The direct numerical simulation (DNS) is carried out for the incompressible viscous turbulent flows over an anisotropic porous wall. Effects of the anisotropic porous wall on turbulence modifications as well as on the...The direct numerical simulation (DNS) is carried out for the incompressible viscous turbulent flows over an anisotropic porous wall. Effects of the anisotropic porous wall on turbulence modifications as well as on the turbulent drag reduction are investigated. The simulation is carried out at a friction Reynolds number of 180, which is based on the averaged friction velocity at the interface between the porous medium and the clear fluid domain. The depth of the porous layer ranges from 0.9 to 54 viscous units. The permeability in the spanwise direction is set to be lower than the other directions in the present simulation. The maximum drag reduction obtained is about 15.3% which occurs for a depth of 9 viscous units. The increasing of drag is addressed when the depth of the porous layer is more than 25 wall units. The thinner porous layer restricts the spanwise extension of the streamwise vortices which suppresses the bursting events near the wall. However, for the thicker porous layer, the wall-normal fluctuations are enhanced due to the weakening of the wall-blocking effect which can trigger strong turbulent structures near the wall.展开更多
Self-similar steady natural convection thermal boundary layer flow from a rotating vertical cone to anisotropic Darcian porous medium is investigated theoretically and numerically. The transformed non-dimensional two-...Self-similar steady natural convection thermal boundary layer flow from a rotating vertical cone to anisotropic Darcian porous medium is investigated theoretically and numerically. The transformed non-dimensional two-point boundary value problem is reduced to a system of coupled, highly nonlinear ordinary differential equations, which are solved subject to robust surface and free stream boundary conditions with the MAPLE 17 numerical quadrature software. Validation with earlier non-rotating studies is included, and also further verification of rotating solutions is achieved with a variational finite element method （FEM）. The rotational （spin） parameter emerges as an inverse function of the Grashof number. The influence of this parameter, primary Darey number, secondary Darcy number and Prandtl number on tangential velocity and swirl velocity, temperature and heat transfer rate are studied in detail. It is found that the dimensionless tangential velocity increases whilst the dimensionless swirl velocity and temperature decrease with the swirl Darcy number, tangential Darcy number and the rotational parameters. The model finds applications in chemical engineering filtration processing, liquid coating and spinning cone distillation columns.展开更多
The effects of hydrodynamic anisotropy on the mixed-convection in a vertical porous channel heated on its plates with a thermal radiation are investigated analytically for fully developed flow regime. The porous mediu...The effects of hydrodynamic anisotropy on the mixed-convection in a vertical porous channel heated on its plates with a thermal radiation are investigated analytically for fully developed flow regime. The porous medium is anisotropic in permeability whose principal axes are oriented in a direction that is oblique to the gravity. The generalized Brinkman-extended Darcy model which allows the no-slip boundary-condition on solid wall is used in the formulation of the problem. The flow reversal, the thermal radiation influence for natural, and forced convection are considered in the limiting cases for low and high porosity media. It was found that the anisotropic permeability ratio, the orientation angle of the principal axes of permeability and the radiation parameter affected significantly the flow regime and the heat transfer.展开更多
We establish the existence of fundamental solutions for the anisotropic porous medium equation, ut = ∑n i=1（u^mi）xixi in R^n × （O,∞）, where m1,m2,..., and mn, are positive constants satisfying min1≤i≤n{...We establish the existence of fundamental solutions for the anisotropic porous medium equation, ut = ∑n i=1（u^mi）xixi in R^n × （O,∞）, where m1,m2,..., and mn, are positive constants satisfying min1≤i≤n{mi}≤ 1, ∑i^n=1 mi 〉 n - 2, and max1≤i≤n{mi} ≤1/n（2 ＋ ∑i^n=1 mi）.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.11572183,91852111,and 11825204)the Program of Shanghai Municipal Education Commission(No.2019-01-07-00-09-E00018)
文摘The direct numerical simulation (DNS) is carried out for the incompressible viscous turbulent flows over an anisotropic porous wall. Effects of the anisotropic porous wall on turbulence modifications as well as on the turbulent drag reduction are investigated. The simulation is carried out at a friction Reynolds number of 180, which is based on the averaged friction velocity at the interface between the porous medium and the clear fluid domain. The depth of the porous layer ranges from 0.9 to 54 viscous units. The permeability in the spanwise direction is set to be lower than the other directions in the present simulation. The maximum drag reduction obtained is about 15.3% which occurs for a depth of 9 viscous units. The increasing of drag is addressed when the depth of the porous layer is more than 25 wall units. The thinner porous layer restricts the spanwise extension of the streamwise vortices which suppresses the bursting events near the wall. However, for the thicker porous layer, the wall-normal fluctuations are enhanced due to the weakening of the wall-blocking effect which can trigger strong turbulent structures near the wall.
文摘Self-similar steady natural convection thermal boundary layer flow from a rotating vertical cone to anisotropic Darcian porous medium is investigated theoretically and numerically. The transformed non-dimensional two-point boundary value problem is reduced to a system of coupled, highly nonlinear ordinary differential equations, which are solved subject to robust surface and free stream boundary conditions with the MAPLE 17 numerical quadrature software. Validation with earlier non-rotating studies is included, and also further verification of rotating solutions is achieved with a variational finite element method （FEM）. The rotational （spin） parameter emerges as an inverse function of the Grashof number. The influence of this parameter, primary Darey number, secondary Darcy number and Prandtl number on tangential velocity and swirl velocity, temperature and heat transfer rate are studied in detail. It is found that the dimensionless tangential velocity increases whilst the dimensionless swirl velocity and temperature decrease with the swirl Darcy number, tangential Darcy number and the rotational parameters. The model finds applications in chemical engineering filtration processing, liquid coating and spinning cone distillation columns.
文摘The effects of hydrodynamic anisotropy on the mixed-convection in a vertical porous channel heated on its plates with a thermal radiation are investigated analytically for fully developed flow regime. The porous medium is anisotropic in permeability whose principal axes are oriented in a direction that is oblique to the gravity. The generalized Brinkman-extended Darcy model which allows the no-slip boundary-condition on solid wall is used in the formulation of the problem. The flow reversal, the thermal radiation influence for natural, and forced convection are considered in the limiting cases for low and high porosity media. It was found that the anisotropic permeability ratio, the orientation angle of the principal axes of permeability and the radiation parameter affected significantly the flow regime and the heat transfer.
基金The research is supported by National 973-Project the Trans-Century Training Programme Foundation for the Talents by the Ministry of Education
文摘We establish the existence of fundamental solutions for the anisotropic porous medium equation, ut = ∑n i=1（u^mi）xixi in R^n × （O,∞）, where m1,m2,..., and mn, are positive constants satisfying min1≤i≤n{mi}≤ 1, ∑i^n=1 mi 〉 n - 2, and max1≤i≤n{mi} ≤1/n（2 ＋ ∑i^n=1 mi）.
