The mathematical equations of 2-D thermal density flow in a channel were developed and a finite layer numerical model was established. In the direction of y, a cubic spline approximations were used for u and θ, and l...The mathematical equations of 2-D thermal density flow in a channel were developed and a finite layer numerical model was established. In the direction of y, a cubic spline approximations were used for u and θ, and linear interpolation were used for du/dx and dθ/dx. The integration of differential equations along the direction of y was made with the subdomain scheme of weighted residual method. In the direction of x, the boundary value problem of differential equations was converted into an initial value problem. It is then solved by shooting method. An effective method for choosing and amending shooting multipoint initial values have been presented. The vertical distribution of u and θ at each x-section were also obtained.展开更多
The perturbation solution of axial and secondary flow behavior in a curved annular duct was presented. First, a nonorthogonal cylindrical coordinate system was introduced. Second, the Navier-Stokes equations and conti...The perturbation solution of axial and secondary flow behavior in a curved annular duct was presented. First, a nonorthogonal cylindrical coordinate system was introduced. Second, the Navier-Stokes equations and continuity equation were established in tensorial form. The zeroth-order, first-order and second-order analytic perturbation solutions were obtained. It is found that there is a secondary flow in the annular section, and four recirculating cells in the cross section.展开更多
文摘The mathematical equations of 2-D thermal density flow in a channel were developed and a finite layer numerical model was established. In the direction of y, a cubic spline approximations were used for u and θ, and linear interpolation were used for du/dx and dθ/dx. The integration of differential equations along the direction of y was made with the subdomain scheme of weighted residual method. In the direction of x, the boundary value problem of differential equations was converted into an initial value problem. It is then solved by shooting method. An effective method for choosing and amending shooting multipoint initial values have been presented. The vertical distribution of u and θ at each x-section were also obtained.
文摘The perturbation solution of axial and secondary flow behavior in a curved annular duct was presented. First, a nonorthogonal cylindrical coordinate system was introduced. Second, the Navier-Stokes equations and continuity equation were established in tensorial form. The zeroth-order, first-order and second-order analytic perturbation solutions were obtained. It is found that there is a secondary flow in the annular section, and four recirculating cells in the cross section.
