A Numberical Vortex Approach to Aerodynamic Modeling of SUAV/VTOL Aircraft

A numerical lifting line method, coupled with a numerical blade element method, is presented as a low computational cost approach to modeling slipstream effects on a finite wing. This method uses a 3D vortex lifting law along with known 2D airfoil data to predict the lift distribution across a wing in the presence of a propeller slipstream. The results are of significant importance in the development of an aerodynamic modeling package for initial stages of vertical takeoff and landing (VTOL) aircraft design. An overview of the algorithm is presented, and results compared with published experimental data

Momentum Theory with Slipstream Rotation Applied to Wind Turbines

A momentum theory which includes the effects of slipstream rotation for wind turbines is presented. The theory accounts for the axial and radial pressure gradients within the slipstream as well as the wake expansion caused by wake rotation. Because of the limiting approximations of previous methods, the effects of slipstream rotation have not been accurately realized. The method included here, which does not suffer from the unrealistic approximations of previous methods, predicts that the effects of slipstream rotation are manifest entirely through an increase in the turbine thrust coefficient. The method predicts, as previous methods do, that the Lanchester-Betz-Joukowski limit of 16/27 is an upper limit for the maximum efficiency, or power coefficient, of a wind turbine. Unlike the results from classical methods that are traditionally reported in terms of the axial induction factor, results of this work are presented in terms of two independent variables, the tip-speed ratio and the torque coefficient. The results included here allow the dependent variables including the thrust coefficient, power coefficient, axial induction factor, and circumferential induction factor to be evaluated in terms of the tip-speed ratio and torque coefficient. Additionally, relationships for the ideal operating conditions of a wind turbine are presented

Lifting-Line Predictions for Induced Drag and Lift in Ground Effect

Closed-form relations are presented for estimating ratios of the induced-drag and lift coefficients acting on a wing in ground effect to those acting on the same wing outside the influence of ground effect. The closed-form relations for these ground-effect influence ratios were developed by correlating results obtained from numerical solutions to Prandtl’s lifting-line theory. Results show that these influence ratios are not unique functions of the ratio of wing height to wingspan, as is sometimes suggested in the literature. These ground-effect influence ratios also depend on the wing planform, aspect ratio, and lift coefficient

A Lifting-Line Approach to Estimating Propeller/Wing Interactions

A combined wing and propeller model is presented as a low-cost approach to first-cut modeling of slipstream effects on a finite wing. The wing aerodynamic model employs a numerical lifting-line method utilizing the 3D vortex lifting law along with known 2D airfoil data to predict the lift distribution across a wing for a prescribed upstream flowfield. The propeller/slipstream model uses a blade element theory combined with momentum conservation equations. This model is expected to be of significant importance in the design of tail-sitter vertical take-off and landing (VTOL) aircraft, where the propeller slipstream is the primary source of air flow past the wings in some flight conditions. The algorithm is presented, and results compared with published experimental data

Low-Fidelity Method for Rapid Aerostructural Optimisation and Design-Space Exploration of Planar Wings

During early phases of wing design, analytic and low-fidelity methods are often used to identify promising design concepts. In many cases, solutions obtained using these methods provide intuition about the design space that is not easily obtained using higher-fidelity methods. This is especially true for aerostructural design. However, many analytic and low-fidelity aerostructural solutions are limited in application to wings with specific planforms and weight distributions. Here, a numerical method for minimising induced drag with structural constraints is presented that uses approximations that apply to unswept planar wings with arbitrary planforms and weight distributions. The method is applied to the National Aeronautics and Space Administration (NASA) Ikhana airframe to show how it can be used for rapid aerostructural optimisation and design-space exploration. The design space around the optimum solution is visualised, and the sensitivity of the optimum solution to changes in weight distribution, structural properties, wing loading and taper ratio is shown. The optimum lift distribution and wing-structure weight for the Ikhana airframe are shown to be in good agreement with analytic solutions. Whereas most modern high-fidelity solvers obtain solutions in a matter of hours, all of the solutions shown here can be obtained in a matter of seconds

A One-Dimensional Finite-Difference Solver for Fully-Developed Pipe and Channel Flows

An algorithm is developed to solve the fundamental flow cases of fully-developed turbulent flow in a pipe and in a channel. The algorithm uses second-order finite-difference approximations for nonuniform grid spacing and is developed in such a way as to easily facilitate the implementation of several two-equation, Reynolds-Averaged-Navier-Stokes turbulence models. Results are included for the Wilcox 1998 k-ω model

Estimating the Subsonic Aerodynamic Center and Moment Components for Swept Wings

An improved method is presented for estimating the subsonic location of the semispan aerodynamic center of a swept wing and the aerodynamic moment components about that aerodynamic center. The method applies to wings with constant linear taper and constant quarter-chord sweep. The results of a computational fluid dynamics study for 236 wings show that the position of the semispan aerodynamic center of a wing depends primarily on aspect ratio, taper ratio, and quarter-chord sweep angle. Wing aspect ratio was varied from 4.0 to 20, taper ratios from 0.25 to 1.0 were investigated quarter-chord sweep angles were varied from 0 to 50 deg. and linear geometric washout was varied from -4.0 to +8.0 deg. All wings and airfoil sections from the NACA 4-digit airfoil sweries with camber varied from 0 to 4% and thickness ranging from 6 to 18%. Within the range of parameters studied, wing camber, thickness and twist were shown to have significant effect on the position of the semispan aerodynamic center. The results of this study provide improved resolution of the semispan aerodynamic center and moment componennts for conceptual designs and analysis

Smooth-Wall Boundary Conditions for Dissipation-Based Turbulence Models

It is shown that the smooth-wall boundary conditions specified for commonly used dissipation-based turbulence models are mathematically incorrect. It is demonstrated that when these traditional wall boundary conditions are used, the resulting formulations allow an infinite number of solutions. Furthermore, these solutions do not enforce energy conservation and they do not properly enforce the no-slip condition at a smooth surface. This is true for all dissipation-based turbulence models, including the k-ε, k-ω, and k-ζ models. Physically correct wall boundary conditions must force both k and its gradient to zero at a smooth wall. Enforcing these two boundary conditions on k is sufficient to determine a unique solution to the coupled system of differential transport equations. There is no need to impose any wall boundary condition on ε, ω, or ζ at a smooth surface and it is incorrect to do so. The behavior of ε, ω, or ζ approaching a smooth surface is that required to force both k and its gradient to zero at the wall

Pitch Dynamics of Unmanned Aerial Vehicles

Dynamic stability requirements for manned aircraft have been in place for many years. However, we cannot expect stability constraints for UAVs to match those for manned aircraft; and dynamic stability requirements specific to UAVs have not been developed. The boundaries of controllability for both remotely-piloted and auto-piloted aircraft must be established before UAV technology can reach its full potential. The development of dynamic stability requirements specific to UAVs could improve flying qualities and facilitate more efficient UAV designs to meet specific mission requirements. As a first step to developing UAV stability requirements in general, test techniques must be established that will allow the stability characteristics of current UAVs to be quantified. This paper consolidates analytical details associated with procedures that could be used to experimentally determine the pitch stability boundaries for good UAV flying qualities. The procedures require determining only the maneuver margin and pitch radius of gyration and are simple enough to be used in an educational setting where resources are limited. The premise is that these procedures could be applied to UAVs now in use, in order to characterize the longitudinal flying qualities of current aircraft. This is but a stepping stone to the evaluation of candidate metrics for establishing flying-quality constraints for unmanned aircraft

Energy-Vorticity Turbulence Model with Application to Flow near Rough Surfaces

Based on a more direct analogy between turbulent and molecular transport, a foundation is presented for an energy–vorticity turbulence model. Whereas traditional k-εk-ε, k-ωk-ω, and k-ζk-ζ models relate the eddy viscosity to a dissipation length scale associated with the smaller eddies having the highest strain rates, the proposed model relates the eddy viscosity to a mean vortex wavelength associated with the larger eddies primarily responsible for turbulent transport. A rigorous development of the turbulent-energy-transport equation from the Navier–Stokes equations includes exact relations for the viscous dissipation and molecular transport of turbulent kinetic energy. Application of Boussinesq’s analogy between turbulent and molecular transport leads to a transport equation, which shows neither molecular nor turbulent transport of turbulent energy to be simple gradient diffusion. The new turbulent-energy-transport equation contains two closure coefficients: a viscous-dissipation coefficient and a turbulent-transport coefficient. To help evaluate closure coefficients and provide insight into the energy–vorticity turbulence variables, fully rough pipe flow is considered. For this fully developed flow, excellent agreement with experimental data for velocity profiles and friction factors is attained over a wide range of closure coefficients, provided that a given relation between the coefficients is maintained