Direct numerical simulation based on OpenFOAM is carried out for two-dimensional RayleighBénard( RB) convection in a square domain at high Rayleigh number of 107 and Pr = 0.71. Proper orthogonal decomposition( PO...Direct numerical simulation based on OpenFOAM is carried out for two-dimensional RayleighBénard( RB) convection in a square domain at high Rayleigh number of 107 and Pr = 0.71. Proper orthogonal decomposition( POD) is used to analyze the flow and temperature characteristics from POD energy spectrum and eigenmodes. The results show that the energy spectrum converges fast and the scale of vortex structures captured by eigenmodes becomes smaller as the eigenmode order increases. Meanwhile,a low-dimensional model( LDM) for RB convection is derived based on POD eigenmodes used as a basis of Galerkin project of Navier-Stokes-Boussinesq equations. LDM is built based on different number of eigenmodes and through the analysis of phase portraits,streamline and isothermal predicted by LDM,it is suggested that the error between LDM and DNS is still large.展开更多
The reduced-order model （ROM） for the two-dimensional supersonic cavity flow based on proper orthogonal decomposition （POD） and Galerkin projection is investigated. Presently, popular ROMs in cavity flows are base...The reduced-order model （ROM） for the two-dimensional supersonic cavity flow based on proper orthogonal decomposition （POD） and Galerkin projection is investigated. Presently, popular ROMs in cavity flows are based on an isentropic assumption, valid only for flows at low or moderate Mach numbers. A new ROM is constructed involving primitive variables of the fully compressible Navier-Stokes （N-S） equations, which is suitable for flows at high Mach numbers. Compared with the direct numerical simulation （DNS） results, the proposed model predicts flow dynamics （e.g., dominant frequency and amplitude） accurately for supersonic cavity flows, and is robust. The comparison between the present transient flow fields and those of the DNS shows that the proposed ROM can capture self-sustained oscillations of a shear layer. In addition, the present model reduction method can be easily extended to other supersonic flows.展开更多
基金Sponsored by the National Natural Science Foundation of China(Grant o.51576051)
文摘Direct numerical simulation based on OpenFOAM is carried out for two-dimensional RayleighBénard( RB) convection in a square domain at high Rayleigh number of 107 and Pr = 0.71. Proper orthogonal decomposition( POD) is used to analyze the flow and temperature characteristics from POD energy spectrum and eigenmodes. The results show that the energy spectrum converges fast and the scale of vortex structures captured by eigenmodes becomes smaller as the eigenmode order increases. Meanwhile,a low-dimensional model( LDM) for RB convection is derived based on POD eigenmodes used as a basis of Galerkin project of Navier-Stokes-Boussinesq equations. LDM is built based on different number of eigenmodes and through the analysis of phase portraits,streamline and isothermal predicted by LDM,it is suggested that the error between LDM and DNS is still large.
基金Project supported by the National Natural Science Foundation of China(Nos.11232011,11402262,11572314,and 11621202)
文摘The reduced-order model （ROM） for the two-dimensional supersonic cavity flow based on proper orthogonal decomposition （POD） and Galerkin projection is investigated. Presently, popular ROMs in cavity flows are based on an isentropic assumption, valid only for flows at low or moderate Mach numbers. A new ROM is constructed involving primitive variables of the fully compressible Navier-Stokes （N-S） equations, which is suitable for flows at high Mach numbers. Compared with the direct numerical simulation （DNS） results, the proposed model predicts flow dynamics （e.g., dominant frequency and amplitude） accurately for supersonic cavity flows, and is robust. The comparison between the present transient flow fields and those of the DNS shows that the proposed ROM can capture self-sustained oscillations of a shear layer. In addition, the present model reduction method can be easily extended to other supersonic flows.
