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Laser doppler velocimetry measurements of mean velocity and turbulent stress tensor components in a free isothermal swirling jet

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Mareh, 1984

LASER DOPPLER VELOCIMETRY MEASUREMENTS

OF MEAN VELOCITY AND TURBULENT STRESS TENSOR COMPONENTS IN A FREE ISOTHERMAL SWIRLING JET

by

/ J. P. Sislian and R. A. Cusworth ~

6 JUNI 1984

TECHrJlSCHE HOGES

LUCHTVAART_ EN

UIMTE~,~~~l DElFT

BfBUOTHe~K' TTECHNIEK

Kluyverweg 1 - DELFT

UTIAS Report No. 281 CN ISSN 0082-5255

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(

Summary

Measured values of three components of mean velocity and the six

components of the' turbulent stress tensor are reported in free, isothermal,

axisymmetric, swirling jet flows representative of combustor swirl flows. The objectives are to provide data against which results of numerical prediction procedures can be compared, and quantitative information on the behaviour of all turbulent stresses and their correlation to spatial

distribution of mean velocity gradients, with a view on improving our understanding of relevant transport processes and on guiding turbulence modelling and prediction efforts of such flows. A laser velocimeter is used

to obtain the measurements. It consists of a 15-mW helium-neon laser,

DISA 55X Modular Optics components with a Bragg cell and an electronic frequency shifter to handle high turbulence intensity and reverse flow regions, and a TS! model 1980A Counter Processor. Signal processing is carried out by a Motorola 6809 microcomputer system which reads and reduces the digital data, from the processor, on-line. Measured values are

presented for the cases of weak (no reverse flow) and strong (with recirculating region) swirling velocities, as well as the case of a

non-swirling straight jet. The streamlines of the flows in all three cases are calculated from measured velocity distributions; in the case of strong swirling velocities the location and extent of the recirculation region is established. Contours of turbulent kinetic energy, derived from measured data, locate the high turbulence intensity zones (i.e. zones of intense mixing). From measured distributions of the mean velocities and various

shear stress components, effective viscosity distributions are derived. Significant radial variation of effective viscosity is shown together with considerable anisotropy of turbulence. These regions of anisotropic

turbulence are identified. Finally, experiment al data indicate a st rong dependence of the turbulent stresses on the local strain of the mean flow, which suggests that an eddy viscosity type turbulence model rat her than a Reynolds stress model could be acceptable for the prediction of such flows.

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Acknowledgements SUll1I1ary

Notation

1. I NTR 00 \JC TI ON

Contents

2. EXPERIMENTAL APPARATUS AND INSTRlJMENTATION

2.1 Test Facility

2.2 Laser Doppler Velocimeter

2.3 Signal Processing and Data Acquisition System

2.4 Measurement Procedure

3. MEASUREMENTS AND OISCIJSSION

3.1 Non-Swirling Jet

3.2 Swiling Jet·Weak Swirl (S

=

0.4)

3.3 Swirling Jet·Strong Swirl (S = 0.79)

4. CONCLUS IONS

5. RECOMMENOATIONS FOR FURTHER RESEARCH

REFERENCES iv i i i i i v 1 4 4 5 6 7 14 14 15 1B 21 22 23

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combustion. Unfortunately, the data presented contain significant scatter both in isothermal and combusting flow situations, and it is virtually

impossible to infer even the general behaviour of certain turbulent stress components. Gouldin et al (Ref. 12) and Sommer (Ref. 13) have investigated nearly similar flow configurations of two confined, concentric co- and counter-swirling jets in a cylindrical combustor with and without

combustion. Measurements were reported on axial and circumferential mean velocity components and of the corresponding turbulent normal stresses in co- and counter-swirl situations. Sommer used a two-component (two-colour) laser Doppler velocimeter to simultaneously measure axial and

circumferential velocity components and hence was able to present, in addition, data on one turbulent shear stress component.

The present report is concerned with laser Doppler velocimetry

measurements of the three mean velocity and the six turbulent stress tensor components in a free isothermal swirling jet. The cases of weak (no reverse flow) and strong (with recirculating flow) swirl velocities were considered, as well as the case of a straight non-swirling jet. The main emphasis is on providing quantitative information on the behaviour and evolution of all turbulent stresses in the flowfield, and their correlation to spatial distribution of gradients of mean velocity components, with a view on

improving our understónding of relevant transport processes and on guiding

turbulence modelling and prediction efforts of such flows. Another

objective is to provide data against which results of numerical prediction procedures can be compared.

In the next paragraph, we present a detailed description of the

experimental apparatus and the relevant instrumentation used throughout this

work. Section 2.1 contains a description of the various components of the

test facility and flow configurations studied. Section 2.2 is devoted to the laser Doppler velocimeter system used to perform the measurements. The function of each optical module, and the succession in which they are

assembled is described and basic parameters of the system derived. This is followed by a presentation of the type of signal processing equipment and the data acquisition system used in Section 2.3. The operating principle and the operating procedures of each component of the signal processing equipment is given. The design and development of the data acquisition system is discussed, and a detailed description of its constituent parts and capabilities presented. The important topic of how measurements are

performed is dealt with in Section 2.4. The measurement procedure employed is thoroughly discussed, with particular emphasis on such critical areas as correct processor filter settings and velocity bias. A brief statement of the estimated accuracy of the measurements performed is also given in this section. Paragraph 3 contains the results of measurements and their

discussion for the three flow situations investigated, i.e., the

non-swirling jet, the weakly swirling jet (no recirculation zone), and the strongly swirling jet (with recirculation zone). The evolution of various measured flow quantities i.e., the three components of the mean velocity and the six components of the (turbulent) Reynolds stress tensor are discussed,

and particular relationships between turbulent quantities and gradients of ·

mean velocity components (local strain rate) noted. Finally, in paragraph

4, certain conclusions are drawn as to theturbulence modelling of such flows, and recommendations for further research in this area, as well as to improve the accuracy of measurements, are enumerated.

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2. EXPERIMENTAL APPARATUS AND INSTRUMENTATION

2.1 Test Facility

A schematic of the experimental set-up is shown in Fig. 1. Air is supplied from a central compressor facility at 90-100 psi. The compressed air is passed through two filters in tandem, to clean it of unwanted

particles, and then regulated down to 60 psi by the first pressure

regulator. The air line then divides into two branches, one going via two diametrical openings to the cylindrical settling chamber of the vertical air duet, and the other leading directly through a pressure regulator and filter to the TSI Model 3076 constant output atomizer. The air flow to the

settling chamber is regulated and controlled by a second pressure regulator and a Fischer

&

Porter flow meter. A 685 mm long and 76.2 mm internal diameter circular duet containing fine mesh screens conneets the settling chamber with the contoured jet nozzle of 25.4 mm exit diameter. The length of this vertical tube assured fully-developed pipe flow at the entrance to swirlers. Swirling motion is imparted to the axial flow by fixed, flat guide vane swirlers. The positions of these swirlers in the duet, for the two càses of swirling jet flow considered, are indicated in Fig. 1. The constancy of the flow rate at the exit of the jet was checked by measuring

the exit centreline axial velocity in the non-swirling jet flow at regular time intervals during a period of approximately two hours. Exit centreline axial veloeities were also measured before and af ter each experimental session. In all cases, the discrepancy between such measured values was always well within the accuracy limits of the measuring technique. The axial symmetry of the flows was assessed by measuring exit axial and circumferential mean velocity components up to a distance of 1/3" on both

sides of the geometrical axis of symmetry. Their relative error, at the corresponding symmetrie position, was within the experimental uncertainty for the weakly swirling jet flow case, with the swirler placed well inside the duct, and of the order of 6% for the case of strongly swirling jet with the swirler placed at the exit of the nozzle (see Fig.

1).

The swirl number S which characterizes the intensity of the swirl, and which is the ratio of the axial flux of angular momentum to the axial flux ofaxial momentum (see Ref. 14) : R

J

2 üwr2d r S

=

_R.::,.l---;:;,---_ _ R2 R2

J

ü2rdr Rl (2.1)

was calculated from measured exit axial, ü, and circumferential,

W,

mean velocity components. Here R2 is the radius of the exit section and Rl the radius of the cent ral hub of the swirler.

The swirling jet flow facility was placed vertically on the lower rigid frame of a three-dimensional traversing mechanism (see Fig. 1). The optical table of this mechanism, to which optical components of the laser Doppler velocimeter is attached, has a circular opening through which the vertical duct protrudes. The traversing mechanism displaces the optical table in two mutually perpendicular horizontal directions and in the

vertical direction. The positioning accuracy of the traversing mechani~n is ±O.125 mm in the horizontal directions and approximately ±1 mm in the

4

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vertical direction. The range of travel was 200 mm in the horizontal and

500 mm in the vertical directions. The traversing mechanism was operated

manually in all three directions.

2.2 Laser Doppler Velocimeter

The opical arrangement has been built up from standard DISA 55X Modular Opties components. A 15 mW Spectra Physics Model 124B helium-neon

laser (wavelength À = 632.8 nm; beam diameter dl = 1.1 mm) provided the

monochromatic and coherent light souree. The beam is folded with the [)ISA 55X45 prism-bench (see Fig. 2) and split into two parallel beams of equal

intensity by the 55X24 beam splitter module. The frequency of the central laser beam is then upshifted by 40 MHz by means of the 55X29 Bragg cello This causes the interference fringe system in the probe volume to move at

the velocity vf

=

40 MHz x of' where of is the fringe spacing, and allows

for the determlnation of fluld motion äirection as well as velocity. The central zero, and first order diffracted beams are then displaced by the 55X28 beam displacer module. The emerging unshifted and diffracted

(shifted) beams pass through the 55X30 backscatter section (not used in the present investigation) 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 probe volume for the present investigation, the separation

of the beams was chosen to be 39 mme The beams then proceed through the

55X12 beam expander which expands the parallel incoming beams by a factor E

=

1.938 and hence decreases the sizes of the probe volume (see Eq. 2.3) and

approximately quadruples the light intensity in it. The resulting pair of

beams leave the beam expander through a f = 300 mm focal length lens at a

beam separation distance of 70 mm and intersect at an angle

e

=

13.3° (see

Fig. 1). The spacing of the interference fringes in the probe volume is then

À

=

2.73x10-6m

2sin ~

The beam waist of the focused laser beam is

df

=

!~

=

1.134x10- 4m

1t Ed 1

The ellipsoidal probe volume dimensions are: .

Major axis (along the optical axis of the system):

a

=

df

=

9.785xl0- 4m

sin ~

2

Minor (lateral) axes:

b = df = 1.142x10-4m; cos ~ 2 5 (2.2) (2.3) (2.4)

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The number of fringes in the probe volume is:

b Nf = - '" 42

of

(2.5)

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 the present investigation consists of two lenses of focal lengths f1 = 150 ll1Tl (close-up lens), and f2 = 100 1llTl. The combined lens,

which has a focal length

f = (.L +

1-

r

1 = 60 mm

c f

1 f2

focuses the collected scattered light onto apinhole aperture of 0.1 mm diameter situated at a distance of 100 mm from the combined lens system. The focused light is then filtered with the 55X38 narrow bandwidth

interference filter (red). The photomultiplier section 55X08 which houses the photomultiplier tube with a quantum efficiency ~13% and high sensitivity

(300 ~A/lumen), converts the photon flux to an electric signal. The optical set-up represents a one-component forward scatter system operating in the differential Doppler mode. Thp entire system is carefully aligned and rigidly mounted to the optical table of the traversing ge ar which makes it quite stable. The transmitting optics can be rotated 360°; the maximum lateral displacement of the probe volume from the axis of rotation, when the system is rotated, is less than 0.11llTl.

2.3 Signal Processing and Data Acquisition System

The photomultiplier output signal carrying the sum of the Doppler frequency, f , and the constant optical frequency, f

=

40 MHz, is fed to the DISA

55N~0

Electronic Frequency Shifter, to

shif~

up or down the signal frequency to a desired level (see Fig. 2). In flow situations of extreme variations of mean velocity and turbulent fluctuation amplitudes, the desired level is chosen 50 as to properly remove the signal pedestal, the

dead zones (velocity directions giving a number of zero crossings that are insufficient for proper counter operation), and to obtain the number of fringes required to optimize the accuracy of measurements, since electronic frequency shifting alters the effective number of fringes in the probe

volume. More importantly, a eombination of optical and eleetronic frequency shifting allows the use of a single linear relationship between the detected frequeneies and all possible positive, zero and negative velocities

encountered at the given point in the flow, and place these frequencies within the range of a pair of high and low pass filters for proper filtering of the photomultiplier signal.

The electronic mixer output signals are analyzed by a TSI Counter Processor, Model 1980A. The TSI 1980A processor is a sophisticated high speed electronic counter capable of resolving 5 ns intervals (100 MHz). The photomultiplier signal af ter being amplified is conditioned by a set of selectable high and low pass filters. The high pass filters remove the de component of the signal ("pedestal") which does not contain any velocity

information. The low pass filters remove the high frequency noise. The filters thus enhance the signal-to-noise ratio which is inversely

proportional to the bandwidth. A high speed Schmitt trigger converts the

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filtered signals, above a certain amplitude, into a square wave that is compatible with the digital counter circuitry to measure the time taken by a single particle passing through the probe volume to generate N = 2n, n

=

1, ••• 5 (selectable) cycles or the total number of cycles. In order to minimize measurement errors due to noise and to the presence of two or more

particles in the probe volume, a comparison is made between the times taken by the particle to generate N and N/2 cycles. The data are validated when the percentage comparison is lower or equal to a preset level. Also, an amplitud~ limit setting is provided in order to reduce the probability of making measurements on large particles that may not follow the flow. A

frequency counter counts the pulses generated each time a new data point is validated by the electronic circuitry and latched into the output register, and provides the data rate (samples/sec) on the readout module (Model 1992) of the TSI processor. The photomultiplier signal and/or the filtered-out

signal (from the processor) was continuously monitored on a Hewlett Packard 1744A oscilloscope.

The TSI 1980A processor has the capability to output the necessary information (i.e., the exponent, mantissa, and cycle number) in digital form. A microcomputer system was developed to read and process the data from the TSI 1980A counter. The microcomputer is based on the Motorola family of microprocessors and interface support devices.

Initially, a 6800 based microcomputer was used to evaluate the

requirements for a data acquisition system. The mantissa and exponent were read through a 6821 PIA (Peripheral Interface Adapter) and stored in the microcomputer's user memory. The data was then stored on cassette tape for further analysis. Software was written to translate the acquired data, which was in packed hexadecimal, to ASCII so that the data could be further reduced by an on-site larger mainframe computer. However, it became

apparent that the limiting transmission speeds available were totally inadequate for the large volumes of data generated by the LDV experiments.

The present computer system incorporates a 6809 microprocessor and has two 5-1/4" disk drives running under the FLEX disk operating system. The exponent, mantissa, and the cycle number, representing 24 bits of

information, are read by two 6821 PIA's and stored in the user memory. The data is reduced during the experiment by the microcomputer system. The

software for this operating system is written in an assembly language

program and was developed at lJTIAS using subroutine packages available from Technical Systems Consultants (TSC). The reduced data is displayed on the CRT terminal and then dumped onto an on-line printer. The data reduction process is quite fast and efficient and permits on-line CRT graphics display with hard-copy capabilities.

A general view of the experimental apparatus is shown in Fig. 3. 2.4 Measurement Procedure

The output from the counter processor consists of a number N of validated instantaneous velocities Vi' i

=

1, 2, ••• ,N. Assuming that this set of measurements constitutes an approximation to the velocity

distribution function, the mean velocity and the mean square of the fluctuating velocity can be obtained from the following statistical formulae:

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N N

L

Vi

L

(V·-V) -2 V· 2 . 1 V = i=1 = 1=1 (2.6) N N

The statistical error caused by the unavoidable limitations of the number of measurements can be estimated if we assume that the velocity fl uctuations form a Gaussian process. If V is the mean of a set of N velocity measurements, Vt the true mean value and at the true standard deviation of the continuous randomly fluctuating velocity, then the confidence levels for the evaluation of the true mean value is given by

(Ref. 15):

Vt ~ V ± Z at (2.7)

IN

where Z = 1.645, 1.96 and 2.58 for 90, 95 and 99% confidence levels,

respectively. Since at is not known a priori, it has to be replaced by the standard deviation om of the set of N measurements (am =

Jv·

2). This is satisfactory if N is large. From (2.7) we get

where Z2 V· 2 N = _ . R 2 V m R m

=

(2.8)

is the relative error in the determination of the mean value. The relation between om and at is given by the following equation:

or N

=

Z2

2R 2'

s

8

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I.)

In the present investigation each set of data points consisted of 2000 instantaneous velocity measurements from which the mean velocity and the mean square fluctuating velocity were determined. Assuming 95% confidence

level, from Eq. (2.9) we get Rs

=

0.031, and for Rm

=

Rs

=

0.031 Eq. (2.8) gives V,2/V2

=

0.50, i.e., mean velocities are determined with an accuracy of 3% if the turbulent intensity does not exceed ~70%. Alternatively, for turbulent intensities of the order of 100% the error in the determination of the mean velocity will be, approximately, 5%.

Figure 4 shows the flow system geometry adopted in the pres~nt investigation to evaluate the local mean flow velocity components and the various correlations of the fluctuating velocity components. The magnitude of the instantaneous Doppler frequency is given by the relationship

V

Vo

= - •

À. V A

e

= -

n2sin -À. 2 (2.10)

where ~1 and ~2 are the unit vxctors in the direction of the two

intersecting laser beams, and n the unit "sensitivity" vector perpendicular to the plane fringes. Equation (2.10) is evaluated in a coordinate system x, r, $ with the origin at the centre of the probe volume, the x-axis parallel to the (vertical) axis of symmetry of the flow, the r-axis in the radial direction, and the $-axis perpendicular to both of them. Let a, ~ and y be the angles formed by the sensitivity vector, ~, with the coordinate axes (see Fig. 4). With the probe volume placed at some point in the flow field, and u, v and w (circumferential velocity component) denoting the components of the instantaneous velocity in the coordinate directions, the above formula (2.10), for a turbulent flow, is written as

2sin ~

_ _ _ 2 [(u+u' )cosa + (v+v' )cos~ + (w+w" )cosyJ (2.11) À.

where the bar indicates a time average quantity and the prime the

instantaneous fluctuation from the average. Averaging Eq. (2.11) yields 2sin ~

C

= _ _

~2

-

-vD = C(ucosa + vcos~ + wcosy);

(2.12)

Squaring Eq. (2.11), time averaging and using Eq. (2.12) to eliminate

v5'

we get

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+ u'w'cosa cosy + v'w'cos~ cosy)] (2.13)

The actual measurements were perfonned in the following way. In any

horizontal section considered, the probe volume was moved, starting from the axis of symmetry, in the direction of the optical axis of the LOV system. At each measurement point A in the flow field along this direction, the unit

vector ~ was placed vertically (a = 00, ~ = y = 900; see Fig.

4).

The

velocimeter measured 2000 instantaneous frequencies v1Di (i = 1, 2, ••• ,2000)

from which the mean velocity component

u

and the turbulent stress u· 2 [see

Eqs. (2.12) and (2.13)J were computed using Eqs. (2.6): 2000

L

(v10i IC) i=l ti = -::-::-::-::----2000 2000

L

i=l u·2

=

-2000 (2.14)

The LOV optical system was then rotated until ~ was in the plane

(r,

~).

Hence a = ~ = 90 0 and y = 00• The velocimeter measured 2000 instantaneous

frequencies v2Di from which, in a similar manner, the mean velocity

component wand the corresponding turbulent normal stress w· 2 were computed.

Next the optical system was rotated +45 0 [a = 45 0, ~ = 90 0, y = {n/2)-450J

and then -45° [a = -45°, ~ = 90 0, y = (n/2)+450J, 2000 measurements of

instantaneous frequencies performed at each of these sensitivity vector positions, and the corresponding mean velocities v 3D/C, v40/C and the mean

-

-square of fluctuating velocities v'5/C2, v45/C2 computed. The turbulent shear stress u'w' was then calculafed by uSlng F.q. (2.13) for positions 3

and 4 and subtracting the resulting equations:

u'w'

=

(2.15)

Af ter traversing the flowfield in this direction, the probe volume was brought back to the axis of symmetry of the flow and moved in a direction

perpendicular to the optical axis of the LOV. At each measurement point B

in this direction (see Fig. 4) the sensitivity vector was given the vertical

position (position 1, a = 00, ~ = y = 90 0), the position in the horizontal

plane (r,~) (position 2, a = y = 90 0, ~ = 00), and then positions ±45°

around the x-axis [position 3, a = 45 0, ~ = {n/2)-450 , y = 900; position 4,

a = -450 , ~ = (n/2)+45°, y = 90°; see Fig. 4]. At each of these positions

of the sensitivity vector ~, 2000 measurements of instantaneous frequencies

were performed and the quantities

v, v·

2 and

ü'V'

computed in a manner

similar to that used in traversing the flow in the optical axis direction.

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In order to determine the remaining turbulent shear stress VIWI, the

flow was traversed a third time along th~ bisector of the right angle formed

by the last two directions. The vector n was placed in the horizontal r, ~

-plane [a

=

90°, ~

=

45°, y

=

(n/2)-450J for all measurement points C (see

Fig. 4), and the probe volume positioned consecutively at the same distances from the axis of symmetry as the corresponding measurement points on the previous two directions. At each point C along this direction, 2000 measurements, vdDi' of the instantaneous frequency were made and the corresponding mean velocity vdD/C and the mean square of the fluctuating

velocity vd5/C2 computed. For this position of the sensitivity vector ~,

Eq. (2.13) yields

---;I 2 2

vdD = Vi + wl + VIW I

C2 2

If we assume that the values of V,2 and W,2 at point C in the

axisymmetric flow are equal to those measured at points A and B, then we can

determine VIWI from the equation

VIW I

12 v 12 + W,2

= vdD _ B A

C2 2 (2.16)

Thus, a11 the mean velocity and turbulent tress tensor components were determined at the measurements points in the considered section of the flowfield.

All the measurements and their reduction were performed according to the following methodology. The counter processor data rate was dependent on

several factors, such as the atomi zer seedi ng density, the photomulti pl ier gain, the gain, the "amplitude limiter" and the "comparison" settings of the processor. In all measurements performed, the gains of the photomultiplier and processor were kept as low as possible in order to minimize electronic noise, and the "amplitude limiter" on the processor was adjusted so as to

eliminate large particles that may not be following the flow. These

sett i ngs were estab 1 i shed by vi sual ob servat ion of the osc i 110scope traces of the direct photomultipli"er signals and of the filtered-out signal from

the processor, as well as the processor. data rates, during a number of test

runs in various flow situations considered, and were seldom changed during the experiments. The seeding density, i.e., the concentration (by number) of particles per unit volume, was varied by operating the TSI model 3076 atomizer at a constant settingand b)L-"'passing a selected portion of the

output. In a11 experiments the level of the particle concentration was

selected in such a way as to maintain almost one particle in the probe volume for most of the time. This level was established by visual

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observation of the oscilloscope traces of the photomultiplier signals, at relatively slow sweep rates, on the basis of the experience gained during seed parti cl e si ze and concentrati on eval uati on experiments. With a IIcompari sonll

sett i ng (accuracy requi red between time enve 1 ope measurement s for N and N/2 cycles) of 5% for the case of the nonswirling jet, of 3% for the case of the weakly swirling jet (S = 0.4), and of 1% for the case of the strongly swirling jet (S

=

0.79), this set of adjustments gave average data rates (as monitored by TSI 1980 processor) of approximately 10,000/s in the case of the non-swirling jet and 5000/s in the cases of swirling jets in the central portion of the exit sections.

Special attention was given to the problem of optimum filtering of the photomultiplier input (to the processor) signals. Correct filter setting is one of the most critical adjustments in any actual LDV set-up (Ref. 16). Theoretically, correct filter setting is only possible with an a priori knowleçige of the expected mean frequency and the standard deviation. In the present investigation the high and low pass filter settings of the TSI

processor were adjusted in the following way. For each individual measuring

point and position of the sensitivity vector ~, the microcomputer takes first a set of digital data with a relatively wide filter range, and computes instantaneous frequencies according to the formula

f

=

Nx109

D x2m n-2

Here N is the number of cycles per Doppler burst, n the exponent and Dm the mantissa of the time envelope. The mean frequency f and the standard

deviation a

=

~

are computed next, according to Eqs. (2.6). The

computer further proceeds to remove IIbadll

data by rejecting all measured instantaneous frequencies which lie outside the range f ±3a. A new mean and standard deviation is recomputed using the remaining data. These final values are used to compute fmax

=

f+3a and f i

=

f-3a. These values are displayed on the CRT monitor and the high an~ 90w pass filters of the processor adjusted so that fmax and fmin can pass; the whole computing process of f 'and f,2 is then repeated again. If the new val ues of fmax and fmin are within the bandwidth of high and low pass filters, the new computed values of

f

and f,2are accepted. The positioning of fmax and fmin within a bandwidth of high and low pass filters is made possible Dy varylng the amount of electronic frequency shift on the DISA 55N10 Frequency Shifter.

The effective number of fringes in the probe volume depends on the amount of electronic frequency shift used and the flow velocity at the

measurement point. In order to minimi ze errors in frequency measurements

due to noise, the maximum possible number of signal cycles N, compatible with the desired data rate, were used. In general , in relatively high velocity regions in the flow, the number of signal cycles timed for

frequency measurements was set to N = 16, whereas in low velocity regions of the flow N was set to 32, the maximum number of measurable cycles for the TSI Model 1980A processor. Values of N lower than the above number of

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signal cycles, as well as the so-called total burst mode (all cycles of the Doppler signal used to measure the instantaneous frequency) were not used in the present experiments.

It is well known that statistical parameters obtained from

instantaneous frequency measurements by counting techniques of individual Doppler signals are subject to biases from several sources (see, for example, Ref. 17), the most significant of these being the so-called velocity bias. In principle, this biasing occurs in turbulent flows,

because the sampling of the fluctuating velocity history at a given point in the flow, by the LDV system, is random. Even when the seeding particles are assumed to be uniformly distributed throughout the fluid, a larger volume of high velocity fluid, and hence a larger number of seed particles, would pass through the probe volume than for low velocity fluid. Thus, the processor would count more fast particles than slow ones and, therefore, the ensemble (based on the randomly sampled velocities of the seed particles) averaged velocity would be higher than the true time averaged velocity; the

difference between the two is the velocity bias. Several correction schemes have been proposed (see Refs. 18-21). Unfortunately, there is still

consi derab 1 e di sagreement as to the proper correcti on approach. In the present work, the error caused by velocity bias was minimized by following the approach used in Ref. 22.

An ensemble average will approximate a time ave rage if the sampling of the velocity history is performed at equal or nearly equal time intervals.

It is possible to obtain a close approximation to sampling at equal time increments by controlling the relationship between the data rate, as

displayed by the TSI processor, and the computer speed, i.e., the number of data per second that the microcomputer processes. Whenever the processor

has a validated data ready, it sends a data ready pulse to the

microcomputer, which then returns a data inhibit pulse to the processor; this causes it to hold that data until the microcomputer records and processes it. Once the data is processed, the microcomputer removes the data inhibit pul se, waits for another data ready pul se, and the process of

data acquisition and processing by the microcomputer continues. In the data

acquisition system used in the present investigation, the data acquisition rate by the computer was made variable, so as to always keep, approximately, a ratio of ten-to-one between the processor data rate and the computer data acquisition rate (i.e., the computer sampled one out of ten validated data supplied by the processor). When the computer is ready for data, the

processor will have it ready in a very short time due to the high processor data rate. As aresult, the actual sampling is performed at nearly equal time intervals. In Ref. 22, it is shown that measurements performed in this way coincide with randomly sampled measurements corrected according to McLaughlin and Tiedermanis one dimensional velocity weighing (Ref. 18). No other attempts have been made, in the present experiments, to correct for velocity bias or for any other biases, for example, the non-uniform seeding bias, the incomplete signal bias, velocity gradient bias, etc. (see Ref. 23). The last two biasing errors in the present data are considered to be

small, because of the significant amount of frequency shift used and the relative smallness of the probe volume, respectively.

It is difficult to assess the accuracy of laser velocimeter

measurements in turbulent flows due to sources of potential signal biasing (at least ten such sources are cited in Ref. 25). However, by paying

careful attention to the choice of components of a laser velocimeter and to their integration, most of the biases can virtually be eliminated.

(15)

Evaluating the accuracy of laser velocimeter data by comparing them to, say, hot-wire measurements in the same flow, although useful, is not quite

convincing, as the hot-wire data have their own inherent sources of errors. Based on a rough estimate of various significant sources of error in the present opt i ca 1 and si gna 1 processi ng arrangement, it is suggested that expected uneertainties in mean velocity measurements are of the order of 3-4% (sl ightly higher for the

v

component), in normal Reynolds stresses of the order of 5%, in the xr- and x~-eomponents of the Reynolds shear stress of the order of 8%, and the r~-comopnent of ~10%.

3. MEASUREMENTS AND DISCUS5ION

Measured values of the three components of the mean velocity and the six components of the turbulent stress tensor are presented for the cases of weakly swirling, S

=

0.4, strongly swirling, S

=

0.79, as well as for a non-swirling, 5 = 0, free jet flows. The exit Reyn~lds numbers, based on

the average axial velocity at the exit, Üo

=

40

0/nD , where

00

is4the exit

volumetrie fl~w rate and 0 the nozzl. exit diameter, were 2.2Hx10 (S

=

0.0), 1.39x10 (5

=

0.4) and 1.16xl0 (S

=

0.79) for average velocities of 13.36, 8.15 and 6.8 mis, respectively. Measurements for the non-swirling jet flow were performed to test the effectiveness of the measurement procedure used. They are also intended to allow a qualitative and quantitative comparison with the swirling jet flow cases.

3.1 Non-Swi rl i ng Jet

Measurements for the non-swi rl i ng jet flow were performed at

distanees x/D

=

0.125, 2, 4, 6, 8, 10, 15 and 20 from the nozzle exit plane. These data are presented in Figs. 5-23. Mean streamlines of the flow are plotted in Fig. 18, where ~ is the stream function

r ~ = 2n

J

pürdr o and R ~ 0 = 2n J p ü rd r o (3.1)

is the exit mean mass flow rate. Figure 5 depicts the centre-line

distribution of mean axial velocity, axial and radial Reynolds stresses and turbulent kinetic energy. The cent ral core extends to, approximately, four nozzle diameters and the turbulent stresses are negligibly small in that region. In the transition region the mean axial velocity decays due to entrainment of ambient fluid by the jet, and the centre-line turbulent

stresses reach maximum values at about 8-10 diameters from the exit. In the fully developed turbulent flow region (x/D ~ 10), the flow variables decay asymptotically. The development of the mean axial velocity distributions in the flow follow the self-similarity rule (Figs. 6-14), and the mean radial velocity is negligibly small everywhere. All turbulent' stresses reach their maxima at the same radial locations in all sections which, close to the exit

section, lie on the streamline ~/~o

=

1.0 separating the flowing fluid from ambient air (shear layer). As the flow develops, these maxima deeay rapidly and in the fully developed turbulent flow region converge to the centre-line (see also Figs. 15-20). The nondimensional turbulent kinetic energy, k, which is a measure of the mixing intensity, reaches its maximum value in the shear layer, somewhere between two and three diameters downstream of the

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exit section. shown in Fig.

Contours of equal nondimensional turbulent kinetic energy are 18. The maximum value of k is close to 0.031. The radial Reynolds stress V,2 is always smaller than the axial U,2, throughout the

flowfield investigated, and the shear stress,

U'V',

is even smaller. Figure 19 shows flow regions where 0.8 ~ V,2/u,2 ~ 1.2. From this figure it can be

seen that turbulence is isotropic in the fully developed turbulent flow zone. Turbulence production characteri zed by the quantity

-ü"?"( ou/or) is

always positive in the investigated flow field, attaining peak values in the shear layer with a maximum peak at about two diameters downstream from the exit. If an eddy viscosity model is assumed to predict turbulent stresses, then from measured val ues of the tangential stress Ui Vi and mean axial

velocity, the eddy (turbulent) viscosity can be evaluated from the relation

~xr

=

_pUIV I

=

~ oü

tï;r

Such di stributions are shown in Fig. 21. The maxima are located in the shear layer and increase gr.aduall:y; as with other flow characteristics, their radial positions move steadily inward and attain the axis of symmetry as one proceeds downstr-eam. Radial distributions of the turbulent length

scale, evaluated from the relation

1/2 ~t "" pK .R.

and measured values of k are presented in Fig. 22. Radial and streamwise variation of.R. is similar to that of turbulent viscosity, ~t. lt is

worthwhile to note that predicted distributions of .R. and ~t, using the k-E model of turbulence (see, for example, Ref. 24), are similar to those derived here from measured val ues of relevant quantities. If a

local-equilibrium turbulence model is assumed, the length scale .R., which is the mixing length, .R.m, in this case, can be evaluated from

k1/ 2 ou/or

Mixing length distributions, depicted in Fig. 23, exhibit regions of

constant magnitude in the central portion of each section. Their behaviour is similar to those calculated in Ref. 5.

3.2 $wirling Jet-Weak Swirl ($

=

0.4)

As shown in Fig. 1, the guide vane swirler for this case was placed 10 inches below the jet exit plane, just before the nozzle contraction.

Measurements were performed at distances x/D

=

0.125, 1.0, 2.0, 3.0, 4.0 and 5.0 downstream of the nozzle exit. Measured values are presented in Figs. 24-55. The mean streamlines of the flow are plotted in Fig. 24. There are

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no recirculating fiow regions, but the spreading rate of the jet is

significantly higher than that for the nonswirling jet (see Fig. 18). The edge of the jet flow is arbitrarily defined as the line along which the magnitude of the axial velocity is one tenth of its maximum value at the section. Figure 25 depicts the centre-line distributions of mean axial velocity, axial and radial Reynolds stresses, and turbulent kinetic energy. Compared to the case without swirl, the mean axial velocity exhibits a much faster decay and the cent ral core has almost disappeared. The evolution of the axial Reynolds stress, u· 2 , is similar to that for the nonswirling case, but its magnitude is, generally, larger. In the initial part of the flow, measured values of the radial Reynolds stress, v· 2 , are quite high. It is believed that this is due to the presence of a central hub of 0.5" diameter on the guide vane swirler. In the central part of the flow, the magnitude of this stress gecays rapidly, and 2.5-3 diameters downstream from the exit, its value approaches that of the axial stress, u· 2, similar to the case without swirl (see Fig. 5). Correspondingly, relatively high values of turbulent kinetic energy prevail in the initial part of the flow; however, they decay rapidly as the jet spreads downstream.

Figures 26-53 represent radial distributions of mean velocity and Reynolds stress tensor components. The mean axial velocity component, ü, is no longer uniform at the exit section (Fig. 26) due to changes of pressure distributions as the cross-sectional area changes along the length of the duet. Af ter a distance of about two diameters the axial velocity profile has a Gaussian form, which it conserves at subsequent sections (see also Fig. 32). The jet expands rapidly in a manner similar to a nonswirling jet af ter about 3-4 diameters downstream of the exit. The exit profile of the rnean circumferential velocity component,

w

(Fig. 26), is, approximately of

the Rankine vortex type, with a small central solid body rotation region near the axis of the flow, with the maximum value at riO ~ 0.15. Oownstream of the exit, maximum values of the swirl velocity decrease rapidly and at x/O ~ 4.0 the swirl velocity is practically negligible (see also Fig. 34). The mean radial velocity component is small throughout the flow field (see also Fig. 33). The mean axial 'velocity component gradient in the axial direction is small compared to its gradient in the radial direction. The mean swirl velocity gradient in the axial direction is larger than that of mean axial velocity and not so small compared to its gradient in the radial direct ion in the central portion of the flow at x/O ~ 1.5-3.

Radial distributions of nonnal Reynolds stresses and turbulent kinetic energy at the nozzle exit are shown in Fig. 35. As noted above, high values of the radial and circumferential stresses in the near-axis region are

attributed to the presence of a central hub on the guide vane swirler. Relatively high turbulent stresses are also generated in the shear layer at the edge of the jet. In the remaining portion of the section all normal stresses are small, and are of similar magnitude for riO ~ 0.1. Similarly, the turbulent kinetic energy is large near the axis and at the edge of the flow. At subsequent sections (Figs. 36-40) the high turbulence levels in the near-axis region decay rapidly and the normal stresses maxima in the shear layer move inward (see also Figs. 41-43). For x/O ~ 3, radial and circumferential stresses in the near-axis region attain the magnitude of the axial stress, and the distributions of all nonnal stresses become similar to those of a nonswirling jet, with maximum values moving towards the axis of

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symmetry. The distributions of the turbulent kinetic energy follow the trend of normal stresses (see also Fig. 44), with values generally higher than those encountered in the equivalent nonswirling jet. Figure 45 shows contours of equal nondimensional turbulent kinetic energy. Relatively high turbulent intensity levels exist in the near-axis region and in the shear

layer region (around the

<vNo

= 1.0 streamline) in the initial zone of the

flow. The extent to which normal Reynolds stresses are isotropic is

examined in Fig. 19. Isotropy was found over a substantial portion of the

flow field. Measured values of the Reynolds shear stresses, Figs. 46-50,

show that

U'V'

and v' w' are 1 arge compared to the shear stress u' w'. In the

initial part of the flow, the shear stresses u'v' and v'w' are,

approximately, of the same order of magnitude. This seems to contradiet the results found in Ref. 5, where these stresses were computed from measured

mean velocity profiles. The results in Ref. 5 suggest that, at x/D = 2, the

stress v'w' is smaller than

UTV',

and that the magnitude of this stress

decreases further as the swirl number increases. The present measurements indicate that the shear stress v'w' decays more rapidly than the stress

UTV'and at about four diameters downstream from the exit,

ü'VI

becomes the

dominant shear stress (in agreement with the results of Ref. 5), as the swirl velocity becomes negligibly small and the jet expands rapidly

downstream, in a manner similar to a nonswirling jet (see also Figs. 51-53).

The second peak in the v'w' value at x/D

=

4.0 (Fig. 50) is probably due to

scatter in measured data. In all sections, except in the shear layer at the

exit and at x/D

=

1.0, the shear stress u'w' was found to be small and can

be discarded in predicting such flows. In general , normal stresses are

higher than the shear stresses in weakly swirling jet flows.

The shear stress distributions also show that regions of maximum shear

stress

.

""üï"VT

correspond to regions of maximum radial gradients ofaxial

velocity. Introducing again turbulent (eddy) viscosities as a framework to

a turbulence model, we can write, for the present case of nonrecirculating swi rl ing (bounday-layer type) flows, the significant shear stresses in the form

"xr

=

-pu'v'

=

~t oü and

xr or "r'" 'I'

=

-pv'w'

=

~t r.(o(w/r) rq, or

Values of eddy viscosities ~~r and ~~ derived from measured values of the

shear stresses and mean veloclty

comp~nents

are presented in Fig. 54. In

the initial region of the 'f1o,w, i.e., for x/D =_1 .... 2, both eddy viscosities

have the same order of magnitude and similar radial distributions. {heir

magnitude increases furtner downstream and ~~ becomes larger than ~xr.

Also, their radial distributions change.

t The<Pradial position of ~Fdl. maximum

moves outwards, whereas the m~ximum of ~xr moves towards the axi s ot

symmetry. The evolution of ~xf becomes slmilar to,that of a nonswirling jet

(see Fig. 21), although its va ue for the swirling case is higher than for

the nonswirling jet. It CM, therefore, be concluded that, for the type of

flow considered and within the framework of eddy viscosity turbulence model,

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~~r and ~~$ are, in general, neither uniform nor similar in magnitude. For turbulence modelling purposes, the further assumption of local equilibrium turbulence can be made, i.e., turbulence can be presumed to be

produced and di ssi pated at the same location. Neglecting the convection and diffusion of energy, the partial differential equation for the turbulent

kinetic energy for the case considered (see, for example, Ref. 25, Eqs. 52 and 80) yields a turbulence length scale

proportional to the mixing length. Radial distributions of this length scale are depicted in Fig. 55. The peak in the central portion of the curve for x/O

=

2 seems to be due to scatter in measured data. It is seen that the behaviour of the curves is similar to that of a nonswirling jet (see

Fig. 23), although regions of approximately constant mixing length

magnitudes of each curve are less accentuated in the present case than for a nonswi rl i ng jet.

3.3 $wirling Jet·$trong Swirl ($

=

0.79)

As shown in Fig. 1, the guide vane swirler, for this case, was placed at the nozzle exit. Measurements were performed at distances x/O

=

0.125, 1.0, 2.0, 3.0, 4.0 and 5.0 downstream of the nozzle exit. The mean

streamlines of the flow, calculated by integrating mean axial velocity components (see Eqs. 3.1), are plotted in Fig. 56. The swirling jet flow has now a substantial region of recirculation in the central part of the flow. The upstream stagnation point is inside the nozzle, close to the trailing edges of the swirler's guide vanes, and could not be determined. The downstream stagnation point is very close to x/O

=

4.0. The zero streaml ine encompasses the internal recircul ation zone; at the exit its position is, approximately, situated at r/O

=

0.375. The zero velocity line, which divides the forward flow from the reverse, is also shown. Oue to insufficient experimental data the eye of the vortex could not be

located. The streamline ~/~o

=

1.0 represents the volumetric fiow rate of the nozzle fluid; values of streamlines above this represent entrainment of fluid from the ambient stagnant air. The spreading rate of the jet is higher than that of the \'teakly swirling jet (see Fig. 24).

Figure 57 depicts the centre-line distributions of mean axial velocity, axial and radial Reynolds stresses, and the turbulent kinetic energy. The axi&l mean velocity component, in absolute value, reaches its maximum at x/O '" 1.0. The axial Reynolds stress is maximum at the exit, and has no apparent peak in the recirculation region. In contrast, the radial Reynolds stress and the turbulent kinetic energy attain maximum values in the central portion of the reci rculation zone. Past this zone, both normal turbulent stresses and the turbulent kinetic energy decay rapidly in a

manner similar to the two previous cases investigated above (see Figs. 5 and 25), and attain values of the same order of magnitude in both swirling cases considered. Their values at the downstream stagnation point are quite low.

Figures 58-63 represent radial distributions of mean velocity components. The maximum values of the positive mean axial velocity

component move outwards and decay as we proceed downstream in the flow (see also Fig. 64). At x/D = 5.0 (Fig. 63), the mean axial velocity distribution

18

(20)

has al ready the well-known hump-type shape peculiar to the far downstream regions of strongly swirling jets. The radial component of the mean

velocity is small; it is negative in the recirculation bubble and positive

outsid~ it. As is the case with the mean axial velocity component, its maximum at the edge of the jet, at the exit, moves radially outwards and decays at subsequent downstream sections (see also Fig. 65). Also, values of the radial mean velocity component are higher in this case than for jets

with S = 0.0 and 0.4. The exit profile of the mean circumferential velocity

component,

w

(Fig. 58), consists of two parts: the inner part, within the

recirculation zone has a linear, rigid body rotation distribution; in the

outer main swirling flow region,

w

reaches maximum at the edge of the flow

and then decreases rapidly. Inside the recirculation zone, the fluid

rotates as a rigid body; the angular velocity of this rigid body rotation

increases initially, reaching a maximum at x/O ~ 1.0, and then decreases

gradually with downstream distance. At approximately x/D

=

1.0 (Fig. 59), a

transition takes place from the exit profile to the Rankine vortex profile. Maximum swirl velocities occur outside the recirculation region. The radial positions of these maxima move radially outwards and decay rapidly (see also

Fig. 66). The magnitude of mean swirl velocity is quite small at x/D = 5.0

(Fig. 63), and is comparable to that of the mean radial velocity component. The positions of maxima of radial gradients of mean axial and

circumferential velocity components approximately coincide with the zero

velocity line in the recirculation zone, up to a distance x/D ~ 2.0.

Double peak values of normal Reynolds stresses, and hence, of

turbulent kinetic energy were found at the exit section (Fig. 67). Similar double peak values have also been reported in Ref. 11. These peaks are produced in regions with high gradients of mean velocity. Measurements show that the inner peak values of normal Reynolds stresses are located close to the zero streamline (i.e., near the edge of the recirculation zone). The outer peak (maximum) values are due to the shear layer at the edge of the

jet flow. These double peak values of u· 2 persist up to a distance x/D ~

?-3, the outer peak value decaying more rapidly than the inner (Figs.

68-70). The double peak values of v· 2 also persist up to the same distance, but although the outer peak decays, the inner peak value first increases

(Figs. 68-70) and then decays slowly at subsequent downstream sections. Inner peak values of u· 2 and v· 2 remain near the edge or move slightly

inside the recirculation zone (at x/D ~ 1.0) up to x/D ~ 2.0. Downstream,

they clearly fall outside the recirculation zone (see also Figs. 73 and 74). The inner peak value of w· 2 (Fig. 67) decays very rapidly and has almost

disappeared at x/O = 1.0 (Fig. 68). Further downstream, the distributions

of normal stresses gradually approach those in a weakly swirling jet. Their

magnitudes are quite small at distances x/D

=

4-5 (see also Figs. 73-75).

The distributions of kinetic energy of turbulence is similar to those of normal stresses (see also Fig. 76). Contours of nondimensional turbulent kinetic energy are depicted in Fig. 77. The figure shows that maximum turbulence is generated in the shear layer existing at the edge of the swirling jet flow immediately af ter the exit. High values of turbulent kinetic energy also exist near the zero streamline at the exit. The kinetic energy of turbulence decays rapidly in the axial and radial directions as the swirling jet expands rapidly into the stagnant surroundings. Except at

(21)

the exit section, the u· 2 and v· 2 stresses are, in general , larger than the

w· 2 ; up to a distance x/D ~ 2.0, the v·2 is larger than u· 2 in the outer

part of the flow and smaller in the inner region of the flow. Further

downstream, u· 2 and v· 2 attain the same order of magnitude in the central region of the flow field, with v· 2 remaining larger than u· 2 in the outer region. The relative orders of magnitude of the normal Reynolds stresses in the flow field can also be inferred from Fig. 19{c), which shows flow

regions where 0.8 ~ v· 2/u· 2, w· 2/u· 2 ~ 1.2 (dark areas) , i.e., flow regions

where near isotropic turbulence prevails.

Reynolds shear stresses, presented in Figs. 78-82, are appreciably smaller than the normal stresses (Figs. 67-72). At the exit section, Fig. 78, the distributions of shear stresses exhibit double peaks. The radial positions of the inner peak values, positive for the u'w' stress and negative for u'v' and v'w' stresses, coincide with those of the normal stresses, i.e., they are near the edge of the recirculation zone; the outer positive peaks are located in the jet flow boundary (shear) layer. Further downstream the shear stresses decay rapidly and become quite small at

distances x/D

=

3.0-4.0 (see also Figs. 83-85). Both peak values of

U'V'

decay at approximately the same rate. , Their radial locations coincide with

those of the normal stress u· 2 at all downstream sections (see Fig. 73),

i.e., up to x/D = 2.0, the negative maxima of

UTV'

are near the edge of the

recirculation zone, and gradually move outwards downstream. The shear stress v'w' is very small in the recirculation zone and attains its maximum

value outside it (see also Fig. 84). These maxima move gradually outwards

at downstream sections. Analysis of the measured data shows that at all

sections where measurements were performed 'radial positions where

üïV'

and

àÜ/àr approach zero coincide. A similar conclusion has also been reached in Ref. 11. Moreover, radial positions of minima and maxima of these

quantities al so coincide at all sections. The same is true for the shear

stress v'w' and rà{w/r)/àr up to the section x/D

=

2.0. Further downstream

the above noted coincidence of these quantities deteriorates. This remarkable experimental fact shows astrong dependence of these shear stresses on the local strain of the mean flow, and suggests an eddy viscosity type turbulence model for these stresses rather than Reynolds stress modelling. Maxima of the shear stress u'w' are located in the

recirculation zone (see also Fig. 85). The peak value of this stress at the

20

(22)

initial section is located at the edge of the recirculation region. At subsequent sections, contrary to the behaviour of the other stresses, these maxima move inward and decay rapidly. At distances x/D "" 3.0-4.0 the

magnitude of u'w' becomes very small (Figs. 81 and 82). Radial locations of negative maxima of this stress seem to coincide with those of positive u'v' stress maxima.

4. CONCLUSIONS

A one-dimensional laser Ooppler velocimeter with optical and

electronic frequency shift has been used to obtain measurements of the th ree components of mean velocity and the six components of the (turbulent)

Reynolds stress tensor under isothermal conditions in a free swirling jet. The cases of weak swirl velocities (S

=

0.4, no recirculation zone) and strong swirl velocities (S

=

0.79, with recirculation zone) were

investigated, as well as the case of a nonswirling jet.

Measurements performed at x/D

=

0.125, 4, 6, 8, 10, 15 and 20 for the case of a nonswirling jet, and at x/D = 0.125, 1, 2, 3, 4 and 5 for the cases of swirling jets, provide a broad data base against which results of calculation procedures, both of parabolic (boundary layer) and elliptic types, embodying various turbulence models, can be compared.

For the weakly swirling jet considered, measured normal Reynolds stresses show little deviations from isotropy. These stresses are larger than the Reynolds shear stresses. The u'w' component of the shear stress is small a'nd can be neglected. The remaining two shear stresses

lJïV'

and v'w' are of the same order of magnitude in the near exit region of the flow; downstream of this region, v'w' decays more rapidly than u'v' which then becomes the dominant shear stress. Within the framewofk of an eddy viscosity turbulence model, eddy viscosities ~~x and ~r$' derived from measured values of shear stresses and mean velocity components, are, i~

general , neither uniform nor similar in magnitude. The evolution of ~rx is similar to that of a nonswirling jet. This suggests that a k-E type

two-equation model of tubulence could be adequate to predict the shear

stress

U'V'.

The v'w' stress should then be determined by an appropriate

algebraic or differential relation.

When the swirl velocity is strong, the normal Reynolds stress results show substantial deviations from isotropy; these stresses are significantly larger than the Reynolds shear stresses. This clearly indicates the need to consider the three normal stresses in any turbulence model of such flows. Maxima of these stresses occur in regions of high gradients of mean

velocity, i.e., near the edge of the recirculation zone and in the boundary (shear) layer of the jet. Radial positions where the shear stress u'v' and êÜ/êr approach zero, maximum and minimum values coincide. The same is true

for the stress v'w' and r(êw/r)/êr up to the middle portion of the

investigated flow. These relationships indicate astrong dependence of

(23)

these stresses on the local strain of the mean flow. Hence an eddy

vi scosi ty type turbul ence model rather than a Reynolds stress model could be acceptable to predict such flows.

5. RECOMMENDATIONS FOR FURTHER RESEARCH

The above noted dependence of the turbulent stresses on the local strain of mean flow is remarkable and deserves further study. To this end, a more detailed mapping of the flow field should be performed for an

accurate evaluation of the derivatives of mean velocity components in both coordinate directions. Moreover, the validity of this dependence should be

investigated for higher swirl number (up to 1.5) jets. Measurements of the length scale of turbulence could shed additional light into the turbulence structure and help devise a viable turbulence model for such flows.

Further, a similar investigation should be performed for a swirling

turbulent diffusion type flame in order to assess the effect of combustion on the turbulence properties of such flows; in addition, simultaneous

measurements of instantaneous velocity components and density should be made in order to clarify the effects of combustion on turbulent stresses, i.e., on turb ul ent tran spo rt processes. Results obta i ned from such a researc h effort could be most valuable for our understanding of the effect of turbulence on various combustor flow properties, and hence for improving combustor performance.

From the point of view of instrumentation, it is highly desirable to improve the accuracy of measurements by using: (a) a more powerful laser (to increase the signal-to-noise ratio), (b) a two-dimensional laser velocimeter (for simultaneous measurements of two velocity components) instead of the one-dimensional used in the present investigation.

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