A comparison of Galerkin and streamline techniques for integrating strains from an Eulerian flow field

Two methods are compared for integrating the strains that can arise in finite element solutions for Eulerian velocity fields associated with large strain material forming processes. With the Galerkin formulation, partial differential equations for the deformation gradient are solved over the entire domain based on a weighted residual; with the streamline integrated technique, the corresponding ordinary differential equations are integrated along characteristic lines. Both methods have yielded accurate integrations for the radial flow and planar rolling problems studied. A finite element technique is also presented for ensuring that the free surfaces of the fluid flow are streamlines. This technique has been used for ensuring proper boundary conditions in the rolling analysis.     

Finite element analysis of internal flows with heat transfer

This paper presents a finite element-based model for the prediction of 2-D and 3-D internal flow problems. The Eulerian velocity correction method is used which can render a fast finite element code comparable with the finite difference methods. Nine different models for turbulent flows are incorporated in the code. A modified wall function approach for solving the energy equation with high Reynolds number models is presented for the first time. This is an extension of the wall function approach of Benim and Zinser and the method is insensitive to initial approximation. The performance of the nine turbulent models is evaluated by solving flow through pipes. The code is used to predict various internal flows such as flow in the diffuser and flow in a ribbed channel. The same Eulerian velocity correction method is extended to predict the 3-D laminar flows in various ducts. The steady state results have been compared with benchmark solutions and the agreement appears to be good.     

Parallel implementation of the EFG Method for heat transfer and fluid flow problems

The parallel implementation of the element free Galerkin (EFG) method for heat transfer and fluid flow problems on MIMD type parallel computer is treated. A new parallel algorithm has been proposed in which parallelization is performed by row-wise data distribution among the processors. The codes have been developed in FORTRAN language using MPI message passing library. Two model (one each in heat transfer and fluid flow) problems have been solved to validate the proposed algorithm. The total time, communication time, user time, speedup and efficiency have been estimated for heat transfer and fluid flow problems. For eight processors, the speedup and efficiency are obtained to be 7.11 and 88.87% respectively in heat transfer problems for a data size of N=2,116 whereas 7.20 and 90.04% respectively in fluid flow problems for a data size of N=2,378.     

Investigation of turbulent heat transfer and nanofluid flow in a double pipe heat exchanger

In present study, heat transfer and turbulent flow of water/alumina nanofluid in a parallel as well as counter flow double pipe heat exchanger have been investigated. The governing equations have been solved using an in-house FORTRAN code, based on finite volume method. Single-phase and standard k-ε models have been used for nanofluid and turbulent modeling, respectively. The internal fluid has been considered as hot fluid (nanofluid) and the external fluid, cold fluid (base fluid). The effects of nanoparticles volume fraction, flow direction and Reynolds number on base fluid, nanofluid and wall temperatures, thermal efficiency, Nusselt number and convection heat transfer coefficient have been studied. The results indicated that increasing the nanoparticles volume fraction or Reynolds number causes enhancement of Nusselt number and convection heat transfer coefficient. Maximum rate of average Nusselt number and thermal efficiency enhancement are 32.7% and 30%, respectively. Also, by nanoparticles volume fraction increment, the outlet temperature of fluid and wall temperature increase. Study the minimum temperature in the solid wall of heat exchangers, it can be observed that the minimum temperature in counter flow has significantly reduced, compared to parallel flow. However, by increasing Reynolds number, the slope of thermal efficiency enhancement of heat exchanger gradually tends to a constant amount. This behavior is more obvious in parallel flow heat exchangers. Therefore, using of counter flow heat exchangers is recommended in higher Reynolds numbers.     

板翅式换热器封头型式的改造

采用计算流体力学(CFD)方法研究大型板翅式换热器封头内的流体流动,根据流动特征提出在封头段加入导流分布板改善流动分布均匀性的方法.与未加入导流分布板比较结果显示,加入导流分布板后,流体分布得到改善,传热系数亦有显著提高.     

二氧化碳翅片管式蒸发器模拟与分析

运用分布参数法建立采用CO2的翅片管式蒸发器的数学模型，分析制冷剂侧和空气侧温度、压力和换热的变化情况。同时讨论迎面风速和制冷剂质量流量对蒸发器换热和流动性能的影响，结果表明提高迎面风速可以增加换热效果，但增加的趋势趋于平缓。制冷剂侧压降则成近似线性增大；随着管内工质流量的增大，蒸发器总换热量和制冷荆侧压降都成近似线性增大。这些工作有助于进一步了解CO2在翅片管式蒸发器中的换热和流动特性，并为换热器的优化设计和系统的匹配提供理论依据。     

Experimental Study of the Relation Between Heat Transfer and Flow Behavior in a Single Microtube

The flow boiling heat transfer in microchannels have become important issue because it is extremely high-performance heat exchanger for electronic devices. For a detailed study on flow boiling heat transfer in a microtube, we have used a transparent heated microtube, which is coated with a thin gold film on its inner wall. The gold film is used as a resistance thermometer to directly evaluate the inner wall temperature averaged over the entire temperature measurement length. At the same time, the transparency of the film enables the observation of fluid behavior. Flow boiling experiments have been carried out using the microtube under the following conditions; mass velocity of 105 kg/m² s, tube diameter of 1 mm, heat flux in the range of 10 ~ 380 kW/m² s, and the test fluid used is ionized water. Under low heat flux conditions, the fluctuations in the inner wall temperature and mass velocity are closely related; the frequency of these fluctuations is the same. However, the fluctuations in the inner wall temperature and heat transfer coefficient are found to be independent of the fluctuation in the mass velocity under high heat flux conditions.     

PIV experimental investigation of entrance configuration on flow maldistribution in plate-fin heat exchanger

Flow characteristics of flow field in the entrance of plate-fin heat exchanger have been investigated by means of particle image velocimetry (PIV). The velocity fields were measured using the two-frame cross-correlation technique. A series of velocity vector and streamline graphs of different cross-sections are achieved in the experiment. The experimental results indicate that performance of fluid maldistribution in conventional entrance configuration is very serious, while the improved entrance configuration with punched baffle can effectively improve the performance of fluid flow distribution in the entrance. Based on the analysis of the fluid flow maldistribution, a baffle with small holes is recommended to install in the entrance configuration in order to improve the performance of flow distribution. When the punched baffle is proper in length, the small holes is distributed in staggered arrangement, and the punched ratio gradually increases from central axis to the boundary along with the baffle length, the performance of flow distribution in plate-fin heat exchanger is effectively improved by the optimum design of the entrance configuration. The flow maldistribution parameter S in plate-fin heat exchanger has been reduced from 1.21 to 0.209 and the ratio of the maximum velocity to the minimum θ is reduced from 23.2 to 1.76 by installing the punched baffle. The results validate that PIV is well suitable to investigate complex flow pattern and the conclusion of this paper is of great significance in the optimum design of plate-fin heat exchanger.     

Finite element formulation of a heat transfer problem for an axisymmetric composite structure

By using weighted residual method, the finite element formulation of a heat transfer problem for axisymmetric composite structures is established from the heat transfer differential equations expressed by heat fluid density. A few examples are included to indicate that the heat transfer anisotropy has an important effect on temperature field and to prove the accuracy and effectiveness of the finite element formulation.Aknowledgement Special thanks are due to the National Natural Science Foundation of China (No: 10272037) for supporting the present work.     

Turbulent flow through a circular pipe: Resistance and heat exchange at the constant boundary temperature

In this work, problems of the velocity profile, hydraulic resistance and heat exchange at constant equal temperature on the walls, steady-state turbulent flow, and established heat exchange in a straight channel limited by coaxial circular cylinders (a circular pipe) are solved. A moving incompressible fluid is considered as the medium, its viscous and heat-conducting properties being defined not only by its physical properties, but also by stable vortex structures that are formed upon the turbulent flow and generate local anisotropy of the medium. A vector called the director is a characteristic parameter of anisotropy. Director dynamics within the flow is assigned by a separate equation. The flow region consists of two near-wall subregions, which are adjacent to solid flow boundaries. The boundary between the subregions is determined during solving the problem. A closed set of equations is formulated for the desired values (velocity, temperature), and boundary conditions are laid. The velocity profile and temperature field in the flow were obtained in form of solutions to the corresponding boundary problems. The results of solution are compared with the experimental data and empirical formulas.     

Turbulent biomagnetic fluid flow in a rectangular channel under the action of a localized magnetic field

The fundamental problem of the turbulent flow of a biomagnetic fluid (blood) between two parallel plates under the action of a localized magnetic field is studied. The blood is considered to be an electrically conducting, incompressible and Newtonian fluid and its flow is steady, two-dimensional and turbulent. The turbulent flow is described by the Reynolds averaged Navier–Stokes (RANS) equations. For the numerical solution of the problem under consideration, which is described by a coupled and non-linear system of PDEs, with appropriate boundary conditions, the stream function–vorticity formulation is used. For the eddy-kinematic viscosity, the low Reynolds number k–ε turbulence model is adopted. The solution of the problem, for different values of the dimensionless parameter entering into it, is obtained by developing and applying an efficient numerical technique based on finite differences scheme. Results concerning the velocity and temperature field, skin friction and rate of heat transfer, indicate that the presence of the localized magnetic field, appreciable influences the turbulent flow field. A comparison is also made with the corresponding laminar flow, indicating that the influence of the magnetic field decreases in the presence of turbulence.     

Heat transfer in turbulent nanofluids: Separation flow studies and development of novel correlations

Convective heat transfer plays a significant role in numerous industrial cooling and heating applications. This method of heat transfer can be passively improved by reconfiguring flow passage, fluid thermophysical properties, or boundary conditions. The broader scope of nanotechnology introduced several studies of thermal engineering and heat transfer. Nano-fluids are one of such technology which can be thought of engineered colloidal fluids with nano-sized particles. In the present study, turbulent forced convection heat transfer to nanofluids in an axisymmetric abrupt expansion heat exchanger was investigated experimentally. During heat transfer investigation, the functionalized multiwalled carbon nanotubes (MWCNT-COOH), polycarboxylate functionalized graphene nanoplatelets (F-GNP), SiO₂ and ZnO water-based nanofluids were used. The convective heat transfer coefficient of fully developed turbulent flow of nanofluids flowing through an abrupt enlargement with the expansion ratio (ER) of 2 was experimentally determined at a constant wall heat flux of 12,128.56 W/m². The experiments were conducted at the Re ranges of 4000–16,000. The observed Nusselt numbers were higher than in the case of fully developed pipe flow indicating the level of the turbulent transport is high even though the recirculating velocities were a few percentages of the bulk mean velocity. The effect of Reynolds number and nanofluid’s volume concentration on heat transfer and friction losses were studied, where all the results reveal that with the increase of weight concentration and Reynolds number, the local Nusselt number enhanced at the increment of axial ratios in all the cases showing greater heat transfer rates than those of the base fluids. Comparison between the examined four types of nanofluids, show that the carbon-based nanofluids have a greater effect on enhancing heat transfer (33.7% and 16.7% heat transfer performance improvement for F-GNP and MWCNT nanofluids respectively at 0.1 wt% concentration) at the downstream of the sudden expansion pipe. There is no reported work dealing with the prediction of the local Nusselt number at the distance equivalent to the axial ratio and flow through sudden expansion. So far, two excellent correlations for the Local Nusselt number are proposed with reasonably good accuracy. Furthermore, a new correlation is developed for the average Nusselt number.     

Effect of periodic reverse flow on the heat transfer performance of microchannel evaporators

Periodic flow reversal are commonly present in microchannel heat exchangers, but have been studied in air conditioning systems only recently. This paper presents the effect of periodic reverse flow on the heat transfer performance of a heat exchanger. Two heat exchangers with identical geometries in the heat transfer areas are employed and an artificial upstream flow resistance is added for one of them. The heat exchanger without artificial flow resistance is subject to more severe boiling instabilities and consequently generates four times more reverse vapor flow than the other one. The comparison of capacities under identical operating conditions reveals that higher intensity of reverse flow helps to improve cooling capacity by up to 13.3%. Meanwhile, numerical simulations of bubble dynamics coupled with heat transfer are carried out for both heat exchangers. Results show that in the heat exchanger with more reverse flow, the refrigerant side heat transfer coefficients are enhanced, especially in the upstream part of a channel where the flow velocity is relatively low.     

A least-squares front-tracking finite element method analysis of phase change with natural convection

This paper focuses on the numerical modelling of phase-change processes with natural convection. In particular, two-dimensional solidification and melting problems are studied for pure metals using an energy preserving deforming finite element model. The transient Navier–Stokes equations for incompressible fluid flow are solved simultaneously with the transient heat flow equations and the Stefan condition. A least-squares variational finite element method formulation is implemented for both the heat flow and fluid flow equations. The Boussinesq approximation is used to generate the bulk fluid motion in the melt. The mesh motion and mesh generation schemes are performed dynamically using a transfinite mapping. The consistent penalty method is used for modelling incompressibility. The effect of natural convection on the solid/liquid interface motion, the solidification rate and the temperature gradients is found to be important. The proposed method does not possess some of the false diffusion problems associated with the standard Galerkin formulations and it is shown to produce accurate numerical solutions for convection dominated phase-change problems.     

不同强化管传热特性的数值模拟与实验研究

对横纹槽管、缩放管和螺旋槽管在夹套间进行了传热特性实验,研究了传热效率指标随雷诺数的变化规律.运用FLUENT软件,采用二维轴对称方法和k-ε模型对夹套间流体流动传热进行了数值模拟,并将模拟结果与实验结果进行对比.从场协同的角度研究了速度场与温度场夹角对传热膜系数的影响.     

凹陷阵列印刷电路板式换热器里超临界甲烷换热和流动特性模拟研究

为了强化液化甲烷在印刷电路板式微通道换热器中的换热能力,提出了一种凹陷阵列的微小通道换热器整体性能提高的被动式强化技术并进行了数值模拟验证。研究了流体温度范围125—265 K范围内的超临界甲烷在凹陷阵列结构微通道内的换热和流动特性,考察了凹陷阵列微通道和光滑微通道下,流体温度、质量流量、雷诺数和进口压力对传热系数、努塞尔数、摩擦因子和综合效益系数(PEC)的影响。此外,通过凹陷结构的局部流动特性分析强化换热机理,数值模拟结果表明相较于光滑微通道,凹陷阵列微通道的换热特性得到大大强化,且随雷诺数(由质量流量或者流体温度改变)的增大而增强,而摩擦因子只是有较弱的劣化。     

An adaptive simplex cut‐cell method for high‐order discontinuous Galerkin discretizations of conjugate heat transfer problems

In this paper, we present a solution framework for high‐order discretizations of conjugate heat transfer problems on non‐body‐conforming meshes. The framework consists of and leverages recent developments in discontinuous Galerkin discretization, simplex cut‐cell techniques, and anisotropic output‐based adaptation. With the cut‐cell technique, the mesh generation process is completely decoupled from the interface definitions. In addition, the adaptive scheme combined with the discontinuous Galerkin discretization automatically adjusts the mesh in each sub‐domain and achieves high‐order accuracy in outputs of interest. We demonstrate the solution framework through several multi‐domained conjugate heat transfer problems consisting of laminar and turbulent flows, curved geometry, and highly coupled heat transfer regions. The combination of these attributes yield nonintuitive coupled interactions between fluid and solid domains, which can be difficult to capture with user‐generated meshes. Copyright © 2016 John Wiley & Sons, Ltd.     

超临界CO2冷却换热特性数值模拟

采用L-B低雷诺数模型对超临界二氧化碳在竖直圆管内的冷却对流换热特性进行了数值模拟.通过分析得到了管内不同截面的径向流体温度、速度、湍动能分布,并进一步分析了二氧化碳和冷却水进口雷诺数对超临界二氧化碳对换热的影响.研究表明,对流传热系数峰值出现在接近准临界温度的截面内,此时截面内湍动能最大,跨过该截面流速小于进口流速;...     

Formulation and solution of hierarchical finite element equations

The paper presents a general hierarchical formulation applicable to both elliptic and hyperbolic problems. Static and eigenvalue linear elastic problems as well as convection–diffusion problems are studied. The hierarchical formulation is well suited for adaptive procedures. For the convection-diffusion problem the hierarchical approximation is made in time only. Different hierarchical functions are proposed for different types of problems. Both weighted residual and least-squares formulations are applied. A combination of these two gives a penalty method with a constraint equation corresponding to the least-squares method. A whole class of time integration formulae is obtained. These are all suitable for adaptive procedures owing to the hierarchical approximation in the time domain. If a linear discontinuous hierarchical base function is used in the Galerkin weak formulation, the method so obtained corresponds to the discontinuous Galerkin method in time and is especially suited for convection dominated problems. The streamline-diffusion method is found to be the aforementioned penalty method. This paper also examines the sequence of nested equation systems that results from a hierarchical finite element formulation. Properties of these systems arising from static problems are investigated. The paper presents some new possibilities for iterative solution of hierarchic element equations, and different procedures are compared in a numerical example. Finally, a simple ID convection-diffusion problem clearly shows that the proposed hierarchical formulation in time gives a stable and accurate solution even for convection dominated flow.     

椭圆管换热器对空调室内机声场影响的数值模拟

椭圆管换热器由于良好的流动和换热特性,在换热设备中有广泛的应用。本文利用计算流体力学方法,对椭圆管翅片换热器应用于空调室内机的流场和声场进行数值模拟,并与圆管作对比。计算结果表明,换热管形状对贯流风机内部偏心涡的形成位置和大小没有影响;与采用相同截面积的圆管翅片换热器的室内机相比,相同条件下,采用椭圆管换热器对于室内机增加风量,改善制冷性能,降低噪声尤其是低频噪声方面有良好的效果。其中,长短轴之比为2的椭圆管可以降低室内机噪声4 d B。