Determination of the aerodynamic characteristics of the tiltrotor with the wingtip-mounted coaxial rotors

The article describes the study of rotor-to-wing aerodynamic interaction for the wingtip-mounted coaxial rotors configuration of the tiltrotor aircraft. The influence of the rotor slipstreams on lift-to-drag ratio characteristic was determined. Obtained results were compared with similar characteristics of the equivalent in thrust conventional single rotor slipstreams impact. Using the computational aerodynamics methods (panel-vortex method) the flow around the tiltrotor model with the wingtip-mounted single and coaxial rotors has been simulated. A study of the basic model configuration with conventional single rotors, based on the technical characteristics of the AgustaWestland AW609 tiltrotor, was conducted. Further researches were conducted for a modified model where single rotors were replaced with equivalent in thrust coaxial rotors. The influence of the rotor slipstreams on the aerodynamic characteristics of the model for both directions of rotors rotation in coaxial combination is considered. Also, the dependence of the maximum lift-to-drag characteristic due to the coaxial rotor diameters change has been determined. The results show that the coaxial rotor slipstreams-to-wing aerodynamic interaction effect is the similar to the effect of conventional single rotor, but less intensive. Comparison of the results showed that a tiltrotor equipped with wingtip-mounted single rotors has approximately 20% greater maximum lift-to-drag characteristic than one equipped with coaxial rotors with the same thrust. However, the use of coaxial rotors allows getting higher maximum speed, when conventional single rotors lose the efficiency significantly. Therefore, it is advisable to conduct further research for the possibility of using coaxial rotors for tiltrotor aircrafts. The research results are presented in graphical form. The obtained data provides a basis for further studies of the described problem, and also will be useful for new tiltrotor design works.

McKean–Vlasov type stochastic differential equations arising from the random vortex method

We study a class of McKean–Vlasov type stochastic differential equations (SDEs) which arise from the random vortex dynamics and other physics models. By introducing a new approach we resolve the existence and uniqueness of both the weak and strong solutions for the McKean–Vlasov stochastic differential equations whose coefficients are defined in terms of singular integral kernels such as the Biot–Savart kernel. These SDEs which involve the distributions of solutions are in general not Lipschitz continuous with respect to the usual distances on the space of distributions such as the Wasserstein distance. Therefore there is an obstacle in adapting the ordinary SDE method for the study of this class of SDEs, and the conventional methods seem not appropriate for dealing with such distributional SDEs which appear in applications such as fluid mechanics.

Vortex Trapping Cavity on Airfoil: High-Order Penalized Vortex Method Numerical Simulation and Water Tunnel Experimental Investigation

This paper presents a two-dimensional implementation of the high-order penalized vortex in cell method applied to solve the flow past an airfoil with a vortex trapping cavity operating under moderate Reynolds number. The purpose of this article is to investigate the fundamentals of the vortex trapping cavity. The first part of the paper treats with the numerical implementation of the method and high-order schemes incorporated into the algorithm. Poisson, stream-velocity, advection, and diffusion equations were solved. The derivation, finite difference formulation, Lagrangian particle remeshing procedure, and accuracy tests were shown. Flow past complex geometries was possible through the penalization method. A procedure description for preparing geometry data was included. The entire methodology was tested with flow past impulsively started cylinder for three Reynolds numbers: 550, 3000, 9500. Drag coefficient, streamlines, and vorticity contours were checked against results obtained by other authors. Afterwards, simulations and experimental results are presented for a standard airfoil and those equipped with a trapping vortex cavity. Airfoil with an optimized cavity shape was tested under three angles of attack: 3°, 6°, 9°. The Reynolds number is equal to Re = 2 × 104. Apart from performing flow analysis, drag and lift coefficients for different shapes were measured to assess the effect of vortex trapping cavity on aerodynamic performance. Flow patterns were compared against ultraviolet dye visualizations obtained from the water tunnel experiment.

A STUDY ON VISCOUS ROLL DAMPING OF A BOX-SHAPED VESSEL IN THE FREQUENCY DOMAIN USING THE DISCRETE VORTEX METHOD

This paper presents a study on viscous roll damping of a floating box-shaped vessel in the frequency domain. The application of the discrete vortex method (DVM) for calculation of the viscous roll damping in regular seas has been validated by model tests. Equivalent roll RAOs associated with a range of regular wave amplitudes are calculated to assess behaviour of the viscous roll damping in relation to incident wave amplitude linearisation. A model test is conducted using the model test facilities of the Marine Hydrodynamics Laboratory at Newcastle University to validate the applicability of the DVM in calculating the roll RAO in regular waves and to study the application of this method to irregular waves. Results of these model tests are presented in this paper.

Conformal Mapping-Based Discrete Vortex Method for Simulating 2-D Flows around Arbitrary Cylinders

A novel technique based on conformal mapping and the circle theorem has been developed to tackle the boundary penetration issue, in which vortex blobs leak into structures in two-dimensional discrete vortex simulations, as an alternative to the traditional method in which the blobs crossing the boundary are simply removed from the fluid field or reflected back to their mirror-image positions outside the structure. The present algorithm introduces an identical vortex blob outside the body using the mapping method to avoid circulation loss caused by the vortex blob penetrating the body. This can keep the body surface streamlined and guarantees that the total circulation will be constant at any time step. The model was validated using cases of viscous incompressible flow passing elliptic cylinders with various thickness-to-chord ratios at Reynolds numbers greater than Re = 1 × 105. The force and velocity fields revealed that this boundary scheme converged, and the resultant time-averaged surface pressure distributions were all in excellent agreement with wind tunnel tests. Furthermore, a flow around a symmetrical Joukowski foil at Reynolds number Re = 4.62 × 104, without considering the trailing cusp, was investigated, and a close agreement with the experimental data was obtained.

Mathematical Modelling of the Elliptical Vortex Ring in a Viscous Fluid with the Vortex Filament Method

The article deals with modelling an elliptical vortex ring in a viscous fluid using the Lagrangian vortex filament method. The novelty is that earlier only inviscid flows restricted vortex filament method application. The proposed viscosity model uses an analogue of the diffusion rate method, which is widely applied to simulate plane-parallel and axisymmetric flows of viscous fluid. A transfer of the formula of a diffusion rate from two-dimensional flows to the model of spatial vortex filament is due to assumption that swirling of vortex lines (helicity of vorticity) is unavailable. Despite the laxity of the diffusion rate model for general spatial flows, its application enables taking into account the effect of viscous diffusion of vorticity, which provides expansion of vortex tubes in space. The paper formulates the vortex filament method in which the filaments are broken into the vortex segments. Such discretization enables turning from the equation of vorticity evolution in partial derivatives to a system of ordinary differential equations with respect to the parameters of the segments. Formulas to calculate a filament system-induced flow rate as well as formulas to perform approximate calculation of an analogue of the diffusion rate are given.The objective is to propose the viscosity model as an application to the vortex filament method by the example of modelling the evolution of an elliptical vortex ring in viscous fluid. The calculation results obtained by the vortex method are compared with the existing experiment and with the calculation performed by the grid method in the OpenFOAM package. A feature of the problem is that there are zones of nonzero helicity of vorticity where the proposed model of viscosity, strictly speaking, is not correct. It is shown that the results of calculations are in good agreement with each other and are in complete agreement with experiment. This allows saying that the effects of swirling vortex lines do not significantly affect the results of modelling a specific example of the spatial flow of viscous fluid by the proposed modification of the vortex filament method.

Comparison between Vortex-In-Cell and Vortex Particle Methods on Two-Dimensional Problem

This research is concerned with the two-dimensional vortex method (VM) solvers. We develop and investigate the performance of the Vortex-In-Cell (VIC) and Vortex Particle Method (VPM) which are well known as the VM’s family members. The advantage of these both methods are that we can accelerate velocity computation procedure, an N-body problem in numerical methods, by using Fast Fourier Transform (FFT) and Fast Multipole Method (FMM), respectively. In addition, the viscous calculation process in VPM can be accelerated by using a scheme of Nearest Neighbor Particle Searching (NNPS) algorithms. Moreover, the no-through boundary condition treatment issue can be easily handled by using an immersed boundary condition for both methods. The accuracy and numerical cost of both numerical methods will be examined by simulating flow over an Impulsively Started Circular Cylinder and comparisons

Lagrangian Vortex Computations of a Four Tidal Turbine Array: An Example Based on the NEPTHYD Layout in the Alderney Race

This study investigates the wake interaction of four full-scale three-bladed tidal turbines with different ambient turbulence conditions, in straight and yawed flows. A three-dimensional unsteady Lagrangian Vortex Blob software is used for the numerical simulations of the turbines’ wakes. In order to model the ambient turbulence in the Lagrangian Vortex Method formalism, a Synthetic Eddy Method is used. With this method, turbulent structures are added in the computational domain to generate a velocity field which statistically reproduces any ambient turbulence intensity and integral length scale. The influence of the size of the structures and their density (within the study volume) on the wake of a single turbine is studied. Good agreement is obtained between numerical and experimental results for a high turbulence intensity but too many structures can increase the numerical dissipation and reduce the wake extension. Numerical simulations of the four turbine array with the layout initially proposed for the NEPTHYD pilot farm are then presented. Two ambient turbulence intensities encountered in the Alderney Race and two integral length scales are tested with a straight flow. Finally, the wakes obtained for yawed flows with different angles are presented, highlighting turbine interactions.