CFD Study of Flow and the 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
September, 2013
(For Graduation December 2013)
© Copyright 2013
by
Reade William James
All Rights Reserved
i
CONTENTS
LIST OF TABLES ............................................................................................................ iii
LIST OF FIGURES .......................................................................................................... iv
LIST OF SYMBOLS ......................................................................................................... v
ABSTRACT ..................................................................................................................... vi
1. Introduction/Background ............................................................................................. 1
2. Problem Description .................................................................................................... 2
3. Methodology/Approach ............................................................................................... 4
4. Results and Discussion ................................................................................................ 9
5. Conclusions................................................................................................................ 23
6. References.................................................................................................................. 25
ii
LIST OF TABLES
Table 1: Boundaries ........................................................................................................... 8
Table 2: Air Properties....................................................................................................... 8
iii
LIST OF FIGURES
Figure 1: Rotating Cavity Oil Egress................................................................................. 3
Figure 2: SIMPLE Algorithm Diagram ............................................................................. 5
Figure 3: Grid .................................................................................................................... 6
Figure 4: Boundary Conditions ......................................................................................... 7
Figure 5: Obstruction ......................................................................................................... 7
Figure 6: 200x20 Grid Pressure Profile ............................................................................. 9
Figure 7: 400x40 Grid Pressure Profile ........................................................................... 10
Figure 8: 800x80 Grid Pressure Profile ........................................................................... 11
Figure 9: Unobstructed Channel - Fortran ....................................................................... 11
Figure 10: Unobstructed Channel - Fortran ..................................................................... 12
Figure 11: Twenty Percent of the Channel Obstructed - Fortran .................................... 13
Figure 12: Twenty Percent of the Channel Obstructed - COMSOL ............................... 13
Figure 13: Pressure Profile for Twenty Percent of the Channel Obstructed ................... 14
Figure 14: Forty Percent of the Flow Passage Obstructed - Fortran ............................... 15
Figure 15: Forty Percent of the Flow Passage Obstructed - COMSOL .......................... 15
Figure 16: Pressure Profile for Forty Percent of the Flow Passage Obstructed .............. 16
Figure 17: Sixty Percent of the Channel Obstructed - Fortran ........................................ 17
Figure 18: Sixty Percent of the Channel Obstructed - COMSOL ................................... 17
Figure 19: Pressure Profile for Sixty Percent of the Channel Obstructed ....................... 18
Figure 20: Eighty Percent of the Channel Obstructed - Fortran ...................................... 19
Figure 21: Eighty Percent of the Channel Obstructed - COMSOL ................................. 19
Figure 22: Pressure Profile for Eighty Percent of the Channel Obstructed ..................... 20
Figure 23: Ninety Percent of the Channel Obstructed – Fortran ..................................... 21
Figure 24: Pressure Profile for Ninety Percent of the Channel Obstructed ..................... 22
iv
Symbol
x
y
u
v
ρ
µ
p
t
LIST OF SYMBOLS
Units
Definition
m
m
m/s
m/s
kg/m3
kg/(m-s)
Pa
s
X distance
Y distance
X component of Velocity
Y component of Velocity
Density
Dynamic Viscosity
Pressure
Time
v
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 was done by expanding on Fortran based codes using the SIMPLE
algorithm developed by Professor Brian Spalding and Suhas Patankar. A model was 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.
vi
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.
1
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 or
egress line, the air will blow the oil up the downwind wall and form a standing wave.
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
3. Methodology/Approach
The SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm
developed by Professor Brian Spalding and Suhas Patankar was used to solve the
Navier-Stokes equations, using Fortran as the computer language and numerical solver.
The system was assumed to be a two dimensional, steady state, single phase flow
problem. Although the problem is by nature dealing with two phases of air and oil, the
quantity of oil is assumed to be small if the oil is being managed properly. COMSOL
was also used to compare results. The Fortran code developed by Peric for a lid driven
cavity and described in Computational Methods for Fluid Dynamics was used as a
starting point.
Algorithm:
The SIMPLE algorithm is a strategy for solving a discretized form of the NavierStokes equations. The Navier-Stokes equations for 2-D flow in Cartesian coordinates are
shown in Equations 1, 2 and 3.
𝜕𝑢 𝜕𝑣
+
=0
𝜕𝑥 𝜕𝑦
Equation 1: Continuity Equation
𝜕𝜌𝑢 𝜕𝜌𝑢2 𝜕𝜌𝑢𝑣 𝜕𝑝
𝜕 2𝑢 𝜕 2𝑢
+
+
+
= 𝜇 [ 2 + 2]
𝜕𝑡
𝜕𝑥
𝜕𝑦
𝜕𝑥
𝜕𝑥
𝜕𝑦
Equation 2: X-Direction Momentum Equation
𝜕𝜌𝑣 𝜕𝜌𝑢𝑣 𝜕𝜌𝑣 2 𝜕𝑝
𝜕 2𝑣 𝜕 2𝑣
+
+
+
= 𝜇 [ 2 + 2]
𝜕𝑡
𝜕𝑥
𝜕𝑦
𝜕𝑦
𝜕𝑥
𝜕𝑦
Equation 3: Y-Direction Momentum Equation
In order to solve these equations simultaneously, the SIMPLE algorithm uses an iterative
process. 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 new values of U and
4
V, denoted as U* and V* respectively. Convergence is checked. If convergence has not
been reached, correction factors are calculated for P, U, and V. These are designated as
P’, U’, and V’ respectively. Finally the corrections are applied to calculate new values of
P, U and V to feed into the momentum equations and the process is repeated. A diagram
of the algorithm process can be seen in Figure 4.
Figure 2: SIMPLE Algorithm Diagram
Grid Selection:
The code developed by Peric is designed to work with a cartesian grid. Although
this still 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.
The code is also designed around a co-located 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).
5
Figure 3: 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 0.005 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.
Boundaries:
There is no heat addition in any of the boundaries, and the entire system was
assumed to be isothermal. The south boundary is a static, no-slip 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 south boundary, to the shaft velocity at the north boundary.
The east boundary is our outflow boundary. The outlet boundary is considered to be
fully developed and there is no change in velocity in the flow direction at the exit. After
the outflow velocity is calculated, and the entire outflow velocity profile is multiplied by
a correction factor that ensures that the mass flow into the east boundary equals the mass
flow out of the west boundary.
6
Figure 4: 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 5: Obstruction
7
A full list of the dimensions and boundary conditions that were used can be found in
Table 1.
Table 1: Boundaries
Boundary Length
0.4 m
Boundary Height
0.005 m
Obstruction Length
0.1 m
Obstruction Height
0.001, 0.002, 0.003, 0.004, 0.0045 m
North Boundary Velocity
1 m/s, no slip
South Boundary Velocity
0 m/s, no slip
Linear gradient from 0 m/s at south edge
West Boundary Velocity
boundary to 1 m/s at north edge
Fully developed - no gradient in velocity
East Boundary Velocity
direction
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. A table of the air
properties used can be found in Table 2.
Table 2: Air Properties
Temperature
120 C
p
1.013E5 Pa
ρ
0.898 kg/m3
µ
2.266E-5 kg/(m-s)
Pr
0.70
8
4. Results and Discussion
Grid Selection:
Multiple grid densities were tried, three of which will be discussed. A coarse grid of
200x20 was tried first, and then applied to a case with an obstruction that extended into
40% of the cavity. This yielded results that had characteristics that matched
expectations. The pressure profile for this grid can be seen in Figure 6. There are some
viscous losses that can be seen through the first 0.1 meters of the passage. There is a
sharp loss in pressure as the fluid experiences contraction losses at the 0.1 meter mark, to
move around the obstruction. This is followed by a gradual loss to the 0.2 meter mark as
the fluid experiences the higher viscous losses around the obstruction. At the 0.2 meter
mark, there is small increase in pressure as the fluid expands on the opposite side of the
obstruction, and then a steady decrease due to viscous losses on the far side of the
obstruction.
Figure 6: 200x20 Grid Pressure Profile
Increasing the grid density to 400x40 resulted in a similar profile in shape. The
viscous losses around the obstruction however increased considerably. A loss through
this section that was 4.5 pascal with the 200x20 grid, and shown to be approximately 8
9
pascal with the 400x40 grid. Fidelity appears to have improved with a minimal increase
in processing time. The profile for this grid can be seen in Figure 7.
Figure 7: 400x40 Grid Pressure Profile
Increasing the grid density further to 800x80 results in a pressure profile that
deviates from expectation. The pressure increases over the length of the channel with the
exception of the contraction loss. The profile for this grid can be seen in Figure 8.
Investigation has shown that steps smaller than approximately 0.0001m result in
unexpected behavior. The Fortran code is set up to use single precision numbers. On the
computers used to run this code this means that the smallest difference that can be
calculated is approximately 5.96E-8. At the 800x80 grid level the change in pressure per
grid interval in the Y direction is less than this minimum number in some 448 locations.
This results in undesirable round-off errors. The 400x40 grid will be used for the Fortran
model analysis since it matches with expected results and shows good fidelity.
10
Figure 8: 800x80 Grid Pressure Profile
The COMSOL grid was a physics controlled mesh set at normal mesh density. This
resulted in between 50698 non-orthogonal elements for the twenty percent obstruction
case up to 57599 non-orthogonal elements for the eighty percent obstruction case.
Obstruction Dimensions:
A solution without an obstruction is first run and a velocity vector field can be seen
in Figure 9. It is a simple case of flow between a static and moving plate, so the flow is
uniform as expected.
Figure 9: Unobstructed Channel - Fortran
11
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 10 below.
Figure 10: Unobstructed Channel - Fortran
A solution for a blocker that obstructs twenty percent of the flow area is shown in
Figure 11. 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.
12
Figure 11: Twenty Percent of the Channel Obstructed - Fortran
Repeating the analysis in COMSOL showed good agreement (Figure 12). The profile
over the obstruction is similar, although COMSOL does show a very small recirculation
zone on the downwind face of the obstruction.
Figure 12: Twenty Percent of the Channel Obstructed - COMSOL
The pressure profile for the Fortran based solution shows results very similar to what
had been seen while testing grids. The three main components of viscous losses,
contraction losses and expansion pressure recovery can be seen. The total pressure loss
across the obstruction can be seen to be approximately 0.4 pascal. This pressure profile
can be seen in Figure 13 below.
13
Figure 13: Pressure Profile for Twenty Percent of the Channel Obstructed
14
As the obstruction size is increased to forty percent of the flow area, a small
recirculation zone is seen starting to form downwind of the obstruction. This can be seen
in Figure 14, 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 14: Forty Percent of the Flow Passage Obstructed - Fortran
The analysis was repeated in COMSOL and shows good agreement (Figure 15). Behind
the obstruction we see the narrow and tall recirculation zone that the Fortran solution
indicated.
Figure 15: Forty Percent of the Flow Passage Obstructed - COMSOL
15
The resulting pressure profile for the Fortran solution result at a forty percent obstruction
is shown in Figure 16. This profile shows similar features to the twenty percent case,
however the pressure loss over the obstruction has increased to 0.8 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 16: Pressure Profile for Forty Percent of the Flow Passage Obstructed
16
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. The velocity profile is shown in Figure 17.
Figure 17: Sixty Percent of the Channel Obstructed - Fortran
The solution in COMSOL shown in Figure 18 demonstrates 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 differences should be expected.
Figure 18: Sixty Percent of the Channel Obstructed - COMSOL
17
The pressure profile for the sixty percent case is shown in Figure 19. This case shows
that the pressure loss across the obstruction has risen to 4.5 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.
Figure 19: Pressure Profile for Sixty Percent of the Channel Obstructed
18
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. In addition, it looks to
be separating from the blocker. This appears to be the edge of the useful sizing. The
velocity profile for this case is shown in Figure 20 below.
Figure 20: Eighty Percent of the Channel Obstructed - Fortran
As before, the COMSOL solution shown in Figure 21 gives reasonable 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 21: Eighty Percent of the Channel Obstructed - COMSOL
19
At the eighty percent obstruction point, the pressure gradient across the obstruction has
risen to nearly 16 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. The pressure profile can be seen in Figure 22.
Figure 22: Pressure Profile for Eighty Percent of the Channel Obstructed
20
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, two changes occur. As shown in
Figure 23 below, the recirculation zone has decreased in size and moved away from the
block. There is also a small recirculation zone in front of the obstruction. This is
undesirable behavior in our application since that would trap fluid on both sides of the
obstruction.
Figure 23: 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 22 Pascal. The pressure profile can be
seen in Figure 24.
21
Figure 24: 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.
In the configuration investigated for this study, no details about the shaft size were
included, but an optimum configuration could still be seen. At an obstruction size of
sixty to eighty percent, the recirculation zone was at its peak in size. The Fortran based
solution concluded that even at eighty percent the recirculation zone was starting to
separate from the obstruction, and consequently from the egress location. This, along
with the additional losses incurred would identify the sixty percent case as the optimal
solution.
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
23
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
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) C. Hirsch; Fundamentals of Computational Fluid Dynamics, Second Edition;
John Wiley & Sons, Ltd; 2007
5) W. Lai, D. Rubin, E. Krempl; Introduction to Continuum Mechanics, Fourth
Edition; Elsevier; 2010
6) Engineeringtoolbox.com
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