Fluids & Structural Mechanics > CM Projects > Optimization (OPT)

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Historically, fluid mechanical hardware design has been a cut-and-try process.  New designs were largely based on familiar existing designs.  Full-scale performance was inferred by building and testing scale models.  In many applications, as design requirements became more demanding, increasingly sophisticated models were required.  This, in turn, led to significant increases in the cost of scale model testing.  In some cases, it could even be physically impossible to design and construct a meaningful small scale test.  Finally, completely new or novel applications forced the examination of concepts outside the realm of familiarity.  A different approach was required.

One way to deal with these difficulties was the introduction of computational fluid dynamic (CFD) flow simulation tools into the design process.  Twenty years ago these tools were one- and two-dimensional flow simulation tools or three-dimensional potential flow models.  Over the past two decades these tools have evolved into very sophisticated, high-fidelity flow models.  Today, three-dimensional steady and unsteady Reynolds-Averaged Navier-Stokes flow solvers are routinely used in the detailed design process for a variety of fluid mechanical devices.  Unfortunately, the typical way these analysis tools are used in support of the design process can best be described as virtual cut-and-try.  That is, they’re used primarily to replace much of the small scale testing that was historically required.  What is needed is a systematic application of these powerful tools to arrive at the best design for a given application.

Optimization is a mathematical process that seeks a set of parameters describing a configuration that extremizes (i.e., minimizes or maximizes) some performance metric or cost function.  In the case of hydrodynamic design, evaluation of the cost function generally requires a high-fidelity flow solution, so the construction of an efficient optimization approach can be a very challenging task.  In general, optimization is either local, where one seeks the best solution in the vicinity of an existing design – or global, where one has no a priori knowledge of where the optimal configuration resides.  At ARL we have different applications where each approach is appropriate.

The goal of hydrodynamic shape optimization is to improve the performance of a marine propulsor design candidate arrived at by our traditional design process.  Obviously this fine-tuning application represents a local optimization problem.  Here, we exploit a simple gradient-based methodology where the cost function gradient is computed from the solution of an adjoint problem.  We have demonstrated this approach to design improvements in a number of applications including: inverse design for both stationary and rotating blade rows in inviscid and turbulent flows; and multipoint efficiency and cavitation inception improvement in Cartesian space and on quasi-three-dimensional, rotating blade sections.

ARL/CM engineers have also been using Genetic Algorithms (GAs) on a wide range of global optimization problems related to fluid dynamics.  One example is using a GA to assimilate sensor data into a dispersion model in order to infer unknown wind direction.  Figure 5 shows how well such a plume assimilated with a GA matches the original synthetic plume.  A GA is also used to back-calculate source characteristics of a contaminant release and to retrieve meteorological conditions given monitored contaminant concentrations.  The GA has been able to back-calculate source location (x,y), source height, source strength, time of release, wind direction, wind speed, and atmospheric stability class.  Other problems optimized with a GA include fitting empirical models of fluid dynamics problems and finding permanent form wave solutions of highly nonlinear high order partial differential equations.  CM personnel regularly teach short courses on genetic algorithms and artificial intelligence methods and contribute to books on such techniques.

Images
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Figure 1:

Inverse Design of the DARPA HIREP inlet guide vane and rotor blade rows from generic NACA symmetric sections using the steepest descent approach with cost function gradients computed from solutions to the continuous adjoint problem.
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Figure 2:

Multipoint optimization of a NACA 0010 hydrofoil section for improved cavitation imception performance over a 10 degree range of incidence; design points are circled in the figure on the left.  In the figure on the right it is shown that the initial and final sections have identical integrated loading, but the optimized section achieves it without suction peaks present giving it much more robust cavitation performance.
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Figure 3:

Experimental verification of the multipoint shape optimization for cavitation inception.  The starting hydrofoil was a NACA 65410.  The goal was to optimize the cavitation inception performance over a 20 degree incidence range and verify this by an experiment in ARL’s 12-inch water tunnel.  The figure on the right shows the excellent agreement for both the baseline 65410 and its optimized counterpart.
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Figure 4:

Multipoint hydrodynamic shape optimization of a notional rim-driven thruster for improved cavitation inception performance in a 5 knot cross-flow condition.  The re-distribution of section loading away from the tip leading edge resulted in an estimated improvement of 115 feet in cavitation-free depth for this scenario.
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Figure 5:

Assimilation of concentration measurements to compute wind direction for a meandering plume