A solver is developed for time-accurate computations of viscous flows based on the conception of Newton's method.A set of pseudo-time derivatives are added into governing equations and the discretized system is so...A solver is developed for time-accurate computations of viscous flows based on the conception of Newton's method.A set of pseudo-time derivatives are added into governing equations and the discretized system is solved using GMRES algorithm.Due to some special properties of GMRES algorithm,the solution procedure for unsteady flows could be regarded as a kind of Newton iteration.The physical-time derivatives of governing equations are discretized using two different approaches,i.e.,3-point Euler backward,and Crank-Nicolson formulas,both with 2nd-order accuracy in time but with different truncation errors.The turbulent eddy viscosity is calculated by using a version of Spalart-Allmaras one-equation model modified by authors for turbulent flows.Two cases of unsteady viscous flow are investigated to validate and assess the solver,i.e.,low Reynolds number flow around a row of cylinders and transonic bi-circular-arc airfoil flow featuring the vortex shedding and shock buffeting problems,respectively.Meanwhile,comparisons between the two schemes of timederivative discretizations are carefully made.It is illustrated that the developed unsteady flow solver shows a considerable efficiency and the Crank-Nicolson scheme gives better results compared with Euler method.展开更多
A basic equation system for meridional throughflow fields in multistage axial flow compressors has been deduced, containing many unknown correlation terms,which describe different kinds of spanwise mixing mechanism in...A basic equation system for meridional throughflow fields in multistage axial flow compressors has been deduced, containing many unknown correlation terms,which describe different kinds of spanwise mixing mechanism in a unified form.The equation system shows that spanwise mixing of meridional flows in compressors is attributed to three kinds of mechanism:molecular motion,turbulent diffusion,and circumferential non-uniformities,the last of which includes secondary flow effects and others.Therefore the equation system unifies the two models for spanwise mixing analyses by Adkins & Smith (1981) and Gallimore & Cumpsty (1986).With three kinds of apparent mixing coefficients defined and introduced into the basic equation system,a novel,much simpler equation system,without additional unknown correlation terms included,has been obtained.This novel equa- tion system makes throughflow computations including mixing far easier for multistage compressors.It has been rigorously shown that these apparent mixing coefficients contain full information of all the three kinds of mixing mechanism,so that the simpler equation system can also be taken as a unified model for meridional flows with all the kinds of the mixing effects.Calculations of the flow through multistage machines have been made by incorporating the new model into a streamline curvature throughflow calculation method and the improved agreement with experimental data has been obtained.It is believed that the simpler equation system can be applied to the flows not only in subsonic but in transonic and supersonic compressors if an appropriate model is proposed for the apparent mixing coefficients.展开更多
文摘A solver is developed for time-accurate computations of viscous flows based on the conception of Newton's method.A set of pseudo-time derivatives are added into governing equations and the discretized system is solved using GMRES algorithm.Due to some special properties of GMRES algorithm,the solution procedure for unsteady flows could be regarded as a kind of Newton iteration.The physical-time derivatives of governing equations are discretized using two different approaches,i.e.,3-point Euler backward,and Crank-Nicolson formulas,both with 2nd-order accuracy in time but with different truncation errors.The turbulent eddy viscosity is calculated by using a version of Spalart-Allmaras one-equation model modified by authors for turbulent flows.Two cases of unsteady viscous flow are investigated to validate and assess the solver,i.e.,low Reynolds number flow around a row of cylinders and transonic bi-circular-arc airfoil flow featuring the vortex shedding and shock buffeting problems,respectively.Meanwhile,comparisons between the two schemes of timederivative discretizations are carefully made.It is illustrated that the developed unsteady flow solver shows a considerable efficiency and the Crank-Nicolson scheme gives better results compared with Euler method.
文摘A basic equation system for meridional throughflow fields in multistage axial flow compressors has been deduced, containing many unknown correlation terms,which describe different kinds of spanwise mixing mechanism in a unified form.The equation system shows that spanwise mixing of meridional flows in compressors is attributed to three kinds of mechanism:molecular motion,turbulent diffusion,and circumferential non-uniformities,the last of which includes secondary flow effects and others.Therefore the equation system unifies the two models for spanwise mixing analyses by Adkins & Smith (1981) and Gallimore & Cumpsty (1986).With three kinds of apparent mixing coefficients defined and introduced into the basic equation system,a novel,much simpler equation system,without additional unknown correlation terms included,has been obtained.This novel equa- tion system makes throughflow computations including mixing far easier for multistage compressors.It has been rigorously shown that these apparent mixing coefficients contain full information of all the three kinds of mixing mechanism,so that the simpler equation system can also be taken as a unified model for meridional flows with all the kinds of the mixing effects.Calculations of the flow through multistage machines have been made by incorporating the new model into a streamline curvature throughflow calculation method and the improved agreement with experimental data has been obtained.It is believed that the simpler equation system can be applied to the flows not only in subsonic but in transonic and supersonic compressors if an appropriate model is proposed for the apparent mixing coefficients.
