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Mass transfer in annuli of grooved or splined microporous tubing twisted to generate swirl
Pergamon Press
I~~HEATANDMASSTRANSFER Vol. 2, 3 . 445 - 450, 1975
Printed in the United States
MASS TRANSFER IN ANNULI OF GROOVED OR SPLINED MICROPOROUS TUBING TWISTED TO GENERATE SWIRL
P. D. Richardson, K. Tanishita and P. M. Galletti Bmown University, Providence, Rhode Island 02912
(C~,~/nicated by J.P. Hartnett and W.J. Minkowycz) ABSTRACT Annuli have been built with longitudinal grooves or splines on both inner and outer tube surfaces, using microporous teflon tubing with appropriate extruded crosssections. Axial twisting of the tubes (which makes the splines helical) gave enhanced mass transfer, counter~twisting being more effective than co-twisting. Introduction In mass transfer devices which handle diffusion processes in liquids having large Schmidt numbers flowing at modest Reynolds numbers, the mass transfer boundary layers are very thin.
FoP good exchange efficiency the fluid passages must be narrow (leading to high
hydrodynamic resistance), or conditions must be created to agitate or disperse the mass transfer boundary layer in wider passages.
Examples of such mass transfer devices are
blood oxygenatoPs which incorporate membranes to separate blood from the gases used fop ventilation.
The dominant resistance to oxygen transfer is the diffusion layer in the
blood, and this has led to various attempts to reduce its resistance by creating secondary motions using e.g. coiled tubes (I,2), oscillation of toroidal tubes (3), and pulsatile flow over ribbed walls (4). Mass transfer results reported here have been measured in annuli which were built with longitudinal splines or grooves on both inner and outer tube surfaces bounding the annulus, using microporous teflon tubing with appropriate extruded cross-sections.
Axial twisting
of the tubes makes the splines helical and generates swirl in the annulus, which is yet another method to create secondary motions.
The pores in the teflon are small - 5~ or less -
and, with modest transmural pressures, surface tension seems adequate to prevent transmission of water or plasma.
The microporous teflon was available as extruded tubes,
the larger diameter tube having 8 splines on its inner surface, Fig. l(a), and the smaller diameter tube having a six-lobed star as its outer surface cross-section, Fig. l(b), the smaller tube fitting easily into the larger tube.
445
The tubes could be considered equally
446
P.D. Richardson, et al.
0
Vol. 2, No. 6
b
C
C7
FIG. 1 Construction of annuli. (a) Outer tube: OD 9.6ram, ID 6.35mm, ID at groove r o o t 8.0ram (b) 6-splined inner tube: OD 5.4ram, OD at spline root 3.Smm, ID 2.6ram (c) 8-splined inner tube: OD 5.9ram, OD at spline Poor 4.3ram (d) Assembly of annulus; inner tube shown twisted, arrows show entr,y and exit ports for liquid flow through annulus. Other parts are for gas flows through inside of inner tube and over outside of outer tube.
well as having the corresponding number of grooves.
The microporous teflon has unusual
mechanical properties, accepting large compressive strains without much change of macroscopic dimensions.
By twisting the tubes, Fig. l(a) - (b), around their axes and fitting
one inside the other it is possible to create annular passages with swirl.
This is similar
to the technique used by Seban and Hunsbedt (5) in heat transfer devices to increase convective transfer rates, except that here swirl-generating ribs were incorporated on both inner and outer walls, and were also contiguous with the walls so that the surfaces were available for mass transfer as well as for generating swirl.
In this way the ribs were
mass-t-~ansfer analogs of fins. A set of units was built each having a single annulus, Fig. l(d).
The annular space
was used for the flow of water or of blood, flows through ports being indicated by arrows
Vol. 2, No. 6
MASS TRANSFER INAI%R~]LI
447
on Fig. l(d), while the inside of the inner tube and the outside of the outer tube were ventilated with puree oxygen.
These units were built with varying degrees of axial twist of
the outer and inner splined tubes, as described in Table i. TABLE 1 Geometry of Annular Units Unit
Le
No.
cm
A cm
Configuration 2
Inner tube
Outer tube
I
29.5
132
straight
s t~aight
2
25.1
112
straight
straight
3
25.1
112
straight
straight
4
24.5
109
straight
2 turns
5
29.5
132
2 turns
2 countel--tuPns
6
24.5
109
4 turns
2 counter-turns
7
24.5
109
8 turns
2 counter-turns
8
24.5
109
8 turns
2 co-turns
9
29.8
8520
~8 turns (av.)
2 counter-Tulals (av.)
In addition, one unit (No. 9 in Table I) was built with 60 annuli in pamallel, following the general form also of FiE. l(d), with the assembly being mounted in a lucite shell, using 1/4 inch diameter side ports for the water or blood access.
However, in this unit
the inner tubes had eight splines on their inner circumference, FiE. l(c).
The outer
tubes were twisted about their axes with a pitch of approximately 6 inches, and the inner tubes were twisted in the opposite direction.
In all cases, the liquid-side sumface areas
(required for calculatinE %-eansfer coefficients) were estimated by sectioning sample tubes, photographing them on a ruled ground and measuming their profiles by projection at great magnification. Methods All units were tested to determine gas teansfeP coefficients for 02 and CO 2 in water passing through them: reser-~oiP.
degassed water, cambomated to about pCO 2 = 60 mmHg, flowed fTom a
Input and output water samples were taken fop electrometric determination of
pO 2 and pCO 2 and the flow rate was found by timed collection:(6) gives more details.
In
vivo testing of gas exchange with blood fop the 60-annulus unit was performed with a chlomolose-anesthetised sheep on veno-arterial partial bypass (7). Results Results plotted as average transfer coefficients obtained from water testing ape shown in Fig. 2 as functions of Reynolds number, the characteristic distance in the latter being the hydmaulic diameter.
The average %-eansfer coefficients can be converted
to Sherwood numbems by use of the hydraulic diameter, 0.98ram for No. 1 through 8 and
448
P.D. Richardson, et al.
Vol. 2, No. 6
:3
U
BQ e
tt
e
Uco2
Q
Q
÷
•
13
I:1
10-3
~
e
f
+
!
3
10-4
4~ D
e~
8
Uo~ 3
+
•
Q ÷
Re-10-5
30
0
3
I00
FIG. 2 Gas transfer coefficients, ml STPD/cm 2 sec arm, for water flow in micPopoPous annuli. Solid circles: straight-splined annuli, units i, 2 and 3. +, unit 4. x, unit 5. , unit 6. ~ , unit 7. O , unit 8.
0.56ram for No. 9, and values of diffusivity (in water) of 2.07 x 10 .5 cm2/sec for 02 and 1.77 x 10 -5 cm2/sec for CO 2 at 20
C.
Certain features of the results for the sinEle-annulus units ape worthy of comment: (i) The transfer coefficient U increases approximately as Re 0"5 for both 02 and C02, a result typical of diffusion at larEe Sc in a laminar boundary layer flow. of twistinE the splined tubes on values of U02 is small but perceptible:
(2) The effect the value of
U02/Re 0"5 for st-eaiEht splined annuli is (8.16 + 1.73) x 10-6 ml 02 STPD/cm 2 sec a~n (mean +- standard deviation) while that for all units with counter-twisted tubes is (8.82 -+ i.~6) x 10 -6 .
(3) The effect of twistinE the splined tubes shows itself more
stronEly in the values fop UCO 2.
The averaEe value of UCo2/Re0" 5 fop straight splined
Vol. 2, No. 6
NI~SS TRANSFER IN ANNULI
449
annuli is (2.08 + 0.64) x 10 -4 ml CO 2 STPD/cm 2 sec arm, whereas t h a t f o r counter-twisted annuli is (2.55 + 0.49) x 10 -4 .
(q) The effect on transfer rates of counter-twisting is
higher than that of co-twisting:
a counter-twisted unit gave Uo2/Re0"5 of 9.42 -+ 0.i0 x 10-6
and a UCO2/Re 0"5 of 3.05 -+ 0.17 x 10 -4 , whereas for the same unit co-twisted the cox~-esponding values were 8.82 -+ 0.55 x i0 -5 and 2.g6 + 0.32 x 10 -4 respectively.
(5) The pitch
ratios - pitch length divided by tube diameter - were limited by the flexibility of the tubing
(the outer tube began to collapse with pitches shorter than 5 inches).
Results from testing the 60-pamallel annulus unit with water also show that: increases approximately as Re 0"5.
(i) U
(2) The average value of UO2/Re 0"5 was (11.5 + 0.9)
x 10 -6 ml 02 STPD/cm 2 sec arm, and of UCO2/Re0'5 was (2.87 + 0.58) x 10 -4 .
These values
are higher than fox" single-annulus units ; the inner tubes for the 50-tube unit had mope grooves (8 instead of 6) ape fitted more tightly in the outer tubes than the single annulus units.
Both features ape likely to increase transfer rates.
from testing this unit with blood.
Fig. 3 shows results
The "rated flow" (blood output saturation 95% with
input saturation 65%) was about 250 ml/min, corresponding to 0.33 L/m 2 min.
This per-
formance level as a blood oxygenator is only about half that of a high-performance design , e.g. the Dow EDO type achieves about 0.67 L/m 2, though at the price of a much higher pressure drop - typically ii0 - 145 mmHg c o ~ a r e d with less than 5 mmHg for the annulus. Discussion Mass transfer data for annuli built in a new configumatlon with longitudinal splines or grooves on both inner and outer tubes show that axial twisting enhances transfer to high Schmidt n u ~ e r liquids in laminar flow, counter-twisting being more effective than cotwisting.
This latter observation may be a consequence of stronger secondary flows.
The
augmentation of mass transfer at the degrees of twist achieved is of the same order as Peached in (5) with similar twist.
The liquid flow pattern in the twisted annular sectors,
at least when co-twisted, is probably somewhat similar (in terme of generating a secondary flow pattern via centrifugal forces) to Dean flows.
With the long pitch of the helix,
the effective coiling ratio is large and the coiling effects small.
The peculiar mechanical
properties of microporous tubing allow helical coils to be made with coiling ratios as small as 4 (2). secondary motion.
These achieve a ETeater level of augmentation of mass transfer by Configurations other than the twisted splined annulus can provide a
more economic deployment of microporous membrane material while keeping the hydraulic resistance small. Acknowledgements W. L. Gore Associates very kindly placed s a b l e s of material at our disposal and built the 60-annulus unit.
This study was supported in part by Grant HL-IIg45 from the National
Heart and Lung Institute.
450
P.D. Richardson, et al.
Vol. 2, No. 6
I00 0
V ML/MIN
| |
50
I
|
S O
ZO
o
8
,o O @
MLIMIN
Qs 5 200
500
103
FIG. 3 Gas transfer rates, V, ml STPD/min, as a function of blood flow rate, % , ml/min, in mica~porous twisted splined annuli, unit no. 9. Open circles: oxygen. Solid circles: eambon dioxide. References i.
W. J. Dorson and K. J. Lateen, Advances in Cardiology 6, 17 (1971).
2.
K. Tanishita, P. D. Richamdson and P. M. Galletti, Trans. Amer. Soc. Artificial Intemnal Organs 21, 215 (1975).
3.
R. A. Moss, J. A. Benn, P. K. Ghadar and P. A. Drinker, Adv. in Cardiology 6, W0 (1971).
4.
B. J. Bellhouse et al., Trans. Amer. Soc. Artificial Internal Organs 1_~9, 72 (1973).
5.
R. A. Seban and A. Hunsbedt, Int. J. Heat Mass Trans. 1_~6, 303 (1973).
6.
P. M. Galletti, P. D. Richamdson and M. T. Snider, Blood 0xygenator Testing and Evaluation, Part I. Evaluation Techniques, Rept NIH 69-20q7-1 (1971)'
7.
P. M. Galletti, P. D. Richar~Ison, M. T. Snider and L. I. Friedman, Trans. Amer. Soc. Artificial Internal Organs 18, 359 (1972).
I~~HEATANDMASSTRANSFER Vol. 2, 3 . 445 - 450, 1975
Printed in the United States
MASS TRANSFER IN ANNULI OF GROOVED OR SPLINED MICROPOROUS TUBING TWISTED TO GENERATE SWIRL
P. D. Richardson, K. Tanishita and P. M. Galletti Bmown University, Providence, Rhode Island 02912
(C~,~/nicated by J.P. Hartnett and W.J. Minkowycz) ABSTRACT Annuli have been built with longitudinal grooves or splines on both inner and outer tube surfaces, using microporous teflon tubing with appropriate extruded crosssections. Axial twisting of the tubes (which makes the splines helical) gave enhanced mass transfer, counter~twisting being more effective than co-twisting. Introduction In mass transfer devices which handle diffusion processes in liquids having large Schmidt numbers flowing at modest Reynolds numbers, the mass transfer boundary layers are very thin.
FoP good exchange efficiency the fluid passages must be narrow (leading to high
hydrodynamic resistance), or conditions must be created to agitate or disperse the mass transfer boundary layer in wider passages.
Examples of such mass transfer devices are
blood oxygenatoPs which incorporate membranes to separate blood from the gases used fop ventilation.
The dominant resistance to oxygen transfer is the diffusion layer in the
blood, and this has led to various attempts to reduce its resistance by creating secondary motions using e.g. coiled tubes (I,2), oscillation of toroidal tubes (3), and pulsatile flow over ribbed walls (4). Mass transfer results reported here have been measured in annuli which were built with longitudinal splines or grooves on both inner and outer tube surfaces bounding the annulus, using microporous teflon tubing with appropriate extruded cross-sections.
Axial twisting
of the tubes makes the splines helical and generates swirl in the annulus, which is yet another method to create secondary motions.
The pores in the teflon are small - 5~ or less -
and, with modest transmural pressures, surface tension seems adequate to prevent transmission of water or plasma.
The microporous teflon was available as extruded tubes,
the larger diameter tube having 8 splines on its inner surface, Fig. l(a), and the smaller diameter tube having a six-lobed star as its outer surface cross-section, Fig. l(b), the smaller tube fitting easily into the larger tube.
445
The tubes could be considered equally
446
P.D. Richardson, et al.
0
Vol. 2, No. 6
b
C
C7
FIG. 1 Construction of annuli. (a) Outer tube: OD 9.6ram, ID 6.35mm, ID at groove r o o t 8.0ram (b) 6-splined inner tube: OD 5.4ram, OD at spline root 3.Smm, ID 2.6ram (c) 8-splined inner tube: OD 5.9ram, OD at spline Poor 4.3ram (d) Assembly of annulus; inner tube shown twisted, arrows show entr,y and exit ports for liquid flow through annulus. Other parts are for gas flows through inside of inner tube and over outside of outer tube.
well as having the corresponding number of grooves.
The microporous teflon has unusual
mechanical properties, accepting large compressive strains without much change of macroscopic dimensions.
By twisting the tubes, Fig. l(a) - (b), around their axes and fitting
one inside the other it is possible to create annular passages with swirl.
This is similar
to the technique used by Seban and Hunsbedt (5) in heat transfer devices to increase convective transfer rates, except that here swirl-generating ribs were incorporated on both inner and outer walls, and were also contiguous with the walls so that the surfaces were available for mass transfer as well as for generating swirl.
In this way the ribs were
mass-t-~ansfer analogs of fins. A set of units was built each having a single annulus, Fig. l(d).
The annular space
was used for the flow of water or of blood, flows through ports being indicated by arrows
Vol. 2, No. 6
MASS TRANSFER INAI%R~]LI
447
on Fig. l(d), while the inside of the inner tube and the outside of the outer tube were ventilated with puree oxygen.
These units were built with varying degrees of axial twist of
the outer and inner splined tubes, as described in Table i. TABLE 1 Geometry of Annular Units Unit
Le
No.
cm
A cm
Configuration 2
Inner tube
Outer tube
I
29.5
132
straight
s t~aight
2
25.1
112
straight
straight
3
25.1
112
straight
straight
4
24.5
109
straight
2 turns
5
29.5
132
2 turns
2 countel--tuPns
6
24.5
109
4 turns
2 counter-turns
7
24.5
109
8 turns
2 counter-turns
8
24.5
109
8 turns
2 co-turns
9
29.8
8520
~8 turns (av.)
2 counter-Tulals (av.)
In addition, one unit (No. 9 in Table I) was built with 60 annuli in pamallel, following the general form also of FiE. l(d), with the assembly being mounted in a lucite shell, using 1/4 inch diameter side ports for the water or blood access.
However, in this unit
the inner tubes had eight splines on their inner circumference, FiE. l(c).
The outer
tubes were twisted about their axes with a pitch of approximately 6 inches, and the inner tubes were twisted in the opposite direction.
In all cases, the liquid-side sumface areas
(required for calculatinE %-eansfer coefficients) were estimated by sectioning sample tubes, photographing them on a ruled ground and measuming their profiles by projection at great magnification. Methods All units were tested to determine gas teansfeP coefficients for 02 and CO 2 in water passing through them: reser-~oiP.
degassed water, cambomated to about pCO 2 = 60 mmHg, flowed fTom a
Input and output water samples were taken fop electrometric determination of
pO 2 and pCO 2 and the flow rate was found by timed collection:(6) gives more details.
In
vivo testing of gas exchange with blood fop the 60-annulus unit was performed with a chlomolose-anesthetised sheep on veno-arterial partial bypass (7). Results Results plotted as average transfer coefficients obtained from water testing ape shown in Fig. 2 as functions of Reynolds number, the characteristic distance in the latter being the hydmaulic diameter.
The average %-eansfer coefficients can be converted
to Sherwood numbems by use of the hydraulic diameter, 0.98ram for No. 1 through 8 and
448
P.D. Richardson, et al.
Vol. 2, No. 6
:3
U
BQ e
tt
e
Uco2
Q
Q
÷
•
13
I:1
10-3
~
e
f
+
!
3
10-4
4~ D
e~
8
Uo~ 3
+
•
Q ÷
Re-10-5
30
0
3
I00
FIG. 2 Gas transfer coefficients, ml STPD/cm 2 sec arm, for water flow in micPopoPous annuli. Solid circles: straight-splined annuli, units i, 2 and 3. +, unit 4. x, unit 5. , unit 6. ~ , unit 7. O , unit 8.
0.56ram for No. 9, and values of diffusivity (in water) of 2.07 x 10 .5 cm2/sec for 02 and 1.77 x 10 -5 cm2/sec for CO 2 at 20
C.
Certain features of the results for the sinEle-annulus units ape worthy of comment: (i) The transfer coefficient U increases approximately as Re 0"5 for both 02 and C02, a result typical of diffusion at larEe Sc in a laminar boundary layer flow. of twistinE the splined tubes on values of U02 is small but perceptible:
(2) The effect the value of
U02/Re 0"5 for st-eaiEht splined annuli is (8.16 + 1.73) x 10-6 ml 02 STPD/cm 2 sec a~n (mean +- standard deviation) while that for all units with counter-twisted tubes is (8.82 -+ i.~6) x 10 -6 .
(3) The effect of twistinE the splined tubes shows itself more
stronEly in the values fop UCO 2.
The averaEe value of UCo2/Re0" 5 fop straight splined
Vol. 2, No. 6
NI~SS TRANSFER IN ANNULI
449
annuli is (2.08 + 0.64) x 10 -4 ml CO 2 STPD/cm 2 sec arm, whereas t h a t f o r counter-twisted annuli is (2.55 + 0.49) x 10 -4 .
(q) The effect on transfer rates of counter-twisting is
higher than that of co-twisting:
a counter-twisted unit gave Uo2/Re0"5 of 9.42 -+ 0.i0 x 10-6
and a UCO2/Re 0"5 of 3.05 -+ 0.17 x 10 -4 , whereas for the same unit co-twisted the cox~-esponding values were 8.82 -+ 0.55 x i0 -5 and 2.g6 + 0.32 x 10 -4 respectively.
(5) The pitch
ratios - pitch length divided by tube diameter - were limited by the flexibility of the tubing
(the outer tube began to collapse with pitches shorter than 5 inches).
Results from testing the 60-pamallel annulus unit with water also show that: increases approximately as Re 0"5.
(i) U
(2) The average value of UO2/Re 0"5 was (11.5 + 0.9)
x 10 -6 ml 02 STPD/cm 2 sec arm, and of UCO2/Re0'5 was (2.87 + 0.58) x 10 -4 .
These values
are higher than fox" single-annulus units ; the inner tubes for the 50-tube unit had mope grooves (8 instead of 6) ape fitted more tightly in the outer tubes than the single annulus units.
Both features ape likely to increase transfer rates.
from testing this unit with blood.
Fig. 3 shows results
The "rated flow" (blood output saturation 95% with
input saturation 65%) was about 250 ml/min, corresponding to 0.33 L/m 2 min.
This per-
formance level as a blood oxygenator is only about half that of a high-performance design , e.g. the Dow EDO type achieves about 0.67 L/m 2, though at the price of a much higher pressure drop - typically ii0 - 145 mmHg c o ~ a r e d with less than 5 mmHg for the annulus. Discussion Mass transfer data for annuli built in a new configumatlon with longitudinal splines or grooves on both inner and outer tubes show that axial twisting enhances transfer to high Schmidt n u ~ e r liquids in laminar flow, counter-twisting being more effective than cotwisting.
This latter observation may be a consequence of stronger secondary flows.
The
augmentation of mass transfer at the degrees of twist achieved is of the same order as Peached in (5) with similar twist.
The liquid flow pattern in the twisted annular sectors,
at least when co-twisted, is probably somewhat similar (in terme of generating a secondary flow pattern via centrifugal forces) to Dean flows.
With the long pitch of the helix,
the effective coiling ratio is large and the coiling effects small.
The peculiar mechanical
properties of microporous tubing allow helical coils to be made with coiling ratios as small as 4 (2). secondary motion.
These achieve a ETeater level of augmentation of mass transfer by Configurations other than the twisted splined annulus can provide a
more economic deployment of microporous membrane material while keeping the hydraulic resistance small. Acknowledgements W. L. Gore Associates very kindly placed s a b l e s of material at our disposal and built the 60-annulus unit.
This study was supported in part by Grant HL-IIg45 from the National
Heart and Lung Institute.
450
P.D. Richardson, et al.
Vol. 2, No. 6
I00 0
V ML/MIN
| |
50
I
|
S O
ZO
o
8
,o O @
MLIMIN
Qs 5 200
500
103
FIG. 3 Gas transfer rates, V, ml STPD/min, as a function of blood flow rate, % , ml/min, in mica~porous twisted splined annuli, unit no. 9. Open circles: oxygen. Solid circles: eambon dioxide. References i.
W. J. Dorson and K. J. Lateen, Advances in Cardiology 6, 17 (1971).
2.
K. Tanishita, P. D. Richamdson and P. M. Galletti, Trans. Amer. Soc. Artificial Intemnal Organs 21, 215 (1975).
3.
R. A. Moss, J. A. Benn, P. K. Ghadar and P. A. Drinker, Adv. in Cardiology 6, W0 (1971).
4.
B. J. Bellhouse et al., Trans. Amer. Soc. Artificial Internal Organs 1_~9, 72 (1973).
5.
R. A. Seban and A. Hunsbedt, Int. J. Heat Mass Trans. 1_~6, 303 (1973).
6.
P. M. Galletti, P. D. Richamdson and M. T. Snider, Blood 0xygenator Testing and Evaluation, Part I. Evaluation Techniques, Rept NIH 69-20q7-1 (1971)'
7.
P. M. Galletti, P. D. Richar~Ison, M. T. Snider and L. I. Friedman, Trans. Amer. Soc. Artificial Internal Organs 18, 359 (1972).