Machine Learning Based Flight Dynamic Framework for eVTOL Aircraft

Recent years have seen a renewed interest in rotary-wing aircraft, due to the emergence of urban air mobility. In the conceptual design of such aircraft, fast estimation of rotor performance is important. A challenge is that rotor performance models require a detailed description of the blade geometry, which is not always available at this stage. We have developed a new, robust method for rapidly computing optimal rotor designs, which is derived from blade element momentum theory. In this paper, we derive the rotor design method and prove its convergence for all reasonable model inputs. We verify the design method by comparing the optimal rotor designs it computes to those found by a nonlinear programming algorithm. Thousands of numerical experiments yield relative errors of less than 13 and 5% in terms of the chord and twist profiles, respectively, and less than 0.3% in terms of efficiency, thrust, torque, and power coefficients. In addition, the design method computes optimal designs 170 times faster compared to the nonlinear programming algorithm. Based on these findings, we expect this new rotor design method to be useful in the conceptual design of rotary-wing aircraft.

This study focuses on the robust aerodynamic design of the bladed rotor of small horizontal axis wind turbines. The optimization process also considers the effects of manufacturing and assembly tolerances on the yearly energy production. The aerodynamic performance of the rotors so designed has reduced sensitivity to manufacturing and assembly errors. The geometric uncertainty affecting the rotor shape is represented by normal distributions of the pitch angle of the blades, and the twist angle and chord of their airfoils. The aerodynamic module is a blade-element momentum theory code. Both Monte Carlo-based and the Univariate Reduced Quadrature technique, a novel deterministic uncertainty propagation method, are used. The performance of the two approaches is assessed both in terms of accuracy and computational speed. The adopted optimization method is based on a hybrid multi-objective evolutionary strategy. The presented results highlight that the sensitivity of the yearly energy production to geometric uncertainties can be reduced by reducing the rotational speed and increasing the aerodynamic blade loads.

The general objective of this paper is to present the initial results obtained as an outcome of applying a coupled Experimentally Derived – Blade Element Momentum Theory (BEMT) model for evaluating the airflow-defining parameters of a hovering helicopter rotor close to obstacles and making performance predictions. Several empirical models are described, and proper comparison with the experimentally obtained data is conducted. In detail, the characterization of the rotor inflow ratio (λ), when operating at fixed rotational frequency (n), at different relative distances to the ground (H/R), varying the pitching angle (θ) is discussed. The dependencies show an increase in the rotor inflow ratio parameter (λ), when increasing the collective pitch angle (θ) in hovering regime at fixed constant relative distance to the ground surface (H/R). On the contrary, the inflow ratio (λ) is experiencing a decline once the helicopter rotor operates closer to the ground surface. Moreover, the inflow ratio characterization (λ) along the blade span can be applied to the total generated thrust (T). As a result, the corresponding thrust coefficients (CT) are calculated and graphically represented. The overall characterization of the thrust coefficients (CT) will allow the definition of the ground effect zone.

The powerful wind generators, producing electric power on the order of megawatts are with significant sizes. The studies on the interaction between the air flow and the wind turbine usually assume that the airflow is homogeneous in vertical direction, which admission is made also in the classical Blade element momentum (BEM) theory. While for the smaller wind turbines this assumption does not lead to significant inaccuracies, for powerful generators the vertical gradient of the wind velocity causes a dependence of the aerodynamic interaction from the angle of rotation of the turbine and leads to a significant cyclic variability of the forces and moments acting on the blades, even for a constant flow velocity without a longitudinal turbulence. The study of this problem is important for the blades loads and fatigue calculations as well as for the synthesis of an individual pitch control of the turbine blades. In this publication adaptation of the BEM theory is proposed in order to account of the influence of the vertical gradient of the wind velocity.

Blade Element Momentum (BEM) theory is a well understood and proven method for modeling blade loads and determining steady state performance characteristics of wind turbines. Recently this theory has successfully been applied to horizontal axis marine current turbines when incorporating modifications that lead to better predictions of turbine performance for a range of operating conditions. Relatively little work exists in the implementation of BEM theory in a marine environment with surface gravity waves. A better understanding of the effects of waves on tidal turbines is necessary to predict fatigue loading that can eventually lead to blade failure. This paper presents a BEM numerical model that incorporates the unsteady velocities due to the presence of waves and assesses the effects of waves on tidal turbine performance. Numerical results of the coefficient of power (CP) and coefficient of thrust (CT) match closely with experimental results for the mean Cp and CT for a range of tip speed ratios. The model is also able to predict the instantaneous amplitudes of the performance characteristics as compared with the measured values except for the BEM calculated thrust which shows a 20% reduction in amplitude.

This paper has illustrated the potential accuracy of often-used Blade Element Momentum Theory (BEMT) model in hovering thrust predictions and a limiting feature of the Blade Element Theory (BET) model during forward flight. When employed in hover, BEMT with the linear lift curve slope assumption and small angle approximation is shown to accurately predict the hover thrust. However, during forward flight an underprediction of the thrust and torque is likely to occur because the lift boost from dynamic stall and the extra torque due to post stall drag are missing. Additionally, without a dynamic stall model the rotor flapping angles for a quadrotor aircraft can contain higher frequencies that are likely fictitious. A state space dynamic stall model has been integrated into BET and it has been shown that reasonable predictions of lift and rotor flapping angle are produced. Finally, a reduced order model amenable to inclusion in 6DOF flight simulations is presented. The reduced order model seeks to make inclusion of the often-neglected time varying thrust due to blade flapping. It also includes the effects of dynamic stall on the thrust generated by the rotor.

The magnetic coupler is the heart of an inductive power transfer (IPT) system, which facilitates wireless power transfer through its air gap. The couplers are designed to maximize efficiency, power density, power transfer distance, and misalignment tolerance while minimizing leakage flux, weight, cost, and volume. The coupler design process becomes complex due to the nonlinear behavior of magnetics, sophisticated geometrical structures, and mandatory design limitations imposed by standards, such as SAE J2954/1, IEC 61980-1:2015, and ISO 19363:2020. Initially, this article reviews the advancements in coil design methodologies and their structures over the last few decades to identify the ongoing challenges and trends. The impacts of the power electronics system, industrial standards, material selection, numerical and analytical modeling methods, and thermal modeling on the coil design process are identified to formalize the design procedure. A coil design example based on finite element analysis (FEA) tools is presented to identify the drawbacks of the existing design and optimization process. A sensitivity analysis, 3-D-Pareto plots, and optimal design selection by considering misalignment variations are proposed to improve the multiobjective optimization process. A generalized guideline for coil design is proposed, which highlights the essential design stages of an IPT coupler. Current trends are identified, and future directions are proposed.

Current engineering design focuses mainly on the geometrical optimization of a component, while the material selection is often limited to picking a material based on a set of properties reported in handbooks. The inherent anisotropic behavior of materials is often ignored in the design process, and is usually assumed to be addressed by the safety factor employed. This simple treatment of material selection in the design and optimization process often leads to inefficient design. In this study, we present a rigorous and a comprehensive procedure that facilitates the treatment of material microstructure as a continuous design variable in the elastic-plastic design of structural components made from anisotropic polycrystalline metals. The mechanical behavior of a metal is influenced by several details of its microstructure, including chemical composition, grain size distribution, crystallographic texture, among others. Here, we focus on the crystallographic texture (also called Orientation Distribution Function or ODF) as the main microstructural parameter controlling the anisotropic elastic-plastic properties of interest. The property closures that we have delineated describe the complete set of feasible property combinations for a given polycrystalline material system, while accounting for all possible textures. The property closures are obtained here using a spectral representation of ODF and its relationship with rigorous first order bounds on the effective properties of interest in design. Using the proposed methodology, we successfully developed a few examples of property closures for face centered cubic (fcc) and hexagonal close-packed (hcp) metals. The mechanical anisotropic behavior at the single crystal level for face centered cubic metals has been characterized using the nanoindentation technique along with orientation imaging mapping. This methodology shows promising possibilities to extract fundamental elastic and plastic parameters. However, the methods proposed in the literature to extract data from the load-displacement curves cause discrepancy between the experimental and expected values. The discrepancy could be attributed to the induced plastic deformation among other factors.

Aircraft manufacturing companies have to consider multiple derivatives to satisfy various market requirements. They modify or extend an existing aircraft to meet the new market demands while keeping the development time and the cost to a minimum. Many researchers have studied the derivative design process, but these research considered the baseline and the derivatives together, while using the whole set of design variables. Therefore, an efficient process that can reduce the cost and the time for the aircraft derivative design is needed. In this dissertation, Aircraft Derivative Design Optimization process (ADDOPT) was developed which obtains the global changes from the local changes in the aircraft design to develop the aircraft derivatives efficiently. The sensitivity analysis was implemented to ignore design variables that have low impact on the objective function. This avoids wasting computational effort and time on low priority variables for design requirements and objectives. Additionally, the classification of uncertainty from its characteristics and sources of uncertainty involved in the aircraft design process were suggested to consider with design optimization. Uncertainty from the fidelity of analysis tools was applied in design optimization to increase the probability of optimization results. To handle uncertainty in low fidelity analysis tools on aircraft conceptual design optimization, Reliability Based Design Optimization (RBDO) and Possibility Based Design Optimization (PBDO) methods were performed. In this research, Extended Fourier Amplitude Sensitivity Test (eFAST) method was implemented in ADDOPT for Global Sensitivity Analysis (GSA) method and Collaborative Optimization (CO) based framework with RBDO and PBDO were also used. These methods were evaluated using numerical examples. ADDOPT was carried through on the civil jet aircraft derivative design. The objective of the optimization problem was to increase cruise range while satisfying the requirement such as the number of passengers. The proposed process reduced computation effort by reducing the number of design variables and achieved the target probability of failure when considering uncertainty from low fidelity analysis tools.

The slotted, natural-laminar-flow (SNLF) airfoil is a low-drag, high-lift airfoil concept that has been explored for commercial and general aviation applications. This work seeks to determine the performance benefits of using an SNLF airfoil on the tail rotor of a small helicopter. Blade element momentum theory (BEMT) and Reynolds-Averaged Navier-Stokes (RANS) computational fluid dynamics (CFD) results for a rotor in hover are compared, including with an SNLF rotor that has the rotational speed reduced to generate the same amount of thrust as the baseline rotor. The BEMT analysis uses polar data generated from two-dimensional RANS CFD with methods and grids validated against wind tunnel data taken from high-quality facilities. Sectional data for the baseline and SNLF airfoils are presented and discussed, such as the higher maximum lift coefficient of the SNLF airfoil and subsonic and transonic Mach numbers and the SNLF airfoils' performance with high levels of freestream turbulence. Skin friction coefficient contours from the rotor CFD indicate the blade operates as intended and show regions of high skin friction on the tip closure geometry, highlighting a region of potential improvement. Integrated results, such as dimensionless and dimensional thrust and power, demonstrate that the SNLF rotor with a reduced rotational speed outperforms the baseline blade in terms of power requirements; however, the magnitude of the gain is substantially different between the BEMT and rotor RANS CFD. Lastly, BEMT results with various freestream turbulence levels and completely turbulent boundary layers indicate that the reduced rotational speed SNLF rotor requires the same amount of power as the fully turbulent baseline.

Optimization methods have been widely applied to the aerodynamic design of gas turbine blades. While applying optimization to high-fidelity computational fluid dynamics (CFD) simulations has proven capable of improving engineering design performance, a challenge has been overcoming the prolonged run-time due to the computationally expensive CFD runs. Reduced-order models and, more recently, machine learning methods have been increasingly used in gas turbine studies to predict performance metrics and operational characteristics, model turbulence, and optimize designs. The application of machine learning methods allows for utilizing existing knowledge and datasets from different sources, such as previous experiments, CFD, low-fidelity simulations, 1D or system-level studies. The present study investigates inserting a machine learning model that utilizes such data into a high-fidelity CFD driven optimization process, and hence effectively reduces the number of required evaluations of the CFD model. Artificial Neural Network (ANN) models were trained on data from over three thousand two-dimensional (2D) CFD analyses of turbine blade cross-sections. The trained ANN models were then used as surrogates in a nested optimization process alongside a full three-dimensional Navier–Stokes CFD simulation. The much lower evaluation cost of the ANN model allows for tens of thousands of design evaluations to guide the search of the best blade profiles to be used in the more expensive, high-fidelity CFD runs, improving the progress of the optimization while reducing the required computation time. It is estimated that the current workflow achieves a five-fold reduction in computational time in comparison to an optimization process that is based on three-dimensional (3D) CFD simulations alone. The methodology is demonstrated on the NASA/General Electric Energy Efficient Engine (E3) high pressure turbine blade and found Pareto front designs with improved blade efficiency and power over the baseline. Quantitative analysis of the optimization data reveals that some design parameters in the present study are more influential than others, such as the lean angle and tip scaling factor. Examining the optimized designs also provides insight into the physics, showing that the optimized designs have a lower amount of pressure drop near the trailing edge, but have an earlier onset of pressure drop on the suction side surface when compared to the baseline design, contributing to the observed improvements in efficiency and power.

The design and evaluation of floating horizontal-axis tidal turbines involves a vast design space, especially in the early conceptual stages. Both the turbine and the floating platform must be carefully considered, as the rotor's performance is directly influenced by the dynamic motion of the platform, which responds to the environmental conditions at the deployment site. This study investigates the relationship between platform design features and turbine performance under wave conditions informed by real world data. An automated workflow has been developed to assess performance metrics for parametric platform designs. This workflow begins with generating hull geometries based on specified design parameters. Using the boundary element method, the radiation and diffraction problems are solved, and the added mass and inertia matrix is obtained for each hull. The Added mass and inertia matrices are converted to WAMIT format for coupled aero-hydro-elastic model analysis within OpenFAST. Rotor performance is evaluated using blade element momentum theory, with the addition of a Beddoes-Leishman correction model for unsteady flows, capturing the effects of platform motion. The workflow is validated against experimental data for the rotor, and computational simulation for the combined platform and rotor. By analysing platform-turbine combinations across real world environmental scenarios, sensitivity to design changes such as the beam of the float, and the tension in the mooring system can be evaluated. Key metrics include blade loads, the presence of flow separation, turbine thrust, and overall power output. Response amplitude operators (RAOs) (Figure 1) quantify the excitation of platform motion by wave direction and frequency, and its subsequent impact on turbine dynamics. By selecting platform-turbine combinations, a parameter space of limiting operating conditions will defined. This workflow offers a cost-effective tool for exploring design impacts on system performance early in the development process, complementing higher-fidelity models that are typically constrained by computational expense and time.

The bifurcation and continuation methodology has evolved over the last two decades into a powerful tool for the analysis of trim and stability problems in aircraft flight dynamics. Over the years, bifurcation methods have been employed to deal with a variety of problems in aircraft dynamics, such as predicting high angle of attack behavior, especially spin, and studying instabilities in rolling maneuvers. The bifurcation methodology has served as a tool for the design of flight control systems, and is promising to be a useful tool in the aircraft design, simulation, testing, and evaluation process. In the present paper, we describe the state-of-theart in the use of bifurcation and continuation methods for the analysis of aircraft trim and stability with a few illustrative examples. Both the standard and extended bifurcation analysis procedures are discussed and typical results for instabilities in high-α flight and inertia-coupled roll maneuvers are shown. This is followed by several problems in nonlinear flight dynamics where bifurcation and continuation methods have been fruitfully applied to yield effective solutions. Finally, the use of bifurcation theory to arrive at analytical instability criteria is demonstrated for the aircraft roll coupling and wing rock problems. 78 references have been cited in the text.

The bifurcation and continuation methodology has evolved over the last two decades into a powerful tool for the analysis of trim and stability problems in aircraft flight dynamics. Over the years, bifurcation methods have been employed to deal with a variety of problems in aircraft dynamics, such as predicting high angle of attack behavior, especially spin, and studying instabilities in rolling maneuvers. The bifurcation methodology has served as a tool for the design of flight control systems, and is promising to be a useful tool in the aircraft design, simulation, testing, and evaluation process. In the present paper, we describe the state-of-the-art in the use of bifurcation and continuation methods for the analysis of aircraft trim and stability with a few illustrative examples. Both the standard and extended bifurcation analysis procedures are discussed and typical results for instabilities in high-α flight and in inertia-coupled roll maneuvers are shown. This is followed by several problems in nonlinear flight dynamics where bifurcation and continuation methods have been fruitfully applied to yield effective solutions. Finally, the use of bifurcation theory to arrive at analytical instability criteria is demonstrated for the aircraft roll coupling and wing rock problems. 76 references have been cited in the text.

A case is made that introducing CAD-based geometry prematurely in the aircraft design process actually hinders multidisciplinary design. Consequently, a design process which allows a designer to quickly build and analyze aerospace configurations without CAD or computational meshing specialists is proposed. This allows higher fidelity analyses to be applied at conceptual design and decreases the turnaround time for trade studies and optimizations. The basic premise of conceptual geometry modeling is presented and discussed. Key features and capabilities which are essential for a successful geometry modeler are identified. Desktop Aeronautics' conceptual geometry modeler, RAGE, is described, with emphasis on recent progress and advances in the tool. A preliminary graphical-user-interface is presented along with an application programming interface. Extensibility of the RAGE modeler is discussed along with the importance of this feature. The applicability of RAGE to simple trade studies is demonstrated in an example problem. The precision of the RAGE modeler is also demonstrated on a complex aircraft design. Future plans for the geometry modeler are also discussed. I. Background In the conceptual phase of aircraft design, there is often a wide range of geometric configurations that the designer wishes to consider, analyze, and assess. A designer’s intuition and creativity are crucial to a successful conceptual design, yet are easily inhibited by the modeling and analysis process itself, particularly if high-fidelity analysis is warranted. If the time between inception and assessment of a candidate design is relatively long, a designer may be forced to limit the number of concepts considered. New data revealed in a design iteration may suggest or require significant changes to the geometry configuration. Since the majority of considered design configurations will eventually be discarded, an ideal conceptual design process should involve a highly efficient and easy to use geometry modeler. Significant changes should be allowed without tedious re-work of the geometry model. Exporting the model for analysis should require little effort and have the capability to be automated. Therefore, any modeling application used in this process should be flexible and not restrict the designer’s choice of user interface, analysis method, and design optimization environment. Most current design processes in the aerospace industry rely heavily on computer-aided-design (CAD) applications. As a general design tool, CAD is a powerful geometry modeler capable of precisely representing practically any shape. Unfortunately, this generality is realized at the cost of requiring specialized training to efficiently and effectively use the software. Also, a CAD model is often not easily modified, especially if significant re-work of the geometry is necessary. This can lead to the premature freeze of an aircraft design due to employing excessively high-fidelity geometry modeling too early in the design process. Parametric CAD modeling could address this issue, but creating a well-designed parametric CAD model is difficult. Not only does it require an extremely skilled operator, but also the designer must have some insight into what parameterization may ultimately be desired. Modifying a parametric CAD model is often more difficult than modifying a conventional CAD model. Significant changes, such as adding or removing cross-sections, may invalidate the parameterization in some cases. In most organizations, CAD modeling (whether it be parametric or conventional) is often assigned to a dedicated CAD specialist. Since the conceptual designer is usually not a CAD specialist, the latter must communicate his design intent to the former, often using sketches, dimensions, and word of mouth. When the CAD specialist interprets the sketches, any part or detail not precisely defined usually requires judgment and artistic license. This interpretation may result in loss of design intent and indeterminate iteration between the CAD specialist and designer to obtain a satisfactory result. Because this process is iterative, CAD operators often must recreate similar geometry