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Computational Improvements to Predict Propeller Performance at Off DesignConditions
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 ofthe 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 ofthis thesis document in whole or in part.
Signature of A uthor.............................................................................................. .... ....Department of Ocean Engineering and Mechanical Engineering
May 10, 2002
Certified by ........................................................................ ... ............................
David V. BurkeSenior Lecturer, epartment of Ocean Engineering
Thesis Supervisor
Read by.........................................................Ain A. Sonin
anical EngineeringThesis Reader
A ccepted by ..................................................... ..... . ...... ..........................Henrik Schmidt
ssor of Ocean EngineeringChairman, Committee on Grad ts for Ocean Engineering
Accepted by .......................................................................Ain A. Sonin
Professor of Mechanical EngineeringChairman, Committee on Graduate Studies for Mechanical Engineering
MASSACHUSETTS INSTITUTEOF TECHNOLOGY
AUG 2 002 BARKER
LIBRARIES
Computational Improvements to Predict Propeller Performance at Off DesignConditions
by
William E. Duncan
Submitted to the Department of Ocean Engineering and the Department of MechanicalEngineering 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 performancefor the 4119 propeller at off design conditions. The 4119 propeller is a conventional threebladed propeller without skew. The existing computational method used is an Euler/IntegratedBoundary Layer Theory (IBLT) axisymmetric flow solver coupled with a propeller liftingsurface design and analysis program. Presently, the coupling will converge to realistic thrust andtorque coefficients at advance coefficients between 0.7 and 1.1. The modified procedureoutlined in this thesis can predict thrust and torque coefficients down to an advance coefficient of0.3, however, the results are lower than expected from model tests. An error analysis is includedto identify reasons for the low thrust and torque coefficients.
Thesis Supervisor: David V. BurkeTitle: 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 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
2 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
3 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
4 Case I, Blade Grid is Fixed 27
4.1 Overview 27
4.2 Grid 27
4.3 Artificial Modifications 28
4
Page
4.4 Effective Velocity 30
5 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
6.1 Overview 35
6.2 PBD Error 35
7 Conclusion 37
7.1 Summary of Results 37
7.2 Recommendations for Future Work 37
A Input Files to PBD/MTFLOW Coupling 38
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
B Changes to MTFLOW Source Code (io.f) 44
5
C Changes made to PBD2MT Source Code 47
D PBD Admin. File for PSF-2 Convection Velocities 50
Bibliography 51
6
List of Figures Page
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
22
24
25
36
List of Tables
3.1 Guidelines to Concentrate Streamlines
3.2 Foil and MTSET values
3.3 X and R values for Foil
6.1 J=0.4, Ifix=O results compared to PSF-2
9
Nomenclature
A
B
D
h
VsnD
TKt T
pn2 D4
Kq 2pn2 D5
m
n
n
p
q
R
S
To
V
r V o
(Veffective)
(Vinsced)
cross sectional area
field parameter
propeller diameter
enthalpy
advance coefficient
thrust coefficient
torque coefficient
mass flow rate
surface normal vector
propeller rotation rate revsec
pressure
meridional speed
radial coordinate
entropy
field parameter
velocity
swirl, tangential velocity
effective velocity
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
radblade rotation rate ---
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 propelleritself." [5]
Induced flow (Vinduced): induced velocity by the propeller and trailing wake vortex
distributions.Nominal flow: 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).
(Vto ta) =(Veective) + (Vinduced (1.2)
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 Gridsurfaces are ideal due to the normal vector from the surface
and the curvature can be uniquely defined everywhere on0.7
the surface. In defining the surface, the user can choose an 60.5:
appropriate grid density to accurately capture the forces. 0.4
0.3
0.2 -0.2 0 0.2 0.4 0.6
Fig. 1. 1: A1IOX 10 grid
13
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).
dFrf(y) - (1.3)
dy
Horseshoe Element
FreeVortexSegment
Bound Control pointVortex 0Segme t
Fig. 1.2: Grid box is one of the boxes fromfigure 1.1. Vorticity is shed from one Freesegment of bound vorticity to two Vortexsegments of free vorticity [7]. 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 (1.4)
Combining equations 1.4, 1.2 and 1.1 results in equation 1.5.
14
[[INF] i] +Veecte -n =0 (1.5)
From equation 1.5, the resultant distribution of force on the blade can be calculated using Kutta-
Joukowski'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, re-
computes 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 AdvanceCoefficients
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
Figure 2.1 shows the close
0.5 -correlation of Kt and IOKq results 5Model Test10 10Kq,Model Test
Kt 0.4 IL KtCoupled no fbilfor advance coefficients between 0.7 K 1 Oq,Coupled nofoit
10Kq _
and 1.1 [4,11]. There are two Kt
problems at low J. First, the grid in 0.2
MTFLOW is too coarse to accurately
model the flow around the tip. %.3 0 0 0 0 0 0 2Advance Coefficient J
Second, PBD2MT does not accurately input Fig. 2.1: Kt/IOKq results forexisting 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
1.5 R
R
0.5
3 4 5 3 V4 5xV
Fig: 2.2: MTFLOW grid Fig. 2.3 MTFLOW grid does not
separates at low J. separate at J above 0.7.
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.
Figure 2.5 shows the resulting wake when the grid separates. As a comparison, Figure 2.4 shows
a wake growing properly downstream.
18
Blade and TransitionJ=0.4
Blade and Transition Wake,J=0.833
0.a5 1 1
0.5
Y0
-0.25
-0.5
-0.75
xFig. 2.4 Wake follows the
streamlines.
xFig. 2.5 Wake can not follow 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 = 0.4PBD Input Swirl Contour Lines, J = 0.833
0.975
0.95
4.02 4.04X
Fig. 2.6: Swirl Contour linesbecome crossed at J= 0.4.
4.02
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
US
0.5
025
1
0.99
0.98
50.97
0.96
0.95
0.94
Y
I 1-5
4.06 4.084.04 4.06
1 .
R
0
0
Blade and MTFLOW Grid, J = 0.833
Notice the jump in streamlinesbetween inside and outside theblade
9
Streamlines Vertical blade.8 in M TFL OW lines are s
are t lines lines
.7
3.7 3.8 3.9 4 4.1 4.2 4.3x
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= 0.4Ifix =I
fine if the streamlines stayed perfectly
horizontal and the MTFLOW grid had
dense streamlines at the tip. TwoR-
problems develop when the streamlinesThe constant sline crosses a t
are not horizontal and the MTFLOW grid 0.95 line twice.
is coarse at the tip. First, at low J
the streamlines become more vertical. 4 4.05 4.1x
This causes streamlines (t lines) to cross s 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<=0.7N number of streamwise grid N should be greater than 150
pointsE exponent for airfoil side E must be correlated with the size of the foil. For a
points: n = N*chord given foil if:(fig. 3.2, 3.3, 3.4) E is too large - mtsol will only grid the leading edge
E is too small - mtsol output grid includes the foilE just right - mtsol will grid the leading and trailingedges 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 Description Guidelines for J<=0.7X x-spacing parameter X should equal one. The vertical lines connecting the
upper and lower grid will then be straight. (fig. 3.1)S number of streamlines S should be greater than 60J j-spacing flag Set J = 1. This will allow WI, W2, T1, T2 and T3 to
be variedW1 streamline bunching weight Wi should be greater than W2. This will put more
between airfoils 1,2 streamlines below the foil. When the stagnation linemoves higher the upper grid upstream will not be toodense
W2 streamline bunching weight W2 should be less than Wi. This will put lessbetween airfoils 2,3 streamlines in the upper grid.
TI airfoil 1 (bottom of grid) TI, T2 and T3 are relative weighting numbers. TIsurface streamtube thickness corresponds to the grid density near the hub and nearfactor the foil but still in the lower grid. TI should be greater
than T2 to bunch the streamlines around the foil. Sincethere are more streamlines in the lower grid Ti shouldbe less than T3 to keep the grid symmetric.
T2 airfoil 2 (foil location) surface T2 should be less than TI and T3. This will allow thestreamtube thickness factor streamlines around the foil to be more dense
T3 airfoil 3 (top of grid) surface T3 corresponds to the grid density at the outerstreamtube thickness factor boundary and near the foil but in the upper grid. T3
should be greater than T2 to bunch the streamlinesabove the foil instead of at the boundary. To keep thegrid symmetric T3 should also be greater than TI.
Foil A diamond is the easiest foil The critical dimension is the distance between the(walls to manipulate. MTSET reads points along the X axis. This distance must befile) the diamond starting at the correlated with the exponent variable, E. The griddownstream point and
proceeds counter-clockwise. reads a diamond but interpolates a circle. (fig 3.7, 3.8)Each point should be on the Xand R axis (X being horizontaland R vertical) and alsosymmetric about the X and Raxis.
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
X R Symbol Value4.001 1.0 N 2004.0 1.001 E 0.9003.999 1.0 X 1.0004.0 0.999 S 604.001 1.0 J 1
W1 0.700W2 0.500TI 0.500T2 0.050T3 0.700
Table 3.2
Foil
MTSOLGridE = 0.900
Fig. 3.2: MTSOL will crash becausethe trailing edge does notcross a grid line. E needs to
be smaller.
Foil
Fig. 3.3: MTSOL will converge.Trailing edge does cross agrid line.
w Grd e=0.4
Fig. 3.4: E is too low. MTSOL output file isgridding a portion of the foil.
1.01 Streamlines will cross as flow goesaround foil to blade
D~an -
&06 4 4.005
24
Foil
MTSOLGridE = 0.600
MTSET
I I
2.5
[ MTFLOW Grid x=0.001
R t. o
0.5
Fig. 3. 1: MTSOL will crash. Upper andlower grid do not meet at right angles. Xneeds to equal one.
Blade and MTFLOW GridI | | | | | | | | | || | | | | 0 | | | | | | | I I I I I I I I I I I
Blade and MTFLOW Grid
16
14-4 -
1.2
R
0.8
0.6
0.43.9 4
x4.1 4.2
xFig. 3.5: Same graph as Fig. 3.6 Fig. 3.6: Illustration of dense gridding in
but zoomed in. MTSOL X and R directions. MTSOLwill converge 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 R4.01 1.04.0 1.013.99 1.04.0 0.994.01 1.0
Table 3.3
Hub and Blade inMTFLOW Grid
R
3
Fig. 3.7:
4 5x
Hub and blade with longer chord.Grid is not as dense in the Xdirection.
Foil
MTSOL-- - - Grid
E = 0.900
Fig. 3.8: The longer chord set in the walls fileallows the trailing edge to cross a gridline even with the higher E.
25
1.15
1.1
Ros
1
0.95
0.9
0.85
Figure 3.9 illustrates a chord set in the walls file for a foil
that is too long even at an exponent equal to 0.9. The
streamlines would cross as the flow goes across the foil to
the blade.
1.3
1.2
Foil in MTFLOW Grid
1.1
R
0.9
0.8
0.7
3.6 3.8 4 4.2xFig. 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 FoilLevel
VX: 1'1
1.01
0. 99 - 1
2 3 45 0.9976 0.9989 0.9997
5 6 7 81.0004 .1.0007 1.0018 1.00499 10 11
1.0060 1.0080 1.0091
x
Fig. 3.10: Axial velocity around the foil is lessthan 1%.
26
-r
. ,,, 1,
4.01
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
blade tip. In this case the blade does not Kt, 1 OKq Vs. Advance Coefficient, Ifix=1
move with the streamlines. There is only - - - - - KtModel Test1 OKq,Model Test
A Kt,Foil at tipix=1
slight movement to maintain a geometrical 0.4 lI 1OKq,FoIl at tip, fx=1
Cr
relationship with the outer domain '0.3 -
AK
boundary. Figure 4.1 shows that the 0.2 'L
coupling converged down to an advance 0.1
coefficient of 0.5, however, there were 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2coeficiet of0.5,howeer, hereAdvance Coefficient, J
artificial modifications to the coupling to force Fig. 4.1: Results for Ifix=1
convergence at J=0.5. These modifications
will be discussed in this chapter.
4.2 Grid
27
Figure 4.2 illustrates the blade and MTFLOW grid for J=0.5 using the MTSET parameters
outlined in Table 3.2. The foil parameters are the same as Table 3.2 except that the X location is
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
0.8 3
x
Fig. 4.2: J=O.5, Ifix=1, Blade and Fig. 4.3: Stagnation line is outside blade
MTFLOW grid. tip. Wake grows properly.
stagnation line crosses the blade. First, the tip wake will begin outside the slip stream where the
velocities are just free stream. This will result in the tip wake pitch not proceeding at the correct
angle and will skew the final Kt and 10OKq results. The second problem is that the tangential
velocity will not be added above the stagnation line. The PBD2MT code sections the lower grid
and upper grid based on the location of the stagnation line. Because the foil tricks the code into
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
Blade Grid (dashed lines) and SwirlInput Grid (solid lines)
-- going- vertical
from lastknown
4 location.
3.7F,.05 403.975 4 4.025 4.05
x
Fig. 4.4: Notice the swirl input outsid the blade
grid.
crossing the s lines went vertically upward to the
Input Swirl at Tip, Ifix=1, J=0.5
3.99 4 4 0 . 4.03 .04 .0
1.03
1.02
1.01
S1
0.99
0.98
0.97
3.99 4 4.01 4.02 4.03 4.04 4.05X
Fig. 4.5: Swirl is input above the blade tip. Swirl isinput from the last known position thenproceeds vertically up inputting swirl equal to
the tip swirl.
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
1.02
R
0.98
0.96
4.4 Effective VelocityEffective Velocity, Ifix=1, J=0.5
The effective velocity ranges +/-12 % which is
an indication of poor coupling. The artificial
modifications are partly to blame. An in depth
error analysis will be conducted in chapter 6.
0.9
0.8
0.7
R 0.6
0.5
0.4
0.3
-
T2
Level Ux14 1.1204313 1.1133812 1.1040611 1. 0955810 1.08708
9 1.011238 0.994208
7 0.9771826 0.9601575 0.9431324 0.:261073 0.909822 0.8920561 0.875031
Fig. 4.6: The large range in effectivevelocity indicates poor coupling.The velocities not shown areconcentrated at the blade tiptrailing edge.
30
0.4 0.6-0.2
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
parallel to the streamlines. Case II resulted Kt I OKq Vs. J, IfIx=O
in converged solutions down to J=0.3 but 0.5 KtFo Downsream
0 1 OKq,Foll Downstream
the solutions were much lower than 04O 0'KqtFoiatTipaY- - KtModel Testc - 1Kq,Model Test
expected from model tests (figure 5.1). The T
10Kqsolutions were converged with the foil 0.2
Ktlocated at the tip and downstream. There 0
were only slight differences in final 3 . 0 0 0 1.2J, Advance Coefficient
Kt/l0Kq with the two methods. However, Fig. 5.1: Kt/1OKQ Vs. J, Ifix=O
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 MTFLOWR
grid after converging at J=0.4. The chord length0.8
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. 0.23.5 4 4.5 5
The dense grid in the X direction used in Fig. 5.2: Blade and MTFLOW grid, Ifix=O,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
downstream and the J from above. Thisresulted in the stagnation line being close to theblade tip (figure 5.3).
* Adjust J such that the stagnation line is justabove the blade tip. This will allow the swirl tobe input at the proper location.
R
If the downstream foil was too high, the0.95
concentrated streamlines would be above the blade
and MTFLOW would crash. If the foil was too
low, the stagnation line would cut through the
blade and swirl would not be input above the
Blade and MTFLOW Grid,Iix=O, J=0.4 (Tip Region)
xFig. 5.3: Stagnation line does not cross blade
tip. Foil is downstream. The foilwas placed in the correct location,thus, not requiring J to be adjusted.
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, Ifix=0, J=0.41.04 1-
15 0.36282714 0.338638
1 0.9261
7 0.169319
2 0.4876
8
Swirl Input Locations to Blade, Ifix=0, J=0.41. 04 1-
1.02k
1
0.98
i0.96
0.94
0.92
0.9
4.05
Fig. 5.4: Swirl input locations. Noticethe contour lines do not cross.
mm-J
4.05 4.1
4x6
Fig. 5.5: Swirl is input properly along the blade.Dashed lines are the blade grid. Solidlines are the input swirl locations.
artificially to the foil (figure 5.5). However, in order for MTSOL to converge, PBD2MT must
33
1.02
1
0.98
M 0.96
0.94
0.92
0.9
1
4.1
4.1
4.1
- 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.
Blade and Wake, Ifix=O,J=0.4
xWake follows streamline.
0.9
0.8
0.7
: 0.6
0.5
0.4
0.3
Effective Velocity, Ifix=O, J=0.4
-
Level LIx1 1 1240(10 1.2209 1.201:
8 1.18117 1.16116 1.1225 1.083
8 4 1.024C3 1.0042 0.984
-71 0.965
6-4 A .11 1 1AI
-0.2 0 0.2 0.4X
Fig. 5.7: The large variance in effectivevelocity indicates poor coupling.
34
1
0.5
Y
0
-0.5
0
Fig. 5.6:
0.6
9427693584
5573
2
0.62
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 Value % Error from Model testKt, model test 0.33 0%IOKQ, model test 0.53 0%Kt, Ifix=O, coupled 0.2367 28%10Kq, Ifix=O, coupled 0.3708 30%Kt, stand-alone 0.3039 7.9%1OKq, stand alone 0.4779 9.8%Table 6.1
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 to PBD/MTFLOW
Coupling
A.1 Walls File Without Foil and Hub
4119 ITTC walls case0.0 7.6 0.00 2.000
7.6 0.25.449084 0.25.340678 0.25.234253 0.25.130387 0.25.029772 0.24.933049 0.24.840815 0.24.753613 0.24.671937 0.24.596230 0.24.526885 0.24.464243 0.24.408596 0.24.360183 0.24.319196 0.24.285772 0.24.260002 0.24.240000 0.24.22 0.24.2 0.24.18 0.24.16 0.24.14 0.24.12 0.24.1 0.24.08 0.24.06 0.24.04 0.24.02 0.24.0 0.23.2375 0.23.2125 0.23.2 0.23.0 0.22.0 0.21.0 0.20.0 0.2
38
A.2 Walls File with Foil and Hub
4119 ITTC0.0
7.65.4490845.3406785.2342535.1303875.0297724.9330494.8408154.7536134.6719374.5962304.5268854.4642434.4085964.3601834.3191964.2857724.2600024.2400004.224.24.184.164.144.124.14.084.064.044.024.03.23753.21253.23.1880163.1651103.1438203.1243043.1066353.0908193.0768093.0645153.0538223.0445943.0366883.0299593.0242633.0194673.015447
qalls case7.6 0.000.2
0.20.20.20.20.20.20.20.20.20.20.20.20.20.20.20.20.20.20.20.20.20.20.20.20.20.20.20.20.20.20.20.20.20.1996410.1969330.1919470.1851220.1768700.1675690.1575560.1471190.1364990.1258930.1154530.1052900.0954810.0860690.077072
2.000
39
3.012093 0.0684923.009314 0.0603223.007026 0.0525473.005163 0.0451503.003665 0.0381123.002482 0.0314143.001573 0.0250383.000901 0.0189683.000436 0.0131943.000148 0.0077053.000016 0.0024983.000000 0.03.000016 -0.0024983.000148 -0.0077053.000436 -0.0131943.000901 -0.0189683.25 -0.200000
999.0 999.04.01 1.04.0 1.013.99 1.04.0 0.994.01 1.0
A.3 Batchfile
bl2body=$HOME/MTFLOW.1/MTCouple/bl2bodyhansonvelcon9=$HOME/MTFLOW.1/VELCON9/SRC/velcon9hansonpbdl43=$HOME/PBD14.36/SRC/pbdl4pbd2mt=$HOME/MTFLOW.1/MTCouple/pbd2mtmtflo=$HOME/MTFLOW.test/Mtflow/bin/mtflomtsol=$HOME/MTFLOW.test/Mtflow/bin/mtsolbuildtflow=$HOME/MTFLOW.1/MTCouple/buildtflowhanson
rm Batch.log
date > Batch.logpwd >> Batch.log
MAX=20COUNT=1
echo 'TITLE = "ITTC 4119 PBD/MTFLOW COUPLING"' >> KTQOUT.TOTecho 'VARIABLES = "N", "Kt", "10Kq"' >> KTQOUT.TOTecho 'ZONE T="Kt / 1OKq", I= ' $MAX >> KTQOUT.TOT
################################################################
#######
while test $COUNT -le $MAX
40
doecho ' ## PBD - MTFLOW ITERATION ' $COUNT >> Batch.log
echo ' ####### PBD - MTFLOW ITERATION ' $COUNT' #######'
################################################################# MTFLOW TO PBD ################################################################## Create VELJOIN.tec from Mtflow results$bl2body >> Batch.logecho ' ## 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.logecho ' ## PBD complete ##'$pbd2mt >> ../Batch.log#cat PBDOUT.CMV >> PBDTOT.CMV#cat PBDOUT.CMF >> PBDTOT.CMF#cat PBDOUT.SGR >> PBDTOT.SGRcat PBDOUT.KTQ >> ktrot.tottail -1 PBDOUT.KTQ > ktq.inread wordi word2 word3 word4 < ktq.inecho $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 loopdone
#######
################################################################################################################################
A. 4 Vel. in
41
VELJOIN.tecrestart.vel4.0 1.011591990
A. 5 Mtcouple. inp
Mtcouple. inp5 !50.0011.00934.01.00041194119.pbd001
! Reynolds numberinlet mach number
! Vship used in PBD to find J! x location of LE tip! r location of LE tipMTFLOW case namepbd input file nameBlinput toggle (0=no,1=yes)
I Nominal velocity toggle (0=no,1=yes)Number of blade rows
A.6 PBD Admin File
admin file4119.BSNrestart.vel.3 25 251 124 1 2 3 4 5 6 7 8 9 10 11 12 13 14
MCTRP3 0.0 0 0.00 00 00.0 00.0 0.010 -10 0 060 0 05 0.001 0.02 2.0 1
1 0 0 8
:FILE NAME FOR BLADE B-SPLINE NET:FILE NAME FOR WAKE FIELD:nblade, nkey, mkey:ispn (0=uniform,1=cos),iffixlat
15 16 17 18 19 20 21 22 23 24 : MC,
:ihub, hgap, iduct, dgapIHUBSUBLAY, IDUCSUBLAYHDWAK, NTWAKECq, MXITEROVHANG(1), OVHANG(3)nx,ngcoeff,mltype,mthick
:IMODE:NWIMAX
niter,tweak,bulge,radwgt,nufix:IBSHAPE, IHUBSL, IDUCSL, NGENLINE
1 0.02 : nplot,hubshk4 6 : NOPT, NBLK0.6 1.0 1.500 0.05 :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 .3000 .4000 .5000 .60000 .7000 .8000 .9000 .9500 1.0000.06576 .05630 .04777 .0396 .03209 .02504 .01828 .0120 .00896 .0000
r/RT/D
42
0.00814 0.0086 0.0085 0.0084 0.0082 0.0081 0.0080.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00000.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00000.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00000.0 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.0079 0.0078 0.0079:Cd0.0000 0.0000 0.000 :UA0.0000 0.0000 0.000 :UAU0.0000 0.0000 0.000 :UT0.0000 0.0000 0.000 :UTU
A.7 MTFLORun MTFLOpr
w
q
A.8 MTSOLRun MTSOLx111110w
q
43
Appendix B
Changes made to MTFLOW SourceCode (io. f)
Note: Corrections are required for MTFLOW to plot grid above
stagnation line.
.... Start corrections made by Bill Duncan 5MAR02REAL 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 formatMtflow velocity info is valid at cell centers only,but X,Y locations are at cell corners.
So ..................Shift X,Y to cell centers and extrapolate velocity info back to boundarywall. Thus, array size info:
Original X,Y,Q,RVT array II,JJ but Q,RVTA valid only inII-1,JJ-1 since already cell centered. For Q,RVTA the IIth column
and JJth row are all zero.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
to cell center. The half cell lost at the inlet and outlet is ignored
since they do not effect the PBD results.
Current version outputs info from t=0 to t=1.0, should be improved
to give up to t=2.0 for the ducted case.
If the extrapolated velocity is < 0 (in case of rapid BL change with
a specific inlet profile), the velocity is "stamped" to zero.!.............................................................................
... 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)-1DO 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 DOEND DO
.... Start corrections made by Bill Duncan 5MAR02DO J=JAIR(2),JAIR(3)-1
DO I=1,II-1XAC(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 DOEND DO
.... End corrections made by Bill Duncan 5MAR02
... Now add in the bottom and top streamlines to recover the half cell on
! bottom and top that was lost during cell center shift. Linearly* extrpolate velocity info from two points outward to get* velocity info.
DO I=1,II-1XC(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)IF (QXC(I,1).LT.0) QXC(I,1)=0 ! Velocity "stamping"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-1XAC(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
&
&
"stamping
&
(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)IF (QAXC(I,JAIR(2)).LT.0) QAXC(IJAIR(2))=0f
QAYC(I,JAIR(2))=VelExtrap(QAYC(I,JAIR(2)+2),QAYC(I,JAIR(2)+3),dAlbot,dA2bot)
Velocity
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!....JAIR(3) instead of JAIR(2)
OPEN(UNIT=169,
WRITE(169,'(A)WRITE(169, '(A)WRITE(169,'(''
&
FILE='OUTVEL.tec',STATUS='UNKNOWN')
TITLE = "MTFLOW Velocity Output"VARIABLES = "X", "R", "Vx", "Vr", "Vt", "Cp"
ZONE T="Cell Velocity", I='',I4,'' J='',I4,'' F=POINT '')') II-1,JAIR(3)+l
to read to
'
DO J=1,JAIR(2)+lDO I=1,II-1
WRITE (169, 1002)&
END DO
XC(IJ),YC(IJ),QXC(I,J),QYC(I,J),RVTC(I,J),CP(I,J)
END DO
.... Start corrections made by Bill Duncan 5MAR02DO J=JAIR(2),JAIR(3)+l
DO I=1,II-1WRITE (169, 1002)
&
XAC(IJ),YAC(I,J),QAXC(IJ),QAYC(IJ),RAVTC (I, J) ,CP (I, J)
END DOEND DO
.... End corrections made by Bill Duncan 5MAR02CLOSE(169)
46
&
&
&
Appendix C
Changes made to PBD2MT SourceCode
Note: This code inputs swirl equal to the tip swirl between
the first crossing of a t line and the stagnation line. Change
Zlast to Zl in the **** section and the program will go to the
tip instead of the first crossing. Uncomment the $$$ section
and swirl will not be input between the tip and stagnation line.
Subroutine GetZRrVt finds Z,R,rVt where the given t line crosses! current blade CP line of interest.
Input: t: t value of interestBFGline: t line number
Output: Z,R coordinate and rVt at the coordinateGlobal Variables used: Blade array, BFG array,MM,JJ
--------------------------------------------------------------------
SUBROUTINE GetZRrVt (BFGline, t, Z,R, rVt, DSdrag, ZLAST,togl)
IMPLICIT NONE
REAL, INTENT(IN) :: tINTEGER, INTENT(IN) :: BFGlineREAL, INTENT(OUT) :: Z,R,rVt,DSdragREAL
Z1,Z2,RlR2,Zhigh,Rhigh,Zlow,Rlow,rVthigh,rVtlow,Ll,L2,L,tt,ZLASTINTEGER :: IREAL, PARAMETER :: Tolerance=1E-7LOGICAL :: Undershoot,Overshoot,togl
Undershoot=.TRUE.Overshoot=.FALSE.
DO I=1,MMZl=BLADE (1, J, I)Rl=BLADE (2, J, I)tt=t Find (Z 1, Rl)
IF (tt>t) THENZLAST=ZlEXITEND IFUndershoot=.FALSE. If here, at least one blade CP is below
t lineEND DO
47
IF (tt<=t) Overshoot=.TRUE. I This can happen above the last bladeCP
... No blade CP above for interpolation ==> extend CP #MM info upIF (Overshoot) THEN
Z=ZLAST I Extend Z info upDO K=1,II
tLineZ(K)=BFG(1,BFGline*II-II+K)tLineR(K)=BFG(2,BFGline*II-II+K)
END DOCALL LININTERP(II,tLineZ,tLineR,Z,R) I Find R given t line and ZrVt=O I For open prop rVt=OIF ((ISDUCT.OR.INTERNAL).AND.(.NOT.togl)) THENrVt=BLADE(3,J,MM)! For ducted/internal extend rVt info up from CP
#MMtogl=.TRUE.END IF
END IF
... No blade CP below for interpolation ==> extend CP #1 info downIF (Undershoot) THEN
Z=Z1 ! Extend Z info downDO K=1,II
tLineZ(K)=BFG(1,BFGline*II-II+K)tLineR(K)=BFG(2,BFGline*II-II+K)
END DOCALL LININTERP(II,tLineZ,tLineR,Z,R) ! Find R given t line and ZrVt= BLADE(3,J,1) ! Extend rVt info down from CP
#1DSdrag=BLADE (4, J, 1)
END IF
... Have blade CP above and below t line of interestInterpolates info from blade CP above and belowUses bisection method to get Z,R of blade span and t line intersection
IF ((.NOT.Overshoot).AND.(.NOT.Undershoot)) THENZ2=BLADE(1,.J, I-1)R2=BLADE(2,J, I-1)
Zhigh=ZlRhigh=RlZlow=Z2Rlow=R2
DOZ=0.5*(Zl+Z2)R=0.5*(Rl+R2)tt=tFind (Z, R)IF (tt<=t) THEN
Z2=ZR2=R
ELSEZl=ZRl=R
END IFIF (ABS(R2-R1)<Tolerance) EXIT
END DO
48
L1=SQRT ((Zhigh-Z) **2+ (Rhigh-R) **2)
L2=SQRT ((Z-Zlow) **2+ (R-Rlow) **2)L=L1+L2
rVthigh=BLADE (3, J, I)rVtlow=BLADE(3,J,I-1)
rVt=rVthigh*L2/L + rVtlow*L1/L Linear
interpolate to get rVtDSdrag=BLADE(4,J,I)*L2/L + BLADE(4,J,I-1)*L1/L !same fore DSdrag
END IF
END SUBROUTINE GetZRrVt
49
Appendix D
PBD Admin. File for PSF-2Convection Velocities
4119.BSN :FILE NAME FOR BLADE B-SPLINE NET
uniform.rotor.vel :FILE NAME FOR WAKE FIELD
3 25 25 :nblade, nkey, mkey11 :ispn (0=uniform,1=cos),iffixiat24 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,
MCTRP3 0.0 0 0.0 :ihub, hgap, iduct, dgap0 0 : IHUB SUBLAY, IDUCSUBLAY
0 0 HDWAK, NTWAKE
0.0 0 Cq, MXITER0.0 0.0 OVHANG(1), OVHANG(3)10 -10 0 0 nx,ngcoeff,mltype,mthick4 :IMODE0 0 0 :NWIMAX5 0.001 0.02 2.0 1 niter,tweak,bulge,radwgt,nufix
1 0 0 8 :1_BSHAPE, IHUBSL, IDUCSL, NGENLINE1 0.02 : nplot,hubshk4 6 : NOPT, NBLK0.4 1.0 1.500 0.05 :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 .3000 .4000 .5000 .60000 .7000 .8000 .9000 .9500 1.0000 :r/R.06576 .05630 .04777 .0396 .03209 .02504 .01828 .0120 .00896 .0000 :T/D0.00814 0.0086 0.0085 0.0084 0.0082 0.0081 0.008 0.0079 0.0078 0.0079:Cd
0.178 0.626 0.935 1.158 1.351 1.535 1.612 1.449 1.238 0.918 :UA
1.122 1.266 1.509 1.714 1.738 1.500 1.145 0.875 0.835 0.891 :UAU
-0.132 -0.802 -1.071 -1.082 -0.976 -0.864 -0.735 -0.544 -0.412 -0.249 :UT
-1.888 -1.218 -0.931 -0.845 -0.775 -0.589 -0.364 -0.226 -0.231 -0.305 :UTU
50
Bibliography
[1] A. Chrisospathis, J.E. Kerwin and T.E. Taylor. PBD-14.36: A Coupled Lifting-Surface
Design/Analysis Program for Marine Propulsors. Technical Report, Department of
Ocean Engineering , Massachusetts of Technology, July 2001.
[2] M. Drela. A User's Guide to MTFLOW 1.2. MIT Fluid Dynamics research Laboratory,
November 1997.
[3] M. Drela and M. Giles. Conservative Streamtube Solution of Steady-State Euler
Equations. Technical Report CFDL-TR-83-6. Department of Aeronautics and
Astronautics, Massachusetts Institute of Technology, November 1983.
[4] C.J. Hanson. Integrated Lifting-Surface and Euler/Boundary-Layer Theory Analysis
Method for Marine Propulsors. Master's thesis, Department of Ocean Engineering,
Massachusetts Institute of Technology, 2000. Also Naval Engineer's thesis.
[5] C. Hsin. Development and Analysis of Panel Methods for Propellers in Unsteady Flow.
PHD thesis, Department of Ocean Engineering, Massachusetts Institute of Technology,
September 1990.
[6] S.D. Jessup. An Experimental Investigation of Viscous Aspects of Propeller Blade Flow.
PHD thesis, School of Engineering and Architecture, The Catholic University of
America, 1989.
[7] J.E. Kerwin. 13.04 Lecture Notes Hydrofoils and Propellers. Department of Ocean
Engineering, Massachusetts Institute of Technology, January 2001.
[8] R.W. Kimball, T.E. Taylor and J.E. Kerwin. PBD-14.6: A Coupled Lifting-Surface
Design/Analysis Program for Marine Propulsors. Technical Report, Department of
Ocean Engineering , Massachusetts of Technology, July 2001.
51
[9] G.P. Mc Huch. Advances in Ducted Propulsor Analysis using Vortex-Lattice Lifting-
Surface Techniques. Master's thesis, Department of Ocean Engineering, Massachusetts
Institute of Technology, January 2001.
[10] A.M. Polsenberg. An Assessment of the PBD/MTFLOW Coupling: 3 Case Studies.
Department of Ocean Engineering, Massachusetts Institute of Technology, 2000.
[11] D.H. Renick. An Analysis Procedure for Advanced Propulsor Design. Master's thesis,
Department of Ocean Engineering, Massachusetts Institute of Technology, January 2001.
Also Naval Engineer's thesis.
[12] T.E. Taylor. Combined Experimental and Theoretical Determination of Effective Wake
For a Marine Propeller. Master's thesis, Department of Ocean Engineering,
Massachusetts Institute of Technology, October 1993.
52
