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Calculation of Sensitivity Derivatives in an MDAO Framework

During gradient-based optimization of a system, it is necessary to generate the derivatives of each objective and constraint with respect to each design parameter. If the system is multidisciplinary, it may consist of a set of smaller "components" with some arbitrary data interconnection and process work ow. Analytical derivatives in these components can be used to improve the speed and accuracy of the derivative calculation over a purely numerical calculation; however, a multidisciplinary system may include both components for which derivatives are available and components for which they are not. Three methods to calculate the sensitivity of a mixed multidisciplinary system are presented: the finite difference method, where the derivatives are calculated numerically; the chain rule method, where the derivatives are successively cascaded along the system's network graph; and the analytic method, where the derivatives come from the solution of a linear system of equations. Some improvements to these methods, to accommodate mixed multidisciplinary systems, are also presented; in particular, a new method is introduced to allow existing derivatives to be used inside of finite difference. All three methods are implemented and demonstrated in the open-source MDAO framework OpenMDAO. It was found that there are advantages to each of them depending on the system being solved.

Moore, Kenneth T.

Design Environment for Multifidelity and Multidisciplinary Components

One of the greatest challenges when developing propulsion systems is predicting the interacting effects between the fluid loads, thermal loads, and structural deflection. The interactions between technical disciplines often are not fully analyzed, and the analysis in one discipline often uses a simplified representation of other disciplines as an input or boundary condition. For example, the fluid forces in an engine generate static and dynamic rotor deflection, but the forces themselves are dependent on the rotor position and its orbit. It is important to consider the interaction between the physical phenomena where the outcome of each analysis is heavily dependent on the inputs (e.g., changes in flow due to deflection, changes in deflection due to fluid forces). A rigid design process also lacks the flexibility to employ multiple levels of fidelity in the analysis of each of the components. This project developed and validated an innovative design environment that has the flexibility to simultaneously analyze multiple disciplines and multiple components with multiple levels of model fidelity. Using NASA's open-source multidisciplinary design analysis and optimization (OpenMDAO) framework, this multifaceted system will provide substantially superior capabilities to current design tools.

Platt, Michael

Parallel Aircraft Trajectory Optimization with Analytic Derivatives

Trajectory optimization is an integral component for the design of aerospace vehicles, but emerging aircraft technologies have introduced new demands on trajectory analysis that current tools are not well suited to address. Designing aircraft with technologies such as hybrid electric propulsion and morphing wings requires consideration of the operational behavior as well as the physical design characteristics of the aircraft. The addition of operational variables can dramatically increase the number of design variables which motivates the use of gradient based optimization with analytic derivatives to solve the larger optimization problems. In this work we develop an aircraft trajectory analysis tool using a Legendre-Gauss-Lobatto based collocation scheme, providing analytic derivatives via the OpenMDAO multidisciplinary optimization framework. This collocation method uses an implicit time integration scheme that provides a high degree of sparsity and thus several potential options for parallelization. The performance of the new implementation was investigated via a series of single and multi-trajectory optimizations using a combination of parallel computing and constraint aggregation. The computational performance results show that in order to take full advantage of the sparsity in the problem it is vital to parallelize both the non-linear analysis evaluations and the derivative computations themselves. The constraint aggregation results showed a significant numerical challenge due to difficulty in achieving tight convergence tolerances. Overall, the results demonstrate the value of applying analytic derivatives to trajectory optimization problems and lay the foundation for future application of this collocation based method to the design of aircraft with where operational scheduling of technologies is key to achieving good performance.

aircraft

Multidisciplinary Conceptual Design for Reduced-Emission Rotorcraft

Python-based wrappers for OpenMDAO are used to integrate disparate software for practical conceptual design of rotorcraft. The suite of tools which are connected thus far include aircraft sizing, comprehensive analysis, and parametric geometry. The tools are exercised to design aircraft with aggressive goals for emission reductions relative to fielded state-of-the-art rotorcraft. Several advanced reduced-emission rotorcraft are designed and analyzed, demonstrating the flexibility of the tools to consider a wide variety of potentially transformative vertical flight vehicles. To explore scale effects, aircraft have been sized for 5, 24, or 76 passengers in their design missions. Aircraft types evaluated include tiltrotor, single-main-rotor, coaxial, and side-by-side helicopters. Energy and drive systems modeled include Lithium-ion battery, hydrogen fuel cell, turboelectric hybrid, and turboshaft drive systems. Observations include the complex nature of the trade space for this simple problem, with many potential aircraft design and operational solutions for achieving significant emission reductions. Also interesting is that achieving greatly reduced emissions may not require exotic component technologies, but may be achieved with a dedicated design objective of reducing emissions.

Rotorcraf

Optimal Control within the Context of Multidisciplinary Design, Analysis, and Optimization

Multidisciplinary design, analysis and optimization involves modeling the interactions of complex systems across a variety of disciplines. The optimization of such systems can be a computationally expensive exercise with multiple levels of nested nonlinear solvers running under an optimizer.The application of optimal control in project development often involves performing trajectory optimization for fixed vehicle designs or parametric sweeps across some key vehicle properties.This information is then relayed to the subsystem design teams who update their designs and relay some bulk characteristics back to the trajectory optimization procedure.This iteration is then repeated until the design closes.However, with increasing interest in more tightly coupled systems, such as electric and hybrid-electric aircraft propulsion and boundary layer ingestion, this process is prone to ignore subtle coupling between vehicle subsystem designs and vehicle operation on a given mission.Integrating trajectory optimization into a tightly coupled multidisciplinary design procedure can be computationally prohibitive, depending on the complexity of the subsystem analyses and the optimal control technique applied.To address these issues a new optimal control software tool, Dymos, has been developed.Dymos is built upon NASA's OpenMDAO software and can leverage its capabilities to efficiently compute gradients for the optimization and optimize complex models in parallel on distributed memory systems.This report provides some explanation into the numerical methods employed in Dymos and provides several use cases that demonstrate its performance on traditional optimal control problems and improvements ino techniques have been used extensively in recent decades to solve a variety of optimal control problems, typically in the form of aerospace vehicle trajectory optimization.

pseudospectral

Gradient-Based Propeller Optimization with Acoustic Constraints

Urban Air Mobility vehicles are intended to operate near or within large cities, where a significant portion of the public will be exposed to the noise they create. If these vehicles are to become acceptable to the public, designers must be able to manage the amount of noise they generate, and understand the relationship between traditional performance metrics (thrust, efficiency, etc.) and noise. As a first step to addressing this need, this work combines a blade element momentum theory tool (OpenBEMT) with an acoustic prediction tool (ANOPP2) to optimize a propeller subject to both aerodynamic and acoustic constraints. These tools are developed within a optimization framework (OpenMDAO) that allows analytic derivatives to be propagated through the models and passed to a gradient-based optimizer. This tool chain is exercised on the cruise propellers from the X-57 Maxwell, and yields propeller designs that reduced the overall sound pressure level by about 5 dB for a cost of 1% propeller efficiency.

Ingraham, Daniel

Load Flow Analysis with Analytic Derivatives for Electric Aircraft Design Optimization

Many of the aircraft concepts of the future are exploring the use of hybrid-, turbo- or all-electric propulsion systems to improve performance and decrease environmental impacts. These aircraft concepts range from small rotorcraft for urban air mobility to conventional commercial transports to large blended wing body designs. Developing the conceptual design for these vehicles presents a challenge, however, as traditional aircraft design tools often were not developed to handle these unique propulsion system architectures. Previous studies on these vehicles have therefore relied on relatively simple models of the electrical transmission and distribution system. This paper presents the development of a hybrid AC-DC load flow (or power flow) analysis capability to enhance the conceptual design of these concept vehicles. Specifically, the desire was to create a load flow analysis capability within the OpenMDAO framework that is also being used to develop a set of compatible tools for rapid optimization of conceptual designs. This load flow analysis capability is unique in its flexible object-oriented structure and implementation of analytic derivatives to facilitate the use of solvers and gradient based optimization in the design process. The developed hybrid load flow analysis capability is first verified against a published 13-bus example then used to model the electrical distribution system for a turbo-electric tiltwing aircraft.

Load flow

How Certain Physical Considerations Impact Aerostructural Wing Optimization

Wing design optimization has been studied extensively and is of continued interest as optimization tools are developed and become more accessible. In each of these studies, certain assumptions and simplifications are made to make the design problem tractable. However, it is difficult to find systematic studies in which several considerations are added or removed one at a time to study how much impact they have. In this work, we examine how certain physical considerations (viscous drag, wave drag, thrust loads, and inertial relief from structural, fuel, and engine masses), impact the aerostructural optimization results for three distinct aircraft wings. The goal is to help develop a rough idea of how important these physical considerations are. We do this using gradient-based optimization and a multidisciplinary design optimization framework, OpenMDAO. We use the open-source tool OpenAeroStruct that couples a vortex lattice method to a finite element method. We establish a baseline aerostructural design optimization problem then perform a series of optimizations, each with one physical consideration removed from the baseline case. We find that depending on the size of the aircraft and flight conditions, the importance of some of these physical considerations varies considerably whereas the importance of others do not. Specifically, the optimal designs change radically without proper viscous and wave drag considerations and smaller aircraft with more distributed propulsion are more affected by the inclusion of engine loads.

Aeropropulsion

Gradient-Based Propeller Optimization with Acoustic Constraints

Urban Air Mobility (UAM) vehicles are intended to operate near or within large cities, where a significant portion of the public will be exposed to the noise they create. If these vehicles are to become acceptable to the public, designers must be able to manage the amount of noise they generate, and understand the relationship between traditional performance metrics (thrust, efficiency, etc.) and noise. As a first step to addressing this need, this work combines a Blade Element Momentum Theory tool (OpenBEMT) with an acoustic prediction tool (ANOPP2) to optimize a propeller subject to both aerodynamic and acoustic constraints. These tools are developed within a optimization framework (OpenMDAO (Multidisciplinary Design Analysis Optimization)) that allows analytic derivatives to be propagated through the models and passed to a gradient-based optimizer. This tool chain is exercised on the cruise propellers from the X-57 Maxwell, and yields propeller designs that reduced the overall sound pressure level by about 8 decibels for a cost of 3 percent propeller efficiency.

Acoustics

Implicit Formulations of Bounded-Impulse Trajectory Models for Preliminary Interplanetary Low-Thrust Analysis

The bounded-impulse approach to low-thrust interplanetary trajectory optimization is widely used. In an effort to efficiently implement this approach using NASA’s OpenMDAO optimization software, the authors have implemented implicit formulations of the forward shooting/backwards-shooting methods commonly used in bounded-impulse models. These implicit approaches allow for vectorization of the underlying calculations which can significantly reduce runtime in interpreted languages. An implicit approach may be either converged by using an underlying nonlinear solver to converge the state propagation, or as a constraint in an optimizer-driven multiple-shooting approach. Significant computational efficiency gains are realized through the utilization of the modular approach to unified derivatives. Further computational efficiency is achieved by capitalizing on the sparsity of the constraint Jacobian matrix. This work demonstrates that a vectorized multiple-shooting approach for propagating a state-time history is superior in terms of computational efficiency as the number of segments in the state-propagation is increased.

Falck, Robert D

Performance Analysis of Optimized STARC-ABL Designs Across the Entire Mission Profile

Boundary layer ingestion (BLI) offers the potential for significant fuel burn reduction by exploiting strong aeropropulsive interactions. NASA’s STARC–ABL concept uses an electri- cally powered BLI tail cone thruster on what is otherwise a traditional airframe. Despite the traditional airframe of this configuration, aeropropulsive integration is critical to the perfor- mance of the BLI propulsor. Furthermore, due to being electrically powered, the fan pressure ratio and efficiency of the BLI tail cone thruster vary widely across the flight envelope, and this variation in fan performance must be accounted for with the aeropropulsive integration of the BLI system. Thus, accurate performance prediction for this novel propulsion configu- ration requires the use of a coupled aeropropulsive model across the flight envelope. In this work, we analyze the off-design performance of 18 optimized designs using an aeropropulsive model that is built with the OpenMDAO framework to couple 3-D RANS CFD simulations to 1-D thermodynamic cycle analyses. The designs are created via high-fidelity aeropropulsive design optimizations that span a range of fan pressure ratio and thrust values at the cruise conditions for the STARC-ABL concept, which was chosen as the aerodynamic design point for the propulsor. Performance analyses we present herein are then performed at a range of off-design flight conditions that span the flight envelope, including low-speed and low-altitude flight conditions. This study provides the first set of high-fidelity data for the STARC–ABL configuration at off-design conditions, and the results quantify the power savings through BLI compared to a traditional propulsion system across the entire mission profile.

optimization

Coupled Aeropropulsive Design Optimization of a Podded Electric Propulsor

New aircraft concepts are increasingly relying on non-traditional propulsion systems to achieve lower energy consumption. These non-traditional technologies, such as boundary layer ingestion or distributed electric propulsion, require a tight integration of the propulsion sys- tem to the airframe, and therefore, a traditional design approach where the aerodynamics and propulsion disciplines are considered separately is likely to result in sub-optimal designs. As a result, we have to rely on coupled aeropropulsive design optimization, in which fully coupled aeropropulsive models are optimized to maximize the advantages of these tightly integrated propulsion systems. Despite its advantages, aeropropulsive design optimization is a relatively new field, and significant advancements are required for wide adoption of this approach, especially in the context of robustness. In this work, we introduce two fully coupled aeropropulsive design optimization approaches that are compatible with CFD models with body-force terms and boundary conditions to model the effects of the propulsion system in the flow field. To test these new approaches, we developed a podded electric fan model based on the aft-propulsor of NASA’s STARC-ABL concept. This simple design problem enables us to rapidly develop and test different aeropropulsive coupling approaches, while including the challenging physical interactions that arise from coupling CFD and propulsion models. The coupled aeropropulsive model is implemented using the MPhys library, which is built with NASA’s OpenMDAO frame- work. Using this benchmark design problem, we demonstrate the robustness of the approaches and our aeropropulsive design optimization framework by performing a sweep of optimizations for a total of 50 CFD-based aeropropulsive design optimizations. Furthermore, the new aero- propulsive coupling approaches enable multi-point design optimizations. We demonstrate this capability in a multi-point design optimization problem where we optimize cruise performance subject to a fan-face distortion constraint at rolling take-off conditions. The aeropropulsive modeling approaches we present in this work represent a significant milestone in the field of aeropropulsive design optimization. The framework we developed is extremely robust and flexible, and these developments will be crucial for future aeropropulsive design optimizations of complete turbofan engines.

Optimization propulsion aerodynamics

A Nonlinear Schur Complement Solver for CFD-Based Multidisciplinary Models

CFD-based multidisciplinary models are the fundamental building blocks of multidis- ciplinary design optimization frameworks. Linear and nonlinear solutions of these coupled models are difficult, especially when the Jacobian matrices represent a saddle point problem, where a block-diagonal corresponding to a discipline is non-invertible. These scenarios necessitate the use of a coupled solver algorithm such as the Newton’s method instead of the popular block Gauss– Seidel-based methods because of this non-invertible block. To address this challenge, we introduce a nonlinear Schur complement solver suitable for CFD-based multidisciplinary models. The solver leverages the specialized linear and nonlinear solvers of the CFD code, and therefore, does not require the solution of a large coupled linear system as the coupled Newton’s method. Further- more, because the solver primarily uses the specialized linear and nonlinear solvers of the CFD code, it does not suffer from the same robustness limitations as the coupled Newton’s method. In this work, we will implement this solver in NASA’s OpenMDAO framework and demonstrate its effectiveness using a CFD-based aeropropulsive model. The solver will contribute to the develop- ment of aeropropulsive design optimization and CFD-based design optimization methods with the ultimate goal of accelerating the design and integration of advanced propulsion systems.

Nonlinear Solvers

Advancement of the General Aviation Synthesis Program Using Python to Enable Optimization-Based Hybrid-Propulsion Aircraft Design

In support of Electrified Powertrain Flight Demonstrator and Advanced Air Transport Technologies programs at NASA, engineers at NASA Ames and NASA Glenn Research Centers have developed a new tool for coupled engine and airframe optimization and analysis. The new tool combines the engineering-level analysis methods of the FORTRAN General Aviation Synthesis Program (GASP) with the OpenMDAO framework to handle highly coupled problems that legacy tools struggle to optimize. The tool has been verified to match GASP with good agreement on a 737 MAX8 baseline vehicle closure problem, and preliminary efforts have been made to integrate the pyCycle thermodynamic cycle analysis tool for electrified engine optimization in the context of a vehicle optimization problem.

Kenneth R. Lyons

Advancement of the General Aviation Synthesis Program Using Python to Enable Optimization-Based Hybrid-Propulsion Aircraft Design

In support of the Electrified Powertrain Flight Demonstrator and Advanced Air Transport Technologies projects at NASA, a new tool has been developed at NASA’s Ames and Glenn Research Centers to enable coupled engine and airframe optimization and analysis. The new tool combines the engineering-level analysis methods and empirical models of the FORTRAN General Aviation Synthesis Program (GASP) with the Python-based OpenMDAO framework to provide a modular framework for efficient gradient-based optimization with the aim of incorporating new subsystem models for unconventional configurations. The tool has been verified against GASP analyses of several aircraft models and mission formulations. Preliminary efforts have been made to integrate pyCycle, a thermodynamic cycle analysis tool, to enable simultaneous optimization of hybrid propulsion system and vehicle parameters while taking full mission performance and constraints into account. This will improve current capabilities to assess impacts of electrified powertrain technologies on future aircraft designs.

Kenneth R. Lyons

Advancement of the General Aviation Synthesis Program Using Python to Enable Optimization-Based Hybrid-Propulsion Aircraft Design

In support of the Electrified Powertrain Flight Demonstrator and Advanced Air Transport Technologies projects at NASA, a new tool has been developed at NASA's Ames and Glenn Research Centers to enable coupled engine and airframe optimization and analysis. The new tool combines the engineering-level analysis methods and empirical models of the FORTRAN General Aviation Synthesis Program (GASP) with the Python-based OpenMDAO framework to provide a modular framework for efficient gradient-based optimization with the aim of incorporating new subsystem models for unconventional configurations. The tool has been verified against GASP analyses of several aircraft models and mission formulations. Preliminary efforts have been made to integrate pyCycle, a thermodynamic cycle analysis tool, to enable simultaneous optimization of hybrid propulsion system and vehicle parameters while taking full mission performance and constraints into account. This will improve current capabilities to assess impacts of electrified powertrain technologies on future aircraft designs.

Kenneth R Lyons

Analysis and Optimization of Baseline Single Aisle Aircraft for Future Electrified Powertrain Flight Demonstrator Comparisons

The purpose of this study is to provide baseline single-aisle vehicles for future comparisons with NASA’s Electrified Powertrain Flight Demonstration (EPFD) turbofan-powered Vision Systems. State-of-the-art single-aisle transports with varying design capacities of 100 to 150 passengers are modeled using NASA Ames Research Center’s General Aviation Synthesis Program (GASP) as well as GASPy. GASPy is a modernized Python-based version of GASP built on the OpenMDAO framework to allow for future, efficient gradient-based optimization and coupled airframe-propulsion design. In order to meet projected NASA Aeronautics goals for 2035, advanced aircraft technologies must be incorporated into these vehicle systems. Methodology to parametrically infuse baseline aircraft models with advanced technologies simulating improvements in aerodynamics, structures, and propulsion systems is detailed, along with the results of technology sensitivity studies. Comparison of the baseline and advanced configurations will allow for future analysis of the benefits of future hybrid and fully electric aircraft concepts in the EPFD project, where fuel consumption and emissions will be modeled and assessed. This study has been conducted under the EPFD project to establish benchmark turbofan models and demonstrate System Analysis capabilities in multi-disciplinary aircraft design, analysis, and optimization for advanced turbofan concepts.

Carl J. Recine

Thermal Management System Modeling in the Heat Transport System Simulation (HeaTSSPy) Package

This paper describes the development of a thermal management system (TMS) concept design and analysis software package called Heat Transport System Simulation (HeaTSSPy). Built within Python using the OpenMDAO framework, HeaTSSPy can be used to size and optimize an active (using liquid/air heat exchangers) or passive (using finned heat sinks) TMS. The package makes use of modular TMS elements that allow for the creation of different system architectures and includes components such as heat sinks, heat exchangers, liquid pumps, fans, ducts, air inlets, air nozzles, and liquid pipes. Modeling methods for these components include a combination of physics-based analytical and empirical equations that relate component sizing criteria to system performance. The HeatSSPy heat sink methods are fully detailed within this paper, while the heat exchanger methods are described and referenced from previous work. This paper also uses high-fidelity simulation to validate two different methods of calculating thermal resistance using CFD results. Once the methods are fully described, the code is exercised to compare an active TMS with that of a passive TMS. Design criteria for this study include rejected heat, system altitude, Mach number, and ambient temperature. These criteria are used to develop a TMS system with estimated performance metrics such as weight, drag, and operational power. Results of this paper show the crossover point when a passive system begins to weigh more than an active system for a given heat rejection.

Thermal management system