- Email: [email protected]
Measurement of the deposition of small particles in stationary and oscillating turbulent pipe flow
J Aerosol Set., Vol 14, N o 5, pp 615 632, 1983 Printed tn Great Brnain
(
0021 850283 $ 3 0 0 + 0 . 0 0 1983 Pergamon Pres~, Ltd
MEASUREMENT OF THE DEPOSITION OF SMALL PARTICLES IN STATIONARY AND OSCILLATING TURBULENT PIPE FLOW J. WILDI a n d H . THOMANN Institute of Aerodynamics, Swiss Federal Institute of Technology, CH-8092 Zfirich, Switzerland ( R e c e i v e d 20 J a n u a r y
1983)
Abstract--The deposition rate of small spherical droplets on the wall of a pipe is measured for fully developed turbulent flow at Reynolds numbers between 10,000 and 20,000 and for oscillating flow. For steady flow and sufficiently large particles, the results agree with k÷ = - 3.4 x 10 -4 r2+ derived from Kneen and Strauss ( i 969). The deposition rate of small particles is considerably larger than predicted by the above equation. For the experiments with oscillating flow, the same equipment is used. Turbulence is observed for A = 2 ~,/x/"v¢o >1 350. The dependence of the deposition rate on particle diameter is as in steady flow. For the present experiments with A /> 350, deposition rates are equal if the peak velocity in the pipe center in oscillating flow equals about twice the mean velocity in steady flow.
NOMENCLATURE A
(m 2)
A = 2~',c vw a . = ( D v) 1 3 c
( ) (_) (Part:m 3)
c+ = c/c,.
(-)
c,. D D DT d F~ f j
(Part,,m 3) (m) (mZ/sec) (me:sec) (pm) (N) (sec- t) (Part/m: sec)
j.
= j'u~cm
h k
(pm) (m.sect ~ )
k~
(pro)
k~+ = k ~ u , / v
(-)
AN N
(Part) (Partl
Re = ~D/v R e ^ = ~D.'v
(-) ( )
r = D2 - y r~ s
(m) (m) (~(m)
5÷ = . ' ¢ ' U r v
( )
t
(sec)
t. = tully
( )
u u.
(m sec) (m sec) = u./u~
u~ = ,, Zo/p
v r.
= t':U~
f f_ = f,u~ y )'. = )'u~v 3 ,. y
Particle concentration in pipe center Pipe diameter Molecular diffusion coefficient Turbulent diffusion coefficient Particle diameter Stokes drag force Frequency o f oscillation Particle flux
( }
k+ = k/u~
u..
Deposition area Number indicating the appearance of turbulence Dimensionless number in equation (16) Particle concentration
Step height between surface elements Deposition rate Equivalent roughness height Number of particles in one diameter class Number of particles Pipe Reynolds number Reynolds number of oscillation Radial distance from center Stroke of piston, see equation (9) Stokes stopping distance, see equation (5) Deposition time Velocity of fluid in axial direction Axial velocity in pipe center
(-)
lm secj (m ,sec) (m secl
Friction velocity Maximum velocity Velocity of fluid in radial direction
( }
(m sec) (-) (m) ( ) (m) (N sec, m 2) (m: sec)
Velocity of particle in radial direction Distance from wall Boundary layer thickness Dynamic viscosity Kinematic viscosity 615
616 ~,/¢ ?z rf~ =~ ck ~o= 2~f
L WILDIand H, THOMANN !kg/m3) (kg/m") IN/m2) I-! (:t Isec- ~i
Density of air Density of particle Wall friction Particle relaxation, equation (5) Crank angle, see Fig. 9 Angular velocityof oscillation
1. I N T R O D U C T I O N The theoretical treatment o f the particle transport is generally based on the diffusion model, in which the particle flux is expressed in terms o f particle diffusivity and concentration gradient. The governing equation is j =
- D" g r a d c.
(1)
The flux j is an abbreviation for the expression d N / A dr, i.e. N particles are transferred through an area A lying perpendicular to the concentration gradient grad c. In turbulent flows both molecular and eddy diffusion are operative, and D has to be replaced by D + Dr . To describe the particle deposition on a fixed wall the following equation is convenient jw = k ( c , , - c~).
{2)
The reference concentration outside o f the boundary layer or, in the case o f pipe flow, in the center is c,, and the concentration at the wall is cw. Using
v. = yu,/v, j+ = j/u~c,,,, C+ = C/Cm,
k+ = k/u~, with u, = V/zo/p, equations (1) and {2) read j+ =
D+ DT dc+ , v dy+
j~+ = k+(l - c ~ + ) .
[3) (3a)
In the present case there is c~+ = 0.
2. C L A S S I C A L D E P O S I T I O N T H E O R I E S 2.1. Free flight model To describe analytically the transportation mechanism, the flow near the wall is split up into three regions: (a)
0~
(b)
s+ < y+ ~< 5;
(c)
14)
y+ > 5.
Particles moving towards the wall, have, according to a model suggested by J. T. Davies (1972), to cross region (a) in a free flight owing to their inertia. They are started at a distance s ÷ away from the wall with a radial velocity ~ imposed by the turbulent motion. The surrounding flow is assumed to be motionless, so that the Stokes-drag Fw = 3 ¶/Mr3 is the only retarding force acting on the particle. The distance a particle flies to its stop is, according to
Particle deposition from turbulent flow
617
this theory,
±(P")
=
(5)
s+ -- 1 8 \ p L f with z+ = 1 8 \ p t ]
Region (b) contains the remaining part of the laminar sublayer. The turbulent diffusion mechanism determines the particle transport in this region.The coefficient of eddy diffusion used by J. T. Davies (1972), is --=
,
y+
~< 5.
(6)
In region (c), the equations of the Reynolds analogy determine the mass flux 1 -- c~+
j+ =
.
(7)
/Am+ -- 1~6+
Integration of equation (3) with Dr from equation (6) between the boundaries y+ = s+ and y+ = 6+ = 5 leads to the concentration at the outside of the laminar sublayer c,.=
_(8.933"+ "~[.1 \ 2 ]Ls~
1] 25
(8}
Eliminating ca+ between equations (7) and (8) leads to the deposition rate 1
k+ = -
(9)
u=+ - 19 + (353/s2+)
with Um+ = axial velocity in the pipe center. The following expressions are used to describe the turbulent pipe flow (Schlichting, 1951): u
/u =
2 = 0.3164Re~ l/a,
(10)
Re o = ~D/v, =
u~
/0.31_64 v Re~/8
X/ /
Um +
8 8
D
' 1/8
= u U¢ = =1.240.~- ~Re D .
(11)
C. N. Davies (1966) uses an empirical relation to describe the root mean square of the radial fluctuation velocities as a function of the wall distance .t
r+ =
Y+
y+ + 10
.
(12)
Equation (12) agrees well with experimental results given by Laufer (1954). The following assumption is now made: e+ = r+. Hence, the stopping distance may be written s+ = z+ - Y+ y+ +10"
(13)
Results are shown in Fig. 1. All particles hitting the wall have to satisfy the condition s+ /> y . - d + / 2 .
(14)
618
J WII.DI and H. THOMANN
"
r--
t 9p !'auz);
-U(--m:/
r+ :
Fr~edlander & ]oht~itone
k÷
N
k+
i
A't-cm'ur
~
8ca/
/
//
,,/
Lane & 5truket~ exper (flat plate) f fheo£
//X
¢ o
t62
Llu & Agarval
/
/~///~I / / / /
/
/
/
•Well5 & Chornbartam
0
Kneen & Strauss ._
// !
3 f Dawes, 1972, Eq {9) combined with Eqs (ll)&(12)
/ / i
/
/
C N Dawes, 1966 Re = lO ~
/
////// //,//
"
~
*
?0!
/
I
I
I
[
/ ~ Oiffu$ion through turbulent boundary layer, Eq (17)
/
~ Re =
o
1
J
r
1
1
tO
Particle
relaxion
I
5000
tO000
I
~+
L
I
102
time
Fig. 1. Deposition rates on smooth walls, experimental data compared with theory. Data from Beal (1968), C. N. Davies (1966), J. T. Davies (1972), Friedlander and Johnstone (1957), Kneen and Strauss (1969), Lane and Stukel (1978), Liu and Agarwal (1974), Liu and Ilori (1973), and Wells and Chamberlain (1967).
This model holds in a very limited range of z +. For s + ~ d . / 2 , equations t 13) and (14) require r+ /> 10 for particles to reach the wall. For r+ /> 15, on the other hand, s+ >/5 and the particles cross the whole sublayer in free flight. The deposition rate is in this case determined by the Reynolds analogy. For still larger particles the assumption no longer holds that particles move exactly with the velocity of the surrounding turbulent fluid. 2.2. Diffusion through the laminar sublayer To determine the deposition of small particles lying outside of the range of the free-flight model, i.e. z + < 10, one has to start from the complete diffusion equation (3), introducing the expressions for the diffusion constants
2kT 3~
0..=--
with the Boitzmann constant k = 1.38 × l0 -23 J / K and
(151
Equation (3) is valid in the whole laminar sublayer. Outside this layer the Reynolds analogy is used again. The integration of the diffusion equation from the first wall contact of a particle aty+ = d . /2 to the outside of the laminar sublayer at l, . = 5withe_ = t ) at v. = d . 2and
Particle deposition from turbulent flow
619
c+ = ca+ at y+ = 5 results in the concentration value ca. c~+ 8.9 f ~ (xa++a+)2(x2+--a+xa"+a2+) J÷ -- 3a2+ , - In (xa+ + a + ) 2 (x2+ --a+xa- +a+) /arctg
+ "v/3 L
----~--x/3a+
arctg
v/3 a+
= g (xa+, xd+, a+), (16) with
aS+ = O / v -
2kT 3nl~vd'
xa+ = 5/8.9,
1 (d/2)u, x~ +
8.9
v
Combining equation (16) with equation (7) results in the deposition rate k+ -
1 Urn+ - - U a +
+g
.
(17)
Combining the expressions for the turbulent pipe flow (u,,+ from equation (11) and ua+ = 6+ = 5) with equation (17)) leads to the numerical results shown in Fig. 1. 2.3. Literature on the particle deposition Figure 1 supplies a summary of existing theoretical and experimental deposition rates, including the present experiments. The papers are discussed in more detail by Wildi (1982). The deposition models based on experimental data for the turbulent fluctuation velocities, i.e. the theories of C. N. Davies and J. T. Davies, give numerical deposition rates which are more than one order of magnitude lower than the experimental results. The experimental results of different authors are in the range 1 < ~ ÷ < 10 in good agreement with k + = - 3.4 x 10- 4 r2 derived from Kneen and Strauss (1969) in spite of very different experimental techniques and different interpretation methods. Browne (1974) and Wood (1981) present analytical methods for the calculation of turbulent deposition to rough surfaces. Their theories follow the general approach of the free flight model and are valid for a roughness height smaller than 5v/u,. To take the roughness into account, the particle free flight distance is extended by an additional distance of the order of magnitude of the roughness height and the position of the origin of the velocity profile is shifted away from the smooth wall. Applying this method, it has been possible to use the Davies assumption for the radial velocity fluctuations. The results suggest that deposition rates of very small particles are extremely sensitive to small changes in surface roughness, even for hydraulically smooth surfaces. Some new attempts to reduce the discrepancy between the theoretical and experimental work are made by Rouihainen and Stachiewicz (1970) and Durst and Lee (1979). These authors consider the behaviour of a single particle in a fluctuating flow. However, they need a very specified knowledge of the turbulent velocities near the wall which is not yet available.
3. D E P O S I T I O N M E A S U R E M E N T S IN STATIONARY P I P E F L O W
3.1. Experimental arrangement The experimental setup is shown in Fig. 2. Saturated air is sucked from the inlet chamber (Position 1) through the deposition pipe (Position 2, Plexiglass, 40mm inner diameter) and
J WILDI and H. THOMANN
620
!
-
,o,,,como,,
r
JL
I
I
!
I
I
~
Honeycomb
Thermometer I
I
j.
lo
~9 Aerosol
generator
...ur,~ section
li
!
J i
~Thermometer
m~,,..~ un,
NIl
Return duct
O.,u,or
Fig. 2. Experimental arrangement, stationary flow.
flows back to the inlet chamber via the return pipe. The mass flow is computed from the pressure difference in the Venturi pipe (Position 6). Three different types of inserts in the pipe are available for measuring the flow parameters (velocity profiles, skin friction), the concentration and the deposition rate. The air in the closed system is saturated prior to the deposition measurements by evaporating water droplets produced in a second aerosol generator (Position 9). During the
0.5
t
i
!
Y~R 0.5 i
0 0
0.5 ]
o
: Exoenmental data for oresent measurement
Re = ~8000,
Re=
~-D
Veloctty profile In fully developl3ed t u r b u l e n t ptpe f l o w , R e = 2 3 0 0 0 , data f r o m S c h l i c h t i n g , 195!
Fig. 3. Velocity profile measured at
Re = 18,600 and comparison with data of Schlichting t195 t ).
Particle deposition from turbulent flow 12 11
•
To
.10 9
g/2 u2
I0
\
621
...
_
Bias,us" 9 ~
= ~
. Re ~
oo.,.s I T /
9 • Davies, experimental
8 ~.'~ ~*-3"/.. • ~.'~.....~
7
present measurement PreSton tubes
w, th
6 5 L
0 2
I
L
10
20
I
;0
Re. 103
40
Fig. 4. Skin frictionmeasuredat 4 Re-numbersand comparison with data by J. T, Davies(1972),and by Blasius (in Schlichting(1951)).
deposition experiment, this aerosol generator is inactive to prevent adding undesired particles and changing the temperature. The droplets to be deposited are generated in an ultrasonic aerosol generator with an oscillation frequency of 1.7 MHz. It produces water droplets in a diameter range between 3 and 30/~m with a mean diameter of about 10/am. The measuring section was located 35 pipe diameters downstream of the inlet. At this location and for Reynolds number Re = ~D/v between 10,000 and 20,000, the velocity profile measurements with a Pitot tube confirm the fully developed turbulent pipe flow characteristics. Figure 3 shows the velocity profile for Re = 18,600. The skin friction is evaluated from Preston-tube data using the interpretation method of Patel (1965). The maximum difference in skin friction along the periphery is + 3 ~o of the mean value. The rotational symmetry of the flow is thus sufficient for the deposition tests. The measured wall friction is compared in Fig. 4 with data by Blasius and by Davies for hydraulically smooth pipe flow. 3.2. Measurement of particle concentration The particle concentration is the number of particles in unit volume of air. As the particle size is not uniform, the particles have to be separated into diameter classes and the concentration has to be evaluated for each class separately. In the present experimental system, the concentration measurement is subdivided into two independent steps: first, the total mass of all droplets per volume is evaluated and, second, the particles in a representative test volume are deposited and counted. If the temperature and the relative humidity are measured, the water content of humid air can be calculated. The same method works for a mixture of saturated air and water droplets if the mixture is heated until all droplets are evaporated. In the present experiment, a small test volume of the air-droplet mixture is sucked isokinetically from the center of the measuring pipe. This volume is heated and the temperature and the humidity of the no longer saturated warm air are recorded. The results are used to calculate the water content. The difference in water content between the heated humid air containing the water mass from the droplets and the saturated air at the temperature in the pipe equals the mass of the droplets. This first step gives the information about the total droplet mass. The particle size distribution is evaluated by counting particles deposited from a representative test volume. The measuring section shown in Fig. 5 is inserted into the deposition pipe at the location of the deposition measurements. The test volume of air containing water droplets is captured by closing the two slides. The enclosed droplets sink due to gravity to a silicone oil bath on the lower slide and are captured in the silicone oil because of the big difference in surface tension between water and silicone fluid. The oil surface is now covered with a thin glass plate to avoid evaporation of the droplets in the oil.
J WILD! and H. THOMANN
622
il
Upper shde
i"
i¸ !
~ Lower slide Silicone oil bath Gasket
Fig. 5. Section used for concentration measurements.
Electric gear motor /
i
~
Deposition cylinder
~\"\ _~
Pipe wall
(4)-
/;;_V///
..,.oo. o. o o , ~ - ~ Surface roughness and step height
vii",
._..._ (1) Pipe l o l l ,
"**~ "" r~Jc~,,, .... 3 S~eap s 2*-3 ( ) Br ss
,.
~,~.=,oooo,...,oooo I~.:~
<<0.5
l
*:<0.01~
<<000Si
I ,o r
~..q o.~ I #
o,, I
I °°°* <15
to3,
I °°'~1 ! 0;2~
i 0.015
~/~/,",/
i
0~;7 003I
Fig. 6. Section used for deposition measurements.
Particle deposition from turbulent flow
623
This arrangement is photographed under the microscope. The measurement of the droplet diameter and the size classification are realized with an electronic analyser (Quantimet 720). With the results from the two steps, i.e. the total mass of all droplets and the size distribution, the particle concentration c,, for each diameter class is determined. 3.3. Measurement of the deposition rate The same technique is used to measure the deposition of droplets on the wall. The droplets are again captured in a silicone oil bath as shown in Fig. 6. The oil bath with a diameter of 6 mm is located on the front surface of a cylindrical part inserted into a hole in the pipe wall. The surface roughness in the gradual transition from the pipe wall to the cylinder and from there to the silicone oil surface is given in Fig. 6. It was evaluated using the Taylor-Hobson Talysurf 10 roughness measuring instrument. The walls are very smooth with their dimensionless surface roughness ks+ < 0.02. The height of the wall steps, although lying in the lower part of the laminar sublayer, may have some influence on the deposition rate. The smoothness of the silicone oil surface can only be checked qualitatively by observing the surface under the microscope. The deposition cylinder with the oil bath is turned with 1/2 revolution" per second to prevent the oil surface from bulging out because of gravity. The measuring time changes from 10 sec to 2 rain depending on the expected deposition rate. The data reduction with the electronic picture analyser required a great number of captured particles which should not contact or overlap each other. During the deposition time, the water content is continuously recorded with the sucking technique mentioned above. 3.4. Deposition results The deposition velocity k = AN(d)/Atc,,(d) is a function of the particle diameter for constant flow parameters. Deposition measurements are realised in stationary flow for Reynolds numbers Re = ~D/v = 10,000, 15,000 and 20,000. The results are given in Fig. 7. The experimental data for Re = 10,000 are determined in 3 independent test-series with a total of 2500 deposited particles. For Re = 15,000, there are 2 test series with 2000 particles and for Re = 20,000, the data contain one series. The measuring error of the number of deposited particles in the mean diameter classes (6/~m ~< d ~< 20/~m) is in the order of 40 and increases for the very small particles because of possible particle evaporation and for the large particles because of the small number of droplets observed. The dimensionless deposition rate k+ = k/u~ is shown as a function of the particle
I -k 16~ [m"4]
k-
4N - A .t---'~m
o ° •
°
S
o
~
o~'1
_ .20000 _^ 150UU ~o~~ r ' ~
-z
~e
_.I:7.. •
"
_ ,00oo
o
d [e,~.7 70 5
0
I
1
I
I
I
I
5
10
15
20
25
30
Fig. 7. Depositionrates, experimentaldata for Re = 10,000, 15,000and 20,000and pipe diameterD = 40 mm.
624
J. WILDIand H. THOMANN 161
1
7:*= ld
@p /dur )2 ©
9t ~ v ./
0
AN A" t Cm'Uz
-k÷ k+
©
o
0
o of /
/ .°/
°
/--
C N Dorms,
1965
R,:tO~
o o o ~O~o~1
162 eu
°
o
•
/
/
• o
/
o© o
u k,,.-t4.10
o o.//~
/
o °/ o "/o ~
I
8
3.2" Dawes, 1972, corn#ined with Eqs. (11) &(12) all Re < 2 . I 0 4
/
-4 2 / T; - - /
/
/
/ /
Dlffuston through turbulent boundary layer, Eq (17)
/
/
/i
//
~ ' / . , x "/ ~
Re = 5000 o - tO000
/
~--.v____--------~/// "
0
135 I
I
16 t
I
I
I
I
I
i
o r = 0.24 r'/s 0.35 "
15000 20000
°
I
I
1
I0
047 I
I
r,
I
" I
I
102
Particle relaxion Mine
Fig. 8. Deposition rotes,comparison of ¢x~rimemai data for Re = 10,000, 15,000and 20,000 with experimental data and theories. 3/6t. = 850, v = 15 x 10-6 m2/sec.
relaxation time T+ in Fig. 8. The same figure gives the comparison of the experimental results with the calculated deposition rates from the free-flight model (equation (9)) and the diffusion theory (equation (17)). The quadratic relation k+ = - 3.4 x 10-* r+ from Kneen and Strauss represents the experimental investigations. The measured deposition rates agree with published experimental results for sufficiently large particles. The deposition of the very small particles on the other hand changes only slightly with the relaxation time (or particle diameter if the pipe Reynolds number is kept constant). With increasing pipe Reynolds number, the transition to quadratic dependence of the deposition rate is shifted to larger particles (or higher relaxation times).
4. D E P O S I T I O N M E A S U R E M E N T S IN O S C I L L A T I N G P I P E F L O W 4.1. E x p e r i m e n t a l
arrangement
The modified experimental arrangement is shown in Fig. 9. An oscillating piston at one end of the pipe allows measurements also in oscillating flow. Other changes became necessary at the aerosol generator and at the concentration measuring system. The piston unit works in a frequency range from 5 to 25 Hz. The amplitude of the piston motion can be varied from 0.015 to 0.08 m with a piston diameter of 0.075 m, this corresponds to a particle amplitude in the measuring pipe (D = 40 ram) from 0,05 to 0.28 m A weak stationary flow is superimposed on the oscillating flow to replace the deposited
Particle deposition from turbulent flow
Inlet comber ~
~
D=~;Omm__~I Optical particle concentration mea'~uring
.
625
"
I
saturatedair Depositionpipe
E ~,
..h. 2r=
eter
ll
Fig. 9. Experimentalarrangement,oscillatingflow.
aerosol particles. The mean velocity of the stationary flow is 0.2 m/sec and the maximum velocity during oscillation varies from 6.0 m/sec ~< u ~< 17.1 m/sec depending on frequency and amplitude of the piston. A new aerosol generator is used. It is driven with compressed air and is small enough to be placed directly into the pipe. The particle diameter distribution resulting from the new generator is comparable with one from the ultrasonic unit. The isokinetical extraction of the small test volume for the water-content measurement does not work properly in oscillating flow. A phototransistor was therefore used to determine the intensity of the scattered light from a beam crossing radially the measuring pipe. This optical system is calibrated in stationary flow with the isokinetical measuring system. Particle size distribution and wall deposition were measured as in the stationary case. The unsteady velocity field was determined with a conventional hot wire equipment. During the velocity measurements, the air was not saturated and the weak mean flow was turned off. Figure 10 shows the range, in which the parameters of the piston driving mechanism can be changed. The maximum velocity in the pipe center during one oscillation period, g, is plotted against the oscillation frequency f. The strong increase of ~ with increasing frequency is caused by resonance in the pipe. The dimensionless number A = 2 a / x ~ is a Reynolds number based on the boundary layer thickness 6 = 2x/2x/2x/2x/2x/2x/~and gives a criterion of the boundary layer stability. If the boundary layer is small compared with the pipe radius, the
626
J. WILDI a n d H. THOMANN
25 rk =5a /~b~ /~a
2O
/
I
,/
i
/ ./I
/
/' ) "
t
/
6
lie' / )" - c~
i
~
/
'1 I I
/oo
"
•
O~~ '
I~.~.--
,/ /
e l
/
," OA
. / ' d d ,; / " ''~ I" i, / , ~ ) I /o o V ~ . . . . - ..~
I0
.~
/
/
li, ~ i" o//,~/
~000/"
/ -//
i...,f/
/ 15
.~
,°38
~
i
o/18 _
it
_^
Io
"6 -
2~
0-/1/
;0
'
~
,5
'
f~s-t]
~
20
'
t
25
F i g . 10. Maximum velocity (a) as function of frequency f and piston amplitude rk.
critical value of A for transition from laminar to turbulent flow is in the range (Merkli, 1973) Acrit = 350 to 700.
(18)
The points A' ./. E' in Fig. 10 determine the parameter combinations for the further experiments. In the sequence C'-A'-B', the frequency is kept constant and the amplitude of the piston is increased. Combination C' is the laminar flow regime, A' is the transition region and B' is a fully turbulent oscillation. In the sequence E'-A'-D', the A-value remains nearly constant with increasing frequency.
I0-
5.
/
, 025 7
0
-5
-I0
Fig. 1 la. Velocities in the pipe center tr = 0 mm) and at a distance y = 0.25 m m f r o m t h e wall f o r combination .4' as a function of the crank angle ~b.
Particle deposition from turbulent flow
627
1.0I I
t I I I I I
I 2
I I I I
O5
T
f
IJ
aa
4 5 6
135 193 22S
e
I/
¢
3 7
I I I
,n" i
12 45
2?0 ~ls
0
£J 0
-£J
.I
d
o
-I
u,4
0
f
Fig. 1lb. Velocities as a function of the wall distance y for fixed crank angles #, combination A'.
The results o f the hot wire measurements for the five parameter combinations A' to E' are summarized in Figs. I 1-15 and in Table 1. 4.2. Deposition results The five flow parameters for the deposition measurements are changed in the same way as for the hot wire measurements, but all points are moved to slightly higher A-values. The five 20-
[ "/+f
10y ,, O.25mm 5 ~// 0 , 5
t
" ~ r = O
- 10 -15
-20 o
,;o
Fig. 12a. Velocities in the pipe center (r = 0 ram) and at a distance y = 0.25 ram from the wall for combination B' as a function of the crank angle ~.
Table 1. Numerical data for the hot wire investigations
Combination A' B' C'
D' E'
Turbulent range at r = O r a m / r = 19.15ram
f (sec- 1)
Stroke of piston (mm)
a (m/sec)
A (-)
Re^ (-)
b (ram)
~(o)
~(o)
12.50 12.50 12.50 19.00 7.50
28 48 18 18 38
9.5 17.1 6.0 12.0 7.4
540 972 342 550 530
23,750 42,750 15,000 30,000 18,500
0.64 0.64 0.64 0.52 0.82
65-140 45-165 65-120 40-130 45-130
0-120 10-180 30-90 0--135 0-120
A = 2a/'x/vog'--~, R e ^ = D•/v, 6 = x / v / n p .
628
], WILDI and H. THOMANN 7 ....... !
, .
-
101.
.
.
.
I I I I Profile
l 1
#5 45
I
I
I
f I
-.¢ . . . . . .
I
I I I I I
I I I
I
#3'5
4 S 6 7 8
0.5
i
I
0
82 #9": 225 265 315
O -6
t -1
0
Fig. 12b. Velocities as a function o f the wall distance y for fixed crank angles ¢, combination B'. #OU
•
5;
,.O,Tr:O 0
-5
- #0
o
9'0
,~o
e~o
3Do ,p f*7
Fig. 13a. Velocities in the pipe center (r -- O m m ) a n d at a distance y = 0.25 m m from the wall for combination C' as a function o f the crank angle @. - ~ - - -
F t
1.0
I I I I 1
I
Profile
r
i i
L.
.
.
.
o.
I I I I
I
l 2 3 4 5 6 7 8
1 I I
i
%
.
.
.
05
.
.
.
.
.
.
~o t I I I I
F
0
I
~3
I
135 188 225 266 315
i 0 -t] J
i I i
1
I
TFig. 13b. Velocities as a function of the wall distance ,v for fixed crank angles ~. combination C".
Particle deposition from turbulent flow
629
I0 u
1%7 5
y = 0.25 rn~o
-5
-10 ¸
!
o
mo'
Fig. 14a. Velocities in the pipe center (r = 0 mm) and at a distance y = 0.25 m m from the wall for combination D' as a function of the crank angle $.
-
-
1.01
I I I I
Profile ~ [ o ]
¢ I I
I i I
IJ
li i:
0.5 I
13
*;5
3
97
5 6 7
135 193 225 27a 315
8
i i
o
0 -0
I I
i
!
pi
I
2
u(~- t)
~
%'-~ -I
/
/
_
o
A
Fig. 14b. Velocities as a function of the wall distance y for fixed crank angles $, combination D'.
points A ./. E are inserted in Fig. 10 and have the numerical data given in Table 2. The deposition rates are shown in Fig. 16. The presentation of the results using the dimensions (m/see) for the deposition velocity and (/~m) for the particle diameter was chosen as the friction velocity in a turbulent oscillating flow is not known well enough. The deposition rate depends strongly on the turbulence intensity. For very small particles, it hardly changes with particle diameter as in the stationary case. The number A, characteristic for the appearance of turbulence in oscillating flows, is obviously not the only parameter determining the deposition rate, which increases with increasing oscillation frequency if A is kept constant. Some additional experiments confirm that the deposition rate given in Figs. 7 and 16 are not influenced by forces on the particles due to an electric field and that the evaporation of
630
J. WILDt and H. THOMANN 10]
°i !=~}! 5
0
-5
1
- I 0 _1
Fig. 15a. Velocities in the pipe center (r 0ram) and at a distance y 0.25 mm from the wall for combination E' as a function of the crank angle 0. =
I
-
=
;.0!
II i
.
!l
.
----0.5
! 2 3
,
~ 5
-
p
tO ,;5
109
0
O
~35
,
7
t92 225 287
i
.
3,5 ]
6
i i
I t 1
0
i
®
_ ~ _ _ _
~o..
_
~
-I
0~._ ~
0
u,.~
Fig. 15b. Velocities as a function o f the wall distance y for fixed crank angles ~, combination E'.
Table 2. Numerical data for the deposition investigations
Combination A B C D E
Turbulent range at r = 0 m m / r = 19.15mm
f (sec- ~)
Stroke of piston (ram)
fi (mlsec)
Ustat (m/see)
A (- )
Re^ (- )
6 tmm)
~ ()
~( )
15.0 15.0 15.0 21.0 9.0
28 48 18 18 48
12.8 22.7 8.0 15.2 10.6
0.2 0.2 0.2 0.2 0.2
660 1170 410 660 700
32,000 56,750 20,000 38,000 26.500
0.58 0.58 0.58 0.49 0.75
45-150 40-180 65- 130 45-130 45-145
0-t30 0-180 15-110 0-120 0 145
Particle deposition from turbulent flow
Combinations
oA, OB,
631
oC, & O , o E l J
-k
[,,,/,]
161
C,["A]
2 . e e
22.70 0 0 ~ O~o ~ 15.21', 0 0 0
e O "
162
t2e. A.
~. ~ * ÷
121 0
~63
o o
o o ° o 0
0
0 o
0
0
1050o 8.00
•
o
o
o
o
o
0
0
d[.m] 10 5
0
30
I
I
I
I
I
)
5
I0
15
20
25
30
C1
[z..'J
25
•1250
/
/
20
A" loOO
/
/
/
/__/
15 /
• A
750
zx/3 500
/
10 /
~
oC ~
5
250
/
r (,-'J 0
5
I
I
I
I
10
15
20
25
Fig, 16. Deposition rates, experimental data for four frequency-amplitude combinations.
small particles in a saturated mixture of air and larger particles becomes important only for the smallest particles used in this investigation. (For details see Wildi (1982).)
5. CONCLUSIONS Deposition experiments with small spherical particles on the wall of a pipe were carried out for steady and for oscillating flows. The appearance of turbulence increases the deposition rate considerably for both cases. In oscillating flow, turbulence was observed for A = 2 ~ / x / v w >>,350. In steady flow, the deposition of"sufficientlylarge" particles agrees with the relation k + = 3.4 x 10- ~ z2+ derived from Kneen and Strauss (1969). The expression 'sufficiently large" depends on the Reynolds number. The critical particle size increases with increasing Reynolds number. The deposition rate of small particles is higher than expected and the particle diameter loses its dominant influence on the deposition rate. The influence of surface roughness on deposition rates may be important for small particles (d < 10/~m). Theoretical predictions of particle deposition to rough surfaces by Browne (1974) and Wood (1981) agree in their tendencies with the deposition rates of this investigation. They predict, however, too small an effect. The deposition rates in oscillating flow were measured with the same arrangement. They show a similar dependence on particle -
632
J. WluDI and H. THOMANN
size. F o r the range of p a r a m e t e r s investigated, the peak velocity in the pipe ceater in oscillating flow (Fig. 16) had to be a b o u t twice the m e a n value for steady flow (Fig. 7) for equa~ d e p o s i t i o n rates, as long as A > 3 5 0
REFERENCES Bed, S. K. (1968) Bettis Atomic Power Lab. Rep. No. WAPD-TM-765, Westinghouse ElectricCorp., Pittsburg, Pa. Browne, L. W. B. (1974) Atraos. Environ. 8, 801. Davies, C. N. (1966) Aerosol Science. Academic Press, London. Davies, J. T. (1972)Turbulence Phenomena. Academic Press, New York. Durst, F. and Lee, S. L. (1979) Techn, Rep. SFB 80/TE/142 of Sonderforschungsbereich 80, Universitat Karlsruhe. Friedlander, S. K. and Johnstone, H. F. (1957) Ind. Engng. Chem. 49, 1151. Kneen, T. and Strauss, W. (1969) Atmos. Environ. 3, 55. Lane, D. D. and Stukel, J. J. (1978) J. Aerosol Sci. 9, 191. Laufer, J. (1954) NACA 1174. Liu, B. Y. H. and Agarwal, J. K. (1974) d. Aerosol Sci. 5, 145. Liu, B. Y. H. and Ilori, T. A. (1973) ASME Syrup. on Flow Studies in Air and Water Pollution. Atlanta, Georgia. Merkli, P. (1973) Diss ETH 5151. Patel, V. C. (1965) J. Fluid Mech. 23, 185. Rouihainen, P. O. and Stachiewicz, J. W. (1970) J. Heat Transfer, Series C 92, 169. Schlichting, H. (1951) Grenzschichttheorie. Verlag G. Braun, Karlsruhe. Wells, A. C. and Chamberlain, A. C. (1967) Brit. J. Appl. Phys. 18, 1793. Wildi, J. (1982) Diss ETH 7119. Wood, N. B. (1981) J. Aerosol Sci. 12, 275.
(
0021 850283 $ 3 0 0 + 0 . 0 0 1983 Pergamon Pres~, Ltd
MEASUREMENT OF THE DEPOSITION OF SMALL PARTICLES IN STATIONARY AND OSCILLATING TURBULENT PIPE FLOW J. WILDI a n d H . THOMANN Institute of Aerodynamics, Swiss Federal Institute of Technology, CH-8092 Zfirich, Switzerland ( R e c e i v e d 20 J a n u a r y
1983)
Abstract--The deposition rate of small spherical droplets on the wall of a pipe is measured for fully developed turbulent flow at Reynolds numbers between 10,000 and 20,000 and for oscillating flow. For steady flow and sufficiently large particles, the results agree with k÷ = - 3.4 x 10 -4 r2+ derived from Kneen and Strauss ( i 969). The deposition rate of small particles is considerably larger than predicted by the above equation. For the experiments with oscillating flow, the same equipment is used. Turbulence is observed for A = 2 ~,/x/"v¢o >1 350. The dependence of the deposition rate on particle diameter is as in steady flow. For the present experiments with A /> 350, deposition rates are equal if the peak velocity in the pipe center in oscillating flow equals about twice the mean velocity in steady flow.
NOMENCLATURE A
(m 2)
A = 2~',c vw a . = ( D v) 1 3 c
( ) (_) (Part:m 3)
c+ = c/c,.
(-)
c,. D D DT d F~ f j
(Part,,m 3) (m) (mZ/sec) (me:sec) (pm) (N) (sec- t) (Part/m: sec)
j.
= j'u~cm
h k
(pm) (m.sect ~ )
k~
(pro)
k~+ = k ~ u , / v
(-)
AN N
(Part) (Partl
Re = ~D/v R e ^ = ~D.'v
(-) ( )
r = D2 - y r~ s
(m) (m) (~(m)
5÷ = . ' ¢ ' U r v
( )
t
(sec)
t. = tully
( )
u u.
(m sec) (m sec) = u./u~
u~ = ,, Zo/p
v r.
= t':U~
f f_ = f,u~ y )'. = )'u~v 3 ,. y
Particle concentration in pipe center Pipe diameter Molecular diffusion coefficient Turbulent diffusion coefficient Particle diameter Stokes drag force Frequency o f oscillation Particle flux
( }
k+ = k/u~
u..
Deposition area Number indicating the appearance of turbulence Dimensionless number in equation (16) Particle concentration
Step height between surface elements Deposition rate Equivalent roughness height Number of particles in one diameter class Number of particles Pipe Reynolds number Reynolds number of oscillation Radial distance from center Stroke of piston, see equation (9) Stokes stopping distance, see equation (5) Deposition time Velocity of fluid in axial direction Axial velocity in pipe center
(-)
lm secj (m ,sec) (m secl
Friction velocity Maximum velocity Velocity of fluid in radial direction
( }
(m sec) (-) (m) ( ) (m) (N sec, m 2) (m: sec)
Velocity of particle in radial direction Distance from wall Boundary layer thickness Dynamic viscosity Kinematic viscosity 615
616 ~,/¢ ?z rf~ =~ ck ~o= 2~f
L WILDIand H, THOMANN !kg/m3) (kg/m") IN/m2) I-! (:t Isec- ~i
Density of air Density of particle Wall friction Particle relaxation, equation (5) Crank angle, see Fig. 9 Angular velocityof oscillation
1. I N T R O D U C T I O N The theoretical treatment o f the particle transport is generally based on the diffusion model, in which the particle flux is expressed in terms o f particle diffusivity and concentration gradient. The governing equation is j =
- D" g r a d c.
(1)
The flux j is an abbreviation for the expression d N / A dr, i.e. N particles are transferred through an area A lying perpendicular to the concentration gradient grad c. In turbulent flows both molecular and eddy diffusion are operative, and D has to be replaced by D + Dr . To describe the particle deposition on a fixed wall the following equation is convenient jw = k ( c , , - c~).
{2)
The reference concentration outside o f the boundary layer or, in the case o f pipe flow, in the center is c,, and the concentration at the wall is cw. Using
v. = yu,/v, j+ = j/u~c,,,, C+ = C/Cm,
k+ = k/u~, with u, = V/zo/p, equations (1) and {2) read j+ =
D+ DT dc+ , v dy+
j~+ = k+(l - c ~ + ) .
[3) (3a)
In the present case there is c~+ = 0.
2. C L A S S I C A L D E P O S I T I O N T H E O R I E S 2.1. Free flight model To describe analytically the transportation mechanism, the flow near the wall is split up into three regions: (a)
0~
(b)
s+ < y+ ~< 5;
(c)
14)
y+ > 5.
Particles moving towards the wall, have, according to a model suggested by J. T. Davies (1972), to cross region (a) in a free flight owing to their inertia. They are started at a distance s ÷ away from the wall with a radial velocity ~ imposed by the turbulent motion. The surrounding flow is assumed to be motionless, so that the Stokes-drag Fw = 3 ¶/Mr3 is the only retarding force acting on the particle. The distance a particle flies to its stop is, according to
Particle deposition from turbulent flow
617
this theory,
±(P")
=
(5)
s+ -- 1 8 \ p L f with z+ = 1 8 \ p t ]
Region (b) contains the remaining part of the laminar sublayer. The turbulent diffusion mechanism determines the particle transport in this region.The coefficient of eddy diffusion used by J. T. Davies (1972), is --=
,
y+
~< 5.
(6)
In region (c), the equations of the Reynolds analogy determine the mass flux 1 -- c~+
j+ =
.
(7)
/Am+ -- 1~6+
Integration of equation (3) with Dr from equation (6) between the boundaries y+ = s+ and y+ = 6+ = 5 leads to the concentration at the outside of the laminar sublayer c,.=
_(8.933"+ "~[.1 \ 2 ]Ls~
1] 25
(8}
Eliminating ca+ between equations (7) and (8) leads to the deposition rate 1
k+ = -
(9)
u=+ - 19 + (353/s2+)
with Um+ = axial velocity in the pipe center. The following expressions are used to describe the turbulent pipe flow (Schlichting, 1951): u
/u =
2 = 0.3164Re~ l/a,
(10)
Re o = ~D/v, =
u~
/0.31_64 v Re~/8
X/ /
Um +
8 8
D
' 1/8
= u U¢ = =1.240.~- ~Re D .
(11)
C. N. Davies (1966) uses an empirical relation to describe the root mean square of the radial fluctuation velocities as a function of the wall distance .t
r+ =
Y+
y+ + 10
.
(12)
Equation (12) agrees well with experimental results given by Laufer (1954). The following assumption is now made: e+ = r+. Hence, the stopping distance may be written s+ = z+ - Y+ y+ +10"
(13)
Results are shown in Fig. 1. All particles hitting the wall have to satisfy the condition s+ /> y . - d + / 2 .
(14)
618
J WII.DI and H. THOMANN
"
r--
t 9p !'auz);
-U(--m:/
r+ :
Fr~edlander & ]oht~itone
k÷
N
k+
i
A't-cm'ur
~
8ca/
/
//
,,/
Lane & 5truket~ exper (flat plate) f fheo£
//X
¢ o
t62
Llu & Agarval
/
/~///~I / / / /
/
/
/
•Well5 & Chornbartam
0
Kneen & Strauss ._
// !
3 f Dawes, 1972, Eq {9) combined with Eqs (ll)&(12)
/ / i
/
/
C N Dawes, 1966 Re = lO ~
/
////// //,//
"
~
*
?0!
/
I
I
I
[
/ ~ Oiffu$ion through turbulent boundary layer, Eq (17)
/
~ Re =
o
1
J
r
1
1
tO
Particle
relaxion
I
5000
tO000
I
~+
L
I
102
time
Fig. 1. Deposition rates on smooth walls, experimental data compared with theory. Data from Beal (1968), C. N. Davies (1966), J. T. Davies (1972), Friedlander and Johnstone (1957), Kneen and Strauss (1969), Lane and Stukel (1978), Liu and Agarwal (1974), Liu and Ilori (1973), and Wells and Chamberlain (1967).
This model holds in a very limited range of z +. For s + ~ d . / 2 , equations t 13) and (14) require r+ /> 10 for particles to reach the wall. For r+ /> 15, on the other hand, s+ >/5 and the particles cross the whole sublayer in free flight. The deposition rate is in this case determined by the Reynolds analogy. For still larger particles the assumption no longer holds that particles move exactly with the velocity of the surrounding turbulent fluid. 2.2. Diffusion through the laminar sublayer To determine the deposition of small particles lying outside of the range of the free-flight model, i.e. z + < 10, one has to start from the complete diffusion equation (3), introducing the expressions for the diffusion constants
2kT 3~
0..=--
with the Boitzmann constant k = 1.38 × l0 -23 J / K and
(151
Equation (3) is valid in the whole laminar sublayer. Outside this layer the Reynolds analogy is used again. The integration of the diffusion equation from the first wall contact of a particle aty+ = d . /2 to the outside of the laminar sublayer at l, . = 5withe_ = t ) at v. = d . 2and
Particle deposition from turbulent flow
619
c+ = ca+ at y+ = 5 results in the concentration value ca. c~+ 8.9 f ~ (xa++a+)2(x2+--a+xa"+a2+) J÷ -- 3a2+ , - In (xa+ + a + ) 2 (x2+ --a+xa- +a+) /arctg
+ "v/3 L
----~--x/3a+
arctg
v/3 a+
= g (xa+, xd+, a+), (16) with
aS+ = O / v -
2kT 3nl~vd'
xa+ = 5/8.9,
1 (d/2)u, x~ +
8.9
v
Combining equation (16) with equation (7) results in the deposition rate k+ -
1 Urn+ - - U a +
+g
.
(17)
Combining the expressions for the turbulent pipe flow (u,,+ from equation (11) and ua+ = 6+ = 5) with equation (17)) leads to the numerical results shown in Fig. 1. 2.3. Literature on the particle deposition Figure 1 supplies a summary of existing theoretical and experimental deposition rates, including the present experiments. The papers are discussed in more detail by Wildi (1982). The deposition models based on experimental data for the turbulent fluctuation velocities, i.e. the theories of C. N. Davies and J. T. Davies, give numerical deposition rates which are more than one order of magnitude lower than the experimental results. The experimental results of different authors are in the range 1 < ~ ÷ < 10 in good agreement with k + = - 3.4 x 10- 4 r2 derived from Kneen and Strauss (1969) in spite of very different experimental techniques and different interpretation methods. Browne (1974) and Wood (1981) present analytical methods for the calculation of turbulent deposition to rough surfaces. Their theories follow the general approach of the free flight model and are valid for a roughness height smaller than 5v/u,. To take the roughness into account, the particle free flight distance is extended by an additional distance of the order of magnitude of the roughness height and the position of the origin of the velocity profile is shifted away from the smooth wall. Applying this method, it has been possible to use the Davies assumption for the radial velocity fluctuations. The results suggest that deposition rates of very small particles are extremely sensitive to small changes in surface roughness, even for hydraulically smooth surfaces. Some new attempts to reduce the discrepancy between the theoretical and experimental work are made by Rouihainen and Stachiewicz (1970) and Durst and Lee (1979). These authors consider the behaviour of a single particle in a fluctuating flow. However, they need a very specified knowledge of the turbulent velocities near the wall which is not yet available.
3. D E P O S I T I O N M E A S U R E M E N T S IN STATIONARY P I P E F L O W
3.1. Experimental arrangement The experimental setup is shown in Fig. 2. Saturated air is sucked from the inlet chamber (Position 1) through the deposition pipe (Position 2, Plexiglass, 40mm inner diameter) and
J WILDI and H. THOMANN
620
!
-
,o,,,como,,
r
JL
I
I
!
I
I
~
Honeycomb
Thermometer I
I
j.
lo
~9 Aerosol
generator
...ur,~ section
li
!
J i
~Thermometer
m~,,..~ un,
NIl
Return duct
O.,u,or
Fig. 2. Experimental arrangement, stationary flow.
flows back to the inlet chamber via the return pipe. The mass flow is computed from the pressure difference in the Venturi pipe (Position 6). Three different types of inserts in the pipe are available for measuring the flow parameters (velocity profiles, skin friction), the concentration and the deposition rate. The air in the closed system is saturated prior to the deposition measurements by evaporating water droplets produced in a second aerosol generator (Position 9). During the
0.5
t
i
!
Y~R 0.5 i
0 0
0.5 ]
o
: Exoenmental data for oresent measurement
Re = ~8000,
Re=
~-D
Veloctty profile In fully developl3ed t u r b u l e n t ptpe f l o w , R e = 2 3 0 0 0 , data f r o m S c h l i c h t i n g , 195!
Fig. 3. Velocity profile measured at
Re = 18,600 and comparison with data of Schlichting t195 t ).
Particle deposition from turbulent flow 12 11
•
To
.10 9
g/2 u2
I0
\
621
...
_
Bias,us" 9 ~
= ~
. Re ~
oo.,.s I T /
9 • Davies, experimental
8 ~.'~ ~*-3"/.. • ~.'~.....~
7
present measurement PreSton tubes
w, th
6 5 L
0 2
I
L
10
20
I
;0
Re. 103
40
Fig. 4. Skin frictionmeasuredat 4 Re-numbersand comparison with data by J. T, Davies(1972),and by Blasius (in Schlichting(1951)).
deposition experiment, this aerosol generator is inactive to prevent adding undesired particles and changing the temperature. The droplets to be deposited are generated in an ultrasonic aerosol generator with an oscillation frequency of 1.7 MHz. It produces water droplets in a diameter range between 3 and 30/~m with a mean diameter of about 10/am. The measuring section was located 35 pipe diameters downstream of the inlet. At this location and for Reynolds number Re = ~D/v between 10,000 and 20,000, the velocity profile measurements with a Pitot tube confirm the fully developed turbulent pipe flow characteristics. Figure 3 shows the velocity profile for Re = 18,600. The skin friction is evaluated from Preston-tube data using the interpretation method of Patel (1965). The maximum difference in skin friction along the periphery is + 3 ~o of the mean value. The rotational symmetry of the flow is thus sufficient for the deposition tests. The measured wall friction is compared in Fig. 4 with data by Blasius and by Davies for hydraulically smooth pipe flow. 3.2. Measurement of particle concentration The particle concentration is the number of particles in unit volume of air. As the particle size is not uniform, the particles have to be separated into diameter classes and the concentration has to be evaluated for each class separately. In the present experimental system, the concentration measurement is subdivided into two independent steps: first, the total mass of all droplets per volume is evaluated and, second, the particles in a representative test volume are deposited and counted. If the temperature and the relative humidity are measured, the water content of humid air can be calculated. The same method works for a mixture of saturated air and water droplets if the mixture is heated until all droplets are evaporated. In the present experiment, a small test volume of the air-droplet mixture is sucked isokinetically from the center of the measuring pipe. This volume is heated and the temperature and the humidity of the no longer saturated warm air are recorded. The results are used to calculate the water content. The difference in water content between the heated humid air containing the water mass from the droplets and the saturated air at the temperature in the pipe equals the mass of the droplets. This first step gives the information about the total droplet mass. The particle size distribution is evaluated by counting particles deposited from a representative test volume. The measuring section shown in Fig. 5 is inserted into the deposition pipe at the location of the deposition measurements. The test volume of air containing water droplets is captured by closing the two slides. The enclosed droplets sink due to gravity to a silicone oil bath on the lower slide and are captured in the silicone oil because of the big difference in surface tension between water and silicone fluid. The oil surface is now covered with a thin glass plate to avoid evaporation of the droplets in the oil.
J WILD! and H. THOMANN
622
il
Upper shde
i"
i¸ !
~ Lower slide Silicone oil bath Gasket
Fig. 5. Section used for concentration measurements.
Electric gear motor /
i
~
Deposition cylinder
~\"\ _~
Pipe wall
(4)-
/;;_V///
..,.oo. o. o o , ~ - ~ Surface roughness and step height
vii",
._..._ (1) Pipe l o l l ,
"**~ "" r~Jc~,,, .... 3 S~eap s 2*-3 ( ) Br ss
,.
~,~.=,oooo,...,oooo I~.:~
<<0.5
l
*:<0.01~
<<000Si
I ,o r
~..q o.~ I #
o,, I
I °°°* <15
to3,
I °°'~1 ! 0;2~
i 0.015
~/~/,",/
i
0~;7 003I
Fig. 6. Section used for deposition measurements.
Particle deposition from turbulent flow
623
This arrangement is photographed under the microscope. The measurement of the droplet diameter and the size classification are realized with an electronic analyser (Quantimet 720). With the results from the two steps, i.e. the total mass of all droplets and the size distribution, the particle concentration c,, for each diameter class is determined. 3.3. Measurement of the deposition rate The same technique is used to measure the deposition of droplets on the wall. The droplets are again captured in a silicone oil bath as shown in Fig. 6. The oil bath with a diameter of 6 mm is located on the front surface of a cylindrical part inserted into a hole in the pipe wall. The surface roughness in the gradual transition from the pipe wall to the cylinder and from there to the silicone oil surface is given in Fig. 6. It was evaluated using the Taylor-Hobson Talysurf 10 roughness measuring instrument. The walls are very smooth with their dimensionless surface roughness ks+ < 0.02. The height of the wall steps, although lying in the lower part of the laminar sublayer, may have some influence on the deposition rate. The smoothness of the silicone oil surface can only be checked qualitatively by observing the surface under the microscope. The deposition cylinder with the oil bath is turned with 1/2 revolution" per second to prevent the oil surface from bulging out because of gravity. The measuring time changes from 10 sec to 2 rain depending on the expected deposition rate. The data reduction with the electronic picture analyser required a great number of captured particles which should not contact or overlap each other. During the deposition time, the water content is continuously recorded with the sucking technique mentioned above. 3.4. Deposition results The deposition velocity k = AN(d)/Atc,,(d) is a function of the particle diameter for constant flow parameters. Deposition measurements are realised in stationary flow for Reynolds numbers Re = ~D/v = 10,000, 15,000 and 20,000. The results are given in Fig. 7. The experimental data for Re = 10,000 are determined in 3 independent test-series with a total of 2500 deposited particles. For Re = 15,000, there are 2 test series with 2000 particles and for Re = 20,000, the data contain one series. The measuring error of the number of deposited particles in the mean diameter classes (6/~m ~< d ~< 20/~m) is in the order of 40 and increases for the very small particles because of possible particle evaporation and for the large particles because of the small number of droplets observed. The dimensionless deposition rate k+ = k/u~ is shown as a function of the particle
I -k 16~ [m"4]
k-
4N - A .t---'~m
o ° •
°
S
o
~
o~'1
_ .20000 _^ 150UU ~o~~ r ' ~
-z
~e
_.I:7.. •
"
_ ,00oo
o
d [e,~.7 70 5
0
I
1
I
I
I
I
5
10
15
20
25
30
Fig. 7. Depositionrates, experimentaldata for Re = 10,000, 15,000and 20,000and pipe diameterD = 40 mm.
624
J. WILDIand H. THOMANN 161
1
7:*= ld
@p /dur )2 ©
9t ~ v ./
0
AN A" t Cm'Uz
-k÷ k+
©
o
0
o of /
/ .°/
°
/--
C N Dorms,
1965
R,:tO~
o o o ~O~o~1
162 eu
°
o
•
/
/
• o
/
o© o
u k,,.-t4.10
o o.//~
/
o °/ o "/o ~
I
8
3.2" Dawes, 1972, corn#ined with Eqs. (11) &(12) all Re < 2 . I 0 4
/
-4 2 / T; - - /
/
/
/ /
Dlffuston through turbulent boundary layer, Eq (17)
/
/
/i
//
~ ' / . , x "/ ~
Re = 5000 o - tO000
/
~--.v____--------~/// "
0
135 I
I
16 t
I
I
I
I
I
i
o r = 0.24 r'/s 0.35 "
15000 20000
°
I
I
1
I0
047 I
I
r,
I
" I
I
102
Particle relaxion Mine
Fig. 8. Deposition rotes,comparison of ¢x~rimemai data for Re = 10,000, 15,000and 20,000 with experimental data and theories. 3/6t. = 850, v = 15 x 10-6 m2/sec.
relaxation time T+ in Fig. 8. The same figure gives the comparison of the experimental results with the calculated deposition rates from the free-flight model (equation (9)) and the diffusion theory (equation (17)). The quadratic relation k+ = - 3.4 x 10-* r+ from Kneen and Strauss represents the experimental investigations. The measured deposition rates agree with published experimental results for sufficiently large particles. The deposition of the very small particles on the other hand changes only slightly with the relaxation time (or particle diameter if the pipe Reynolds number is kept constant). With increasing pipe Reynolds number, the transition to quadratic dependence of the deposition rate is shifted to larger particles (or higher relaxation times).
4. D E P O S I T I O N M E A S U R E M E N T S IN O S C I L L A T I N G P I P E F L O W 4.1. E x p e r i m e n t a l
arrangement
The modified experimental arrangement is shown in Fig. 9. An oscillating piston at one end of the pipe allows measurements also in oscillating flow. Other changes became necessary at the aerosol generator and at the concentration measuring system. The piston unit works in a frequency range from 5 to 25 Hz. The amplitude of the piston motion can be varied from 0.015 to 0.08 m with a piston diameter of 0.075 m, this corresponds to a particle amplitude in the measuring pipe (D = 40 ram) from 0,05 to 0.28 m A weak stationary flow is superimposed on the oscillating flow to replace the deposited
Particle deposition from turbulent flow
Inlet comber ~
~
D=~;Omm__~I Optical particle concentration mea'~uring
.
625
"
I
saturatedair Depositionpipe
E ~,
..h. 2r=
eter
ll
Fig. 9. Experimentalarrangement,oscillatingflow.
aerosol particles. The mean velocity of the stationary flow is 0.2 m/sec and the maximum velocity during oscillation varies from 6.0 m/sec ~< u ~< 17.1 m/sec depending on frequency and amplitude of the piston. A new aerosol generator is used. It is driven with compressed air and is small enough to be placed directly into the pipe. The particle diameter distribution resulting from the new generator is comparable with one from the ultrasonic unit. The isokinetical extraction of the small test volume for the water-content measurement does not work properly in oscillating flow. A phototransistor was therefore used to determine the intensity of the scattered light from a beam crossing radially the measuring pipe. This optical system is calibrated in stationary flow with the isokinetical measuring system. Particle size distribution and wall deposition were measured as in the stationary case. The unsteady velocity field was determined with a conventional hot wire equipment. During the velocity measurements, the air was not saturated and the weak mean flow was turned off. Figure 10 shows the range, in which the parameters of the piston driving mechanism can be changed. The maximum velocity in the pipe center during one oscillation period, g, is plotted against the oscillation frequency f. The strong increase of ~ with increasing frequency is caused by resonance in the pipe. The dimensionless number A = 2 a / x ~ is a Reynolds number based on the boundary layer thickness 6 = 2x/2x/2x/2x/2x/2x/~and gives a criterion of the boundary layer stability. If the boundary layer is small compared with the pipe radius, the
626
J. WILDI a n d H. THOMANN
25 rk =5a /~b~ /~a
2O
/
I
,/
i
/ ./I
/
/' ) "
t
/
6
lie' / )" - c~
i
~
/
'1 I I
/oo
"
•
O~~ '
I~.~.--
,/ /
e l
/
," OA
. / ' d d ,; / " ''~ I" i, / , ~ ) I /o o V ~ . . . . - ..~
I0
.~
/
/
li, ~ i" o//,~/
~000/"
/ -//
i...,f/
/ 15
.~
,°38
~
i
o/18 _
it
_^
Io
"6 -
2~
0-/1/
;0
'
~
,5
'
f~s-t]
~
20
'
t
25
F i g . 10. Maximum velocity (a) as function of frequency f and piston amplitude rk.
critical value of A for transition from laminar to turbulent flow is in the range (Merkli, 1973) Acrit = 350 to 700.
(18)
The points A' ./. E' in Fig. 10 determine the parameter combinations for the further experiments. In the sequence C'-A'-B', the frequency is kept constant and the amplitude of the piston is increased. Combination C' is the laminar flow regime, A' is the transition region and B' is a fully turbulent oscillation. In the sequence E'-A'-D', the A-value remains nearly constant with increasing frequency.
I0-
5.
/
, 025 7
0
-5
-I0
Fig. 1 la. Velocities in the pipe center tr = 0 mm) and at a distance y = 0.25 m m f r o m t h e wall f o r combination .4' as a function of the crank angle ~b.
Particle deposition from turbulent flow
627
1.0I I
t I I I I I
I 2
I I I I
O5
T
f
IJ
aa
4 5 6
135 193 22S
e
I/
¢
3 7
I I I
,n" i
12 45
2?0 ~ls
0
£J 0
-£J
.I
d
o
-I
u,4
0
f
Fig. 1lb. Velocities as a function of the wall distance y for fixed crank angles #, combination A'.
The results o f the hot wire measurements for the five parameter combinations A' to E' are summarized in Figs. I 1-15 and in Table 1. 4.2. Deposition results The five flow parameters for the deposition measurements are changed in the same way as for the hot wire measurements, but all points are moved to slightly higher A-values. The five 20-
[ "/+f
10y ,, O.25mm 5 ~// 0 , 5
t
" ~ r = O
- 10 -15
-20 o
,;o
Fig. 12a. Velocities in the pipe center (r = 0 ram) and at a distance y = 0.25 ram from the wall for combination B' as a function of the crank angle ~.
Table 1. Numerical data for the hot wire investigations
Combination A' B' C'
D' E'
Turbulent range at r = O r a m / r = 19.15ram
f (sec- 1)
Stroke of piston (mm)
a (m/sec)
A (-)
Re^ (-)
b (ram)
~(o)
~(o)
12.50 12.50 12.50 19.00 7.50
28 48 18 18 38
9.5 17.1 6.0 12.0 7.4
540 972 342 550 530
23,750 42,750 15,000 30,000 18,500
0.64 0.64 0.64 0.52 0.82
65-140 45-165 65-120 40-130 45-130
0-120 10-180 30-90 0--135 0-120
A = 2a/'x/vog'--~, R e ^ = D•/v, 6 = x / v / n p .
628
], WILDI and H. THOMANN 7 ....... !
, .
-
101.
.
.
.
I I I I Profile
l 1
#5 45
I
I
I
f I
-.¢ . . . . . .
I
I I I I I
I I I
I
#3'5
4 S 6 7 8
0.5
i
I
0
82 #9": 225 265 315
O -6
t -1
0
Fig. 12b. Velocities as a function o f the wall distance y for fixed crank angles ¢, combination B'. #OU
•
5;
,.O,Tr:O 0
-5
- #0
o
9'0
,~o
e~o
3Do ,p f*7
Fig. 13a. Velocities in the pipe center (r -- O m m ) a n d at a distance y = 0.25 m m from the wall for combination C' as a function o f the crank angle @. - ~ - - -
F t
1.0
I I I I 1
I
Profile
r
i i
L.
.
.
.
o.
I I I I
I
l 2 3 4 5 6 7 8
1 I I
i
%
.
.
.
05
.
.
.
.
.
.
~o t I I I I
F
0
I
~3
I
135 188 225 266 315
i 0 -t] J
i I i
1
I
TFig. 13b. Velocities as a function of the wall distance ,v for fixed crank angles ~. combination C".
Particle deposition from turbulent flow
629
I0 u
1%7 5
y = 0.25 rn~o
-5
-10 ¸
!
o
mo'
Fig. 14a. Velocities in the pipe center (r = 0 mm) and at a distance y = 0.25 m m from the wall for combination D' as a function of the crank angle $.
-
-
1.01
I I I I
Profile ~ [ o ]
¢ I I
I i I
IJ
li i:
0.5 I
13
*;5
3
97
5 6 7
135 193 225 27a 315
8
i i
o
0 -0
I I
i
!
pi
I
2
u(~- t)
~
%'-~ -I
/
/
_
o
A
Fig. 14b. Velocities as a function of the wall distance y for fixed crank angles $, combination D'.
points A ./. E are inserted in Fig. 10 and have the numerical data given in Table 2. The deposition rates are shown in Fig. 16. The presentation of the results using the dimensions (m/see) for the deposition velocity and (/~m) for the particle diameter was chosen as the friction velocity in a turbulent oscillating flow is not known well enough. The deposition rate depends strongly on the turbulence intensity. For very small particles, it hardly changes with particle diameter as in the stationary case. The number A, characteristic for the appearance of turbulence in oscillating flows, is obviously not the only parameter determining the deposition rate, which increases with increasing oscillation frequency if A is kept constant. Some additional experiments confirm that the deposition rate given in Figs. 7 and 16 are not influenced by forces on the particles due to an electric field and that the evaporation of
630
J. WILDt and H. THOMANN 10]
°i !=~}! 5
0
-5
1
- I 0 _1
Fig. 15a. Velocities in the pipe center (r 0ram) and at a distance y 0.25 mm from the wall for combination E' as a function of the crank angle 0. =
I
-
=
;.0!
II i
.
!l
.
----0.5
! 2 3
,
~ 5
-
p
tO ,;5
109
0
O
~35
,
7
t92 225 287
i
.
3,5 ]
6
i i
I t 1
0
i
®
_ ~ _ _ _
~o..
_
~
-I
0~._ ~
0
u,.~
Fig. 15b. Velocities as a function o f the wall distance y for fixed crank angles ~, combination E'.
Table 2. Numerical data for the deposition investigations
Combination A B C D E
Turbulent range at r = 0 m m / r = 19.15mm
f (sec- ~)
Stroke of piston (ram)
fi (mlsec)
Ustat (m/see)
A (- )
Re^ (- )
6 tmm)
~ ()
~( )
15.0 15.0 15.0 21.0 9.0
28 48 18 18 48
12.8 22.7 8.0 15.2 10.6
0.2 0.2 0.2 0.2 0.2
660 1170 410 660 700
32,000 56,750 20,000 38,000 26.500
0.58 0.58 0.58 0.49 0.75
45-150 40-180 65- 130 45-130 45-145
0-t30 0-180 15-110 0-120 0 145
Particle deposition from turbulent flow
Combinations
oA, OB,
631
oC, & O , o E l J
-k
[,,,/,]
161
C,["A]
2 . e e
22.70 0 0 ~ O~o ~ 15.21', 0 0 0
e O "
162
t2e. A.
~. ~ * ÷
121 0
~63
o o
o o ° o 0
0
0 o
0
0
1050o 8.00
•
o
o
o
o
o
0
0
d[.m] 10 5
0
30
I
I
I
I
I
)
5
I0
15
20
25
30
C1
[z..'J
25
•1250
/
/
20
A" loOO
/
/
/
/__/
15 /
• A
750
zx/3 500
/
10 /
~
oC ~
5
250
/
r (,-'J 0
5
I
I
I
I
10
15
20
25
Fig, 16. Deposition rates, experimental data for four frequency-amplitude combinations.
small particles in a saturated mixture of air and larger particles becomes important only for the smallest particles used in this investigation. (For details see Wildi (1982).)
5. CONCLUSIONS Deposition experiments with small spherical particles on the wall of a pipe were carried out for steady and for oscillating flows. The appearance of turbulence increases the deposition rate considerably for both cases. In oscillating flow, turbulence was observed for A = 2 ~ / x / v w >>,350. In steady flow, the deposition of"sufficientlylarge" particles agrees with the relation k + = 3.4 x 10- ~ z2+ derived from Kneen and Strauss (1969). The expression 'sufficiently large" depends on the Reynolds number. The critical particle size increases with increasing Reynolds number. The deposition rate of small particles is higher than expected and the particle diameter loses its dominant influence on the deposition rate. The influence of surface roughness on deposition rates may be important for small particles (d < 10/~m). Theoretical predictions of particle deposition to rough surfaces by Browne (1974) and Wood (1981) agree in their tendencies with the deposition rates of this investigation. They predict, however, too small an effect. The deposition rates in oscillating flow were measured with the same arrangement. They show a similar dependence on particle -
632
J. WluDI and H. THOMANN
size. F o r the range of p a r a m e t e r s investigated, the peak velocity in the pipe ceater in oscillating flow (Fig. 16) had to be a b o u t twice the m e a n value for steady flow (Fig. 7) for equa~ d e p o s i t i o n rates, as long as A > 3 5 0
REFERENCES Bed, S. K. (1968) Bettis Atomic Power Lab. Rep. No. WAPD-TM-765, Westinghouse ElectricCorp., Pittsburg, Pa. Browne, L. W. B. (1974) Atraos. Environ. 8, 801. Davies, C. N. (1966) Aerosol Science. Academic Press, London. Davies, J. T. (1972)Turbulence Phenomena. Academic Press, New York. Durst, F. and Lee, S. L. (1979) Techn, Rep. SFB 80/TE/142 of Sonderforschungsbereich 80, Universitat Karlsruhe. Friedlander, S. K. and Johnstone, H. F. (1957) Ind. Engng. Chem. 49, 1151. Kneen, T. and Strauss, W. (1969) Atmos. Environ. 3, 55. Lane, D. D. and Stukel, J. J. (1978) J. Aerosol Sci. 9, 191. Laufer, J. (1954) NACA 1174. Liu, B. Y. H. and Agarwal, J. K. (1974) d. Aerosol Sci. 5, 145. Liu, B. Y. H. and Ilori, T. A. (1973) ASME Syrup. on Flow Studies in Air and Water Pollution. Atlanta, Georgia. Merkli, P. (1973) Diss ETH 5151. Patel, V. C. (1965) J. Fluid Mech. 23, 185. Rouihainen, P. O. and Stachiewicz, J. W. (1970) J. Heat Transfer, Series C 92, 169. Schlichting, H. (1951) Grenzschichttheorie. Verlag G. Braun, Karlsruhe. Wells, A. C. and Chamberlain, A. C. (1967) Brit. J. Appl. Phys. 18, 1793. Wildi, J. (1982) Diss ETH 7119. Wood, N. B. (1981) J. Aerosol Sci. 12, 275.