Study of Flow and Sizing of an Air Blocker for use in Bearing
Compartment Scavenge
by
Reade William James
A Thesis Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the degree of
MASTER OF ENGINEERING IN MECHANICAL ENGINEERING
Approved:
_________________________________________
Ernesto Gutierrez, Project Adviser
Rensselaer Polytechnic Institute
Troy, New York
Month, 2013
(For Graduation Month 2013)
© Copyright 2013
by
Reade William James
All Rights Reserved
ii
CONTENTS
LIST OF FIGURES .......................................................................................................... iv
ACKNOWLEDGMENT ................................................................................................... v
ABSTRACT ..................................................................................................................... vi
Introduction/Background ................................................................................................... 1
Problem Description .......................................................................................................... 2
Methodology/Approach ..................................................................................................... 4
Results................................................................................................................................ 8
Conclusions...................................................................................................................... 18
References........................................................................................................................ 20
Appendix.......................................................................................................................... 21
iii
LIST OF FIGURES
Figure 1: Rotating Cavity Oil Egress................................................................................. 3
Figure 2: Boundary Conditions ......................................................................................... 5
Figure 3: Obstruction ......................................................................................................... 5
Figure 4: Grid .................................................................................................................... 6
Figure 5: Twenty Percent of the Channel Obstructed - Fortran ........................................ 8
Figure 6: Twenty Percent of the Channel Obstructed - COMSOL ................................... 9
Figure 7: Pressure Profile for Twenty Percent of the Channel Obstructed ....................... 9
Figure 8: Forty Percent of the Flow Passage Obstructed - Fortran ................................. 10
Figure 9: Forty Percent of the Flow Passage Obstructed - COMSOL ............................ 10
Figure 10: Pressure Profile for Forty Percent of the Flow Passage Obstructed .............. 11
Figure 11: Sixty Percent of the Channel Obstructed - Fortran ........................................ 12
Figure 12: Sixty Percent of the Channel Obstructed - COMSOL ................................... 12
Figure 13: Pressure Profile for Sixty Percent of the Channel Obstructed ....................... 13
Figure 14: Eighty Percent of the Channel Obstructed - Fortran ...................................... 14
Figure 15: Eighty Percent of the Channel Obstructed - COMSOL ................................. 14
Figure 16: Pressure Profile for Eighty Percent of the Channel Obstructed ..................... 15
Figure 17: Ninety Percent of the Channel Obstructed - Fortran ...................................... 16
Figure 18: Pressure Profile for Ninety Percent of the Channel Obstructed ..................... 17
Figure 19: Entrance Pressure Profile for Ninety Percent of the Channel Obstructed ..... 17
iv
ACKNOWLEDGMENT
v
ABSTRACT
Turbomachine bearing compartments typically have a rotating shaft within a
static outer compartment wall. Lubricating and cooling oil is introduced into the
compartment at specific locations, and after lubricating and gaining heat, the oil is
scavenged out of the bottom of the compartment. The rotating air in the compartment
tends to drive a standing wave up the downwind side of the compartment, away from the
scavenge or drain port. To manage this, a blocker is introduced and the oil is collected in
the recirculation zone downwind. In this project we will develop a CFD code to do an
analysis of this blocker and investigate some design specifics. A model will also be
developed
in
COMSOL
as
a
point
vi
of
reference
and
comparison
Introduction/Background
Efficient oil management within a bearing compartment is important for several
reasons. Increased oil compartment residency time increases the amount of oil that is
required to run the engine as a whole and as a result increases oil tank size requirements
and impacts engine weight on the whole. Additionally the oil will churn while it is in the
compartment and that churning results in wasted energy and additional heat pickup in
the oil. Unnecessary heat pickup by the oil results in a need to increase oil cooler sizes,
which impacts the overall performance of the engine as well as again increasing engine
weight. Oil delivery in the compartment to the proper locations is a fairly
straightforward task, but once the oil has become entrained in what is sometimes rapidly
moving air, it can be difficult to get the oil back out in an efficient manner.
A patented strategy for efficient oil management is to use a windward blocker to
provide a relatively quiet spot to scavenge oil. Not only does the blocker reduce the air
velocity over the hole, but the recirculation zone that it creates has a tendency to pull the
oil back into the hole. With this scheme high scavenge efficiency can be achieved in
high velocity compartments.
1
Problem Description
A common configuration for a bearing compartment in turbomachinery is to have
a rotating inner wall such as a shaft, and a static outer wall. This configuration is of
course present for the main engine shafts, but will also show up in accessory gearboxes
and other locations. The rotation of the inner wall creates an air velocity profile
throughout the compartment or cavity. If the air is not calmed near the scavenge line, the
air will blow the oil up the downwind wall and form a wave there. This oil will not be
recoverable, which will add to the necessary size of the oil volume.
An intuitive solution to this issue would be to use a scoop and actively force oil
into the egress. In some configurations, this might be an advantageous solution. In a
compartment that is actively scavenged using a scavenge pump however, this solution
does not offer a benefit. The volumetric flow out of the compartment is defined by the
scavenge pump capacity itself and is not assisted with pressurization. Unless this scoop
manages to segregate the air/oil mixture that it is delivered, it does not offer a benefit.
Another solution to this problem is by adding an obstruction in the flow path,
with the egress location just downwind of this obstruction. This obstruction will create a
zone of low velocity downstream of the obstruction. This will reduce or eliminate the
standing wave. Additionally, if a recirculation zone forms, this configuration can trap oil
above the egress location. A description of this flow behavior can be seen in Figure 1.
The size of this blocker, and limitations are not well established and will be investigated
in this project.
2
Figure 1: Rotating Cavity Oil Egress
3
Methodology/Approach
The SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm
developed by Professor Brian Spalding and Suhas Patankar is used to solve the NavierStokes equations, using Fortran as the computer language and numerical solver. The
system is assumed to be a two dimensional, steady state, single phase flow problem.
Although the problem is by its nature dealing with two phases of air and oil, the amount
of oil is assumed to be small if the oil is being managed properly. COMSOL will also be
used to compare results.
The Fortran code developed by Peric and described in Computational Methods for
Fluid Dynamics was used as a starting point. The initial code used was for a lid driven
cavity.
The code developed by Peric is designed to work with a cartesian grid. Although
this leaves several options for grid optimization, the speed of the code and the relatively
low complexity of the problem means that an evenly spaced orthogonal grid is sufficient.
This simplification allows for more easily implementing the flow blocker as will be
discussed later.
There is no heat addition in any of the boundaries, and the entire system is assumed
to be isothermal. The south boundary is a static, no-slip boundary. There is a section
behind the obstruction that is used as the scavenge. This has a prescribed velocity out of
the bottom of the boundary. The north boundary was used to represent the rotating shaft.
It is a no-slip condition and is moving with a prescribed velocity from west to east. The
west boundary was altered to be a defined inlet velocity. The profile was assumed to be a
linearly increasing from zero at the bottom surface, to the shaft velocity at the top
surface. The east boundary is our outflow boundary. The velocity is calculated, and then
afterwards the entire velocity profile is multiplied by a correction factor that ensures that
the mass flow into the boundaries equals the mass flow out of the boundaries. This
correction factor has been modified from its original code to account for the mass flow
lost through the scavenge outlet on the south boundary.
4
Figure 2: Boundary Conditions
The obstruction itself is handled as described by XXXXX. As described earlier, the
grid is using an evenly spaced orthogonal grid. The obstruction itself is of rectangular
cross section, so representing it in the grid is straightforward. The velocities in both the
U and V direction are set to be zero at the grid points over the obstruction. This enforces
a no-slip condition for the obstruction itself.
Figure 3: Obstruction
The SIMPLE algorithm by making an initial guess at P, U, and V. The momentum
balances are solved to calculate U* and V* respectively. The pressures P* are solved for
5
from those conditions from the U* and V* values. The SIMPLE algorithm then uses a
correction for P, U, and V.
P=P*+P'
U=U*+U'
V=V*+V'
Finally the process is iterated until convergence is reached.
Grid Selection:
The algorithm developed by Peric and used for this problem is designed around a
colocated variable scheme. This means that the pressure and velocities are calculated at
the same locations on the grid. This can cause mathematical problems with the solution,
which caused it to fall out of favor, but Peric suggests ways to mitigate this (Peric p184).
An orthogonal grid was selected for use in this problem.
Figure 4: Grid
Several dimensions must be defined. This type of design can be used in many
applications, the one we will explore is intended as use for a drain. The depth of the
cavity is 0.006 meters, and the length that we will investigate is 0.4 meters. The
obstruction itself will be 0.1m in width, and the height will be varied to investigate the
size of the resulting recirculation zone.
Fluid Properties:
Properties for the air were pulled from www.engineeringtoolbox.com. The air was
assumed to be 120 degrees Celsius and of ambient pressure. The purpose of this exercise
6
is to understand the nature of the problem and determine some design principles, not to
explore a particular application. The temperature selected is one that might be typical of
many locations in a turbine engine. Sea level ambient pressures were assumed. The
resulting density, dynamic viscosity, and Prandtl number were used.
Temperature = 120C
Density = 0.898 kg/m3
Kinematic viscosity = 25.23E-6 m2/s
Pr = 0.70
7
Results
A solution for a blocker that obstructs twenty percent of the flow area is shown in
Figure 5. This shows no recirculation zone, which means that there will be no trap for
any entrained oil. It does result in a slight slowing of the flow on the downwind side of
the obstruction. With this lower velocity profile any downwind standing wave that forms
will be smaller, even though the oil segregating effects of the recirculation zone will not
be realized. It is not completely without merit if design constraints result in an
obstruction of this size, although improvements can be made.
Figure 5: Twenty Percent of the Channel Obstructed - Fortran
Repeating the analysis in COMSOL shows good agreement (Figure 6). The entrance
velocity profile for the COMSOL case is constant, so how the flow develops near the
entrance varies from the Fortran solution. The profile over the obstruction is similar, and
shows the lack of a recirculation zone.
8
Figure 6: Twenty Percent of the Channel Obstructed - COMSOL
The pressure profile for the Fortran based solution shows two things of importance. First
there is an increase in pressure as the flow leaves the inlet. This is the result of the
velocity at the inlet condition not matching it's unobstructed steady state profile. This
stabilizes by the 0.05 meter mark. Secondly at the 0.1 meter mark, the obstruction starts
and there is a total pressure loss across it of 0.15psi. This pressure profile can be seen in
Figure 7 below.
Figure 7: Pressure Profile for Twenty Percent of the Channel Obstructed
9
As the obstruction size is increased to forty percent of the flow area, a small
recirculation zone can be seen starting to form downwind of the obstruction. This can be
seen in Figure 8, where flow reversals are shown in red and flow in the same direction as
the bulk flow is shown in blue. The size of this recirculation zone is very small at
approximately 0.01meters.
Figure 8: Forty Percent of the Flow Passage Obstructed - Fortran
The analysis is repeated in COMSOL and shows good agreement (Figure 9). Again the
inlet profiles are different, so differences in the development of the flow prior to the
obstruction are expected. Behind the obstruction we see the narrow and tall recirculation
zone that the Fortran solution indicated.
Figure 9: Forty Percent of the Flow Passage Obstructed - COMSOL
The resulting pressure profile for the Fortran solution result at a forty percent obstruction
is shown in Figure 10. This profile shows similar features to the twenty percent, however
10
the pressure loss over the obstruction has increased to 0.7psi. This is to be expected since
the smaller available flow path above the obstruction is yielding higher velocities and
increasing the losses. Although this effect is still not very large, it will be something to
note since this will result in additional shaft work.
Figure 10: Pressure Profile for Forty Percent of the Flow Passage Obstructed
11
As the obstruction increases to sixty percent, the recirculation zone is growing as
expected. The depth of the recirculation zone had approximately doubled in size. In
addition, the height of the recirculation zone has grown along with the size of the
obstruction itself. This will be beneficial since the volume of oil that can be trapped here
will depend on this area of reversed flow.
Figure 11: Sixty Percent of the Channel Obstructed - Fortran
The solution in COMSOL shows good agreement again. The recirculation zone in the
COMSOL solution appears to be slightly larger. The grid density of the COMSOL
solution is larger, so some disagreement should be expected.
Figure 12: Sixty Percent of the Channel Obstructed - COMSOL
The pressure profile for the sixty percent case is shown in Figure 13. This case shows
that the pressure loss across the obstruction has risen to 3.5psi. At this point the pressure
rise is becoming significant. Depending on the application, this may be unacceptable if
there are seals or other compartment features nearby that would be adversely impacted
by such a local pressure rise.
12
Figure 13: Pressure Profile for Sixty Percent of the Channel Obstructed
13
As the obstruction size is increased to eighty percent of the flow channel, the
recirculation zone increases in size further. In dimensions, it is only slightly larger than
the sixty percent case. This is only a marginal increase in benefit.
Figure 14: Eighty Percent of the Channel Obstructed - Fortran
As before, the COMSOL solution shows good agreement. The overall size of the
recirculation zone in the COMSOL solution is slightly larger and extends out to the 0.25
meter mark.
Figure 15: Eighty Percent of the Channel Obstructed - COMSOL
At the eighty percent obstruction point, the pressure gradient across the obstruction has
risen to 18psi. This is becoming a very significant loss in pressure and depending on the
application may be enough additional work for the rotor as to not make it the optimal
configuration. It is also much more likely to have an adverse effect on a nearby
component that might be sensitive to a localized pressure increase.
14
Figure 16: Pressure Profile for Eighty Percent of the Channel Obstructed
15
Although the eighty percent case was already reaching some practical limitations,
the ninety percent case was run to help define the envelope. As the obstruction increases
in size to cover ninety percent of the flow channel, the flow no longer appears to be
steady. As shown in Figure X below, the recirculation zone has decreased in size.
Importantly though, a periodic behavior has developed that is showing velocities that are
alternatingly increasing and decreasing with each iteration through the X axis.
Figure 17: Ninety Percent of the Channel Obstructed - Fortran
Investigating the pressure profile of the flow channel shows what would be expected
over the entire length of the flow path. The majority of the pressure loss occurs as the
flow passes over the obstruction itself, with a sharper pressure drop associated with the
contraction and expansion losses on either end of the obstruction. In this case the
pressure loss across the obstruction has reached 41psi.
16
Figure 18: Pressure Profile for Ninety Percent of the Channel Obstructed
Closer investigation of the pressure profile as the flow approaches the obstruction
indicates that there is a periodic pressure fluctuation. The fluctuation is shown in Figure
X. This fluctuation is symptomatic of the checkerboarding effects described by
Ferzinger and Peric in section 7.5.2.
Figure 19: Entrance Pressure Profile for Ninety Percent of the Channel Obstructed
COMSOL was unable to converge on a solution at all for the ninety percent obstructed
case. Grid fidelity was increased several times, but without success.
17
Conclusions
The sizing of this recirculation zone is the important part of this design. The
blocker cannot be so large as to completely block flow. This is unnecessary and also
wasteful since it will result in additional work for the shaft. In ideal circumstances, the
scavenge port would be located at bottom dead-center. The recirculation zone should
always be sized to be larger than the scavenge port so that oil is always directed towards
the port itself and never diverted away. It is unnecessary for the recirculation zone to be
any larger than 90 degrees downstream of the obstruction. The reason for this is that any
oil that is flung from the shaft below this line will be trapped in the recirculation zone.
Oil that is flung from the shaft between 90 and 180 degrees from the obstruction will
either fall back into the recirculation zone, or fall back onto the shaft to be flung around
again. A small amount of oil will cling to the wall due to adhesion, but it will not be able
to form a standing wave, which is the objective. Finally, oil that is flung between the 180
degree and 360 degree marks will be carried around by the air velocity to be deposited in
the scavenge area.
There are two areas where additional work is warranted. The first is to include an air
velocity out of the south boundary. The significance of this flow will depend greatly on
the application of this technique. In some applications, such as in a drain to manage a
small amount of leakage, the amount of oil that needs to be recovered is minimal and no
air at all needs to be recovered from the cavity. In an application such as this, the
analysis described above would be adequate. Some applications may have a relatively
large amount of oil that needs to be recovered, or possibly the air itself needs to be
removed from the cavity. The analysis described in this paper may be inadequate for
conditions like this since the air velocity out may have a significant influence on the
recirculation zone.
With additional work, the recirculation zone could be optimized to a smaller size.
With gravity acting on the wave, there is already a motive force discouraging wave
formation at the 90 degree mark. A recirculation zone of smaller size, perhaps 45
degrees, might be more than adequate to eliminate any significant wave and would
further reduce waste. This is especially true when considering that the air velocity
beyond the recirculation zone will have been decreased and its ability to support a wave
18
against gravity diminished. This analysis would be considerably more complex however
since it would require an analysis of the behavior of a two-phase mixture and is beyond
the scope of this task.
19
References
1) S. Patankar; Numerical Heat Transfer and Fluid Flow; Hemisphere Publishing
Corporation; 1980
2) J. Herziger, M Peric; Computational Methods for Fluid Dynamics
3) J. Tannehill, D. Anderson, R Pletcher; Computational Fluid Mechanics and Heat
Transfer, Second Edition; Taylor & Francis; 1997
4) Engineeringtoolbox.com
20
Appendix
21