SNAME H-8 Panel Meeting No. 124 Oct. 18, 2004 NSWC-CD Research Update from UT Austin Ocean...

SNAME H-8 Panel Meeting No. 124Oct. 18, 2004

NSWC-CDResearch Update from UT Austin

Ocean Engineering GroupDepartment of Civil EngineeringThe University of Texas at Austin

Prof. Spyros A. KinnasDr. Hanseong Lee, Research Associate

Mr. Hua Gu, Doctoral Graduate StudentMs. Hong Sun, Doctoral Graduate Student

Mr. Yumin Deng, Graduate student

10/18/2004 SNAME panel H-8 mtg. No. 124, NSWC-CD 2

Topics

►MPUF/HULLFPP .vs. PROPCAV/HULLFPP

►Effective wake evaluation at blade control points

►Modeling of cavitating ducted propeller

►Blade design using optimization method


MPUF3A- and PROPCAV- /HULLFPP (Steady wetted case: H03861 Propeller)

* 4 blades* 4 blades

* User input thickness * User input thickness

* User input camber* User input camber

►Propeller and hull geometriesPropeller and hull geometries

* uniform wake* uniform wake * Froude number Fr=9999.0* Froude number Fr=9999.0 * Advance Ratio Js =0.976* Advance Ratio Js =0.976 * IHUB = OFF * IHUB = OFF


► From MPUF3A/HULLFPP ► From PROPCAV/HULLFPP

MPUF3A- and PROPCAV- /HULLFPP(Pressure distribution on the hull)


MPUF3A- and PROPCAV- /HULLFPP

►Circulations from MPUF3A and PROPCAVCirculations from MPUF3A and PROPCAV

* Not considering induced velocity effect * Not considering induced velocity effect

* Match the transition wake geometry from PROPCAV with that from MPUF3A* Match the transition wake geometry from PROPCAV with that from MPUF3A


MPUF3A- and PROPCAV- /HULLFPP ►Field Point Potential from MPUF3A and PROPCAVField Point Potential from MPUF3A and PROPCAV


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


MPUF-3A/HULLFPP► General wake geometry


* Cavitation number * Froude number Fr = 3.0789 * Advance Ratio Js =1.177

731.1n

►Hull geometry and run conditions * Uniform wake * IHUB =ON * TLC = ON

MPUF-3A/HULLFPP(Steady cavitating case)


MPUF-3A/HULLFPP(Pressure distribution on the hull)

► Improved Approximation ►Using decay function


MPUF-3A/HULLFPP (Unsteady cavitating case)

►Cavitating run conditions

* Effective wake

* Cavitation number

* Froude number Fr=4.0

* Advance Ratio Js =1.0

* IHUB = OFF

* TLC = ON

►Cavity patterns

20x18

7.2n


MPUF-3A/HULLFPP(Pressure distribution on the hull)

► Improved approximation ►Using decay function


NEW EFFECTIVE WAKE

CALCULATION

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.


Interpolation of total axial velocity on control points

Interpolation of total tangential velocity on 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.


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.


The error brings lower circulation for this case, which still needs improvement.


CAVITATING DUCTED

PROPELLER

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


Straight Panel Paneled with pitch angle (45o)

Modeling of ducted propeller►NACA0015 Duct + N3745 Propeller

* Uniform wake * Advance ratio Js =0.6

Circulation Distribution


BLADE DESIGNVIA OPTIMIZATION

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


New Optimization Method

►Start with a base propeller geometry.

►Given conditions are: Js, inflow (can be non-axisymmetric), cavitation number, Froude number, and thrust coefficient.

►The optimum design is searched for within a family of propeller geometries such that:

1

2

3

/ *( / )

/ *( / )

/ *( / )

base

base

base

P D X P D

c D X c D

f c X f c

X1, X2, X3 are factors (constant initially, to be varied later)


► Hydrodynamic coefficients and cavity planform area are expressed in terms of polynomial functions of X1, X2 and X3.

,7

1 1 2 32 4

2 1 2 32 5

3 1 2 3

2 2 2,1 1 ,2 2 ,3 3 ,4 1 ,5 2 ,6 3

1 2 ,8 1 3 ,9 2 3 ,10

( , , )

( , , )

( , , )

i

T

Q

i i i i i i i

i i i

TK f X X X

n D

QK f X X X

n D

cavity areaCA f X X X

blade area

f a X a X a X a X a X a X

a X X a X X a X X a

min max1 1 1

min max2 2 2

min max3 3 3

X X X

X X X

X X X

While:

The function coefficients are determined by Least Square Method (LSM), using the predictions of a large array (e.g. 10x10x10) of MPUF-3A runs


The Optimization Scheme (based on CAVOPT-2D, optimization method for cavitating 2-D hydrofoils)

► The optimization problem of the propeller design is :

( )f xMinimize :

Subject to : ( ) 0

( ) 0i

i

g x

h x

Where is the objective function to be minimized. is the solution vector of n components. ( i=1…m ) are inequality constrains and

( i=1…l ) are equality constrains.

( )f x x( ) 0ig x

( ) 0ih x

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.


In current case, the problem reduces to:

The function to be minimized is , while x is the vector (X1, X2, X3), and are Lagrange multipliers, and are penalty function coefficients.

( )QK x

1 1c 1c

1 0

1

( ) ( ) 0

( ) ( ) 0T Th x K x K

g x CA x CAMAX

With:

0TK CAMAX and are user defined.

Augmented Lagrange function:

])([~

)()()~,,~

,,( 2111111111 sxgxhxKccxF Q

1

~

22111

211 ][~)( sxgcxhc

Optimization Samples:

Sample 1: Fully wetted run based on N4148 propeller (with prescribed skew distribution)

-- Design conditions:

• , to be minimized

• , ,

• uniform inflow

• 20x9 grid size

-- Range of variables:

0 0.15TK QK

1.0SJ 999n 999nF

1

2

3

0.8 2.2

0.8 2.0

0.8 2.0

x

x

x


-- Database and Interpolation :


How good is the interpolation method?


-- 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


Propeller geometry comparison: OPT vs. CAVOPT-3D


Circulation comparison: OPT vs. CAVOPT-3D


Pressure distribution comparison: OPT vs. CAVOPT-3D


Blade geometry comparison: OPT vs. CAVOPT-3D


Sample 2: Cavitating run based on N4148 propeller and presribed skew distribution

-- Design conditions:

0 0.25TK

1.2SJ 2.5n 5.0nF QK

-- Range of variables:

1

2

3

1.0 2.0

0.8 2.0

0.8 2.0

x

x

x

• , to be minimized

• , ,

•

• effective wake file

• 10x9 and 20x9 grid size

40%CAMAX


-- Wake file used:


-- Database and Interpolation :


-- 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

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

Initial guess: ( 0.8, 1.0, 1.0 )

Several initial guesses were tested, they led to the almost same optimization results.


Propeller geometry comparison: OPT (10x9) vs. CAVOPT-3D (10x9)


Circulation comparison: OPT (10x9) vs. CAVOPT-3D (10x9)


Blade geometry comparison: OPT (10x9) vs. CAVOPT-3D (10x9)


Cavitations comparison: OPT (10x9) vs. CAVOPT-3D (10x9)

18.97 %18.51 %


-- 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.


Propeller geometry of OPT (20x9):


Circulation of OPT


Blade geometry and cavity of OPT (20x9)


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.

SNAME H-8 Panel Meeting No. 124 Oct. 18, 2004 NSWC-CD Research Update from UT Austin Ocean...

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