w - c c o u n t e r - s 1 N i r l . F I G . 8 C d ) STREAMLINES IN CASE D

5~---~

•••••••••••••••••••

~-~~--~~

_••

~.~·~·~~----.---~---.--~---r----~---~4 o \ \ i

I

i

I

I

'

~ \ \ \ I , I ,

I

1\,

\

\ \

'

,

I , , , \ I " I , , 15 , \ \ \ ' , I , , \ , \ \ I , I' I , , , \ I I , I I I

\ \ \ \

I

, ' I

I \ \ I \ I , I I ,

\ \ I,

I .J I I , \ \ I • • • 11 • • -t • el • • ' • • • 1 , o ,I'" ' . . . ~ \ , I

I

I

I·.,

10 5 • • " • • \ \ i \ \ , " I I I

~-4/~-+~~~\+-~\-4'--~!~--~I--~j--~'~--~/----t---~3

/ \ , \ \ \ ' I

1 /

/

I

. I \ I \ \ ' I / I / I / \ l ' I / I / I I \ " I I / I / 5 _/ / II " , _{\ I "} , I / _{/ / I I} / _/ / / III I, " / / 1 / I / I , I / / / / 10 / .... , II " 1 I I / / / / I / \ 1 , / / , , , 5 I ,/ \ \ . '

+ ., ••• /.

j / 1 / I , . , / ' . / • • • .I. ' [ m / s ] O I _t / _{• •} • \e _\ 1 1 '" _" / / ,

i.· .,

I / / 1 r 1

~,_·~~~/

__

~~\~\~~'i+ i'~I __ ~I-+'-1/ ____ ~J ____ -L! ______________ -12

I '

\ \\

I

1

1

1

t

15 I

I

1 , I ' I t l / I " , l i J I 1 1 1 1 I 1 ,,\ I ,,1 / / I 1 10 I ' / \ I 11

I

~

' I 1 5 I 1 / ~

+

~

r

1

··t.

1 I

I

I / • 1

dil'

' i • ,'. • • •

o " . A : - " 1 I , " I I , " . , ' \ " 11" / / , I

'.J.,

I I I, // / / / I -5 • et 'T I \ I 1 / / ' 1 / I

I

t / \

I 11/ /

I I I

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~~~+-~~~-r~~+-~---~1 11 f ' , /11

I

! /

'" I I // / / I / '" ' / 1// / / I '" ~/I / I I " I .~/ / / 1 I I • //1 11 I I /

" , Ij/I / /. / /

" ,~ ~ 1/1 I ./ ' I " 1 /1/1 I l , " \. 1111 1 / •• I 1 1 ..111 ///1, I I -5 r 1 \ '\

/j// / /

15 10 5 S t r e a r n l i n e s o o o

o

0.5 1.0 1.5 r / D

F I G . 9 . DISTRIBUTIONS OF MEAN AXIAL VELOCITV COMPONENTS: CASE A

Cm/sJ

...

o • • • • • •

-••••••••••••

r~~~~~ __ ,--.~-. __ :-~---~4 I- \ ' " I , i ' \ \ I , , " , ' \ \ I , I ' I I I 8 ~ \ \ I , I " , " :\, \ \ I , , " I , , \ \ I , I " 1 I , \ \ \ , I ' I I I , \ \ I I I I , I \ \ \ \ , I " I I , \ \ \ I ' " ,

I

\ \ I \ , , " , , \ \ \ \ I , " , ,

/" ,\ \ \...l •• '..

1 •

~

•

~

• • • ,..

I 6 4 2 o . . . ~\.\. 1" "I

r , "

, ,

L-~/~~~'~\~~\~\~~I--~i----~-1iL-~---;r'----r---~3

/

\ \\ \, I

I

I : I

I

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\

I \ \ , , " I I I \ \ \ " , I , I ' 6 I II \ I ' ' : I I : I \\ \ ' I " / I I I II I I 1 I I I J I 4

f

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~\

\

1

I: /

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2 , I \ \ \ , ' , I I I I 8

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______________________________ --,1/8 o ,.... -r ~ 1 \

1/1/' l· /

Is

o

0.5 1.0 1.5 r / D

F I G . 1 0 . DISTRIBUTIONS OF MEAN RADIAL

VELOCITY COMPONENTS: CASE A

4 ~---, 16 12 8 4 16 12 8 W 4 [ m / s J 16 12 8 4 16 12 8 4 ~L!.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~~---14 \ \ i " , ' " ' 3 \

\ ,

'

,

,

,

,

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1\ \ \ , 1 1 , 1 1 1 :>., \ \ I , , I I , ' , \ \ I , , , , , ' , \ \ I , , , , , ' \ \ I I , I , , , I , \ I \ , , " , ' " _{\ , I} \ I _{I ,} '

, ' I ,

I " ,

'

' \ , I I I " I , ' / ' , \ \ \ I ,

' I

I I ' I \ \ ' • • ' • • I , I I

I

.1.. ., \.

1 I ~ • • ., • • .'. 1 , \ - \ I 1 " " I .\ \ \ I I I , , , I \\ I I I

I ' ,

I

,

\\ I ,

I , " ,

, II , ,

I , "

I , II , ,

I , "

,

, II , ,

I , ' I

,

, 11' I , I ' I , , I I , ,

I, /

/

,

I

I ' ",',

,"

I " , _{1 ' I , " 1} , 1 \ \" ,

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~~.~~~/~·_·-+--~\~'HI~~/---f'-+~-;·~·~·~~~.~~---~2

, \ I, I , I I I I '11 I , " I , \ , ' 1 1 1

I

, 1 \ , " , 1 ' " , 1 \ " / I ' , 1 , 1 \ I ,11

I

I

I

I

'I \,

,11 I I I I

I

I I , I 1/ I I " I I \ , , " , , , , , I / ' \ "

,11,

, ,

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ftl I \

i TI' /.'. .'

I

I

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,e., •• ,

~'~I~-4-+~I~~~'---r/~'--~'·--·~~---;1

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" ' , " , 1 1 1

"

,,;;.1., / /

"

IJ

1// / / / I ' .J 111,. I / " rf/II 1 1 / , , ~ ,11/1 1 1 1 \ , " " " I .; I I , • 1/11 1 ., 1 , I /111 1 I 1 x / D /1/1 1 I . 1

o~~~~~/~~~/~~/~~~----~---4~8

o

0.5 1.0 1.5 r / D F I G . 1 1 . DISTRIBUTIONS OF MEAN TANGENTIAL VELOCITY COMPONENTS: CASE A

u ' 2 10~---~ 0~~~~~~LL~~~~LI~~~YL~~---~4

,

\ /

,

\ / \ \ /

\

\ /

"

\ \ \ /

, \

_{, \}

\ \

_{\ I}

I

_/ \ \ \ \ I

\ \ \ \

_{\ I \}

I

_/ ;' , \ I \ \ I / ,~\ I \ \ I 40 30 20 10

I.. .'

I • • • 1 • • O~~~~~·~~~~~~~~~~~--t---~3 , \ \ \ \ I I o , \, , \ I I

I

\,

I I

I

/

I ,\ \ \ I

I

I

\1 I I

I

I I ,\ \ \ I

I

I

I', \

I I I I / I \ I I I I I

I

I \ I I I

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