Vortex lattice method

About: Vortex lattice method is a research topic. Over the lifetime, 779 publications have been published within this topic receiving 9242 citations.

Flight Dynamics Analyses of a Propeller-Driven Airplane (II): Building a High-Fidelity Mathematical Model and Applications

Abstract: This paper is the second in a series and aims to build a high-fidelity mathematical model for a propeller-driven airplane using the propeller’s aerodynamics and inertial models, as developed in the first paper. It focuses on aerodynamic models for the fuselage, the main wing, and the stabilizers under the influence of the wake trailed from the propeller. For this, application of the vortex lattice method is proposed to reflect the propeller’s wake effect on those aerodynamic surfaces. By considering the maneuvering flight states and the flow field generated by the propeller wake, the induced velocity at any point on the aerodynamic surfaces can be computed for general flight conditions. Thus, strip theory is well suited to predict the distribution of air loads over wing components and the viscous flow effect can be duly considered using the 2D aerodynamic coefficients for the airfoils used in each wing. These approaches are implemented in building a high-fidelity mathematical model for a propeller-driven airplane. Flight dynamic analysis modules for the trim, linearization, and simulation analyses were developed using the proposed techniques. The flight test results for a series of maneuvering flights with a scaled model were used for comparison with those obtained using the flight dynamics analysis modules to validate the usefulness of the present approaches. The resulting good correlations between the two data sets demonstrate that the flight characteristics of the propeller-driven airplane can be analyzed effectively through the integrated framework with the propeller and airframe aerodynamic models proposed in this study.

Modeling of aerodynamic forces in flapping flight with the Unsteady Vortex Lattice Method

Abstract: This thesis concerns the extensive study and comparison of two approaches commonly used to compute the aerodynamic forces with the unsteady vortex lattice method. The first approach was introduced by Katz and Plotkin and is based on Bernoulli’s equations, the second approach was based Joukowski’s equations for the computation of forces. This report is divided in two main sections: the study of one wing undergoing simple movements (steady, pure harmonic pitching and pure harmonic plunging) and the study of two separate wings undergoing a combination of flapping and pitching such as seen in avian flight. For the simple test cases, the results obtained with both methods of computation were first compared to an analytical solution for a (quasi) 2D case. Then the comparison of both methods was made for finite wings. For the 3D problem a convergence study was done with respect to the chordwise discretisation of the airfoils. This section showed that for all the cases, the two methods give almost the same answer and therefore they could be considered as equivalent. The convergence study realised for finite wings showed however that Joukowski’s method converges quicker than Katz’s for symmetric airfoils, but it is the other way around when it comes to cambered airfoils. The study of the flapping and pitching motion is based on the work of N. Abdul Razak in [2]. The influence of pitch leading was extensively studied as this phenomenon presents a flow attached at all time, so these kinematics are well suited for the vortex lattice method. Both pure flapping and pitch lagging were also discussed but more briefly. For pitch leading, the study showed that in general both methods give the same results for the drag and the lift. Moreover, the UVLM solutions were very close to the experimental ones, especially for the drag. The convergence showed a small advantage for the Katz method for the coarser meshes, but in the end both methods appear to reach convergence for the same discretisation.

Application of the Vortex Lattice Method to the Three-Dimensional Theory of a Cavitating Propeller

Abstract: A new theory on a cavitating propeller is proposed, treating the cavitation threedimensionally, and using a lifting surface theory. A numerical method has also been developed based on this theory, appying the vortex lattice method and replacing the cavitation and the blade thickness by source elements, for a cavitating propeller operating in a uniform flow.To evaluate the present method, the calculations are carried out for a model propeller and compared with other prediction methods and the model test results.It is confirmed that the present method gives considerable improvements, in comparison with the conventional methods, on the evaluation of the cavity thickness due to the three-dimensional flow, and on the elimination of the instability of the solution caused by the two-dimensional theory.

Global and Local Optimization of Flapping Kinematics

Abstract: In this work, optimization methodologies of the kinematics of flapping wings in forward and hover flights are considered. Particularly, local and global optimization algorithms are combined with the unsteady vortex lattice method (UVLM) to determine the most efficient kinematics. In the first problem, the kinematic optimization of a three-dimensional flapping wing in forward flight with active shape morphing is aimed at maximizing the propulsive efficiency under lift and thrust constraints. Results show that due to the quasi-concavity of the objective function associated with the flapping kinematics employed in forward flight, local gradient-based optimizers perform very well in terms of accuracy and computational cost. In the second problem, the objective is to identify the optimized kinematics of a twodimensional hovering wing that minimize the aerodynamic power under lift constraint. The results show that using a hybrid optimization algorithm (combination of local and global schemes) accelerates the convergence to optimal points and avoids being trapped at local minimum points. While the efficiency of using a local optimizer, a global optimizer, or a hybrid of the two depends on the nature of the problem and associated design space, it is determined that hybrid optimization is best suited for determining local minima.

Wing and Airfoil Optimized Design of Transport Aircraft

Abstract: An efficient methodology for multi-disciplinary design and optimization of transport was elaborated and developed. The methodology was implemented in a commercial known optimization framework. Semi-empirical methods were employed for wing weight estimation; a multi-block full-potential code was used for drag calculation; Vortex Lattice method was implemented for spanwise lift distribution in order to compute de aircraft maximum-lift coefficient via critical section method; a calibrated single- point Breguet simplified equation was considered for aircraft performance calculation. The optimization design variables are related to the wing planform and airfoil geometry and cruise speed. The design constraints were the fuel tank capacity, flight quality of the aircraft, and takeoff field length. A simple stability augmentation control system was implemented in order to compute its effects on optimal configurations. Multi-objective optimization tasks were performed accomplishing minimization of the block time and block fuel for a specified mission.