Bharath Govindarajan M

eVTOL sizing is tackled with a Multi-Disciplinary Optimization problem with nonlinear constraints in this work, focusing on UAVs with distributed vertical lift. Several optimization schemes are investigated for including airframe sizing with finite element analysis, vehicle trim, and blade aerodynamic shape design. The iterative weight convergence loop is replaced by a slack variable and equality constraint for the sizing optimizer. Airframe sizing and weight minimization (with stress inequality constraints) may be driven either by the sizing optimizer, or by a separate optimizer within the various constraint functions in a nested structure. It is preferable to drive the trim variables using the sizing optimizer; if a particular design cannot be trimmed, this information is propagated to the sizing optimizer through the corresponding equality constraints. The all-at-once optimization strategy yields results in the shortest time compared to the other methods. Using modified momentum theory for rotor performance, all gradient-based optimizations from different starting points converged to the same minimum, indicating that the design space is convex for the chosen bounds and objective function. Blade shape design with BEMT is also included in the sizing, either directly with blade twist and taper as additional design variables, or indirectly through a response surface. The methodology is demonstrated on the sizing of two package delivery vehicle configurations (a quadrotor and a lift-augment quadrotor biplane tailsitter) for a mission with 10 km radius of action. The cruise airspeeds for the two configurations are also identified as part of the sizing/optimization. The quadrotor is more suited for this point mission owing to its lower empty weight compared to the quad-biplane, which has better cruise efficiency but higher empty weight.

This paper presents an approach to reframe the sizing problem for vertical-lift unmanned aerial vehicles (UAVs) as an optimization problem and obtains a weight-optimal solution with up to two orders of magnitude of savings in wall clock time. Because sizing is performed with higher fidelity models and design variables from several disciplines, the Simultaneous Analysis aNd Design (SAND) approach from fixed-wing multidisciplinary optimization literature is adapted for the UAV sizing task. Governing equations and disciplinary design variables that are usually self-contained within disciplines (airframe tube sizes, trim variables, and trim equations) are migrated to the sizing optimizer and added as design variables and (in)equality constraints. For sizing consistency, the iterative weight convergence loop is replaced by a coupling variable and associated equality consistency constraint for the sizing optimizer. Cruise airspeed is also added as a design variable and driven by the sizing optimizer. The methodology is demonstrated for sizing a package delivery vehicle (a lift-augment quadrotor biplane tailsitter) with up to 39 design variables and 201 constraints. Gradient-based optimizations were initiated from different starting points; without blade shape design in sizing, all processes converged to the same minimum, indicating that the design space is convex for the chosen bounds, constraints, and objective function. Several optimization schemes were investigated by moving combinations of relevant disciplines (airframe sizing with finite element analysis, vehicle trim, and blade aerodynamic shape design) to the sizing optimizer. The biggest advantage of the SAND strategy is its scope for parallelization, and the inherent ability to drive the design away from regions where disciplinary analyses (e.g., trim) cannot find a solution, obviating the need for ad hoc penalty functions. Even in serial mode, the SAND optimization strategy yields results in the shortest wall clock time compared to all other approaches.

Techniques allowing for robust six degree-of-freedom vehicle trim are explored within the iterative rotorcraft sizing framework HYDRA. An optimization-based approach allows designers to find an acceptable local minimum solution of the trim problem for over-actuated vehicle configurations for which an infinite number of trim solutions exist. The performance and robustness of optimization algorithms suitable for the minimization of a nonlinear objective function subject to design variable bounds and equality constraints are compared using both a four degree-of-freedom and a six degree-of-freedom vehicle trim problems. The SciPy implementation of the sequential least squares programming algorithm was found to converge to a target objective function value up to 96% faster than a trust region algorithm for both problems. The six degree-of-freedom trim methodology using sequential least squares programming was then applied to the problem of sizing an omni-directional ocotocopter to be able to complete a mission taking into account multiple motor/rotor failures during the flight.

A computational study is conducted on thin flat plates to simulate flows of Reynolds numbers at 104 to provide understanding and guidance for micro air vehicles and other low-Reynolds-number airfoil designs. A synergistic effort between experiments and validated and computational fluid dynamics (CFD) tools were used as part of this study. The CFD tool used in this study is an established Reynolds-averaged Navier–Stokes (RANS) solver with a Spalart–Allmaras turbulence model and a correlation-based laminar–turbulent boundary-layer transition model. The computational method was validated against experimental data for flat plates under steady and unsteady kinematic conditions. The objective of the study was to understand unsteady characteristics of a thin flat plate undergoing harmonic pitching (no plunging) around the quarter chord under incompressible flow conditions. Pitching amplitudes were limited to 10 deg to ensure there was no effect of dynamic stall. The focus of this study is to characterize unsteady aerodynamics based on reduced frequency, which was varied between 0.005, 0.05, and 0.5. The unsteady condition of 0.05 was compared against experiments, 2-D RANS, and 3-D hybrid RANS/large-eddy simulation formulations. It was observed that the lift characteristics were reasonably well predicted by the CFD tools when compared to experimental observations. At a reduced frequency of 0.05, the pitching motion causes an apparent stabilization of vortices resulting in higher oscillatory lift amplitude than the static value. The 3-D RANS better predicted the pitching-moment characteristics compared to the 2-D RANS, attributed to the breakdown of the leading-edge vortex. It was observed that, although thinner flat-plate airfoils have a higher maximum lift coefficient compared to the thicker NACA 0012, they also produce higher instantaneous pitching moment.

Conceptual sizing and performance estimation of four configurations for a package delivery mission is presented in this work. The multi-fidelity VTOL design framework HYDRA is used to size a notional quadcopter, hexacopter, quad-rotor bi-plane tailsitter (QBiT), and a lift-augmented tricopter for weight classes of 10 kg, 15 kg, 20 kg, and 25 kg. Sizing is performed using a combination of physics-based empty weight models for the airframe, rotor blades and wings, along with empirical models. A longitudinal trim methodology was implemented that minimizes the power required for a configuration for a given flight condition. Representative payload drop scenarios were constructed from different cruise speeds and ranges to identity a vehicle design in each configuration that can complete the most number of payload drop missions successfully. It is identified that the hexacopter performed better over the quadcopter in terms of requiring lower installed power and deliver heavier payload packages for a given radius of action. Wing-based designs such as the QBiT and tricopter are capable of delivering packages in a short time owing to either full/partial conversion to airplane mode during cruise flight.

Conceptual sizing and performance estimation of four vertical takeoff and landing (VTOL) configurations for a package delivery mission is presented in this Paper. The multifidelity VTOL design framework HYDRA is used to size a notional quadrotor, hexarotor, quadrotor biplane tailsitter (QBiT), and a lift-augmented tricopter for weight classes of 10, 15, 20, and 25 kg. Sizing is performed using a combination of physics-based empty weight models for the airframe, rotor blades, and wings, along with statistical models for predicting motor and battery weights. A gradient- based optimization methodology was implemented to identify the best designs for each configuration under each weight class. An optimization-based longitudinal trim methodology was used to identify the appropriate shaft power settings for each vehicle at various trimmed flight conditions along the mission profile. Representative payload delivery and return scenarios were constructed from different cruise speeds and ranges to identity a vehicle design in each configuration that can complete the highest number of payload drop missions successfully. The hexarotor performed better than the quadrotor in terms of requiring lower installed power and deliver heavier payload packages for a given radius of action. Wing-borne designs such as the QBiT and tricopter are capable of delivering packages in a short time owing to full/partial conversion to airplane mode during cruise flight but may require careful fine-tuning of the trimline and flight control system to successfully transition between hover and cruise flight modes.

This work explores the use of high-order finite-difference schemes along Hamiltonian lines to solve conservation laws on unstructured two-dimensional meshes. To demonstrate these procedures, the paper focuses on explicit and compact spatial discretizations of up to sixth-order coupled with implicit low-pass filters of up to tenth-order along the identified line-structures. The spatial discretization schemes are then extended for the simulation of high-speed flows to capture embedded shocks. A WENO-type switch is used to identify potential regions of shock, where two distinct shock-capturing approaches are investigated. The “adaptive filter" approach, which combines a sixth-order compact scheme with a locally reduced-order filter, is one method, while the second approach is a “hybrid compact-Roe" wherein a compact scheme is replaced with a third-order upwind-biased MUSCL scheme within the shock regions. These spatial discretization schemes are used with explicit time integration approaches to investigate canonical problems defined by the compressible Navier–Stokes equations. The applicabililty of the methodology is demonstrated by solving representative problems and for both inviscid and viscous flows. It is seen that even in the presence of significant grid discontinuities, the low-pass high-order filter preserves the advantages of the high-order technique.

This study enables the use of explicit and compact high-order finite-difference schemes with a line-based solver to solve conservation laws on unstructured grids. A quadrilateral subdivision process is used to identify unique line structures (also known as Hamiltonian loops) before formulating stencil-based discretizations. To demonstrate the methodology for canonical flows represented by the Navier–Stokes equations, up to sixth-order spatial discretization and a maximum of tenth-order low-pass filters are implemented along with the Hamiltonian loops. The filter restores the benefits of the high-order approach even in the presence of abrupt grid discontinuities that cause abrupt changes in loop curvature. Isentropic vortex convection, lid-driven cavity, double periodic shear layer, and inviscid and viscous flow past a cylinder and NACA 0012 airfoil are all used to demonstrate the formulation. The ability of some schemes, particularly the fourth-order explicit, to nearly achieve the formal order of accuracy and successfully predict the flow following available results in the literature is one of the key findings. Compact schemes have been found to be more sensitive to loop curvature than explicit schemes.

This paper presents a methodology for using a neural network to predict airfoil behavior in the context of rapid airfoil design and prop-rotor blade shape optimization. To train the neural network, the 1620 shapes in the UIUC airfoil database were each evaluated using XFOIL at various angles of attack. The Class Shape Transformation approach is used to parameterize airfoil upper and lower surface geometries, using Chebyshev polynomials as shape functions. Three separate neural networks were trained, one each for lift, drag, and pitching moment. After training the neural network, isolated airfoil shape optimization was performed using the NSGA2 algorithm, targeting minimum average drag over an operating lift coefficient range for 10%, 12%, and 16% thick airfoils. Additionally, prop-rotor aerodynamic optimization was carried out by designating airfoil shape parameters, blade twist distribution, and blade chord distribution as simultaneous design variables for two objectives: hover figure of merit and cruise-mode propeller efficiency. A Blade Element Momentum Theory is used to predict rotor performance, using airfoil tables generated by the neural network. Pareto frontiers and an analysis of the resulting designs are presented. Using a neural network is advantageous for both applications considered, because it results in a 40 × speed-up over XFOIL, and decouples the computational cost of shape optimization from that of the physics-based model generating truth data.