DRIFT -
A NUMERICAL SIMULATION SOLUTION
FOR COOLING TOWER DRIFT ELIMINATOR PERFORMANCE
by
Joseph K. Chan and
Michael W. Golay
Energy Laboratory
and
Department of Nuclear Engineering
Massachusetts Institute of Technology
Cambridge, Massachusetts
02139
Topical Report for Task #3 of the
Waste Heat Management
Research Program
sponsored by
New England Electric System
Northeast Utilities Service Co.
under the
MIT Energy Laboratory Electric Power Program
Energy Laboratory Report No. MIT-EL 77-006
June
1977
DRIFT --
A NUMERICAL SIMULATION SOLUTION
FOR COOLING TOWER DRIFT ELIMINATOR PERFORMANCE
by
Joseph K. Chan and
Michael W. Golay
Energy Laboratory Report No. MIT-EL 77-006
June 1977
1
'ABSTRACT
A method for the analysis of the performance 'of
standard industrial evaporative cooling tower drift
eliminators using numerical simulation methods is reported.
The simulation methods make use of the computer code
SOLASUR as a subroutine of the computer code DRIFT to calculate the two dimensional laminar flow velocity field
and pressure loss in a drift eliminator geometry.
This
information is then used in the main program to obtain the'
eliminator collection efficiency by performing trajectory
calculations for droplets of a given size by.a fourth'
order Runge-Kutta numerical method.
2
ACKNOWLEDGEMENT
This work was funded through the Waste Heat Management
Program of the M.I.T. Energy Laboratory, supported Jointly
by the New England Electric System and Northeast Utilities.
3
TABLE OF CONTENTS
Page
ABSTRACT
1
ACKNOWLEDGEMENT
2
TABLE OF CONTENTS
3
LIST OF FIGURES
NOMENCLATURE
5
CHAPTER 1.
INTRODUCTION
6
CHAPTER 2.
THEORY
7
CHAPTER 3.
PROGRAM DESCRIPTION
10
CHAPTER 4.
INPUT DESCRIPTION
18
CHAPTER 5.
NUMERICAL STABILITY CONSIDERATIONS
26
REFERENCES
28
APPENDIX A.
LISTING OF THE DRIFT PROGRAM
29
APPENDIX B.
SAMPLE PROBLEM
74
B.1.
INPUT DATA OF SAMPLE PROBLEM
75
B.2.
OUTPUT OF SAMPLE PROBLEM
90
4
LIST OF FIGURES
Page
3.1
The Flow Chart of the DRIFT Code
11
3.2
The Flow Chart of the SOLASUR Subroutine
13
3.3
Convention
of Wall Definition
for the
Main Program
3.4
Convention
15
of Wall Definition
for the
16
SOLASUR Subroutine
B.1
Velocity
Distribution
of Air Flow for th e
Sample Problem at Cycle 20
B.2
Velocity
Sample
B.3
Distribution
of Air Flow for th e
Problem at Cycle 40
Velocity
Distribution
137
138
of Air Flow for th e
Sample Problem at Cycle 60
139
B.4
Droplet Trajectory
Plot for the Sample Problem
140
B.5
Droplet Trajectory
Plot for the Sample Problem
141
B.6
Droplet Trajectory
Plot for the Sample Problem
142
B.7
Droplet
Trajectory
Plot for the Sample P'roblem
143
NOMENCLATURE
Cd
=
drag coefficient
g
=
2 )
gravity acceleration (m/s
h
=
time step size (s)
md
=
droplet mass (kg)
p
=
pressure
R
=
droplet radius (m)
Re
=
Reynolds number
t
=
time
u
=
horizontal velocity component (m/s)
v
=
vertical velocity component (m/s)
Va
=
air velocity (m/s)
Vd
=
droplet velocity (m/s)
Vt
=
terminal
x
=
horizontal position coordinate
y
=
vertical position coordinate
p
=
3
air density (kg/m )
(N)
(s)
velocity
(m/s)
water density (kg/m3)
Pw
Ia
=
air viscosity (kg/s-m)
v
=
kinematic
viscosity
6
CHAPTER
1
INTRODUCTION
In order to evaluate cooling tower drift eliminators,
a computer program, DRIFT, is written to simulate eliminator
performance. (1
2)
The main program of the code calculates
the droplet trajectory such that the capture efficiency of
the eliminator can be determined.
The air velocity distribu-
tion within the eliminator is calculated by the subroutine
SOLASUR,(3 ) which is then input into the main program for
droplet trajectory calculation.
SOLASUR also calculates the
pressure drop across the eliminator when no-slip condition
is used at the rigid boundaries of the eliminator.
The
standard eliminator geometries that have been included in
this code for evaluation
are the single-layer
louvre elimina-
tor, the double-layer louvre eliminator, the sinus-shaped
eliminator, zig-zag eliminator, Hi-V eliminator, and the
asbestos-cement eliminator.
Other geometries can also be
evaluated if the user will provide the boundary information
in appropriate subroutines.
This program is written in FORTRAN IV computer language,
and is run on IBM 370/168 system.
The plotting is done by
CALCOMP machine.
This report describes the details of the structure of
the code, the input parameters
considerations.
are also given.
and some numerical
stability
A listing of the program and a sample problem
7
CHAPTER
2
THEORY
Some theoretical basis of the DRIFT code are described
The main program of the code solves the
in this chapter.
equation of motion of droplets by using the fourth order
Runge-Kutta
The equation
technique.
dV
dad
9
dt
2
-Pa
R2
CdRe
-
Vd)+
2T -(Va
to be solved is
+(2.1)
(21)
where
CdRe
064
63
'
-R = 1 + 0.197Re
+ 2.6 x 10-4Re
.3
8
(2.2)
and
Re
=
21V - VdIRpa
a
In two dimensional
coordinates,
dV d
fx
(2.3).
Eq. (2.1) can be written
9p a CdRe
2pwR 2
24
(Va,x
dt
dt
2
(Va
, - Vd,
) +g
as
(2.4)
and
dV
yE
dt
=~
_9va
2p2
CdRe
2
(Va,y - Vd,y) + gy
(2.5)
These two equations are coupled by the Reynold's number deterThe position of the droplet at any instant can be
mination.
determined from the velocities as
dx
dt
=
d,x ,
(2.6)
and
dy
dt
Vd,y
(2.7)
Knowing the initial conditions of the four parameters at the
beginning
of the time step, these four coupled nonlinear
dif-
ferential equations can then be solved by standard fourth
order Runge-Kutta technique.(4)
The initial conditions
of the droplets
at the entrance
of the eliminator is determined from the local air velocities
and the droplet terminal velocity.
This terminal velocity
is determined by solving the steady-state form of Eq. (2.1)
which
is
Vt
2
Pwg R 2
2V~~
9
CdRe
~~~~V
a
Vd
=
(2.8)
This nonlinear algebraic equation is solved by Newton's method
of tangent
(4)
with a calculational accuracy of 0.1%.
A variable time-step size is used in the trajectory calculation.
The step size is determined from consideration of the
4)
propagation of error((4)
The propagation error in this numeri-
cal method will tend to diminish if at any time step
1 + h af
<
i,
1 ,
(2.9)
ti,a
where
a
Vd(ti+l).
is a velocity value within the interval
Vd(ti) and
Therefore at the beginning of each time step
is determined
af/aVd
(which is always less than zero in the present
cases) from which a time-step
size can be determined
such that
9
the propagation error will diminish.
Subroutine SOLASUR calculates the air velocity distribution within eliminators by solving the Navier-Stokes equations
au
au2
auv
at
ax
ay
_
-
-
2u
+
ax+
gX
a2 u
+
2u
ay2
Vax2
(2.10)
av + auv
ax
at
av 2
p + g+
y
ay
ay
a2v
+
ax2
ax
a2 v
2
ay2
together with the mass continuity equation
au + a
ax
ay
=
(2.11)
0
An implicit finite difference
technique
is used.
First the
guesses for the new velocities for the entire mesh are computed
from the difference
the previous
forms of Eq. (2.10), which involve only
time values for the contributing
velocities in the various flux contributions.
pressures
and
These velocities
are then adjusted iteratively to satisfy the continuity equation
(2.11) by making appropriate
changes in the cell pressures.
In
the iteration, each cell is considered successively and is
given a pressure change that drives its instantaneous velocity
divergence to zero.
the velocity
Finally, when convergence has been achieved,
and pressure
fields are at the advanced
time level
and may be used as starting values for the next cycle.
10
CHAPTER
3
PROGRAM DESCRIPTION
The DRIFT code is written in FORTRAN
system.
IV for IBM 370/168
The main program calculates the droplet trajectory
within eliminators and the collection efficiency for specified
droplet
sizes.
Fig. 3.1.
A flow chart of the main program
is shown in
It starts by reading some appropriate input para-
meters for the case to be studied..
The air velocity
distribu-
tion can either be calculated by the SOLASUR subroutine or
supplied by the user.
Then calculation starts for droplet
trajectory of different droplet sizes.
The initial conditions
of the droplet are first determined and trajectory calculation
is done step by step, advances
the time-step
beginning
in time.
size is determined
At each time step,
from the conditions
of the step, then the final conditions
step are calculated by Runge-Kutta method.
stops when the location
eliminator
walls
at the
in that time
The calculation
of the droplet is either outside the
(captured) or is out of the top of the
eliminator (escape). For each droplet size this calculation
starts at the left wall of the eliminator
tion in wall definition
entrance.
is shown in Fig. 3.3.)
(Conven-
When the
droplet is captured by or escapes from the eliminator, another
calculation is done by placing the droplet at a certain
distance
to the right of the previous
tor entrance.
location at the elimina-
The procedure is repeated until the starting
11
(READ INPUT PARAMETERS
CALCULATE THE
AIR VELOCITY
DISTRIBUTION BY
SOLASUR SUBROUTINE
OES USER SUPPLY
THE AIR VELOCITY
\_
YES
! E~~
IBUTIO
INPUT AIR VELOCITY
O CALCULATE
COLLECTION
FFICI
ENCY? / YES
NO
DIRIBUTION?/
CALCULATE DROPLET
TERMINATE VELOCITY
_
FOR ALL GIVEN
DROPLET SIZES
I_
,·
IFIND INITIAL CONDITION I -- _
....
.
,.,,
,
.-
IS THE ENTRANCE POINT
CALCULATE THE
OF THE ELIMINATOR?
YES
COLLECTION
EFFICIENCY
NO
I
FINI
CONDNTTTNNS
BEGINNING
i
ENTRANCE
'DECREASE
CALCULATE TIME,,
AT
OF TIME STEP
DIVISION SIZE FOR
IMORE ACCURATE RESULTI
STEP SIZE
I
ml
II
I
CALCULATE CONDITIONS
AT END OF TIME STEP I
YES
/T
10
DETERMINE THE
BOUNDARY
ELIMINATOR
:
m
,,-,,,,,.
, ,
,
I
WTRANCE POINT TRAPPQ_(--
!
,,
.
NO
i1C \X
lf'
lI f'Tr AT Dr \lT'
C )RVrLC1
Ml KCYVU0_,
YE
I
1(
--
-
--
-
DKULt
-
.
I
I
,,
UU I
,
IS
DRPLETOUT OF \
U
-ELIMINATOR BOUNDARY?!
NO
OP
O
e~~~~~~~~~~~~~~~~~~~~~i
,
NO
ELMINATOR.
YES
J.
lb
*
,,
,
.
__
KU'Ltl
Al V'I=VIUUS
-I
NU
ENTRANCE POINT TRAPPEDORE
YE
r-I
I DECREASE
~1
i
i
i
ii
i
iii
ENTRANCE
I
ACCURATE RESULT
D DROPLET
J
iRECORD TRAPPED DROPLET,
Fig. 3.1
Flow Chart of the DRIFT Code
12
point coincides with the right wall of the eliminator.
During
these calculations, if a droplet starting at a certain location at the eliminator entrance is found to be captured while
the previous droplet starting at the adjacent location has
been found to escape, or vice versa, then a more detailed
calculation will be performed between these two locations for
more accurate results.
This is done by dividing this distance
into smaller intervals for trajectory calculation.
The
fraction of this distance starting from which the droplet
will be trapped is determined.
This information, together
with the recorded information from "coarse" calculation, can
then be used to determine the collection efficiency for that
droplet
size.
The procedure
SOLASUR subroutine
Fig. 3.2.
for air velocity
calculation
in the
is shown in the flow chart of the code in
A more detailed
description
of this subroutine
is
given in Ref. (3).
The boundaries for many standard eliminator geometries
are defined
in the code.
Boundaries
for arbitrary
geometries
should be supplied by the user through several subroutines.
A simple description of the main program and the subroutines
of the code are listed below.
Main program:
calculates droplet trajectory and collection
efficiency.
-LJ
P
SET INITIAL
CONDITIONS FOR
PROBLEM
!,*
]
COMPUTE INITIA
-
GUESS VELOCITIES
_SET
BOUNDARY
I
Ir"t !IT T ' T AF I I
,VIJ.1JI
1vv4j ]~
f/SET
I
SPECIAL\
URES•COBOUNDARY
TI ONS
nn
!SS
/HAVE PR,ESSRES
-7-- -- -/
\ 5 CONVERGED(-
I
ldd
vF:
Z---
-L-
NO
I! !
-
1
.
I
.
....
UPDATE CELL
PRESSURE AND
VELOCITIES
.
_
.
|
|
UPDATE FREE
SURFACE
_ ...
I-|~
POSITION
.
.
I
ir
ADVANCE
·
ii
iii
PRINT
T I ME
AND CYCLE
PLOT
i
.
1
i
iii_
ii
PRESSURE
·
,
_
DROP
-CALCUL
NO TIME TOSTOP?;
YES
I
t
OP
Fig.
3
Flow Chart of the SOLASUR Code
.,
_.._
/
14
Subroutines
SOLASUR:
calculates air velocity distribution and pressure
drop.
HIVBT:
defines the bottom boundary of the Hi-V eliminator.
HIBTB:
defines the top boundary of the Hi-V eliminator
ASBCEM:
defines the bottom boundary of the asbestos-cement
eliminator.
BOUNPL:
plots the boundaries of arbitrary eliminator
geometry as defined by user.
BOUNTS:
defines the boundaries of arbitrary eliminator
geometry for testing whether droplets are captured.
This information is supplied by user if needed.
BTBOUN:
defines the boundaries of arbitrary eliminator
geometry
for air velocity
calculation.
This in-
formation is supplied by user if needed.
It should be noted that the convention
in defining
boundaries is different between the main program and the
SOLASUR subroutine.
Fig. 3.3 shows the convention
of defining
boundaries in the main program for either boundary plotting
or for testing of the capturing possibility
of droplets.
The
reference point and the coordinate system are shown in the
figure.
SOLASUR
The left boundary
is the top boundary
as defined in
(see Fig. 3.4) while the right boundary
boundary in SOLASUR.
is the bottom
Convention for defining the boundary
in the SOLASUR subroutine to be used for air velocity calculation
is shown in Fig. 3.4.
Therefore,
in defining
boundaries
for
15
Outlet
Left
Right (Bottom)
(r
Boundai
;oundary
r
F
J
Inlet
A
Air Flow
Fig. 3.3
Convention of Wall Definition for
the Main Program
16
H
4-a)
)
a)
d
>5
cl
C0
ro
4-3
0
0
-
000
:d
z
0
CQ
bO
4-,
4-,
a)
a)
-4.
0
H
0o
EA
m
rl
o
o
X
a)
0
a)
O
O
0o)
._1
rU ~
bO
do
-H
0
H(
cr~
17
arbitrary eliminator geometries in subroutines BOUNPL and
BOUNTS, convention as shown in Fig. 3.3 should be used, while
in subroutine
BTBOUN the convention
should be adopted.
as shown in Fig. 3.4
18
CHAPTER
INPUT
4
DESCRIPTION
The input parameters of the DRIFT program are described
below.
MKS units are used throughout the program.
Recommended
values are given in brackets after the concerned parameters.
Card No. 1
Case identification
(AA(I),I=1,20)
FORMAT (20A4)
Any information
to eighty.
can be put on this card from column one
The purpose
of this input is to identify
the
case to be executed.
Card No. 2
Option definitions
NCAL, NTYPE, NTJ, NDATA
FORMAT(5I3)
(a)
NCAL defines calculation mode.
<0 for air velocity distribution calculation only.
=0 for collection efficiency calculation with air
velocity distribution being calculated by subroutine
SOLASUR.
>0 for collection efficiency calculation with air
velocity distribution being input by user.
19
(b)
NTYPE defines types of eliminator.
=1 for single-layer louvre eliminator.
=2 for double-layer louvre eliminator.
=3 for sinus-shaped eliminator.
=4 for zig-zag eliminator.
=5 for Hi-V eliminator.
=6 for asbestos-cement eliminator.
=7 for other arbitrary geometry defined by user.
(c)
NTJ defines droplet trajectory plot option.
#O for droplet trajectory
plot.
=0 for omitting droplet trajectory plot.
(d)
NDATA is used to number the data sets.
=1 for the first set of input data.
>1 for the other cases to be executed
any.
if there are
(Note that either all cases use the same plotting
options or that the cases with plotting option should
be placed
(A)
first.)
If NCAL>O
Card No. 3A
(If NCAL>O)
IMAX, XL, TTY, A, DELX, DELY
FORMAT(I10,5F10.3)
(a)
IMAX is the maximum number of nodes in x-direction
the input velocity distribution.
(b)
XL is the length of the eliminator.
for
20
(c)
TTY is the pitch of the eliminator.
(d)
A is the eliminator
inclinded
angle for single-,
double-layer louvre and zig-zag eliminators, or the
amplitude for other eliminators.
(e)
DELX is the mesh size in x-direction used for the
input velocity distribution determination.
(f)
DELY is the mesh size in y-direction
used for the
input velocity distribution determination.
Card No. 4A to Card No. (IMAX+4)A
(If NCAL>0)
(JB(I),JT(I),I=l,IMAX)
FORMAT(2I3)
(a)
JB(I)=node number in y-direction for the bottom
boundary of the eliminator used in input air velocity
distribution determination.
(b)
JT(I)=node
number
in y-direction
for the top boundary
of the eliminator used in input air velocity distribution determination.
Card No. (IMAX+5)A and onward
(If NCAL>0)
I,J, U(I,J), V(I,J)
FORMAT(I3,5X,I3,2(6X,E12.5))
(a)
I is the nodal point number in x-direction.
(b)
J is the nodal point number in y-direction.
(c)
U(I,J) is the velocity
component
in x-direction
at (I,J).
(d)
V(I,J)
is the velocity
component
in y-direction
at (I,J).
(The velocities
are read in at each I from JB(I)-l to JT(I)+l.)
21
(B)
If NCAL=O or NCAL<O
Card No. 3B
(If NCAL<O)
NUM
FORMAT(6X,I2)
NUM is the number of input parameters
necessary
for air
velocity distribution calculation in subroutine SOLASUR.
(NUM=33 for present study)
Card No. 4B to Card No. 12B
(If NCAL<O)
(XPUT(I) ,I=1,NUM)
FORMAT(4(6X,E12.5))
4B
XPUT(1)=IBAR=number of cells in the x-direction, excluding
boundary cells.
XPUT(2)=JBAR=number of cells in the y-direction, excluding
boundary cells.
XPUT(3)=XL=length
of the eliminator.
XPUT(4)=TTY=pitch
of the eliminator.
5B
XPUT(5)=DELT=time increment.
XPUT(6)=NU=v=coefficient of kinematic viscosity.
XPUT(7)=CYL=C=geometry indicator (1.0 for cylindrical
coordinates, 0.0 for plane coordinates).
XPUT(8)=EPSI=c=pressure iteration convergence criterion
(0.005 to 0.01).
22
6B
XPUT(9)=DZRO=Do=scaling factor for convergence test. (1.0)
XPUT(10)=GX=gx=body acceleration in positive x-direction.
XPUT(1ll)=GY=gy=bodyacceleration in positive y-direction
XPUT(12)=UI=x-direction velocity used for initializing mesh
and/or setting special boundary conditions.
7B
XPUT(13)=VI=y-direction velocity for initializing mesh and/
or setting special boundary conditions.
XPUT(14)=VELMX=maximum velocity expected in problem, used to
scale velocity vector plot.
XPUT(15)=TWFIN-problem
time when calculation
is to be termi-
nated.
XPUT(16)=CWPRT=number of cycles between long prints output
on paper.
8B
XPUT(17)=CWPLT=number of cycles between velocity vector plots.
XPUT(18)=OMG=w=over-relaxation factor used in pressure iteration.
(1.95)
XPUT(19)=ALPHA=a=controls amount of donor cell fluxing : 1.0
for full donor cell differencing and 0.0 for centered
differencing.
XPUT(20)=GAMMA=y=controls the amount of donor cell fluxing
in kinematic
equations
for free surface position.
concerned with the present study)
22
(Not
23
9B
XPUT(21)=WL=indicator for boundary condition to be used
along the left side of the mesh:l.0=rigid
free-slip
wall, 2.0=rigid no-slip wall, 3.0=continuative boundary,
4.0=periodic boundary. (3.0)
XPUT(22)=WR=indicator for boundary condition along right
side of mesh.
(3.0)
XPUT(23)=WT=indicator for boundary condition along top of
mesh.
(Not concerned with the present study)
XPUT(24)=WB=indicator for boundary condition along bottom
of mesh.
(Not concerned with the present study)
10B
XPUT(25)=TB=top boundary definition:0.0 for top boundary
coincident
with the top mesh boundary,
surface, 2.0 for rigid top boundary.
1.0 for free
(2.0)
XPUT(26)=BB=bottom boundary definition: 0.0 for bottom
boundary coincident with the bottom mesh boundary,
1.0 for free surface,
2.0 for rigid bottom boundary.
(2.0)
XPUT(27)=A=eliminator inclined angle for single-, doublelayer louvre or zig-zag eliminators, or the amplitude
for other eliminators.
XPUT(28)=IPUNCH=>O.O for punch output of final velocities,
<0.0 for no punch output.
llB
XPUT(29)=VANG=angle between the air flow and the normal to
the eliminator inlet transverse cross section.
XPUT(30)=INVEL=#0.O for initial velocity distribution
supplied by user,
=0.0 assume constant initial velocity distribution of UI and VI.
XPUT(31)=NSLIP=>0.0 for free-slip condition at the rigid
boundaries.
<0.0 for no-slip condition at the rigid
boundaries.
XPUT(32)=LIER=limiting number of iteration per cycle. (1500)
12B
XPUT(33)=LC=maximum cycle number beyond which velocity calculation will stop if iteration is greater than LIER. (60)
0.0
If INVEL
Card No. 13B and onward
(If NCAL
0 and INVEL M 0.0)
I,J, U(I,J), V(I,J)
FORMAT(I3,5X,I3,2(6X,E12.5))
(a)
I is the nodal point number in x-direction.
(b)
J is the nodal point number in y-direction.
(c)
U(I,J) is the velocity
component
in x-direction
at (I,J).
(d)
V(I,J) is the velocity
component
in y-direction
at (I,J).
(C) If NCAL > 0
Card
No
3
Trajectory calculation information
(If NCAL > 0)
NY,DN,ERR,EANG
FORMAT(I10,5F10.3)
(a)
NY=the number of points at eliminator entrance where
trajectory calculation will start.
(20)
(b) DN=number of points within 1/NY of the entrance width
of the eliminator which will be tested when change of
trapping conditions is detected.
(10)
(c) ERR=the control parameter for time step determination.
(0.1)
(d) EANG=angle between the eliminator length and the vertical.
Card No. 4
(If NCAL > 0)
ND
FORMAT(I3)
ND=number of droplet sizes for which trajectory calculation
will be performed.
Card No. 5
(If NCAL
0)
(DD(I),I=l,ND)
FORMAT(8F10.6)
DD(I)=droplet diameter in
will be performed.
m for which trajectory calculation
26
CHAPTER
5
NUMERICAL STABILITY CONSIDERATIONS
Numerical calculations frequently exhibit unstable
behavior in which computed quantities develop large, high
frequency
oscillations
type of behavior
in space, time, or both.
occurs it is usually referred
When this
to as a
numerical instability, especially if the physical problem
being studied is known not to possess such behavior.
When
the physical problem does have unstable solutions, if the
calculated results exhibit significant variations over distances
comparable
time increment,
on.
to a cell width or times comparable
the accuracy
of the results
To avoid this type of numerical
in the velocity
calculation
to the
cannot be relied
instability
by the Subroutine
or inaccuracy
SOLASUR,
certain
restrictions must be observed in defining the mesh increments
6x
and
y, the time increment
ferencing parameter
a.
t, and the upstream
dif-
The restrictions to these parameters
are as follows:
(1)
The curved rigid boundaries must be definable by single
valued functions, e.g., y=H(x) for the top boundary and
y=HB(x) for the bottom boundary.
(2)
The slope of the rigid boundaries
cell aspect ratio
(3)
must not exceed the
6y/6x.
The mesh increments must be chosen small enough to resolve
the expected spatial variations in all dependent variables.
27
. (4)
Fluid cannot move through more than one cell in one
time step.
Therefore the time increment must satisfy
the inequality
6t < min I 6x
6
where the minimum is with respect
mesh.
Typically,
the minimum
(5)
(5.1)
,
to every cell in the
t is chosen equal to 1/4 to 1/3 of
cell transit time.
When a non-zero value of kinematic viscosity is employed,
momentum must not diffuse more than approximately one
cell in one time step.
6x26y2
vt <1
2
2 x
(6)
a
and
y
This implies
+
(5.2)
y2
should satisfy the following inequality
in
order to insure numerical stability:
1
>
> max
As a rule of thumb,
I{
I'- I
a = y
approximately
times larger than the right hand member
inequality
is a good choice.
(5.3)
1.2 to 1.5
of the last
28
REFERENCES
(1)
Chan, J. and Golay, M.W., "Numerical
Simulation
of
Cooling Tower Drift Eliminator Performance," Numerical/
Laboratory Computer Methods in Fluid Mechanics, presented
at the ASME Annual Winter Meeting, edited by A.A. Pouring
and U.L. Shah, ASME, New York, Dec., 1976, pp. 229.
(2)
Chan, J., "Comparative Evaluation of Cooling Tower Drift
Eliminator Performance," Ph.D. Thesis, Massachusetts
Institute of Technology, Cambridge, Massachusetts, June,
1977.
(3)
Hirt, C.W., Nichols,
B.D. and Romero,
N.C., "SOLA--
A Numerical Solution Algorithm for Transient Fluid
Flows," LA-5832,
(4)
1974, Los Alamos Scientific
Carnahan, B., Luther, H.A. and Wilkes,
Lab.
J.O., Applied
Numerical Method, John Wiley & Sons, Inc., 1969.
29
APPENDIX A
LISTING OF THE DRIFT PROGRAM
30
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APPENDIX B
SAMPLE PROBLEM
A sample problem is presented
of the DRIFT code.
In this case the performance
Hi-V eliminator is studied.
all the cells are input.
the use
of the
Section B.1 lists the input
values for this particular case.
in Section B.2.
to demonstrate
Initial velocities at
The output of the code is shown
Figs. B.1 to B.3 are the velocity
vector
plots for this case and Figs. B.4 to B.7 are the droplet
trajectory plots for this sample problem.
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