The variation of spray characteristics along a radial distance downstream of a pressure-swirl atomizer was measured by laser light-scattering technology. An analytical model was developed to predict the variation of spray characteristics along the radial distance. A comparison of the predicted and experimental data showed excellent agreement. Therefore, the spray model proposed, although relatively simple, is correct and can be used, with some expansion and modification of the prepared model, to predict more complicated spray systems

Chin, J. S.

Li, W. M.

Wang, X. F.

English

NASA Technical Reports Server

N87-20271
EXPERIMENTAL AND ANALYTICAL INVESTIGATION OF THE VARIATION OF SPRAY
CHARACTERISTICS ALONG A RADIAL DISTANCE DOWNSTREAM OF A
PRESSURE-SWIRL ATOMIZER
J.S. Chin, W.M. LI, and X.F. Wang
BelJlng Institute of Aeronautics and Astronautics
BelJlng, People's Republic of China
The variation of spray characteristics along a radial distance downstream
of a pressure-swlrl atomizer was measured by laser llght-scatterlng technology.
An analytical model was developed to predict the variation of spray character-
istics along the radial distance. A comparison of the predicted and experi-
mental data showed excellent agreement. Therefore, the spray model proposed,
although relatively simple, is correct and can be used, with some expansion
and modification of the prepared model, to predict more complicated spray
systems.
INTRODUCTION
The characteristics of the spray formed by an atomizer in a llquld-fueled
combustion device are extremely important to the performance, stability, and
pollutant formation of the combustor. The spray characteristics should be
measured accurately, and a model should be developed to predict the variation
of spray characteristics, droplet trajectory, spray dispersion, and evapora-
tion history. It is also important to understand the influence of various
factors on the measurement of spray characteristics. A comparison between
predicted and measured spray characteristics provides useful insight into
spray combustion. Such research has a slgnlflcant effect on engineering
applications and on the fundamental understanding of spray combustion.
The authors analyzed the variation of spray characteristics along the
axial distance downstream of a pressure-swirl atomizer. The effect of spray
evaporation on the variation of spray characteristics is discussed in
reference 1 and was presented by J.S. Chin and J.Y. Zhu at this symposium.
(Paper, entitled The Interdependence of Spray Characteristics and Evaporation
History of Fuel Sprays in High Temperature Airflows, was unavailable for
printing at the time of publication.) The influence of downstream distance on
the spray characteristics of pressure-swirl atomizers is caused by the effects
of spray dispersion and drop acceleration or deceleration. This condltlon is
analyzed in reference 2. These analyses have been partially substantiated by
some experimental data. Until now there have been few experimental data of
the variation of spray characteristics along the radial distance downstream of
the pressure-swlrl atomizer. Lee Dodge published his measurement results as
shown in figure 1 (ref. 3). He shows that both the Sauter mean diameter SMD
and drop-slze distribution parameter N increase with radial distance. There
is no analysis on this aspect available at the present time.
We are interested in comparing the experimental and predicted values of
the variation of spray characterlstlcs along the radial distance. Therefore,
we carefully measured this variation in a well-deflned experimental condition,
"developed an analytical model to predict the variation, and then compared the
47
https://ntrs.nasa.gov/search.jsp?R=19870010838 2020-03-20T11:08:36+00:00Z
experimental and predicted data. These comparisons promote our understanding
of spray dispersion and the factors influencing drop-slze measurement. After
we have predicted the simple spray system, we will be able to expand and
modify the proposed spray model to extend its capability to more complicated
spray systems.
Cao and Chin proposed a flat-fan spray model for the fuel distribution
downstream of a plain orifice injector under cross airflow (ref. 4). The
model was validated by fuel distribution measured by gas analysis and drop
size. It is obvious that, for the validation of a given spray model, the
spray characteristics measurement is reliably accurate and much simpler than
the fuel distribution measurement. It is this author's intention to validate
a spray model by measuring the spray characteristics along the radial distance.
The same spray model has also been validated by measuring the spray character-
istics along different B angles (as shown in fig. 5).
TEST APPARATUS, ATOMIZER, AND PARTICLE SIZER
The test section was a rectangular chamber with transparent windows for
optical drop-slze measurement. The test apparatus included an air system and
a fuel system, as shown in figure 2.
The atomizer tested (fig. 3) was a pressure-swlrl atomizer taken from an
existing aircraft gas-turblne engine. The atomizer had a pilot-fuel flow and
a main-fuel flow. In this test we used the pilot-fuel passage. Because the
flow rate is relatively lower with pilot-fuel flow, the obscuratlon was In the
right range.
A Malvern drop-slze analyzer model 2200 was used. The principle of the
particle slzer is shown in figure 4. The instrument was set on the Rosin-
Rammler distribution mode. The direct results from the instrument are the
characteristic diameter B and the drop-slze distribution parameter N in
the R-R distribution which is expressed by
exo[,N] (I)
where Q is the fractlon of the total volume contained in drops that have a
diameter less than D.
The Sauter mean diameter SMD can be obtained from
where r is the gamma function.
(2)
EXPERIMENTAL RESULTS
During drop-size measurement tests, the laser light beam was first
adjusted so that it was in the same horizontal plane as the central line of
the atomizer and that it was perpendicular to this central llne. At this
48
position (defined as the y = 0 position), the spray characteristics were
measured. Then the Malvern particle slzer was put on some stze blocks of
known dimension. This changed the height of the laser beam so that the radtal
distance where the parttcle stzer measured the drop stze was changed. The
summation of the size block was defined as the radlal distance y. The dlmen-
slons of the blocks chosen were 2.5, 3.0, and l0 mm. Thus, the following
radial distance y could be obtained by different combinations of the size
blocks: y = 0, 5.5, 10.0, 15.5, 20.0, 25.5, and 30.0 mm. The experimental
results are shown In figures 6 to 13. From these figures it Is clear that the
Sauter mean diameter and drop-size distribution parameter increase with radial
distance until the edge of the spray has been reached. The experlmental
results obtained by the present authors are quantitatively tn good agreement
with Lee Dodge's results. The obvious explanation of the measured results
shown in figures 6 to 13 is that wtth larger radial distances the possibility
of the laser light beam meeting the large drops ts greater than tt is with
smaller radtal distances. Thts shows that when we measure the drop size it ts
necessary to take a sample that Is representative of the spray formed; how-
ever, it ls impossible to define the sample which would fully represent the
spray. The most reasonable sample can be obtained by measuring the spray at
the y = 0 position.
Comparing figure 6 wlth 8 and 7 wlth 9 shows that, at a higher airflow
velocity, the change of spray characteristics along the radial distance Is
weaker. A comparison of figures 8, lO, and 12 and of 9, II, and 13 shows
that, wlth a lower pressure drop across the nozzle, the change of the spray
characteristics along the radial distance Is weaker. These results tell us
that when the spray Is expanded less radially the change of spray characteris-
tics is also flatter. The reverse Is also true.
The experimental data obtained In thls way were used to check the pro-
posed spray model.
PHYSICAL MODEL
The spray formed by a pressure-swlrl atomizer Is shown In figure 5. The
physical model was proposed wlth the following assumptions:
(I) The atomization process is completed as soon as the fuel leaves the
atomizer nozzle; that Is, droplets of different sizes start their movement at
the nozzle exit. Droplets of different sizes have the same initial velocity.
Because It Is suitable to use a cylindrical coordinate system to describe
droplet motion, the tangential velocity and the radial velocity component can
be combined and treated as one velocity component.
(2) The airflow Is uniform.
(3) The air Is at ambient temperature, so droplet evaporation can be
neglected.
(4) The influence of different droplet velocities on the drop-slze meas-
urements made by the Malvern particle slzer Is neglected.
The initial drop-slze distribution can be expressed by Do(SMDo) and No
wlth the initial volume fraction (dQ/dD) o as
49
N -l
No l°dD o DO (3)
At a downstream distance x, the droplets of diameter D move from the origin
and then distribute themselves on a circumference of radius R(D) while the
laser light beam of diameter dj only meets some of these droplets:
(4)
where
1
Yo - 2 dj
mI = arcsln R(D) (5)
1
Yo + 2 dj
m2 = arcsln R(D) (6)
The definitions of m2 and _I are shown in figure 5. When
Yo - 1 dj <_ R(D) <_ Yo + 1 dj
then
_o2 =
where Yo is the radial distance and dj the diameter of the light beam.
The summation of the liquid fraction of the droplets of various diameters
passing through the laser light beam is given by
dD (7)
The minimum diameter Dml n that the laser light beam can see is determined
by
R(Dmln) = Yo - ½ dj
That is, at the downstream distance x, if
will not pass through the laser light beam.
determined by the droplet motion equation.
exist in the spray, can be approximated by
R(D) < Yo - 1/2 dj, this droplet
The relationship R(D) can be
The maximum diameter that may
50
Omax = 3.5(SMD)
If we take the droplets within the laser light beam as a new spray (a
sample), the liquid volume fraction of droplets of diameter D in this new
spray (sample) is
dQ _2 - _l
dQ'_ dD o
dD
-f Dmax (dd-d-_D/o_2- _l
J Dml n
dD
Since this Is actually the drop-slze dlstrlbution of the sample (new spray)
the laser light beam is to measure, we may obtain Q' as a function of D.
Then, if we assume that the Rosln-Rammler (R-R) distribution can be used for
data fitting the sample (new spray), we obtain new SMD' and N' for the
sample. These values, SMD' and N', change with the distance Yo- If we
delete the prime, we obtain the functional relationships SMD = f(y) and
N = f(y).
(8)
DROPLET TRA3ECTORY EQUATION
If we use a coordinate system which is moving with the airflow, then the
droplet motion equation is
where
m droplet mass, (_/6)ptO3
p_ liquid density
w droplet relative velocity
CD droplet drag coefficient, CD
Pa density of air
_a viscosity of air
Equation (9) can be rewritten as
dt - -
where Wo
2
dw Paw
m _ = -CO 2
= 15/_/'_ for Re = PaDW/Pa
45 (PaPaWo )l/2D_3/2(W _3/2
4 Pl. \Wo)
is the droplet initial relative velocity.
(9)
(lO)
51
Integrating equation (lO) yields
W )-2
_--= (Bt + 1 (II)
0
where
45 (Pa"aWo )I/2
= -- D-3/2
B 8 p_ (12)
We know that, at the downstream distance x, droplet velocity, air veloc-
ity, and the relative velocity of these two have the following relations:
+( wVx = Va Vxo - Va)_--
0
and (13)
W
VR = VRo _--
0
where Vx and VR are the axial and radial velocity components of the drop-
let, and Vxo and VRo are the initial values of these components. Thus, we
obtain the droplet trajectory equations
and
_o t Wx = Vat + (Vxo - Va) Woo dt
_o t WR = VRo Woo dt
(14)
From equation (ll) we have
t
_o W dt too -Bt+l
(15)
From equations (14) and (15) we have the radial position (droplet size D) at
downstream distance x:
l
R(D) = VRo ] (16)
B+_
52
Time t can be determined by
r )2 4VaBX]I/2XB - Vxo + L(XB - Vxo ÷
t =
2VaB
(17)
where B Is determined by equation (12).
From equations (14) and (15), by substituting x and Rml n = R(Dml n) =
Yo - (1/2) d_, we obtain
I v 1Vxo - a _2 2/3Dmln = 84_55(Pa"aWo)I/2 VR0- Kml n - XRmlVxo m n- " (18)
CALCULATION METHOD AND RESULTS
In order to calculate the variation of spray characteristics along the
radial distance the following parameters must be known:
(1) Axial distance x
(2) Pressure drop across the nozzle aP_
(3) Fuel properties and physical properties of alr
(4) Atomizer spray cone angle
(5) Initial spray characteristics (SMD)o and No
The calculation method used In thls paper may be summarized as follows:
(1) Use the measured SMD and N values at y = 0 and the downstream
distance x as the approximation of (SMD) o and NO. We know that there Is
some difference between (SMD) o and SMDy= O, NO, and Ny= 0 (ref. 2). So far
these are the most reasonable approximate values that can be used.
(2) Calculate the initial droplet velocity Vt = _(2ap_Ipt) I/2 where
Is the flow coefficient for the pressure drop. For the atomizer used In the
present research, the spray angle Is close to 90°; therefore,
Vxo = 0.566
2Aptll/2
VRo = 0.566
(19)
(3) Determine the Omln value for a different Yo value by
equation (18). We assume Dmax = 3.5(SMD).
(4) Use the Simpson method to solve equation (8), wlth the R(D) value
calculated from equations (16) and (17).
53
(5) Determine the integration
Q' = dD
mln
From this, we are able to obtain a set of the data of Q' and D.
(6) Assume that Q' can be fitted by R-R distribution:
Q' = 1 - exp -
By using the least-square method, we can obtain D and N'; then, SMD' and
N' can be calculated. These SMD' and N' values are plotted against y
in figures 6 to 13.
The results of the calculations for different airflow velocities and for
the nozzle pressure drop are shown in figures 6 to 13. These are compared
with the corresponding experimental data. It is obvious that the predictions
are in excellent agreement with the experimental results.
CONCLUDING REMARKS
In the present study, droplet evaporation was neglected (discussed by
J.S. Chin and J.Y. Zhu in the unpublished paper cited previously), and it is
not difficult to take into consideration the effect of droplet evaporation.
After this model has been validated, it is relatively simple to predict
the fuel distribution downstream of a pressure-swirl atomizer (ref. 6).
One interesting point that was noticed from the experiments and the anal-
ysis was that the larger droplets are always at the spray edge. Because the
ignition spark plug is also always positioned close to the spray edge, the
spark might meet the larger droplets, which would harm the ignition.
We measured the variation of spray characteristics along the radial dis-
tance was by laser light-scatterlng technology. And we found that the predic-
tion based on the proposed spray model was in excellent agreement with the
experimental data.
l °
.
REFERENCES
J.S. Chin; R. Durrent; and A.H. Lefebvre: The Interdependence of Spray
rh_+o_+_ _,a _,,_^_+_ _+.... ^_ _,,ol _,,_ Transacti_ _....................... _, _,on Hi , j ....... v ........
ASME Journal of Engineering for Gas Turbine and Power. July, lgB4.
J.S. Chin; D. Nickolaus; and A.H. Lefebvre: Influence of Downstream
Distance on the Spray Characteristics of Pressure-Swirl Atomizers. ASME
85-GT-138, Transactions of the ASME, Journal of Engineering for Gas
Turbine and Power, Jan., 1986.
54
..
.
.
L.G. Dodge; and C.A. Moses: Mechanisms of Smoke Reduction In the Htgh
Pressure Combustion of Emulsified Fuels. Vol. 1, Construction of Appara-
tus and Preliminary Experiments, Yearly Progress Report No. l, Sept. 29,
1980 to Sept. 29, 1981.
M.H. Cao; J.S. Chin; et al.: Semi-Empirical Analysis of Liquid Fuel
Distribution Downstream of a Plain Orifice Injector Under Cross-stream
Air Flow. Transactions of the ASME, Journal of Engineering for Power,
Oct., 1982.
3.S. Chtn; X.F. Wang; W.M. Lt; and A.H. Lefebvre: The Influence on
Measured Spray Characteristics of Variations In the Radtal and Angular
Positions of the Sampling Laser Beam. Spring Technical Meeting Central
States Sectlon/The Combustion Institute, Paper CSS/CI 86-5C1, 1986.
3.S. Chin; and A.H. Lefebvre: Predlctlon of Ltquid Fuel Dlstrlbution
Downstream of a Swirl Atomtzer In Flowing Air. Sprlng Technical Meettng,
Central States Section/The Combustion Institute, Paper CSS/CI 83-20, 1983.
55
E _
E
t_
t-
f_
aJ
E
i-
V3
gO
8£,
70
6o
40
IOO
9o
80
qo
6o
50
J
; S /
J
i , I , I I _ I I J I ,
0 2 _ 6 8 10 1_ 1@ 16
(a) x = 25.4 mm.
-",0
_8
(b) x = 50.8 ram.
,2.4,
2.2,
_0
i
;:1.._,
._6
_2
_,o
2.6
2.4,
2.0
16
30
z
C
_u
E
11:1
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o
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I
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Figure 1. - Lee Dodge's measurement resu]ts (ref. 4). Atomlzer
pressure drop, _P, ]00 ]b/In. 2
56
24 5
f
12
lO
f .._-
14/5__ )
Figure 2. - Experimental system. Plenum chamber, 1; air
temperature, 2; air flowmeter, 3; test section, 4; exhaust
pipe, 5; fuel tank, 6; fl]ter, 7; pump, 8; return valve, 9;
valve, 10; pilot-fuel flow valve, 11; pressure gauge, 12;
atomizer, 13; main-fuel flow valve, 14; pressure gauge, 15.
2
Figure 3. - Atomizer. Pllot-fuel
flow, I; maln-fuel flow, 2.
57
12
Figure 4. - Laser drop particle slzer. Laser, l; beam expander, 2; test
section, 3; fuel nozzle, 4; lens, 5; photo detector, 6; solid valve, 7;
amplifier, 8; A/D converter, 9; data transfer, lO; interface, ll;
computer, 12; printer, 13; micro tune, 14.
--" Spray--_. i Light
t Y .J_ Beam
---_ / f ,T-'Cq)-
- o_- _O%v,
-Xv- i
z Fuel
Laser Light
Beam
Figure 5. - Physical model.
58
E:E
80
70
60
50
• Experimental
Predicted
40 , ,
o lO 20 30
y, mm
Ftgure 6. - Variation of Sauter mean diameter (SMD) along radtal
distance (y) for x = 70 mm, Va = 9 m/sec, and AP = 12 kg/cm2.
z 3
• Experimental
n Predtcted
o 3b
y, Inm
Figure 7. - Varlatlon of drop-size distribution parameter (N)
along radial dlstance (y) for x = 70 mm, Va = 9 m/sec, and
&P = 12 kg/cm 2.
59
Eu_
8O
70
6O
5O
40
• Experimental
Predicted
i i
0 I0 20 30
y, mm
Figure 8. - Variation of Sauter mean diameter (SMO) along radial
distance (y) for x = 70 mm, Va = 6 m/sec, and AP = 12 kg/cm2.
z 3
0
Experimental
Predicted
10 20 30
y, mm
Figure 9. - Variation of drop-slze distribution parameter (N) along
radial distance (y) for x = 70 mm, Va = 6 m/sec, and
AP = 12 kg/cm2.
60
80
E 7o
s'-
6O
50
40
• Experimental A
-- Predicted ,&_
0 I 0 20 30
y, mm
Figure I0. - Variation of Sauter mean diameter (SMD) along radial
distance (y) for x = 70 mm, Va = 6 m/sec, and AP = 8 kg/cm2.
z 3
___ Experlmental
k
L t i
0 I0 20 30
y, mm
Figure II. - Variation of drop-slze distribution parameter (N)
along radial distance (y) for x = 70 mm, Va = 6 m/sec, and
AP = 8 kg/cm2.
61
E
;z
C:3
z
u3
7O
6O
50
• Experimental
-- Predlcted
4O
0 10 20 30
Figure 12. - Variation of Sauter mean diameter (SRD) along radial
distance (y) for x = 70 mm, Va = 6 m/sec, and AP = 4 kg/cm L.
z 3
• Experimental
-- Predicted
I I |
0 I0 20 30
Figure 13. - Variation of drop-size distribution parameter (N)
along radial dlstance (y) for x = 70 mm, Va = 6 m/sec, and
_P = 4 kglcm 2.
62


Experimental and analytical investigation of the variation of spray characteristics along a radial distance downstream of a pressure-swirl atomizer

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