Increasing interest has been give to swirl brakes as a means of reducing destabilizing rotordynamic forces due to leakage flows in new high speed rocket turbopumps.  Although swirl brakes have been used successfully in practice (such as with the Space Shuttle HPOTP), no experimental test until now have been performed to demonstrate their beneficial effect over a range of leakage flow rates.  The present study investigates the effect of swirl brakes on rotordynamic forces generated by discharge-to-suction leakage flows in the annulus of shrouded centrifugal pumps over a range of subsynchronous whirl ratios and various leakage flow rates.  In addition, the effectiveness of swirl brakes in the presence of leakage inlet (pump discharge) swirl is also demonstrated.  The experimental data demonstrates that with the addition of swirl brakes a significant reduction in the destabilizing tangential force for lower flow rates is achieved.  At higher flow rates, the brakes are detrimental.  In the presence of leakage inlet swirl, brakes were effective over all leakage flow rates tested in reducing the range of whirl frequency ratio for which the tangential force is destabilizing

Acosta, Allan J.

Brennen, Christopher E.

Caughey, Thomas K.

Sivo, Joseph M.

English

Caltech Authors - Main

FED-Vol. 154, Pumping Machinery 
ASME 1993 
THE INFLUENCE OF SWIRL BRAKES ON THE ROTORDYNAMIC 
FORCES GENERATED BY DISCHARGE-TO-SUCTION LEAKAGE 
FLOWS 1N CENTRIFUGAL PUMPS 
Joseph M. Sivo, Allan J. Acosta, 
Christopher E. Brennen, and Thomas K. Caughey 
Department of Mechanical Engineering 
California Institute of Technology 
Pasadena, California 
ABSTRACT 
Increasing interest has been given to swirl brakes as 
a means of reducing destabilizing rotordynarnic forces 
due to leakage flows in new high speed rocket tur- 
bopumps. Although swirl brakes have been used suc- 
cessfully in practice (such as with the Space Shuttle 
HPOTP), no experimental tests until now have been 
performed to demonstrate their beneficial effect over a 
range of leakage flow rates. The present study investi- 
gates the effect of swirl brakes on rotordynarnic forces 
generated by discharge-to-suction leakage flows in the 
annulus of shrouded centrifugal pumps over a range of 
subsynchronous whirl ratios and various leakage flow 
rates. In addition, the effectiveness of swirl brakes in 
the presence of leakage inlet (pump discharge) swirl 
is also demonstrated. The experimental data demon- 
strates that with the addition of swirl brakes a signifi- 
cant reduction in the destabilizing tangential force for 
lower flow rates is achieved. At higher flow rates, the 
brakes are detrimental. In the presence of leakage inlet 
swirl, brakes were effective over all leakage flow rates 
tested in reducing the range of whirl frequency ratio for 
which the tangential force is destabilizing. 
NOMENCLATURE 
[A*] Rotordynamic force matrix 
B Depth of logarithmic spiral channel on swirl 
vane 
c Cross-coupled damping coefficient, 
normalized by p?rw2 R2 Le 
C Direct damping coefficient, normalized by 
p ? r ~ 2 ~ 2 2  LC 
Lateral horizontal force in the laboratory 
frame 
Lateral vertical force in the laboratory frame 
Steady horizontal force 
Steady vertical force 
Force normal to whirl orbit 
Force normal to  whirl orbit normalized by 
p m 2  ~2~ Le 
Force tangent to whirl orbit 
Force tangent to whirl orbit normalized by 
p?rw2 R~~ LC 
Lateral forces in rotating frame 
Clearance between impeller shroud and 
housing 
Crosscoupled stiffness coefficient normalized 
by pnw2R22 LE 
Direct stiffness coefficient normalized by 
pnw2 R~~ LE 
Axial length of impeller 
Direct added mass coefficient normalized by 
p . m 2  R~~ LE 
Volumetric leakage flow rate 
Radius of impeller at  leakage inlet 
Mean leakage inlet path velocity of fluid 
Mean leakage inlet swirl velocity of fluid 
Horizontal displacement of impeller on its 
orbit 
Vertical displacement of impeller on its orbit 
Turning angle of logarithmic spiral channel 
on swirl vane 
Leakage inlet swirl ratio, u e / w R a  
Eccentricity of impeller's circular whirl orbit 
Density of leakage fluid 
Leakage flow coefficient, u, /w  Rz 
Main shaft radian frequency 
Whirl radian frequency 
INTRODUCTION 
Previous experimental and analytical results have 
shown that discharge-to-suction leakage flows in the an- 
nulus of a shrouded centrifugal pump contribute sub- 
stantially to the fluid induced rotordynamic forces (Ad- 
kins, 1988). Experiments conducted in the Rotor Force 
Test Facility (RFTF) at Caltech on an impeller un- 
dergoing a prescribed whirl have indicated that the 
leakage flow contribution to the normal and tangential 
forces can be as much as 70% and 30% of the total, re- 
spectively (Jery, 1986). Recent experiments at  Caltech 
have examined the rotordynamic consequences of leak- 
age flows and have shown that the rotordynamic forces 
are functions not only of the whirl ratio but also of 
the leakage flow rate and the impeller shroud to pump 
housing clearance. The forces were found to be in- 
versely proportional to the clearance and a region of 
forward subsynchronous whirl was found for which the 
average tangential force was destabilizing. This region 
decreased with flow coefficient (Guinzburg, 1992a). 
The motivation for the present research is that 
the previous experiments have shown that leakage inlet 
(pump discharge) swirl can increase the cross-coupled 
stiffness coefficient (in some tests by over 100%) and 
hence increase the range of positive whirl for which the 
tangential force is destabilizing. One might therefore 
surmise that if the swirl velocity within the leakage 
path were reduced, then the destabilizing tangential 
force might be reduced. One way of reducing the leak- 
age flow swirl is with the use of ribs or swirl brakes on 
the housing. In fact, swirl brakes installed upstream of 
the interstage seal on the Space Shuttle Main Engine 
High Pressure Oxygen Turbopump completely elimi- 
nated the subsynchronous whirl motion over the steady 
state operating range of the unit (Childs, 1990). The 
present study investigates the influence of swirl brakes 
on the rotordynamic forces generated by discharge-to- 
suction leakage flows in shrouded centrifugal pumps 
over a range of subsynchronous whirl ratios and various 
leakage flow rates typical of present rocket turbopump 
designs. In addition, the effectiveness of swirl brakes in 
the presence of leakage inlet (pump discharge) swirl is 
also demonstrated. 
ROTORDYNAMIC FORCES 
Figure (1) shows a schematic of the hydrodynamic 
forces that act on a rotating impeller whirling in a cir- 
cular orbit. F*, and F* are the instantaneous lateral 
forces in the laboratory frame. C? is the whirl radian fre- 
quency and w is the main shaft radian frequency. The 
eccentricity of the orbit is given by E .  The lateral forces 
are given in linear form as: 
F,*, and F,; are the steady forces which result from 
flow asymmetries in the volute. [A*] is the rotordy- 
namic force matrix. It is a function of the mean flow 
conditions, pump geometry, whirl frequency ratio R/w 
and if outside the linear range it may also be a func- 
tion of the eccentricity E. In the case of a circular whirl 
orbit: 
x*(t) = ~cos(C?t) (2) 
y*(t) = ~sin(C?t) (3) 
The normal and tangential forces for a circular whirl 
orbit are given by (Jery, 1986 and Ranz 1989): 
ROTORDYNAMIC COEFFICIENTS 
AND STABILITY 
To study the stability of an impeller, it is conve- 
nient for rotordynamicists to fit the dimensionless nor- 
mal force Fn to a quadratic function of the whirl ratio 
and to fit the dimensionless tangential force Ft to a 
linear function of the whirl ratio. The expressions are 
given by: 
CIRCULAR 
WHIRL ORBIT 
FIGURE 1. SCHEMATIC OF THE FLUID-INDUCED 
FORCES ACTING ON AN IMPELLER WHIRLING IN A CIR- 
CULAR ORBIT. 
SEAL RING -J ROTATING SHROUD 
FIGURE 2. LEAKAGE FLOW TEST SECTION (ZHUANG. 
1989). 
where the dimensionless coefficients are the direct 
added mass (M), direct damping (C), crosscoupled 
damping (c), direct stiffness (K), and cross-coupled 
stiffness (k). As can be seen from equation (7), a pos- 
itive cross-coupled stiffness is destabilizing because it 
starts the forward whirl of the impeller since it is equal 
to the tangential force at zero whirl ratio. Also, from 
equation (6), a large negative direct stiffness is destabi- 
lizing because it promotes a positive normal force which 
increases the eccentricity of the whirl orbit. 
A convenient measure of the rotordynamic stability 
is the ratio of the cross-coupled stiffness to the direct 
damping (i.e. k /C)  termed the whirl ratio. This is just 
a measure of the range of positive whirl frequency ratios 
for which the tangential force is destabilizing. 
TEST APPARATUS 
The present experiments were conducted in the Ro- 
tor Force Test Facility (RFTF) at Caltech. The leakage 
flow test section of the facility is shown in Figure (2). 
The working fluid is water. The main components 
of the test section apparatus consist of a solid or dummy 
impeller (or rotating shroud), a housing (or stationary 
shroud) instrumented for pressure measurements, a ro- 
tating dynamometer (or internal force balance), an ec- 
centric whirl mechanism (not shown), a leakage exit seal 
ring and a leakage inlet swirl vane (shown installed in 
Figure (3)). The solid impeller is used so that leakage 
flow contributions to the forces are measured but the 
main through flow contributions are not experienced. 
The inner surface of the housing has been modified to 
accommodate meridional ribs or swirl brakes along the 
entire length of the leakage annulus. The ribs are each 
3/16 of an inch wide and 2 rnm high. Up to 8 equally 
spaced ribs can be installed. The leakage flow annulus 
between the impeller and housing is inclined at 45' to 
the axis of ratation. The nominal clearance between the 
solid impeller and the housing can be varied by axial ad- 
justment of the housing. The flow through the leakage 
path is generated by an auxiliary pump. The solid im- 
peller is mounted on a spindei attached to the rotating 
dynamometer connected to a data acquisition system 
which permits measurements of the rotordynamic force 
matrix. Jery, 1986 and Franz, 1989 describe the oper- 
ation of the dynamometer. The eccentric drive mecha- 
nism imposes a circular whirl orbit on the basic main 
shaft rotation. The radius of the circular whirl orbit (or 
eccentricity) can be varied. The seal ring at  the leak- 
age exit models a wear ring. The clearance between the 
seal ring and impeller face is adjustable. The effect of 
swirl was investigated by installing a swirl vane a t  the 
leakage inlet to introduce pre-rotated fluid in the direc- 
tion of shaft rotation. Figure (3) shows that the vane 
consists of a logarithmic spiral channel with a turning 
angle of 2'. The swirl ratio I' (the ratio of the leakage 
flow circumferential velocity to the impeller tip veloc- 
ity) is varied by changing the leakage flow rate. The 
CH 
FOR 
FRONT VIEW SECTION A - A  
FIGURE 3. INSTALLATION OF LEAKAGE INLET SWIRL 
VANE. DIMENSIONS IN MM (GUINZBURG, 1992b). 
swirl ratio depends on the flow coefficient according to: 
B is the depth of the logarithmic spiral channel equal 
to 0.125 in. A derivation of equation (8) can be found 
in Guinzburg, 1992a. 
TEST MATRIX 
This experiment is designed to measure the rotor- 
dynamic forces due to simulated leakage flows for dif- 
ferent parameters such as whirl frequency ratio, shaft 
speed, leakage flow coefficient, number of swirl brake 
ribs and leakage inlet swirl ratio. For all tests a nomi- 
nal annulus clearance H of 0.167 in, a whirl eccentricity 
E of 0.0465 in and a leakage exit face seal clearance 
of 0.04 in were maintained. Tests without leakage inlet 
swirl were conducted a t  shaft speeds w of 1000 and 2000 
RPM, leakage flow rates Q of 0, 10, 20 and 30 GPM 
and 0, 4 and 8 brake ribs. For the 1000 RPM runs, 
the above flow rates correspond to flow coefficients 4 of 
0.0, 0.026, 0.052 and 0.077, respectively. For the 2000 
RPM runs, the above flow rates correspond to flow co- 
efficients 4 of 0.0, 0.013, 0.026 and 0.039, repectively. 
The above flow coefficients cover the range of typical 
leakage rates for the new Space Shuttle Alternate Tur- 
bopump (ATP) presently being developed. For the 1000 
RPM runs, tests are performed for whirl frequency ra- 
tios in the range -0.9 5 5 5 +0.9 at 0.1 increments. 
For the 2000 RPM runs, tests are performed for whirl 
frequency ratios in the range -0.6 5 2 L +0.7 a t  0.1 
increments. Tests with the swirl vane installed are con- 
ducted at  a shaft speed of 2000 RPM and the same flow 
rates as above. With the swirl vane, the above leakage 
flow rates yield swirl ratios r of 0.0, 0.5, 1.0 and 1.5, 
respectively. The above test matrix is summarized in 
Tables 1 and 2. 
TABLE 1. TESTS WITHOUT SWIRL 
RPM R/w Brakes Q (GPM) 4 
TABLE 2. TESTS WITH SWIRL 
RPM Q/w Brakes Q (GPM) 4 I' 
RESULTS FOR TESTS WITHOUT LEAKAGE INLET 
SWIRL 
Figures (4) and (5) show plots of the dimensionless 
rotordynamic coefficients for 2000 and 1000 RPM, re- 
spectively for the three different number of brake ribs. 
Figures (6) and (7) show the whirl ratio. Tests are done 
at two different rotor speeds to access the Fteynolds 
Number effects. The 2000 RPM runs are shown first 
since they give the results at a lower flow coefficient 
range. A comparison of Figures (4) and (5) show dif- 
ferences between corresponding coefficient plots at the 
lower flow coefficients indicating that Reynolds Num- 
ber effects are important at low flow rates. At flow 
coefficients above about 0.03 there seems to be little dif- 
ference between corresponding coefficient plots at 1000 
and 2000 RPM. Reynolds Number effects are stronger 
with no brake ribs installed. C and k seem to have the 
greatest discrepencies between the 1000 and 2000 RPM 
runs. 
Focusing on the coefficients corresponding to the 
tangential force, we can see that with no brakes the 
tangential force decreases with increasing leakage flow 
rate, as was found previously by Guinzburg, (1992a). 
The cross-coupled stiffness coefficient, k, is decreased 
by increasing the flow from 0 to 30 GPM, and for the 
1000 RPM case, C remains essentially constant. Hence 
the range for which the tangential force is destabilizing, 
k/C, decreases with increasing flow rate. This can be 
seen in Figure (7). However, looking at k for the case 
with 4 or 8 brake ribs, the opposite trend with flow 
rate is observed. The crosscoupled stiffness increases 
as the flow rate increases from 0 to 30 GPM in both 
the 1000 and 2000 RPM runs. The above may appear 
to indicate that brakes are not beneficial. On the con- 
trary, although the destabilizing tangential force with 
brakes increases with flow rate, there is a flow rate be- 
low which the tangential force with brakes is less than 
the tangential force without brakes. From the k plots 
in Figures (4) and (5) we can see that below I$ = 0.025 
the cross-coupled stiffness coefficient is reduced by the 
addition of 4 or 8 brakes. 8 brakes are only marginally 
more effective than 4. The beneficial effect of brakes is 
better exemplified by looking at the whirl ratio plots in 
Figures (6) and (7). Below about I$ = 0.03, the range 
of destabilizing tangential force is much less with the 
addition of brakes. 
Focusing on the coefficients corresponding to the 
normal force, we can see that with no brakes, the nor- 
mal force increases with increasing leakage flow rate. K 
becomes more negative with increasing flow, hence in- 
creasing the normal force at zero whirl frequency and 
therfore is destabilizing. The same is true with 4 or 8 
brakes, but we can also see from K that the destabiliz- 
ing normal force is significantly reduced by the addition 
of brakes throughout the range of flow rates tested. 
FIGURE 4. ROTORDYNAMIC COEFFICIENTS AT 2000 
RPM, NO SWIRL. 
I ~ i b  w = 1000 rpm 1 + 4 ~ i i  e = 0.0465 in ( 
FIGURE 5. ROTORDYNAMIC COEFFICIENTS AT 1000 
RPM. NO SWIRL. 
[7 0 Ribs 
4 Ribs 
8 Ribs 
FIGURE 6. WHIRL RATIO AT 2000 RPM, NO SWIRL. 
FIGURE 7. WHIRL RATIO AT 1000 RPM, NO SWIRL. 
RESULTS FOR TESTS WlTH LEAKAGE INLET 
SWIRL 
Figure (8) shows plots of the dimensionless rotor- 
dynamic coefficients for the 2000 RPM runs with leak- 
age inlet swirl for the three different number of ribs. 
Figure (9) shows the whirl ratio. As was previously 
found by Guinzburg, (1992b), swirl dramatically in- 
creases the tangential force. This is evident by com- 
paring the plot of k without swirI from Figure (4) with 
the plot of k with swirl from Figure (8). Once again, 
with no brakes, it can be seen that as the leakage rate 
increases, the tangential forces decrease, even though in 
the process the swirl ratio is increased. The stabilizing 
effect of an increase in flow rate dominates the destabi- 
lizing effect of an increase in swirl ratio. When 4 or 8 
brake ribs are used, the opposite trend with flow rate is 
observed, as shown with the results without swirl. With 
brakes, the tangential force increases with flow rate and 
swirl ratio. But, for the entire flow range tested, the 
cross-coupled stiffness is decreased by the addition of 
brakes. 
Focusing on the coefficient K corresponding to the 
normal force, K is much large in the presence of swirl. 
We can see that with no brakes the normal force in- 
creases with increasing leakage flow rate. The same is 
true with 4 or 8 brakes, although from K, the destabiliz- 
ing normal force is significantly reduced by the addition 
of brakes throughout the range of flow rates tested. 
The most dramatic beneficial effect of brakes is 
found by comparing the whirl ratio plots for 4 or 8 
brakes without and with swirl, figures (6) and (9), re- 
spectively. The 4 or 8 brake runs with and without swirl 
are almost identical. This indicates that the brakes al- 
most completely eliminated the effect of swirl. With 
brakes present, swirl produces only a slight increase in 
the range for which the tangential force is destabilizing. 
Also, looking at Figure (9), for all flow rates tested, the 
addition of brakes reduces the range for which the tan- 
gential force is destabilizing. 
"'m 
0 Ribs 6l = 2000 rpm 
+ 4 Ribs E = 0.0465 in 
FIGURE 8. ROTORDYNAMIC COEFFICIENTS AT 2000 
RPM WlTH SWIRL. 
0 0 Ribs 
4 Ribs 
I 8 Ribs 
FIGURE 9. WHIRL RATIO AT 2000 RPM WITH SWIRL. 
CONCLUSIONS 
The influence of swirl brakes on the rotordynamic 
forces generated by discharge-to-suction leakage flows 
in centrifugal pumps with and without leakage inlet 
swirl has been investigated. The destabilizing normal 
force at zero whirl is reduced by the addition of brakes. 
The tangential force and the range of whirl frequency 
ratios for which the tangential force is destabilizing is 
reduced by the addition of brakes for low leakage flow 
rates. Brakes are beneficial in reducing the tangential 
force up to a higher leakage flow rate in the presence of 
leakage inlet swirl. Finally, the increase in the range of 
whirl frequency ratios for which the tangential force is 
destabilizing due to an increase in the leakage inlet swirl 
is nearly eliminated by the addition of swirl brakes. 
ACKNOWLEDGEMENTS 
The assistance provided by Asif K h a m  and Kyh 
Roof with the experimental program is greatly appre- 
ciated. We would also like to thank the NASA George 
Marshall Space Flight Center for support under Grant 
NAG8-118 and technical monitor Henry Stinson. 
Childs, D. W., Baskharone, E. and Ramsey, C., 1990, 
Test Results for Rotordynamic Coefficients of the 
SSME HPOTP Turbine Interstage Seal with Two Swirl 
Brakes, 7 h . n ~  of ASME, Journal of aibology, 90-nib- 
45. 
Franz, R. J., 1989, Experimental Investigation of the 
Effect of Cavitation on the Rotordynamic Forces on 
a Whirling Centrifugal Pump Impeller, Ph.D. Thesis, 
California Institute of Technology. 
Guinzburg, A., 1992a, Rotordynamic Forces Generated 
By Discharge-To-Suction Leakage Flows in Centrifugal 
Pumps, Ph.D. Thesis, California Institute of Technol- 
O D .  
Guinzburg, A., 1992b, The Effect of Inlet Swirl on the 
Rotordynamic Shroud Forces in a Centrifugal Pump, 
ASME Paper 92-GT-126. 
Jery, B., 1986, Experimental Study of Unsteady Hydro- 
dynamic Force Matrices on Whirling Centrifugal Pump 
Impellers, Ph.D. Thesis, California Institute of Tech- 
nology. 
Zhuang, F., 1989, Experimental Investigation of the 
Hydrodynamic Forces on the Shroud of a Centrifugal 
Pump Impeller, E249.9, Division of Engineering and 
Applied Science, California Institute of Technology. 
REFERENCES 
Adkins, D. R. and Brennen, C. E., 1988, Analysis of 
Hydrodynamic Radial Forces on Centrifugal Pump Im- 
pellers, ASME J. Fluids Eng., Vol. 110, No. 1, pp. 


The Influence of Swirl Brakes on the Rotordynamic Forces Generated by Discharge-to-Suction Leakage Flows in Centrifugal Pumps

Adkins, D. R. and Brennen, C. E., 1988, Analysis of Hydrodynamic Radial Forces on Centrifugal Pump Impellers, ASME J. Fluids Eng., Vol. 110, No. 1, pp.

Analysis of Hydrodynamic Radial Forces on Centrifugal Pump Impellers,

http://authors.library.caltech.edu/147/1/SIV131.pdf

The Influence of Swirl Brakes on the Rotordynamic Forces Generated by Discharge-to-Suction Leakage Flows in Centrifugal Pumps

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