We propose an efficient and robust algorithm to solve the steady Euler equa- tions on unstructured grids.The new algorithm is a Newton-iteration method in which each iteration step is a linear multigrid method using b...We propose an efficient and robust algorithm to solve the steady Euler equa- tions on unstructured grids.The new algorithm is a Newton-iteration method in which each iteration step is a linear multigrid method using block lower-upper symmetric Gauss-Seidel(LU-SGS)iteration as its smoother To regularize the Jacobian matrix of Newton-iteration,we adopted a local residual dependent regularization as the replace- ment of the standard time-stepping relaxation technique based on the local CFL number The proposed method can be extended to high order approximations and three spatial dimensions in a nature way.The solver was tested on a sequence of benchmark prob- lems on both quasi-uniform and local adaptive meshes.The numerical results illustrated the efficiency and robustness of our algorithm.展开更多
This paper presents the results of an investigation to use arc-length mesh generation and finite volume TVD scheme to calculate Euler equations for predicting the effect of geometry parameters in reducing the drag for...This paper presents the results of an investigation to use arc-length mesh generation and finite volume TVD scheme to calculate Euler equations for predicting the effect of geometry parameters in reducing the drag force and improving the lift-drag ratio of grid fin in the supersonic flow regime. The effects of frame and web, whose cross section shape and thickness and spacing,on the aerodynamic character of the grid fin were studied. Calculations were made at Mach 2.5 and several angles of attack. The results were validated by comparing the computed aerodynamic coefficients against wind tunnel experimental data. Good agreement was found between computed and experimental results. The computed results suggest that parameters of the grid fin's frame have the greatest effect on the grid fin aerodynamic character, especially on its drag force. It was concluded proper choice of appropriate grid fin geometry parameters could reduce the drag force and improve the lift-drag ratios.展开更多
Conventional coupled BE/FE （Boundary-Element/Finite-Element） method and modeling of structural-acoustic interaction has shown its promise and potential in the design and analysis of various structural-acoustic inter...Conventional coupled BE/FE （Boundary-Element/Finite-Element） method and modeling of structural-acoustic interaction has shown its promise and potential in the design and analysis of various structural-acoustic interaction applications. Unified combined acoustic and aerodynamic loading on the structure is synthesized using two approaches. Firstly, by linear superposition of the acoustic pressure disturbance to the aeroelastic problem, the effect of acoustic pressure disturbance to the aeroelastic structure is considered to consist of structural motion independent incident acoustic pressure and structural motion dependent acoustic pressure, which is known as the scattering pressure, referred here as the acoustic aerodynamic analogy. Secondly, by synthesizing the acoustic and aerodynamic effects on elastic structure using an elegant, effective and unified approach, both acoustic and aerodynamic effect on solid structural boundaries can be formulated as a boundary value problem governed by second order differential equations which lead to solutions expressible as surface integral equations. The unified formulation of the acousto-aeroelastic problem is amenable for simultaneous solution, although certain prevailing situations allow the solution of the equations independently. For this purpose, the unsteady aerodynamic problem which was earlier utilizes well-established lifting surface method is reformulated using Boundary Element （BE） approach. These schemes are outlined and worked out with examples.展开更多
There were for a long time two invariant forms of hydrodynamic equations： one was related to coordinate system of references, and the other was versus to measure units of characteristics. These both invariant forms h...There were for a long time two invariant forms of hydrodynamic equations： one was related to coordinate system of references, and the other was versus to measure units of characteristics. These both invariant forms had important roles in the development of theoretical and practical applications of hydro-aerodynamics and related industries. The third invariant form of hydrodynamic equations is one for the dimensions of spaces. For this goal, the hyper quantities （space and physics） are introduced. Then these are created we can easily cover all problems in arbitrary dimensions （3D, 2D, 1D, separate space for liquids or constituent matters）. In particularly, when they are applied to water hammer problem, which is an especially problem, we can receive immediately celerity and pressure of the event.展开更多
Unsteady effect of seriously separated flow is the main factor of modern aircraft buffeting. So accurate simulation of this complex flow becomes the basis associated with the research of aircraft buffeting. This paper...Unsteady effect of seriously separated flow is the main factor of modern aircraft buffeting. So accurate simulation of this complex flow becomes the basis associated with the research of aircraft buffeting. This paper constructs an unsteady numerical simulation method for separation flow based on modified delayed detached eddy simulation (MDDES) method by considering both modern computer resources and the credibility of simulating separation flow. The proposed method is also verified through the simulation of the separated flow by a typical fighter at high angle of attack. And then a robust and efficient technology for deforming mesh is established using radial basis function (RBF) and infinite interpolation method. Moreover, the platform for numerical simulation of buffeting is set up in combination with the structural dynamics equations in the modal space, by which the research of vertical tail buffeting caused by edge vortex is carried out on a fighter at large angle of attack. Through spectrum analysis of time-domain response of pressure pulsation on the location of vortex rupture, the results show that the pulsation frequency of vortex structure with different scales covers the inherent modal frequency of vertical tail structure. Compared to the Reynolds-averaged Navier-Stokes equations, the MDDES method can distinguish the more detailed and higher frequency small-scale vortex structure. Unlike flutter, displacement acceleration response of each mode in buffeting is dominated by its own mode. There exists strong coupling between the first bending mode and first torsion mode, and it leads to acceleration and large inertia impact of structure, which is the main factor causing structural fatigue. In sum, the obtained results verify the validity of the numerical means and the corresponding methods in the paper.展开更多
Based on the idea of adjoint method and the dynamic evolution method,a new optimum aerodynamic design technique is presented in this paper.It can be applied to the optimum problems with a large number of design variab...Based on the idea of adjoint method and the dynamic evolution method,a new optimum aerodynamic design technique is presented in this paper.It can be applied to the optimum problems with a large number of design variables and is time saving.The key of the new method lies in that the optimization process is regarded as an unsteady evolution,i.e.,the optimization is executed,simultaneously with solving the unsteady flow governing equations and adjoint equations.Numerical examples for both the inverse problem and drag minimization using Euler equations have been presented,and the results show that the method presented in this paper is more efficient than the optimum methods based on the steady flow solution and the steady solution of adjoint equations.展开更多
In this paper,a coupled CFD-CSD method based on N-S equations is described for static aeroelastic correction and jig-shape design of large airliners.The wing structural flexibility matrix is analyzed by a finite eleme...In this paper,a coupled CFD-CSD method based on N-S equations is described for static aeroelastic correction and jig-shape design of large airliners.The wing structural flexibility matrix is analyzed by a finite element method with a double-beam model.The viscous multi-block structured grid is used in aerodynamic calculations.Flexibility matrix interpolation is fulfilled by use of a surface spline method.The load distributions on wing surface are evaluated by solving N-S equations with a parallel algorithm.A flexibility approach is employed to calculate the structural deformations.By successive iterations between steady aerodynamic forces and structural deformations,a coupled CFD-CSD method is achieved for the static aeroelastic correction and jig-shape design of a large airliner.The present method is applied to the static aeroelastic analysis and jig-shape design for a typical large airliner with engine nacelle and winglet.The numerical results indicate that calculations of static aeroelastic correction should employ tightly coupled CFD-CSD iterations,and that on a given cruise shape only one round of iterative design is needed to obtain the jig-shape meeting design requirements.展开更多
The unsteady Reynolds-averaged Navier-Stokes equations coupled with the k-co SST turbulence model are solved to obtain the steady and unsteady aerodynamic forces for airfoils and wings. The effects of vibration types ...The unsteady Reynolds-averaged Navier-Stokes equations coupled with the k-co SST turbulence model are solved to obtain the steady and unsteady aerodynamic forces for airfoils and wings. The effects of vibration types and amplitudes on aerody- namic forces of airfoils and wings are studied. The deformation characteristics of a swept wing induced by steady aerodynamic load are presented. It is found that for a vibrating elastic wing at small and medium incidences, its mean aerodynamic loads are almost the same as those obtained from the static one. On the contrary, at high incidences especially around the stall incidence, the vibration may change the mean values. In addition, the larger amplitude is, the larger discrepancy will be. For a swept wing, the steady aerodynamic loads usually lead to the ＂pitching down＂ effect on the wing tip which delays the stall compared with a rigid one; But this phenomenon dose not occur on a aeroelastic wing which can induce the separation ahead and trigger the stall. The above conclusions are in good agreement with the scatter characteristics of wind-tunnel data. The reason why the data obtained from wind tunnel and CFD are different is also analyzed. Meanwhile, it can be an explanation for scatter phe- nomenon of wind-tunnel data, especially for high incidence cases, which remains a puzzle so far.展开更多
The paper presents the formulation to compute numerically the unsteady aerodynamic forces on the vibrating annular cascade blades.The formulation is based on the finite volume method.By applying the TVD scheme to the ...The paper presents the formulation to compute numerically the unsteady aerodynamic forces on the vibrating annular cascade blades.The formulation is based on the finite volume method.By applying the TVD scheme to the linear unsteady calculations,the precise calculation of the peak of unsteady aerodynamic forces at the shock wave location like the delta function singularity becomes possible without empirical constants.As a further feature of the present paper,results of the present numerical calculation are compared with those of the double linearization theory(DLT),which assumes small unsteady and steady disturbances but the unsteady disturbances are much smaller than the steady disturbances.Since DLT requires far less computational resources than the present numerical calculation,the validation of DLT is quite important from the engineering point of view.Under the conditions of small steady disturbances,a good agreement between these two results is observed,so that the two codes are cross-validated.The comparison also reveals the limitation on the applicability of DLT.展开更多
In recent years many long-span bridges have been or are being constructed in the world, especially in China. Wind loads and responses are the key factors for their structural design. This paper introduces some importa...In recent years many long-span bridges have been or are being constructed in the world, especially in China. Wind loads and responses are the key factors for their structural design. This paper introduces some important achievements of wind-resistant studies of the author's research team on long-span bridges. First, new concepts and identification methods of aerodynamic derivatives and aerodynamic admittances were proposed. Then mechanical and aerodynamic control strategies and methods of wind-induced vibrations of long-span bridges were the great concerned problems, and valuable achievements were presented. Especially, great efforts which have been theoretically and experimentally made on rain-wind induced vibration of cables of cable-stayed bridges were described. Finally, some new progresses in computation wind engineering were introduced, and a new method for simulating an equilibrium boundary layer was put forward as well.展开更多
The ship hull is simplified as a free beam with varying sections. Based on hydroelasticity and explosion mechanics theory,mechanical model and kinetic equation for hull girder vibration under non-contact explosion are...The ship hull is simplified as a free beam with varying sections. Based on hydroelasticity and explosion mechanics theory,mechanical model and kinetic equation for hull girder vibration under non-contact explosion are established. The equation is solved by Wilson-θ algorithm. On the basis of the above principles,a structure kinetics analysis program is compiled. The dynamic response of supposed warship under air explosion is calculated conveniently and quickly. Under the explosion condition designed in the paper,the positive pressure period of non-contact explosion wave is much less than the natural periods of the first four modes of hull girder and the resonance of ship girder overall vibration can be avoided. The ratio of midship maximum moment to ultimate bearing strength under non-contact explosion accelerates with the increment of impact factor.展开更多
文摘We propose an efficient and robust algorithm to solve the steady Euler equa- tions on unstructured grids.The new algorithm is a Newton-iteration method in which each iteration step is a linear multigrid method using block lower-upper symmetric Gauss-Seidel(LU-SGS)iteration as its smoother To regularize the Jacobian matrix of Newton-iteration,we adopted a local residual dependent regularization as the replace- ment of the standard time-stepping relaxation technique based on the local CFL number The proposed method can be extended to high order approximations and three spatial dimensions in a nature way.The solver was tested on a sequence of benchmark prob- lems on both quasi-uniform and local adaptive meshes.The numerical results illustrated the efficiency and robustness of our algorithm.
基金Project supported by National Defence Science and Technology Advance Research Foundation of China (No. 413130305) and Postdoctor Science Foundation of China (No. 2003034510)
文摘This paper presents the results of an investigation to use arc-length mesh generation and finite volume TVD scheme to calculate Euler equations for predicting the effect of geometry parameters in reducing the drag force and improving the lift-drag ratio of grid fin in the supersonic flow regime. The effects of frame and web, whose cross section shape and thickness and spacing,on the aerodynamic character of the grid fin were studied. Calculations were made at Mach 2.5 and several angles of attack. The results were validated by comparing the computed aerodynamic coefficients against wind tunnel experimental data. Good agreement was found between computed and experimental results. The computed results suggest that parameters of the grid fin's frame have the greatest effect on the grid fin aerodynamic character, especially on its drag force. It was concluded proper choice of appropriate grid fin geometry parameters could reduce the drag force and improve the lift-drag ratios.
文摘Conventional coupled BE/FE （Boundary-Element/Finite-Element） method and modeling of structural-acoustic interaction has shown its promise and potential in the design and analysis of various structural-acoustic interaction applications. Unified combined acoustic and aerodynamic loading on the structure is synthesized using two approaches. Firstly, by linear superposition of the acoustic pressure disturbance to the aeroelastic problem, the effect of acoustic pressure disturbance to the aeroelastic structure is considered to consist of structural motion independent incident acoustic pressure and structural motion dependent acoustic pressure, which is known as the scattering pressure, referred here as the acoustic aerodynamic analogy. Secondly, by synthesizing the acoustic and aerodynamic effects on elastic structure using an elegant, effective and unified approach, both acoustic and aerodynamic effect on solid structural boundaries can be formulated as a boundary value problem governed by second order differential equations which lead to solutions expressible as surface integral equations. The unified formulation of the acousto-aeroelastic problem is amenable for simultaneous solution, although certain prevailing situations allow the solution of the equations independently. For this purpose, the unsteady aerodynamic problem which was earlier utilizes well-established lifting surface method is reformulated using Boundary Element （BE） approach. These schemes are outlined and worked out with examples.
文摘There were for a long time two invariant forms of hydrodynamic equations： one was related to coordinate system of references, and the other was versus to measure units of characteristics. These both invariant forms had important roles in the development of theoretical and practical applications of hydro-aerodynamics and related industries. The third invariant form of hydrodynamic equations is one for the dimensions of spaces. For this goal, the hyper quantities （space and physics） are introduced. Then these are created we can easily cover all problems in arbitrary dimensions （3D, 2D, 1D, separate space for liquids or constituent matters）. In particularly, when they are applied to water hammer problem, which is an especially problem, we can receive immediately celerity and pressure of the event.
文摘Unsteady effect of seriously separated flow is the main factor of modern aircraft buffeting. So accurate simulation of this complex flow becomes the basis associated with the research of aircraft buffeting. This paper constructs an unsteady numerical simulation method for separation flow based on modified delayed detached eddy simulation (MDDES) method by considering both modern computer resources and the credibility of simulating separation flow. The proposed method is also verified through the simulation of the separated flow by a typical fighter at high angle of attack. And then a robust and efficient technology for deforming mesh is established using radial basis function (RBF) and infinite interpolation method. Moreover, the platform for numerical simulation of buffeting is set up in combination with the structural dynamics equations in the modal space, by which the research of vertical tail buffeting caused by edge vortex is carried out on a fighter at large angle of attack. Through spectrum analysis of time-domain response of pressure pulsation on the location of vortex rupture, the results show that the pulsation frequency of vortex structure with different scales covers the inherent modal frequency of vertical tail structure. Compared to the Reynolds-averaged Navier-Stokes equations, the MDDES method can distinguish the more detailed and higher frequency small-scale vortex structure. Unlike flutter, displacement acceleration response of each mode in buffeting is dominated by its own mode. There exists strong coupling between the first bending mode and first torsion mode, and it leads to acceleration and large inertia impact of structure, which is the main factor causing structural fatigue. In sum, the obtained results verify the validity of the numerical means and the corresponding methods in the paper.
文摘Based on the idea of adjoint method and the dynamic evolution method,a new optimum aerodynamic design technique is presented in this paper.It can be applied to the optimum problems with a large number of design variables and is time saving.The key of the new method lies in that the optimization process is regarded as an unsteady evolution,i.e.,the optimization is executed,simultaneously with solving the unsteady flow governing equations and adjoint equations.Numerical examples for both the inverse problem and drag minimization using Euler equations have been presented,and the results show that the method presented in this paper is more efficient than the optimum methods based on the steady flow solution and the steady solution of adjoint equations.
基金supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘In this paper,a coupled CFD-CSD method based on N-S equations is described for static aeroelastic correction and jig-shape design of large airliners.The wing structural flexibility matrix is analyzed by a finite element method with a double-beam model.The viscous multi-block structured grid is used in aerodynamic calculations.Flexibility matrix interpolation is fulfilled by use of a surface spline method.The load distributions on wing surface are evaluated by solving N-S equations with a parallel algorithm.A flexibility approach is employed to calculate the structural deformations.By successive iterations between steady aerodynamic forces and structural deformations,a coupled CFD-CSD method is achieved for the static aeroelastic correction and jig-shape design of a large airliner.The present method is applied to the static aeroelastic analysis and jig-shape design for a typical large airliner with engine nacelle and winglet.The numerical results indicate that calculations of static aeroelastic correction should employ tightly coupled CFD-CSD iterations,and that on a given cruise shape only one round of iterative design is needed to obtain the jig-shape meeting design requirements.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11072199 and 10872171)
文摘The unsteady Reynolds-averaged Navier-Stokes equations coupled with the k-co SST turbulence model are solved to obtain the steady and unsteady aerodynamic forces for airfoils and wings. The effects of vibration types and amplitudes on aerody- namic forces of airfoils and wings are studied. The deformation characteristics of a swept wing induced by steady aerodynamic load are presented. It is found that for a vibrating elastic wing at small and medium incidences, its mean aerodynamic loads are almost the same as those obtained from the static one. On the contrary, at high incidences especially around the stall incidence, the vibration may change the mean values. In addition, the larger amplitude is, the larger discrepancy will be. For a swept wing, the steady aerodynamic loads usually lead to the ＂pitching down＂ effect on the wing tip which delays the stall compared with a rigid one; But this phenomenon dose not occur on a aeroelastic wing which can induce the separation ahead and trigger the stall. The above conclusions are in good agreement with the scatter characteristics of wind-tunnel data. The reason why the data obtained from wind tunnel and CFD are different is also analyzed. Meanwhile, it can be an explanation for scatter phe- nomenon of wind-tunnel data, especially for high incidence cases, which remains a puzzle so far.
文摘The paper presents the formulation to compute numerically the unsteady aerodynamic forces on the vibrating annular cascade blades.The formulation is based on the finite volume method.By applying the TVD scheme to the linear unsteady calculations,the precise calculation of the peak of unsteady aerodynamic forces at the shock wave location like the delta function singularity becomes possible without empirical constants.As a further feature of the present paper,results of the present numerical calculation are compared with those of the double linearization theory(DLT),which assumes small unsteady and steady disturbances but the unsteady disturbances are much smaller than the steady disturbances.Since DLT requires far less computational resources than the present numerical calculation,the validation of DLT is quite important from the engineering point of view.Under the conditions of small steady disturbances,a good agreement between these two results is observed,so that the two codes are cross-validated.The comparison also reveals the limitation on the applicability of DLT.
基金supported by the National Natural Science Foundation of China (Grant Nos. 59238161,59725818,50178049,50321803,and 50621062)
文摘In recent years many long-span bridges have been or are being constructed in the world, especially in China. Wind loads and responses are the key factors for their structural design. This paper introduces some important achievements of wind-resistant studies of the author's research team on long-span bridges. First, new concepts and identification methods of aerodynamic derivatives and aerodynamic admittances were proposed. Then mechanical and aerodynamic control strategies and methods of wind-induced vibrations of long-span bridges were the great concerned problems, and valuable achievements were presented. Especially, great efforts which have been theoretically and experimentally made on rain-wind induced vibration of cables of cable-stayed bridges were described. Finally, some new progresses in computation wind engineering were introduced, and a new method for simulating an equilibrium boundary layer was put forward as well.
文摘The ship hull is simplified as a free beam with varying sections. Based on hydroelasticity and explosion mechanics theory,mechanical model and kinetic equation for hull girder vibration under non-contact explosion are established. The equation is solved by Wilson-θ algorithm. On the basis of the above principles,a structure kinetics analysis program is compiled. The dynamic response of supposed warship under air explosion is calculated conveniently and quickly. Under the explosion condition designed in the paper,the positive pressure period of non-contact explosion wave is much less than the natural periods of the first four modes of hull girder and the resonance of ship girder overall vibration can be avoided. The ratio of midship maximum moment to ultimate bearing strength under non-contact explosion accelerates with the increment of impact factor.
