Study of Flow and Sizing of an Air Blocker for use in Bearing
Compartment Scavenge
by
Reade William James
An Engineering Project 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
Hartford, CT
August, 2013
(For Graduation August 2013)
© Copyright 2013
by
Reade William James
All Rights Reserved
ii
CONTENTS
LIST OF FIGURES ........................................................................................................... 2
ACKNOWLEDGMENT ..................................................Error! Bookmark not defined.
ABSTRACT ...................................................................................................................... 3
1. Introduction/Background ............................................................................................. 4
2. Problem Description .................................................................................................... 5
3. Methodology/Approach ............................................................................................... 7
4. Results........................................................................................................................ 11
5. Conclusions................................................................................................................ 23
6. References.................................................................................................................. 25
7. Appendix.................................................................................................................... 26
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1
LIST OF FIGURES
Figure 1: Rotating Cavity Oil Egress................................................................................. 6
Figure 2: Boundary Conditions ......................................................................................... 8
Figure 3: Obstruction ......................................................................................................... 8
Figure 4: SIMPLE Algorithm Diagram ............................................................................. 9
Figure 5: Grid .................................................................................................................... 9
Figure 6: Unobstructed Channel - Fortran ....................................................................... 11
Figure 7: Unobstructed Channel - Fortran ....................................................................... 11
Figure 8: Twenty Percent of the Channel Obstructed - Fortran ...................................... 12
Figure 9: Twenty Percent of the Channel Obstructed - COMSOL ................................. 12
Figure 10: Pressure Profile for Twenty Percent of the Channel Obstructed ................... 13
Figure 11: Forty Percent of the Flow Passage Obstructed - Fortran ............................... 14
Figure 12: Forty Percent of the Flow Passage Obstructed - COMSOL .......................... 14
Figure 13: Pressure Profile for Forty Percent of the Flow Passage Obstructed .............. 15
Figure 14: Sixty Percent of the Channel Obstructed - Fortran ........................................ 16
Figure 15: Sixty Percent of the Channel Obstructed - COMSOL ................................... 16
Figure 16: Pressure Profile for Sixty Percent of the Channel Obstructed ....................... 17
Figure 17: Eighty Percent of the Channel Obstructed - Fortran ...................................... 18
Figure 18: Eighty Percent of the Channel Obstructed - COMSOL ................................. 18
Figure 19: Pressure Profile for Eighty Percent of the Channel Obstructed ..................... 19
Figure 20: Ninety Percent of the Channel Obstructed - Fortran ...................................... 20
Figure 21: Pressure Profile for Ninety Percent of the Channel Obstructed ..................... 21
Figure 22: Entrance Pressure Profile for Ninety Percent of the Channel Obstructed ..... 22
2
ABSTRACT
In this project a computational fluid dynamics study is completed to provide an
analysis of fluid driven in a cavity similar to those found in turbomachine bearing
compartments. This is done by expanding on Fortran based codes using the SIMPLE
algorithm developed by Professor Brian Spalding and Suhas Patankar. A model is also
developed in COMSOL as a point of reference and comparison.
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. This increases the weight of the engine since it increases the amount of oil
needed for the engine to function, and also decreases the efficiency of the machine since
it increases churning within the compartment. To manage this behavior a blocker is
introduced and the oil is collected in the recirculation zone downwind. This project
investigates one such configuration and looks at the benefits achieved through the sizing
of this obstruction.
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1. 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.
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2. 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.
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Figure 1: Rotating Cavity Oil Egress
6
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 of 1 meter per second
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.
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Figure 2: Boundary Conditions
The obstruction itself is handled as described by Patankar (Numerical Heat Transfer
and Fluid Flow, pp147). 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
8
The SIMPLE algorithm is started by making an initial guess at P, U, and V. The
Navier-Stokes momentum balance equations are solved to calculate U* and V*
respectively. If convergence has not been reached, the pressure correction P’ is
calculated. Finally the corrections are applied to calculate new values of P, U and V to
feed into the momentum equations.
Figure 4: SIMPLE Algorithm Diagram
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 5: Grid
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Several dimensions must be defined. This type of design can be used in many
aplications, 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
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
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4. Results
A solution without an obstruction is first run and a velocity vector field can be seen
in Figure 6. Next to the west boundary just after the inlet condition is defined, there is a
perturbation that can be seen. In the cell next to the inlet, there is an upwards draft,
which then corrects itself in the next cells to the east. The flow is such that in the southwest corner of the grid it can be seen that there is an additional recirculation zone. Since
the inlet condition is correctly applied, and this is present in all studies, it is possibly an
error in the implementation of the algorithm in the Fortran code. The error is dissipated
before the flow reaches the area of interest, so our results do not appear to be adversely
impacted, but it would be worthy of closer inspection in the future.
Figure 6: Unobstructed Channel - Fortran
Once the flow is developed, it can be seen that the flow exhibits a profile that linearly
increases from the static bottom boundary to the sliding upper boundary. This is the
expected profile from this simple case. This profile can be seen in Figure 7 below.
Figure 7: Unobstructed Channel - Fortran
11
A solution for a blocker that obstructs twenty percent of the flow area is shown in
Figure 8. 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 8: Twenty Percent of the Channel Obstructed - Fortran
Repeating the analysis in COMSOL shows good agreement (Figure 9). 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.
Figure 9: Twenty Percent of the Channel Obstructed - COMSOL
12
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 0.15 Pascal. This pressure profile can be
seen in Figure 10 below.
Figure 10: Pressure Profile for Twenty Percent of the Channel Obstructed
13
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 11, 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 11: Forty Percent of the Flow Passage Obstructed - Fortran
The analysis is repeated in COMSOL and shows good agreement (Figure 12). 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 12: 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 13. This profile shows similar features to the twenty percent, however
14
the pressure loss over the obstruction has increased to 0.7 Pascal. 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 13: Pressure Profile for Forty Percent of the Flow Passage Obstructed
15
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 14: 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 15: Sixty Percent of the Channel Obstructed - COMSOL
The pressure profile for the sixty percent case is shown in Figure 16. This case shows
that the pressure loss across the obstruction has risen to 3.5 Pascal. The pressure rise is
growing considerably, however in magnitude this is a small number and it is unlikely to
have any adverse impacts on local components or unacceptable resistance to rotation.
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Figure 16: Pressure Profile for Sixty Percent of the Channel Obstructed
17
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 17: 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 18: Eighty Percent of the Channel Obstructed - COMSOL
At the eighty percent obstruction point, the pressure gradient across the obstruction has
risen to 18 Pascal. This is still a relatively small pressure loss, however depending on the
application it may have an adverse effect on a nearby component that might be sensitive
to a localized pressure increase.
18
Figure 19: Pressure Profile for Eighty Percent of the Channel Obstructed
19
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 20 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 20: 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 41 Pascal.
20
Figure 21: 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
22. This fluctuation is symptomatic of the checkerboarding effects described by
Ferzinger and Peric in section 7.5.2.
21
Figure 22: 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.
22
5. 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
23
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.
24
6. References
1) S. Patankar; Numerical Heat Transfer and Fluid Flow; Hemisphere Publishing
Corporation; 1980
2) J. Ferziger, M Peric; Computational Methods for Fluid Dynamics; Springer;
1996
3) J. Tannehill, D. Anderson, R Pletcher; Computational Fluid Mechanics and Heat
Transfer, Second Edition; Taylor & Francis; 1997
4) Engineeringtoolbox.com
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7. Appendix
26