The 22nd Offshore Symposium - University of Texas at Austin€¦ · Ope n turbine (w itho ut duc t)...
Transcript of The 22nd Offshore Symposium - University of Texas at Austin€¦ · Ope n turbine (w itho ut duc t)...
The 22nd Offshore SymposiumRedefining Offshore Development: Technologies and Solutions
Feb 2, 2017 | Houston, USA
In this method, the propeller/turbine
blade is solved in the lifting line
model, and the duct is solved in the
axisymmetric RANS solver. The blade
is represented as an actuator disk with a pressure jump
profile. 𝑻𝑷: thrust on the propeller, 𝑻𝑫: thrust on the duct.
“RANS/Lifting Line Model Interaction Method for the Design of Ducted Propellers and Tidal Turbines”
Weikang DU*, Spyros A. Kinnas*, Robin Martins Mendes**, Thomas Le Quere**
*Ocean Engineering Group, The University of Texas at Austin
**Ecole Navale, France
Introduction
Methodology
Objectives
Conclusions
Results
• Propeller and turbine design tools developed at UT’s OEG:
• LLOPT: lifting line theory based optimization
• LLOPT-BASE: circulation database searching method
• CAVOPT-BASE: database-searching method for the design
of propeller (coupled with VLM method)
• CAVOPT-3D: nonlinear optimization method for propeller
design (coupled with VLM method)
• Wake alignment procedure:
• Lerbs-Wrench formulas: assuming a constant pitch along
the x-direction (LLOPT-LW)
• Simplified Wake Alignment (LLOPT-SWA)
• Full wake alignment (LLOPT-FWA)
• However, the duct geometry is not taken into consideration in
those methods
In this paper, a RANS/lifting line model interaction method is
proposed to consider the duct geometry in the design of
propellers and tidal turbines. XY
Z
Blade (actuator disk)
Lerbs-Wrench wake (helical wake)
Real duct geometry
X
Y
-1.5 -1 -0.5 0 0.5 1 1.5
0
0.5
1
1.5
2
2.5
RANS domain
axis
hub
∆𝑝
circulation
pressure low pressure high
𝑇𝐷
𝑇𝑃
𝑉𝑠𝑈𝑖𝑛
actuator disk
τ =𝑇𝑃
𝑇𝑃 + 𝑇𝐷=𝑇𝑃𝑇𝑇
𝐽𝑠 =𝑉𝑠𝑛𝐷
𝐽𝑙 =𝑈𝑖𝑛𝑛𝐷
𝐶𝑇𝑠 =𝑇𝑇
12𝜌𝜋𝑉𝑠
2𝑅2
𝐶𝑇𝑙 =𝑇𝑃
12𝜌𝜋𝑈𝑖𝑛
2 𝑅2= τ𝐶𝑇𝑠
𝑉𝑠2
𝑈𝑖𝑛2
𝐶𝑄 =Q
12𝜌𝜋𝑉𝑠
2𝑅3
η =𝑇𝑇𝑉𝑠
Q𝜔=
𝐽𝑠𝐶𝑇𝑠
𝜋𝑪𝑸
𝑈𝑖𝑛 = U𝑅𝐴𝑁𝑆 − 𝑢𝑎∗
Previous iteration
τ =𝑇𝑇 − 𝑇𝐷𝑇𝑇
• Viscous effect is included in two parts:
• Non-slip boundary condition on duct
• Drag-to-lift coefficient κ
κ =𝐶𝐷𝐶𝐿
𝑈𝑖𝑛 = U𝑅𝐴𝑁𝑆 + 𝑢𝑎∗
Propeller_case1Without duct.
LLOPTDuct is considered as image model
(blade inside cylindrical tunnel).
LLOPT
LLOPT2NSflowchart
Real duct geometry is considered.
LLOPT2NS
x
r
-0.4 -0.2 0 0.2 0.4
1
1.05
1.1
1.15
1.2
f0=-0.02, t
0=0.15
x
r
-0.4 -0.2 0 0.2 0.41
1.05
1.1
1.15
1.2
f0=-0.04, t
0=0.15
x
r
-0.4 -0.2 0 0.2 0.41
1.1
1.2
1.3
f0=-0.04, t
0=0.30
x
r
-0.4 -0.2 0 0.2 0.41
1.1
1.2
1.3
f0=-0.02, t
0=0.30
t0
Eff
icie
nc
y
0.15 0.2 0.25 0.3
0.64
0.66
0.68
0.7
Propeller_case3 f0
= -0.02
Propeller_case3 f0
= -0.03
Propeller_case3 f0
= -0.04
Propeller_case1
Propeller_case2
t0
KT
on
the
bla
de
0.15 0.2 0.25 0.3
0.08
0.085
0.09
0.095Propeller_case3 f
0= -0.02
Propeller_case3 f0
= -0.03
Propeller_case3 f0
= -0.04
Propeller_case1
Propeller_case2
t0
KQ
0.15 0.2 0.25 0.3
0.112
0.114
0.116
0.118
0.12
Propeller_case3 f0
= -0.02
Propeller_case3 f0
= -0.03
Propeller_case3 f0
= -0.04
Propeller_case1
Propeller_case2
Propeller case: Js=0.5, CTs=1.0
t0
Uin
0.15 0.2 0.25 0.3
1.15
1.2
1.25
1.3
1.35
1.4
Propeller_case3 f0
= -0.02
Propeller_case3 f0
= -0.03
Propeller_case3 f0
= -0.04
t0
0.15 0.2 0.25 0.3
0.8
0.85
0.9
0.95
Propeller_case3 f0
= -0.02
Propeller_case3 f0
= -0.03
Propeller_case3 f0
= -0.04
• With the increase of duct camber, the
efficiency increases
• With the increase of duct camber and
thickness, both the inflow velocity
and thrust on the duct increase
Propeller case: Js=0.5
t0
Eff
icie
nc
y
0.15 0.2 0.25 0.3
0.54
0.56
0.58
0.6
0.62
0.64
0.66
Propeller_case3 f0
= -0.02
Propeller_case3 f0
= -0.03
Propeller_case3 f0
= -0.04
Propeller_case1
Propeller_case2
t0
Eff
icie
nc
y
0.15 0.2 0.25 0.3
0.48
0.5
0.52
0.54
0.56
0.58
0.6
0.62
0.64
Propeller_case3 f0
= -0.02
Propeller_case3 f0
= -0.03
Propeller_case3 f0
= -0.04
Propeller_case1
Propeller_case2
CTs=2.0 CTs=3.0
CTs
Eff
icie
nc
y
1 1.5 2 2.5 30.45
0.5
0.55
0.6
0.65
0.7Propeller_case1
Propeller_case2
Propeller_case3
Propeller case, fixed duct geometryJs=0.5
Js
Eff
icie
nc
y
0.5 0.6 0.7 0.8 0.9 1
0.6
0.65
0.7
0.75
Propeller_case1
Propeller_case2
Propeller_case3
CTs=1.0
Turbine case, different duct angles
• A RANS/lifting line model interaction method is proposed for the design of
ducted propellers and tidal turbines.
• The NACA a=0.8 camber and NACA 00 thickness are used.
• For the propeller case, the influence of camber and thickness is studied; for
the turbine case, the influence of duct angle is studied.
• It is shown that the duct geometry has influence on the inflow velocity and
KT on the blade for ducted propellers and turbines, which can not be taken
into account in the image model. Proper designed duct can increase the
efficiency significantly.
• This method is proved to be reliable and efficient in designing ducted
propellers and tidal turbines.
• Turbine case:
• Only Uin is updated
• The pressure jump is in the opposite direction, compared
with the propeller case
Propeller_case2 Propeller_case3
x
r
-0.2 -0.1 0 0.1 0.2
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
1.3
1.35
Duct angle=11 degree
Duct angle=13 degree
Duct angle=15 degree
X
Y
-1 -0.5 0 0.5 1
0
0.5
1
1.5
Pressure
300
240
180
120
60
0
-60
-120
-180
-240
-300
TSR
Eff
icie
nc
y
7 7.5 8 8.5 9 9.5 10
0.42
0.44
0.46
0.48
0.5
0.52
Duct angle=11 degree
Duct angle=13 degree
Duct angle=15 degree
Open turbine (without duct)
(0,1)
(0,0)
cduct
f0
t0
dxle
axis
x
r
-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
0
0.2
0.4
0.6
0.8
1
1.2
1.4
duct
camber line
blade (actuator disk)
nose-tail line
11% to 22% efficiency increase