Andrew Ning

Automatic Evaluation of Multidisciplinary Derivatives Using a Graph-Based Problem Formulation in OpenMDAO

The optimization of multidisciplinary systems with respect to large numbers of design variables is best pursued using a gradient-based optimization together with a method that efficiently evaluates coupled derivatives, such as the coupled adjoint method. However, implementing such a method in a problem with more than a few disciplines is time consuming and error prone. To address this issue, we develop an automated procedure for assembling and solving the coupled derivative equations that takes into account the disciplinary couplings using the interdisciplinary dependency graph of the problem. The coupled derivatives can be computed completely analytically, if analytic derivatives are available for all disciplines; otherwise, the coupled derivatives are computed semi-analytically. The procedure determines the disciplinary analyses execution order, detects iterative cycles, and uses this information to converge the coupled analysis, and evaluate the coupled derivatives as efficiently as possible by exploiting sparsity. Sparsity can occur at two levels within a multidisciplinary problem: between disciplines, when certain analyses do not affect all outputs, and within a discipline when, the Jacobian of that discipline is sparse. The numerical procedures are implemented in NASA’s OpenMDAO framework, providing a flexible API for declaring discipline-level derivatives that can handle sparsity within a discipline. The tool is demonstrated in two MDO problems: the design of a small satellite and its operation with the objective of maximizing downloaded data to a ground station, and the design of a horizontal-axis wind turbine with the objective of minimizing the cost of energy. In both cases, the method demonstrated improved efficiency by taking advantage of analytic gradients considering sparsity. This new capability in OpenMDAO greatly facilitates the implementation of system-level direct and adjoint coupled derivative evaluations, and is applicable for general problems.

Sensitivity Analysis of Wind Plant Performance to Key Turbine Design Parameters: A Systems Engineering Approach

This paper introduces the development of a new software framework for research, design, and development of wind energy systems which is meant to 1) represent a full wind plant including all physical and nonphysical assets and associated costs up to the point of grid interconnection, 2) allow use of interchangeable models of varying fidelity for different aspects of the system, and 3) support system level multidisciplinary analyses and optimizations. This paper describes the design of the overall software capability and applies it to a global sensitivity analysis of wind turbine and plant performance and cost. The analysis was performed using three different model configurations involving different levels of fidelity, which illustrate how increasing fidelity can preserve important system interactions that build up to overall system performance and cost. Analyses were performed for a reference wind plant based on the National Renewable Energy Laboratory’s 5-MW reference turbine at a mid-Atlantic offshore location within the United States. Three software configurations were used: 1) a previously published wind plant cost model using simplified parametric scaling relationships, 2) an integrated set of wind turbine and plant engineering and cost models that use a “bottom-up” approach to determine overall wind plant performance and cost metrics, and 3) the second set of models plus the addition of a plant layout and flow model for calculation of energy production. Global sensitivity analysis was performed on each analysis set with respect to key wind turbine configuration parameters including rotor diameter, rated power, hub height, and maximum tip speed. The analyses show how the latter approaches capture important coupling throughout the wind plant in a way that has not previously been achieved. In addition, while deficiencies even in the newer model set are readily identifiable, the flexibility of the new framework shows how extension and gradual buildup of model fidelity for various parts of the system provide a powerful tool that enables analysis for an ever-expanding set of wind energy research and design problems.

Aircraft Route Optimization for Heterogeneous Formation Flight

network Network optimization objective function Jsolo Optimal fuel burn or cost for each solo route from mission optimization JthreeAC Optimal fuel burn or cost for each three aircraft formation from mission optimization JtwoAC Optimal fuel burn or cost for each two aircraft formation from mission optimization uPh.D. Department of Aeronautics & Astronautics. Student Member AIAA †Ph.D. Department of Aeronautics & Astronautics. Student Member AIAA ‡Ph.D. Department of Aeronautics & Astronautics. Student Member AIAA §Professor, Department of Aeronautics & Astronautics. Fellow AIAA

Understanding the Benefits and Limitations of Increasing Maximum Rotor Tip Speed for Utility-Scale Wind Turbines

For utility-scale wind turbines, the maximum rotor rotation speed is generally constrained by noise considerations. Innovations in acoustics and/or siting in remote locations may enable future wind turbine designs to operate with higher tip speeds. Wind turbines designed to take advantage of higher tip speeds are expected to be able to capture more energy and utilize lighter drivetrains because of their decreased maximum torque loads. However, the magnitude of the potential cost savings is unclear, and the potential trade-offs with rotor and tower sizing are not well understood. A multidisciplinary, system-level framework was developed to facilitate wind turbine and wind plant analysis and optimization. The rotors, nacelles, and towers of wind turbines are optimized for minimum cost of energy subject to a large number of structural, manufacturing, and transportation constraints. These optimization studies suggest that allowing for higher maximum tip speeds could result in a decrease in the cost of energy of up to 5% for land-based sites and 2% for offshore sites when using current technology. Almost all of the cost savings are attributed to the decrease in gearbox mass as a consequence of the reduced maximum rotor torque. Although there is some increased energy capture, it is very minimal (less than 0.5%). Extreme increases in tip speed are unnecessary; benefits for maximum tip speeds greater than 100-110 m/s are small to nonexistent.

Objectives and Constraints for Wind Turbine Optimization

Efficient extraction of wind energy is a complex, multidisciplinary process. This paper examines common objectives used in wind turbine optimization problems. The focus is not on the specific optimized designs, but rather on understanding when certain objectives and constraints are necessary, and what their limitations are. Maximizing annual energy production, or even using sequential aero/structural optimization, is shown to be significantly suboptimal compared to using integrated aero/structural metrics. Minimizing the ratio of turbine mass to annual energy production can be effective for fixed rotor diameter designs, as long as the tower mass is estimated carefully. For variable diameter designs, the predicted optimal diameter may be misleading. This is because the mass of the tower is a large fraction of the total turbine mass, but the cost of the tower is a much smaller fraction of overall turbine costs. Minimizing the cost of energy is a much better metric, though high fidelity in the cost modeling is as important as high fidelity in the physics modeling. Furthermore, deterministic cost of energy minimization can be inadequate, given the stochastic nature of the wind and various uncertainties associated with physical processes and model choices. Optimization in the presence of uncertainty is necessary to create robust turbine designs.

Compressibility Effects of Extended Formation Flight

Aircraft own in formations may realize signi cant reductions in induced drag by ying in regions of wake upwash. However, most transports y at transonic speeds and compressibility e ects in formation ight are not well understood. This study uses an Euler solver to analyze the inviscid aerodynamic forces and moments of transonic wing/body con gurations ying in a 2-aircraft formation. We consider formations with large streamwise separation distances (10-50 wingspans) in an arrangement we term extended formation ight. Compressibility-related drag penalties in formation ight may be eliminated by slowing 2-3% below the nominal out-of-formation drag divergence Mach number, at xed lift coe cient or xed altitude. The latter option has the additional bene t that the aerodynamic performance of the formation improves slightly at higher lift coe cients. Optimal in-formation lift coe cients are not nearly as high as those estimated by incompressible analyses, but if not limited by engine performance, modest increases in altitude can yield further improvements in aerodynamic e ciency. Increasing the lateral separation of the aircraft can allow for slightly higher cruise speeds in exchange for higher induced drag. For the con gurations examined here, a 1-2% reduction in Mach number combined with a lateral spacing increase of 5% span achieves a total formation drag savings of about 10%.

UAV Path-Planning using Bézier Curves and a Receding Horizon Approach

Unmanned aerial vehicles (UAVs) are used in an increasing number of applications. Such applications may include navigating through heavy traffic and highly congested airways, where numerous static and dynamic obstacles impinge upon a UAV’s flight. It is imperative that a UAV successfully avoids these obstacles, while improving its planned flight path according to certain criteria. We have modeled UAV path planning as a single objective optimization problem that utilizes a receding horizon approach, where the path is constrained to avoid obstacle collision and to account for flight aerodynamic constraints. The proposed method is gradient based, allowing for quick and robust convergence to a near optimal solution. This heuristic method converges closely to full-knowledge optimal solutions and will allow UAVs to be implemented in a greater amount of tasks and missions than before while lessening the risk to the safety of others and the safety of the UAV.

Development and Validation of a New Blade Element Momentum Skewed-Wake Model within AeroDyn

Blade element momentum methods, though conceptually simple, are highly useful for analyzing wind turbines aerodynamics and are widely used in many design and analysis applications. A new version of AeroDyn is being developed to take advantage of new robust solution methodologies, conform to a new modularization framework for National Renewable Energy Laboratorys FAST, utilize advanced skewed-wake analysis methods, fix limitations with previous implementations, and to enable modeling of highly flexible and nonstraight blades. This paper reviews blade element momentum theory and several of the options available for analyzing skewed inflow. AeroDyn implementation details are described for the benefit of users and developers. These new options are compared to solutions from the previous version of AeroDyn and to experimental data. Finally, recommendations are given on how one might select from the various available solution approaches.

Large-Scale Multidisciplinary Optimization of an Electric Aircraft for On-Demand Mobility

Distributed electric propulsion is a key enabling technology for on-demand electric aircraft concepts. NASA’s X-57 Maxwell X-plane is a demonstrator for this technology, and it features a row of high-lift propellers distributed along the leading edge of its wing to enable better aerodynamic efficiency at cruise and improved ride quality in addition to less noise and emissions. This study applies adjointbased multidisciplinary design optimization to this highly coupled design problem. The propulsion, aerodynamics, and structures are modeled using blade element momentum theory, the vortex lattice method, and finite element analysis, respectively, and the full mission profile is discretized and analyzed. The design variables in the optimization problem include the altitude profile, the velocity profile, battery weight, propeller diameter, blade profile parameters, wing thickness distribution, and angle of attack. Optimizations take on the order of 10 hours, and a 12% increase in range is observed.

Improving the FLORIS wind plant model for compatibility with gradient-based optimization:

The FLORIS (FLOw Redirection and Induction in Steady-state) model, a parametric wind turbine wake model that predicts steady-state wake characteristics based on wind turbine position and yaw angle, was developed for optimization of control settings and turbine locations. This article provides details on changes made to the FLORIS model to make the model more suitable for gradient-based optimization. Changes to the FLORIS model were made to remove discontinuities and add curvature to regions of non-physical zero gradient. Exact gradients for the FLORIS model were obtained using algorithmic differentiation. A set of three case studies demonstrate that using exact gradients with gradient-based optimization reduces the number of function calls by several orders of magnitude. The case studies also show that adding curvature improves convergence behavior, allowing gradient-based optimization algorithms used with the FLORIS model to more reliably find better solutions to wind farm optimization problems.