The preconditioning method is used to solve the low Mach number flow. The space discritisation scheme is the Roe scheme and the DES turbulence model is used. Then, the low Mach number turbulence flow around the NACA00...The preconditioning method is used to solve the low Mach number flow. The space discritisation scheme is the Roe scheme and the DES turbulence model is used. Then, the low Mach number turbulence flow around the NACA0012 airfoil is used to verify the efficiency of the proposed method. Two cases of the low Mach number flows around the multi-element airfoil and the circular cylinder are also used to test the proposed method. Numerical results show that the methods combined the preconditioning method and compressible Navier-Stokes equations are efficient to solve low Mach number flows.展开更多
The operator splitting method is used to deal with the Navier-Stokes equation, in which the physical process described by the equation is decomposed into two processes： a diffusion process and a convection process; a...The operator splitting method is used to deal with the Navier-Stokes equation, in which the physical process described by the equation is decomposed into two processes： a diffusion process and a convection process; and the finite element equation is established. The velocity field in the element is described by the shape function of the isoparametric element with nine nodes and the pressure field is described by the interpolation function of the four nodes at the vertex of the isoparametric element with nine nodes. The subroutine of the element and the integrated finite element code are generated by the Finite Element Program Generator （FEPG） successfully. The numerical simulation about the incompressible viscous liquid flowing over a cylinder is carded out. The solution agrees with the experimental results very well.展开更多
A complete boundary integral formulation for incompressible Navier Stokes equations with time discretization by operator splitting is developed by using the fundamental solutions of the Helmhotz operator equation wit...A complete boundary integral formulation for incompressible Navier Stokes equations with time discretization by operator splitting is developed by using the fundamental solutions of the Helmhotz operator equation with different orders. The numerical results for the lift and the drag hysteresis associated with a NACA0012 aerofoil oscillating in pitch are good in comparison with available experimental data.展开更多
The authors propose a numerical algorithm for the two-dimensional Navier-Stokes equations written in stream function-vorticity formulation. The total time derivative term is treated with a first order characteristics ...The authors propose a numerical algorithm for the two-dimensional Navier-Stokes equations written in stream function-vorticity formulation. The total time derivative term is treated with a first order characteristics method. The space approximation is based on a piecewise continuous finite element method. The proposed algorithm is used to simulate the mechanical aeration process in lakes. Such process is used to combat the degradation of the water quality due to the eutrophication phenomena. For this application high computing facilities and capacities are required. In order to optimize the computing time and make possible the simulation of real applications, the authors propose a parallel implementation of the numerical algorithm. The parallelization technique is performed using the Message Passing Interface. The efficiency of the proposed numerical algorithm is illustrated by some numerical results.展开更多
Gridless method is developed for unsteady viscous flows involving moving boundaries. The point distri- bution of gridless method is implemented in an isotropic or anisotropic way according to the features of viscous f...Gridless method is developed for unsteady viscous flows involving moving boundaries. The point distri- bution of gridless method is implemented in an isotropic or anisotropic way according to the features of viscous flows. In the area far away from the body, the traditional cloud of isotropic points is used, while in the adjacent area, the cloud of anisotropic points is distributed. In this way, the point spacing normal to the wall can be small enough for simulating the boundary layer, and meanwhile, the total number of points in the computational do- main can be controlled due to large spacing in other tangential direction through the anisotropic way. A fast mov- ing technique of clouds of points at each time-step is presented based on the attenuation law of disturbed motion for unsteady flows involving moving boundaries. In the mentioned cloud of points, a uniform weighted least- square curve fit method is utilized to discretize the spatial derivatives of the Navier-Stokes equations. The pro- posed gridless method, coupled with a dual time-stepping method and the Spalart-Allmaras turbulence model, is implemented for the Navier-Stokes equations. The computational results of unsteady viscous flows around a NLR7301 airfoil with an oscillating flap and a pitching NACA0012 airfoil are presented in a good agreement with the available experimental data.展开更多
An unstructured Reynolds-averaged Navier-Stokes flow solver using the finite volume method is studied. The spatial discretisation is based on the Osher approximate Riemann solvers. A two-equation turbulence model (k-...An unstructured Reynolds-averaged Navier-Stokes flow solver using the finite volume method is studied. The spatial discretisation is based on the Osher approximate Riemann solvers. A two-equation turbulence model (k-ω model) is also developed for hybrid grids to compute the turbulence flow. The turbulence flow past NACA0012 airfoil and the double ellipsolids are computed, and the numerical results show that the above methods are very efficient.展开更多
Residual-based a posteriori error estimate for conforming finite element solutions of incompressible Navier-Stokes equations, which is computed with a new two-level method that is different from Volker John, is derive...Residual-based a posteriori error estimate for conforming finite element solutions of incompressible Navier-Stokes equations, which is computed with a new two-level method that is different from Volker John, is derived. A posteriori error estimate contains additional terms in comparison to the estimate for the solution obtained by the standard finite element method. The importance of the additional terms in the error estimates is investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than the convergence of discrete solution. The two-level method aims to solve the nonlinear problem on a coarse grid with less computational work, then to solve the linear problem on a fine grid, which is superior to the usual finite element method solving a similar nonlinear problem on the fine grid.展开更多
Motivated by the results of J. Y. Chemin in ＂J. Anal. Math., 77, 1999, 27- 50＂ and G. Furioli et al in ＂Revista Mat. Iberoamer., 16, 2002, 605-667＂, the author considers further regularities of the mild solutions ...Motivated by the results of J. Y. Chemin in ＂J. Anal. Math., 77, 1999, 27- 50＂ and G. Furioli et al in ＂Revista Mat. Iberoamer., 16, 2002, 605-667＂, the author considers further regularities of the mild solutions to Navier-Stokes equation with initial data uo ∈ L^d（R^d）. In particular, it is proved that if u C ∈（[0, T^＊）; L^d（R^d）） is a mild solution of （NSv）, then u（t,x）- e^vt△uo ∈ L^∞（（0, T）;B2/4^1,∞）~∩L^1 （（0, T）; B2/4^3 ,∞） for any T 〈 T^＊.展开更多
Fourier analysis methods and in particular techniques based on Littlewood-Paley decomposition and paraproduct have known a growing interest recently for the study of nonlinear evolutionary equations. In this survey pa...Fourier analysis methods and in particular techniques based on Littlewood-Paley decomposition and paraproduct have known a growing interest recently for the study of nonlinear evolutionary equations. In this survey paper, we explain how these methods may be implemented so as to study the compresible Navier-Stokes equations in the whole space. We shall investigate both the initial value problem in critical Besov spaces and the low Mach number asymptotics.展开更多
Following the idea of Speziale＇s Very Large Eddy Simulation （VLES） method, a new unified hybrid simulation approach was proposed which can change seamlessly from RANS （Reynolds-Averaged Navier-Stokes） to LES （La...Following the idea of Speziale＇s Very Large Eddy Simulation （VLES） method, a new unified hybrid simulation approach was proposed which can change seamlessly from RANS （Reynolds-Averaged Navier-Stokes） to LES （Large Eddy Simulation） method depending on the numerical resolution. The model constants were calibrated in accordance with other hybrid methods. Besides being able to approach the two limits of RANS and LES, the new model also provides a proper VLES mode between the two limits, and thus can be used for a wide range of mesh resolutions. Also RANS simulation can be recovered near the wall which is similar to the Detached Eddy Simulation （DES） concept. This new methodology was implemented into Wilcox＇s κ- ω model and applications were conducted for fully developed turbulent channel flow at ReT = 395 and turbulent flow past a square cylinder at Re = 22000. Results were compared with LES predictions and other studies. The new method is found to be quite efficient in resolving large flow structures, and can predict satisfactory results on relative coarse mesh.展开更多
A novel circulation control technique is proposed to overcome the shortcomings of blowing jet circulation control, which uses the synthetic jet as the actuator and avoids the limitation about air supply requirement. T...A novel circulation control technique is proposed to overcome the shortcomings of blowing jet circulation control, which uses the synthetic jet as the actuator and avoids the limitation about air supply requirement. The effectiveness of synthetic jet circulation control to enhance lift of NCCR1510-7067N airfoil is confirmed by solving the 2-D unsteady Reynolds-averaged Na- vier-Stokes equations. The aerodynamic characteristics and the flow structure （especially close to the trailing edge） of NCCR 1510-7067N airfoil at zero angle of attack are also presented to discuss the mechanism of lift enhancement of the airfoil with synthetic jet circulation control. The results indicate that the synthetic jet can effectively delay the separation point on the airfoil trailing edge and increase the circulation and lift of the airfoil by Coanda effect. The numerical simulation results demonstrate that the lift augmentation efficiency with synthetic jet circulation control reaches △C1/Cμ,=114 in the present study, which is much higher than the value 12.1 in the case with steady blowing jet circulation control.展开更多
With the development of computational power and numerical algorithms,computational fluid dynamics(CFD) has become an important strategy for the design of aircraft,which significantly reduces the reliance on wind-tunne...With the development of computational power and numerical algorithms,computational fluid dynamics(CFD) has become an important strategy for the design of aircraft,which significantly reduces the reliance on wind-tunnel and flight tests.In this paper,we conducted a numerical investigation on the flow past a full commercial aircraft at Mach number 0.2 and 14 degrees angle of attack by means of Reynolds-averaged Navier-Stokes(RANS),detached-eddy simulation(DES) and our newly developed constrained large-eddy simulation(CLES).The objective of this paper is to study the capability of these models in simulating turbulent flows.To our knowledge,this is the first large-eddy simulation method for full commercial aircraft simulation.The results show that the CLES can predict the mean statistical quantities well,qualitatively consistent with traditional methods,and can capture more small-scale structures near the surface of the aircraft with massive separations.Our study demonstrates that CLES is a promising alternative for simulating real engineering turbulent flows.展开更多
In this study,based on the dynamic Biot＇s theory ＂u-p＂ approximation,a 3D finite element method（FEM） numerical soil model is developed,in which the Generalized Newmark-β method is adopted to determine the time i...In this study,based on the dynamic Biot＇s theory ＂u-p＂ approximation,a 3D finite element method（FEM） numerical soil model is developed,in which the Generalized Newmark-β method is adopted to determine the time integration.The developed 3D FEM soil model is a part of the coupled model PORO-WSSI 3D for 3D wave-seabed-marine structures interaction problem,and is validated by the analytical solution proposed by Wang（2000） for a laterally infinite seabed loaded by a uniform force.By adopting the developed 3D soil model,the consolidation of seabed under a caisson breakwater and hydrostatic pressure is investigated.The numerical results show that the caisson breakwater built on seabed has very significant effect on the stresses/displacements fields in the seabed foundation after the transient deformation and primary consolidation are completed.The parametric study indicates that the Young＇s modulus E of seabed is the most important parameter to affect the settlement of breakwater,and the displacement fields in seabed foundation.Taking the consolidation status as the initial condition,the interaction between ocean wave,caisson breakwater and seabed foundation is briefly investigated.The 3D ocean wave is determined by solving the Navier-Stokes equations with finite volume method（FVM）.The numerical results indicate that there is intensive interaction between oceean wave, caisson breakwater and seabed foundation; and the breakwater indeed can effectively block the wave energy propagating to the coastline.展开更多
The governing equations are derived by circumferentially averaging the three-dimensional （3D） Navier-Stokes equations, which are solved using a time marching finite volume approach. Both Euler throughflow model and ...The governing equations are derived by circumferentially averaging the three-dimensional （3D） Navier-Stokes equations, which are solved using a time marching finite volume approach. Both Euler throughflow model and Navier-Stokes （N-S） throughflow model are employed to investigate the performance and flow fields of a highly loaded transonic single-stage fan ATS-2 and a four-stage fan. The results are compared with the experimental and three-dimensional computational results. It shows that the throughflow models can provide reasonable perform- ance characteristics and N-S throughflow model gives better predictions in endwall regions. A throughflow com- putation in which all the non-axisymmetric terms are included has been performed at off-design condition and the radial distributions of the flow field can be well described.展开更多
文摘The preconditioning method is used to solve the low Mach number flow. The space discritisation scheme is the Roe scheme and the DES turbulence model is used. Then, the low Mach number turbulence flow around the NACA0012 airfoil is used to verify the efficiency of the proposed method. Two cases of the low Mach number flows around the multi-element airfoil and the circular cylinder are also used to test the proposed method. Numerical results show that the methods combined the preconditioning method and compressible Navier-Stokes equations are efficient to solve low Mach number flows.
文摘The operator splitting method is used to deal with the Navier-Stokes equation, in which the physical process described by the equation is decomposed into two processes： a diffusion process and a convection process; and the finite element equation is established. The velocity field in the element is described by the shape function of the isoparametric element with nine nodes and the pressure field is described by the interpolation function of the four nodes at the vertex of the isoparametric element with nine nodes. The subroutine of the element and the integrated finite element code are generated by the Finite Element Program Generator （FEPG） successfully. The numerical simulation about the incompressible viscous liquid flowing over a cylinder is carded out. The solution agrees with the experimental results very well.
文摘A complete boundary integral formulation for incompressible Navier Stokes equations with time discretization by operator splitting is developed by using the fundamental solutions of the Helmhotz operator equation with different orders. The numerical results for the lift and the drag hysteresis associated with a NACA0012 aerofoil oscillating in pitch are good in comparison with available experimental data.
文摘The authors propose a numerical algorithm for the two-dimensional Navier-Stokes equations written in stream function-vorticity formulation. The total time derivative term is treated with a first order characteristics method. The space approximation is based on a piecewise continuous finite element method. The proposed algorithm is used to simulate the mechanical aeration process in lakes. Such process is used to combat the degradation of the water quality due to the eutrophication phenomena. For this application high computing facilities and capacities are required. In order to optimize the computing time and make possible the simulation of real applications, the authors propose a parallel implementation of the numerical algorithm. The parallelization technique is performed using the Message Passing Interface. The efficiency of the proposed numerical algorithm is illustrated by some numerical results.
基金Supported by the National Natural Science Foundation of China(10372043,11172134)the Fundingof Jiangsu Innovation Program for Graduate Education(CXZZ11-0192)~~
文摘Gridless method is developed for unsteady viscous flows involving moving boundaries. The point distri- bution of gridless method is implemented in an isotropic or anisotropic way according to the features of viscous flows. In the area far away from the body, the traditional cloud of isotropic points is used, while in the adjacent area, the cloud of anisotropic points is distributed. In this way, the point spacing normal to the wall can be small enough for simulating the boundary layer, and meanwhile, the total number of points in the computational do- main can be controlled due to large spacing in other tangential direction through the anisotropic way. A fast mov- ing technique of clouds of points at each time-step is presented based on the attenuation law of disturbed motion for unsteady flows involving moving boundaries. In the mentioned cloud of points, a uniform weighted least- square curve fit method is utilized to discretize the spatial derivatives of the Navier-Stokes equations. The pro- posed gridless method, coupled with a dual time-stepping method and the Spalart-Allmaras turbulence model, is implemented for the Navier-Stokes equations. The computational results of unsteady viscous flows around a NLR7301 airfoil with an oscillating flap and a pitching NACA0012 airfoil are presented in a good agreement with the available experimental data.
文摘An unstructured Reynolds-averaged Navier-Stokes flow solver using the finite volume method is studied. The spatial discretisation is based on the Osher approximate Riemann solvers. A two-equation turbulence model (k-ω model) is also developed for hybrid grids to compute the turbulence flow. The turbulence flow past NACA0012 airfoil and the double ellipsolids are computed, and the numerical results show that the above methods are very efficient.
基金The research is SUpported by the NatlOllal Science Foundation of China(No.10371096)
文摘Residual-based a posteriori error estimate for conforming finite element solutions of incompressible Navier-Stokes equations, which is computed with a new two-level method that is different from Volker John, is derived. A posteriori error estimate contains additional terms in comparison to the estimate for the solution obtained by the standard finite element method. The importance of the additional terms in the error estimates is investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than the convergence of discrete solution. The two-level method aims to solve the nonlinear problem on a coarse grid with less computational work, then to solve the linear problem on a fine grid, which is superior to the usual finite element method solving a similar nonlinear problem on the fine grid.
基金the National Natural Science Foundation of China(Nos.10525101,10421101)the 973 Project of the Ministry of Science and Technology of China and the innovation grant from Chinese Academy of Sciences.
文摘Motivated by the results of J. Y. Chemin in ＂J. Anal. Math., 77, 1999, 27- 50＂ and G. Furioli et al in ＂Revista Mat. Iberoamer., 16, 2002, 605-667＂, the author considers further regularities of the mild solutions to Navier-Stokes equation with initial data uo ∈ L^d（R^d）. In particular, it is proved that if u C ∈（[0, T^＊）; L^d（R^d）） is a mild solution of （NSv）, then u（t,x）- e^vt△uo ∈ L^∞（（0, T）;B2/4^1,∞）~∩L^1 （（0, T）; B2/4^3 ,∞） for any T 〈 T^＊.
文摘Fourier analysis methods and in particular techniques based on Littlewood-Paley decomposition and paraproduct have known a growing interest recently for the study of nonlinear evolutionary equations. In this survey paper, we explain how these methods may be implemented so as to study the compresible Navier-Stokes equations in the whole space. We shall investigate both the initial value problem in critical Besov spaces and the low Mach number asymptotics.
基金supported by the National Natural Science Foundation of China (Grant No. 50936005)the National Basic Research Program of China (Grant No. 2010CB227302)
文摘Following the idea of Speziale＇s Very Large Eddy Simulation （VLES） method, a new unified hybrid simulation approach was proposed which can change seamlessly from RANS （Reynolds-Averaged Navier-Stokes） to LES （Large Eddy Simulation） method depending on the numerical resolution. The model constants were calibrated in accordance with other hybrid methods. Besides being able to approach the two limits of RANS and LES, the new model also provides a proper VLES mode between the two limits, and thus can be used for a wide range of mesh resolutions. Also RANS simulation can be recovered near the wall which is similar to the Detached Eddy Simulation （DES） concept. This new methodology was implemented into Wilcox＇s κ- ω model and applications were conducted for fully developed turbulent channel flow at ReT = 395 and turbulent flow past a square cylinder at Re = 22000. Results were compared with LES predictions and other studies. The new method is found to be quite efficient in resolving large flow structures, and can predict satisfactory results on relative coarse mesh.
基金supported by the National Natural Science Foundation of China (Grant No. 10872021)the Open Research Project of the State Key Laboratory of Mechanical System and Vibration (Grant No. MSV-2012-09)
文摘A novel circulation control technique is proposed to overcome the shortcomings of blowing jet circulation control, which uses the synthetic jet as the actuator and avoids the limitation about air supply requirement. The effectiveness of synthetic jet circulation control to enhance lift of NCCR1510-7067N airfoil is confirmed by solving the 2-D unsteady Reynolds-averaged Na- vier-Stokes equations. The aerodynamic characteristics and the flow structure （especially close to the trailing edge） of NCCR 1510-7067N airfoil at zero angle of attack are also presented to discuss the mechanism of lift enhancement of the airfoil with synthetic jet circulation control. The results indicate that the synthetic jet can effectively delay the separation point on the airfoil trailing edge and increase the circulation and lift of the airfoil by Coanda effect. The numerical simulation results demonstrate that the lift augmentation efficiency with synthetic jet circulation control reaches △C1/Cμ,=114 in the present study, which is much higher than the value 12.1 in the case with steady blowing jet circulation control.
基金supported by the National Natural Science Foundation of China(Grant Nos.10921202 and 91130001)the National Basic Research Program of China(Grant No. 2009CB724101)
文摘With the development of computational power and numerical algorithms,computational fluid dynamics(CFD) has become an important strategy for the design of aircraft,which significantly reduces the reliance on wind-tunnel and flight tests.In this paper,we conducted a numerical investigation on the flow past a full commercial aircraft at Mach number 0.2 and 14 degrees angle of attack by means of Reynolds-averaged Navier-Stokes(RANS),detached-eddy simulation(DES) and our newly developed constrained large-eddy simulation(CLES).The objective of this paper is to study the capability of these models in simulating turbulent flows.To our knowledge,this is the first large-eddy simulation method for full commercial aircraft simulation.The results show that the CLES can predict the mean statistical quantities well,qualitatively consistent with traditional methods,and can capture more small-scale structures near the surface of the aircraft with massive separations.Our study demonstrates that CLES is a promising alternative for simulating real engineering turbulent flows.
基金the financial support from EPSRC #EP/ G006482/1the funding support of Oversea Research Student Award from Scottish Government, UK
文摘In this study,based on the dynamic Biot＇s theory ＂u-p＂ approximation,a 3D finite element method（FEM） numerical soil model is developed,in which the Generalized Newmark-β method is adopted to determine the time integration.The developed 3D FEM soil model is a part of the coupled model PORO-WSSI 3D for 3D wave-seabed-marine structures interaction problem,and is validated by the analytical solution proposed by Wang（2000） for a laterally infinite seabed loaded by a uniform force.By adopting the developed 3D soil model,the consolidation of seabed under a caisson breakwater and hydrostatic pressure is investigated.The numerical results show that the caisson breakwater built on seabed has very significant effect on the stresses/displacements fields in the seabed foundation after the transient deformation and primary consolidation are completed.The parametric study indicates that the Young＇s modulus E of seabed is the most important parameter to affect the settlement of breakwater,and the displacement fields in seabed foundation.Taking the consolidation status as the initial condition,the interaction between ocean wave,caisson breakwater and seabed foundation is briefly investigated.The 3D ocean wave is determined by solving the Navier-Stokes equations with finite volume method（FVM）.The numerical results indicate that there is intensive interaction between oceean wave, caisson breakwater and seabed foundation; and the breakwater indeed can effectively block the wave energy propagating to the coastline.
基金supported by National Natural Science Foundation of China (50736007, 51006005)
文摘The governing equations are derived by circumferentially averaging the three-dimensional （3D） Navier-Stokes equations, which are solved using a time marching finite volume approach. Both Euler throughflow model and Navier-Stokes （N-S） throughflow model are employed to investigate the performance and flow fields of a highly loaded transonic single-stage fan ATS-2 and a four-stage fan. The results are compared with the experimental and three-dimensional computational results. It shows that the throughflow models can provide reasonable perform- ance characteristics and N-S throughflow model gives better predictions in endwall regions. A throughflow com- putation in which all the non-axisymmetric terms are included has been performed at off-design condition and the radial distributions of the flow field can be well described.
