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August, 2016
AMOL NARENDRA PAWAR
Dynamic positioning of hydrofoil using
RANS computations
Thesis submitted to École Centrale de Nantes in fulfillment of the requirement
for the Degree of Master of Science in Computational Mechanics
Supervisor: Dr. Jeroen WACKERS, LHEEA, C.N.R.S.
Introduction
Motivation
14/09/2016Dynamic positioning of hydrofoil2
AC72 yacht- America’s Cup 2013
Contents
 Introduction
 Algorithm for 3d hydrofoil
 Principle of adapted algorithm
 Case study
 Tests performed on the algorithm
 Parameter Extractions
 Mathematical model
 Least square fitting
 Tests on extracted parameters
 Conclusion and future scope
14/09/2016Dynamic positioning of hydrofoil3
Introduction
Objective
14/09/2016Dynamic positioning of hydrofoil4
 Current situation: dynamic positioning algorithm for hydrofoils (2d)
 Target : To have an algorithm to search for a stable elevation height of the
hydrofoil for a given imposed vertical force.
Algorithm for 3d hydrofoil
Principle of adapted algorithm
14/09/2016Dynamic positioning of hydrofoil5
Vertical Velocity
Imposed Force
Variable imposed
force
Target lifting
force
Corrected Actual
Lift Force
Added mass
correction in X
direction
Added mass
Correction in Z
direction
Vertical Velocity
Influence
Correction
i
z
v
i
z
e
zIMP
z F
D
FF
F 

 LAMAMFF xaxzazz
COR
z 
2
v
e
z
IMP
z
COR
z
z
DF
FF
CV


Algorithm for 3d hydrofoil
Principle of adapted algorithm- Corrected lift force
14/09/2016Dynamic positioning of hydrofoil6
 Added mass correction in z direction
 Added mass correction in x direction
 Vertical velocity influence correction
Az
Fz
az
D
D
M 
Ax
Fx
ax
D
D
M 
LCSVL  2
2
1
Algorithm for 3d hydrofoil
Case study- AC72 hydrofoil
14/09/2016Dynamic positioning of hydrofoil7
Hydrofoil
elevation(m)
Generated Lift
force(N)
0.5 -4456
0 22465
-0.5 58374
-1 69685
-2 80531
Span (b) 2.5 m
Chord (c) 1 m
Speed (V) 20 m/s
Angle of attack ( ) 1 deg.
Tests performed on the algorithm
Test 1: Analysis of the effect of added mass correction in x direction
14/09/2016Dynamic positioning of hydrofoil8
Induced noise x acceleration No effect of noise on the lifting force
Tests performed on the algorithm
Test 2: Analysis of the vertical velocity influence correction
14/09/2016Dynamic positioning of hydrofoil9
Case1: Lifting force coefficient approximation using infinite wing theory
Case 2: Lifting force coefficient approximation using finite wing theory
Where:
 2LC




AR
a
a
CL
0
0
1
 20a
S
b
AR
2

bcS 
2
1
Tests performed on the algorithm
Test 2 Analysis of the vertical velocity influence correction
14/09/2016Dynamic positioning of hydrofoil10
Infinite wing theory approximation Finite wing theory approximation
Partially immersed hydrofoil position h=0
Tests performed on the algorithm
Test 2 Analysis of the vertical velocity influence correction
14/09/2016Dynamic positioning of hydrofoil11
Infinite wing theory approximation Finite wing theory approximation
Completely immersed hydrofoil position h=-1m
Tests performed on the algorithm
Reference computations for parameter extraction
14/09/2016Dynamic positioning of hydrofoil12
8339.214
)(*10*2 IMP
zFC 

Power law fit
Geometry dependent !!!
Optimal values of C constant
Parameter Extraction
Mathematical model
14/09/2016Dynamic positioning of hydrofoil13
 Aim: To build a model to predict the vertical position of hydrofoil to converge
to an imposed force.
 Saved values:
 Real function:
 To make it easy to integrate in developed dynamic library
),,,(
..
zzxFz
),,(
..
zzxfFz 
..
4
2
.
32
2
.
1 )()( zxazxazaxaFz 
..
4
2
.
3
2
.
1 )()( zxazxaxaFAMFF i
zzazz
P
z 
Parameter Extraction
Least square fitting
14/09/2016Dynamic positioning of hydrofoil14
bAx 
bAAxA TT

Over determined System
Number of unknowns = Number of equations
Parameter Extraction
Test 1: Imposing parametric solution just once after 300 time steps
14/09/2016Dynamic positioning of hydrofoil15
 Test settings:
 Forces are saved after every 5 time steps
 Parameters extracted at 300th time step: from 60 saved forces
 Initial guess for C constant : Power law
 C after 300th time step :
3
170
a
C 
Parameter Extraction
Test 1: Imposing parametric solution just once after 300time steps
14/09/2016Dynamic positioning of hydrofoil16
Hydrofoil elevation : -1m Hydrofoil elevation : -2m
Parametric solution is imposed very late !
Still geometry dependent – power law !
Parameter Extraction
Test 2: Imposing parametric solution after every 100 time step
14/09/2016Dynamic positioning of hydrofoil17
 Test settings:
 Forces are saved after every 5 time steps
 Parameters extracted after every 100th time step: from last 20 saved
forces
 Initial guess for C constant : 1
Geometry dependence of algorithm is removed
 C after every 100th time step :
where, P= 60, for the case of h =-1m
and P= 30, for the case of h =-2m
3a
P
C 
Parameter Extraction
Test 2: Imposing parametric solution after every time 100 time step
14/09/2016Dynamic positioning of hydrofoil18
Hydrofoil elevation : -1m Hydrofoil elevation : -2m
Parametric solution Vs Reference solution is not matching !
Failed to compute parameters consistently !
Parameter Extraction
Test 3: Verification of model with continues saving of forces
14/09/2016Dynamic positioning of hydrofoil19
Number of
saved forces
Hydrofoil elevation height
-0.5 -1 -2
25
50
Predicted elevation height converges faster than simulation height !
In early phase of computations, model over predicts the height !
Parameter Extraction
Test 3: Validation of model with continues saving of forces
14/09/2016Dynamic positioning of hydrofoil20
Number of
saved forces
Hydrofoil elevation height
-0.5 -1 -2
100
200
Conclusion and Future work
14/09/2016Dynamic positioning of hydrofoil21
 Conclusion
 With developed algorithm – dynamic positioning of hydrofoil is possible
 With derived mathematical model – convergence rate of predicted elevation of
hydrofoil is faster
 Future work
 Position control procedure
 Integration of mathematical model into the algorithm
14/09/2016Dynamic positioning of hydrofoil22
Thank you very much for your time!
Questions ?

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PPT

  • 1. August, 2016 AMOL NARENDRA PAWAR Dynamic positioning of hydrofoil using RANS computations Thesis submitted to École Centrale de Nantes in fulfillment of the requirement for the Degree of Master of Science in Computational Mechanics Supervisor: Dr. Jeroen WACKERS, LHEEA, C.N.R.S.
  • 2. Introduction Motivation 14/09/2016Dynamic positioning of hydrofoil2 AC72 yacht- America’s Cup 2013
  • 3. Contents  Introduction  Algorithm for 3d hydrofoil  Principle of adapted algorithm  Case study  Tests performed on the algorithm  Parameter Extractions  Mathematical model  Least square fitting  Tests on extracted parameters  Conclusion and future scope 14/09/2016Dynamic positioning of hydrofoil3
  • 4. Introduction Objective 14/09/2016Dynamic positioning of hydrofoil4  Current situation: dynamic positioning algorithm for hydrofoils (2d)  Target : To have an algorithm to search for a stable elevation height of the hydrofoil for a given imposed vertical force.
  • 5. Algorithm for 3d hydrofoil Principle of adapted algorithm 14/09/2016Dynamic positioning of hydrofoil5 Vertical Velocity Imposed Force Variable imposed force Target lifting force Corrected Actual Lift Force Added mass correction in X direction Added mass Correction in Z direction Vertical Velocity Influence Correction i z v i z e zIMP z F D FF F    LAMAMFF xaxzazz COR z  2 v e z IMP z COR z z DF FF CV  
  • 6. Algorithm for 3d hydrofoil Principle of adapted algorithm- Corrected lift force 14/09/2016Dynamic positioning of hydrofoil6  Added mass correction in z direction  Added mass correction in x direction  Vertical velocity influence correction Az Fz az D D M  Ax Fx ax D D M  LCSVL  2 2 1
  • 7. Algorithm for 3d hydrofoil Case study- AC72 hydrofoil 14/09/2016Dynamic positioning of hydrofoil7 Hydrofoil elevation(m) Generated Lift force(N) 0.5 -4456 0 22465 -0.5 58374 -1 69685 -2 80531 Span (b) 2.5 m Chord (c) 1 m Speed (V) 20 m/s Angle of attack ( ) 1 deg.
  • 8. Tests performed on the algorithm Test 1: Analysis of the effect of added mass correction in x direction 14/09/2016Dynamic positioning of hydrofoil8 Induced noise x acceleration No effect of noise on the lifting force
  • 9. Tests performed on the algorithm Test 2: Analysis of the vertical velocity influence correction 14/09/2016Dynamic positioning of hydrofoil9 Case1: Lifting force coefficient approximation using infinite wing theory Case 2: Lifting force coefficient approximation using finite wing theory Where:  2LC     AR a a CL 0 0 1  20a S b AR 2  bcS  2 1
  • 10. Tests performed on the algorithm Test 2 Analysis of the vertical velocity influence correction 14/09/2016Dynamic positioning of hydrofoil10 Infinite wing theory approximation Finite wing theory approximation Partially immersed hydrofoil position h=0
  • 11. Tests performed on the algorithm Test 2 Analysis of the vertical velocity influence correction 14/09/2016Dynamic positioning of hydrofoil11 Infinite wing theory approximation Finite wing theory approximation Completely immersed hydrofoil position h=-1m
  • 12. Tests performed on the algorithm Reference computations for parameter extraction 14/09/2016Dynamic positioning of hydrofoil12 8339.214 )(*10*2 IMP zFC   Power law fit Geometry dependent !!! Optimal values of C constant
  • 13. Parameter Extraction Mathematical model 14/09/2016Dynamic positioning of hydrofoil13  Aim: To build a model to predict the vertical position of hydrofoil to converge to an imposed force.  Saved values:  Real function:  To make it easy to integrate in developed dynamic library ),,,( .. zzxFz ),,( .. zzxfFz  .. 4 2 . 32 2 . 1 )()( zxazxazaxaFz  .. 4 2 . 3 2 . 1 )()( zxazxaxaFAMFF i zzazz P z 
  • 14. Parameter Extraction Least square fitting 14/09/2016Dynamic positioning of hydrofoil14 bAx  bAAxA TT  Over determined System Number of unknowns = Number of equations
  • 15. Parameter Extraction Test 1: Imposing parametric solution just once after 300 time steps 14/09/2016Dynamic positioning of hydrofoil15  Test settings:  Forces are saved after every 5 time steps  Parameters extracted at 300th time step: from 60 saved forces  Initial guess for C constant : Power law  C after 300th time step : 3 170 a C 
  • 16. Parameter Extraction Test 1: Imposing parametric solution just once after 300time steps 14/09/2016Dynamic positioning of hydrofoil16 Hydrofoil elevation : -1m Hydrofoil elevation : -2m Parametric solution is imposed very late ! Still geometry dependent – power law !
  • 17. Parameter Extraction Test 2: Imposing parametric solution after every 100 time step 14/09/2016Dynamic positioning of hydrofoil17  Test settings:  Forces are saved after every 5 time steps  Parameters extracted after every 100th time step: from last 20 saved forces  Initial guess for C constant : 1 Geometry dependence of algorithm is removed  C after every 100th time step : where, P= 60, for the case of h =-1m and P= 30, for the case of h =-2m 3a P C 
  • 18. Parameter Extraction Test 2: Imposing parametric solution after every time 100 time step 14/09/2016Dynamic positioning of hydrofoil18 Hydrofoil elevation : -1m Hydrofoil elevation : -2m Parametric solution Vs Reference solution is not matching ! Failed to compute parameters consistently !
  • 19. Parameter Extraction Test 3: Verification of model with continues saving of forces 14/09/2016Dynamic positioning of hydrofoil19 Number of saved forces Hydrofoil elevation height -0.5 -1 -2 25 50 Predicted elevation height converges faster than simulation height ! In early phase of computations, model over predicts the height !
  • 20. Parameter Extraction Test 3: Validation of model with continues saving of forces 14/09/2016Dynamic positioning of hydrofoil20 Number of saved forces Hydrofoil elevation height -0.5 -1 -2 100 200
  • 21. Conclusion and Future work 14/09/2016Dynamic positioning of hydrofoil21  Conclusion  With developed algorithm – dynamic positioning of hydrofoil is possible  With derived mathematical model – convergence rate of predicted elevation of hydrofoil is faster  Future work  Position control procedure  Integration of mathematical model into the algorithm
  • 22. 14/09/2016Dynamic positioning of hydrofoil22 Thank you very much for your time! Questions ?