# Browsing by Author "Hall, Kenneth C"

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Item Open Access Aerodynamic Optimization of Helicopter Rotors using a Harmonic Balance Lifting Surface Technique(2018) Tedesco, Matthew BraxtonThis thesis concerns the optimization of the aerodynamic performance of conventional helicopter rotors, given a set of design variables to control the rotor's pitching angle, twist and chord distributions. Two models are presented for use. The lifting line model is a vortex lattice model that uses assumptions on the size and shape of the blade to simplify the model, but is unable to account for unsteady and small aspect ratio effects. The lifting surface model removes these assumptions and allows for a wider variety of accurate solutions, at the cost of overall computational complexity. The lifting surface model is chosen for analysis, and then condensed using static condensation and harmonic balance. The final system is discretized and pertinent values of power, force, and moment calculated using Kelvin's theorem and the unsteady Bernoulli equation. This system is then optimized in one of two ways: using a direct linear solve if possible, or the open source package IPOPT where necessary. The results of single-point and multi-point optimization demonstrate for low speed forward flight, the lifting line model is sufficient for modeling purposes. As the speed of the rotor increases, more unsteady effects become prominent in the system, and therefore the lifting surface model becomes more necessary. When conducting a chord optimization on the rotor, hysteresis effects and local minima are calculated for the non-linear optimization. The global minima within the set of captured local minima can be found through simple data visualization, and the global minima is confirmed to have similar behavior to the results of lifting line; a large spike in induced power at a critical advance ratio, with a sharp decline in induced power as the rotor flies faster. Within the realm of practical forward flight speeds of a conventional rotor, smooth, continuous results are demonstrated.

Item Open Access Aeroelastic Modeling of Blade Vibration and its Effect on the Trim and Optimal Performance of Helicopter Rotors using a Harmonic Balance Approach(2020) Tedesco, MatthewThis dissertation concerns the optimization of the aeroelastic performance of conventional

helicopter rotors, considering various design variables such cyclic and higher

harmonic controls. A nite element model is introduced to model the structural

eects of the blade, and a coupled induced velocity/projected force model is used

to couple this structural model to the aerodynamic model constructed in previous

works. The system is then optimized using two separate objective functions: minimum

power and minimum vibrational loading at the hub. The model is validated

against several theoretical and experimental models, and good agreement is demonstrated

in each case. Results of the rotor in forward

ight demonstrate for realistic

advance ratios the original lifting surface model is sucient for modeling normalized

induced power. Through use of the dynamics model the vibrational loading minimization

is shown to be extremely signicant, especially when using more higher

harmonic control. However, this decrease comes at an extreme cost to performance

in the form of the normalized induced power nearly doubling. More realistic scenarios

can be created using multi-objective optimization, where it is shown that vibrational

loading can be decreased around 60% for a 5% increase in power.

Item Open Access Efficient Solution of Unsteady Nonlinear Flows Using a Multiple Zone Harmonic Balance Technique(2010) Gentilli, Nicholas CharlesAn efficient two-dimensional multiple zone harmonic balance solver for calculating unsteady nonlinear flows is presented. The solver adapts Roe's flux difference splitting algorithm such that it can be used to discretize the harmonic balance equations. It is demonstrated that the numerical solutions produced by this solver are in good agreement with known results for a variety of unsteady flows, including cascade flows. The solver incorporates a multiple zone technique in which the number of harmonics is allowed to vary in different zones of a flow domain. In the present study, the multiple zone technique is optimized for unsteady nonlinear transonic flows. It is shown that the multiple zone technique reduces computational time by 50-60% in comparison to single zone solutions. It is additionally shown that these computational savings come with no change in the accuracy of the solution.

An analysis of the temporal and spatial behavior of the waves associated with harmonic balance discretization schemes is also presented. In the temporal analysis, the numerical stability limits of several discretization schemes are worked out in detail, and a numerical instability associated with the first-order upwind discretization is removed. The numerical stability limits are verified through experimentation. In the spatial analysis, spatial wave amplification factors are derived for the same set of discretization schemes. A novel upwind approximation of the harmonic source term is introduced, and it is demonstrated that, for one-dimensional flows, this approximation eliminates the spatial wave dissipation associated with previously used cell-centered discretizations of the source term. However, it is found that the difference between the dissipation associated with each approximation of the source term is less pronounced in two-dimensions.

Item Open Access Minimum Power Requirements and Optimal Rotor Design for Conventional, Compound, and Coaxial Helicopters Using Higher Harmonic Control(2013) Giovanetti, Eli BattistaThis thesis presents a method for computing the optimal aerodynamic performance of conventional, compound, and coaxial helicopters in trimmed forward flight with a limited set of design variables, including the blade's radial twist and chord distributions and conventional and higher harmonic blade pitch control. The optimal design problem, which is cast as a variational statement, minimizes the sum of the induced and viscous power required to develop a prescribed lift and/or thrust. The variational statement is discretized and solved efficiently using a vortex-lattice technique. We present two variants of the analysis. In the first, the sectional blade aerodynamics are modeled using a linear lift curve and a quadratic drag polar, and flow angles are assumed to be small. The result is a quadratic programming problem that yields a linear set of equations to solve for the unknown optimal design variables. In the second approach, the problem is cast as a constrained nonlinear optimization problem, which is solved using Newton iteration. This approach, which accounts for realistic lift and drag coefficients including the effects of stall and the attendant increase in drag at high angles of attack, is capable of optimizing the blade planform in addition to the radial twist distribution and conventional and higher harmonic blade pitch control. We show that for conventional rotors, coaxial counterrotating rotors, and a wing-rotor compound, using radially varying twist and chord distributions and higher harmonic blade pitch control can produce significant reductions in required power, especially at high advance ratios.

Item Open Access Optimal Aerodynamic Design of Conventional and Coaxial Helicopter Rotors in Hover and Forward Flight(2015) Giovanetti, Eli BattistaThis dissertation investigates the optimal aerodynamic performance and design of conventional and coaxial helicopters in hover and forward flight using conventional and higher harmonic blade pitch control. First, we describe a method for determining the blade geometry, azimuthal blade pitch inputs, optimal shaft angle (rotor angle of attack), and division of propulsive and lifting forces among the components that minimize the total power for a given forward flight condition. The optimal design problem is cast as a variational statement that is discretized using a vortex lattice wake to model inviscid forces, combined with two-dimensional drag polars to model profile losses. The resulting nonlinear constrained optimization problem is solved via Newton iteration. We investigate the optimal design of a compound vehicle in forward flight comprised of a coaxial rotor system, a propeller, and optionally, a fixed wing. We show that higher harmonic control substantially reduces required power, and that both rotor and propeller efficiencies play an important role in determining the optimal shaft angle, which in turn affects the optimal design of each component. Second, we present a variational approach for determining the optimal (minimum power) torque-balanced coaxial hovering rotor using Blade Element Momentum Theory including swirl. We show that the optimal hovering coaxial rotor generates only a small percentage of its total thrust on the portion of the lower rotor operating in the upper rotor's contracted wake, resulting in an optimal design with very different upper and lower rotor twist and chord distributions. We also show that the swirl component of induced velocity has a relatively small effect on rotor performance at the disk loadings typical of helicopter rotors. Third, we describe a more refined model of the wake of a hovering conventional or coaxial rotor. We approximate the rotor or coaxial rotors as actuator disks (though not necessarily uniformly loaded) and the wake as contracting cylindrical vortex sheets that we represent as discrete vortex rings. We assume the system is axisymmetric and steady in time, and solve for the wake position that results in all vortex sheets being aligned with the streamlines of the flow field via Newton iteration. We show that the singularity that occurs where the vortex sheet terminates at the edge of the actuator disk is resolved through the formation of a 45 degree logarithmic spiral in hover, which results in a non-uniform inflow, particularly near the edge of the disk where the flow is entirely reversed, as originally hypothesized by previous authors. We also quantify the mutual interference of coaxial actuator disks of various axial spacing. Finally, we combine our forward flight optimization procedure and the Blade Element Momentum Theory hover optimization to form a variational approach to the multipoint aerodynamic design optimization of conventional and coaxial helicopter rotors. The resulting nonlinear constrained optimization problem may be used to map the Pareto frontier, i.e., the set of rotor designs for which it is not possible to improve upon the performance in one flight condition without degrading performance in the other. We show that for both conventional and coaxial rotors analyzed in hover and high speed flight, a substantial tradeoff in performance must be made between the two flight conditions. Finally, computational results demonstrate that higher harmonic control is able to improve the Pareto efficiency for both conventional and coaxial rotors.

Item Open Access Optimization of the Aerodynamics of Small-scale Flapping Aircraft in Hover(2008-06-27) Lebental, SidneyFlapping flight is one of the most widespread mean of transportation. It is a complex unsteady aerodynamic problem that has been studied extensively in the past century. Nevertheless, by its complex nature, flapping flight remains a challenging subject. With the development of micro air vehicles, researchers need new computational methods to design these aircrafts efficiently.

In this dissertation, I will present three different methods of optimization for flapping flight with an emphasis on hovering with each their advantages and drawbacks. The first method was developed by Hall et al. It is an extremely fast and powerful three-dimensional approach. However, the assumptions made to develop this theory limit its use to lightly loaded wings. In addition, it only models the motion of the trailing edge and not the actual motion of the wing.

In a second part, I will present a two-dimensional unsteady potential method. It uses a freely convected wake which removes the lightly loaded restriction. This method shows the existence of an optimal combination of plunging and pitching motion. The motion is optimal in the sense that for a required force vector, the aerodynamic power is minimal.

The last method incorporates the three-dimensional effects. These effects are especially important for low aspect ratio wings. Thus, a three-dimensional unsteady potential vortex method was developed. This method also exhibits the presence of an optimal flapping/pitching motion. In addition, it agrees really well with the two previous methods and with the actual kinematics of birds during hovering flapping flight.

To conclude, some preliminary design tools for flapping wings in forward and hovering flight are presented in this thesis.

Item Open Access The Effect of Wing Damage on Aeroelastic Behavior(2009) Conyers, Howard J.Theoretical and experimental studies are conducted in the field of aeroelasticity. Specifically, two rectangular and one cropped delta wings with a hole are analyzed in this dissertation for their aeroelastic behavior.

The plate-like wings are modeled using the finite element method for the structural theory. Each wing is assumed to behave as a linearly elastic and isotropic, thin plate. These assumptions are those of small-deflection theory of bending which states that the plane sections initially normal to the midsurface remain plane and normal to that surface after bending. The wings are modeled in low speed flows according to potential flow theory. The potential flow is governed by the aerodynamic potential equation, a linear partial differential equation. The aerodynamic potential equation is solved using a distribution of doublets that relates pressure to downwash in the doublet lattice method. A hole in a wing-like structure is independently investigated theoretically and experimentally for its structural and aerodynamic behavior.

The aeroelastic model couples the structural and aerodynamic models using Lagrange's equations. The flutter boundary is predicted using the V-g method. Linear theoretical models are capable of predicting the critical flutter velocity and frequency as verified by wind tunnel tests. Along with flutter prediction, a brief survey on gust response and the addition of stores(missile or fuel tanks) are examined.