3D Numerical Simulation of Overbank Flow in Non-Orthogonal Curvilinear Coordinates

The velocity field in meandering compound channels with overhank flow is highly three dimensional. To date, its features have been investigated experimentally and little research has been undertaken to investigate the feasibility of reproducing these velocity fields with computer models. If computer modeling were to prove successful in this context, it could become a useful prediction technique and research tool to enhance our understanding of natural river dynamics. A 3-D k-E turbulence hydrodynamic model in curvilinear coordinates is established to simulate the overhank flow. The bodyfitted coordinate is adopted in the horizontal plane, the part grid is adopted in the vertical direction, and the wall-function method is employed to simulate the bed resistance. The model is applied to the simulation of the meandering channel with straight flood plain banks, and the main velocities and secondary velocities for both the longitudinal and cross sections are presented. Comparison and analysis show that the results of simulation are fit to reflect the results of experiment. These results show the application value of the model to 3D overhank flow.

Characteristics of a Terrain-Following Sigma Coordinate

This study quantifies the main characteristics of a terrain-following, G-coordinate through mathematical analyses of its covariant and contravariant basis vectors as well as the vertical coordinate of σ. A 3-D schematic of the σ-coordinate in a curvilinear coordinate system is provided in this study. The characteristics of the basis vectors were broken down into their ＂local vector charac- teristics＂ and ＂spatial distribution characteristics＂, and the exact expressions of the covariant; in addition, the con- travariant basis vectors of the G-coordinate used to eluci- date their detailed characteristics were properly solved. Through rewriting the expression of the vertical coordi- nate of G, a mathematical expression of all the cr-coor- dinate surfaces was found, thereby quantifying the so- called terrain-following characteristics and lack of flexi- bility to adjust the slope variation of G-coordinate sur- faces for the classic definition of G. Finally, an analysis on the range value of the vertical coordinate demonstrated that the general value range of G could be obtained by eliminating the G-coordinate surfaces below the Earth＇s surface. All these quantitative descriptions of the charac- teristics of G-coordinate were the foundation for improv- ing the G-coordinate or creating a new one.

非正交坐标系下NPC三电平逆变器控制方法

对于二极管钳位式三电平逆变器,采用传统的空间矢量脉宽调制方法在大扇区判断、小三角形判断和矢量作用时间等方面需进行大量的三角函数运算,这大大增加了控制器的计算量。研究了一种非正弦坐标系的空间脉宽调制方法,对传统的空间矢量脉宽调制进行简化。仿真结果和实验结果证明了该非正弦坐标系下的NPC三电平逆变器控制方法的有效性。

A New Approach to Implement Sigma Coordinate in a Numerical Model

This study shows a new way to implement terrain-following s-coordinate in a numerical model,which does not lead to the well-known"pressure gradient force(PGF)"problem.First,the causes of the PGF problemare analyzedwith existing methods that are categorized into two different types based on the causes.Then,the new method that bypasses the PGF problem all together is proposed.By comparing these threemethods and analyzing the expression of the scalar gradient in a curvilinear coordinate system,this study finds out that only when using the covariant scalar equations of s-coordinate will the PGF computational form have one term in each momentum component equation,thereby avoiding the PGF problem completely.A convenient way of implementing the covariant scalar equations of s-coordinate in a numerical atmospheric model is illustrated,which is to set corresponding parameters in the scalar equations of the Cartesian coordinate.Finally,two idealized experimentsmanifest that the PGF calculated with the new method is more accurate than using the classic one.This method can be used for oceanic models as well,and needs to be tested in both the atmospheric and oceanic models.

Energy Efficiency Maximization for Cooperative NOMA with Hardware Impairments

The massive connectivity and limited energy pose significant challenges to deploy the enormous devices in energy-efficient and environmentally friendly in the Internet of Things(IoT).Motivated by these challenges,this paper investigates the energy efficiency(EE)maximization problem for downlink cooperative non-orthogonal multiple access(C-NOMA)systems with hardware impairments(HIs).The base station(BS)communicates with several users via a half-duplex(HD)amplified-and-forward(AF)relay.First,we formulate the EE maximization problem of the system under HIs by jointly optimizing transmit power and power allocated coefficient(PAC)at BS,and transmit power at the relay.The original EE maximization problem is a non-convex problem,which is challenging to give the optimal solution directly.First,we use fractional programming to convert the EE maximization problem as a series of subtraction form subproblems.Then,variable substitution and block coordinate descent(BCD)method are used to handle the sub-problems.Next,a resource allocation algorithm is proposed to maximize the EE of the systems.Finally,simulation results show that the proposed algorithm outperforms the downlink cooperative orthogonal multiple access(C-OMA)scheme.

THREE-DIMENSIONAL SIMULATION OF MEANDERING RIVER BASED ON 3-D RNG k-ε TURBULENCE MODEL

A 3-D numerical model for calculating flow in non-curvilinear coordinates was established in this article. The flow was simulated by solving the full Reynolds-averaged Navier-Stokes equations with the RNG κ-ε turbulence model. In the horizontal x-y-plane, a boundary-fitted curvilinear co-ordinate system was adopted, while in the vertical direction, a σ co-ordinate transformation was used to represent the free surface and bed topography. The water level was determined by solving the 2-D Poisson equation derived from 2-D depth averaged momentum equations. The finite-volume method was used to discretize the equations and the SIMPLEC algorithm was applied to acquire the coupling of velocity and pressure. This model was applied to simulate the meandering channels and natural rivers, and the water levels and the velocities for all sections were given. By contrasting and analyzing, the agreement with measurements is generally good. The feasibility studies of simulating flow of the natural fiver have been conducted to demonstrate its applicability to hydraulic engineering research.

Stream Surface Theory of Bird-like Flapping Flight

Through analyzing the motion characteristics of bird-like flapping flight, it is considered that the wing angular acceleration is equal to zero at the point of maximum angular speed. Thus, the flapping flight is equivalent to a uniform rotating motion which can be analyzed by using the stream surface theory of turbomachinery during a micro period of time. In this article, the N-S equations of the motion are expanded in a non-orthogonal curvilinear coordinate system, and simplified on stream surfaces of the flapping flight model. By using stream function me- thod, the three-dimensional unsteady flow equations are simplified as a two-order partial differential equation with variable coefficients eventually and the equation＇s iterative solving method on S1 and $2 stream surfaces of the flapping flight model is presented. Through expanding the relatively steady equations of flapping flight at an arbitrary time point of a stroke on meridional plane of the flapping flight model, it can use a relatively steady mo- tion to approximate the real flapping flight at that time point, and analyze the flow stability influenced by the wing＇s flexibility. It can be seen that the wing flexibility is related to the higher pressurization capacity and the flow stability, and the pressurization capacity of flexible wing is proportional to the angular speed, angular distor- tion rate and radius square.

NUMERICAL SOLUTIONS OF REYNOLDS AVERAGED NAVIER-STOKES EQUATIONS FOR 3-D TURBULENT FLOW OVER CONCAVE SURFACES OF DISCHARGING STRUCTURES

This paper is conserned with a numerical method for the solution of complete Reynolds averaged Navier Stokes equations for three dimensional flows over the concave surfaces of discharging structures. A non orthogonal body fitted coordinate system was used to deal with the complex physical geometry, and finite volume method (FVM) was employed to solve the convective transport equations for mean velocities and turbulence parameters (k, ε). It is indicated through the numerical example that the calculated results are in good agreement with the experimental ones, and it is also proved that this numerical method used to predict the characteristics of turbulent flow over the concave surfaces of discharging structures is feasible.