Trawl-door Performance Analysis and Design Optimization with CFD
Eirikur Jonsson, Leifur Leifsson and Slawomir Koziel
Engineering Optimization & Modeling Center, School of Science and Engineering, Reykjavik University, Reykjavik, Iceland
Keywords:
Trawl-doors, CFD, Design Optimization, Space Mapping, Surrogate-based Optimization, Variable-resolution
Modeling, Simulation-driven Design.
Abstract:
Rising fuel prices and inefficient fishing gear are hampering the fishing industry. In this paper, we present a
computational fluid dynamic (CFD) model to analyse the hydrodynamic performance of trawl-doors, which
are a major contributor to the high fuel consumption of fishing vessels. Furthermore, we couple the CFD
model with an efficient design optimization technique and demonstrate how to redesign the trawl-door shapes
for minimum drag at a given lift. The optimization techinique is surrogate-based and employs a coarse discriti-
zation CFD model with relaxed convergence criteria. The surrogate model is constructed using the physics-
based low-fidelity model and space mapping. The CFD model is applied to the analysis of current trawl-door
shapes and reveals that they are operated at low efficiency (with lift-to-drag ratios lower than 1), mainly due to
massively separated flow. An example design optimization case study reveals that the angle of attack can be
reduced significantly by re-positioning and tilting the leading-edge slats. The performance can be improved
by as much as 24 times (attaining lift-ro-drag ratios around 24).
1 INTRODUCTION
Efficient trawler ships are vital for the fishing indus-
try. Rising fuel prices have an enormous impact on
the fishing industry as a whole as the cost of fuel is a
major part of the operation cost. Most of the fuel (of-
ten over 80%) is spent during the trawling operation,
which can take days at a time, although the trawling is
normally performed at low speeds (less than 3 knots).
The reason is the high drag of the fishing gear assem-
bly. Therefore, a careful study and redesign of the
assembly is necessary in order to reduce the fuel con-
sumption and improve the efficiency.
A typical fishing gear assembly, shown in Fig. 1,
consists of a large net, a pair of trawl-doors to keep
the net open, and a cable assembly extending from
the trawl-doors to the boat and the net. Although
the trawl-doors are a small part of the fishing gear,
they are responsible for roughly 30% of the total drag
(Garner, 1967). A typical trawl-door is shown in Fig.
2.
Almost all the trawl-doors that have been de-
veloped over the years are fundamentally the same.
Trawl-door designs are essentially steel plates, cut
down, bent with a certain radius and welded together.
These designs have two key elements, namely, the
main element (ME), which is the largest part, and one
or more slats or slots, located at the leading edge. Mi-
nor design changes have been made to trawl-doors
over the years, mainly because their designs are solely
based on time consuming and expensive physical ex-
periments.
Although, computational fluid dynamics (CFD) is
widely used in design of a variety of engineering de-
vices, such as aircraft, ships, and cars, very few ap-
plications are reported for trawl-doors in the litera-
ture (Haraldsson et al., 1996). Therefore, there is
an opportunity to apply state-of-the-art CFD methods
and optimizatin techniques to analyse and redesign
the trawl-doors, before using physical experiments for
verification purposes only. The trawl-doors have a
low aspect ratio and are operated at high angles of
attack (up to 50 degrees). As a result, the flow is
highly three-dimensional and transient. A full three-
dimensional simulation is required to capture the flow
physics accurately. However, such simulation can be
time consuming, and if used directly within the op-
timization loop (requiring a large number of simula-
tions), the overall time of the design process becomes
prohibitive. An efficient design methodology is there-
fore essential for such design applications.
In this paper, we develop a robust high-fidelity
CFD method for the performance analysis of trawl-
doors. As a first step in this development, we use
479
Jonsson E., Leifsson L. and Koziel S..
Trawl-door Performance Analysis and Design Optimization with CFD.
DOI: 10.5220/0004163904790488
In Proceedings of the 2nd International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SDDOM-2012), pages
479-488
ISBN: 978-989-8565-20-4
Copyright
c
2012 SCITEPRESS (Science and Technology Publications, Lda.)
Figure 1: Trawl gear drag decomposition diagram (Garner,
1967). Approximately 30% of the drag of the entire fishing
gear assembly is due to the trawl-doors. Cables account for
about 10% and the net and other parts the rest.
Figure 2: A CAD drawing of the F11 trawl-door elements.
Main element (ME), Slat 1 and Slat 2. The span is b = 5.8m
and the extended chord length is c
0
= 2.4m. This is a low
aspect ratio wing with AR = 2.07
a steady-state two-dimensional approach. The CFD
model is used to investigate the performance of a
typical trawl-door design. The CFD model is inte-
grated within a recently developed surrogate-based
optimization algorithm (Koziel and Leifsson, 2012)
to demonstrate how trawl-doors can be redesigned for
minimum drag at a given lift.
2 CFD MODELING
In this section, we describe the CFD model for two-
dimensional trawl-door shapes. In particular, we de-
scribe the geometry, the computational grid, and the
flow solver. We present results of a grid convergence
study. Finally, we validate the model by comparing
it’s evaluations with experimental data.
2.1 Geometry
We consider a simple chord-wise cross-sectional cut
of the F11 trawl-door (shown in Fig. 2). The two-
dimensional cut is shown in Fig. 3. There are three
elements, the main element (ME), which is the largest
element of the assembly, slat 1, the middle element,
and slat 2, the element farthest from the ME. The
trawl-door is normalized with the chord length of the
ME (c).
−0.2 0 0.2 0.4 0.6 0.8 1
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
0.4
0.5
x/c
y/c
Slat 2 Slat 1 Main Element (ME)
Figure 3: Cross-section of the normalized F11 trawl-door
with three elements, main element (ME), slat 1 and slat 2.
2.2 Governing Equations
Trawl-doors are devices used in seawater, hence, we
can safely assume that the flow is incompressible.
We, furthermore, assume that the flow is steady, vis-
cous and with no body forces. The Reynolds Average
Navier-Stokes (RANS) equations are taken to be the
governing equations with Menter’s k-ω-SST turbu-
lence model (see for example (Tannehill et al., 1997)).
2.3 Computational Grid
The farfield is configured in a box-topology where the
trawl-door geometry is placed in the center of the box.
The main element leading edge (LE) is placed as the
origin (x/c, y/c) = (0,0), with the farfield extending
100 main element chord lengths away from the ori-
gin. The grid is an unstructured triangular grid where
the elements are clustered around the trawl-door ge-
ometry, growing in size as they move away from the
origin. The maximum element size on the geometry
is set to 0.1% of c. The maximum element size in do-
main is 10c. In order to capture the viscous boundary
layer well, a prismatic inflation layer is extruded from
all surfaces. The inflation layer has a initial height of
5 × 10
−6
c, growing with exponential growth ratio of
1.2 and extending 20 layers from the surface. The ini-
tial layer height is chosen so that y
+
< 1. In the wake
region aft of the trawl-door, the grid is made denser by
applying a density grid with an element size of 5% of
c, extending 20c aft of the trawl-door geometry. The
density mesh is configured in an adaptive manner so
that it aligns with the flow direction. An example grid
is shown in Fig. 4.
SIMULTECH 2012 - 2nd International Conference on Simulation and Modeling Methodologies, Technologies and
Applications
480
(a)
(b)
Figure 4: High-fidelity mesh for the angle of attack α = 50
degrees.
2.4 Flow Solver
Numerical fluid flow simulations are performed us-
ing the computer code ANSYS FLUENT (ANSYS,
2010). The flow solver is set to a coupled velocity-
pressure-based formulation. The spatial discretiza-
tion schemes are second order for all variables and the
gradient information is found using the Green-Gauss
node based method. Additionally, due to the difficult
flow condition at high angle of attacks, the pseudo-
transient option and high-order relaxation terms are
used in order to get a stable converged solution (AN-
SYS, 2010). The iterative solution is performed with
relaxation factors to prevent a numerical oscillation
of the solution that can lead to a no solution or er-
rors. The residuals, which are the sum of the L
2
norm
of all governing equations in each cell, are monitored
and checked for convergence. The convergence cri-
terion for the high-fidelity model is such that a so-
lution is considered to be converged if the residuals
have dropped by six orders of magnitude, or the total
number of iterations has reached 1000. Also, the lift
and drag coefficients are monitored for convergence.
The working fluid used is water and the inlet
boundary is a velocity-inlet with a freestream velocity
V
∞
= 2 m/s, (which is typical during trawling), split
into its x and y components depending on the angle
of attack α. The outlet boundary is a pressure-outlet.
Reynolds number is Re
c
= 2 × 10
−6
. The inlet flow
is assumed to be calm, with turbulent intensity and
viscosity ratio of 0.05% and 1, respectively.
2.5 Grid Convergence
A sufficiently fine enough mesh is found by carrying
out a grid convergence study using the NACA 0012
airfoil at V
∞
= 2m/s, Re = 2 × 10
6
, and α = 3
◦
. The
results are shown in Fig. 5 and reveal that 197,620
grid elements are needed for convergence. The over-
all simulation time needed for one high-fidelity CFD
simulation was around 16 minutes, executed on four
Intel-i7-2600 processors in parallel (1000 solver iter-
ations where required).
2.6 Model Validation
Due to a lack of available two-dimensional experi-
mental data for trawl-door shapes, we use other types
of geometries to validate the high-fidelity CFD model.
The NACA 4 digit airfoils (Abbott and Von Doenhoff,
1959) have been studied extensively in the past and
we consider the NACA 0012 airfoil as the validation
case. The results are shown in Fig. 6. There is good
agreement between the CFD model and the experi-
mental data in terms of lift up to the stall region, and
up to α < 10
◦
for drag.
3 OPTIMIZATION WITH SPACE
MAPPING
In this paper, the airfoil design is carried out in a com-
putationally efficient manner by exploiting the space
mapping (SM) methodology (Bandler et al., 2004).
Space mapping replaces the direct optimization of an
expensive (high-fidelity or fine) airfoil model f ob-
tained through high-fidelity CFD simulation, by an
iterative updating and re-optimization of a cheaper
surrogate model s. The key component of SM is a
physics-based low-fidelity (or coarse) model c that
embeds certain knowledge about the system under
Trawl-door Performance Analysis and Design Optimization with CFD
481
10
3
10
4
10
5
10
6
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Number of grid elements
C
l
,10 x C
d
C
l
10 x C
d
(a)
10
3
10
4
10
5
10
6
0
5
10
15
20
25
30
Number of grid elements
Time [min]
(b)
Figure 5: Grid convergence study using the NACA 0012
airfoil at V
∞
= 2m/s,Re = 2 × 10
6
and angle of attack α =
3
◦
. a) Lift (C
l
) and drag (C
d
) coefficient versus number
of grid elements, b) simulation time versus number of grid
elements.
consideration and allows us to construct a reliable sur-
rogate using a limited amount of high-fidelity model
data. Here, the low-fidelity model is evaluated using
the same CFD solver as the high-fidelity one, so that
both models share the same knowledge of the airfoil
performance.
3.1 Optimization Problem
The simulation-driven design can be generally formu-
lated as a nonlinear minimization problem
x
∗
= arg min
x
H ( f (x)), (1)
where x is a vector of design parameters, f the high-
fidelity model to be minimized at x and H is the ob-
jective function. x
∗
is the optimum design vector. The
high-fidelity model will represent the aerodynamic
forces, i.e., the lift and drag coefficients. The response
will have to form
f (x) =
C
l, f
(x),C
d, f
(x))
T
, (2)
(a)
−5 0 5 10 15 20
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
α [deg]
C
d
2D CFD ME only
Ladson data Re=6M Fixed Transition
(b)
Figure 6: Results of the CFD model validation. The model
is compared with experimental data (LADSON, 1988) at
Re
c
= 6 × 10
6
. (a) Lift curve, and (b) drag curve.
where C
l, f
and C
d, f
are the lift and drag coeffi-
cient, respectively, generated by the high-fidelity CFD
model. We are interested in minimizing the drag for a
given lift, so the objective function will take the form
of
H ( f (x)) = C
d
, (3)
with the design constraint written as
c( f (x)) = −C
l, f
(x) +C
l,min
≤ 0, (4)
(5)
where C
l,min
is the minimum required lift coefficient.
3.2 Space Mapping Basics
Starting from an initial design x
(0)
, the generic space
mapping algorithm produces a sequence x
(i)
,i =
0,1 .. . of approximate solution to 1 as
x
(i+1)
= arg min
x
H
s
(i)
(x)
, (6)
where
s
(i)
(x) =
h
C
(i)
l,s
(x),C
(i)
d,s
(x)
i
T
, (7)
SIMULTECH 2012 - 2nd International Conference on Simulation and Modeling Methodologies, Technologies and
Applications
482
is the surrogate model at iteration i. As previously
described, the accurate high-fidelity CFD model f is
accurate but computationally expensive. Using Space
Mapping, the surrogate s is a composition of the low-
fidelity CFD model c and a simple linear transforma-
tions to correct the low-fidelity model response (Ban-
dler et al., 2004). The corrected response is denoted
as s(x, p) where p represent a set of model parameters
and at iteration i the surrogate is
s
(i)
(x) = s(x,p). (8)
The SM parameters p are determined through a
parameter extraction (PE) process. In general this
process is a nonlinear optimization problem where the
objective is to minimize the misalignment of surro-
gate response at some or all previous iteration high-
fidelity model data points (Bandler et al., 2004). The
PE optimization problem can be defined as
p
(i)
= arg min
p
i
∑
k=0
w
i,k
k f (x
(k)
) − s(x
(k)
,p)k
2
, (9)
where w
i,k
are weight factors that control how much
impact previous iterations affect the SM parameters.
Popular choices are
w
i,k
= 1 ∀i,k , (10)
and
w
i,k
=
1 k = i
0 otherwise
. (11)
In the first case, all previous SM iterations influence
the parameters; in the second case, the parameters de-
pend only on the most recent SM iteration.
3.3 Low-fidelity CFD Model
The general underlying low-fidelity model c used for
all cases is constructed in the same way as the high-
fidelity model f , but with a coarser grid discretization
and relaxed convergence criteria. Referring back to
the grid study, carried out in Section 2.5, and inspect-
ing Fig. 5, we select the coarse low-fidelity model.
Based on time and accuracy, with respect to lift and
drag, we select the grid parameters representing the
fourth point from the right, giving 16,160 elements for
the low-fidelity CFD model. The evaluation time of
the low-fidelity model is 2.3 minutes on four Intel-i7-
2600 processors in parallel. Inspecting further the lift
and drag convergence plot for the low-fidelity model
in Fig. 7, we note that the solution has converged af-
ter 150-200 iterations. However, the maximum num-
ber of iterations for the low-fidelity model is set to
50 100 150 200 250 300 350 400 450
0
0.5
1
1.5
2
2.5
3
3.5
4
C
l
,10 x C
d
Iterations
C
l
10 x C
d
Figure 7: Lift and Drag coefficient convergence plot for
low-fidelity model obtained in grid convergence study sim-
ulation for NACA 0012 at Reynolds number Re = 2 × 10
6
and angle of attack α = 3
◦
.
three times that, or 700 iterations, due to the nature
of problem and different geometries to be optimized.
This reduces the overall simulation time to 1.6 min-
utes. The ratio of simulation times of the high- and
low- fidelity model in this case is high/low = 16/1.6 =
10. This is based on the solver uses all 700 iterations
in the low-fidelity model to obtain a solution.
3.4 Surrogate Model Construction
As mentioned above, the SM surrogate model s is
a composition of the low-fidelity CFD model c and
corrections or linear transformations where model pa-
rameters p are extracted using one of the PE processes
described above. Parameter extraction and surrogate
optimization create a certain overhead on the whole
process which can be up to 80-90 % of the computa-
tional cost. This is due to the fact that physics-based
low-fidelity models are in general relatively expensive
to evaluate.
To alleviate this problem, an output SM with both
multiplicative and additive response correction is ex-
ploited here with the surrogate model parameters ex-
tracted analytically. We use the following formulation
s
(i)
(x) = A
(i)
◦ c(x) + D
(i)
+ q
(i)
, (12)
or
s
(i)
(x) =
h
a
(i)
l
C
l,c
(x) + d
(i)
l
+ q
(i)
l
,
a
(i)
d
C
d,c
(x) + d
(i)
d
+ q
(i)
d
i
T
.
(13)
The parameters A
(i)
and D
(i)
are obtained by solving
Trawl-door Performance Analysis and Design Optimization with CFD
483
h
A
(i)
,D
(i)
i
= argmin
A,D
i
∑
k=0
k f
x
(k)
− A ◦ c
x
(k)
+ Dk
2
,
(14)
where w
i,k
= 1, i.e., all previous iteration points are
used to improve globally the response of the low-
fidelity model. The additive term q
(i)
is defined such it
ensures a perfect match between the surrogate and the
high-fidelity model at design x
(i)
, namely f (x
(i)
) =
s(x
(i)
) or a zero-order consistency (Alexandrov and
Lewis, 2001). We can write the additive term as
q
(i)
= f
x
(i)
−
h
A
(i)
◦ c(x
(i)
) + D
(i)
i
. (15)
Since an analytical solution exists for A
(i)
,D
(i)
and q
(i)
there is no need for non-linear optimization
solving Eq. 9 to obtain the parameters. We can obtain
A
(i)
and D
(i)
by solving
"
a
(i)
l
d
(i)
l
#
=
C
T
l
C
l
−1
C
T
l
F
l
, (16)
"
a
(i)
d
d
(i)
d
#
=
C
T
d
C
d
−1
C
T
d
F
d
, (17)
where
C
l
=
C
l,c
(x
(0)
) C
l,c
(x
(1)
) ... C
l,c
(x
(i)
)
1 1 ... 1
T
,
(18)
F
l
=
C
l, f
(x
(0)
) C
l, f
(x
(1)
) ... C
l, f
(x
(i)
)
1 1 .. . 1
T
,
(19)
C
d
=
C
d,c
(x
(0)
) C
d,c
(x
(1)
) ... C
d,c
(x
(i)
)
1 1 ... 1
T
,
(20)
F
d
=
C
d, f
(x
(0)
) C
d, f
(x
(1)
) ... C
d, f
(x
(i)
)
1 1 ... 1
T
,
(21)
which are the least-square optimal solutions to the lin-
ear regression problems
C
l
a
(i)
l
+ d
(i)
l
= F
l
, (22)
C
d
a
(i)
d
+ d
(i)
d
= F
d
. (23)
Note that C
T
l
C
l
and C
T
d
C
d
are non-singular for i >
1 and assuming that x
(k)
6= x
(i)
for k 6= i. For i = 1 only
the multiplicative SM correction with A
(i)
is used.
3.5 Optimization Algorithm
Here we formulate the optimization algorithm ex-
ploiting the SM based surrogate and a trust-region
convergence safeguard (Forrester and Keane, 2009).
The trust-region parameter λ is updated after each it-
eration. This algorithm will be used in applications
presented in this thesis.
1. Set i = 0; Select λ, the trust region radius; Eval-
uate the high-fidelity model at the initial solution,
f (x
(0)
);
2. Using data from the low-fidelity model c, and f
at x
(k)
,k = 0,1,.. . , i, setup the SM surrogate s
(i)
;
Perform PE;
3. Optimize s
(i)
to obtain x
(i+1)
;
4. Evaluate f (x
(i+1)
);
5. If H( f (x
(i+1)
)) < H( f (x
(i)
)), accept x
(i+1)
; Oth-
erwise set x
(i+1)
= x
(i)
;
6. Update λ;
7. Set i = i + 1;
8. If the termination condition is not satisfied, go to
2, else proceed;
9. End; Return x
(i)
as the optimum solution.
The termination condition is set to kx
(i)
− x
(i−1)
k <
10
−3
.
4 PERFORMANCE ANALYSIS
In this section, we present the results of the CFD anal-
ysis of the two-dimensional cut of the F11 trawl-door,
shown in Fig. 3. The CFD model, presented in Sec-
tion 2, is evaluated at number of different angle of
attacks or from α = −5
◦
to α = 60
◦
with 5 degree
increments at a free-stream velocity V
∞
= 2 m/s, and
Reynolds number Re
c
= 2 × 10
6
. Three different con-
figurations were studied: the main element only, the
main element with one slat, and the main element
with two slats (the F11 trawl-door design). Figure 8
shows the lift and drag curves.
Inspecting Fig. 8 reveals that the flow remains at-
tached for relatively low angles of attack when con-
sidering the main element only, and stall occurs close
to α = 10
◦
. For the main element with one slat,
the stall occurs at α = 20
◦
and for the F11 design
(the main element with two slats) the stall occurs at
α = 25
◦
. Adding the slats therefore to improves the
performance by delaying the stall, as well as increas-
ing the C
l,max
. This effect is expected as it is well
known for multi-element high-lift devices on aircraft.
SIMULTECH 2012 - 2nd International Conference on Simulation and Modeling Methodologies, Technologies and
Applications
484
We can split Fig. 8(b) into three regions, first
where the stall has not occurred where α < 20
◦
, and
after stalling 20
◦
< α < 35
◦
and α > 35
◦
. As seen
in part α < 20
◦
, prior to stall, the drag increases as
more slats are added to the assembly simply because
of more area that the flow needs bypass. As the an-
gle of attack is increased beyond stall, the drag rises
due to a massive flow separation as can be seen in Fig.
9. Effectiveness of slats are evident here, whereas by
adding slats the flow remains attached longer reduc-
ing separation and drag. In the last region, α > 35
◦
,
the flow simply needs to pass through more area as
more slats are added, increasing the drag further.
It should be noted that the flow is highly unsteady,
especially for large angles of attack, i.e., higher than
20 degrees. Therefore, the steady-state model does
not give an accurate description of the flow and only
provides an estimate of the averaged characteristics.
Any flow analysis or design optimization at high an-
gles of attack should be performed using an unsteady
analysis. However, a steady-state model gives a rea-
sonable estimate at moderate angles of attack.
5 DESIGN OPTIMIZATION
We proceed with a low angle of attack steady-state
analysis working only in the range where separation
is limited, thus, avoiding strong unsteady effects. The
objective is to optimize the location of the one slat
design to match or exceed the performance of the F11
trawl-door. We consider a drag minimization formu-
lation solved using both direct optimization using the
pattern-search technique (Kolda et al., 2003) and the
space mapping (SM) methodology presented in Sec-
tion 3.
5.1 Problem Formulation
To simplify the geometry, the slat furthest upstream
of the F11 design is removed and we consider only
the remaining geometry for optimization. The de-
sign variables considered are the location of the slat
(x
S1
/c,y
S1
/c), the slat orientation θ
S1
, and the angle
of attack α of the flow. This is shown in Fig. 10. The
design vector is written as x = [x
S1
/c,y
S1
/c,θ
S1
,α]
T
.
The free-stream velocity is fixed at V
∞
= 2 m/s and
the Reynolds number is Re
c
= 2 × 10
6
.
The objective is to minimize the drag coefficient
C
d, f
subject to a constraint on the lift coefficient
C
l, f
≥ C
l,min
= 1.5. Additional constraints include a
geometry validity check where the design is checked
at every iteration such that the optimizer rejects de-
signs if the slat and the main element cross, or vio-
−10 0 10 20 30 40 50 60
−0.5
0
0.5
1
1.5
2
2.5
3
α [deg]
C
l
2D CFD ME only
2D CFD ME+1 Slat
2D CFD ME+2 Slats (F11 design)
(a)
−10 0 10 20 30 40 50 60
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
α [deg]
C
d
2D CFD ME only
2D CFD ME+1 Slat
2D CFD ME+2 Slats (F11 design)
(b)
Figure 8: Lift and drag curves at V
∞
= 2m/s,Re
c
= 2 × 10
6
.
Computational results are shown with dotted dash line (.-.),
dashed line (- -) and solid line (–) for Main Element only
(ME), ME + 1 slat and ME + 2 (the F11 trawl-door design)
respectively. (a) lift coefficient, (b) drag coefficient.
late a minimum gap, Gap ≥ Gap
min
, or a maximum
overlap, Overlap ≤ Overlap
max
. The minimum gap
between elements is defined as the minimum distance
from any point on the main element to any point on
the slat. Maximum overlap is defined as the distance
x/c which the trailing edge of the slat overlaps the
leading edge of the main element.
The nonlinear minimization problem is formu-
lated as
x
∗
= arg min
x
C
d
, (24)
subject to
C
l, f
≥ C
l,min
= 1.5,
Gap ≥ Gap
min
= 0.05,
Overlap ≤ Overlap
max
= 0.1,
(25)
with the following design variable bounds
Trawl-door Performance Analysis and Design Optimization with CFD
485
(a)
−0.4 −0.2 0 0.2 0.4 0.6 0.8 1 1.2
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
x/c
C
f
Main Element
Slat 1
Slat 2
(b)
−0.4 −0.2 0 0.2 0.4 0.6 0.8 1 1.2
−2.5
−2
−1.5
−1
−0.5
0
0.5
1
1.5
x/c
C
p
Main Element
Slat 1
Slat 2
−0.4 −0.2 0 0.2 0.4 0.6 0.8 1 1.2
0
0.05
0.1
0.15
0.2
x/c
y/c
(c)
Figure 9: F11 trawl-door characteristics at V
∞
=
2m/s,Re
c
= 2 × 10
6
, angle of attack α = 40
◦
. (a) Veloc-
ity contours, (b) Skin friction coefficient (C
f
), (c) Pressure
coefficient (C
p
).
−0.3 ≤ x
S1
/c ≤ 0.2,
−0.3 ≤ y
S1
/c ≤ 0.2,
20 ≤ θ
S1
≤ 50,
2 ≤ α ≤ 8.
(26)
5.2 Results
The numerical results are given in Table 1. Results
using the proposed SM method are compared to the
initial design of the modified F11 geometry design
(two elements, main element and one slat), and the
c
ME
c
S
1
x
S1
y
S1
θ
S1
(x
ME
,y
ME
) = (0,0)
x
y
t
ME
R
ME
c‘
(x
S1
,y
S1
)
Figure 10: Shift (x
S1
,y
S1
) relative to (0,0) and orientation
θ
S1
of one slat. The second slat is omitted for simplicity.
The chord length c of each element is defined from its lead-
ing edge to trailing edge and c
0
is the extended chord length
for the assembly. Thickness t
ME
and radius R
ME
for the ME
are shown but omitted for slat.
direct optimization of that design. Figure 11 shows
the initial and optimized designs. Figure 12 shows
the flow field, as well as the skin friction and pressure
distributions.
Similar results are obtained by the direct approach
and the SM approach. The slat is moved down and
forward, and tilted clockwise. The angle of attack is
reduced to between 2 to 3 degrees. The optimized
trawl-door design has approximately 90% less drag
for a lift coefficient of approximately 1.5 (the SM ap-
proach slightly violates the lift constraint by less than
5%). The proposed method requires less than 31 high-
fidelity model evaluations, 250 surrogate and 5 high-
fidelity which is considerably lower than if direct op-
timization is applied which required 180 high-fidelity
model evaluations.
A comparison of the optimized SM design with
the F11 design is given in Table 2 at C
l
= 1.4382. At
this C
l
, the F11 design is operating at 56 degrees (re-
ferring to Fig. 8), with a drag coefficient of about 96%
lower than the optimized design. The drag reduction
comes about due to a reduction in the angle of attack
and associated attached flow on the upper surface as
can be seen from Fig. 12. The F11 design has a lift-
to-drag ratio around 1, whereas the optimized design
lift-to-drag-ratio is around 23.
6 CONCLUSIONS
A robust and efficient design optimization method-
ology of fishing gear trawl-doors using high-fidelity
CFD models has been presented. The steady-state
two-dimensional high-fidelity CFD model captures
the essence of the clomplex flow physics of the trawl-
door flow. The computational cost of the design pro-
cess is reduced significantly by using a surrogate-
based optimization technique with variable-resolution
SIMULTECH 2012 - 2nd International Conference on Simulation and Modeling Methodologies, Technologies and
Applications
486
Table 1: Numerical results initial, direct and surrogate
based optimization using space mapping. The ratio of the
high-fidelity model evaluation time to the low-fidelity is 10.
The ratio is the SM optimized design over the initial design.
Variable Initial Direct SM Ratio
x/c -0.1192 -0.2515 -0.2107 -
y/c 0.0085 -0.0298 -0.0100 -
θ [deg] 33.9 22.3648 24.0113 -
α [deg] 30.0 2.8058 2.0000 -
C
l
1.7925 1.5634 1.4382 0.8
C
d
0.5875 0.0613 0.0614 0.1
C
l
/C
d
3.0511 25.5041 23.4235 7.7
N
c
- 300 250
N
f
- 150 6
Total Cost - 180 < 31
Table 2: Space mapping optimum design compared to the
F11 trawl-door design at lift coefficient C
l
= 1.4382. The
ratio is the SM optimized design over the F11 design.
Variable F11 design SM Ratio
α [deg] 55.9 2.0000 -
C
d
1.5044 0.0614 0.04
C
l
/C
d
0.9560 23.4235 24.5
CFD models.
The results of a performance analysis show that
the current trawl-door designs are poorly designed in
terms of efficiency. The flow is massively separated
at the high operation angle of attack (between 30 to
50 degrees), resulting in large vortices being shed and
yielding a highly unsteady response. However, the
leading-edge slats aleviate the lift loss a bit by extend-
ing the stall angle of attack up to 25 to 30 degrees.
A design optimization of the slat position shows
that the operation angle of attack can be lowered sig-
−0.2 0 0.2 0.4 0.6 0.8 1
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
0.4
0.5
x/c
y/c
Optimized Initial Main Element (ME)
Figure 11: Optimum design geometry obtained using space
mapping with the initial design shown as well.
(a)
−0.4 −0.2 0 0.2 0.4 0.6 0.8 1 1.2
0
0.005
0.01
0.015
0.02
0.025
x/c
C
f
Main Element
Slat 1
(b)
−0.4 −0.2 0 0.2 0.4 0.6 0.8 1 1.2
−2
−1.5
−1
−0.5
0
0.5
1
1.5
x/c
C
p
Main Element
Slat 1
−0.4 −0.2 0 0.2 0.4 0.6 0.8 1 1.2
0
0.05
0.1
0.15
0.2
x/c
y/c
(c)
Figure 12: Space Mapping optimization results V
∞
=
2m/s,Re
c
= 2 × 10
6
. Optimized design characteristics at
angle of attack α = 2
◦
. a) Velocity contour, b) Skin friction
coefficient (C
f
), c) Pressure coefficient (C
p
).
nificantly (to almost zero) and still retain the required
lift. As a result, the flow remains attached and the
drag is reduced dramatically, yield a large improve-
ment in efficiency, which could translate to lowered
fuel consumption of the fishing vessel. These results
give rise to further study of trawl-door shapes, as the
potential benefit is very important.
ACKNOWLEDGEMENTS
This work was funded by RANNIS, The Icelandic Re-
search Fund for Graduate Students, grant ID: 110395-
0061
Trawl-door Performance Analysis and Design Optimization with CFD
487
REFERENCES
Abbott, I. and Von Doenhoff, A. (1959). Theory of wing
sections: including a summary of airfoil data. Dover
Pubns.
Alexandrov, N. and Lewis, R. (2001). An overview of first-
order model management for engineering optimiza-
tion. Optimization and Engineering, 2(4):413–430.
ANSYS (2010). ANSYS FLUENT Theory Guide. AN-
SYS, Southpointe 275 Thecnology Drive Canonburg
PA 15317, release 13.0 edition.
Bandler, J., Cheng, Q., Dakroury, S., Mohamed, A., Bakr,
M., Madsen, K., and Sondergaard, J. (2004). Space
mapping: the state of the art. Microwave Theory and
Techniques, IEEE Transactions on, 52(1):337–361.
Forrester, A. and Keane, A. (2009). Recent advances in
surrogate-based optimization. Progress in Aerospace
Sciences, 45(1-3):50–79.
Garner, J. (1967). Botnvarpan og bunadur hennar. Fiskife-
lag Islands.
Haraldsson, H. O., Brynjolfsson, S., and Jnsson, V. K.
(1996). Reiknileg hermun iustreymis umhverfis togh-
lera. Vlabrg, 17.rg.:31–35.
Kolda, T., Lewis, R., and Torczon, V. (2003). Optimization
by direct search: New perspectives on some classical
and modern methods. SIAM review, pages 385–482.
Koziel, S. and Leifsson, L. (2012). Knowlegde-based air-
foil shape optimization using space mapping. In 22nd
AIAA Applied Aerodynamics Conference.
LADSON, C. (1988). Effects of independent variation of
mach and reynolds numbers on the low-speed aerody-
namic characteristics of the naca 0012 airfoil section.
Tannehill, J., Anderson, D., and Pletcher, R. (1997). Com-
putational fluid mechanics and heat transfer. Taylor
& Francis Group.
SIMULTECH 2012 - 2nd International Conference on Simulation and Modeling Methodologies, Technologies and
Applications
488