Abstract
Blade element momentum methods are widely used for initial aerodynamic analysis of propellers and wind turbines. A wide variety of correction methods exist, but common to all variations, a pair of residuals are converged to ensure compatibility between the two theories. This paper shows how to rearrange the sequence of calculations reducing to a single residual. This yields the significant advantage that convergence can be guaranteed and to machine precision. Both of these considerations are particularly important for gradient-based optimization where a wide variety of atypical inputs may be explored, and where tight convergence is necessary for accurate derivative computation. On a moderate-sized example optimization problem we show over an order of magnitude increase in optimization speed, with no changes to the physics. This is done by using the single residual form, providing numerically exact gradients using algorithmic differentiation with an adjoint, and by leveraging sparsity in the Jacobian using graph coloring techniques. Finally, we demonstrate a revised formulation for cases when no inflow exists in one of the directions (e.g., a hovering rotor or a parked rotor). These new residuals allow for robust convergence in optimization applications, avoiding the occasional numerical difficulties that exist with the standard formulation.
Notes
The resulting OpenBEMT code has since been folded back into the CCBlade repository to consolidate efforts.
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Funding
This research was partially supported by the Department of Energy (DOE) Advanced Research Projects Agency-Energy (ARPA-E) Program award DE-AR0001186 entitled “Computationally Efficient Control Co-Design Optimization Framework with Mixed-Fidelity Fluid and Structure Analysis.”
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Replication of results
A full implementation of the methodology in the Julia programming language, with documentation, is available in an open source repository called CCBlade (https://github.com/byuflowlab/CCBlade.jl). The scripts used to generate the results and figures from the paper are available in separate repository (https://github.com/byuflowlab/ning2020-bem).
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Ning, A. Using blade element momentum methods with gradient-based design optimization. Struct Multidisc Optim 64, 991–1014 (2021). https://doi.org/10.1007/s00158-021-02883-6
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DOI: https://doi.org/10.1007/s00158-021-02883-6