•
February 1986
LASER DOPPLER VELOCIMETRY INVESTIGATION
OF THE TURBULENCE STRUCTURE
OFAXISYMMETRIC DIFFUSION FLAMES
by
2 MEI
1986
J. P. Sislian, L.-Y. Jiang and R. A. Cusworth
TECH, ISGHE ;WGESCHOOL
DELFT
LUCHTVAART· EN JiMTEVAARITECHNlEACBIBLIOTHEEK
Kluyverweg 1 -
DElFT
UTIAS Report No. 291
CN ISSN 0082-5255
•
LASER DOPPLER VELOCIMETRY INVESTIGATION
OF THE TURBULENCE STRUCTURE
OF AXISYMMETRIC DIFFUSION FLAMES
by
J. P. Sislian, L.-Y. Jiang and R. A. Cusworth
Submitted September 1985
February 1986
UTIAS Report No. 291
CN ISSN 0082-5255
•
Acknowledgements
The authors wi sh to thank Prof. J. J. Gl ass for hi s support and encouragement throughout the course of this work.
The calculation procedure for power spectra and autocorrelation functions employed in the present investigation was developed by M.A.Sc. candidate, ~1r. P. A. Robinson. He has also written Appendix A of the present Report. He acknowledge his valuable contribution with thanks.
Thanks are due to Mrs. ~l. I)illon for typing the manuscript and to '~s. J. Krauze for preparing the figures.
The financial support of the Natural Sciences and Engineering Research Council of Canada under Strategic Grant r,0691 is gratefully acknowledged •
•
Summary
Measurements of mean velocity components, turbul ent intens it ies,
velocity probability density functions, power spectra and autocorrelation functions of axial velocity fluctuation, and spatial turbulence macroscale, are reported in a turbulent round jet flow, issuing vertically into stagnant
air, in non-combusting and combusting situations. The fuel density (a
mixture of methane and argon) is chosen to be equal to the cold flow gas density (a mixture of air and helium) in order to minimize cold fueljcold gas mixture density difference effects on measured turbulence properties. The objectives are to study the influence of the combustion process on the turbulence structure of the combustible jet flows considered, and to provide data against which results of numeri cal prediction methods for such flows embodying various turbulence and combustion models can be compared, with a view to improving our understanding of relevant transport processes and on
guiding modelling and prediction efforts of such flows. A one-dimensional
laser velocimeter operating in forward scatter differential Doppler mode was
used to obtain the measurements. Gas temperatures were measured by
thermocouples. A visual study by schlieren photography has also been
conducted. It is found that the exi stence of the fl ame suppresses
turbulence in the upstream region of the jet flow and enhances it in the
downstream region, where turbulence intensities are substantially higher
than in the corresponding cold jet flow. However, the relative intensities,
i.e., the ratio of the local turbulent intensity to the local mean velocity, are smaller in the jet diffusion flame and become comparable to relative turbulent intensities found in the cold jet flow in the downstream region of
the flow. Turbulence in the jet diffusion flame is appreciably more
anisotropic than in the corresponding cold jet in all regions of the flow, suggesting the eventual desirability of multi-stress models of turbulence
for the prediction of such flames. The combustion process has been found to
have also a marked influence on the turbulence macroscale. It is
significantly smaller than in the cold jet flow in the upstream region and increases appreciably at downtream distances, the rate of this increase
closely following the rate of temperature increase. The experimental
results obtained will guide the development of an improved prediction method for such combusting systems •
•
T,ARLE OF CONTE NTS Ac knowl edgements·
. . . .
Summary.
.
. . .
.
· . .
.
Notation. .
.
. .
. .
.
. . . .
.
1.0 INTRODlICTION •.
. . .
. . . .
2.0 EXPERIMENTAL APPARATUS • 3.0 r~EASlIREMENT TECHf\lIOIiES •3.1 The La ser Doppl er Vel oc imeter Arrangement • • • • • • 3.2 Temperature rleasurement Procedure . . . .. 3.3 Schl ieren Photography • • • • • • • • • • • • • • 4.0 RESULTS OF MEASUREMEfIITS • • • • • •
. . . .
. . . .
2 3 5 7 8 9 9 15 15 16 4.1 Schl ieren Photograph (lbservations • • • • • • • • • • • • • • • • 16 4.2 Mean Temperature, rlean Velocity Components and Turbul enceIntensities • • • • • • • • • • • • • • • • • • • • • • • •• 17 4.3 Velocity probab il ity [)ensi ty Functions. • • • • • • • • • •• ?O 4.4 Power Spectra, Autocorrelation Functions and Turbulence Macroscale 20 5.0 CONCLUSIONS R EF ERE NCES TAB LES FI GURES
.
. . .
. .
.
.
·
. . . .
APPENDIX A: POWER SPECTRAL DENSJTY AND AUTOCORRELATION FlJNCTION ESTIMATES VIA FAST FOUR IER TRANSFORM C(}r1PUTATIONS APPENDIX B: TEMPERATURE MEASUREMENT PROCEDURE
4
21
•
d D f ~ G( f) h k L r u vx
~fVf
ÀfSubscri pts
9th
Notation
thermocouple bead diameter
nozzle exit diameter
frequency
power spectral density estimate
analog-to-digital converter sampling interval; convection heat
transfer coefficient
turbul ent kinetic energy
spatial turbulence macroscale
radial distance
autocorrelation function
time length of analog record; temperature
axial velocity component
radial velocity component
longitudinal (vertical) distance
no~alized
standard error of power spectra calculation
thermocouple emissivity
Stephen-Boltzmann constant
viscosity of the gas mixture
kinematic viscosity of the gas mixture
thermal conductivity of the gas mixture
gas
thermocoupl e
Superscripts
time-averaged value
fiuctuating quantity
•
•
1.0 INTRODUCTION
Turbul ent fl ames are of importance i n a v ari ety of power and propulsion devices in aerospace and other applications. In these systems, the combustion process is characterized, in a large number of cases, by the mixing of the fuel gas and air streams. The propagation of combustion is then part ly dependent on the rate of the physi ca 1 mi xi ng process, whi ch is determi ned by the state of the flow tu rbul ence, and part lyon the rate of the chemical reactions in the mixture produced. Moreover, there can be a strong interaction between the mixing and chemical processes. A basic understanding of such "diffusion" flames is greatly facilitated by studying somewhat simpler systems. Of these, the diffusion flame resulting from the burning of a fuel gas issuing vertically from a circular tube into stagnant or co-flowing ambient air has been the subject of intensive research. This system is quite simple compared to the complex flame structure in practical combustion devices, but nevertheless it is of considerable interest and pertinence to the modelling of such systems.
Turbulent jet diffusion flames have been extensively studied, theoretically and experimentally (see, for example, Refs. 1-4). In earlier studies the flame properties of interest were its length, mean temperature and mean species distributions. However, recent advances in the size and speed of digital computers, computational fluid dynamics, turbulence theory and diagnostic techniques have encouraged the development of "mathematical models" of turbulent combusting flows. A considerable aid to such modelling effort is the creation of an extensive and detailed data base for many statistical properties. However, hostile and complex conditions within flames have been responsible for a deficiency of experimental information on these properties. Recent advances in the laser Doppler velocimetry technique enable us to measure the instantaneous fluctuating flow velocity in turbulent flames which was almost impossible by other measuring techniques. The LDV technique has been used for the study of turbulent diffusion flames (Refs. 5-7), but measurements are mostly concerned with turbulence intensities and only a few examples of other turbulence properties are available. The aim of this report is to present some results of an experimental investigation into the turbulent structure of a jet diffusion flame, using the laser Doppler velocimetry technique, thermocouple probes and i nstantaneous schl i eren photography. Measurements were made in combusting and non-combusting situations of the following quantities:
(1) components of mean velocity, (2) all turbulent intensities,
(3) velocity probability density distributions, (4) power spectra ofaxial velocity component, (5) auto-correlation ofaxial velocity component, (6) turbulence length scale
(7) mean temperature distributions.
In the next paragraph, we present a detailed description of the various components of the test facility, the investigated flame configuration and the fuel and inert gas es used. Paragraph 3 contains a thorough description of the measurement techniques employed. Section 3.1 ;s
devoted to the laser Doppler velocimeter system, the signal processing equipment and the data acquisition system used to perform instantaneous velocity measurements. The procedure to obtai n such data is thoroughly discussed, as well as the measurement and calculation techniques of the power spectral density, autocorrelation function and spatial turbulence macroscale from a continuous laser Doppler velocimeter signal. Additional details concerning the determination of these latter quantities are given in Appendix A. A brief statement of the estimated accuracy of the measurements perforrned is also given in this section. Section 3.2 describes briefly the mean temperature measurement technique used, the detailed description of the technique being given in Appendix B. Section 3.3 discusses the components and optical parameters of the schlieren apparatus. Results of all measurements are presented in Paragraph 4, where the evolution of all the investigated properties is discussed and particular relationships between these properties in flame and no-flame conditions noted. Finally, in paragraph 5, certain major findings, as well as deficiencies of the present investigation, are enumerated.
2.0 EXPERIMENTAL APPARATUS
A schematic of the apparatus used in the present investigation is shown in Figs. 1 and 2. A vertical steel tube, 1250 mm long of variable cross-section, contains three perforated plates, 1, 2, 3, and a honeycomb flow straightener, 4 (see Fig. 1). It connects the mixing chamber near the bottom of the tube to a contoured jet nozzl e made of brass and hav i ng an area contraction ratio of 26:1, and a throat diameter of 10 mmo The nozzle profile was designed according to the specifications given in Ref. 8 in order to obtain a uniform velocity at the throat. This contraction is followed by a 60 mm long and 10 mm diameter brass tube. This relatively large burner diameter was selected in order to obtain adequate spatial resolution during measurements of the initial conditions near the burner exit. The fuel jet, which issued vertically upwards into stagnant air, was a mixture of industrial methane (96% methane) and argon, whose volume ratio was 2.33. In the cold flowexperiments the nozzle gas was a mixture of
21.4% helium and 78.6% air by volume. Thus the cold fuel mixture/cold gas
mixture density and molecular viscosity ratios were 1 and 1.3, respectively. The average gas velocity at the nozzle exit for combusting and noncombusting cases was 17.2 mis, corresponding to cold fuel mixture and cold gas mixture Reynolds numbers (based on the exit diameter) of 0.785x1Q4 and 1.02 x104,
respectively. The compositions of all gases used during the experiments are presented in Table I. The flame was stabilized and attached to the rim of the exit port at all times. No externalflame holders were used during the experiments.
Two independent methane/argon (for the combusting jet) and helium/air (for the cold jet) circuits supplied and controlled the flow of gases to the mixing chamber, 11 (see Fig. 2), through pressure regulators and Fischer and
Porter rotameters. This mixture was then fed into the nozzle mixing chamber 5 (Fig. 1) via two diametrically placed injectors. A third circuit formed by diverting part of the ai r or argon flow was used to seed the flow with aluminum oxide particles for laser Doppler velocimeter measurements. The suspension formed by aluminum oxide particles in water was sucked through a
8
t
1.5 mm diameter tube from an open reservoir to the atomizer, 12 (Fig. 2). Excess suspension was returned to the same reservoir. A sonic probe, 18 (Sonicator, Model W185-F, Heat Systems, U1trasonic, Inc.), Fig. 2, was used to disperse the partieles in the suspension continuous1y. The wet partieles exiting from the atomizer passed through a diffusion drier, 13 (TSI t-bde1 3062), and then were neutra1ized e1ectrostatically by the charge neutralizer, 14 (TSI Model 3077). Agg10meration of partieles was thus minimized. The aeroso1 was then fed into the mixing chamber, 5 (Fig. 1), of the nozz1e burner via two diametrica11y p1aced injectors where it mixed with the appropri ate gas mi xtu re. The constancy of the flow rate at the exit of the jet was checked by measuring the exit centre1ine axia1 velocity before each experimenta1 sessi on, and by constant1y monitori ng, duri ng the experiments, the f10wmeter and precision pressure gauge readings. In all cases the error was 1ess than 1%. The axia1 symmetry of the flow was assessed by performing complete traverses of the velocity field at the exit section and at a section ten diameters downstream of the exit (see, for examp1e, Figs. 20 and 28). The re1ative error, at corresponding symmetrie positions, were very sma11 for the mean axia1 velocity component, and on the order of 12% maximum for the mean square radial velocity f1uctuations.
The burner was p1aced vertica11y upward on the 10wer rigid frame of a three-dimensiona1 traversing mechanism, which was positioned in a square, 0.6m deep, pit in the floor (see Fig. 3). The traversing mechanism disp1aced the burner ih two mutua11y perpendicu1ar horizontal directions and in the vertica1 direction. The positioning accuracy of the traversing mechanism was ±0.125 mm in the horizontal directions and approximately ±1 mm in the vertica1 direction. The range of travel was 200 mm in the horizontal and 500 rnm in the vertical directions. The traversing mechanism was operated manually in all three directions.
The experiments were conducted within a room having dimensions 6.9m x 8.05m x 4.0m high. In order to minimize room disturbances, the burner was p1aced within a fixed screened enelosure having dimensions 1.4m x 1.2m x 2.7m high, consisting of one 1ayer of mesh screen (690
wires/m x 490 wires/m, 0.25 mm wire diameter). Combustion produets were
eo11eeted in a hood 10cated above the enelosure and were removed through a fan-driven exhaust system (see Fig. 3). With this arrangement the flame or the cold jet was not always in the centre of the enelosure. However, because of relative1y short lateral displacements eneountered during the experiments ( ... 100 mm) the biasing of the flame or the jet entrainment is considered sma11. The laser Dopp1er velocimeter for instantaneous velocity measurements was kept fixed in space.
3.0 MEASUREMENT TECHNIQUES
3.1 The Laser Dopp1er Velocimeter Arrangement
Instantaneous velocity measurements in eo1d and combusting f10ws were performed with a one-dimensiona1 laser Dopp1er velocimeter operating in the dua1-beam, forward scatter mode. The optica1 arrangement was built up from standard DISA 55X Modu1ar Opties components and is identica1 to the system used in Ref. 9 (see Fi g. 4). In the opt i ca 1 system used in the present
i nv es t i gat i on, the foca 1 1 ength of the transmitt i ng opt i cs 1 ens was
f
=
600
mm,and the beam intersection angle was 6.5°. Hence the spacing of
the interference fringes in the probe volume was öf
=
5.72
~,the waist
diameter of the focused laser beam, df
=226.8
1Jffi,and the probe volume
dimensions (major axis), a
=
4.1
mm, and (minor axis) b
=0.227
mmoThe
light scattered from the seed particles in the probe volume was collected in
the forward off-axis direction, at an angle
9 =20° from the optical axis of
the system, via the 55X34 receiving optics (Fig. 4).
The co11ected
scattered light was focused onto apinhole aperture of 0.1
mm diameter. The
focused scattered light was then filtered with the OISA 55X38 narrow
bandwidth interference fi lter (red), to reduce interference of the flame
luminosity and other unwanted light sources with the LOV signal.
In this
arrangement, the effective probe volume length seen by the photomultiplier
was -û.6
mm, which greatly enhanced the spatial resolution of the LOV
measurements.
The entire optical system was carefu11y aligned and rigidly
mounted on massive optical tables.
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 0.1
mmoThe LOV actually measures the instantaneous velocities of small
seeding particles in the flow, which act as light scattering centres. These
particles should be sma11
enough to fo11ow the local gas velocity.
Particles in the size range 0.1 - 1
l.lITIare usually considered appropriate
(see Refs. 10 and 11).
In the present investigation aluminum oxide
particles were used for seeding the cold and combusting jets. Their nominal
diameter was determined from electron microscope photographs (x100,000) and
was found to be 0.5
l.lITI(see Fig. 5). The operation of the seeder described
in Section 2 yielded a range of particle densities on the order of
10
9 - 1010particles/m
3•The outer air surrounding the cold jet and the
flame was not seeded.
The details of the signal and data acquisition system, as well as the
procedure for rejection of "bad" data points are given in Ref. 9.
The LOV
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 the CRT terminal and then dumped onto an on-line
printer. A constant time interval saMpling mode, suggested in Ref. 12, was
used to correct for velocity bias. No other attempts have been made, in the
present experiments, to correct for other biases, for example, the
non-uniform seeding bias, the incomplete signal bias, and velocity gradient
bias. The last two biasing errors in the present data were considered to be
sma 11, i n v i ew of the si gn ifi cant amount of frequency shift used and the
relative smallness of the probe volume, respectively.
Measurements of the mean velocity components, turbulence intensities
and velocity probability density distributions were performed by sparsely
seeding the cold and combusting flows, so that only one particle was present
in the probe volume at a given instant of time.
The average data rates (as
monitored by the TSI 1980A processor) were 1O,000/s at the exit central
portion of the flow (cold or combusting), 5000/s in the central portion 50
exit diameters downstream, and about 200/s at the edges of the flow.
The
measurement procedure is similar to the method outlined in detail in Ref. 9.
10
,
For each data point, 2000 individual real izations were averaged for the cold flow, ilnd 8000 for the combusting jet flow. lhe various possible errors associated with the processing of individual Doppl er bursts have been discussed in some detail in Refs. 12 and 13. It is estimated that with the optical and signal processing arrangement used here, the values of the mean velocity components and turbulent intensities may be expected to be accurate to 3-4% and 6-8%, respectively.
Power spectra and autocorrel ations of the axial velocity component were obta ined from an essenti ally continuous record of instantaneous axial velocity versus time by the use of high seeding levels and the analog output of the counter processor. Typical analog outputs of the instantaneous axial velocityare shown in Fig. 6. The level of seeding was 1 imited by the maximum seeding rate of the atomizer used and, more importantly, hy the possible interaction of the gas and particulate phase causing modification of the turbulence structure of the fiow and of the heat release mechanism in the combusting jet. Moreover, ilS a consequence of only the cold gas or the fuel jets being seeded, the time resolved velocity measurements were limited to the central lower portion of the cold and combusting jets. In this high seeding level mode typical data rates were ~O,OOO/s at the exit and ~10,OOO
in the upper part of the investigated region of the flow.
The turbulence macroscale, L, of the jet flows considered were determined, ()n the basis of Taylor's hypothesis, by multiplying the Eulerian
integral time scale of turbulence, defined as
'llnax
o
=f
R('t)d'to
with the local mean axial velocity component. Therefore,
'llnax
L = u
f
R('t)d't (1)o
Here R('t) is the normalized autocorrelation function of the axial fluctuating velocity component
Rh) = Ui (t)u l
(t+'t)
,
(2 )U'2
'tmax the value of the time lag for which R('t)
=
0, and ~ is the local turbul ent intensi ty of the axi al velocity fl uctuation. Tayl orls hypothesi s
merely assumes that turbulent eddies are convected with the mean axial
velocity. This hypothesis is an approximation which is quite accurate as
long as the level of turbulence is not too high (see Ref. 14, p. 40).
The above autocorrelation function was obtained as the inverse
Fourier transform of the power spectral density function G(f) (see, for example, Ref. 15), where and
f
G( f)cos2rtf-oof o T Xk(f,t)=
f
u~(t)e-i2rtftdt o (3) (4 )represents the finite Fourier transform of the fluctuating axial velocity
uk(t). Here T is the time length of the continuous analog record of
uk (t), f the frequency, and E the expected val ue operat i on over the
ensemble index kor, equivalently, the ensemble average CNer the sample
functions Xk(f,T).
An estimate of G(f) can be obtained by omitting the limiting and expectation operations in Eq. (4). We get
where '" G(f)
=
~
/X(f,T)/2 T T X(f,T) =f
u'(t)e- i21tftdt o (5) (6)In the present investigation it is assumed that the highest
anticipated frequency of the axial velocity fluctuations is f
max
=
10 kHz.Hence the analog output signals from the counter processor were low-pass filtered with a frequency cutoff of f max • The filtered out signals are
shown in Fig. 6. The low-pass filtered signals were then digitized
(sampled) at equal time intervals h so as to produce a Nyquist folding frequency f N which is somewhat higher than fmax • The sampling interval was chosen as
12
./
h
=
1
2.7fmaxThe maximum number of sampled points, the sample size, was N
=
215=
32768 and was limited only by the available memory space in the microcomputer. Hence the observed record length T=
Nh=
1.21 sec. For arbi rary f, the discrete version of Eq. (6) isN-l
X(f,T)
= h
L
un exp[-i21tfnh] I (7)n=O
At the Fast Fourier Transform discrete frequency values
f - k - k
k -
T -
"Nh'
k=
0, 1, 2, ••• , N-lthe transformed values give the Fourier components
N-l
L
un exp[-i 21tkn]N (8)
n=O
The results are unique only out to k
=
N/2 since the Nyquist cutoff frequency occurs at this point. Hence, from Eq. (5), the power spectral estimate becomes(9 )
with only N/2 values unique and a frequency resolution (intervals between selected frequencies)
(l0)
The normalized l'1ean square error introduced by using Eqs. (5)-(9)
i nstead of Eq. (4) to determi ne the power spect ra 1 dens ity funct i on is defined as
E2
=
E[(G(f) - G(f) )2] G2( f)and can be shown to be (see Ref. 15) the sum of the v ari ance of the estimate, which defines the random portion of the estimation error
E[(G(f) - E[G(f)]
)2]
G2(f) = E[G2(f)] - E2[G(f)] = G 2(f) ~ ~ a2[ G ( f)] ... 1 G2(f) BeTwhere Be is the resolution bandwidth of G(f), and a bias term which describes the systematic portion of the error
As the power spectra of interest in the present investigation do not display sharp peaks (large second derivatives) this part of the error is considered small. Therefore, the normalized mean square error is approximately equal to the normalized standard error
(11 )
From Eqs. (l0) and (11) it is seen that i f a power spectrum is estimated by direct Fourier transform operations, the normalized standard error Er
=
1, which means that the standard deviation of the estimate a is as great as the quantity being estimated.This random error of the estimate produeed by Eq. (9) ean be redueed by smoothing the estimate further over frequeney. This ean be aeeomplished by averaging the results for ~ contiguous speet ral eomponents in the estimate from a single sample record (analog output). This smoothing operation approximates the expeetation operation in Eq. (4). Sinee the spectral eomponents are spaeed at intervals l1f
=
I/T, it follows that ~M=
B~=
~/T. Henee14
,
I,., '
It can be seen that smoothing reduces Er but increases the frequency
resolution (the resolution bandwidth Be). For a given Er, and hen ce .R.,
the frequency resolution can be decreased by increasing the sample size N,
as T
=
Nh=
1/6.f. In the present calculations .R.=
64, and hen ce Er=
12.5%. It should also be noted th at the resolution bandwidth can be halved
by initially adding N zeroes to the original N data points. This data
augmentation is employed in the present case.
The autocorrelation of the axial fluctuating velocity component is calculated from the inverse Fourier transform of the measured power spectral
density function G'(f) from .Eq. (3). The upper limit of integration is
f max • The quantity 't = I/Be af ter smoothing. Finally, the length scale is
determi ned from Eq. (1). Further detail s of power spectra and
auto-correlation calculations are given in Appendix A.
3.2 Temperature Measurement Procedure
For flame temperature measurements Pt/Pt-10% Rh thermocouples were
employed with 0.074 or 0.11 mm diameter wires. To eliminate catalytic
effects the wires were coated with silica at a temperature of about 1300°C.
An electronic ice-point was used instead of an ice tank. The output of the
thermocouple was amplified and converted into digital output by an A/D
converter. The rate and duration time of data acquisition were carefully
chosen in order to follow signal fluctuations. The data were processed on a
microcomputer. The results obtained were quite stable and symmetric. The
non-symmetry of radial temperature profiles was less than 1% (see Fig. 7). Radiation error for the thermocouple was estimated considering the thermocouple to gain heat by convection from the local gas flow and to lose
it by radiation to the room through a transparent flame. Details of
temperature measurement procedures are discussed in Appendix B. Radial and
axial distributions of the mean temperature in the jet diffusion flame at
all measured sections are given in Fig. 8.
3.3 Schlieren Photography
A schemat i c of th'e sch 1 i eren system used is shown in Fi g. 9. A Ruby
laser was used as the light source for the following reasons: high
intensity directional light source, very short duration light pulse (30
nsec), small diameter output beam (9
mm),
monochromatic (wavelength of 694.7nm). Due to the coherent nature of the laser light a scatter plate had to
be put directly in front of the first knife edge, which stopped the light
formi ng an i nterference pattern with itself. The scatter plate was a 2 mm
thick piece of frosted glass. Since the wavelength of the laser was in the
upper red part of the spectrum, the film sensitivity was much less than if the laser light was in the green or blue part of the visible spectrum.
A condenser lens with a focal length of 4.2 cm was placed the laser so as to focus the light onto the scattering plate and
first knife edge. The lens was moved 4.2 to 10 cm away from the
edge so as to maximize light collection of the first mirror.
15
i n front of through the fi rst kni fe The fi rst
knife edge was located at the focal point of the first mirror. Bath
rectangular and circular knife edges were used. lhe rectangular knife edge
was made from a razor blade, while the circular one was an adjustable lrlS
diaphragm. Since the scatter plate scatters light in all directions, a
piece of black cardboard was placed between the scatter plate and the mirror, which stopped extraneous light from imaging on the mirror.
Bath spherical mi rrors were 30.5 on in d ial'1eter and had a focal
lenyth of 181.6 011. lhe angle of tilt of both mirrors was 8.85 degrees.
lhe fi rst mirror was posi tioned 279.5 on from the centre pl ane of the
d iffus i on fl ame. lhe second mi rror was pl aced 348.4 on from the centre
plane of the diffusion flame.
lhe second knife edge was posi tioned at the focal pl ane of the second
mirror. The knife edge was capable of being rotated around the beam of
light and translated in all three directions. A 7.2
on
diameter achromaticlens was placed 10.0 cm in front of the knife edge (i.e., between the knife
edge and film). lhe focal length of the lens was 50
on.
Since the laser isa monochromatic 1 ight source, a bandpass interference filter with a centre
wavelength of 694.7
nm
was placed directly in front of the knife edge. lhisfilter was used to reduce unwanted illumination, c1ue to the flame, from
imaging on the film. lhe di stance between the 1 ens and film pl ane was
calculated and placed at 39.45 on.
[)je to the very short fl ash. duration, p-xtremely high speed 4x5"
Royal-X Pan 4166 film was used.
lhe investigated flame is shown in Fig. 10. Figure 11 shows the
entire test facility, the laser Doppler velocimeter and the data acquisition and proces si ng apparatus.
4.0 RE SU LTS OF MEASUREMENTS
4.1 Schlieren Photograph Observations
Schlieren photographs of the investigated jet flows, with and without
coobustion, are shown in Figs. 12-15. lhey clearly indicate that the
turbul ence structure of the jet fl ow is considerably al tered by the heat addition due to the coobustion process.
Figures 14(a) , (b) and (c) show clearly a sharp density change due to steep grad ients of temperature and concentration between the col d inner fuel
flow and the hot surround ing gas mixture of coobust ion products. lhe
turbulent flame zone, where a mean temperature peak exists, coincides with the boundary dividing the black and white regions, il1 the left-hand side of
the photo. In the region of the flow close to the nozzle exit, turbulence
is limited to the core region of the jet. lhe outer layers of the flow,
near the turbulent flow zone, seem to be "l am inarized" due to the increase
of the kinematic viscosity of the gas mixture with temperature. This
"l am inarization" prevents the mixing of the jet flame with the éITIbient air. Consequently, the angle of spread of the diffusion flame, at the nozzle
exit, is smaller than that in the cold jet flow (see Fig. 12). lhe
'
.
turbul ence intensities in the fuel jet exiting from the nozzl e are qui te smal 1 (the smal 1 eddies are not visible because of their uniform density). Af ter a distance of the order of the nozzle diameter, the level of turbul ence in the inner jet increases and the turbul ent region spreads out downstream in the form of a cone. The "laminari zed" outer fl ame zone shi fts inwards and becomes turbul ent \'A1ere the two regions meet. Therefore, the section at which this transition to turbulence occurs in the jet diffusion fl ame is infl uenced by the stabil ity of the inner fuel jet flow, which in turn depends on the magnitude of the kinematic viscosity of the fuel jet. Oownstream from this zone, the jet diffusion flame becomes turbulent and the apparent dimensions of the eddies becOl'1e considerably larger than those for the cold jet flow (see Fig. 12). This fact is corroborated by the measured integral scales of turbulence presented in Section 4.4.
4.2 Mean Temperature, Mean Velocity Components and Turbulent Intens it, es
Measurements of the mean temperature, mean velocity coolponents and turbul ent intensi ties for non-cOO1bust ing and combust ing si tuations, presented in Fi gs. 16-41, provide quantitative information on the infl uence of the heat release on the turbulence structure of the combustible jet flow. Figure 16 depicts the centre-line distributions of the mean axial velocity, turbul ent kinetic energy and mean temperature. As mentioned above, hecause of the 1 imitations of the seeder capacity and of the vertical travel of the traversing gear, measurements \\ere performed only up to x/O
=
50 and the fl ame tip was never reached. Figure 16 indicates higher centre-l ine mean axial velocities in the case of flame, rlue to the expansion of the flow caused by the temperature risee The jet diffusion flame flow decays much less rapidly in the axial directon than the non-combusting jet. In the near exit region of the diffusion fl ame the magnitude of the turbul ence kinetic energy, k, is sm all , whereas in the corresponding cold jet flow k reaches a maximum value and then decays rapidly. This "suppression" of turbulence is probably caused partly by the increase of the kinematic viscosity of the fuel gas mixture due to the temperature rise, and partly by the acceleration of the flow in the jet flame and the ensuing changes of the velocity gradients. The turbul ent kinetic energy in the fl ame increases graduall y and reaches a rel ative peak at x/O .. 25. The magnitude of thi s rel ative peak of k is appreciably less than the maximum value of k in the non-combusting jet. However, in the downstream region, i .e., at x/D ~ 20, the turbulent kinetic energy in the diffusion flame changes less rapidly and remains always higher than that in the inert cold flow. Centre-line distributions of the normal turbulent intensities, ~ and Vi 2 (see Fig. 17), are simil ar to those of turbul ent kinetic energy, k. It can be seen that turbulence in the near exit region of the non-combusting jet is anisotropic, ~ being always larger than ~, whereas in the same region of the corresponding jet diffusion flame, these normal stresses are small andalmost equal. However, in the downstream region turbulence in the flame becomes more anisotropic than in the non-cOO1busting turbul ent jet, with higher val ues of Ui 2 and Vi 2 than those in the col d flow.
Radial distributions ef mean axial velocity, turbulent kinetic energy and temperature are presented in Figs. 18-25, at axial distances x/D = 0.3, 5, 10, 15, 20, 30, 40 and 50. The initial values of these quantities are shown in Fig. 18. It can be seen that at the exit, the non-combusting and combusting jet flows are quite symmetrie, and that there are no appreciable differences between the cold and hot flow quantities. The combusting jet widens slightly due to expansion effects of the temperature rise (see also Fig. 14). The values of the turbulent kinetic enegy in the shear layer at the ed ge of the flow are somewhat smalle rin the combust i ng case. Th is 1 oca 1 "1 ami na ri zat i on" of the flow is pri marily due to the i ncrease of the kinematic viscosity of the fuel gas mixture with temperature. This laminarization of the outer layer of the jet diffusion flame is also apparent at the section x/D
=
5.0 (see Fig. 19), where the mean position of the flame front (determined by the radial position of the maximum mean temperature) is located in a region of low turbulent kinetic energy values, although higher values of k are encountered in a region closer to the axis of the jet. The magnitude of the kinetic energy of turbulence is appreciably smaller in the jet diffusion flame than in the non-combusting jet. Compared to the cold flow, the central portion (r/D ~ 0.25) of the jet flame is almost laminar (very low levels of turbulence). The peak value of k in the combusting jet is shifted slightly outwards relative to the maximum value of k reached in the cold flow, due to changes in the radial gradient of the mean axial velocity, ü, created by temperature effects. The mean axial velocities are consistently higher in the combusting jet. The same qualitative picture of the flow and turbulence structure for non-combusting and combusting situations prevails at the downstream section x/D=
10.0 (Fig. 20). At this section complete traverses of both flows were performed to check the symmetry of the investigated flows. The non-combusting turbulent jet flowfield seems to be quite symmetrie. The mean axial velocity distributien in the diffusion flame is also symmetrie. However, the turbulent kinetic energy profile in the flame exhibits some asymmetry. The relative error in the right and left peak values of k in the flame is of the order of 9%. At this axial distance, the "potential core" in the jet flame has disappeared and the gap between the turbulent kinetic energies in both flows has decreased, except in the central near-axis region of the flows. The peak value of the turbulent kinetic energy in the flame is quite close to that of the cold flow. The increasing growth of the turbulence level in the jet flame is due to steeper radial gradients of the mean axial velocity,ü.
At axial distances x/D ~ 15 (see Figs. 21-25), the relative magnitudes of the turbulent kinetic energies in cold and hot flows is reversed. At x/D
=
15 (Fig. 21), the mean axial velocity in the flame is still quite high, whereas in the cold jet the mean axial velocity has decreased appreci ably. The tu rbul ent ki neti c energy in the combusti ng flow is higher almost everywhere in the section. At this, and subsequent axial distances, the growth of turbulence due to higher velocity gradients outweighs the decay of turbulence due to higher kinematic viscosities caused by the existence of the flame. The radial position where the turbulent kinetic energy attains its maximum value, and which is a measure of the maximum turbulent mixing intensity in the flame, does not coincide with the radial position of the flame front. At x/D=
20 (Fig. 22), the turbulent kinetic energy in the cold jet flow decreases further, whereas it increasesin the hot jet flow and attains its greatest values at this section. At subsequent downstream sections, x/D = 30, 40 and 50, the magnitude of k in the fl ame sl owl y dec reases, having al ways a saddl e-type profil e, and its peak values gradually approach the mean radial position of the flame front. Turbul ent kinetic energy 1 evel s at the corresponding sections in the non-combusting jet are canparatively very low. The magnitude of the mean axial velocity component, although decreasing gradually, is still appreciable, at distances x/D = 50, compared to the cold jet flow case.
Radial profiles of the turbulent normal intensities, IJl 2 and Vi 2, at the considered axial sections, are shown in Figs. 26-33. For the sake of clarity, the initial values ofU"2 are depicted, in Fig. 26, on the right-hand side of the centre-line, while those for
V'2
are presented in the left-hand side. As in the case of turbulent kinetic energy, the magnitude of these stresses in the jet flame are smaller than those in the cold jet flow up to x/O ... 10; further downstream they become appreciably larger than the corresponding cold flow values. In both flows, maximum values ofT2 and ~ occur at the same radial positions. In the jet flame, they approach the mean position of the flame front at distances x/O ~40 (Figs. 32, 33). In the non-combusting jet flow, ~ and ~ are largest at a distance x/O = 5.0 downstream of the nozzl e exit (Fig. 27), whereas in the canbusting j et these val ues occu!' at x/D .. 15. The s)1llmetry of the invest igated col d and hot turbulent jet flow is once again shown in Fig. 28. The relative er ro rin the right and 1 eft peak val ues of Ui 2 in the fl ame i s of the orderof "'8%, the corresponding rel ative error for ~ being "'12%. The cold turbulent jet flow is quite s)1llmetric.
Figures 34-41 depict radial distributions of the turbulent shear intensi ty, Ui Vi, in non-canbusting and combusting jet fl ows. In both cases
the turbul ent shear intensi ty i s zero on the jet ax is and has a peak near the positions of maximum radial gradients of the corresponding mean axial velocities. The radial positions of these peaks in the hot flow tend towards the mean position of the fl ame front at x/D '" 40t50. At x/D '" 10, the val ues of Ui Vi are approximately equal. Further downstream Ui Vi in the
cold jet flow decreases rapidly, its value at x/D
=
30 being al ready very small (see Fig. 39), while in the combusting jet, IJIVI increases slightly, up to d i stances x/D '" 15 (Fi 9 0 37) and then sl owl y dec reases furtherdownstream, its val ue being still appreciably higher than in the cold jet flow. The rel at i ve error in the right and left peak val ues of Ui Vi in the
jet fl ame is of the order of 13% (see Fig. 36). In general , in both flows, val ues of the turbul ent shear intensity Ui Vi are appreciably smaller than
the correspond ing val ues of the no rmal turbul ent intensities •
The above comparisons between burning and non-burning situations show that changes occur in both the magnitudes of mean velocities, as well as the magnitudes of the fluctuating velocity canponents. Therefore, it would be of interest to see how their ratios, ; .e., the relative intensities, change due to heat release by canbustion. Figures 42-48 depict the distributions
of the ratio of the axial fluctuating velocity component to the local mean axial velocity component,
lü
'2/U, for flame and no-flame conditions. Thevariations in relative axial turbulence intensity on the centreline with x/D, for flame and no-flame conditions, are shown in Fig. 42. It can be seen that the relative axial intensity is always smaller in the jet diffusion flame; although the curve for the cold jet flow has levelled off farther downstream, the corresponding curve for the combusting jet shows a marked rising trend downstream. Figures 43 and 44 show that up to axial distances of the order of x/D '" 10+15, the magnitudes of the radial distributions of the relative axial turbulent intensity in the flame are lower than in the cold flow, even in the flame region. Profiles of !Q72/ü at x/D = 10 (Fig. 44) are quite symmetrie both for cold and hot flows. At distances x/D ;t 20, the relative axial turbulent intensities in the cold and hot flows tend to have the same order of magnitude in the flame front region. These figures also show that values of
fu72"/ü
of the order of 50% were measured in the flame and of the order of 100% at the edge of the cold jet.4.3 Velocity Probability Density Functions
Some typical probability density functions ofaxial velocity fluctuations u' at x/D
=
5, 20 and 50 are shown in Figs. 49-54 for various radii in flame and no-flame situations. Deviations from the normal (Gaussian) distribution (positive skewness) for both cases occur at the edges of the jet flows, and in the combusting case on the inner side of the flame front. The deviation is more pronounced in the case with flame. A small amount of negative skewness is observed near the flame centreline, but the skewness is almost zero near the axis of the cold jet flow. The probability density functions of radial velocity fluctuations v' shown in Fig. 55 are similar to those ofaxial fluctuating velocity.4.4 Power Spectra, Autocorrelation Functions and Turbulence Macroscale Figures 56 and 57 depiet the power spectrum of axial velocity fl uctuat i on u I at v ari ous poi nts on the jet flow axi s, and at the
cross-section x/D
=
15 at various nondimensional radii for combusting and non-combust i ng situati ons. In these fi gures the ordi nate represents the magnitude of the power spectral estimate determined from Eq. (9) divided by the local value of U'2 , which has been computed fromf max
u' 2 =
J
G(f)dfo
The abscissa representing the value of the frequency has been replaced by the wave number k
=
21tf/O. Obviously, E(k)=
G'(f)O/21t.20
Figure 56 shows that at the initial section of the flow at the exit, i .e., at x/O = 0.3, the power spectra for the inert and burning jet flows have the typical form of the power spectrum for homogeneous grid turbulence. In both cases, turbulence energy is mostly contained in the wave number range below 10 in the investigated region of the jet flows. The energy density in this wave number range increases downstream, this increase being more pronounced in the case of jet diffusion flame, especially in the low wave number (frequency) range. In the high wave number range (high frequency region) turbulence energy density decreases with downstream distance in both flows. From Fig. 57 it can be seen that turbulence energy density increases, in the low wave number range, in the outer part of the jet flows in both cases (the value r/O
=
2.0 in the cold jet flow corresponds to the near edge region of the jet, while the value r/O = 1.15 in the case of flame corresponds to the inner part of the flame zone, i.e., power spectra in the flame zone and in the outer part of the flame zone are not presented in Fig. 57). In the high wave number region a more rapid spectral fall-off occurs in the flame at greater radial distances, which may be due to the temperature dependent dissipation. Spectra, in the combusting case, exhibit more marked differences at each radial position than in the cold jet flow, indicating a still developing pattern of turbulence at this section in the jet diffusion flame.Typical autocorrelation functions from which turbulence macroscales, L, were calculated, Eq. (1), are presented in Figs 58 and 59.
Axial distributions of L are presented in Fig. 60. In the non-combust i ng jet it monotoni ca lly i ncreases along the jet axi s, whil e in the combusting jet L is initially smaller than the cold jet values, but increases sharply downstream, and for x/O ~ 30 attains values much larger than those in the cold jet at the same locations. This increase of the turbulence macroscale in the combusting jet flow is also observed in schlieren photographs shown in Figs 12-15. Radial distributions of Land temperature for the entire (cold and hot) jet flow sections are presented in Fig. 61, and show again the degree of symmetry of the investigated flows and the accuracy of the performed measurements. Radial profiles of L at other sections: x/O
=
0.3 (initial section), 15 and 30 are depicted in Fig. 62. At the initial section, measured values of L in both cold and hot flows were found to be approximately the same and equal to 0.4 mmo At all other sections in the non-combusting jet, L initially increases gradually, attains a maximum and then slightly decreases in the outer region of the jet flow. But in the case with flame L increases rapidly with radial distance, the rate of increase following closely the rate of temperature increase. The magnitude of the turbulence macroscale is appreciably larger than those for the cold jet flow at the same radial locations, especially for axial di stances x/O ) 30. Va 1 ues of L at the fl ame front 1 ocat i ons were not measured in the present investigation because of limited capacity of the seed generator.5.0 CONCLUSIONS
The main objective of this investigation was to determine the i nfl uence of the heat rel eased by the combust i on process on the tu rbul ence
properties i n a jet d iffus i on fl ame. Experimental information was obta ined by 1 aser [):)ppl er velocimetry technique, thermocoupl e probes and schl ieren photog raphy, on a variety of stati st ical properties of turbul ence in non-combusting and combusting situations, on the meán temperature field, and on the qualitative structure of the cold and hot jet flows. The measuranents performed also provide useful initial and flow field data for eval uating the val idity of various turbul ence model s desc ribing turbul ent jet diffusion flames, in particular data on the turbulent kinetic energy and the turbul ence macroscal e.
~asurenents were performed at axial distances x/D
=
0.3, 5, 15, 20, 30, 40 and 50. The main findings of the study are as foll ows:1. The ex i stence of the fl ame suppresses turbul ence in the upstream reg ion of the jet, p.specially at the outer edge of the jet where the gas temperature is high. This apparent "l am inarization" phenomenon is probably caused by the increase in kinematic viscosity of the fuel gas due to temperature rise, which lowers the flow Reynolds number and retards the onset of turbulence. However, downstream of this near nozzl e exit region turbul ence 1 evel s in the jet diffusion fl ame gradually increase and at x/D ~ 15-20 appreciably exceed those in the corresponding cold jet flow. Turbulence generated by higher velocity 9 rad ients in the fl ame by far overcomes the suppressi on mechan i sm due to the increase of viscous dissipative effects caused by high temperatures.
2. The rel ative intensi ties, i.e, the ratio of the local turbul ent intensity to the local mean velocity, are smaller in the jet diffusion flame and become comparable to those found in the cold jet flow in the downstream region of the flow.
3. Turbulence in the jet diffusion flame is more anisotropic than in the corresponding cold jet in all flow regions, indicating that a more el aborate than the commonly used k-e: model of turbul ence (Reynol ds stress modell ing) may be required to predict axis)1Tlmetric jet diffusion flame flow fields.
4. Radial positions of the peak values of the turbulent kinetic energy in the jet flame, which are a measure of the maximum mixing intensity, do not correspond to radial positions of maximum mean temperatures, i.e., of the mean fl ame front, in the upstream reg ion of the fl ame. The fl ame
front is reveal ed to be located in the 1 aminari zed reg ion where turbulence levels are very low, although the central part of the jet is markedly turbulent. As the jet flame develops downstream, the peaks of turbulent kinetic energy gradually shift to coincide with the flame
front.
5. The existence of the flame increases the low frequency (low wave number) energy density of turbul ence.
6. lhe magnitudes of the spatial macroscale of turbulence in the jet diffusion flame are smaller than those in the corresponding
non-combusting jet flow in the upstream region of the investigated
flows. However, at axial distances x/D ~ 20 it increases si gnifi cantly, the rate of thi s increase closely foll owi ng the rate of temperature increase.
The performed measurements prov ide a broad data base agai nst whi ch results of calculation procedures, of jet diffusion flames, embodying various turbulence models, can be compared. These data are presented in
Table Il.
Measured data are restricted to stations up to x/D
=
50 and to the central portion of the jet flame, partly by seeding problems and partly due to vertical travel limitations of the traversing gear used. Work is continuing to alleviate these limitations.REFERENCES
1. Hawthorne, W. R., Weddell, D. S., and I-bttel, H. C., "t4ixing and
Combustion in Turbul ent Gas Jets", 3rd (International) Symposi urn on
Combustion, The Combustion Jnstitute, Baltimore, 1949, pp. 266-28~.
2. Wo hl, K., Ga z 1 e y , C., a n d Kap p , N.,
(International) Symposi urn on Combust ion,
l3altimore, 1949, pp. 288-300.
11 Di ffus ion Fl ames", 3rd
lhe Combustion Institute,
3. Becker, H. A., "Effects of Concentration Fluctuations on Turbulent
Di ffusion Fl ames", Fi fteenth Symposi urn (International) on Combust ion,
lhe Combustion Institute, Tokyo, ,Jiipan, 1975, p. 601.
4. Bilger, R. W., 11 Turbul ent Jet Diffusion Flames", Prog. Energy &
Combust. Sci., 1976,1., pp. 87-109.
5. Ballantyne, A. and Bray, K. N. C., "Jnvestigation into the Structure of
Jet Diffusion Fl ames Using Time-Resolved ~tical t>'easuring Techniques",
Si xteenth Symposi urn (International) on Combust ion, The Combust ion
Institute, Pittsburgh, 1977, pp. 777-787.
6. Glass, M. and Bilger, R. W., "The Turbulent Jet Diffusion Flame in a
Co-flowing Stream - Some Vel ocity ~~asurements", CI.lmbust. 9:i. Techn.,
1978,~, pp. 165-177.
7. Toshimi, T., Hyun-Dong, S., and Aki za, I., "Properties of Turbul ence in
Turbulent Diffusion Flames", CI.lmbustion and Flame, 1981, 40, pp.
121-140.
8. 9nith, R. H. and ~~ang, C.-T., "Contracting Cones Giving U1iform lhroat
Speeds", J. ftero. Sci., 1944,
1l,
pp. 356-3~0.9. Sislian, ,J. P. and Cus\'oQrth, R. A., 11 Laser I'>ppler Velocimetry
t-'easuranents of t-'ean Velocity and Turbul ent Stress Tensor Components in
a Free Isothermal Swirling Jet", UTIAS Report t-b. 281,1984.
10. I\lrst, F., t-'elling, A., and Whitelaw, J. H., "Principles and Practice
of Laser Doppl er Anemometry", Academic Press, 1976.
11. Self, S. A. and Whitelaw, ,J. H., "Laser Anemometry for Combustion
Research", Comb. Sci. Techn., 1976,
Q,
pp. 171-197.12. Stevenson, W. H., lhompson, O. H., and Roesler, T., "Direct t>'easuranent
of Laser Velocimeter Bias Errors in a Turbulent Flow", .AIAA J., 1982,
20, ttl. 12, pp. 1720-1723.
13. lhompson, H. and Flack, R., Jr., "An Application of Laser Velocimetry
to the Interpretation of Turbul ent Structure", Proc. ISL/ AGARD Workshop
on Laser Memometry, ~rman/French Research Inst., Eds. H. J. Pfeiffer
and J. Haertig, St. Louis, France, 1976, pp. 189-231.
14. Hinze, J. 0., "Turbu1ence: An Introduction to lts Mechanism and Theory", McGraw-Hi 11, New Vork, 1959.
15. Bendat, J. S. and Piersol, A. G., IRandom Data: Ana1ysis and t1easurement Procedures", Wi1ey-Interscience, New Vork, 1971.
- - -- - - -- - - -- - - ,
Species
Argon, Liquid Carbonic Canada
Commercial purity:
Helium, Canox
Commercial purity:
Table I
Natural Gas, t1atheson, Typical Composition
Methane:
Ethane:
Propane:
Nitrogen:
Carbon di oxide:
Percent by Vol ume
99.9 99.9 95.75 2.00 0.10 1.95 0.24
TABLE 11
Non-combu8 t ing
x/D r/D u u '2 V'2 u'v' k
(mi 8) {mi 8)2 {mi 8)2 {mI 8)2 (mi 8) 2
0.300 -0.5080 3.2918 0.2915 0.0183 -0.1304 0.1549 -0.4953 4.0370 0.9544 0.0030 -0.2489 0.4787 -0.4826 4.8941 2.1252 0.0240 -0.4345 1.0746 -0.4699 6.7574 4.6881 0.0074 -0.1508 2.3477 -0.4572 8.5639 5.5719 0.0061 0.0902 2.7890 -0.4445 10.056 5.2127 0.0070 0.0656 2.6098 -0.4318 11.723 3.7191 0.0103 0.0996 1.8647 -0.4064 13.785 1. 7902 0.0107 -0.0183 0.9005 -0.3810 15.264 0.4800 0.0084 -0.0019 0.2442 -0.3302 16.831 0.0206 0.0095 0.0051 0.0151 -0.2540 17.172 0.0052 0.0073 0.0011 0.0062 -0.1270 17.166 0.0049 0.0167 0.0017 0.0108 0.0000 17.166 0.0066 0.0138 -0.0044 0.0102 0.1270 17.173 0.0068 0.0091 0.0000 0.0079 0.2540 17.160 0.0073 0.0147 0.0030 0.0110 0.3302 16.827 0.0977 0.0142 0.0172 0.0560 0.3810 15.763 0.9481 0.0124 0.0101 0.4802 0.4064 14.533 2.2085 0.0066 -0.0511 1.1076 0.4318 12.258 3.5973 0.0055 -0.1066 1.8014 0.4445 10.680 3.9104 0.0048 -0.2160 1.9576 0.4572 9.0343 3.7899 0.0053 -0.2265 1. 8976 0.4699 6.1681 2.5995 0.0037 -0.2653 1.3016 0.4826 4.4768 1.0041 0.0034 -0.1458 0.5038 5.000 0.0000 16.196 3.2264 1.0937 0.0000 2.1600 0.1270 15.431 4.1775 2.1941 0.9896 3.1858 0.2540 13.779 5.5384 3.5400 1. 7346 4.5392 0.3175 12.458 6.6209 4.4165 2.1830 5.5187 0.3810 11.414 6.8163 4.5828 2.3940 5.6995 0.4445 10.010 6.5906 4.6000 2.4242 5.5953 0.5080 8.4720 5.9258 4.6009 2.2674 5.2633 0.6350 6.7136 4.7721 3.7072 1.6599 4.2396 0.7620 5.1086 3.5746 2.7176 1.0888 3.1461 0.8890 3.9378 2.7723 1.9444 0.8429 2.3583 1.0160 2.9629 2.1000 1.4304 0.6618 1.7652 1.1430 2.2886 1.4699 1.0123 0.5360 1.2411 1.2700 1.1709 0.8651 0.6710 0.3008 0.7680 1.6510 0.5023 0.4453 0.4617 0.1859 0.4535 10.000 -2.2860 0.3234 0.2315 0.1000 0.0572 0.1657 -2.0320 0.6504 0.4099 0.2320 0.0831 0.3210 -1. 7780 1.1233 0.5997 0.3609 0.2051 0.4303 -1.5240 1.8130 1.0136 0.6101 0.3326 0.8118 -1.2700 2.7621 1.5989 1.0747 0.4566 1.3368 -1.0160 3.7907 2.6766 1.5604 0.8665 2.1185 -0.7620 5.6533 3.7466 2.1226 1.3090 2.9346 -0.5080 7.7698 4.6762 2.5740 1.3941 3.6251 -0.2540 9.7898 4.7390 2.6673 1.1769 3.7031 -0.1270 0.6562 0.0000 .10.714 4.3753 2.7193 -0.0358 3.5473 0.1270 0.4347
- - -
-TABLE I I
Non-combust ing
x/D r/D U u 'Z v' z u'v' k
(mI s) {mI S)2 {mI S)2 {mI S)2 {mI S)2
10.000 0.2540 10.064 4.6894 2.6940 1.0150 3.6917 0.5080 7.9246 4.3510 2.7140 1.4083 3.5325 0.7620 5.5978 4.0204 2.3037 1.2077 3.1620 1.0160 4.0939 2.6793 1.7127 0.8241. 2.1960 1.2700 2.7331 1. 7366 1.1114 0.5042 1.4240 1.5240 1.9256 1.0612 0.7554 0.2839 0.9083 1. 7780 1.1200 0.5755 0.5748 0.2054 0.5752 2.0320 0.6464 0.3846 0.2993 0.0840 0.3422 2.2860 0.3701 0.2206 0.1000 0.0254 0.1603 15.000 0.0000 7.3124 2.4912 1.4680 -0.0352 1. 9796 0.2540 7.1640 2.5317 1.4789 0.2892 2.0053 0.3810 0.4610 0.5080 6.3535 2.5715 1.4975 0.5875 2.0345 0.6350 0.7311 0.7620 5.4704 2.5877 1.4453 0.7833 2.0165 1.0160 4.6817 2.3676 1.3455 0.7374 1. 8565 1.2700 3.5256 1.8967 1.2134 0.6314 1.5550 1.5240 2.7601 1.4738 1.0193 0.5353 1.2465 1. 7780 2.0505 1.0170 0.8750 0.4040 0.9460 2.0320 1.5250 0.7020 0.6959 0.2954 0.6990 2.5400 0.6335 0.3705 0.4131 0.1745 0.3918 3.0480 0.2768 0.2149 0.1300 0.1725 20.000 0.0000 5.4274 1.5383 0.9645 0.0278 1. 2514 0.2540 5.2860 1.5511 0.9500 0.1845 1.2505 0.5080 4.9393 1.5792 0.9455 0.3266 1.2623 0.7620 4.4901 1.6206 0.9300 0.4449 1.2750 1.0160 3.7158 1.3650 0.9266 0.5150 1.1458 1.2700 0.4557 1.5240 2.7437 1.0720 0.7710 0.4218 0.9215 2.0320 1.9913 0.7910 0.6032 0.2871 0.6971 2.5400 1.2933 0.5320 0.4431 0.1984 0.4875 2.7940 0.3937 3.0480 0.6252 0.2891 0.3396 0.0801 0.3143 3.5560 0.3162 0.1969 0.2067 0.0259 0.2018 4.0640 0.1000 0.1100 0.1117 0.1108 30.000 0.0000 3.4373 0.7262 0.4376 0.0287 0.5819 0.5080 3.2924 0.7170 0.4190 0.1398 0.5680 1.0160 2.9226 0.7138 0.4223 0.1977 0.5680 1.5240 2.3892 0.7108 0.4072 0.2359 0.5590 2.0320 2.0151 0.5686 0.3908 0.2195 0.4797 2.2860 0.3535 2.5400 1.5501 0.5121 0.3083 0.2006 0.4102 3.0480 1.1881 0.3951 0.2778 0.1423 0.3364 3.5560 0.9255 0.2834 0.2487 0.1138 0.2661 4.0640 0.6882 0.2214 0.2037 0.0701 0.2126 4.5720 0.4279 0.1708 0.1576 0.1642
TABLE 11
Non-combus t ing
x/D r/D U u '2 v' 2 u'v' k
(mI s) {Dl/s)2 {mI S)2 {mI s)2 {mI S)2
40.000 0.0000 2.4740 0.3791 0.2447 0.3119 0.5080 2.3780 0.3803 0.2436 0.3120 1.0160 2.3090 0.3816 0.2498 0.3157 1.5240 2.1123 0.3755 0.2415 0.3085 2.0320 1.9469 0.3735 0.2430 0.3083 2.5400 1.5653 0.3386 0.2292 0.2839 3.0480 1.3794 0.2941 0.2130 0.2536 3.5560 1.1379 0.2545 0.1894 0.2219 4.0640 0.8700 0.2165 0.1638 0.1902 4.5720 0.6670 0.1785 0.1533 0.1659 5.0800 0.4731 0.1504 0.1316 0.1410 6.0960 0.2378 0.0878 0.0976 0.0927 50.000 0.0000 1.8648 2.1860 0.1606 0.1896 0.5080 1.8742 0.2108 0.1574 0.1841 1.0160 1. 8593 0.2230 0.1576 0.1903 1.5240 1. 7599 0.2184 0.1612 0.1898 2.0320 1.6605 ·0.2175 0.1558 0.1866 2.5400 1.5451 0.2132 0.1524 0.1828 3.5560 1.2483 0.2069 0.1369 0.1719 4.5720 0.9987 0.1753 0.1152 0.1453 5.5880 0.7462 0.1353 0.0911 0.1132 6.6040 0.4840 0.0924 0.0757 0.0840 7.6200 0.2849 0.0622 0.0614 0.0618
- - - -- - ----.
TABLE II
Combusting
x/D r/D U u I Z V I Z U 'V I k
(mI s) {m/s)2 (mI s) 2 (mI s) 2 (mI s) 2
0.300 -0.5207 3.5115 0.0946 0.0014 -0.0191 0.0480 -0.5080 3.8895 0.3609 0.0019 -0.0722 0.1814 -0.4953 4.6965 1.2091 0.0105 -0.2011 0.6098 -0.4826 6.6748 2.9632 0.0108 -0.2628 1.4870 -0.4699 8.5283 3.9611 0.0131 -0.1990 1. 9871 -0.4572 10.246 4.5194 0.0155 -0.0321 2.2670 -0.4445 11. 979 3.8873 0.0176 0.0562 1.9524 -0.4318 13.381 3.0549 0.0051 0.1325 1. 5300 -0.4064 15.626 1.0236 0.0062 0.0894 0.5149 -0.3810 16.499 0.4712 0.0092 0.0542 0.2402 -0.3302 17.151 0.0210 0.0146 0.0124 0.0178 -0.2540 17.202 0.0075 0.0337 -0.0016 0.0206 -0.1270 17.294 0.0186 0.0215 -0.0002 0.0200 0.0000 17.267 0.0049 0.0158 0.0000 0.0103 0.1270 17.219 0.0066 0.0170 0.0004 0.0118 0.2540 17.289 0.0050 0.0123 0.0013 0.0086 0.3302 17.078 0.0656 0.0101 0.0179 0.0379 0.3810 16.351 0.8510 0.0115 0.0402 0.4312 0.4064 15.632 2.1578 0.0080 0.0698 1.0829 0.4318 13.762 4.8507 0.0051 0.0891 2.4279 0.4445 12.373 6.0515 0.0041 0.0012 3.0378 0.4572 10.762 6.3493 0.0119 -0.0170 3.1806 0.4699 7.9308 4.2215 0.0034 -0.0638 2.1124 0.4826 6.2690 2.4177 0.0036 -0.0713 1.2106 0.4953 4.5381 0.6438 0.0031 -0.0172 0.3235 0.5080 3.8839 0.1365 0.0030 0.0697 5.000 0.0000 17.188 0.0467 0.0245 -0.0006 0.0356 0.1270 17.148 0.0695 0.0378 0.0018 0.0536 0.2540 17.086 0.1923 0.1272 0.0208 0.1598 0.3048 16.932 0.3569 0.2347 0.0261 0.2958 0.3556 16.525 0.7766 0.6315 0.0774 0.7040 0.4064 15.361 2.1344 1.4648 0.5375 1. 7996 0.4572 13.841 3.2753 2.1560 1.1476 2.7157 0.5080 12.010 4.2523 2.1193 3.1858 0.5588 10.962 4.5114 1.9519 1.3483 3.2316 0.6096 9.6964 3.9975 1.3872 1.2652 2.6920 0.6604 8.6816 3.4688 1.0217 1.0427 2.2450 0.7112 7.9545 2.5688 0.8763 0.8198 1.7225 0.7620 7.1854 2.1330 0.7959 0.5181 1.4640 10.000 -1.1430 4.1228 2.0135 0.7380 0.5026 1.3757 -1.0160 5.4268 2.7038 1.0024 0.7668 1.8531 -0.8890 7.0909 3.6432 1.2137 1.1735 2.4284 -0.7620 8.9159 4.2601 1.5900 1.2477 3.0882
