Transcript Slide 1

SNAME H-8 Panel Meeting No. 124
Oct. 18, 2004
NSWC-CD
Research Update from UT Austin
Ocean Engineering Group
Department of Civil Engineering
The University of Texas at Austin
Prof. Spyros A. Kinnas
Dr. Hanseong Lee, Research Associate
Mr. Hua Gu, Doctoral Graduate Student
Ms. Hong Sun, Doctoral Graduate Student
Mr. Yumin Deng, Graduate student
Topics
►MPUF/HULLFPP .vs. PROPCAV/HULLFPP
►Effective wake evaluation at blade control
points
►Modeling of cavitating ducted propeller
►Blade design using optimization method
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MPUF3A- and PROPCAV- /HULLFPP
(Steady wetted case: H03861 Propeller)
►Propeller and hull geometries
* 4 blades
* User input thickness
* User input camber
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* uniform wake
* Froude number Fr=9999.0
* Advance Ratio Js =0.976
* IHUB = OFF
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MPUF3A- and PROPCAV- /HULLFPP
(Pressure distribution on the hull)
► From MPUF3A/HULLFPP
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► From PROPCAV/HULLFPP
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MPUF3A- and PROPCAV- /HULLFPP
►Circulations from MPUF3A and PROPCAV
* Not considering induced velocity effect
* Match the transition wake geometry from PROPCAV with that from MPUF3A
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MPUF3A- and PROPCAV- /HULLFPP
►Field Point Potential from MPUF3A and PROPCAV
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MPUF3A/HULLFPP
(Effects of the ultimate wake singularities)
►Previously, it was assumed that only the
steady part of the circulation at the blade TE
shed into the ultimate wake, and a decay
function was applied to the transition wake
►In the improved approximation the unsteady
vorticity is shed into the ultimate wake
►This improvement was verified by several
cases using uniform inflow
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MPUF-3A/HULLFPP
► General wake geometry
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MPUF-3A/HULLFPP
(Steady cavitating case)
►Hull geometry and run conditions
* Uniform wake
* IHUB =ON
* TLC = ON
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* Cavitation number  n  1.731
* Froude number Fr = 3.0789
* Advance Ratio Js =1.177
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MPUF-3A/HULLFPP
(Pressure distribution on the hull)
► Improved Approximation
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►Using decay function
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MPUF-3A/HULLFPP
(Unsteady cavitating case)
►Cavitating run conditions
►Cavity patterns
20x18
* Effective wake
* Cavitation number  n
* Froude number Fr=4.0
* Advance Ratio Js =1.0
* IHUB = OFF
* TLC = ON
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 2 .7
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MPUF-3A/HULLFPP
(Pressure distribution on the hull)
► Improved approximation
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►Using decay function
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NEW EFFECTIVE
WAKE
CALCULATION
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Effective wake evaluation
at blade control points
Previous method: evaluates effective
wake at a plane ahead (by one cell) of the
blade.
New method: Evaluates the effective
wake at the blade control points.
Effective wake evaluation
at blade control points
Interpolation of total axial velocity on
control points
Interpolation of total tangential velocity
on control points
Effective wake evaluation
at blade control points
At the MPUF-3A control
points, the induced
velocity may be in error
due to the local effect of
blade singularities. The
bad points need to be
removed before the
induced velocity is (time)
averaged. The figure
shows the induced
velocity at a control point
at chord index 9 and
span index 8.
Effective wake evaluation
at blade control points
At each control point, Ue = Ua -Uin is applied, the expected effective wake
should be 1.00 at all points, there is still a maximum of 4% error in this case.
Effective wake evaluation
at blade control points
The error brings lower circulation for this case, which still needs improvement.
CAVITATING DUCTED
PROPELLER
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Modeling of cavitating ducted propeller
(duct: panel method, propeller: PROPCAV)
►NACA0015 Duct
Straight Panel
Paneled with pitch angle (45o)
Modeling of ducted propeller
►NACA0015 Duct
Modeling of ducted propeller
►NACA0010 Duct
Straight Panel
Paneled with pitch angle (45o)
Modeling of ducted propeller
►NACA0010 Duct
Modeling of ducted propeller
►NACA0015 Duct + N3745 Propeller
* Uniform wake
* Advance ratio Js =0.6
Circulation Distribution
BLADE DESIGN
VIA OPTIMIZATION
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CAVOPT-3D
(CAVitating Propeller Blade OPTimization method)
Mishima (PhD, MIT, ’96), Mishima & Kinnas (JSR ’97), Griffin & Kinnas (JFE’98)
CAVOPT-3D
►Allows for design of propeller in non-axisymmetric
inflow and includes the effects of sheet cavitation
DURING the design process
►MPUF-3A is running inside the optimization scheme
until all requirements and constraints are satisfied
►Takes about 600-1000 MPUF-3A runs to produce the
final design (3-6 hrs)
►New versions of MPUF-3A (that include duct, pod,
etc) can be incorporated
►Not practical as a web based instructional tool
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New Optimization Method
►Start with a base propeller geometry.
►Given conditions are: Js, inflow (can be nonaxisymmetric), cavitation number, Froude number,
and thrust coefficient.
►The optimum design is searched for within a family
of propeller geometries such that:
P / D  X 1 * ( P / D)base
c / D  X 2 * (c / D)base
f / c  X 3 * ( f / c)base
X1, X2, X3 are factors (constant initially, to be varied later)
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► Hydrodynamic coefficients and cavity planform area are
expressed in terms of polynomial functions of X1, X2 and X3.
KT 
KQ 
CA 
T
n D
2
4
Q
n D
2
5
 f1 ( X 1 , X 2 , X 3 )
 f2 ( X1, X 2 , X 3 )
cavity  area
blade  area
 f3 ( X 1 , X 2 , X 3 )
f i  ai ,1 X 1  ai ,2 X 2  ai ,3 X 3  ai ,4 X 1  ai ,5 X 2  ai ,6 X 3
2
2
2
 a i ,7 X 1 X 2  ai ,8 X 1 X 3  ai ,9 X 2 X 3  ai ,10
While:
min
 X1  X1
min
 X2  X2
min
 X3  X3
X1
X2
X3
max
max
max
The function coefficients are determined by Least Square Method (LSM),
using the predictions of a large array (e.g. 10x10x10) of MPUF-3A runs
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The Optimization Scheme (based on CAVOPT-2D, optimization method for
cavitating 2-D hydrofoils)
► The optimization problem of the propeller design is :
Minimize :
f ( x)
Subject to :
gi ( x)  0
hi ( x)  0
Where f ( x) is the objective function to be minimized. x is the solution
vector of n components. gi ( x)  0 ( i=1…m ) are inequality constrains and
hi ( x)  0 ( i=1…l ) are equality constrains.
The constrained optimization problem is changed to an unconstrained
optimization problem by using Lagrange multipliers and penalty functions.
For more information, please refer to the JSR paper by Mishima & Kinnas, 1996.
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In current case, the problem reduces to:
Augmented Lagrange function:
~
~
2
~
F ( x, 1 , 1 , c1 , c1 )  K Q ( x)  1h1 ( x)  1[ g1 ( x)  s1 ]
2 2
~


 c h ( x)  c1[ g1 x  s1 ]
2
1 1
With:
h1 ( x)  KT ( x)  KT 0  0
g1 ( x)  CA( x)  CAMAX  0
KT 0 and CAMAX are user defined.
The function to be minimized is KQ ( x) , while x is the vector
~
(X1, X2, X3), 1 and 1 are Lagrange multipliers, c1 and c1
are penalty function coefficients.
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Optimization Samples:
Sample 1: Fully wetted run based on N4148 propeller (with prescribed
skew distribution)
-- Design conditions:
• K T 0  0.15 , K Q to be minimized
• J  1.0 ,  n  999 , Fn  999
S
• uniform inflow
• 20x9 grid size
-- Range of variables:
0 .8  x1  2 .2
0 .8  x 2  2 .0
0 .8  x 3  2 .0
-- Database and Interpolation :
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How good is the interpolation method?
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-- Optimum solution and comparisons with CAVOPT-3D
3rd order functions are used to approximate both KT and KQ
code
KT
10KQ
Efficiency
OPT
0.1490
0.2994
0.7921
CAVOPT-3D
0.1504
0.2996
0.7991
The solution of OPT are :
X1 = 1.28865
X2 = 0.80000
X3 = 2.00000
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Propeller geometry comparison: OPT vs. CAVOPT-3D
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Circulation comparison: OPT vs. CAVOPT-3D
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Pressure distribution comparison: OPT vs. CAVOPT-3D
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Blade geometry comparison: OPT vs. CAVOPT-3D
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Sample 2: Cavitating run based on N4148 propeller and presribed skew
distribution
-- Design conditions:
• K T 0  0.25 , K Q to be minimized
• J  1.2 ,  n  2.5 , Fn  5.0
S
• C AM AX  40%
• effective wake file
• 10x9 and 20x9 grid size
-- Range of variables:
1 .0  x1  2 .0
0 .8  x 2  2 .0
0 .8  x 3  2 .0
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-- Wake file used:
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-- Database and Interpolation :
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-- Optimization solution from OPT (MPUF-3A: 10X9) and comparisons with
CAVOPT-3D (MPUF-3A: 10X9)
4th order functions are used for KT, KQ and CAMAX
Initial guess: ( 0.8, 1.0, 1.0 )
code
KT
10KQ
CA
Efficiency
OPT (10x9)
0.2505778
0.5528295
18.51%
86.6%
CAVOPT-3D
0.2267294
0.5193282
18.97%
83.4%
The solution of OPT are :
X1 =1.43586
X2 =2.00000
X3 =1.89869
Several initial guesses were tested, they led to the almost same optimization
results.
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Propeller geometry comparison: OPT (10x9) vs. CAVOPT-3D (10x9)
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Circulation comparison: OPT (10x9) vs. CAVOPT-3D (10x9)
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Blade geometry comparison: OPT (10x9) vs. CAVOPT-3D (10x9)
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Cavitations comparison: OPT (10x9) vs. CAVOPT-3D (10x9)
18.51 %
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18.97 %
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-- Optimization solution of OPT (20x9)
4th order functions are used for KT, KQ and CAMAX
Initial guess: ( 0.8, 1.0, 1.0 )
code
Grid
KT
10KQ
CA
Efficiency
OPT
20x9
0.2497656
0.5558742
20.85%
85.8%
CAVOPT-3D
10x9
0.2267294
0.5193282
18.97%
83.4%
The solution of OPT are :
X1 =1.44072
X2 =1.94383
X3 =2.00000
Several initial guesses were tested, they led to almost the same optimization
results.
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Propeller geometry of OPT (20x9):
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Circulation of OPT
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Blade geometry and cavity of OPT (20x9)
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Conclusions and Future work (on optimization)
►The interpolation scheme can approximate the
database very well using higher order functions.
►The optimization scheme works well for the fully
wetted run. For cavitating runs, both CAVOPT-3D
and OPT should be improved.
►Include more parameters in current optimization
scheme.
►Improve the approximation of cavity area.
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