CONVERGENCE OF THE POINT VORTEX METHODS FOR EULER EQUATION ON HALF PLANE

In this paper, we study the point vortex method for 2-D Euler equation of incompressible how on the half plane, and the explicit Euler's scheme is considered with the reflection method handling the boundary condition. Optimal error bounds for this fully discrete scheme are obtained.

CONVERGENCE OF VORTEX METHODS FOR 3-D EULER EQUATIONS

Presents a study on the convergence of vortex methods for the three-dimensional Euler equations in bounded domains. Related studies on the convergence of vortex methods; Formulation of vortex methods; Convergence for initial-boundary value problems.

Review of vortex methods for rotor aerodynamics and wake dynamics

Electric vertical take-off and landing(eVTOL)aircraft with multiple lifting rotors or prop-rotors have received significant attention in recent years due to their great potential for next-generation urban air mobility(UAM).Numerical models have been developed and validated as predictive tools to analyze rotor aerodynamics and wake dynamics.Among various numerical approaches,the vortex method is one of the most suitable because it can provide accurate solutions with an affordable computational cost and can represent vorticity fields downstream without numerical dissipation error.This paper presents a brief review of the progress of vortex methods,along with their principles,advantages,and shortcomings.Applications of the vortex methods for modeling the rotor aerodynamics and wake dynamics are also described.However,the vortex methods suffer from the problem that it cannot deal with the nonlinear aerodynamic characteristics associated with the viscous effects and the flow behaviors in the post-stall regime.To overcome the intrinsic drawbacks of the vortex methods,recent progress in a numerical method proposed by the authors is introduced,and model validation against experimental data is discussed in detail.The validation works show that nonlinear vortex lattice method(NVLM)coupled with vortex particle method(VPM)can predict the unsteady aerodynamic forces and complex evolution of the rotor wake.

Recent development of vortex method in incompressible viscous bluff body flows

Vortex methods have been alternative tools of finite element and finite difference methods for several decades. This paper presents a brief review of vortex method development in the last decades and introduces efficient vortex methods developed for high Reynolds number bluff body flows and suitable for running on parallel computer architectures. Included in this study are particle strength exchange methods, core-spreading method, deterministic particle method and hybrid vortex methods. Combined with conservative methods, vortex methods can comprise the most available tools for simulations of three-dimensional complex bluff body flows at high Reynolds numbers.

Numerical simulation of unsteady interaction of centrifugal impeller with its diffuser using Lagrangian discrete vortex method

In this study, an advanced Lagrangian vortex- boundary element method is applied to simulate the unsteady impeller-diffuser interactions in a diffuser pump not only for design but also for off-design considerations. In velocity calculations based on the Biot-Savart law we do not have to grid large portions of the flow field and the calculation points are concentrated in the regions where vorticity is present. Lagrangian representation of the evolving vorticity field is well suited to moving boundaries. An integral pressure equation shows that the pressure distribution can be estimated directly from the instantaneous velocity and vorticity field. The numerical results are compared with the experimental data and the comparisons show that the method used in this study can provide us insight into the complicated unsteady impeller-diffuser interaction phenomena in a diffuser pump.

Analysis of Influencing Factors on Lift Coefficients of Autonomous Sailboat Double Sail Propulsion System Based on Vortex Panel Method

Sail is the core part of autonomous sailboat and wing sail is a new type of sail. Wing sail generates not only propulsion but also lateral force and heeling moment. The latter two will affect the navigation status and bring resistance. Double sail can effectively reduce the center of wind pressure and heeling moment. In order to study the effect of distance between two sails, airfoil and attack angle on the total lift coefficient of double sail propulsion system, pressure coefficient distribution and lift coefficient calculation model have been established based on vortex panel method. By using the basic finite solution, the fluid dynamic forces on the two-dimensional sails are computed.The results show that, the distance in the range of 0 to 1 time chord length, when using the same airfoil in the fore and aft sail, the total lift coefficient of the double sail increases with the increase of distance, finally reaches a stable value in the range of one to three times chord length. Lift coefficients of thicker airfoils are more sensitive to the change of distance. The thicker the airfoil, the longer distance is required of the total lift coefficient toward stable.When different airfoils are adopted in fore and aft sail, the total lift coefficient increases with the increase of the thickness of aft sail. The smaller the thickness difference is, the more sensitive to the distance change the lift coefficient is. The thinner the fore sail is, the lower the influence will be on the lift coefficient of aft sail.

A NUMERICAL STUDY OF THE VORTEX MOTION IN OSCILLATING FLOW AROUND A CIRCULAR CYLINDER AT LOW AND MIDDLE Kc NUMBERS

A new hybrid model, which is based on domain decomposition and proposed by the authors is used for calculating the flow around a circular cylinder at low and middle Keulegan-Carpenter numbers (Kc=2～18)respectively.The vortex motion patterns in asymmetric regime,single pair(or transverse)regime and double pair(or diagonal)regime are successfully simulated.The calculated drag and inertial force coefficients are in better agreement with experimental data than other recent computational results.

NUMERICAL STUDY OF PARTICLE DISTRIBUTION IN WAKE OF LIQUID-PARTICLE FLOWS PAST A CIRCULAR CYLINDER USING DISCRETE VORTEX METHOD

Particle-laden water flows past a circular cylinder were numerically investigated. The discrete vortex method （DVM） was employed to evaluate the unsteady water flow fields and a Lagrangian approach was applied for tracking individual solid particles. A dispersion function was defined to represent the dispersion scale of the particle. The wake vortex patterns, the distributions and the time series of dispersion functions of particles with different Stokes numbers were obtained. Numerical results show that the particle distribution in the wake of the circular cylinder is closely related to the particle＇s Stokes number and the structure of wake vortices： （1） the intermediate sized particles with Stokes numbers, St, of 0.25, 1.0 and 4.0 can not enter the vortex cores and concen- trate near the peripheries of the vortex structures, （2） in the circular cylinder wake, the dispersion intensity of particles decreases as St is increased from 0.25 to 4.0.

Vortex interactions between forewing and hindwing of dragonfly in hovering flight

Two tandem flapping wings in viscous flow were modeled by using the immersed boundary method for exploration of the aerodynamics of dragonfly in hovering flight. Interaction between the forewing and the hindwing, and its effect on the lift forces, were examined by varying the phase difference of the wing motions and the inter-distance of the two wings. Two vortex interaction modes were identified at different phase differences and inter-distances, which give rise to significant variations of the lift forces. The first interaction mode increases the lift of the forewing and the second one enhances the lift of the hindwing. The two modes occur at different time during a flapping period and have different influence on the lift ofwings as the ohase difference varies.

Simulation on motion of particles in vortex merging process

In a two-phase flow, the vortex merging influences both the flow evolution and the particle motion. With the blobs-splitting-and-merging scheme, the vortex merging is calculated by a corrected core spreading vortex method （CCSVM）. The particle motion in the vortex merging process is calculated according to the particle kinetic model. The results indicate that the particle traces are spiral lines with the same rotation direction as the spinning vortex. The center of the particle group is in agreement with that of the merged vortex. The merging time is determined by the circulation and the initial ratio of the vortex radius and the vortex center distance. Under a certain initial condition, a stretched particle trail is generated, which is determined by the viscosity, the relative position between the particles and the vortex, and the asymmetrical circulation of the two merging vortices.

WAKE GEOMETRY CALCULATIONS FOR TILT-ROTOR USING VISCOUS VORTEX METHOD

A tilt-rotor unsteady flow analytical method has been developed based upon viscous vortex-particle method.In this method,the vorticity field is divided into small assembled vortex particles.Vortex motion and diffusion are obtained by solving the velocity-vorticity-formed incompressible Navier-Stokes equations using agrid-free Lagrangian simulation method.Generation of the newly vortex particles is calculated by using the Weissinger-L lifting surface model.Furthermore,in order to significantly improve computational efficiency,a fast multiple method(FMM)is introduced into the calculation of induced velocity and its gradient.Finally,the joint vertical experimental(JVX)tilt-rotor is taken as numerical examples to analyze.The wake geometry and downwash are investigated for both hover and airplane modes.The proposed method for tilt-rotor flow analysis is verified by comparing its results with those available measured data.Comparison indicates that the current method can accurately capture the complicated tilt-rotor wake variation and be suitable for aerodynamic interaction simulation in complex environments.Additionally,the aerodynamic interactional characteristics of dual-rotor wake are discussed in different rotor distance.Results show that there are significant differences on interactional characteristics between hover mode and airplane mode.

Design and experimental test of an optical vortex coronagraph

Using an optical vortex coronagraph （OVC） is one of the most promising techniques for di- rectly imaging exoplanets because of its small inner working angle and high throughput. This paper presents the design and laboratory demonstration performance of an OVC based on liquid crystal polymers （LCPs） at 633 nm and 1520 nm. The OVC can deliver good performance in laboratory tests and achieve a contrast of 10-6 at an angular distance of 3A/D, which can be implemented for imaging young giant exoplanets in combination with extreme adaptive optics.

A DETERMINISTIC VORTEX METHOD FOR SOLVING THE NAVIER-STOKES EQUATIONS

In this paper, a new 2-D vortex method is developed, which treats the vorticity diffusion in a deterministical way. The Laplacian operator, which describes vorticity diffusion, is approximated by a contour integral. The numerical results of two model problems show that this method has a good accuracy. A primary error estimation is given, and the self-adaptive vortex blob and the boundary conditions are discussed.

ON THE FORMATION OF VORTEX RINGS AND PAIRS

The axisymmetric vortex sheet model developed by Nitsche and Krasny had been extended to study the formation of vortex rings (pairs) at the edge of circular (2D) tube and opening. Computations based on this model were in good agreement with the experiments (Didden (1979) for circular tube and Auerbach (1987) for 2D tube and opening). Using this new model, evidences are provided to show that the main failure of the similarity theory (the false prediction of axial trajectory of vortex ring) is due to its ignorance of the self-induced ring velocity (mutual induction for vortex pair). The Glezer (1988)'s summary on the influence of piston speed upon the shedding circulation was also discussed, and finally the variation of core distribution of vortex ring with turning angle and piston speed was given. (Edited author abstract) 22 Refs.

IMPROVED UVLM FOR FLAPPING-WING AERODYNAMICS COMPUTATION

To calculate the aerodynamics of flapping-wing micro air vehicle（MAV） with the high efficiency and the engineering-oriented accuracy,an improved unsteady vortex lattice method （UVLM） for MAV is proposed. The method considers the influence of instantaneous wing deforming in flapping,as well as the induced drag,additionally models the stretching and the dissipation of vortex rings,and can present the aerodynamics status on the wing surface. An implementation of the method is developed. Moreover,the results and the efficiency of the proposed method are verified by CFD methods. Considering the less time cost of UVLM,for application of UVLM in the MAV optimization,the influence of wake vortex ignoring time saving and precision is studied. Results show that saving in CPU time with wake vortex ignoring the appropriate distance is considerable while the precision is not significantly reduced. It indicates the potential value of UVLM in the optimization of MAV design.

The Full Non‑linear Vortex Tube‑Vorton Method: the pre‑stall condition

The present hybrid vortex tube-vorton method is based entirely on the Full Multi-wake Vortex Lattice Method(FMVLM)concepts,which means detaching vorticity with pre-cise vortex strength and orientation along all separation lines between each discretized element of a shell-body,including all external edges.Since the classic Vortex Particle Method(VPM)is unstable by itself because it does not conserve the total amount of circulation as time evolves(Kelvin’s circulation theorem),an isolated Vortex(regular-ized)Filament Method(VFM)approach is implemented to obtain advection of vorti-city,while the induced velocity field is obtained through its corresponding full vorton cloud.Further,a novel vortex squeezing/stretching scheme for such a vortex cylinder-sphere approach is proposed based on variation in time for vortex volumes in order to precisely(zero residual)conserve both circulation and vorticity at each time step(for each detached vortex element),while the viscous effect can be accounted for via the Core Spreading Method(CSM).

Influence of Autonomous Sailboat Dual-Wing Sail Interaction on Lift Coefficients

To analyze the influence of the chord length ratio and angle of attack on lift coefficients and explore the interaction mechanism between the two,we established a calculation model of the pressure distribution coefficient on the airfoil surface and lift coefficient of a dual-wing sail on the basis of the vortex panel method.Computational fluid dynamics was used in auxiliary calculation and analysis.Results revealed a reciprocal interference between the front-wing and rear-wing sails.The total lift coefficient of the dual-sail increased with an increase in the front sail chord length.The lift coefficient of the rear sail decreased with an increase in the front sail chord length or angle of attack.The front sail wake affected the pressure distribution on the upper and lower surfaces of the rear sail leading edge.

Vortex analysis of water flow through gates by different vortex identification methods

The pre-gate suction vortex,gate-bottom-edge transverse vortex,gate-slot vertical vortex,and downstream-of-gate return vortex are important factors affecting the flow instability of flat gates,which may lead to fatigue failure in severe cases.This study used the volume of fluid(VOF)model and large eddy simulation(LES)method to accurately capture the transient turbulence characteristics of flow under different water flow conditions and reveal the flow field and vortex structure.The Q—criterion,Omega(Ω)method,and latest third-generation Liutex vortex identification method were used to analyze and compare the pre-gate suction vortex,gate-slot vertical vortex,and downstream-of-gate return vortex,focusing on the ability of each vortex identification method to capture the flow field information and vortex characteristics.The results reveal that theΩmethod and Liutex method are less dependent on the threshold value,and the Liutex method captures a wide range of pre-gate vortices.Different flow conditions cause changes in the vortex structure of over-gate flow.When the relative opening of the gate is smaller,the intensity of the vortices in the flow field around the gate is greater,the return vortices downstream of the gate are more disordered,and the vortex changes are more violent,which in turn affects the efficient and stable operation of the gate.

Drag on a Cylinder with an Apple-Shaped Cross Section

The drag on a cylinder with an apple-shaped cross section was studied numerically in this paper. This cross section is adopted because the drag on an apple is known to be lower than that of a sphere. Since the hollows of an apple seem to be points of drag reduction, two-dimensional numerical simulations of cylinders with hollows of several shapes are carried out at a Reynolds number of 6.7 × 104 by using the vortex method to check their effects. The cylinder with hollows like those of a real apple attained a 13% reduction in drag compared with a circular cylinder. Other geometrical hollow-shapes, namely, V-shaped and U-shaped grooves, also reduced drag from the circular model, but these effects were less pronounced than those of the apple-shaped cross section. It was concluded that an apple-like hollows were effective for drag reduction of a cylin-der as well as a sphere.

FLOW STRUCTURES AND FORCE CHARACTERISTICS FOR FLAT PLATE IN OSCILLATORY FLOWS WITH K_c NUMBER FROM 2 TO 40 AND IN COMBINED FLOWS

The evolution of wake structures and variation of the forces on a flat plate in harmonic oscillatory and in-line combined flows are obtained numerically by improved discrete vortex method. For the oscillatory oncoming flow cases, when K_c number varies from 2 to 40, the vortex pattern changes from a 'harmonic wave' shaped (in a range of small K_c numbers) to a slight inclined 'harmonic wave' shaped (in a range of moderate K_c numbers), then to inclined vortex clusters with an angle of 50 ° to the oncoming flow direction (at K_c = 20), at last, as K_c number becomes large, the vortex pattern is like a normal Karman vortex street. The well predicted drag and inertia force coefficients are obtained, which are more close to the results of Keulegan & Carpenter's experiment as compared with previous vortex simulation by other au- thors. The existence of minimum point of inertia force coefficient C_m near K_c = 20 is also well predicted and this phenomenon can be interpreted according to the vortex structure. For steady-oscillatory in-line combined flow cases, the vortex modes behave like a vortex street, exhibit a 'longitudinal wave' structure, and a vor- tex cluster shape corresponding to the ratios of U_m to U_0 which are of O (10^(-1)), O(1)and O (10), respectively. The effect on the prediction of forces on the flat plate from the disturbance component in a combined flow has been demon- strated qualitatively. In addition to this, the lock-in phenomenon of vortex shedding has been checked.