Computational studies of the rotors aerodynamic characteristics of multirotor drones

The article presents the results of computational studies of aerodynamic characteristics for unmanned lift-generating multi-rotor drones of various configurations. The distinctive features of rotors flow were characterized. The rotor interaction was evaluated. The computations were based on the nonlinear rotor blade vortex theory in a non-stationary arrangement. The combinations of four, eight (four coaxial) and fourteen two-bladed rotors at velocity V = 100, 150, 200 km/h were considered. Semi-empirical methods were employed to select the rotor angles of attack, rotation speed, blade installation angles and geometric parameters at the given take-off weight for each combination of rotors and flight airspeed. The computations showed that for a four-rotor lift-generating design (quad-rotor), two rotors installed downstream, depending on the velocity due to the mutual effect, have values of the thrust coefficients ≈10...20% less than those of the rotors located upstream. For a coaxial quad-copter, the effect of the upper front rotor on the upper rear rotor is similar to the effect of the front rotors on the rear ones in a four-rotor lift-generating design. The effect of the upper front rotor on the lower rear rotor does not vary in terms of the average thrust value, and variations are only local in nature. The interaction of other rotors is identical to that of the four-rotor version. A fourteen-rotor lift-generating multi-rotor drone has a complex flow pattern, which generates deviance in the thrust coefficients variation with respect to time. Depending on the mode and rotors location, the average rotor thrust coefficient can vary approximately twice. The computations showed that with the similar geometric parameters and kinematics characteristics, rotors thrust is substantially subject to variation, which causes destabilizing moments to a significant degree without additional control input. Thrust pulsations and, respectively, vibrations grow in intensity as the flight airspeed increases. Probably, the right choice of the rotor configuration and the automatic control system can counterbalance thrust surge by so-called "phasing", i.e. selecting an initial azimuth angle for each rotor.

Propeller aerodynamic optimisation to minimise energy consumption for electric fixed-wing aircraft

An electric propulsion model for propeller-driven aircraft is developed with the aim of minimising the power consumption for a given airspeed and thrust. Blade Element Momentum Theory (BEMT) is employed for propeller performance predictions fed with aerodynamic aerofoil data obtained from a proposed combined Computational Fluid Dynamics (CFD)–Montgomerie method, which is also validated. The Two-Dimensional (2D) aerofoil data are corrected to consider compressibility, three-dimensional, viscous and Reynolds-number effects. The BEMT model showed adequate fitting with experimental data from the University of Illinois Urbana Champaign (UIUC) database. Additionally, Goldstein optimisation via vortex theory is employed to design pitch and chord distributions minimising the induced losses of the propeller. Particle swarm optimisation is employed to find the optimal value for a wide range of geometrical and operational parameters considering some constraints. The optimisation algorithm is validated through a study case where an existing optimisation problem is approached, leading to very similar results. Some trends and insights are obtained from the study case and discussed regarding the design of an optimal propulsion system. Finally, CFD simulations of the study case are carried out, showing a slight relative error of BEMT.

Performance Prediction and Design of Stratospheric Propeller

In this paper, a performance prediction method is proposed for the design of a stratospheric propeller. The Spalart–Allmaras (S–A) model was used to calculate the airfoil performance of FX63, and the polynomial fitting method was utilized to establish the airfoil database of the lift and drag coefficient. A computational fluid dynamics (CFD) model was applied at different altitudes to prove the feasibility of the method. The CFD results were compared with the results of the vortex theory and prediction; the prediction result accuracy was improved compared with that of the vortex theory over a greater range of advance ratios. The airfoil performance data requirements and the number of iterative calculations were reduced. These results indicate that the proposed propeller design meets the requirements of stratospheric airship propulsion systems.

Charles Porter Ellington. 31 December 1952—30 July 2019

Charles Ellington graduated at Duke University, North Carolina, and came to Cambridge in 1973 to work for a PhD on insect flight dynamics. He developed novel methodology and software for the kinematic analysis of freely hovering insects and applied them to his own high-speed films of a range of species. He identified five new non-steady-state mechanisms for lift generation, was the first to develop a vortex theory for flapping flight and developed and extended the use of morphometric parameters in calculating the forces and power requirements of flight. He remained in Cambridge, married a colleague, joined the staff of the Department of Zoology, became a fellow of Downing College and continued to work on insect aerodynamics and energetics, publishing on flight muscle efficiency, the factors limiting flight performance and the aerodynamic implications of the origin of insect flight. Building a closed-circuit wind tunnel connected with a sensitive oxygen analyser, he studied with colleagues how the aerodynamics and metabolic power input of bumblebees vary with flight speed, challenging the orthodox theory that this should follow a U-shaped curve. Outstanding among later research was the discovery that hawkmoths, and by implication many other insects, gain high levels of lift by generating a vortex above the leading edge, stabilized by spiralling out along the span—a major focus of animal flight research ever since. His many administrative roles included editorship of theJournal of Experimental Biology. He became a British citizen in 1995, was elected FRS in 1998 and to a chair of animal mechanics in 1999. Awards include the Scientific Medal of the Zoological Society and the University of Cambridge Pilkington Prize for teaching excellence. He was diabetic throughout his adult life, and suffered progressive ill health following a heart attack in 1996. He took early retirement in 2010, lived quietly with his wife and two sons at home near Newmarket, and died in July 2019.

Ways to improve the energy efficiency of shaft centrifugal pumps

The increase in the efficiency and competitiveness of mining enterprises is limited by the insufficient efficiency and adaptability of the currently used centrifugal pumps. Using the vortex theory of turbomachines, Theorems Stokes’ and Helmholtz, the principles of hydrodynamic analogy and superpositions, a mathematical model of the hydrodynamic calculation of centrifugal pumps with adaptive vortex sources integrated into the impeller blades is obtained. A significant influence on the hydrodynamic parameters and adaptability of pumps of the energy characteristics of adaptive vortex sources has been proved. Criteria for the similarity of the hydrodynamic process of fluid flow in the interscapular channels of impellers and adaptive vortex sources and their influence on the hydrodynamic characteristics of pumps are obtained. Mathematical and experimental modeling uses a regression equation to calculate the parameters of vortex chambers and their impact on the efficiency and adaptability of pumps. The optimal geometric parameters of the vortex chambers, the diameter of which does not exceed 5…7 % of the impeller diameter, increase the hydrodynamic loading by at least 13 %, the nominal efficiency. not less than 6 %, adaptability not less than 8 %. On the basis of the proposed developed mathematical model, after the positive test results obtained on the laboratory pump K 20/30, tests were carried out on the CNS 300-300 pump

Combined Momentum Theory and Simple Vortex Theory Inflow Model for Multirotor Configurations

For conventional main/tail rotor helicopters, momentum theory-based inflow models are still popular for design trade studies and flight simulations. However, simple momentum theory-based inflow models are not readily applicable in design trade studies of multirotor configuration vehicles where complex flow interactions among rotors can have a significant impact on vehicle overall performance, and hence, can impact vehicle sizing. The use of empirically corrected ad hoc inflow models is not often satisfactory. In this study, momentum theory is combined with a simple vortex theory in the development of a combined momentum theory and simple vortex theory (CMTSVT) based inflow model that is readily applicable to generic multirotor configurations. The developed model is validated against some multirotor inflow models and experimental data from the literature through comparisons of inflow predictions and performance predictions for different dual-rotor configurations. Further, inflow predictions using the proposed inflow model for a partially overlapping quad-rotor configuration are presented to illustrate the significance of rotor-on-rotor flow interactions in multirotor vehicle configurations.

Discrete Vortex Cylinders Method for Calculating the Helicopter Rotor-Induced Velocity

A new vortex model of a helicopter rotor with an infinite number of blades is proposed, based on Shaidakov’s linear disk theory for calculating inductive speeds at any point in space in the helicopter area. It is proposed to consider the helicopter rotor and the behind vortex column as a system of discrete vortex cylinders. This allows building a matrix of the influence of the vortex system under consideration on any set of points, for example, the calculated points on the rotor itself, on the tail rotor, etc. The model allows calculating inductive velocities at any point near the helicopter using matrix multiplication operation. It is shown that the classical results for the momentum theory remain constant even in the discrete simulation of the helicopter rotor vortex system. The structure of the air flow behind the rotor and the simulation results obtained by the proposed method is compared with the structure of the tip vortices and the results of the blade vortex theory. In addition, the experimental data were compared with the simulation results to verify the correctness of the model under real operating conditions by the helicopter trimming.

Helical vortices and wind turbine aerodynamics

All rotating blades shed helical vortices which have a significant effect on the velocity over the blades and the forces acting on them. Nevertheless, knowledge of vortex behavior is not used in blade element theory (BET), the most common method to calculate the thrust produced by propellers and the power by wind turbines. Helical vortices of constant pitch and radius are also of fundamental interest as one of only three geometries that do not deform under their “self-induced” motion. This aspect of vortex theory is reviewed historically and the relationship with the forces acting on submerged bodies briefly reviewed. The development of helical vortex theory (HVT) in the 20th century is then described. It is shown that HVT allows BET to be used for a number of important problems that cannot be analyzed by current versions of the theory.