COMPIT 2010 in Gubbio - TUHH

with the more precise flow solver. This strategy aims to minimize the number of time consuming flow
calculations. The Meta-model Assisted Evolutionary Algorithm was developed at the Department of
Computer Science, Chair of Algorithm Engineering TU Dortmund. The integration of the MAEA
optimisation algorithm into a propulsor optimisation process is described by Hundemer et al. (2006).
3. Flow Solvers
Two different solvers are used in the present study. In all optimisation processes the in-house
potential theory solver ISThydro is included, which is a first-order 3D- panel method. The ISThydro
solver represents the propulsor by a distribution of constant strength sources and dipoles on the
panelised geometry. The strength of the sources and dipoles are to be determined during the
calculation. The method can be applied to simulate steady or unsteady flow problems.
The used RANSE solver is the commercial code ANSYS-CFX, www.ansys.com. It is utilised to
optimise the duct geometry and the hub of the propulsor. The SST-turbulence model is applied and a
hexahedral mesh is employed for the viscous flow calculations in the study.
4. Optimisation Process
The optimisation starts with the generation of a set of design variables. Then this set is used to create
the first geometry and a mesh for the numerical computation. The mesh is passed to the solver, which
simulates the flow generated by the propulsor which finally leads to its hydrodynamic performance.
The calculated performance data is used to estimate the objective function. For an automatic
optimisation of a propulsor geometry, all these steps are combined in one optimisation process.
For a successful realisation of an optimisation process the geometry of the propulsor has to be
described by an appropriate parametric model, which does not necessarily follow the common
description of a propeller blade in cylinder coordinates. Such a parametric model is only valid in a
certain range, in which the parameters may vary during the optimisation. This range has to be defined
before starting the optimisation. The number of design variables should be kept as small as possible;
otherwise the optimisation algorithm will not be able to handle the large number of design variables
efficiently. Furthermore an appropriate objective function has to be defined, which represents the
optimisation targets in a satisfactory way.
The propeller blade is parameterized according to Hundemer et al. (2006). This can be summarised
for the case of chord length as follows: The radial chord distribution can be considered as a product of
two functions and a factor, which allows adjusting the blade area to a desired aspect ratio.
f
r r r
( ) = f1( ) ⋅ f
2
( ) ⋅ c1
R
R
R
f 1 is a square root function, which describes the general shape of the blade. The square root enables a
round tip with a chord length reducing to zero at the tip. f 2 is a spline curve defined by its values at
hub and tip and the derivation at both points. While the value of the function at the hub is set to 1, the
three other values are considered as parameters. Factor c 1 scales the function so that a desired
expanded blade area ratio is obtained. The radial pitch distribution is generated in a similar way. The
pitch is defined by the product of a factor c 2 and B-spline curve g 1 . The points defining the spline
curve are related to each other, so that a typical pitch distribution with an unloaded tip and a reduced
hub loading is achieved.
g
r
r
( ) = g 1
( ) ⋅ c2
R
R
Factor c 2 scales the pitch distribution to obtain a desired pitch at the relative radius r/R = 0.7.
The propeller geometry is modified by varying the radial distribution of the chord length and the pitch
while the propeller diameter, number of blades, number of revolution and skew are fixed. The profile
geometry is kept also constant. The investigated propeller in this study is a seven bladed one.
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