The formulations and approximations of the branch flow model for general(radial and mesh) power networks(General-BranchFlow) are given in this paper. Using different sets of the power flow equations, six formats of th...The formulations and approximations of the branch flow model for general(radial and mesh) power networks(General-BranchFlow) are given in this paper. Using different sets of the power flow equations, six formats of the exact General-BranchFlow model are listed. The six formats are mathematically equivalent with each other. Linear approximation and second-order cone programming(SOCP) are then used to derive the six formats of the convex General-BranchFlow model. The branch ampacity constraints considering the shunt conductance and capacitance of the transmission line Π-model are derived. The key foundation of deriving the ampacity constraints is the correct interpretation of the physical meaning of the transmission line Π-model. An exact linear expression of the ampacity constraints of the power loss variable is derived. The applications of the General-BranchFlow model in deriving twelve formats of the exact optimal power flow(OPF) model and twelve formats of the approximate OPF model are formulated and analyzed. Using the Julia programming language, the extensive numerical investigations of all formats of the OPF models show the accuracy and computational efficiency of the General-BranchFlow model. A penalty function based approximation gap reduction method is finally proposed and numerically validated to improve the AC-feasibility of the approximate General-BranchFlow model.展开更多
Fiber orientation and dispersion in the dilute fiber suspension that flows through a T-shaped branching channel are simulated numerically based on the slender-body theory. The simulated results are consistent qualitat...Fiber orientation and dispersion in the dilute fiber suspension that flows through a T-shaped branching channel are simulated numerically based on the slender-body theory. The simulated results are consistent qualitatively with the experimental data available in the literature. The results show that the spatial distribution of fibers is dependent on the fiber aspect ratio, but has no relation with the volume fraction of fiber. The content ratio of fibers near the upper wall increases monotonically with an increasing Re number, and the situation is reverse for the region near the bottom wall. The orientation of fibers depends on Re number, however, the function of fiber volume fraction and aspect ratio is negligible. The fibers near the wall and in the central region of the channel align along the flow direction at all times, but the fibers in the other parts of the channel tend to align along the flow direction only in the downstream region.展开更多
Flow distribution in branch piping system is affected by flow characteristics and different geometric variations.Most of the flow distribution studies are performed with one-dimensional analysis to yield overall infor...Flow distribution in branch piping system is affected by flow characteristics and different geometric variations.Most of the flow distribution studies are performed with one-dimensional analysis to yield overall information only.However,detailed analysis is required to find effects of design parameters on the flow distribution.For this aspect,three-dimensional turbulent flow analysis was performed to assess turbulence model performance and effects of upstream pressure and branch pipe geometry.Three different turbulence models of standard k-ε model,realizable k-ε model and standard k-ω yield similar results,indicating small effects of turbulence models on flow characteristics analysis.Geometric variations include area ratio of main and branch pipes,branch pipe diameter,and connection shape of main and branch pipes.Among these parameters,area ratio and branch diameter and shape show strong effect on flow distribution due to high friction and minor loss.Uniform flow distribution is one of common requirements in the branch piping system and this can be achieved with rather high total loss design.展开更多
The concentration and orientation of fiber in a turbulent T-shaped branching channel flow are investi-gated numerically. The Reynolds averaged Navier-Stokes equations together with the Reynolds stress turbulent model ...The concentration and orientation of fiber in a turbulent T-shaped branching channel flow are investi-gated numerically. The Reynolds averaged Navier-Stokes equations together with the Reynolds stress turbulent model are solved for the mean flow field and the turbulent kinetic energy. The fluctuating velocities of the fluid are assumed as a random variable with Gaussian distribution whose variance is related to the turbulent kinetic energy. The slender-body theory is used to simulate the fiber motion based on the known mean and fluctuating velocities of the fluid. The results show that at low Reynolds number, fiber concentration is high in the flow separation regions, and fiber orientation throughout the channel is widely distributed with a slight preference of aligning along the horizontal axis. With increasing of Re, the high concentration region disappears, and fiber orientation becomes ho-mogeneous without any preferred direction. At high Reynolds number, fiber concentration increases gradually along the flow direction. The differences in the distribution of concentration and orientation between different fiber aspect ratio are evident only at low Re. Both Re and fiber aspect ratio have small effect on the variance of orientation angle.展开更多
文摘The formulations and approximations of the branch flow model for general(radial and mesh) power networks(General-BranchFlow) are given in this paper. Using different sets of the power flow equations, six formats of the exact General-BranchFlow model are listed. The six formats are mathematically equivalent with each other. Linear approximation and second-order cone programming(SOCP) are then used to derive the six formats of the convex General-BranchFlow model. The branch ampacity constraints considering the shunt conductance and capacitance of the transmission line Π-model are derived. The key foundation of deriving the ampacity constraints is the correct interpretation of the physical meaning of the transmission line Π-model. An exact linear expression of the ampacity constraints of the power loss variable is derived. The applications of the General-BranchFlow model in deriving twelve formats of the exact optimal power flow(OPF) model and twelve formats of the approximate OPF model are formulated and analyzed. Using the Julia programming language, the extensive numerical investigations of all formats of the OPF models show the accuracy and computational efficiency of the General-BranchFlow model. A penalty function based approximation gap reduction method is finally proposed and numerically validated to improve the AC-feasibility of the approximate General-BranchFlow model.
基金The project supported by the National Natural Science Foundation of China(10372090)Doctoral Program of Higher Education in China(20030335001)
文摘Fiber orientation and dispersion in the dilute fiber suspension that flows through a T-shaped branching channel are simulated numerically based on the slender-body theory. The simulated results are consistent qualitatively with the experimental data available in the literature. The results show that the spatial distribution of fibers is dependent on the fiber aspect ratio, but has no relation with the volume fraction of fiber. The content ratio of fibers near the upper wall increases monotonically with an increasing Re number, and the situation is reverse for the region near the bottom wall. The orientation of fibers depends on Re number, however, the function of fiber volume fraction and aspect ratio is negligible. The fibers near the wall and in the central region of the channel align along the flow direction at all times, but the fibers in the other parts of the channel tend to align along the flow direction only in the downstream region.
基金Project supported by Changwon National University in 2010
文摘Flow distribution in branch piping system is affected by flow characteristics and different geometric variations.Most of the flow distribution studies are performed with one-dimensional analysis to yield overall information only.However,detailed analysis is required to find effects of design parameters on the flow distribution.For this aspect,three-dimensional turbulent flow analysis was performed to assess turbulence model performance and effects of upstream pressure and branch pipe geometry.Three different turbulence models of standard k-ε model,realizable k-ε model and standard k-ω yield similar results,indicating small effects of turbulence models on flow characteristics analysis.Geometric variations include area ratio of main and branch pipes,branch pipe diameter,and connection shape of main and branch pipes.Among these parameters,area ratio and branch diameter and shape show strong effect on flow distribution due to high friction and minor loss.Uniform flow distribution is one of common requirements in the branch piping system and this can be achieved with rather high total loss design.
基金Supported by the Major Program of the National Natural Science Foundation of China (No.10632070).
文摘The concentration and orientation of fiber in a turbulent T-shaped branching channel flow are investi-gated numerically. The Reynolds averaged Navier-Stokes equations together with the Reynolds stress turbulent model are solved for the mean flow field and the turbulent kinetic energy. The fluctuating velocities of the fluid are assumed as a random variable with Gaussian distribution whose variance is related to the turbulent kinetic energy. The slender-body theory is used to simulate the fiber motion based on the known mean and fluctuating velocities of the fluid. The results show that at low Reynolds number, fiber concentration is high in the flow separation regions, and fiber orientation throughout the channel is widely distributed with a slight preference of aligning along the horizontal axis. With increasing of Re, the high concentration region disappears, and fiber orientation becomes ho-mogeneous without any preferred direction. At high Reynolds number, fiber concentration increases gradually along the flow direction. The differences in the distribution of concentration and orientation between different fiber aspect ratio are evident only at low Re. Both Re and fiber aspect ratio have small effect on the variance of orientation angle.
