Trans RINA, Vol 152, Part B1, Intl J Small Craft Tech, 2010 Jan-Jun 3.2 NUMERICAL MODELLING
The CFD calculations were all performed using ANSYS CFX10 with two partitions on a Dual 2.2 GHz 64 bit Opteron with 4 GB RAM. Typical CPU time was 15h for mesh size of 2,418,871 cells.
3.2 (a) Domain size and mesh
The domain size encompassed the wind-tunnel’s working section: width = 4.6m, height = 3.7m, depth = 11m.
A study of the actual mesh density and size was made and after
several iterations
Figure 3: Aft view of the picture and digitalized shape 3.
THE CFD MODEL 3.1 MATHEMATICAL THEORY
The flow solver ANSYS CFX 10.0 uses a finite volume formulation of the Reynolds Average Navier Stokes equations to model fluid flow. In Cartesian coordinates, the continuity and momentum equations written in tensor form become:
∂ =∂
u x
i 0 i
ρ⎜⎟ − ⎜⎟ ∂xji j
⎝⎠ ∂xj ∂∂ ∂ tx x
ii j
ττ μ== ∂ +
ij ⎜⎟⎜⎟ ⎝⎠
⎛⎞i ∂∂x
u x
∂u ji And, −ρuu is the so called Reynolds stress tensor, P '' ij
the mean pressure, ui are the mean velocity vector components, u’ the fluctuating velocity vector, ρ the density of the fluid and μ the dynamic viscosity.
Turbulence models are required to close the RANS equations by providing models for the computation of the Reynolds stresses. One proposal suggests that turbulence consists of small eddies which are continuously forming and dissipating, and in which the Reynolds stresses are assumed to be proportional to mean velocity gradients. This assumption is the basis of the so-called eddy viscosity models. The turbulence model used here, the Shear Stress Transport (SST) model developed in 1994 by Menter [8], follows this assumption. The SST model accounts for the transport of the turbulent shear stress and gives highly accurate predictions of the onset and the amount
of flow separation under
gradients, as noted by Collie et al [9] in their review of turbulence models for sail flow simulations.
©2010: The Royal Institution of Naval Architects
uu P u
+
⎛⎞ ∂τ ρuu ∂∂ ∂∂+=−
τ is the molecular stress tensor: j
(' ' )ij (1) (2) of
following was considered accurate enough in terms of the repeatability of CFD results and also the smallness of the y+ parameter.
The 3D structured mesh used to model the wind-tunnel’s walls, jib, main and mast without hull was made of 2,418,871 hexahedrons distributed as follows:
• Spanwise : 60 nodes for the jib and 80 for the main • Chord wise: 50 nodes for the jib and 45 for the main • Slot between the sails: 25 nodes • Wake (longitudinally): 50 nodes • Gap between sails’ foot and deck: 15 nodes
these parameters the
(3)
Figure 4: Views of the mesh with, and without hull adverse pressure
As seen from figure 4, the nodes were distributed hyperbolically to allow for refinement at the leading and trailing edges, foot and head of the sails, in the direction normal to the sails (with y+=O(10)) and in the wake. An
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