A complex problem involving convective flow of a binary mixture containing a condensable vapor and noncondensable gas in a partially enclosed chamber was modelled and results compared to transient experimental values. The finite element model successfully predicted transport processes in dead-ended tubes with inside diameters of 0.4 to 1.0 cm. When buoyancy driven convective flow was dominant, temperature and mixture compositions agreed with experimental data. Data from 0.4 cm tubes indicate diffusion to be the primary air removal method in small diameter tubes and the diffusivity value in the model to be too large

Lasher, William C.

Young, Jack H.

English

NASA Technical Reports Server

N94"23669
COMPARISON OF NUMERICAL SIMULATION
AND EXPERIMENTAL DATA
FOR STEAM-IN-PLACE STERILIZATION
Jack H. Young
William C. Lasher
Pennsylvania State University at Erie
Erie, PA 16563
SUMMARY
A complex problem involving convective flow of a binary
mixture containing a condensable vapor and noncondensable gas in
a partially enclosed chamber was modelled and results compared to
transient experimental values. The finite element model
successfully predicted transport processes in dead-ended tubes
with inside diameters of 0.4 to 1.0 cm. When buoyancy driven
convective flow was dominant, temperature and mixture
compositions agreed with experimental data. Data from 0.4 cm
tubes indicate diffusion to be the primary air removal method in
small diameter tubes and the diffusivity value in the model to be
too large.
NOMENCLATURE
Cp = mixture specific heat at constant pressure, J/kg-°C
C, = mass fraction of air
g = gravitational vector, m/s 2
h = convective heat transfer coefficient, W/m2-°C
k - thermal conductivity, W/m-°C
P = mixture total pressure, Pa
P_ - saturated water vapor pressure, Pa
q = heat transfer rate, W
t z time, s
T = mixture temperature, °C
T_h = ambient temperature, *C
T_ = saturated steam temperature, °C
u = velocity vector, m/s
= mixture dynamic viscosity, Pa-s
ux - x-component of velocity, m/sec
0 = mixture density, kg/m 3
00 = mixture density at reference temperature and
concentration, kg/m 3
p" - mixture density used in momentum equation, kg/m 3
p_ S saturated water vapor density, kg/m 3
= binary mass diffusivity, m2/s
_c _ mixture coefficient of concentration expansion
_T = mixture coefficient of thermal expansion
513
https://ntrs.nasa.gov/search.jsp?R=19940019196 2020-06-16T15:22:38+00:00Z
Subscripts
f = fluid
t = tube
INTRODUCTION
Availability of commercial computational fluid dynamic (CFD)
packages have made finite element modeling available for use as a
tool in studying complex reaI-worid fluid engineering problems.
Previously most CFD work involved selection of a problem based on
availability of software or study of simple geometries and very
idealized problem formulations. This study describes application
of a commercial CFD package to a complex problem, compromises
made during model development and how the model was used in
conjunction with experimental data to gain an understanding and
start in quantizing the important physical parameters.
Steam-in-place (SIP) steriiization has arisen in th@
biotechnology and--pharmaceuticai industries as result of the
increased need to sterilize large devices which can not be placed
in an autoclave. SIP offers the additional advantage of
sterilizing complete systems (i.e., filters, holding tanks and
interconnecting piping) without t_e need for aseptic assembly of
individually sterilized components. This provides greater
sterility assurance, improved productivity and reduced cost over
convectional sterilization in an autoclave.
SIP sterilization requires that an adequate amount of
moisture at the proper temperature be delivered for a required
time to all sterilization sites. The factor most often resulting
in sterilization failure is air entrapment which results in
inadequate temperature and moisture. Failures are most likely to
occur in dead-ended geometries, deadlegs, such as safety valves,
gauges/transducers and closed inlet/outlet lines. Displacement
of air can result from molecular diffusion and/or buoyancy driven
convective flow resulting from temperature and solutal gradients.
Published studies have focused on general SIP principles
(refs. i and 2) or recommendations for specific pieces of
equipment (ref. 3). Recently experimental data have been
reported describing effect of deadleg tube orientation (ref. 4)
and diameter (ref. 5) on sterilization, but no quantitative
guidelines exist for design engineers and scientists. Currently,
biological testing is conducted to determine if sterilization has
occurred. This is time-consuming and expensive. A mathematical
model is needed for the transient air/steam mixing process
occurring during SIP sterilization. The model would predict
temperatures and steam concentrations at locations within various
deadleg geometries and could be used to determine general
transport processesand critical parameters.
EXPERIMENTAL METHODS
Temperature and biological measurements were taken in tubes
514
orientated vertically up or 5 degrees above horizontal. Inside
diameters (IDs) of the tubes were 0.4, 1.0 and 1.7 cm with tube
lengths ranging from 7.8 to 18.0 cm. Thermocouples or biological
indicators were attached to a nylon string which ran along the
tube centerline. The test fixture was pressurized with saturated
steam having an average temperature of 122.4°C and pressure of
217 kPa. Details of experimental methods are given elsewhere
(ref. 5).
Linear regression analysis was performed on the segment of
the semi-logarithmic plots of surviving population versus time
showing decreasing population. Slope of the regression line was
used to determine time required to reduce the population by one
log. This was termed cycle log reduction (CLR) time. Time at
which the regression line intersected the initial population was
termed time to start of kill (TSK). These two parameters
characterized experimental kill at a location within a tube.
NUMERICAL SIMULATION
Simulation of deadleg SIP sterilization required:
I. Compressibility of air be taken into account
2. Development of expressions for physical properties
of air/steam mixtures over wide ranges of
composition (C I equal 0 to i) and temperature (27 to
123°C).
3. Modeling of condensation from a mixture containing a
noncondensable gas and condensable vapor.
Major effects associated with compressibility occur during
initial pressurization with steam since the pressure is constant
thereafter. This allows inclusion of these effects into the
initial conditions for the problem (fig. lb). It was assumed
that all air was removed from the cross by steam flow and that
the air in the tube was isentropically compressed to 217 kPa with
no mixing of air and steam. This results in the top 56% of the
tube initially containing all air at 100°C. The mixture was then
considered to be incompressible with density Po and the
Boussinesq approximation applied to the momentum equation to
account for temperature and concentration induced density
variations.
Actual mixture density at 217 kPa is given by :
p
217
0.287 T CI + Psa= (l-Cz)
P sa_
(1)
Density used to calculate buoyant forces in the momentum
equation was determined by assuming density to be a linear
function of temperature and mass fraction with coefficient of
515
volume expansion due to concentration to be a function of
temperature. Least squares analysis resulted in:
P" = Po (0.00407 T + (0.01638-0.00178 _C I) (2)
Variations in other mixture properties were determined using
published values for steam and air at 25 to 125°C and assuming
properties to be proportional to mass fraction of each component.
Published diffusivity values could not be found for air/steam
mixtures at 217 kPa and over the appropriate temperature and mass
fraction ranges. A semiemperical equation for diffusivity of low
density gases which depends on total pressure, temperature and
molecular properties of constituent gases was used. Diffusivity
was evaluated at 217 kPa and 123°C and assumed constant (0.15
cm 2/s).
Heat transfer resulting from condensation of a condensable
vapor from a binary mixture containing a noncondensable gas is
complex and depends on mixture composition , as well as, fluid
flow near condensation sites. Convective heat transfer
coefficients can vary from 24 to 2500 W/m2-°C as composition
varies from C_ equals 0 to I. Heat transfer reductions of over
50% can result when only 2 to 5% mass of air is present during
free convection (ref. 6 and 7). Substantially higher heat
transfer occurs if forced flow is present and condensation is
minimal (ref. 8 and 9).
The condensation model was kept simple since this
represented a first attempt at modeling SIP sterilization and
substantial computational time was required. The tube was divided
into six segments and temperature of a tube wall segment was set
equal to the saturated steam temperature corresponding to steam
concentration in that segment when the mass fraction of air was
less than 0.i (fig. la). This simulates the high convective heat
transfer associated with condensation and availability of an
infinite steam supply. When C_ was greater than 0.i, the mixture
was treated as a simple mixture of two noncondensable _a2es and a
constant convective heat transfer coefficient of 7 W/m - C
corresponding to free convection was specified on external
surfaces of the tube segment. Heat transfer between the tube
wall and mixture within the tube was specified as:
OT @T (3)
The commercially available CFD package FIDAP Version 6
(Fluid Dynamics International, Inc.) was Used on a Silicon
Graphics 4D35 workstation with 48 mg of memory. The governing
equations were:
516
Continuity equation
V • u = 0 (4)
Concentration equation
aC l
+ u • VC I = _V2Cl (S)
Momentum equation
Po + u • Vu = -VP ÷ _V2u
pog[ , +B c,]
Energy equation
(6)
PO _ + U • V = kl V ZT (7)
Quadrilateral finite elements were used with non-uniform
meshes containing 1923 to 3464 nodes. A preliminary study was
performed to evaluate the effect of two versus three dimensional
modeling and to ensure grid-independence. The three-dimensional
model required two weeks of CPU time to simulate 2.56 seconds of
actual fluid flow, whereas the two-dimensional required 12 hours.
Comparison of tube centerline temperatures showed a maximum
average difference of 9.4%. Doubling the number of elements in
the two dimensional model resulted in a 2.0% difference in
average temperatures. Since five different tube simulations
covering up to 40 minutes of real time were needed, two-
dimensional models were used.
RESULTS AND DISCUSSION
Typical model velocity vector plots show steam rising at the
tube centerline and the cooler air being displaced downward along
the tube walls (fig. 2a). This results in a pair of
counterrotating vortices. A second pair of vortices develop
below the initial interface and the shear layers between the
517
vortices become unstable (fig. 2b). The vortices pair and roll
up resulting in a more homogeneous mixture in the tube (fig. 2c).
The buoyant forces eventually diminish until only weak structures
remain (fig. 2d).
Magnitude of convective flow is indicated by mean fluid
speed (Table I). 0.4 cm ID tubes were predicted to have minimal
flow. This was experimentally investigated by comparing
centerline temperature profiles and biological results from
vertically orientated tubes and those positioned 5 degrees above
horizontal. Average temperatures were within 3.7% and neither
tube showed significant biological kill above the interface after
2 hours, thereby confirming diffusion to be the primary mode of
air removal.
The model predicted significant increases in convective flow
with increasing tube diameter (Table I). since mixture density
depends on temperature and mixture composition (eq. (i)) and not
diameter, buoyant forces are independent of diameter, Viscous or
retarding forces increase with decreasing tube diameter and tend
to damp out convective flow. In the case of 0.4 cm ID tubes,
viscous forces quickly damp out flow and diffusion dominates.
Temperature and biological data confirmed diameter to be a
critical parameter for sterilization. Sterilization was achieved
throughout an 18 cm long tube with 1.7 cm ID within 75 minutes
whereas 185 minutes were required for a 7.8 cm long tube with 1.0
cm ID (fig. 2). Sterilization could be achieved in only the
lower half of 0.4 cm ID tubes with lengths of 7.8 cm.
Model predicted and experimental temperature profiles were
quantitatively compared for three different lengths of 1.7 cm ID
tubes, as well as, 7.8 cm long tubes with diameters from 0.4 to
1.7 cm (fig. 4). % differences were less than 12% for all
lengths of 1.7 cm ID tubes with average differences increasing
with increasing tube length. % differences increased with
decreasing tube diameter. Model temperatures were higher than
experimental values for 0.4 and 1.0 cm tubes with % differences
as high as 28%.
The model must quantitatively predict transient mixture
composition, in addition to temperature, if it is to be used to
predict sterilization times. Mixture composition can not be
measured experimentally but can be inferred from CLR times and
TSK. Young (ref. 5) has shown a correlation between CLR and
saturated steam temperatures for vertical deadlegs. Therefore,
experimental CLR times can be used to calculate mixture mass
fraction. Model predictions of time required to reach this mass
fraction can then be compared to experimental TSK. Due to %
differences in temperatures for 0.4 and 1.0 cm tubes, comparisons
of predicted and experimental TSK were carried out for 1.7 cm ID
tubes only. % differences increased with increasing tube length,
For the shortest tube, 7.8 cm, experimental TSK for the uppermost
location was 2.6 minutes while the model predicted 2.2 minutes.
Experimental values for 13.0 and 18.0 cm tubes were 10.2 and 17.5
minutes. Corresponding predicted values were 5.4 and 7.9
518
minutes.
Model and experimental data show diffusion to be the primary
transport process in 0.4 cm ID tubes, but the value of
diffusivity used in the model was too large. A smaller value
would result in a greater time required for steam to diffuse to
top of the tubes when convective flow is not present. In the
case of 7.8 cm long tubes with 1.7 cm IDs, a smaller diffusivity
will have minimal effect on temperatures and TSK since air is
removed from the tubes within 2-3 minutes by buoyant driven
convective flow. In the longer 1.7 cm tubes, convective flow
dies out prior to complete removal of air. Therefore, diffusion
becomes important in these 1.7 cm tubes. A smaller diffusivity
would increase model predicted TSK and thereby increase agreement
between model and experimental data. A similar argument can be
made for 1.0 cm tubes.
An empirical value for diffusivity can be obtained by
comparison of model and experimental results for 0.4 cm tubes.
This value could be used in the model as a next level of
refinement•
The present condensation model does not allow for
accumulation of non-condensable gas at the site of condensation.
This does not appear to be a problem when convective flow is
present, but may present a problem in 0.4 cm tubes and larger
diameter tubes when convection is minimal.
CONCLUSIONS
Although many simplifying assumptions had to be made, use of
a commercial CFD package has been extremely useful in
understanding transport processes and critical parameters in SIP
sterilization. It correctly predicted diffusion to be the
primary air removal mechanism in 0.4 cm ID tubes and diameter to
have a significant effect on magnitude of buoyant driven
convective flow. When convective flow is the only significant
transport mechanism the model and experimental data were in good
agreement. Interactive use of numerical model and experimental
data has proven effective towards development of quantitative SIP
guidelines.
REFERENCES
.
•
3.
•
Berman, D., Myers, T. and Suggy, C., Factors Involved in
Cycle Development of a Steam-in-Place System, J.
Parenter. Sci. Technol., Vol.40, No. 4, 1986, 119-121.
Agalloco, J., Steam Sterilization-in-Place Technology, J.
Parenter. Sci. Technol., Voi.44, No. 5, 1990, 253-256.
Myers, T. and Chrai, S., Steam-in-Place Sterilization of
Cartridge Filters In-Line with a Receiving Tank. J.
Parenter. Sci. Technol., Vol. 36, No. 3, 1982, 108-112.
Young, J. H., Ferko, B. L., Temperature Profiles and
Sterilization Within a Dead-ended Tube. J. Parenter.
Sci. Technol. Vol. 46, No. 4, 1992, 100-107.
519
••
g
•
•
Young, J. H., Sterilization of Varying Diameter Dead-
ended Tubes. Biotechnology and Engineering. Vol. 42,
No. i, 1993, 125-132.
Mori, Y., Hijikata, K., Free Convective Condensation
Heat Transfer with Noncondensable Gas on a Vertical
Surface. Int. J. Heat Mass Transfer. Vol. 16, 1973,
2229-2240 .........
Sparrow, E. M., Lin, S. H., Condensation Heat
Transfer in the Presence of a Noncondensable Gas. J.
of Heat Transfer. August 1964, 430-436.
AI-Diwany, H. K, Rose, J. W., Free Convection Film
Condensation of Steam in the Presence of Non-condensing
Gas. Int. J. Heat Mass Transfer. Vol. 16, 1973, 1359 &
1369.
Sparrow, E. M., Mincowycz, W. J. and Saddy, M., Forced
Convection Condensation in the Presence of Non-
Condensables and Interfacial Resistance. int. J. Heat
Mass Transfer. Vol. 93, No. 3, 1967, 1829-1838.
520
B
. cl >o.1,
h'7 W/(m 2 I0
if C4<0.1,
T"Tut
T- 122.4 C
(a)
Boundary Conditions
E-l
T.mb- 27C
I____
Ux =.88(1-(y/r) 2)
X
(b)
Initial Conditions
[ilT" 100 C
U-O mlNc >C _ Sta(nlett Steel
>C
C1 ,,0
_ T..12:L,Cuaomlu¢ ._ _ 5talnlellSteqdTm122.4C
C 1 ..o _'
D "1T- 122.4 CUx-.. m/.c _ g
Figure i- Schematic represent-
ation of numerical model (a)
boundary conditions and (b)
initial conditions.
(a) (b) (c) (d)
Figure 2- Velcity vector plots
from 13.0 cm long tubes with
1.7 cm ID; (a) 0.48 seconds,
(b) 1.75 seconds, (c) 1.02
minutes and (d) 4.75 minutes
after pressurization with
steam.
521
Time
Mean Speed
(cm/sec)
(Minutes} 0.4 cm
ID Tube
1.0 cm
ID Tube
5.0 0.005
1.7 cm
ID Tube
0.02
0.02 0.029 1.43 3.55
0.05 0.007 0.97 3.42
0.50 0.005 1.14 2.37
1.0 0.005 0.89 2.05
3.0 0.005 0.74 0.ii
0.03
Table I- Transient mean fluid
speed for 7.8 cm long tubes.
500
_400C
.m
_300
E
.i
C2O0
O
sm
4-a
N
100
0
-0-0.4 cm ID x 7.8 cm
--1.0 cm ID x 7.8 cm
-.-1.7 cm ID x 7.8 cm
--1.7 cm ID x 18.0 cm
• , . I j i | i _ * ' • • I
5 10 15
Distance Up Tube (cm)
Figure 3- Time required for
12 log reduction of B.
stearothermophilus spores
3O
Z25
O
20
%_
13 15
(D
:3
10L-
O.
E
5
0
-o.IO=0.4 cm, L=7.8 cm
÷10=1.0 cm, L=7.8 cm
-,-ID=1.7 cm, L=7.8 cm
_1D=1.7 cm, L=13.0 cm
-,,-ID=1.7 crn, L=18.0 cm
3 6 9
TIME (Minutes)
Figure 4- % difference
between model and
experimentally measured
centerline temperatures.
12
522


Comparison of numerical simulation and experimental data for steam-in-place sterilization

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