Deepwater drilling riser is the key equipment connecting the subsea wellhead and floating drilling platform.Due to complex marine environment,vortex-induced vibration(ViV)will be generated on riser,which will induce f...Deepwater drilling riser is the key equipment connecting the subsea wellhead and floating drilling platform.Due to complex marine environment,vortex-induced vibration(ViV)will be generated on riser,which will induce fatigue failure and even cause unpredictable drilling accidents.Therefore,it is important to study the ViV characteristics of deepwater drilling riser and reveal the main controlling factors for ensuring the safe and efficient operation of deepwater drilling engineering.In this paper,the ViV of deepwater drilling riser is numerically simulated in time domain based on the discrete vortex method(DvM).A hydrodynamic analysis model and governing equation of VIV is proposed with considering the effect of riser motion using DVM and slice method,where the governing equation is solved by Runge-Kutta method.Model validation is performed,which verified the correctness and accuracy of the mechanical model and the solution method.On this basis,the influence of the number of control points,current velocity,riser outer diameter,shear flow and top tension on the ViV characteristics of deepwater drilling risers are discussed in detail.The results show that with the increase of current velocity,the vibration amplitude of deepwater drilling riser decreases obviously,while the vibration frequency increases gradually.However,if the outer diameter of riser increases,the vibration amplitude increases,while the vibration frequency decreases gradually.The top tension also has great influence on the VIV of riser.When the top tension is 1.25 G,the VIV is suppressed to a certain extent.This study has guiding significance for optimal design and engineering control of deepwater drilling riser.展开更多
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. I...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.展开更多
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 t...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.展开更多
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...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.展开更多
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 effici...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.展开更多
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. T...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.展开更多
The Vortex Particle Method(VPM)is a meshless Lagrangian vortex method.Its low numerical dissipation is exceptionally suitable for wake simulation.Nevertheless,the inadequate numerical stability of VPM prevents its wid...The Vortex Particle Method(VPM)is a meshless Lagrangian vortex method.Its low numerical dissipation is exceptionally suitable for wake simulation.Nevertheless,the inadequate numerical stability of VPM prevents its widespread application in high Reynolds number flow and shear turbulence.To better simulate these flows,this paper proposes the stability-enhanced VPM based on a Reformulated VPM(RVPM)constrained by conservation of angular momentum,integrating a relaxation scheme to suppress the divergence of the vorticity field,and further coupling the Sub-Grid Scale(SGS)model to account for the turbulence dissipation caused by vortex advection and vortex stretching.The validity of the RVPM is confirmed by simulating an isolated vortex ring's evolution.The results also demonstrate that the relaxation scheme of vorticity enhances the numerical stability of the VPM by mitigating the divergence of the vorticity field.The leapfrogging vortex rings simulation demonstrates that the RVPM with the present SGS model can more precisely feature the leapfrog and fusion of vortex rings and has improved numerical stability in high Reynolds number flows.The round turbulent jet simulation confirms that the stability-enhanced VPM can stably simulate shear turbulence and accurately resolve fluctuating components and Reynolds stresses in the turbulence.展开更多
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 sec...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.展开更多
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...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.展开更多
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...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.展开更多
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 condit...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.展开更多
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 ...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.展开更多
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 dis...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 coupling, 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 first proposed and then used in numerical simulation of two-dimensional gas-particle mixing 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 structure larger and the distance needed for development of large-scale vortex structure shorter.展开更多
A rapid and efficient method for static aeroelastic analysis of a flexible slender wing when considering the structural geometric nonlinearity has been developed in this paper. A non-planar vortex lattice method herei...A rapid and efficient method for static aeroelastic analysis of a flexible slender wing when considering the structural geometric nonlinearity has been developed in this paper. A non-planar vortex lattice method herein is used to compute the non-planar aerodynamics of flexible wings with large deformation. The finite element method is introduced for structural nonlinear statics analysis. The surface spline method is used for structure/aerodynamics coupling. The static aeroelastic characteristics of the wind tunnel model of a flexible wing are studied by the nonlinear method presented, and the nonlinear method is also evaluated by comparing the results with those obtained from two other methods and the wind tunnel test. The results indicate that the traditional linear method of static aeroelastic analysis is not applicable for cases with large deformation because it produces results that are not realistic. However, the nonlinear methodology, which involves combining the structure finite element method with the non-planar vortex lattice method, could be used to solve the aeroelastic deformation with considerable accuracy, which is in fair agreement with the test results. Moreover, the nonlinear finite element method could consider complex structures. The non-planar vortex lattice method has advantages in both the computational accuracy and efficiency. Consequently, the nonlinear method presented is suitable for the rapid and efficient analysis requirements of engineering practice. It could be used in the preliminary stage and also in the detailed stage of aircraft design.展开更多
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...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.展开更多
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, whic...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展开更多
The Unsteady Vortex Lattice Method(UVLM) is a medium-fidelity aerodynamic tool that has been widely used in aeroelasticity and flight dynamics simulations. The most timeconsuming step is the evaluation of the induced ...The Unsteady Vortex Lattice Method(UVLM) is a medium-fidelity aerodynamic tool that has been widely used in aeroelasticity and flight dynamics simulations. The most timeconsuming step is the evaluation of the induced velocity. Supposing that the number of bound and wake lattices is N and the computational cost is O (N2), we present an OeNT Dipole Panel Fast Multipole Method(DPFMM) for the rapid evaluation of the induced velocity in UVLM. The multipole expansion coefficients of a quadrilateral dipole panel have been derived in spherical coordinates, whose accuracy is the same as that of the Biot-Savart kernel at the same truncation degree P.Two methods(the loosening method and the shrinking method) are proposed and tested for space partitioning volumetric panels. Compared with FMM for vortex filaments(with three harmonics),DPFMM is approximately two times faster for N2 [103,106]. The simulation time of a multirotor(N~104) is reduced from 100 min(with unaccelerated direct solver) to 2 min(with DPFMM).展开更多
This paper presents a new non-linear formulation of the classical Vortex Lattice Method （VLM） approach for calculating the aerodynamic properties of lifting surfaces. The method accounts for the effects of viscosity...This paper presents a new non-linear formulation of the classical Vortex Lattice Method （VLM） approach for calculating the aerodynamic properties of lifting surfaces. The method accounts for the effects of viscosity, and due to its low computational cost, it represents a very good tool to perform rapid and accurate wing design and optimization procedures. The mathematical model is constructed by using two-dimensional viscous analyses of the wing span-wise sections, according to strip theory, and then coupling the strip viscous forces with the forces generated by the vortex rings distributed on the wing camber surface, calculated with a fully three-dimensional vortex lifting law. The numerical results obtained with the proposed method are validated with experimental data and show good agreement in predicting both the lift and pitching moment, as well as in predicting the wing drag. The method is applied to modifying the wing of an Unmanned Aerial System to increase its aerodynamic efficiency and to calculate the drag reductions obtained by an upper surface morphing technique for an adaptable regional aircraft wing.展开更多
The Contra-Rotating Open Rotor(CROR)design confronts significant noise challenges despite being one of the possible options for future green aeroengines.To efficiently estimate the noise emitted from a CROR,a three-di...The Contra-Rotating Open Rotor(CROR)design confronts significant noise challenges despite being one of the possible options for future green aeroengines.To efficiently estimate the noise emitted from a CROR,a three-dimensional unsteady prediction model based on the meshless method is presented.The unsteady wake flow and the aerodynamic load fluctuations on the blade are solved through the viscous vortex particle method,the blade element momentum theory and vortex lattice method.Then,the acoustic field is obtained through the Farassat’s formulation 1A.Validation of this method is conducted on a CROR,and a mesh-based method,e.g.,Nonlinear Harmonic(NLH)method,is also employed for comparison.It is found that the presented method is three times faster than NLH method while maintaining a comparable precision.A thorough parametric analysis is also carried out to illustrate the effects of rotational speed,rotor-rotor spacing and rear rotor diameter on the noise level.The rotor speed is found to be the most influencing factor,and by optimizing the speed difference between the front and rear rotors,a notable noise reduction can be expected.The current findings not only contribute to a deeper comprehension of the CROR’s aeroacoustic properties but also offer an effective tool for engineering applications.展开更多
Applications of a novel curve-fitting technique are presented to efficiently predict the motion of the vortex filament, which is trailed from a rigid body such as wings and rotors. The gov- erning equations of the mot...Applications of a novel curve-fitting technique are presented to efficiently predict the motion of the vortex filament, which is trailed from a rigid body such as wings and rotors. The gov- erning equations of the motion, when a Lagrangian approach with the present curve-fitting method is applied, can be transformed into an easily solvable form of the system of nonlinear ordinary dif- ferential equations. The applicability of Bezier curves, B-spline, and Lagrange interpolating polyno- mials is investigated. Local Lagrange interpolating polynomials with a shift operator are proposed as the best selection for applications, since it provides superior system characteristics with minimum computing time, compared to other methods. In addition, the Gauss quadrature formula with local refinement strategy has been developed for an accurate prediction of the induced velocity computed with the line integration of the Biot-Savart law. Rotary-wing problems including a vortex ring problem are analyzed to show the efficiency, accuracy, and flexibility in the applications of the pro- posed method.展开更多
基金the financial support from National Key R&D Program of China(Grant number:2024YFC2815100)Natural Science Foundation of China(Grant number:52322110)Beijing Nova Program(Grant number:20230484341).
文摘Deepwater drilling riser is the key equipment connecting the subsea wellhead and floating drilling platform.Due to complex marine environment,vortex-induced vibration(ViV)will be generated on riser,which will induce fatigue failure and even cause unpredictable drilling accidents.Therefore,it is important to study the ViV characteristics of deepwater drilling riser and reveal the main controlling factors for ensuring the safe and efficient operation of deepwater drilling engineering.In this paper,the ViV of deepwater drilling riser is numerically simulated in time domain based on the discrete vortex method(DvM).A hydrodynamic analysis model and governing equation of VIV is proposed with considering the effect of riser motion using DVM and slice method,where the governing equation is solved by Runge-Kutta method.Model validation is performed,which verified the correctness and accuracy of the mechanical model and the solution method.On this basis,the influence of the number of control points,current velocity,riser outer diameter,shear flow and top tension on the ViV characteristics of deepwater drilling risers are discussed in detail.The results show that with the increase of current velocity,the vibration amplitude of deepwater drilling riser decreases obviously,while the vibration frequency increases gradually.However,if the outer diameter of riser increases,the vibration amplitude increases,while the vibration frequency decreases gradually.The top tension also has great influence on the VIV of riser.When the top tension is 1.25 G,the VIV is suppressed to a certain extent.This study has guiding significance for optimal design and engineering control of deepwater drilling riser.
文摘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.
基金Project supported by the National Natural Science Foundation of China (No.70371011) the Science Development Foundation of Shanghai Municipal Commission of Education (No.03GK04)
文摘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.
基金Supported by the National Natural Science Foundation of China(11302103)
文摘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.
基金Project (No. 50236030) supported by the National Natural Science Foundation of China
文摘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.
基金The project supported by the National Natural Science Foundation of China
文摘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.
基金co-supported by the National Natural Science Foundation of China(No.12402272)the Natural Science Basic Research Program of Shaanxi Province,China(No.2024JC-YBQN-0024)the Fundamental Research Funds for the Central Universities,China(No.D5000240030)。
文摘The Vortex Particle Method(VPM)is a meshless Lagrangian vortex method.Its low numerical dissipation is exceptionally suitable for wake simulation.Nevertheless,the inadequate numerical stability of VPM prevents its widespread application in high Reynolds number flow and shear turbulence.To better simulate these flows,this paper proposes the stability-enhanced VPM based on a Reformulated VPM(RVPM)constrained by conservation of angular momentum,integrating a relaxation scheme to suppress the divergence of the vorticity field,and further coupling the Sub-Grid Scale(SGS)model to account for the turbulence dissipation caused by vortex advection and vortex stretching.The validity of the RVPM is confirmed by simulating an isolated vortex ring's evolution.The results also demonstrate that the relaxation scheme of vorticity enhances the numerical stability of the VPM by mitigating the divergence of the vorticity field.The leapfrogging vortex rings simulation demonstrates that the RVPM with the present SGS model can more precisely feature the leapfrog and fusion of vortex rings and has improved numerical stability in high Reynolds number flows.The round turbulent jet simulation confirms that the stability-enhanced VPM can stably simulate shear turbulence and accurately resolve fluctuating components and Reynolds stresses in the turbulence.
文摘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.
基金The National Research Foundation of Korea(NRF-2017-R1A5A1015311 and 2021R1C1C1010198),South Korea.Author information。
文摘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.
基金supported by the Innovation Program of Shanghai Municipal Education Commission(Grant No.10ZZ95)the Leading Academic Discipline Project of Shanghai Municipal Education Commission(Grant No.J50502)
文摘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.
文摘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.
文摘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.
文摘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 coupling, 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 first proposed and then used in numerical simulation of two-dimensional gas-particle mixing 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 structure larger and the distance needed for development of large-scale vortex structure shorter.
基金National Natural Science Foundation of China(Nos.11172025,91116005)Research Fund for the Doctoral Program of Higher Education of China(No.20091102110015)
文摘A rapid and efficient method for static aeroelastic analysis of a flexible slender wing when considering the structural geometric nonlinearity has been developed in this paper. A non-planar vortex lattice method herein is used to compute the non-planar aerodynamics of flexible wings with large deformation. The finite element method is introduced for structural nonlinear statics analysis. The surface spline method is used for structure/aerodynamics coupling. The static aeroelastic characteristics of the wind tunnel model of a flexible wing are studied by the nonlinear method presented, and the nonlinear method is also evaluated by comparing the results with those obtained from two other methods and the wind tunnel test. The results indicate that the traditional linear method of static aeroelastic analysis is not applicable for cases with large deformation because it produces results that are not realistic. However, the nonlinear methodology, which involves combining the structure finite element method with the non-planar vortex lattice method, could be used to solve the aeroelastic deformation with considerable accuracy, which is in fair agreement with the test results. Moreover, the nonlinear finite element method could consider complex structures. The non-planar vortex lattice method has advantages in both the computational accuracy and efficiency. Consequently, the nonlinear method presented is suitable for the rapid and efficient analysis requirements of engineering practice. It could be used in the preliminary stage and also in the detailed stage of aircraft design.
基金financially supported by the JIANG Xinsong Innovation Fund(Grant No.Y8F7010701)
文摘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.
基金Project supported by the National Natural Science Foundation of China
文摘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
文摘The Unsteady Vortex Lattice Method(UVLM) is a medium-fidelity aerodynamic tool that has been widely used in aeroelasticity and flight dynamics simulations. The most timeconsuming step is the evaluation of the induced velocity. Supposing that the number of bound and wake lattices is N and the computational cost is O (N2), we present an OeNT Dipole Panel Fast Multipole Method(DPFMM) for the rapid evaluation of the induced velocity in UVLM. The multipole expansion coefficients of a quadrilateral dipole panel have been derived in spherical coordinates, whose accuracy is the same as that of the Biot-Savart kernel at the same truncation degree P.Two methods(the loosening method and the shrinking method) are proposed and tested for space partitioning volumetric panels. Compared with FMM for vortex filaments(with three harmonics),DPFMM is approximately two times faster for N2 [103,106]. The simulation time of a multirotor(N~104) is reduced from 100 min(with unaccelerated direct solver) to 2 min(with DPFMM).
基金the Natural Sciences and Engineering Research Council of Canada (NSERC) for the funding of the Canada Research Chair in Aircraft Modeling and Simulation Technologiesthe Canada Foundation of Innovation (CFI), the Ministerèdu Développement économique, de l’Innovation et de l’Exportation (MDEIE) and Hydra Technologies for the acquisition of the UAS-S4 using the Leaders Opportunity Funds+2 种基金the financial support obtained in the framework of the CRIAQ MDO-505 projectthe implication of our industrial partners Bombardier Aerospace and Thales CanadaNSERC for their support
文摘This paper presents a new non-linear formulation of the classical Vortex Lattice Method （VLM） approach for calculating the aerodynamic properties of lifting surfaces. The method accounts for the effects of viscosity, and due to its low computational cost, it represents a very good tool to perform rapid and accurate wing design and optimization procedures. The mathematical model is constructed by using two-dimensional viscous analyses of the wing span-wise sections, according to strip theory, and then coupling the strip viscous forces with the forces generated by the vortex rings distributed on the wing camber surface, calculated with a fully three-dimensional vortex lifting law. The numerical results obtained with the proposed method are validated with experimental data and show good agreement in predicting both the lift and pitching moment, as well as in predicting the wing drag. The method is applied to modifying the wing of an Unmanned Aerial System to increase its aerodynamic efficiency and to calculate the drag reductions obtained by an upper surface morphing technique for an adaptable regional aircraft wing.
基金the financial support from the National Natural Science Foundation of China(Nos.52276045 and 52206062)the Fundamental Research Funds for the Central Universities,China(Nos.3122019171,3122021087 and 3122022QD06).
文摘The Contra-Rotating Open Rotor(CROR)design confronts significant noise challenges despite being one of the possible options for future green aeroengines.To efficiently estimate the noise emitted from a CROR,a three-dimensional unsteady prediction model based on the meshless method is presented.The unsteady wake flow and the aerodynamic load fluctuations on the blade are solved through the viscous vortex particle method,the blade element momentum theory and vortex lattice method.Then,the acoustic field is obtained through the Farassat’s formulation 1A.Validation of this method is conducted on a CROR,and a mesh-based method,e.g.,Nonlinear Harmonic(NLH)method,is also employed for comparison.It is found that the presented method is three times faster than NLH method while maintaining a comparable precision.A thorough parametric analysis is also carried out to illustrate the effects of rotational speed,rotor-rotor spacing and rear rotor diameter on the noise level.The rotor speed is found to be the most influencing factor,and by optimizing the speed difference between the front and rear rotors,a notable noise reduction can be expected.The current findings not only contribute to a deeper comprehension of the CROR’s aeroacoustic properties but also offer an effective tool for engineering applications.
基金supported by the EDISON Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Science,ICT and Future Planning(No.2011-0020560)
文摘Applications of a novel curve-fitting technique are presented to efficiently predict the motion of the vortex filament, which is trailed from a rigid body such as wings and rotors. The gov- erning equations of the motion, when a Lagrangian approach with the present curve-fitting method is applied, can be transformed into an easily solvable form of the system of nonlinear ordinary dif- ferential equations. The applicability of Bezier curves, B-spline, and Lagrange interpolating polyno- mials is investigated. Local Lagrange interpolating polynomials with a shift operator are proposed as the best selection for applications, since it provides superior system characteristics with minimum computing time, compared to other methods. In addition, the Gauss quadrature formula with local refinement strategy has been developed for an accurate prediction of the induced velocity computed with the line integration of the Biot-Savart law. Rotary-wing problems including a vortex ring problem are analyzed to show the efficiency, accuracy, and flexibility in the applications of the pro- posed method.
