Trans RINA, Vol 153, Part B2, Intl J Small Craft Tech, 2011 Jul-Dec
The method of resolution is based on Barnes studies [30], using dynamic relaxation and kinematic damping. The model is based on membrane elements for sail modelling and beam elements for battens. This model is described
by a parametric surface (u,v local
coordinates). The sail materials can be described as a composite material: each ply contains a filament laid or a film. The behaviour of the material can be non linear. The resolution method is based on an explicit scheme with a first order time and space discretization.
RELAX has a sophisticated meshing tool which can automatically mesh sail geometry given by a CAD software, such as RHINO 3D. Sail meshing is realized using Delaunay triangulation. The grid relates to boundaries of panels and is refined in regions of greatest curvature. During analysis the nodes move to their new equilibrium position. There is no remeshing of the structure.
Knowing that a membrane element has no resistance in compression, a wrinkling model is implemented in RELAX to take into account the compressive stresses. As a membrane has an infinite number of kinematics degree of freedom (possibility to deform without a change of stress) and a grid has a finite number of kinematics degrees, the wrinkling modelling allows a better prediction by adding degrees of freedom. At that time, the membrane is considered as an orthotropic material with a linear behaviour.
RELAX is a robust solver but excess material which is not supported by a batten is a source of instability. This is a consequence of the choice of membrane elements which have no resistance in bending. Also, extended foot modelling can be problematic.
The RELAX interface presents various possibilities for trimming. This is useful to modify the sail shape in a realistic way. In particular, halyard, stay and clew lengths can be changed, as carriage location.
All data are saved from the last analysis. This is a useful point in the case of an FSI loop. From a loop to the next one, just the pressure field has to be updated, while stresses, geometry and the mesh are conserved in the memory by the software. This allows a saving in computing time.
4. FLUID STRUCTURE COUPLING
With actual computing power and accessibility of specialized software, it is now possible to predict the flying shape of sails through FSI coupling [8]. The resolution in the same time of aerodynamic and structural equations is the best way to achieve this goal but it is a computationally expensive way [31]. A loose coupling method allows a reasonable prediction with
In a loose coupling method, aerodynamic and structural equations are solved independently. It is possible to use two
different sets of software, one dedicated to
structural analysis and the other dedicated to fluid analysis, even if they are not developed to communicate together. Once the loop is initialized with the sail design shape and an arbitrary constant pressure field, the structural code sends the sail displacements to the fluid code and the fluid code sends back the pressure field on the sail surfaces to the structural code. Iterations are made until convergence.
4.2 INTERFACING
The aerodynamic and structural solvers are different and don’t have the same needs concerning the meshing. Their respective meshes are different and independent and an efficient
interfacing method needs to be
developed to link these modules. In the FSI loop, the aerodynamic solver sends the pressure field on the geometry to the structural solver and the structural solver communicates the new shape of the geometry resulting from the given pressure field. Also, it is necessary to provide a mapping of the pressure field from the fluid mesh to the structural mesh with no prior knowledge of the target mesh.
To achieve this, the coordinate of the structural surface is mapped onto the unit square using a development of the texture-mapping method described in Desbrun [32].
When the structural mesh geometry is exported for CFD, we also save a record of the relation between the texture-map coordinates and
the current global
Cartesian coordinates. We do this by constructing a NURBS surface approximating the structural model with surface parameterization chosen to match the texture coordinates. This provides a good record of the relation
between global coordinates, although the
smallest resources by using specialized software for the fluid and the structural part.
4.1 PRINCIPLE
Cartesian and texture tensor product NURBS
surface cannot capture all the shape details. This NURBS surface is saved in a neutral CAD format.
The CFD typically returns a surface pressure field at global Cartesian positions of the fluid mesh. For each pressure sample point, we associate the pressure value to texture coordinates by finding the closest point on the NURBS surface. This operation is loss-less because every pressure sample is mapped. It introduces position errors of second order relative to the error of NURBS approximation.
the
Then the new sail shape corresponding to this pressure field is given by the structural solver using an IGES file. The new sail shape is used by the aerodynamic mesher
B-106
©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