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(a)
0.1
0.1
7
4
3
5
6
0.08
0.08
8
2
0.06
0.06
0.04
0.04
0.02
0.02
1
0
0
9
0
0.05
0.1
0.15
0.2
0.8
0.85
0.9
0.95
1
x/L
x/L
(b)
(c)
Fig. 2. (a) A sketch of a typical torpedo shaped hull form (axisymmetric with three sections:
nose, middle, tail); typically, equipment such as the computer, sensors, electronics, batteries,
and payload are housed in the nose and the midsection, whereas the propulsion system is in the
tail; (b) Bézier curve representing the nose (5 control points); and (c) Bézier curve representing
the tail (4 control points). Control points 3 and 8 are free, while the other points are essentially
fixed (depend on L , a , b , and D ).
Fig. 3. The computational solution domain and the boundary conditions
3.3
Low-Fidelity CFD Model
The most important component of the design optimization methodology described in
this work is a low-fidelity model, which is a simplified representation of the
high-fidelity one. The two most important features for the low-fidelity model to be
efficiently used in the surrogate-based optimization process is that it should be com-
putationally much cheaper than the high-fidelity model, and, at the same time, contain
sufficient knowledge about the latter so that it can be used as a reliable prediction tool
to yield an approximate location of the optimum design.
To satisfy the aforementioned requirements, the low-fidelity model is based on the
same CFD model as the high-fidelity one. The simulation time is substantially re-
duced by making the grid coarser (Fig. 4(b)). Grid number 6 needs the lowest simula-
tion time and is the least accurate. A closer look at that grid reveals that it is too
coarse (the responses were too “grainy”). Consequently, we selected grid number 5,
with 504 elements, to be used for the low-fidelity model.
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