Determination of principal characteristics of turbulent swirling flow along annuli: Part 2: Measurement of turbulence components

Turbulence data for swirling flows along the annulus formed between two co-axial tubes are presented. The swirl was generated by a set of inlet guide vanes which produced, after settling and removal of wall boundary layers, a nominally free vortex flow over the complete entry plane of the test section. The work complements that described in Part 1 of the paper which considered the behaviour of time mean values under the same entry conditions¹. A hot wire anemometer was used to detect turbulence quantities and techniques have been developed for the measurement of these using the minimum number of simple probe geometries. The theory leading to the derivation of the separate turbulence parameters from hot wire measurements is described. A series of radial profiles are given as representative examples of the extensive data collected in addition to longitudinal variations of friction factor and shear stress. A brief discussion is given on the determination of eddy diffusivity as a function of radial and axial location.     

圆环中的亚纯函数及其导数在重值条件下的一个唯一性定理

In this paper, we first obtain the famous Xiong Inequality of meromorphic functions on annuli. Next we get a uniqueness theorem of meromorphic function on annuli concerning to their multiple values and derivatives by using the inequality.     

Thermal Energy Storage and Heat Transfer of Nano-Enhanced Phase Change Material (NePCM) in a Shell and Tube Thermal Energy Storage (TES) Unit with a Partial Layer of Eccentric Copper Foam

Thermal energy storage units conventionally have the drawback of slow charging response. Thus, heat transfer enhancement techniques are required to reduce charging time. Using nanoadditives is a promising approach to enhance the heat transfer and energy storage response time of materials that store heat by undergoing a reversible phase change, so-called phase change materials. In the present study, a combination of such materials enhanced with the addition of nanometer-scale graphene oxide particles (called nano-enhanced phase change materials) and a layer of a copper foam is proposed to improve the thermal performance of a shell-and-tube latent heat thermal energy storage (LHTES) unit filled with capric acid. Both graphene oxide and copper nanoparticles were tested as the nanometer-scale additives. A geometrically nonuniform layer of copper foam was placed over the hot tube inside the unit. The metal foam layer can improve heat transfer with an increase of the composite thermal conductivity. However, it suppressed the natural convection flows and could reduce heat transfer in the molten regions. Thus, a metal foam layer with a nonuniform shape can maximize thermal conductivity in conduction-dominant regions and minimize its adverse impacts on natural convection flows. The heat transfer was modeled using partial differential equations for conservations of momentum and heat. The finite element method was used to solve the partial differential equations. A backward differential formula was used to control the accuracy and convergence of the solution automatically. Mesh adaptation was applied to increase the mesh resolution at the interface between phases and improve the quality and stability of the solution. The impact of the eccentricity and porosity of the metal foam layer and the volume fraction of nanoparticles on the energy storage and the thermal performance of the LHTES unit was addressed. The layer of the metal foam notably improves the response time of the LHTES unit, and a 10% eccentricity of the porous layer toward the bottom improved the response time of the LHTES unit by 50%. The presence of nanoadditives could reduce the response time (melting time) of the LHTES unit by 12%, and copper nanoparticles were slightly better than graphene oxide particles in terms of heat transfer enhancement. The design parameters of the eccentricity, porosity, and volume fraction of nanoparticles had minimal impact on the thermal energy storage capacity of the LHTES unit, while their impact on the melting time (response time) was significant. Thus, a combination of the enhancement method could practically reduce the thermal charging time of an LHTES unit without a significant increase in its size.     

Waveguides with Combined Dirichlet and Robin Boundary Conditions

We consider the Laplacian in a curved two-dimensional strip of constant width squeezed between two curves, subject to Dirichlet boundary conditions on one of the curves and variable Robin boundary conditions on the other. We prove that, for certain types of Robin boundary conditions, the spectral threshold of the Laplacian is estimated from below by the lowest eigenvalue of the Laplacian in a Dirichlet-Robin annulus determined by the geometry of the strip. Moreover, we show that an appropriate combination of the geometric setting and boundary conditions leads to a Hardy-type inequality in infinite strips. As an application, we derive certain stability of the spectrum for the Laplacian in Dirichlet–Neumann strips along a class of curves of sign-changing curvature, improving in this way an initial result of Dittrich and Kříž (J. Phys. A, 35:L269–275, 2002).      

Integrated radial basis functions‐based differential quadrature method and its performance

In this paper, indirect radial basis function networks (IRBFN) proposed by Nam and Tranh (Neural Networks 2001; 14 (2):185–199; Appl. Math. Modelling 2003; 27 :197–220) are incorporated into the differential quadrature (DQ) approximation of derivatives. For simplicity, this new variant of RBF‐DQ approach is named as iRBF‐DQ method. The proposed approach is validated by its application to solve the one‐dimensional Burger's equation, and simulate natural convection in a concentric annulus by solving Navier–Stokes equations. It was found that as compared to the benchmark data, the iRBF‐DQ approach can provide more accurate results than the original RBF‐DQ method. Copyright © 2006 John Wiley & Sons, Ltd.     

环内亚纯函数的特征函数

应用亚纯函数的Nevanlinna理论,研究了定义在圆环内的亚纯函数的特征函数.证明了定义在圆环内的具有最大亏量和的有限级允许亚纯函数f(名)与其各阶导函数f~((k))(z)的特征函数之间满足如下关系:当δ_0(∞,f)=1时,T_0(r,f~((k)))~T_0(r,f)(r→+∞);当δ_0(∞,f)=0时,T_0(r,f~((k)))~(k+1)T_0(r,f)(r→+∞),其中k为任意正整数.所得结果推广了定义在全平面上亚纯函数的一些相关结果.     

Determination of principal characteristics of turbulent swirling flow along annuli: part 4: an asymptotic solution

An asymptotic solution of the momentum equation is given that describes the decay of swirling flow passing along the annulus formed between two concentric, straight, circular-section pipes having a common starting point. The flow is considered turbulent and approximations are made consistent with the notion of fully developed flow conditions. Applications of this approach are reviewed and shortcomings highlighted. A series of calculations are presented and compared with experimental and theoretical data previously obtained by the authors. It is shown that acceptable predictions of the overall flow behavior can be obtained over a wide range of initial conditions provided the calculations procedure is applied in regions of validity, which has not been the case in some published work. Substantial errors are found if, for example, the procedure is allowed to commence at inlet to the annulus owing to the inconsistency of the assumptions in the initially developing-flow region, which for this work extends at least five outer-pipe diameters downstream from inlet. The authors' previous numerical integration scheme may be used to predict flows satisfactorily in the developing-flow region and the present asymptotic solution used subsequently to reduce computation time and cost.     

On the multiple values and uniqueness of algebroid functions on annuli

In this paper, we discuss the influence of multiple values and Valiron deficiencies on the uniqueness problem of algebroid functions on annuli, we get the several uniqueness theorems of algebroid functions on annuli, and also we extend the Nevanlinna value distribution theory for algebroid functions on annuli.     

研究流体在偏心环空内流动的新方法

使用双极坐标系研究流体在偏心环空内的流动。给出该坐标系下流体力学基本方程组。对牛顿流体的轴向流、旋转流求得它们的精确级数解和相应的数值结果。     

不连续双斜内肋管的管外换热性能

实验和数值研究了不连续双斜内肋管管外的换热性能.在不连续双斜内肋管管外倾斜凹坑的作用下,不连续双斜内肋管和光滑圆管组成的套管内出现了纵向涡流动,雷诺数为30000~90000时比光滑套管换热增强50%,阻力增加60%～70%.