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.

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.

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.

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.

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.

A numerical study on dispersion of particles from the surface of a circular cylinder placed in a gas flow using discrete vortex method

The dispersion of particles emitted from the surface of a circular cylinder placed in a gas flow at the Reynolds number of 200 000 is numerically investigated using the discrete vortex method coupled with a Lagrangian approach for solid particle tracking. The wake vortex patterns, the temporal-spatial distributions and trajectories as well as the dispersion functions for particles with various Stokes numbers（St） ranging from 0.001 to 1.0 are obtained. The numerical results reveal that：（1） Solid particles on the cylinder surface are picked up and then transported away from the cylinder by the wake vortex flow.（2） Solid particles emitted from the cylinder surface always follow the vortices in the cylinder wake, and the response of particles to wake vortices is directly related to their Stokes numbers（particles with St= 0.001, 0.0038, 0.01 can distribute both in the vortex core and around the vortex periphery, whereas those with St= 0.1, 1.0 can not enter the vortex core and congregate mainly around the vortex periphery）.（3） The particles move in rolling state in the wake region, and the dispersion intensity of particles in the lateral direction decreases remarkably as the Stokes number of particles is increased from 0.001 to 1.0.

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.

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.

Fast Vortex Method for the Simulation of Flows Inside Channels With and Without Injection

A fast vortex method is presented for the simulation of fluid flows inside two-dimensional channels,The first channel studied is formed by two parallel walls simulating the entrance length of a developing flow.The second channel is similar to the first one but with an injection of a secondary fluid through a slot on one of its walls,In both cases,results are presented for flows at low Reynolds numbers and for flows at a high Reynolds number The numerical method used is based on the Random Vortex Method and on the Vortex-In-Cell Algorithm.Physical analyses of the numerical results are also presented.mostly in application to film cooling.

A NOTE ON 3-D VORTEX METHODS

Vortex methods are frequently used for the numerical simulation of incompressible flow, especially for the flow with high Reynold’s number. Three dimensional vortex methods are a kind of large-scale computation, which can be further divided into some different approaches. However, whatever approach is applied, one step to determine the velocity field from the vorticity field is necessary, which is often carried out by

Two-Way Coupling Vortex Method and Its Application

Because of the success of the discrete vortex method for the simulation of large-scale vortex structure.many researchers extend this method to two-phase flow simulations,especially,to the simulation of particle dispersion in mixing layer,which is characterized by large-scale vortex structure,But the previous work is limited to one-way couplin,which neglects the effect of particles on fluid flow.In this paper a discrete vortex method involving two-way coupling for two-phase flows is frist proposed and then used in numerical simulation of two-dimensional gas-particle mixin layers The numerical results show that the introduction of particles into the mixing layer has significant effects on the creation,development and merging process of large-scale vortex structures.It makes the mean size of large-scale vortex stucture large and the distance needed for development of large-scale vortex sturcture shorter.

Numerical Investigation on Vortex-Induced Rotations of A Triangular Cylinder Using An Immersed Boundary Method

A numerical study of vortex-induced rotations(VIRs) of an equivalent triangular cylinder, which is free to rotate in the azimuthal direction in a uniform flow, is presented. Based on an immersed boundary method, the numerical model is established, and is verified through the benchmark problem of flow past a freely rotating rectangular body.The computation is performed for a fixed reduced mass of m~*=2.0 and the structural stiffness and damping ratio are set to zero. The effects of Reynolds number(Re=25-180) on the characteristics of VIR are studied. It is found that the dynamic response of the triangular cylinder exhibits four distinct modes with increasing Re: a rest position,periodic rotational oscillation, random rotation and autorotation. For the rotational oscillation mode, the cylinder undergoes a periodic vibration around an equilibrium position with one side facing the incoming flow. Since the rotation effect, the outset of vortex shedding from cylinder shifts to a much lower Reynolds number. Further increase in Re leads to 2 P and P+S vortex shedding modes besides the typical 2 S pattern. Our simulation results also elucidate that the free rotation significantly changes the drag and lift forces. Inspired by these facts, the effect of free rotation on flow-induced vibration of a triangular cylinder in the in-line and transverse directions is investigated. The results show that when the translational vibration is coupled with rotation, the triangular cylinder presents a galloping response instead of vortex-induced vibration(VIV).

Study on the Wake Shape behind a Wing in Ground Effect Using an Unsteady Discrete Vortex Panel Method

The unsteady evolution of trailing vortex sheets behind a wing in ground effect is simulated using an unsteady discrete vortex panel method. The ground effect is included by image method. The present method is validated by comparing the simulated wake roll-up shapes to published numerical results. When a wing is flying in a very close proximity to the ground, the optimal wing loading is parabolic rather than elliptic. Thus, a theoretical model of wing load distributions is suggested, and unsteady vortex evolutions behind lifting lines with both elliptic and parabolic load distributions are simulated for several ground heights. For a lifting line with elliptic and parabolic loading, the ground has the effect of moving the wingtip vortices laterally outward and suppressing the development of the vortex. When the wing is in a very close proximity to the ground, the types of wing load distributions does not affect much on the overall wake shapes, but parabolic load distributions make the wingtip vortices move more laterally outward than the elliptic load distributions.

Simulation of vortex shedding behind a bluff body flame stabilizer using a hybrid U-RANS/PDF method

The present study aims at the investigation of the effects of turbulence-chemistry interaction on combus- tion instabilities using a probability density function （PDF） method. The instantaneous quantities in the flow field were decomposed into the Favre-averaged variables and the stochastic fluctuations, which were calculated by unsteady Reynolds averaged Navier-Stokes （U-RANS） equations and the PDF model, respectively. A joint fluctuating velocity- frequency-composition PDF was used. The governing equa- tions are solved by a consistent hybrid finite volume/Monte- Carlo algorithm on triangular unstructured meshes. A non- reacting flow behind a triangular-shaped bluff body flame stabilizer in a rectilinear combustor was simulated by the present method. The results demonstrate the capability of the present method to capture the large-scale coherent struc- tures. The triple decomposition was performed, by divid- ing the coherent Favre-averaged velocity into time-averaged value and periodical coherent part, to analyze the coherent and incoherent contributions to Reynolds stresses. A sim- ple modification to the coefficients in the turbulent frequency model will help to improve the simulation results. Unsteady flow fields were depicted by streamlines and vorticity con- tours. Moreover, the association between turbulence produc- tion and vorticity saddle points is illustrated.

Direct Numerical Simulation of a Jet Issuing from Rectangular Nozzle by the Vortex in Cell Method

Direct numerical simulation of a jet issuing from a nozzle having a rectangular cross-section is conducted. The vortex in cell (VIC) method, of which computational accuracy was heightened by the authors in a prior study, is used for the DNS. The aspect ratio of the nozzle cross-section is 15, and the Reynolds number based on the shorter side length of the nozzle exit is 6700. The turbulence statics, such as the mean velocity and the turbulence intensity, are favorably compared with the experimentally measured results. The behavior of the large-scale eddies as well as the development of the turbulent flow is also confirmed to agree with the measurement. These indicate that the authors’ VIC method is successfully employed for the DNS of rectangular jet.

舰载直升机主动甲板着舰气动载荷特性

被动与主动流动控制可减小舰艇艉流强度,但直升机着舰甲板处仍存在明显回流现象,由此导致直升机气动载荷变化显著。提出了自动升降的舰艇主动甲板,建立基于格子玻尔兹曼方法 (LBM)的舰艇主动甲板流场分析方法,并结合单向耦合模型,嵌入旋翼黏性涡粒子法,研究直升机主动甲板着舰气动载荷特性。通过与SFS2舰艇流场试验、分离涡模拟(DES)方法、大涡模拟(LES)方法比较,验证了所建方法的准确性。随后研究主动甲板对舰艇流场和直升机着舰气动载荷的影响特性。结果表明:相比于标准SFS2舰艇,主动甲板有效抑制了直升机着舰甲板处回流,以及直升机旋翼拉力损失、滚转和俯仰力矩,最大降幅分别为21.6%、55.1%、74.6%。

红外照相机的热浮法湍射流流态转捩机理探究

为了探究湍射流3种流动状态的转捩机理,设计并搭建了可控式湍射流实验仪,利用热浮法红外拍摄了3种流态,实现了湍射流的可视化及精确测量。通过实验观察和分析了包络态中流体转捩速度与雷诺数的关系,确定了转捩临界雷诺数大小范围,并推导和验证了涡环态中推进力与流体流速的半经验公式;同时通过颜色仿真展示了喷口截面处的压强分布图像;利用网格剖分的方式分析了涡环转捩机理,完善了流体运动过程的精细测量,为实验室测量雷诺数提供了一种可行方法。

电推进涵道风扇气动快速求解方法及性能分析研究

随着绿色航空发展,为了能在设计阶段快速获得涵道风扇气动性能参数和非定常流场特征,有必要开发一种高效的数值求解方法。基于小型电推进风扇内流弱可压和尾迹耗散特性,本文将转子和涵道的面元与尾迹涡粒子耦合,使用面元法求解固壁流场,使用涡量输运方程求解远场尾迹传播特征,克服了有限体积法尾迹耗散快的问题。研究表明,本文发展的面元-涡粒子耦合方法对涵道风扇叶表压力与有限体积法趋势一致,整体推力误差为7.83%,能满足工程快速预测需求。本文发展的高效非定常计算方法的尾迹计算数值耗散低,能揭示更为复杂的非定常流动现象,仿真结果显示风扇涵道对尾迹发展有明显约束,而当尾迹传播至外部时,涡量呈现出明显的收缩和对称分布特征。在计算效率方面,本文发展的耦合方法非定常计算效率高,计算相同非定常时间步耗时仅为有限体积法的1/6,具有潜在的涵道动力非定常设计应用价值。