Trans RINA, Vol 153, Part B2, Intl J Small Craft Tech, 2011 Jul-Dec
distribution on the flying sail shape and the stress distribution.
Section 3.1 describes the aerodynamic analysis method, while section 3.2 describes the sail structural analysis method. Details of validation tests are also included.
3.1 AERODYNAMIC ANALYSIS
The evaluation of the aerodynamic loads on the sailplan is carried out using a modified version of the Vortex Lattice Method (VLM), which represents the most widely used potential method for solving the inviscid sail aerodynamic problem. In 1968 Milgram started to apply this method to sail aerodynamic analysis [3]. After his basic development the method has been developed in several ways and is demonstrated to be an effective tool for sail analysis [4]. Low costs in terms of computational and human resources make VLM popular and efficient with respect to RANS techniques and Wind Tunnel Tests (WTT), which are mostly used at the final stage of the design.
The implemented Modified Vortex Lattice
Method (MVLM) converts the sail surface into a vortex sheet, which means that the surface has zero thickness (in this paper the mast aerodynamic influence is ignored) and the jump in velocity across it is equal to the local strength of the vortex sheet. The local vorticity is evaluated by imposing the condition that there is no flow through the surface of the sail and, hence, the velocity field is tangent to the surface. Furthermore, to obtain a unique solution, it
is assumed that the flow separates
from the sail surface at the trailing edge – the so-called Kutta condition. For an extensive description of the method please refer to Malpede-Baraldi assumptions are:
[2]. Essential
Flow field is irrotational everywhere. No flow separation on the sail surface. Zero pressure gradient across the wake.
The irrotational condition can be considered satisfied because sails can be modelled as thin lifting surfaces. Such sails are characterised by high Reynolds number and low speed flow. The second assumption is more problematic due to the fact that sails are cambered lifting surfaces working at high angle of attack and a wrong trim can generate even leading edge separation. Thus, the method accuracy decreases for high angles of attack [2]. The third assumption is performed through the wake relaxation process.
The MVLM calculates the jump of the tangential flow velocity over the sail. Thus, the aerodynamic loads are calculated via the Bernoulli principle for calculating the pressure coefficient distribution:
C p
P p V V
Q 1
2 (1)
Figure 2: Pin head mainsail (from left: wind tunnel model, vortex lattice and pressure force distribution).
Figure 1: Square top mainsail (from left: wind tunnel model, vortex lattice and pressure force distribution).
where CP, p and V are pressure coefficient, local pressure and velocity at a control point respectively. Subscript ∞ denotes asymptotic flow [2].
3.1 (a) Validation Using Wind Tunnel Testing
The scarcity of experimental data for loads on yacht sails makes the validation for sails problematic. The authors have carried out many tests comparing the MVLM results with published case studies but the paucity of geometric data makes the reproduction of the geometry approximate. Thus, a series of WTT was carried out at the University of Sydney for a scaled 18ft skiff model; the comparison of the aerodynamic analysis and the WTT results is presented in [5].
The two sailplans are composed of the same jib and square top and pin head (or elliptical) mainsails. The wind tunnel tests were performed in [6] with the following key phases:
SMAR Azure designed the sails and produced the file of panels to be manufactured in a 1:10 scale.
Evan Walker produced the sails, carried out the WTT at the University of Sydney and measured the flying sail shape from photos taken during the tests.
SMAR Azure then reproduced the flying sail shape using the data measured in the WTT, calculated the aerodynamic forces in the same conditions and compared the results.
©2011: The Royal Institution of Naval Architects
B-119
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