Aerodynamic characteristics of propeller in non-axial flow

Flow on running propellers installed on aircraft in general case is not axial what results in off-axis forces and moments at the propeller. Lifting line method is applied for propeller blade model using set of discrete vortex filaments. Propeller wake defined by vortex sheet of discrete vortex filaments is modelled with application of free-wake method. Presented propeller model combines the blade and the wake model and with its low computational cost realization it is suitable for preliminary prediction of propeller contribution to the aircraft aerodynamic characteristics. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical study of helicopter blade–vortex mechanism of interaction using the potential flow theory

The blade–vortex interaction (BVI) phenomenon plays a key role in the rotorcraft aerodynamics. Numerical investigations of BVI using classical CFD approaches are computationally expensive. In the present research we propose a numerical approach, based on the potential flow theory, for the numerical investigation of helicopter blade–vortex mechanism of interaction. This approach overcomes the computational expenses posed by the CFD techniques. The influence of vertical miss distance, angle of attack, airfoil camber, and vortex strength on the helicopter blade–vortex mechanism of interaction is subject of investigation. The study reveals that the magnitude of the aerodynamic coefficients decreases with the increase of vertical miss distance and angle of attack, and the decrease of vortex strength and core size.     

开敞式索膜结构的气动失稳临界风速

考虑几何非线性的影响,利用无限薄的旋涡薄层模拟气流在结构表面形成的扰动,由非稳态Bernoulli方程和环量定理将空气压力表示成旋涡密度的函数;然后由涡格法结合耦合边界条件求出旋涡密度,根据系统的稳定性判据得到结构发散失稳临界风速的解析表达式．通过三维开敞式膜结构的计算分析,发现空间膜结构的曲率是影响结构气动失稳临界风速的主要因素．     

Dynamic properties of wing panels made of composite materials

The dynamic characteristics of an elastic wing panel made of composite material are investigated in relation to the transient processes in a gas flow. The problem is solved using the geometrically nonlinear equations of shallow orthotropic shells and the numerical methods of linearized nonsteady aerodynamics. The displacements are determined by a finite-difference method and the aerodynamic load intensity by means of a model of a thin lifting surface. The numerical results are presented in the form of graphs reflecting the laws of deformation of the middle surface of the panel and pressure distribution and their development with time. Curves characterizing the motion of individual points in relation to the parameters reflecting the anisotropic properties of the panel are also constructed.Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 662–669, July–August, 1974.     

Numerical simulation of laminar flow past a circular cylinder

The present paper focuses on the analysis of two- and three-dimensional flow past a circular cylinder in different laminar flow regimes. In this simulation, an implicit pressure-based finite volume method is used for time-accurate computation of incompressible flow using second order accurate convective flux discretisation schemes. The computation results are validated against measurement data for mean surface pressure, skin friction coefficients, the size and strength of the recirculating wake for the steady flow regime and also for the Strouhal frequency of vortex shedding and the mean and RMS amplitude of the fluctuating aerodynamic coefficients for the unsteady periodic flow regime. The complex three dimensional flow structure of the cylinder wake is also reasonably captured by the present prediction procedure.     

Instability of a Vortex Sheet Leaving a Semi-Infinite Plate

The growth of undulations along an infinite vortex sheet is a classical problem of stability theory. Here we modify that problem by including the effects of a boundary: the vortex sheet is assumed to leave a rigid semi-infinite plate and to undergo spatially growing undulations downstream. The usual solution for a doubly infinite sheet is corrected by the Wiener-Hopf technique to account for the presence of the plate. The correction depends sensitively on whether a Kutta condition is enforced at the trailing edge. Two Kutta conditions, called rectified and full, are suggested to apply depending on conditions in the unperturbed flow. In either case, the correction due to the plate becomes negligible half a wavelength downstream from the trailing edge.     

Analytical modelling for a three-dimensional hydrofoil with winglets operating beneath a free surface

The current study focuses on establishing a theoretical lifting surface model for predicting the hydrodynamic loads acting on the three-dimensional hydrofoil with winglets, which is considerably influenced by the proximity to the free surface through finding the three-dimensional Green’s function for the planar and vertical horseshoe vortices operating below a free surface. The hydrofoil surface is decomposed into a finite number of elements along the span direction and the chord directions, each of which can then be represented by a horseshoe vortex. The linearized free surface boundary condition is applied to analyze the influence of the free surface on the hydrofoil as well as the winglets. The thickness problem is considered using the source distribution among the hydrofoil and winglets surfaces and the analytical Green’s function that satisfies the linearized free surface boundary condition is used. As a sample application, numerical examples were conducted to show the performance of the hydrodynamic characteristics for the hydrofoil with winglets as a function of the Froude number. It was concluded that there are significant efficiency benefits from using winglets inside the free surface proximity effect. These results are substantiated by the comparison with the available published data.     

Comparison of analytical and numerical solution for optimal vortex diffuser design

The contribution deals with optimization of wing tip devices, so called vortex diffusers. A comparison is given between an analytical approach for obtaining the optimal circulation loading and the results of a numerical investigation using a lifting line method. The purpose of most wing tip devices is to reduce the induced drag of the main wing by converting vortex energy into thrust. In order to achieve an optimal design, a variational formulation originally proposed by Betz and Prandtl for air screws is applied to the circulation distribution of the diffuser blades. In extension to the inviscid formulation, a viscous correction is applied in order to account for frictional forces. In an effort to validate the analytical results, a comparison is given with numerical solutions from a lifting line method. The loading of the diffuser blades is parametrized and optimized with respect to resulting thrust by use of a quasi-Newton gradient method. Comparison shows that, knowing the velocity distribution in the near wake of the wing, considerable decrease of induced drag may be achieved making use of vortex diffusers. Although actual circulation loading may differ between the analytical and numerical estimation, resulting thrust agrees within a few percent. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical simulation of unsteady vortex structures in near wake of poorly streamlined bodies on multiprocessor computer system

On the basis of the conservative difference method, spatially unsteady flows near complexly shaped objects are studied. The mathematical model is based on the inviscid gas model. For subsonic, transonic, and supersonic regimes, the nonstationary aerodynamics of various aerospace objects is examined. The three-dimensional structure of the unsteady vortex near wake and its influence on the basic aerodynamic characteristics of aerial vehicles are visualized. The numerical simulation is performed using parallel algorithms on supercomputers of cluster architecture.     

A further note on the force discrepancy for wing theory in Euler flow

Uniform steady potential flow past a wing aligned at a small angle to the flow direction is considered. The standard approach is to model this by a vortex sheet, approximated by a finite distribution of horseshoe vortices. In the limit as the span of the horseshoe vortices tends to zero, an integral distribution of infinitesimal horseshoe vortices over the vortex sheet is obtained. The contribution to the force on the wing due to the presence of one of the infinitesimal horseshoe vortices in the distribution is focused upon. Most of the algebra in the force calculation is evaluated using Maple software and is given in the appendices. As in the two previous papers by the authors on wing theory in Euler flow [E Chadwick, A slender-wing theory in potential flow, Proc. R. Soc. A461 (2005) 415–432, and E Chadwick and A Hatam, The physical interpretation of the lift discrepancy in Lanchester-Prandtl lifting wing theory for Euler flow, leading to the proposal of an alternative model in Oseen flow, Proc. R. Soc. A463 (2007) 2257–2275], it is shown that the normal force is half that expected. In this further note, in addition it is demonstrated that the axial force is infinite. The implications and reasons for these results are discussed.     

A modified discrete-vortex method algorithm with shedding criterion for aerodynamic coefficients prediction at high angle of attack

Low-order methods require less computing power than classical computational fluid dynamics and can be implemented on a laptop computer, which is needed for engineering tasks. Discrete vortex methods are such low order methods that can describe the unsteady separated flow around an airfoil. After a presentation of the leading edge suction parameter discrete vortex method, a modified algorithm is proposed, in order to reduce the computing cost, and compared with the previous one. Several reference unsteady airfoil motions are discussed in terms of gain in the computation time with comparisons between the previous scheme and the present one. The accuracy of the new method is demonstrated through aerodynamic coefficients. The application of the present discrete vortex method to a transient pitching motion of an airfoil is also presented, in order to understand the leading edge vortex formation, and its implication in terms of lift and drag coefficients. The method is not limited to unsteady or transient motions but can also simulate the flow around a constant angle of attack airfoil. In that case, an original method of fast summation of the vortices located far away from the airfoil, allows a linear dependence of the computation time versus the number of vortices shed, which is a great improvement over the quadratic dependence observed in the classical discrete vortex methods. The development of the aerodynamic coefficients with angle of attack, from values ranging between −10° and 90°, is obtained for a purely two-dimensional flow. In particular, the shape of the lift coefficient of the airfoil in the fully detached flow region is established. Comparisons with relevant experimental or computational fluid dynamics data are discussed in order to grasp the influence of upstream turbulence level and three-dimensional effects in the measured data in the fully detached flow region.     

Turbulent Flow with Embedded Vortical Structures Induced by Vortex Generators in a Cascade

Presented work is the next step after several experimental examinations of vortex generator influence on a flow separation occurring on a model of the NACA 63A421 airfoil with deflected simple flap. In this stage of research the vortices produced by vortex generators (VGs) were studied using Particle Image Velocimetry technique (PIV) and numerical simulations. Vane type VGs with two spacings among VGs pairs in straight channel with turbulent flow were tested. The average velocity flow field, peak of vorticity and circulation decay downstream of VGs were evaluated. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Approximations of a Ginzburg-Landau model for superconducting hollow spheres based on spherical centroidal Voronoi tessellations

In this paper the numerical approximations of the Ginzburg- Landau model for a superconducting hollow spheres are constructed using a gauge invariant discretization on spherical centroidal Voronoi tessellations. A reduced model equation is used on the surface of the sphere which is valid in the thin spherical shell limit. We present the numerical algorithms and their theoretical convergence as well as interesting numerical results on the vortex configurations. Properties of the spherical centroidal Voronoi tessellations are also utilized to provide a high resolution scheme for computing the supercurrent and the induced magnetic field.

     

Integral representation of velocity in a flow with separation simulated by a vortex sheet

The goal of this paper is to present a new integral operator that defines the velocity of a streamline flow in terms of the intensity of a free vortex sheet. This operator is important for numerical simulation of flows.     

The Effect of Surface Tension on the Moore Singularity of Vortex Sheet Dynamics

We investigate the regularization of Moore’s singularities by surface tension in the evolution of vortex sheets and its dependence on the Weber number (which is inversely proportional to surface tension coefficient). The curvature of the vortex sheet, instead of blowing up at finite time t ₀, grows exponentially fast up to a O(We) limiting value close to t ₀. We describe the analytic structure of the solutions and their self-similar features and characteristic scales in terms of the Weber number in a O(We⁻¹) neighborhood of the time at which, in absence of surface tension effects, Moore’s singularity would appear. Our arguments rely on asymptotic techniques and are supported by full numerical simulations of the PDEs describing the evolution of vortex sheets.     

An Improved Vortex Lattice Method for Nonstationary Problems

The vortex lattice method is improved for modeling nonlinear highly nonstationary processes appearing in an interaction of bodies that undergo an irregular motion in a proximity of solid boundaries with large-scale vortex structures. We show that keeping the condition of freezing the vortex buildups in the medium leads, in the vortex lattice method, to eliminating the arbitrariness in the calculated time step, singularity radius, and the buffer-zone radius.For the ensemble of discrete vortices that model the surface of tangential discontinuity of the velocity, we propose an economical method for solving the Cauchy problem. The method decreases the discretization error related to the replacement of this surface with a system of discrete vortices.A test for the improved vortex lattice method has been conducted for a nonstationary nonlinear problem on nonharmonic angular oscillations of a wing in a stationary medium near a solid surface in the case where there is no gap between the wing and the surface.By using the improved vortex lattice method, one succeeded, for the first time, in obtaining a solution of a problem of this type that converges from the numerical point of view. A comparison of the obtained results with known experimental data shows a good agreement.     

Computational fluid dynamics based dynamic modeling of parafoil system

The calculation of aerodynamic coefficients has been one of the key issues when modeling parafoil systems, that directly affects model precision. This study relates to investigate limitations of traditional calculation methods. As a result, we achieve aerodynamic parameters of a parafoil using computational fluid dynamics simulations. Also we employ the least square method as a tool for the rapid identification of deflection factors of aerodynamic coefficients. The estimated aerodynamic coefficients of the system were incorporated into the dynamic equations of the parafoil to implement a six degree of freedom model of a parafoil system according to the Kirchhoff equations. Numerical results generated by simulation and airdrop testing demonstrate that the established model can accurately describe the flight characteristics of the parafoil system.     

Nonlinear Dynamics of Non-uniform Current-Vortex Sheets in Magnetohydrodynamic Flows

A theoretical model is proposed to describe fully nonlinear dynamics of interfaces in two-dimensional MHD flows based on an idea of non-uniform current-vortex sheet. Application of vortex sheet model to MHD flows has a crucial difficulty because of non-conservative nature of magnetic tension. However, it is shown that when a magnetic field is initially parallel to an interface, the concept of vortex sheet can be extended to MHD flows (current-vortex sheet). Two-dimensional MHD flows are then described only by a one-dimensional Lagrange parameter on the sheet. It is also shown that bulk magnetic field and velocity can be calculated from their values on the sheet. The model is tested by MHD Richtmyer–Meshkov instability with sinusoidal vortex sheet strength. Two-dimensional ideal MHD simulations show that the nonlinear dynamics of a shocked interface with density stratification agrees fairly well with that for its corresponding potential flow. Numerical solutions of the model reproduce properly the results of the ideal MHD simulations, such as the roll-up of spike, exponential growth of magnetic field, and its saturation and oscillation. Nonlinear evolution of the interface is found to be determined by the Alfvén and Atwood numbers. Some of their dependence on the sheet dynamics and magnetic field amplification are discussed. It is shown by the model that the magnetic field amplification occurs locally associated with the nonlinear dynamics of the current-vortex sheet. We expect that our model can be applicable to a wide variety of MHD shear flows.     

Unsteady Flow and its Influence to Aerodynamic and Aeroacoustic of VAWT's

A study is reported of the influence of unsteady flow on the aerodynamics and aeroacoustics of vertical axis wind turbines by numerical simulation. The combination of aerodynamic predictions with a discrete vortex method and aeroacoustic predictions based on Ffowcs Williams-Hawkings equation is used to achieve this goal. The numerical results show that unsteady flow of the turbine has a significant influence on the turbine aerodynamics and can lead to a decrease in generated noise as compared to the conventional horizontal axis wind turbine at the similar aerodynamic performance. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear dynamics of a simplified engine-propeller system

This paper presents a procedure for studying dynamical behaviors of a simplified engine-propeller dynamical system consisting of a number of bodies of plane motions. The equation of motion of the complex system is obtained using the Lagrange equation and solved numerically using the 4th order Runge–Kutta method. Various simulations were performed to investigate the transient and steady state behaviors of the multiple body system while taking into consideration the engine pressure pulsations, nonlinear inertia of moving bodies, and nonlinear aerodynamic load. Sub-harmonics and super harmonics in the steady state responses for different power and propeller pitch settings are obtained using the fast Fourier transform. Numerical simulations indicate that the 1.5 order is the dominant order of harmonics in the steady state oscillatory motion of the crankshaft. The findings and procedure presented in the paper are useful to the aerospace industry in certifying reciprocating engines and propellers. The crankshaft oscillatory velocities obtained from the simplified rigid body model are in good agreement with the experimental data for a SAITO-450 engine and a SOLO propeller at a 6″ pitch setting.