Computational Improvements to Predict Propeller Performance at Off Design
Conditions
by
William E. Duncan
B.S., Naval Architecture and Marine Engineering, U.S. Coast Guard Academy, 1996
Submitted to the Departments of Ocean Engineering and Mechanical Engineering in partial fulfillment of
the requirements for the degrees of
Master of Science in Naval Architecture and Marine Engineering
and
Master of Science in Mechanical Engineering
at the
Massachussets Institute of Technology
JUNE 2002
C 2002 William E. Duncan. All rights reserved.
The author hereby grants to MIT permission to reproduce and to distribute publicly paper and electronic copies of
this thesis document in whole or in part.
.... ....
Signature of Author..............................................................................................
Department of Ocean Engineering and Mechanical Engineering
May 10, 2002
...
Certified by ........................................................................
............................
David V. Burke
Senior Lecturer, epartment of Ocean Engineering
Thesis Supervisor
Read by.........................................................
Ain A. Sonin
anical Engineering
Thesis Reader
A ccepted by .....................................................
..... .
Chairman, Committee on Grad
...... ..........................
Henrik Schmidt
ssor of Ocean Engineering
ts for Ocean Engineering
Accepted by .......................................................................
Ain A. Sonin
Professor of Mechanical Engineering
Chairman, Committee on Graduate Studies for Mechanical Engineering
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
AUG 2
002
LIBRARIES
BARKER
Computational Improvements to Predict Propeller Performance at Off Design
Conditions
by
William E. Duncan
Submitted to the Department of Ocean Engineering and the Department of Mechanical
Engineering in partial fulfillment of the requirements for the degrees of Master of Science in
Naval Architecture and Marine Engineering and Master of Science in Mechanical Engineering.
Abstract
The purpose of this thesis is to modify an existing computational method to predict performance
for the 4119 propeller at off design conditions. The 4119 propeller is a conventional three
bladed propeller without skew. The existing computational method used is an Euler/Integrated
Boundary Layer Theory (IBLT) axisymmetric flow solver coupled with a propeller lifting
surface design and analysis program. Presently, the coupling will converge to realistic thrust and
torque coefficients at advance coefficients between 0.7 and 1.1. The modified procedure
outlined in this thesis can predict thrust and torque coefficients down to an advance coefficient of
0.3, however, the results are lower than expected from model tests. An error analysis is included
to identify reasons for the low thrust and torque coefficients.
Thesis Supervisor: David V. Burke
Title: Senior Lecturer, Department of Ocean Engineering
2
Acknowledgments
Thanks to Professor Emeritus Justin Kerwin and Dr. Richard Kimball for their assistance.
3
Table of Contents
1
2
3
4
Page
Introduction
12
1.1 Overview
12
1.2 Propeller Blade Design (PBD) Theory
12
1.3 MTFLOW
15
1.4 Coupling PBD with MTFLOW
15
1.5 Purpose
16
Identifying the Problem at Low Advance Coefficients
17
2.1 Overview
17
2.2 MTFLOW Grid
18
2.3 PBD Wake
18
2.4 Input Swirl to MTFLOW
19
2.5 Results
21
Concentrating the streamlines with a Foil
22
3.1 Overview
22
3.2 Guidelines to an Optimum MTFLOW Grid
22
3.3 Examples
23
3.4 Using a Longer Chord
25
3.5 Axial Velocity Around Foil
26
Case I, Blade Grid is Fixed
27
4.1 Overview
27
4.2 Grid
27
4.3 Artificial Modifications
28
4
4.4 Effective Velocity
30
Case II, Blade Tip Follows Trailing Edge
31
5.1 Overview
31
5.2 Grid
31
5.3 Procedure
32
5.4 Swirl Input
33
5.5 Verification
34
6 Error Analysis
35
5
6.1 Overview
35
6.2 PBD Error
35
Conclusion
37
7.1 Summary of Results
37
7.2 Recommendations for Future Work
37
A Input Files to PBD/MTFLOW Coupling
38
7
A. 1 Walls File without Foil and Hub
38
A.2 Walls File with Foil and Hub
39
A.3 Batchfile
40
A.4 Vel.in
41
A.5 Mtcouple.inp
42
A.6 PBD Admin file
42
A.7 MTFLO
43
A.8 MTSOL
43
44
B Changes to MTFLOW Source Code (io.f)
5
C Changes made to PBD2MT Source Code
47
D PBD Admin. File for PSF-2 Convection Velocities
50
Bibliography
51
6
Page
List of Figures
1.1
B-Spline Grid
13
1.2
Horseshoe Element
14
2.1
Kt, 1OKq Vs. Advance Coefficient
17
2.2
Blade and MTFLOW Grid, J=0.4
18
2.3
Blade and MTFLOW Grid, J=0.833
18
2.4
Blade and Transition Wake, J=0.833
19
2.5
Blade and Transition, J=0.4
19
2.6
PBD Input Swirl Contour Lines, J=0.4
19
2.7
PBD Input Swirl Contour Lines, J=0.833
19
2.8
Blade and MTFLOW Grid, J=0.833
20
2.9
Blade Boundary and MTFLOW Grid, J=0.4, Ifix=1
20
3.1
MTFLOW Grid x-0.001
24
3.2
MTSOL grid E = 0.900
24
3.3
MTSOL grid E = 0.600
24
3.4
MTFLOW Grid e=0.4
24
3.5
Blade and MTFLOW Grid
25
3.6
Blade and MTFLOW Grid
25
3.7
Hub and Blade in MTFLOW Grid
25
3.8
MTSOL Grid E=0.900
25
3.9
Foil in MTFLOW Grid
26
3.10
Axial Velocity Around Foil
26
4.1
Results for Ifix=1
27
7
4.2
Blade Grid and MTFLOW Grid
28
4.3
Blade and Wake, Ifix=l, J=0.5
28
4.4
Blade Grid and Swirl Input Grid
29
4.5
Input Swirl at Tip, Ifix=1, J=0.5
29
4.6
Effective Velocity, Ifix=1, J=0.5
30
5.1
Kt, lOKq Vs. J, Ifix = 0
31
5.2
Blade and MTFLOW Grid, Ifix=O, J=0.4
32
5.3
Blade and MTFLOW Grid, Ifix=0, J=0.4
33
5.4
Swirl Input, Ifix=O, J=0.4
33
5.5
Swirl Input Locations to Blade, Ifix=0, J=0.4
33
5.6
Blade and Wake, Ifix=0, J=0.4
34
5.7
Effective Velocity, Ifix=0, J=0.4
34
8
Page
List of Tables
3.1
Guidelines to Concentrate Streamlines
22
3.2
Foil and MTSET values
24
3.3
X and R values for Foil
25
6.1
J=0.4, Ifix=O results compared to PSF-2
36
9
Nomenclature
A
cross sectional area
B
field parameter
D
propeller diameter
h
enthalpy
Vs
nD
Kt
Kq
advance coefficient
T
T
2 4
pn D
2
pn D 5
2
thrust coefficient
torque coefficient
m
mass flow rate
n
surface normal vector
n
propeller rotation rate rev
p
pressure
q
meridional speed
R
radial coordinate
S
entropy
To
field parameter
V
velocity
sec
rV o
swirl, tangential velocity
(Veffective)
effective velocity
(Vinsced)
induced velocity
10
VS
ship velocity
(Vto tal)
total velocity
AH
enthalpy addition
AS
entropy addition
AW
work addition
IF
circulation
p
fluid density
Yf
free vorticity
blade rotation rate
rad
--Ssec)
11
Chapter 1
Introduction
1.1 Overview
The purpose of this research was to use computational techniques to predict propeller
performance at low advance coefficients. The computational techniques used is a propeller blade
design (PBD) lifting surface code (developed by Kerwin' et al) coupled with an axisymmetric
through flow solver called MTFLOW (developed by Drela2 ). The history of this type of an
analysis started with a Reynolds Average Navier Stokes (RANS) method coupled with a lifting
surface code. The RANS coupling proved to be computationally inefficient and required
significant user experience. The coupling with PBD and MTFLOW proved to be robust and
efficient but only for advance coefficients near design.
1.2 Propeller Blade Design (PBD) Theory
PBD is a lifting surface method to determine the resultant distribution of force on a propeller
blade, hub and duct. The mathematics used to determine the force starts with identifying the
kinematic boundary condition which states that the flow normal to a surface is zero (1.1).
1Justin E. Kerwin, Professor Emeritus of Naval Architecture, Ocean Engineering Department, MIT.
2 Mark
Drela, Associate Professor, Department of Aeronautics and Astronautics, MIT.
12
V-n=O
(1.1)
Next step is to identify the types of flow around a propeller. There are four types:
Total flow (Vot&a):
total velocity with the propeller operating.
Effective flow (Veffective): "total time-averaged velocity in the presence of the propeller minus the
time-average potential flow velocity field induced by the propeller
itself." [5]
Induced flow (Vinduced): induced velocity by the propeller and trailing wake vortex
Nominal flow:
distributions.
velocity in the region of the propeller with the propeller not operating.
The effective flow and the induced flow are not physical velocities that may be measured. The
total flow is divided into effective and induced flow for computational purposes. PBD analyzes
the forces using the effective flow. The total velocity equals the effective plus the induced
velocity (1.2).
(1.2)
(Vt o ta) =(Veective) + (Vinduced
For inviscid flow there is zero vorticity in the inflow. Therefore, the induced velocity from the
propeller can not interact with zero vorticity in the inflow. This results in the unique case when
the effective velocity equals the nominal velocity. The cases analyzed in this thesis are inviscid,
thus, the relationship between nominal and effective flow is used to verify the accuracy in the
MTFLOW/PBD coupling.
The propeller blade, hub and duct are identified using B-Spline surfaces. B-Spline
B-Spline Grid
surfaces are ideal due to the normal vector from the surface
and the curvature can be uniquely defined everywhere on
0.7
the surface. In defining the surface, the user can choose an
6
0.5:
appropriate grid density to accurately capture the forces.
0.4
0.3
0.2
-0.2
0
0.2
0.4
Fig. 1. 1: A1IOX 10 grid
13
0.6
Figure 1.1 uses a blade grid density of 10 X 10, but the cases analyzed in this thesis use a density
of 25 X 25. Contained within each grid box PBD calculates the position of a control point.
Along each grid segment PBD assigns a constant-strength bound vortex. Also, PBD assigns a
coincident line source to account for thickness. From each bound vortex segment vorticity must
be shed in the flow (then to the wake) as free vorticity to stay consistent with Kelvin's Theorem
(1.3). The bound vorticity shedding to free vorticity can be visualized as a horseshoe element
(figure 1.2).
rf(y) -
dF
dy
(1.3)
Horseshoe Element
Free
Vortex
Segment
Bound
Vortex
Segme t
Control point
0
Fig. 1.2: Grid box is one of the boxes from
figure 1.1. Vorticity is shed from one
segment of bound vorticity to two
segments of free vorticity [7].
Free
Vortex
Segment
An influence matrix is developed by calculating the distance from every control point to every
bound and free vortex segment. The induced velocity at every control point is then calculated by
multiplying the influence matrix by the vortex segment strength matrix (1.4).
[ INF][I-] =Vi.uced
Combining equations 1.4, 1.2 and 1.1 results in equation 1.5.
14
(1.4)
[[INF] i] +Veecte -n =0
(1.5)
From equation 1.5, the resultant distribution of force on the blade can be calculated using KuttaJoukowski's and Lagally's theorems [1].
1.3 MTFLOW
MTFLOW consists of three programs; MTSET, MTSOL and MTFLO. MTSET reads a
geometry or walls file and generates an initial grid (Appendix A. 1, A.2). MTSOL then solves
the Euler equations. MTFLO manages the input and output data from MTSOL (data in this
thesis is location and magnitude of tangential velocity or swirl and drag). The programs provide
an inviscid/viscous analysis and design capability for axisymmetric bodies. The theory is based
on the conservation of mass, energy and momentum to solve for the total velocity everywhere in
the flow field [2].
1.4 Coupling PBD with MTFLOW
PBD by itself is limited to inviscid open propeller cases because the user can assume the
effective velocity is equal to the nominal velocity. To expand PBD's capability, it is usually
coupled with a through flow solver. The MTFLOW/PBD coupling procedure used in this thesis
was completed in reference [4] and [11]. It uses an iterative process between MTFLOW and
PBD to converge to the correct thrust coefficient, Kt, and torque coefficient, 1 OKq, for a
particular advance coefficient. Essentially, MTFLOW passes the total velocity field to PBD, and
PBD inputs the tangential velocity and drag due to the blade, hub and duct. MTFLOW, then, recomputes the total velocity field. This process is repeated until convergence. Appendix A
outlines the input files for the PBD/MTFLOW couplings used in this thesis.
In addition to the MTFLOW and PBD programs, this thesis focuses on the coupling code
PBD2MT. PBD2MT inputs the swirl and drag from PBD to MTFLOW.
15
1.5 Purpose
The following thesis presents two methods of how to converge the PBD and MTFLOW coupling
at low advance coefficients for the 4119 propeller. The 4119 propeller is a three bladed propeller
without skew. Data about the 4119 propeller has been extensively documented, therefore, it is
used to validate the PBD/MTFLOW coupling. The converged solutions at low advance
coefficients resulted in the thrust and torque coefficients being lower than expected from model
tests. An error analysis is included to identify reasons for the low thrust and torque coefficients.
16
Chapter 2
Identifying the Problem at Low Advance
Coefficients
2.1 Overview
The coupling between PBD and MTFLOW will converge to the correct Kt and 1 OKQ for
advance coefficients near design.
Kt, I OKq Vs. Advance Coefficient
0.5
correlation of Kt and IOKq results
for advance coefficients between 0.7
-
Figure 2.1 shows the close
5Model
Test
10
10Kq,Model Test
IL
Kt
K 0.4
_
10Kq
and 1.1 [4,11]. There are two
problems at low J. First, the grid in
KtCoupled no fbil
1Oq,Coupled nofoit
Kt
0.2
MTFLOW is too coarse to accurately
model the flow around the tip.
%.3
0
0
0
0
0
0
Advance Coefficient J
2
Fig. 2.1: Kt/IOKq results for
Second, PBD2MT does not accurately input
existing coupling routine.
swirl and drag from PBD coordinates to
MTFLOW coordinates. The streamlines moving when running MTSOL also presents a problem
with swirl and drag input.
17
2.2 MTFLOW Grid
The coarse MTFLOW grid results in three types of program failures. First, the grid separates as
shown in figure 2.2. In this case, the streamlines are not able to adjust sufficiently to follow the
flow. As a comparison, figure 2.3 shows the grid uniformity required for MTSOL to converge.
Second, MTSOL will crash when the streamlines cross. The streamlines usually cross at a J well
below design (J<0.4). The streamlines try to go more vertical to follow the flow and
subsequently cross. A final way MTSOL crashes is when the grid is over-constrained. An
indication of an over-constrained grid is the addition of artificial entropy added to MTSOL to
converge the Euler equations. MTSOL will converge if the artificial entropy approaches zero.
Blade and MTFLOW Grid,
Blade and MTFLOW Grid, J=0.4
J=a.833
R
1.5
R
0.5
3
4
xV
3
5
V4
5
Fig. 2.3 MTFLOW grid does not
separate at J above 0.7.
Fig: 2.2: MTFLOW grid
separates at low J.
MTSOL crashes if the artificial entropy approaches infinity.
2.3 PBD Wake
The wake is unable to grow properly downstream as a result of the MTFLOW grid separating.
shows
Figure 2.5 shows the resulting wake when the grid separates. As a comparison, Figure 2.4
a wake growing properly downstream.
18
Blade and Transition
J=0.4
Blade and Transition Wake,
J=0.833
US
0.5
0.5
025
Y
Y
0
-0.25
-0.5
-0.75
0.a5
1
1-5
x I
Fig. 2.5 Wake can not follow the
streamlines.
1
x
Fig. 2.4 Wake follows the
streamlines.
2.4 Input Swirl to MTFLOW
The second problem that causes the coupling not to converge at low J is the program PBD2MT
PBD Input Swirl Contour Lines, J = 0.4
PBD Input Swirl Contour Lines, J = 0.833
1
0.99
0.98
50.97
0.975
0.96
0.95
0.95
0.94
4.02
4.04
X
4.06
Fig. 2.6: Swirl Contour lines
become crossed at J= 0.4.
4.08
4.02
4.04
4.06
Fig. 2.7: Contour lines are smooth at design J.
not accurately inputting swirl and drag from PBD coordinates to MTFLOW coordinates. Figure
2.6 illustrates how the contour lines become scrambled at low J. As a comparison, figure 2.7
illustrate the smooth contour lines at design J. The method that PBD2MT inputs swirl to
MTFLOW is not robust. PBD2MT labels the horizontal MTFLOW streamlines as t lines and the
vertical blade grid lines as s lines (figure 2.8). It inputs swirl by following a constant s line until
19
Blade and MTFLOW Grid, J = 0.833
Notice the
jump in streamlines
between inside and outside the
blade
.
1
R
9
0
.8
Streamlines
Vertical blade
in M TFL OW
are t lines
lines
lines are s
0 .7
3.7
3.8
4.1
4
3.9
4.2
4.3
x
Fig. 2.8: Blade grid and MTFLOW grid
it finds a t line within the blade grid. When it finds a t line it inputs the given swirl from PBD to
that location in MTFLOW. This process is repeated until all the t lines within the blade have
inputted swirl. If following an s line and not finding a t line within the blade, the program jumps
to the next t line above the blade (figure 2.8). At that location the swirl is input equal to the swirl
at the blade tip. This process would work
Blade Boundary and MTFLOW Grid, J= 0.4
Ifix =I
fine if the streamlines stayed perfectly
horizontal and the MTFLOW grid had
dense streamlines at the tip. Two
R-
problems develop when the streamlines
are not horizontal and the MTFLOW grid
The constant s
line crosses a t
0.95
line twice.
is coarse at the tip. First, at low J
the streamlines become more vertical.
This causes streamlines (t lines) to cross s
4
4.05
x
4.1
Fig. 2.9: Blade grid boundary and MTFLOW grid.
lines twice (Figure 2.9). The program can
20
only input one value of swirl for every s and t coordinate, therefore, the second crossing of the s
line does not receive an input swirl value. This causes the swirl contour lines to cross. The
second problem is the jump from inside the blade to outside the blade. A coarse MTFLOW grid
near the blade tip will cause the swirl contour lines to jump because the space between t lines is
too great.
The movement of streamlines with each iteration also presents a problem with swirl and
drag input. After PBD2MT inputs the swirl and drag, MTSOL converges the total velocity field.
During the MTSOL convergence the streamlines contract, therefore, the original input from
PBD2MT changes with the contracting streamlines. This results in PBD obtaining a skewed
inflow, and PBD will output a skewed distribution of swirl and drag.
2.5 Results
The result of the MTFLOW grid separating, the wake not able to follow the streamlines, the
method that PBD2MT inputs swirl and drag to MTFLOW and the streamlines contracting after
receiving swirl and drag from PBD2MT is the PBD/MTFLOW coupling not converging.
21
Chapter 3
Concentrating the Streamlines with a Foil
3.1 Overview
A small, artificial foil is used to concentrate the streamlines at the blade tip to keep the
streamlines from separating. The foil allows the user to test the ability of MTFLOW to converge
with concentrated streamlines without re-writing the MTFLOW source code. The foil is created
such that MTFLOW only identifies the leading and trailing edge. During convergence at low J,
the leading and trailing edge move to stay inline with the flow. Table 3.1 outlines the parameters
in MTSET and the walls file to create an optimum MTFLOW grid. MTFLOW source code was
modified to output the grid above the foil (Appendix B).
3.2 Guidelines to an Optimum MTFLOW Grid
Symbol
Description
Guidelines for J<=0.7
N
number of streamwise grid
points
exponent for airfoil side
N should be greater than 150
points: n = N*chord
(fig. 3.2, 3.3, 3.4)
given foil if:
E is too large - mtsol will only grid the leading edge
E
E must be correlated with the size of the foil. For a
E is too small - mtsol output grid includes the foil
E just right - mtsol will grid the leading and trailing
edges and the output file will not grid the foil
Table 3.1: Parameters in MTSET and the walls file to create an optimum grid.
22
Symbol
X
Description
x-spacing parameter
S
number of streamlines
S should be greater than 60
J
j-spacing flag
W1
streamline bunching weight
between airfoils 1,2
W2
streamline bunching weight
between airfoils 2,3
airfoil 1 (bottom of grid)
surface streamtube thickness
factor
Set J = 1. This will allow WI, W2, T1, T2 and T3 to
be varied
Wi should be greater than W2. This will put more
streamlines below the foil. When the stagnation line
moves higher the upper grid upstream will not be too
dense
W2 should be less than Wi. This will put less
streamlines in the upper grid.
TI, T2 and T3 are relative weighting numbers. TI
corresponds to the grid density near the hub and near
the foil but still in the lower grid. TI should be greater
than T2 to bunch the streamlines around the foil. Since
there are more streamlines in the lower grid Ti should
be less than T3 to keep the grid symmetric.
T2 should be less than TI and T3. This will allow the
streamlines around the foil to be more dense
T3 corresponds to the grid density at the outer
boundary and near the foil but in the upper grid. T3
should be greater than T2 to bunch the streamlines
above the foil instead of at the boundary. To keep the
grid symmetric T3 should also be greater than TI.
The critical dimension is the distance between the
points along the X axis. This distance must be
correlated with the exponent variable, E. The grid
reads a diamond but interpolates a circle. (fig 3.7, 3.8)
TI
T2
airfoil 2 (foil location) surface
streamtube thickness factor
T3
airfoil 3 (top of grid) surface
streamtube thickness factor
Foil
(walls
file)
A diamond is the easiest foil
to manipulate. MTSET reads
the diamond starting at the
downstream point and
proceeds counter-clockwise.
Guidelines for J<=0.7
X should equal one. The vertical lines connecting the
upper and lower grid will then be straight. (fig. 3.1)
Each point should be on the X
and R axis (X being horizontal
and R vertical) and also
symmetric about the X and R
axis.
Table 3.1 (continued): Parameters in MTSET and the walls file to create an optimum grid.
3.3 Examples
The following Tables and Graphs illustrate the guidelines outlined in Table 3.1. All graphs use
values identified in Table 3.2 unless otherwise noted.
23
Foil
X
4.001
4.0
3.999
4.0
4.001
R
1.0
1.001
1.0
0.999
1.0
2.5
MTSET
Symbol Value
200
N
0.900
E
1.000
X
60
S
1
J
0.700
W1
0.500
W2
0.500
TI
0.050
T2
0.700
T3
[
R
MTFLOW Grid x=0.001
t.
o
0.5
Fig. 3. 1: MTSOL will crash. Upper and
lower grid do not meet at right angles. X
needs to equal one.
Table 3.2
Foil
Foil
MTSOL
Grid
E = 0.600
MTSOL
Grid
E = 0.900
I I
Fig. 3.3: MTSOL will converge.
Trailing edge does cross a
grid line.
Fig. 3.2: MTSOL will crash because
the trailing edge does not
cross a grid line. E needs to
be smaller.
wGrd e=0.4
Fig. 3.4: E is too low. MTSOL output file is
gridding a portion of the foil.
Streamlines will cross as flow goes
around foil to blade
1.01
-
D~an
&06
4
4.005
24
Blade and MTFLOW Grid
Blade and MTFLOW Grid
I| | | | | | | | ||| || | | 0 | | | | | | |IIII
14-4
-
16
1.15
1.2
1.1
Ros
R
1
0.8
0.95
0.6
0.9
0.4
0.85
3.9
4
x
4.2
4.1
Fig. 3.5: Same graph as Fig. 3.6
but zoomed in. MTSOL
will converge
x
Fig. 3.6: Illustration of dense gridding in
X and R directions. MTSOL
will converge.
3.4 Using a Longer Chord
The following graphs use the same MTSET parameters as outlined in Table 3.2 but the foil is
identified in Table 3.3. The foil in Table 3.3 has a longer chord.
X
4.01
4.0
3.99
4.0
4.01
R
1.0
1.01
1.0
0.99
1.0
Table 3.3
Foil
Hub and Blade in
MTFLOW Grid
R
--
4
3
-
-
MTSOL
Grid
E = 0.900
5
x
Fig. 3.7: Hub and blade with longer chord.
Grid is not as dense in the X
direction.
Fig. 3.8: The longer chord set in the walls file
allows the trailing edge to cross a grid
line even with the higher E.
25
Foil in MTFLOW Grid
Figure 3.9 illustrates a chord set in the walls file for a foil
1.3
that is too long even at an exponent equal to 0.9. The
1.2
1.1
streamlines would cross as the flow goes across the foil to
R
0.9
the blade.
0.8
0.7
-r
. ,,, 1,
3.6
3.8
x
4
4.2
Fig. 3.9: Chord length for this
foil is 0.2.
3.5 Axial Velocity Around Foil
As a final check, the foil must not significantly disturb the velocity at the blade tip for an
accurate coupling. Plotting the axial velocity in figure 3.10 shows that the influence of the foil is
less than 1% of the nominal flow. The impact of the induced velocity will be shown to be
negligible on the final Kt and lOKq in chapter 5.
Axial Velocity Around Foil
11
10
9
5
4
3
2
Level
6
7
1.0060 1.0080 1.0091
1.0049
8
VX: 1'1 5 0.9976 0.9989 0.9997 1.0004 .1.0007 1.0018
1.01
0. 99
-
1
4.01
x
Fig. 3.10: Axial velocity around the foil is less
than 1%.
26
Chapter 4
Case I, Blade Grid is Fixed
4.1 Overview
The first case that will be analyzed at low J is a fixed blade grid lattice (also known as Ifix =1)
with the concentrated streamlines at the
Kt, 1 OKq Vs. Advance Coefficient, Ifix=1
blade tip. In this case the blade does not
move with the streamlines. There is only
- - - - KtModel Test
-
A
slight movement to maintain a geometrical
lI
0.4
1 OKq,Model Test
Kt,Foil at tipix=1
1OKq,FoIl at tip, fx=1
'0.3
-
Cr
relationship with the outer domain
AK
boundary. Figure 4.1 shows that the
0.2
coupling converged down to an advance
0.1
were
there
however, of0.5,howeer,
coefficient of 0.5,
hereAdvance
coeficiet
0.3
artificial modifications to the coupling to force
'L
0.4
0.5
0.6
0.9 J
0.8
0.7Coefficient,
Fig. 4.1: Results for Ifix=1
convergence at J=0.5. These modifications
will be discussed in this chapter.
4.2 Grid
27
1
1.1
1.2
Figure 4.2 illustrates the blade and MTFLOW grid for J=0.5 using the MTSET parameters
is
outlined in Table 3.2. The foil parameters are the same as Table 3.2 except that the X location
moved to begin at 4.051 instead of 4.001. It is necessary to move the X location downstream to
avoid the stagnation line from crossing the blade tip. Two problems will develop if the
Blade Grid and MTFLOW Grid
Blade and Wake, lfix=1, J=0.5
0.9
R
3
0.8
x
Fig. 4.3: Stagnation line is outside blade
Fig. 4.2: J=O.5, Ifix=1, Blade and
tip. Wake grows properly.
MTFLOW grid.
stream where the
stagnation line crosses the blade. First, the tip wake will begin outside the slip
velocities are just free stream. This will result in the tip wake pitch not proceeding at the correct
tangential
angle and will skew the final Kt and 10OKq results. The second problem is that the
velocity will not be added above the stagnation line. The PBD2MT code sections the lower grid
into
and upper grid based on the location of the stagnation line. Because the foil tricks the code
thinking it is a ducted case, there is not any tangential velocity input above the foil and
stagnation line.
4.3 Artificial Modifications
The solution would not converge at a J=0.5 without modifying the swirl input from PBD. There
are two problems that required attention. First problem was the gap of zero swirl between the
blade tip and the stagnation line. This gap prevented MTSOL from converging. The PBD2MT
28
code was modified to input swirl between the blade tip and the stagnation line equal to the blade
tip swirl, thus, forcing MTSOL to converge (figure 4.5). The second problem was the t lines
were crossing constant s lines at two locations (chapter 2). This resulted in the swirl input
contour lines to cross. To fix this problem, the PBD2MT code was modified such that the tip
swirl was input between the first crossing of the t line and the stagnation line. After the first
Input Swirl at Tip, Ifix=1, J=0.5
Blade Grid (dashed lines) and Swirl
Input Grid (solid lines)
going
vertical
from last
--
1.02
1.03
-
1.02
1.01
known
4
R
location.
S1
0.99
0.98
0.98
3.994 4 0 . 4.03 .04 .0
0.96
0.97
40
3.7F,.05
3.975
4
x
4.025
3.99
4.05
4
4.01
4.02
X
4.03
4.04
4.05
Fig. 4.5: Swirl is input above the blade tip. Swirl is
input from the last known position then
proceeds vertically up inputting swirl equal to
the tip swirl.
Fig. 4.4: Notice the swirl input outsid the blade
grid.
crossing the s lines went vertically upward to the stagnation line (figure 4.4). Essentially the
blade tip was cut at the first crossing of a t line and swirl was equal to the tip swirl between the
cut and the stagnation line (figure 4.5). Appendix C outlines the changes to PBD2MT source
code.
29
4.4 Effective Velocity
Effective Velocity, Ifix=1, J=0.5
The effective velocity ranges +/-12 % which is
0.9
an indication of poor coupling. The artificial
0.8
Level
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0.7
modifications are partly to blame. An in depth
0.6
-
R
error analysis will be conducted in chapter 6.
0.5
0.4
0.3
-0.2
T2
Ux
1.12043
1.11338
1.10406
1. 09558
1.08708
1.01123
0.994208
0.977182
0.960157
0.943132
0.:26107
0.90982
0.892056
0.875031
0.4
Fig. 4.6: The large range in effective
velocity indicates poor coupling.
The velocities not shown are
concentrated at the blade tip
trailing edge.
30
0.6
Chapter 5
Case II, Blade Follows the Streamlines
5.1 Overview
The difference with case II is that the blade moves with the streamlines (also known as Ifix =0)
such that the horizontal blade grid lines are
Kt I OKq Vs. J, IfIx=O
parallel to the streamlines. Case II resulted
in converged solutions down to J=0.3 but
KtFo Downsream
0.5
1 OKq,Foll Downstream
0
the solutions were much lower than
0'KqtFoiatTip
04O
aYc
-
-
KtModel Test
1Kq,Model Test
expected from model tests (figure 5.1). The
T
10Kq
solutions were converged with the foil
0.2
located at the tip and downstream. There
0
Kt
3.
were only slight differences in final
0
0
0
J, Advance Coefficient
1.2
Fig. 5.1: Kt/1OKQ Vs. J, Ifix=O
Kt/l0Kq with the two methods. However,
the lowest J for the foil downstream was 0.4
and the lowest J for the foil at the tip was 0.3. The MTFLOW grid lines crossed at J=0.3 with
the foil downstream which resulted in MTSOL crashing.
5.2 Grid
31
The grid used for this case was the MTSET
Blade and MTFLOW Grid,
Ifix=O, J=0.4
parameters outlined in Table 3.2 and the foil
2
parameters outlined in Table 3.3. Figure 5.1
1.6
illustrates the resulting blade and MTFLOW
R
grid after converging at J=0.4. The chord length
0.8
of the foil used in this case is longer than in case
0.6
I, thus, the grid density in the X direction is less.
0.2
3.5
4
4.5
5
Fig. 5.2: Blade and MTFLOW grid, Ifix=O,
The dense grid in the X direction used in
J=0.4.
Chapter 4 proved to increase the chances of the
streamlines crossing with this case.
5.3 Procedure
The procedure for this case was aimed at testing the foil. There were two major concerns after
completing the Kt/lOKq curve in Chapter 4. First, it was suspected that the foil was significantly
constraining the streamlines causing the increase in effective velocity. Second, it was suspected
that the induced velocity from the foil was having an impact on the blade's induced velocity near
the blade tip. To address both of these concerns the solution was converged with the foil at the
tip and with the foil downstream of the tip. Converging solutions downstream requires a strict
procedure to keep the MTFLOW streamlines from separating. The foil had to be located
downstream in a position such that the stagnation line was just above the blade tip after
convergence. The following procedure was used:
*
The solution was converged for a specific advance coefficient with the foil at the blade tip.
From this converged solution the vertical location of the stagnation line at X = 5.5 was noted.
The X position was determined through an iterative process considering two guidelines.
First, the position had to be downstream far enough not to interact with the blade flow.
32
EJINEW
U
U
~IJ
Second, the position could not be too far downstream such that it interacted with the
downstream boundary.
* The solution was re-converged with the foil
Blade and MTFLOW Grid,
Iix=O, J=0.4 (Tip Region)
downstream and the J from above. This
the
to
close
being
line
stagnation
the
resulted in
blade tip (figure 5.3).
* Adjust J such that the stagnation line is just
1
above the blade tip. This will allow the swirl to
location.
proper
be input at the
R
If the downstream foil was too high, the
0.95
concentrated streamlines would be above the blade
and MTFLOW would crash. If the foil was too
4.1
x
Fig. 5.3: Stagnation line does not cross blade
tip. Foil is downstream. The foil
was placed in the correct location,
thus, not requiring J to be adjusted.
low, the stagnation line would cut through the
blade and swirl would not be input above the
stagnation line. By first finding the location of the downstream foil with the solution from the
foil at the tip saves time by not having to re-compute various foil locations downstream.
5.4 Swirl Input
Following the procedure outlined in section 5.3 will result in zero additional swirl being added
Swirl Input Locations to Blade, Ifix=0, J=0.4
Swirl Input, Ifix=0, J=0.4
1. 04
1.04 11.02
15
14
1
0.362827
0.338638
1.02k
10.9261
1
0.98
0.98
7
0.169319
2
0.4876
M 0.96
i0.96
0.94
0.94
mm
-J
8
0.92
1-
0.92
0.9
0.9
4.05
4.05
4.1
4.1
4x6
Fig. 5.4: Swirl input locations. Notice
the contour lines do not cross.
4.1
Fig. 5.5: Swirl is input properly along the blade.
Dashed lines are the blade grid. Solid
lines are the input swirl locations.
artificially to the foil (figure 5.5). However, in order for MTSOL to converge, PBD2MT must
33
-
U---
initially input swirl between the tip and the stagnation line. This swirl is reduced with each
iteration until equaling zero as long as the final solution has the stagnation line just above the tip.
Additionally, with the blade grid following the MTFLOW streamlines, there are not any jumps in
the swirl contour lines (figure 5.4).
5.5 Verification
The blade wake and the effective velocity are used to verify that the MTFLOW grid did not
separate and the coupling accuracy respectively. Figure 5.6 shows the wake growing properly
downstream. However, figure 6.7, illustrates an error in the coupling with up to 24% increase in
effective velocity. The source of this error is explored in Chapter 6.
Effective Velocity, Ifix=O, J=0.4
Blade and Wake, Ifix=O,
J=0.4
-
0.9
1
0.8
Level
0.5
: 0.6
Y
0
8
0.5
-71
0.4
-0.5
0.3
0
x
Fig. 5.6: Wake follows streamline.
6
-4 1AI11
-0.2
2
LIx
1240(
1.220 94
1.201: 27
8 1.1811 6
1.1611 93
7
1.122 58
6
1.083 4
5
1.024C
4
1.004 55
3
0.984 73
2
0.965 2
11
10
9
0.7
0
A
.1
0.2
0.4
X
Fig. 5.7: The large variance in effective
velocity indicates poor coupling.
34
0.6
0.6
Chapter 6
Error Analysis
6.1 Overview
One obvious source of error for case I and II is the method of inputting swirl and drag into
MTFLOW. Case one is artificially inputting swirl between the stagnation line and the first
crossing of a t line. Case two is inputting zero swirl and drag above the stagnation line which
cuts through the blade tip. Also, both cases are not accounting for the movement in streamlines
after PBD2MT inputs swirl and drag at a particular streamline and X position. These errors
should, however, only result in a few percent error in the final Kt/l OKq. This chapter explores
other sources of error.
6.2 PBD Error
Since both cases were inviscid and with an open propeller, PBD can be used in stand-alone
mode. An effective velocity equal to one and a convective wake velocity equal to values
obtained from an older lifting surface code called PSF-2 resulted in the stand-alone values
outlined in table 6.1 (Appendix D contains the PBD input file). Table 6.1 shows that if PBD
uses the correct effective velocity and convective wake velocity it will calculate answers close to
answers obtained by model tests. Kt and IOKq is 7.9% and 9.8% respectively less than the
35
answer obtained by model tests. Part of this error can be accounted for using Polhamus' leading
edge suction analogy described in the next paragraph.
Reference [5] predicted Kt and 1 OKq for a DTRC N4118 propeller using the propeller
panel method PSF1O. PSF10 was able to predict Kt/lOKq down to a J of 0.4 with minimal
variance between PSF10 results and experimental data. However, the solution included a
leading edge suction force correction to increase 1 OKq up to 5% but minimal increase in Kt. The
correction was based on Polhamus' leading edge suction analogy. If PBD included this suction
loss, the IOKq for stand alone mode would only be lower than model tests by 4.8%. Kt,
however, would still be less than model tests by 7.9%.
Comparison Between Stand-alone, Model Test and Coupled, J=0.4
Test
Kt, model test
IOKQ, model test
Kt, Ifix=O, coupled
10Kq, Ifix=O, coupled
Kt, stand-alone
1OKq, stand alone
Table 6.1
Value
0.33
0.53
0.2367
0.3708
0.3039
0.4779
% Error from Model test
0%
0%
28%
30%
7.9%
9.8%
Sources of other error include vortex tip formulation and wake roll up. Currently PBD
only sheds vorticity from the trailing edge, however, at low J vorticity is also shed from the blade
tip. To account for this vortex tip formulation at low J, PBD needs to be modified to shed a
wake from the tip chord. Wake roll up relates to the wake influencing itself as it progresses
downstream. Currently PBD does not account for wake roll up.
36
Chapter 7
Conclusion
7.1 Summary of Results
Using a fixed blade grid lattice and concentrated streamlines, the coupling converges down to an
advance coefficient of 0.5. Using a blade grid lattice that follows the concentrated streamlines,
the coupling converges down to an advance coefficient of 0.3. Both methods result in converged
solutions that are lower than expected by model tests. Possible errors include wake generation,
leading edge suction losses, swirl and drag input to MTFLOW and wake roll up.
7.2 Recommendations for Future Work
1. Change MTFLOW to facilitate the concentration of streamlines at any point in the flow. The
duct in this thesis proves that concentrating streamlines near critical areas enable MTSOL to
converge. MTSET should allow users to input a point in the flow domain that requires
concentrated streamlines.
2. Create a more robust method of inputting swirl and drag from PBD to MTFLOW.
3. Change PBD to input a weighting function to account for leading edge suction losses at low
advance coefficients. Also, change PBD to account for wake roll up.
37
Appendix A
Input Files
Coupling
to PBD/MTFLOW
A.1 Walls File Without Foil and Hub
4119 ITTC walls case
0.0
7.6
0.00
2.000
7.6
0.2
5.449084
0.2
0.2
5.340678
5.234253
0.2
5.130387
0.2
5.029772
0.2
4.933049 0.2
0.2
4.840815
4.753613
0.2
4.671937
0.2
4.596230
0.2
0.2
4.526885
4.464243 0.2
4.408596 0.2
0.2
4.360183
0.2
4.319196
4.285772
0.2
4.260002
4.240000
0.2
0.2
4.22
4.2
4.18
4.16
4.14
4.12
4.1
0.2
0.2
0.2
0.2
0.2
0.2
0.2
4.08
4.06
4.04
4.02
4.0
0.2
0.2
0.2
0.2
0.2
3.2375
3.2125
3.2
0.2
0.2
0.2
3.0
2.0
1.0
0.0
0.2
0.2
0.2
0.2
38
A.2 Walls File with Foil and Hub
4119 ITTC
0.0
7.6
5.449084
5.340678
5.234253
5.130387
5.029772
4.933049
4.840815
4.753613
4.671937
4.596230
4.526885
4.464243
4.408596
4.360183
4.319196
4.285772
4.260002
4.240000
4.22
4.2
4.18
4.16
4.14
4.12
4.1
4.08
4.06
4.04
4.02
4.0
3.2375
3.2125
3.2
3.188016
3.165110
3.143820
3.124304
3.106635
3.090819
3.076809
3.064515
3.053822
3.044594
3.036688
3.029959
3.024263
3.019467
3.015447
qalls case
7.6
0.00
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
2.000
0.199641
0.196933
0.191947
0.185122
0.176870
0.167569
0.157556
0.147119
0.136499
0.125893
0.115453
0.105290
0.095481
0.086069
0.077072
39
3.012093
3.009314
3.007026
3.005163
3.003665
3.002482
3.001573
3.000901
3.000436
3.000148
3.000016
3.000000
3.000016
3.000148
3.000436
3.000901
3.25
0.068492
0.060322
0.052547
0.045150
0.038112
0.031414
0.025038
0.018968
0.013194
0.007705
0.002498
0.0
-0.002498
-0.007705
-0.013194
-0.018968
-0.200000
999.0 999.0
4.01
1.0
4.0
1.01
3.99 1.0
4.0
0.99
4.01
1.0
A.3 Batchfile
bl2body=$HOME/MTFLOW.1/MTCouple/bl2bodyhanson
velcon9=$HOME/MTFLOW.1/VELCON9/SRC/velcon9hanson
pbdl43=$HOME/PBD14.36/SRC/pbdl4
pbd2mt=$HOME/MTFLOW.1/MTCouple/pbd2mt
mtflo=$HOME/MTFLOW.test/Mtflow/bin/mtflo
mtsol=$HOME/MTFLOW.test/Mtflow/bin/mtsol
buildtflow=$HOME/MTFLOW.1/MTCouple/buildtflowhanson
rm Batch.log
date > Batch.log
pwd >> Batch.log
MAX=20
COUNT=1
echo 'TITLE = "ITTC 4119 PBD/MTFLOW COUPLING"' >> KTQOUT.TOT
echo 'VARIABLES = "N", "Kt", "10Kq"' >> KTQOUT.TOT
echo 'ZONE T="Kt / 1OKq", I= ' $MAX >> KTQOUT.TOT
################################################################
#######
while test $COUNT -le $MAX
40
do
echo ' ## PBD - MTFLOW ITERATION ' $COUNT >> Batch.log
echo ' ####### PBD - MTFLOW ITERATION ' $COUNT' #######'
#
################################################################
MTFLOW TO PBD
#
################################################################
# Create VELJOIN.tec from Mtflow results
$bl2body >> Batch.log
echo ' ## Done with bl2body ##'
# Run velcon
$velcon9 < vel.in >> Batch.log
#
#
############################################################
PBD / PBD to MTFLOW
#
################################################################
# Run PBD14.3 and create tflow.xxx
$pbdl43 < pbd.in >> Batch.log
echo ' ## PBD complete ##'
$pbd2mt >> .. /Batch.log
#cat PBDOUT.CMV >> PBDTOT.CMV
#cat PBDOUT.CMF >> PBDTOT.CMF
#cat PBDOUT.SGR >> PBDTOT.SGR
cat PBDOUT.KTQ >> ktrot.tot
tail -1 PBDOUT.KTQ > ktq.in
read wordi word2 word3 word4 < ktq.in
echo $COUNT $word3 $word4 >> KTQOUT.TOT
#############################################################
#
MTFLOW
#
################################################################
# Combine tflow files and run Mtflow
$mtflo 4119 < runMTFLO >> Batch.log
$mtsol 4119 < runMTSOL >> Batch.log
####################################################### #########
COUNT='expr $COUNT + 1'
# End of while loop
done
#######
################################################################
################################################################
A. 4 Vel. in
41
VELJOIN.tec
restart.vel
4.0 1.0
1
1
59
199
0
A. 5 Mtcouple. inp
Mtcouple. inp
! Reynolds number
5 !5
0.001
inlet mach number
! Vship used in PBD to find J
! x location of LE tip
! r location of LE tip
MTFLOW case name
pbd input file name
Blinput toggle (0=no,1=yes)
I Nominal velocity toggle (0=no,1=yes)
Number of blade rows
1.0093
4.0
1.000
4119
4119.pbd
0
0
1
A.6 PBD Admin File
admin file
4119.BSN
restart.vel.
3 25 25
1 1
24 1 2 3 4 5 6 7 8
MCTRP
3
0
0.0
:FILE NAME FOR BLADE B-SPLINE NET
:FILE NAME FOR WAKE FIELD
:nblade, nkey, mkey
:ispn (0=uniform,1=cos),iffixlat
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 : MC,
0.0
0
0
0 0
0.0 0
0.0 0.0
10 -10
0 0
6
0 0 0
5 0.001 0.02 2.0 1
1 0 0 8
1 0.02
4 6
0.05
1.0
1.500
0.6
:ihub, hgap, iduct, dgap
IHUBSUBLAY, IDUCSUBLAY
HDWAK, NTWAKE
Cq, MXITER
OVHANG(1), OVHANG(3)
nx,ngcoeff,mltype,mthick
:IMODE
:NWIMAX
niter,tweak,bulge,radwgt,nufix
:IBSHAPE, IHUBSL, IDUCSL, NGENLINE
: nplot,hubshk
: NOPT, NBLK
:ADVCO XULT XFINAL DTPROP
0.0080 0.0100 0.0200 0.0300 0.0350 0.03500 0.0300 0.0200 .0100 0.0000
:G(design)
.2000
.06576
.3000 .4000 .5000 .60000
.05630 .04777 .0396 .03209
.7000 .8000 .9000
.02504 .01828 .0120
42
.9500 1.0000
.00896 .0000
r/R
T/D
0.00814 0.0086 0.0085 0.0084 0.0082 0.0081 0.008
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.0
A.7 MTFLO
Run MTFLO
p
r
w
q
A.8 MTSOL
Run MTSOL
x
1
1
1
1
1
0
w
q
43
0.0079
0.0000
0.0000
0.0000
0.0000
0.0078
0.0000
0.0000
0.0000
0.0000
0.0079:Cd
0.000 :UA
0.000 :UAU
0.000 :UT
0.000 :UTU
Appendix B
Changes made to MTFLOW Source
Code (io. f)
Corrections are required for MTFLOW to plot grid above
Note:
stagnation line.
.... Start corrections made by Bill Duncan 5MAR02
REAL XAC(II-1,JAIR(3)+1)
REAL YAC (II-1, JAIR (3) +1)
REAL QAXC (II-1, JAIR (3) +1)
REAL QAYC(II-lJAIR(3)+1)
REAL RAVTC (II-1, JAIR (3)+1)
REAL dAlbot, dA2bot, dAltop, dA2top
.. .. End corrections made by Bill Duncan 5MAR02
!...CJH 7/24/00.............................................................
Output cell info to OUTVEL.tec in TecPlot format
Mtflow velocity info is valid at cell centers only,
but X,Y locations are at cell corners.
So ..................
centers and extrapolate velocity info back to boundary
Shift X,Y to cell
Thus, array size info:
wall.
but Q,RVTA valid only in
Original X,Y,Q,RVT array II,JJ
For Q,RVTA the IIth column
since already cell centered.
II-1,JJ-1
zero.
all
row
are
and JJth
New XCYC,Q,RVTA arrays are II-1,JJ+l due to adding streamline at bottom
and top of domain to recover the half cell which drops out in the shift
The half cell lost at the inlet and outlet is ignored
to cell center.
since they do not effect the PBD results.
Current version outputs info from t=0 to t=1.0,
to give up to t=2.0 for the ducted case.
should be improved
If the extrapolated velocity is < 0 (in case of rapid BL change with
the velocity is "stamped" to zero.
profile),
a specific inlet
!.............................................................................
...
Shift X & Y to cell center and shift all info up one row to make room
for wall streamline to be added later.
DO J=1,JAIR(2)-1
DO I=1,II-1
XC(I, J+l) = 0.25* (X(I,J)+X(I+1,J)+X(I,J+1)+X(I+1, J+1))
YC(I,J+l) = 0.25*(Y(I,J)+Y(I+1,J)+Y(I,J+1)+Y(I+lJ+1))
44
QXC (I, J+1) =QX (I, J)
QYC (I, J+1) =QY(I, J)
RVTC (I, J+1)=RVT (I, J)
END DO
END DO
.... Start corrections made by Bill Duncan 5MAR02
DO J=JAIR(2),JAIR(3)-1
DO I=1,II-1
XAC(I,J+l) = 0.25*(X(IJ)+X(I+1,J)+X(I,J+1)+X(I+1,J+1))
YAC(I,J+l) = 0.25*(Y(I,J)+Y(I+1,J)+Y(I,J+1)+Y(I+1,J+1))
QAXC (I, J+1) =QX (I, J)
QAYC (I, J+1) =QY (I, J)
RAVTC (I, J+1) =RVT (I, J)
END DO
END DO
.... End corrections made by Bill Duncan 5MAR02
... Now add in the bottom and top streamlines to recover the half cell on
Linearly
bottom and top that was lost during cell center shift.
!
*
extrpolate velocity info from two points outward to get
*
velocity info.
DO I=1,II-1
XC(I,1)=0.5*(X(I,1)+X(I+l,1))
YC(I,1)=0.5* (Y(I,1)+Y(I+l,1))
XC(I,JAIR(2)+1)=0.5*(X(I,JAIR(2))+X(I+1,JAIR(2)))
YC(I,JAIR(2)+l)=0.5*(Y(I,JAIR(2))+Y(I+1,JAIR(2)))
dlbot=SQRT((XC(I,2)-XC(I,1))**2+(YC(I,2)-YC(I,1))**2)
d2bot=SQRT ((XC (1,3) -XC (1,1)) **2+ (YC (1,3) -YC (1,1) ) **2)
dltop=SQRT((XC(I,JAIR(2))-XC(I,JAIR(2)+l))**2+(YC(I,JAIR(2))
-YC(IJAIR(2)+1))**2)
&
d2top=SQRT((XC(I,JAIR(2)-1)-XC(I,JAIR(2)+1))**2+
(YC(I,JAIR(2)-1)-YC(IJAIR(2)+l))**2)
&
QXC(I,1)=VelExtrap(QXC(I,2),QXC(I,3),d1bot,d2bot)
! Velocity "stamping"
IF (QXC(I,1).LT.0) QXC(I,1)=0
QYC(I,1)=VelExtrap(QYC(I,2),QYC(I,3),d1bot,d2bot)
RVTC(I, 1)=VelExtrap(RVTC(I,2),RVTC(I, 3) ,dlbot,d2bot)
QXC(I,JAIR(2)+l)=VelExtrap(QXC(I,JAIR(2)),QXC(I,JAIR(2)-l),
d1top,d2top)
&
QYC(I,JAIR(2)+l)=VelExtrap(QYC(I,JAIR(2)),QYC(IJAIR(2)-l),
dltop,d2top)
&
RVTC(I,JAIR(2)+l)=VelExtrap(RVTC(I,JAIR(2)),RVTC(I,JAIR(2)-l),
dltop,d2top)
&
END DO
....
Start
corrections
made
by Bill
Duncan
5MAR02
DO I=1,II-1
XAC(I,JAIR(2))=0.5*(X(I,JAIR(2))+X(I+1,JAIR(2)))
YAC(I,JAIR(2))=0.5*(Y(I,JAIR(2))+Y(I+1,JAIR(2)))
XAC(I,JAIR(3)+l)=0.5*(X(I,JAIR(3))+X(I+1,JAIR(3)))
YAC(IJAIR(3)+l)=0.5*(Y(I,JAIR(3))+Y(I+l,JAIR(3)))
dAlbot=SQRT((XAC(I,JAIR(2)+2)-XAC(I,JAIR(2)+l))**2+
(YAC(I,JAIR(2)+2)-YAC(I,JAIR(2)+1))**2)
&
dA2bot=SQRT((XAC(I,JAIR(2)+3)-XAC(IJAIR(2)+1))**2+
(YAC(I,JAIR(2)+3)-YAC(IJAIR(2)+l))**2)
&
dAltop=SQRT((XAC(I,JAIR(3))-XAC(I,JAIR(3)+1))**2+
&
&
(YAC(I,JAIR(3))
-YAC(I,JAIR(3)+1))**2)
dA2top=SQRT((XAC(I,JAIR(3)-1)-XAC(IJAIR(3)+l))**2+
45
&
(YAC(IJAIR(3)-1)-YAC(IJAIR(3)+1))**2)
QAXC(I,JAIR(2))=VelExtrap(QAXC(I,JAIR(2)+2),
QAXC(I,JAIR(2)+3),dAlbot,dA2bot)
Velocity
IF (QAXC(I,JAIR(2)).LT.0) QAXC(IJAIR(2))=0
"stamping f
&
&
QAYC(I,JAIR(2))=VelExtrap(QAYC(I,JAIR(2)+2),
QAYC(I,JAIR(2)+3),dAlbot,dA2bot)
RAVTC(I,JAIR(2))=VelExtrap(RAVTC(I,JAIR(2)+2),
RAVTC(I,JAIR(2)+3),dAlbot,dA2bot)
&
QAXC(I,JAIR(3)+l)=VelExtrap(QAXC(I,JAIR(3)),QAXC(I,JAIR(3)-l),
dAltop,dA2top)
QAYC(I,JAIR(3)+1)=VelExtrap(QAYC(I,JAIR(3)),QAYC(I,JAIR(3)-1),
dAltop,dA2top)
RAVTC(I,JAIR(3)+1)=VelExtrap(RAVTC(I,JAIR(3)),
RAVTC(I,JAIR(3)-1),dAltop,dA2top)
END DO
....
...
End
corrections made by Bill Duncan 5MAR02
.Corrections made by Bill Duncan 5MAR02 - changed OUTVEL.tec to read to
!....JAIR(3) instead of JAIR(2)
TITLE = "MTFLOW Velocity Output"
VARIABLES = "X", "R", "Vx", "Vr", "Vt", "Cp"
ZONE T="Cell Velocity", I='',I4,'' J='',I4,
&
''
&
DO J=1,JAIR(2)+l
DO I=1,II-1
WRITE (169, 1002)
F=POINT
'')')
II-1,JAIR(3)+l
XC(IJ),YC(IJ),QXC(I,J),QYC(I,J),RVTC(I,J),
CP(I,J)
END DO
END DO
Start corrections made by Bill
&
....
'
OPEN(UNIT=169, FILE='OUTVEL.tec',STATUS='UNKNOWN')
WRITE(169,'(A)
WRITE(169, '(A)
WRITE(169,'(''
Duncan 5MAR02
DO J=JAIR(2),JAIR(3)+l
DO I=1,II-1
WRITE (169, 1002) XAC(IJ),YAC(I,J),QAXC(IJ),QAYC(IJ),
RAVTC (I, J) ,CP (I, J)
END DO
END DO
.... End corrections made by Bill
Duncan 5MAR02
CLOSE(169)
46
Appendix C
Changes made to PBD2MT Source
Code
Note:
This code
the first crossing
Zlast to Zl in the
tip instead of the
and swirl will not
!
inputs swirl equal to the tip swirl between
Change
of a t line and the stagnation line.
**** section and the program will go to the
Uncomment the $$$ section
first crossing.
be input between the tip and stagnation line.
Subroutine GetZRrVt finds Z,R,rVt where the given t
current blade CP line of interest.
line crosses
Input:
t: t value of interest
BFGline: t line number
Z,R coordinate and rVt at the coordinate
Output:
Blade array, BFG array,MM,JJ
Global Variables used:
-------------------------------------------------------------------SUBROUTINE GetZRrVt (BFGline, t, Z,R, rVt, DSdrag, ZLAST,togl)
IMPLICIT NONE
:: t
REAL, INTENT(IN)
INTEGER, INTENT(IN) :: BFGline
:: Z,R,rVt,DSdrag
REAL, INTENT(OUT)
REAL
Z1,Z2,RlR2,Zhigh,Rhigh,Zlow,Rlow,rVthigh,rVtlow,Ll,L2,L,tt,ZLAST
:: I
INTEGER
:: Tolerance=1E-7
REAL, PARAMETER
:: Undershoot,Overshoot,togl
LOGICAL
Undershoot=.TRUE.
Overshoot=.FALSE.
DO I=1,MM
Zl=BLADE (1, J, I)
Rl=BLADE (2, J, I)
tt=t Find (Z 1, Rl)
IF (tt>t) THEN
ZLAST=Zl
EXIT
END IF
Undershoot=.FALSE.
If here,
t line
END DO
47
at least one blade CP is below
IF
(tt<=t) Overshoot=.TRUE.
I This can happen above the last blade
CP
...
No blade CP above for interpolation ==> extend CP #MM info up
IF (Overshoot) THEN
Z=ZLAST
I Extend Z info up
DO K=1,II
tLineZ(K)=BFG(1,BFGline*II-II+K)
tLineR(K)=BFG(2,BFGline*II-II+K)
END DO
I Find R given t line and Z
CALL LININTERP(II,tLineZ,tLineR,Z,R)
I For open prop rVt=O
rVt=O
IF ((ISDUCT.OR.INTERNAL).AND.(.NOT.togl)) THEN
rVt=BLADE(3,J,MM)! For ducted/internal extend rVt info up from CP
#MM
togl=.TRUE.
END IF
END IF
...
No blade CP below for interpolation ==> extend CP #1 info down
IF (Undershoot) THEN
Z=Z1
! Extend Z info down
DO K=1,II
tLineZ(K)=BFG(1,BFGline*II-II+K)
tLineR(K)=BFG(2,BFGline*II-II+K)
END DO
! Find R given t line and Z
CALL LININTERP(II,tLineZ,tLineR,Z,R)
rVt= BLADE(3,J,1)
! Extend rVt info down from CP
#1
DSdrag=BLADE (4, J, 1)
END IF
...
Have blade CP above and below t line of interest
Interpolates info from blade CP above and below
Uses bisection method to get Z,R of blade span and t line intersection
IF ((.NOT.Overshoot).AND.(.NOT.Undershoot)) THEN
Z2=BLADE(1,.J, I-1)
R2=BLADE(2,J, I-1)
Zhigh=Zl
Rhigh=Rl
Zlow=Z2
Rlow=R2
DO
Z=0.5*(Zl+Z2)
R=0.5*(Rl+R2)
tt=tFind (Z, R)
IF (tt<=t) THEN
Z2=Z
R2=R
ELSE
Zl=Z
Rl=R
END IF
IF (ABS(R2-R1)<Tolerance) EXIT
END DO
48
L1=SQRT
L2=SQRT
L=L1+L2
((Zhigh-Z) **2+ (Rhigh-R) **2)
((Z-Zlow) **2+ (R-Rlow) **2)
rVthigh=BLADE (3, J, I)
rVtlow=BLADE(3,J,I-1)
rVt=rVthigh*L2/L + rVtlow*L1/L
interpolate to get rVt
DSdrag=BLADE(4,J,I)*L2/L + BLADE(4,J,I-1)*L1/L
END IF
END SUBROUTINE GetZRrVt
49
Linear
!same fore DSdrag
Appendix D
PBD Admin. File for PSF-2
Convection Velocities
:FILE NAME FOR BLADE B-SPLINE NET
4119.BSN
:FILE NAME FOR WAKE FIELD
uniform.rotor.vel
:nblade, nkey, mkey
3 25 25
:ispn (0=uniform,1=cos),iffixiat
11
24 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 : MC,
MCTRP
:ihub, hgap, iduct, dgap
0.0
0.0
0
3
: IHUB SUBLAY, IDUCSUBLAY
0
0
HDWAK, NTWAKE
0 0
Cq, MXITER
0.0 0
OVHANG(1), OVHANG(3)
0.0 0.0
nx,ngcoeff,mltype,mthick
10 -10 0 0
:IMODE
4
:NWIMAX
0 0 0
niter,tweak,bulge,radwgt,nufix
5 0.001 0.02 2.0 1
:1_BSHAPE, IHUBSL, IDUCSL, NGENLINE
1 0 0 8
: nplot,hubshk
1 0.02
: NOPT, NBLK
4 6
:ADVCO XULT XFINAL DTPROP
0.4
1.0
1.500
0.05
0.0080 0.0100 0.0200 0.0300 0.0350 0.03500 0.0300 0.0200 .0100 0.0000
:G (design)
.9000
.9500 1.0000 :r/R
.8000
.5000 .60000
.7000
.2000
.3000
.4000
.00896 .0000 :T/D
.02504 .01828 .0120
.05630 .04777 .0396 .03209
.06576
0.00814 0.0086 0.0085 0.0084 0.0082 0.0081 0.008 0.0079 0.0078 0.0079:Cd
1.238 0.918 :UA
1.612
1.449
1.535
1.158
1.351
0.935
0.626
0.178
0.835 0.891 :UAU
0.875
1.500
1.145
1.714 1.738
1.266
1.509
1.122
-0.802 -1.071 -1.082 -0.976 -0.864 -0.735 -0.544 -0.412 -0.249 :UT
-0.132
-0.226 -0.231 -0.305 :UTU
-1.888 -1.218 -0.931 -0.845 -0.775 -0.589 -0.364
50
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