(example-nose-opt)=
This page illustrates how pysagas can be used for design optimisation. The example is applied to a nose cone at an operating point of Mach 6, 0 degrees angle-of-attack.
(literature-review)=
A review of literature reveals that the optimal shape for an axisymmetric nose at supersonic speeds which minimises drag for a given length and base diameter is given by the exponential function:
(optimal-equation)= $$ y = R(x/L)^n $$
The exponent
The difference in drag for these exponnents is very slim, so
previous experimental studies have made approximations with
The nose geometry is defined by a Bezier curve with two internal control points, as shown in the figure below. These control points can move in both the horizontal and vertical direction. Therefore, there are 4 design parameters in this problem.
The optimisation process follows the schematic in the figure below.
Starting with a nominal set of geometric parameters,
HyperVehicle is used
to generate STL files. These files are passed into an aerodynamic modelling
package, in order to obtain the nominal flow solution for that geometry.
HyperVehicle is also
used to generate the geometry sensitivities, pysagas.optimisation.cartd.ShapeOpt
.
In this example, the objective function is the drag coefficient of the nose cone, neglecting the base drag (as per the prior art).
As mentioned above, the geometry and geometry-parameter
sensitivities,
(nose-cart3d-modelling)=
Given the STL files from the geometry generation module, the geometry will be simulated in the inviscid CFD solver, Cart3D. The figure below shows an example mesh produced by Cart3D.
The corresponding flow solution for this mesh is visualised in the figure below.
With the modules described above in place, the following output will
be displayed when running ShapeOpt
.
After 7 iterations, the following convergence plot can be created. Also shown on this plot is the 'theoretical convergence', which refers to the drag coefficient of the nose defined by the exponential function above, when simulated in the same manner used in the optimisation.
Finally, the nose geometry produced by pysagas can be compared to the theoretical optimal nose geometry, defined by the exponential function above. This comparison is shown in the figure below.
Footnotes
-
W. H. Mason and Jaewoo Lee. “Minimum-drag axisymmetric bodies in the supersonic/hypersonic flow regimes”. In: Journal of Spacecraft and Rockets 31.3 (1994) ↩
-
Perkins, E.W., Jorgensen, L. H., and Sommer, S. C., “Investigation of the Drag of Various Axially Symmetric Nose Shapes of Fineness Ratio 3 for Mach Numbers from 1.24 to 7.4,” NACA-TR-1386, 1958. ↩
-
Eggers, A. J. Jr., Resnikoff, M. M., and Dennis, D. H., “Bodies of Revolution Having Minimum Drag at High Supersonic Airspeeds,” NACA-TR-1306, 1957. ↩