滇池夏季营养盐空间分布特征研究

基于2014年8月滇池外海空间23个采样点的水质采样数据,考虑化学需氧量(COD)、悬浮颗粒物(SS)、总磷(TP)、溶解性总磷(DTP)、总氮(TN)、溶解性总氮(DTN)、叶绿素a(Chla)七种理化变量并加入空间坐标信息,采用K-means聚类分析方法将采样点划分为三组,并对加入空间坐标信息前后的变量进行聚类效果分析,应用相关性分析方法分析聚类后不同组中各测点水质指标之间的相关性,结合七个水质指标的熵权评价结果研究了水质的空间分布特征。结果表明,加入空间坐标信息后的聚类可避免聚类后同组点的空间分布分散的情况,有助于优化常规的水质监测点位;各水质指标之间并不存在明显相关性,叶绿素a的空间差异明显,呈现出北高南低的空间分布特征,这与流域上的营养盐排放主要集中在东北部区域,并随水流由北向南对流扩散有关。     

Melting of PCM around a horizontal cylinder with constant surface temperature

A numerical study of melting of phase change material (PCM) around a horizontal circular cylinder of constant wall temperature and in the presence of the natural convection in the melt region is presented. A two dimensional mathematical model is formulated in terms of primitive variables and a coordinate transformation technique is used to fix the moving front. The finite volume approach is used to discretize the system of governing equations to obtain a system of linear algebraic equations. An implicit scheme is used for the momentum and energy equations and an explicit scheme for the energy balance at the interface. The numerical predictions were compared with available results to establish the validity of the model and additional results are obtained to demonstrate the effects of Rayleigh and Stefan numbers as well as the wall temperature on the time for complete fusion and total melt volume.     

APPLICATION OF GDQ METHOD FOR THE STUDY OF NATURAL CONVECTION IN HORIZONTAL ECCENTRIC ANNULI

A generalized differential-integral quadrature (GDQ) discretization technique developed by one of the authors was used to solve a natural convection problem in a body-fit coordinate system in their primitive variables form. A special treatment of the boundary conditions to satisfy the continuity and momentum equations along the boundaries with the implementation of the GDQ method was investigated. Comparisons with the experimental and numerical results of other investigators are presented and discussed. In contrast with the existing published results, this highly accurate method was able to reveal extremely weak net circulation around the inner eccentric cylinder that was not found previously by other investigators. This net circulation has its maximum value when the inclination angle of eccentricity is in the horizontal position.     

Numerical solution of the phase change problem around a horizontal cylinder in the presence of natural convection in the melt region

This paper deals with the numerical study of melting of phase change material around a horizontal circular cylinder in the presence of the natural convection in the melt phase. A two dimensional unsteady mathematical model has been formulated in terms of primitive variables and a coordinate transformation technique has been used to fix the moving front. The finite volume approach was used to discretize the system of governing equations, boundary and initial conditions and obtain a system of linear algebraic equations. In the numerical solution an implicit scheme was used for the momentum and energy equations and an explicit scheme for the energy balance at the interface. The numerical predictions were compared with available results to establish the validity of the model and the numerical approach.     

Point source in weak shear flow

This note is an analytic study of the temperature field due to a point heat source placed in a two-dimensional shear flow. The governing three-dimensional equation is perturbed using a small shear parameter. The resulting successive partial differential equations are further reduced into ordinary differential equations by utilizing a proper mixture of Cartesian and polar coordinate variables. The results show the isotherms are skewed towards the lower velocity regions. In certain cases a second temperature maximum may appear on downstream planes perpendicular to the flow.     

Heat transfer in duct flow of non-Newtonian fluids with axial conduction

A special eigenfunction expansion is used to derive an exact solution for heat transfer in laminar flow of a non-Newtonian fluid inside a circular or parallel-plate duct, including axial heat conduction, where the wall is either maintained at a constant temperature or convects heat. The flow is hydrodynamically fully-developed and the velocity distribution may have an arbitrary dependence on the cross flow coordinate. The main features of the present solution are: the eigenfunctions are the same for a given geometry, independent of the velocity distribution; separation of variables of the seemingly non-separable governing partial differential equation; and any velocity distribution, complicated as it may be, is handled easily. The solution accuracy is validated against many published results. It is shown that, as expected, axial heat conduction is significant at the duct inlet.     

Numerical Simulation of Sub-cooled Cavitating Flow by Using Bubble Size Distribution

A new cavitating model by using bubble size distribution based on mass of bubbles is proposed. Liquid phase is treated with Eulerian framework as a mixture containing minute cavitating bubbles. Vapor phase consists of various sizes of minute vapor bubbles, which is distributed to classes based on their mass. The change of bubble number density for each class was solved by considering the change of bubble mass due to phase change as well as generation of new bubbles due to heterogeneous nucleation. In this method the mass of bubbles is treated as an independent variable, in other word, a new coordinate, and dependant variables are solved in Eulerian framework for spatial coordinates and bubble-mass coordinate. The present method is applied to a cavitating flow in a convergent-divergent nozzle, and the two-phase flow with bubble size distribution and phase change was successfully predicted.     

Heatline method for the visualization of natural convection in a complicated cavity

In this paper, natural convection inside a two-dimensional cavity with a wavy right vertical wall has been carried out. The bottom wall is heated by a spatially varying temperature and other three walls are kept at constant lower temperature. The integral forms of the governing equations are solved numerically using finite-volume method in non-orthogonal body-fitted coordinate system. SIMPLE algorithm with higher-order upwinding scheme are used. The method of numerical visualization of heat transport for convective heat transfer by heatlines is studied. The heatfunction equation in the transformed plane is solved in terms of dimensionless variables. Results are presented in the form of streamlines, isotherms, heatlines, local and average Nusselt number distribution for a selected range of Rayleigh number (10⁰–10⁶). The results are presented for three different undulations (1–3) with different wave amplitude (0.00–0.10) and a fluid having Prandtl number 0.71.     

Dynamic response of curved pipes

The problem of the linear elastic response of a thin curved pipe subjected to a local impulsive loading is considered. A series solution based on the Sanders shell theory is developed in the toroidal coordinate system. This solution covers the case of a pipe with arbitrary circular curvature of the torus center line. The loading is represented as a double series in the geometric variables, and direct time integration is carried out using the Newmark method. Sample results are presented for loadings concentrated at the intrados and extrados for both short and long pipes.     

Unsteady heat conduction involving phase changes for an irregular bubble/particle entrapped in a solid during freezing – An extension of the heat-balance integral method

Temperature distributions in the molten layer and solid with distinct properties around a bubble or particle entrapped in the solid during unidirectional solidification are determined by applying a heat-balance integral approximation method. The present model can be used to simulate growth, entrapment or departure of a bubble or particle inclusion in solids encountered in manufacturing and materials processing, MEMS, contact melting processes, drilling, etc. In this work, the proposed heat-balance equations are derived by integrating unsteady elliptic heat diffusion equations and introducing the Stefan boundary condition. Due to the time-dependent irregular shapes of phases, coefficients of assumed quadratic temperature profiles are considered to be functions of longitudinal coordinate and time. Temperature coefficients in distinct regions therefore are determined by solving equations governing temperature coefficients derived from heat-balance equations, imposing boundary conditions, and introducing a fictitious boundary condition. The computed temperature fields show agreement with predictions from the finite-difference method. Since the number of independent variables is reduced by one, this work provides an effective method to solve unsteady elliptic diffusion problems experiencing solid–liquid phase changes in irregular shapes.     

Thermal buckling of FGEM plates integrated with surface-bonded piezoelectric layers and temperature-dependent material properties

Based on Reissner’s mixed variational theorem (RMVT), a unified formulation of finite layer methods (FLMs) is developed for the quasi three-dimensional (3-D) thermal buckling analysis of simply-supported, sandwich piezoelectric plates embedded with a functionally graded elastic material (FGEM) core, the material properties of which are considered to be thickness- and temperature-dependent. The plate is subjected to a uniform temperature change and with open-/closed-circuit boundary conditions on the lateral surfaces. A 3-D linear buckling theory is used, in which a set of membrane stresses is assumed to exist just before buckling occurs, and these membrane stresses are determined using a set of predefined 3-D deformations for the pre-buckling state. The material properties of the FGEM core are assumed to obey the power-law distributions varying through the thickness coordinate of the core according to the volume fractions of the constituents. The effective material properties are estimated using the rule of mixtures and Mori-Tanaka’s model. The accuracies and convergence rates of the FLMs with various orders, as used for expanding the elastic and electric variables in the thickness direction, are assessed by comparing their solutions with the exact 3D and accurate two-dimensional ones available in the literature.     

Numerical Simulation of Natural Convection in Circular Enclosures with Inner Polygonal Cylinders,with Confirmation by Experimental Results

Numerical computations are performed for the natural convection in circular enclosures with inner polygonalcylinders.The polygon surface and the outer envelope are at constant but different temperatures,A body-fittedcoordinate system is used,The coordinate system is generated via simple algebraic equations.The transformedgoverning equations are discretized on a control volume basis with power-law finite difference scheme.TheSIMPLE-like algorithm is used to deal with the linkage between pressure and velocities.The numerical resultsare compared with the experimental data available in the literature,and the agreement between the numericaland experimental results are very good.     

PARALLEL COMPUTATION OF FORCED CONVECTION USING DOMAIN DECOMPOSITION

Boundary-fitted coordinate transformation broadens the applicability of finite difference methods. However, for a large class of geometries, coordinate transformation introduces singularities and increases grid skewness, which results in large numerical error and slow convergence rate. In this paper, we present the results of combining a finite difference scheme with domain decomposition to obtain a parallel scheme. This scheme is used to simulate steady-state forced convection in irregular axisymmetric and two-dimensional domains. The irregular domain is first dissected into subdomains that have smooth curves as their boundaries. Curvilinear coordinate systems are then generated for each subdomain. Each subdomain is mapped onto a processor in the BBN Butterfly computer. After the tasks of inner domain computation are completed in parallel, the inner boundary values are updated (also in parallel). This sets up an iterative (block Gauss-Seidel) procedure that terminates when convergence is achieved. The structure of our scheme allows a straightforward treatment of the load balance problem and alleviates memory contention.     

Numerical Solution of the Navier-Stokes Equations for Arbitrary Blunt Bodies in Supersonic Flows

Abstract

A time-dependent, two-dimensional Navier-Stokes code employing the body-fitted coordinate technique has been developed for supersonic flows past blunt bodies of arbitrary shape. The computer program is based on the finite-difference approximation of the compressible Navier-Stokes equations transformed to nonorthogonal curvilinear coordinates with the contravariant components of the velocity vector as dependent variables. The bow shock ahead of the body is obtained as part of the solution, by “shock capturing.” Numerical solutions of the complete equations are presented in detail for free-stream Mach number 4.6, Reynolds number 104, and an isothermal wall temperature of 556 K for a circular cylinder with the free-stream outer boundaries forming a hyperbola in the front and a circular are in the back.     

Modeling and coordinate control of photovoltaic DC building module based BIPV system

This paper presents the modeling method and coordinate control strategy for photovoltaic dc building module (PV-DCBM) based building integrated photovoltaic (BIPV) system. The PV-DCBM based BIPV system consists of plenty of PV-DCBMs and a centralized inverter which are coupled to the common dc bus in parallel. Each PV-DCBM is integrated with a PV building material to extract maximum power from it and then a centralized inverter is used to transfer the power to the grid. The PV-DCBM based BIPV system has some significant advantages for building integrated applications, such as individual MPPT, inherent data monitor, low cost and excellent expandability. A coordinate control strategy based on energy balance of the PV-DCBM based BIPV system is proposed to realize the individual control for each PV-DCBM and the centralized inverter. The accurate small-signal model of the PV-DCBM based BIPV system is built based on the proposed operation principle and a detailed design approach of the coordinate controller is proposed. Experimental results on the laboratory prototype verify the validity of the proposed modeling and coordinate control method.     

Calcul par iteration d'une couche limite tridimensionnelle et comparaison experimentale

An iterative procedure is described for studying the three-dimensional compressible laminar boundary layer with heat transfer. The equations of motion are first written using a coordinate system tied to the external streamlines and the iterative equations are obtained by isolating and linearizing the transverse equation of motion, hence reducing the number of independent variables from three to two. When the weighting coefficient is zero the first iteration corresponds to the case of very weak cross-flows. The method is then applied to the integral equations of the boundary layer on a cone in supersonic flow. Convergence is obtained after five or six iterations even under severe conditions of strong cross-flows with heated walls. A comparison is made with measurements of pressure, wall-streamline directions, and heat transfer, carried out on a cone for a wide range of wall temperatures and incidence.     

Study on a BFC-Based POD-Galerkin Reduced-Order Model for the Unsteady-State Variable-Property Heat Transfer Problem

A proper orthogonal decomposition–reduced-order model (POD-ROM) method for unsteady-state heat conduction problems with variable physical properties is developed based on the body-fitted coordinate. Two mathematically equivalent forms of the ROM are derived, but their performance is quite different for finite volume. It is found that to obtain accurate prediction by the POD-ROM, the operators of the Jacobi factor and other variables in the ROM should be consistent with those in the finite-volume method (FVM). Validated by a complicated unsteady-state heat conduction problem, the established ROM can obtain accurate prediction of the unsteady-state heat conduction problem with variable properties in which the maximum ratio of thermal conductivity reaches 333.     

THERMOELASTIC DEFORMATION OF MICROSTRETCH ELASTIC BEAMS

This article addresses the problem of thermal stresses for isotropic microstretch elastic cylinders subjected to a temperature distribution that is linear in the axial coordinate. A direct method is used to reduce the problem to solving plane strain problems. The results are used to study the deformation of circular cylinders.     

An improved model of an ASR pyrolysis reactor for energy recovery

In this work, we model a countercurrent tubular reactor where an automotive shredder residue (ASR) is subject to pyrolysis. An inert gas is adopted to convey the pyrolysis products; the solid entering the reactor undergoes an endothermic chemical process which is very sensitive with respect to the temperature. Pressure effects and friction loss of the gas phase are taken into account to better match the real operative conditions. The reaction is modelled by a system of boundary-value differential-algebraic equations (DAEs) where the thermodynamic variables of both phases are investigated with respect to the axial coordinate of the tube. This algorithmic strategy has shown a greater robustness and reliability in comparison with a more traditional approach relying upon well-known ODE solver codes. In particular, the effects of different gas-solid ratios on conversion and the relevant configurations in the inner phase geometries have been investigated.     

Natural convection heat transfer from an inclined wavy plate in a bidisperse porous medium

This work studies the natural convection heat transfer from an inclined wavy plate in a bidisperse porous medium with uniform wall temperature. The two-velocity two-temperature formulation is used to derive the governing equations of this system. The Prandtl coordinate transformation is used to transform the wavy surface into a regular plane, and the obtained equations are then simplified further by the order-of-magnitude analysis to give the boundary layer equations. The cubic spline collocation method is used to solve the boundary layer governing equations. The effects of dimensionless amplitude, angle of inclination, inter-phase heat transfer parameter, modified thermal conductivity ratio, and permeability ratio on the heat transfer and flow characteristics are studied. Increasing the modified thermal conductivity ratio and the permeability ratio can effectively enhance the natural convection heat transfer of the inclined plate in bidisperse porous media. Moreover, the thermal non-equilibrium effects are significant for low values of the inter-phase heat transfer parameter. As the dimensionless amplitude increases, both the fluctuations of the local Nusselt number for the f-phase and the p-phase with the streamwise coordinate are enhanced.