Trans RINA, Vol 153, Part B2, Intl J Small Craft Tech, 2011 Jul-Dec and the number of design variables is large [33].
However in a simple optimization problem in CFD with a subset of the total design variables it has been shown that the objective function may be multi-modal [21].
is one of the reasons we have chosen to use an evolutionary strategy rather ones.
It than more conventional
An evolution strategy (ES) is an optimization method based on Darwinian ideas of the natural evolution. These techniques, created in the early 1960s, have been developed further for fluid flow problems in the 1970s and later [34].
In this work, CMA-ES (Covariance Matrix Adaptation - Evolution Strategy) an evolutionary algorithm is used in most of the paper except in section 7.2 and 7.3 where a gradient based algorithm is used. It is well adapted for non linear non convex optimization problems in a continuous domain. It is also well adapted for noisy problems when derivative based methods fail. Because it doesn’t presume or require the existence of a derivative of the objective function, it is feasible on non-smooth and even non-continuous problems, as well as on multi-modal problems. Following Hansen [35] it is a particularly reliable and highly competitive evolutionary algorithm for local optimization and also for global optimization problems [36, 37]. One more advantage of using CMA-ES is that it doesn’t require a tedious parameter tuning for its application as opposed to commonly used genetic algorithms.
Now we have defined all the ingredients of our
computational framework, examples will be given to illustrate the possibility it opens up for sailing yacht rig optimization through an aerodynamic or an aeroelastic modelling of the problem.
7. RESULTS
Results will be presented in five sections. The first section illustrates the importance of viscous flow modelling through RANS. The second, third and fourth sections illustrate the interest of optimization studies for sails. The fifth section illustrates FSI applications.
7.1 VISCOUS FLOW PREDICTION A first
point about viscous flow modelling is to
understand why and when it is needed for sail and rig performance prediction, design and optimization.
To illustrate this point, it may be that three-dimensional sails should be considered. In this case, one may refer to the Jones [38] study as an illustrative example. In the paper, it is shown on an IACC rig with a mainsail and a jib that viscous and inviscid solutions predict opposite rankings for
conditions. It will be of
two sail camber design in same wind interest to know which
modelling is right but there are no experimental results given. Probably RANS is the right solution because it takes into account
one more important
physical
phenomenon, the viscous effects. Hence, viscous drag is taken into account. However more critically, with RANS modelling, pressure drag associated with flow separation may be qualitatively predicted as shown in a previous
paper on sail sections with detailed
comparisons to the Wilkinson wind-tunnel tests [19]. A few results from this paper are used in this section to illustrate the abilities and limitations modelling for sail flows.
of RANS
Let us look in more details a simple case with only one two-dimensional sail. RANS prediction is more demanding in mesh resolution and CPU time than panel methods, also this should not be underestimated. Because sail camber is an important sail parameter, highly
related to flow separation
design and
pressure drag, the ability of RANS modelling to predict variations of sail aerodynamic performances for various sail cambers has been evaluated.
In Figures 4 and 5 the maximum lift coefficient Clmax and the maximum lift-to-drag ratio (L/D)max are presented as
functions of sail camber for RANS
simulations conducted over a range of angles of attack with first and second order numerical schemes. It is interesting to note that, for both schemes, RANS predicts a saturation of Clmax with f/c. The maximum Clmax value obtained for f/c ranging from 25% to 30% can’t be surpassed by increasing the sail camber as is known by experiments [39]. This is related to flow separation which is qualitatively well predicted by RANS and not by inviscid methods [19, 40]. This is not to say that the maximum Clmax value predicted by RANS is highly accurate but that RANS is sufficient to detect a trade-off on the sail camber design parameter. This is a major difference between the inviscid and the viscous model.
In the same way, accurate RANS modelling with a second-order scheme is able to predict that there is an optimum camber value which maximizes (L/D)max as shown in wind-tunnel
experiments [20] and
Bethwaite observed on sea tests [39]. The value of the predicted optimum camber agrees with the Bethwaite experimental values
as (10%-13%). The accurate
prediction of the maximum (L/D)max may be dependent on the numerical choices made for the simulation (mesh resolution, numerical scheme, etc…) and need expertise. Best practices should be defined [40] and more detailed validation conducted for accurate prediction. As an example, for
a given mesh, the influence of the
numerical scheme used is illustrated for a sail with various camber values in Figure 5. On this figure, the second-order scheme is able to predict an optimum camber value but the first order scheme doesn’t. This example clearly illustrates that when conducting RANS simulations around sails, an important best practice is
B-108
©2011: The Royal Institution of Naval Architects
Page 1 |
Page 2 |
Page 3 |
Page 4 |
Page 5 |
Page 6 |
Page 7 |
Page 8 |
Page 9 |
Page 10 |
Page 11 |
Page 12 |
Page 13 |
Page 14 |
Page 15 |
Page 16 |
Page 17 |
Page 18 |
Page 19 |
Page 20 |
Page 21 |
Page 22 |
Page 23 |
Page 24 |
Page 25 |
Page 26 |
Page 27 |
Page 28 |
Page 29 |
Page 30 |
Page 31 |
Page 32 |
Page 33 |
Page 34 |
Page 35 |
Page 36 |
Page 37 |
Page 38 |
Page 39 |
Page 40 |
Page 41 |
Page 42 |
Page 43 |
Page 44 |
Page 45 |
Page 46 |
Page 47 |
Page 48 |
Page 49 |
Page 50 |
Page 51 |
Page 52 |
Page 53 |
Page 54 |
Page 55 |
Page 56 |
Page 57 |
Page 58 |
Page 59 |
Page 60 |
Page 61 |
Page 62