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Design of High-Order Difference Scheme and Analysis of Solution Characteristics - Part II: A Kind of Third-Order Difference Scheme and New Scheme Design Theory

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Numerical Heat Transfer: Part B -- Fundamentals 2007年第3期52卷 271-295页

作者： Jin, W. W. Tao, W. Q. wqtao@*** State Key Laboratory of Multiphase Flow in Power Engineering School of Energy &Power Engineering Xi''an Jiaotong University Xi''an People''s Republic of China

In this Part II, on the basis of the general style design of second-order difference scheme and the analysis of the absolutely stable scheme proposed in Part I, the companion article, the general design method of any high-order difference scheme is proposed. Based on this method, a new kind of third-order difference scheme including 17 different variants is constructed, which uses the same grid points as existing second-order difference schemes but is different from them in that the grids are chosen symmetrically from two sides of the interface. Because they have the same matrix style created by the same grid plots of the discretization equation, these third-order schemes require the same CPU time and memory as the second-order schemes; however, this kind of symmetrical third-order difference scheme will keep the consistency between the false diffusion and the stability, and the stability of the scheme is better than that of the existing biased second-order scheme. Further research shows that under the conditions of matrix style and computer memory, the scheme constituted by symmetrically numbered grids from two sides of the interface with odd order of accuracy can maintain consistency between numerical accuracy and stability better than any kind of scheme designed according to the 'upwind' idea. Based on this understanding, a new scheme design theory called symmetric and odd-order accuracy scheme design theory is proposed. [ABSTRACT FROM AUTHOR]

关键词： power (Mechanics) NUMERICAL analysis HEAT transfer multiphase flow NUMERICAL calculations

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Experimental study on optical properties of the collector

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International Solar Energy Society Solar World Congress 2007, ISES 2007

作者： Wang, Juan Zhao, Liang Li, Huashan School of Science Xi'an Jiaotong University P.O. Box 2264 Xi'an 710049 China State Key Laboratory of Multiphase Flow in Power Engineering Xi'an Jiaotong University Xi'an 710049 China

ISBN: (纸本)9781622765447

Solar collector is one of the most important parts of solar chimney power plant. It plays an important role in improving the efficiency and saving the cost of the whole system. In this paper, several transparent materials which could be used as the collector were chosen to study the optical properties. The materials include polymethyl methacrylate (PMMA), polycarbonate (PC), perspex (PS) and ordinary glass. Firstly, an experiment device was designed with the collector angles varying from 15° to 60°. Secondly, different thickness of glass and different slope angles of the collector of these materials mentioned above on transmittance was compared. The effect of pollutions caused by the natural environment such as dust, rain and aging on these materials was considered in the experiment. Based on the experimental results, a conclusion was made that PMMA has the highest transmittance among the four materials without considering other factors.

关键词： Optical properties

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An efficient and robust numerical scheme for the SIMPLER algorithm on non-orthogonal curvilinear coordinates: CLEARER

An efficient and robust numerical scheme for the SIMPLER alg...

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作者： Cheng, Y.P. Lee, T.S. Low, H.T. Tao, W.Q. Laboratory of Fluid Mechanics Department of Mechanical Engineering National University of Singapore Singapore Singapore State Key Laboratory of Multiphase Flow in Powering Engineering School of Energy and Power Engineering Xian Shaanxi China Laboratory of Fluid Mechanics Department of Mechanical Engineering National University of Singapore 119260 Singapore Singapore

In this article, an Improved SIMPLER (CLEARER) algorithm is formulated to solve the incompressible fluid flow and heat transfer on the nonstaggered, nonorthogonal curvilinear grid system. By virtue of a modified momentum interpolation method in calculating the interface contravariant velocity in both the predictor step and the corrector step, the coupling between pressure and velocity is fully guaranteed, and the conservation law is also satisfied. A second relaxation factor is introduced in the corrector step, of which the convergent solution is independent. By setting the second relaxation factor less than the underrelaxation factor for the velocity to some extent, both the convergence rate and robustness can be greatly enhanced. Meanwhile, the CLEARER algorithm can also overcome the severe grid nonorthogonality. With the simplified pressure-correction equation, the convergent solution can still be obtained even when the intersection angle among grid lines is as low as 1, which may provide valuable guidance in studying the fluid flow in complex geometries.

关键词： Computational fluid dynamics

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Improvement of SIMPLER algorithm for incompressible flow on collocated grid system

Improvement of SIMPLER algorithm for incompressible flow on ...

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作者： Cheng, Y.P. Lee, T.S. Low, H.T. Tao, W.Q. Laboratory of Fluid Mechanics Department of Mechanical Engineering National University of Singapore Singapore Singapore State Key Laboratory of Multiphase Flow in Power Engineering School of Energy and Power Engineering Xi'an Jiaotong University Xi'an Shaanxi China Laboratory of Fluid Dynamics Department of Mechanical Engineering National University of Singapore 10 Kent Ridge Crescent 119260 Singapore Singapore

In this article an Improved SIMPLER (CLEARER) algorithm is proposed to solve incompressible fluid flow and heat transfer problems. Numerical study shows with the CLEARER algorithm on a collocated grid, in the correction stage the velocities on the main nodes are overcorrected with the pressure correction, which lowers the convergence rate;hence a second relaxation factor is introduced to overcome this disadvantage. By setting this factor less than the underrelaxation factor for velocities, the convergence performance can be significantly enhanced;meanwhile, the robustness can also be increased. Four numerical examples with reliable solutions are computed to validate the CLEARER algorithm, and the results show that this algorithm can predict the numerical results accurately. Compared with the SIMPLER algorithm, CLEARER can enhance the convergence rate greatly, and in some cases it only needs as little as 17% of the iterations required by SIMPLER to reach the same convergence criterion.

关键词： Incompressible flow

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Heat transfer performance of a solar LiBr absorption refrigeration system

Heat transfer performance of a solar LiBr absorption refrige...

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5th International Energy Conversion engineering Conference

作者： Gu, Yaxiu Wu, Yuyuan Liu, Ting Chen, Liufang Zhang, Qinming Institute of Refrigerating and Cryogenic Engineering Xi'an Jiaotong University Xi'an 710049 China State Key Laboratory of Multiphase Flow in Power Engineering Xi'an Jiaotong University Xi'an 710049 China Institute of Refrigerating and Cryogenic Engineering Xi'an Xianning West Road 28# China Department of Thermal Engineering Xi'an Xianning West Road 28#

ISBN: (纸本)1563479028

The utilization of solar heat and waste heat in order to energize absorption chillers is an important issue for increasing the energy efficiency of cooling machines. A compact pump-free LiBr absorption refrigeration system (without the generator-pump, the evaporator-pump and the absorber-pump) driven by solar energy is designed and reconstructed. The required minimum driving temperature of the heat source is only 68°C compared to above 100°C in traditional absorption refrigeration systems. This paper aims to present the effects of various running parameters on the heat transfer performance of a solar refrigeration system, and typical experimental data. The phase change heat transfer is intensified in both the lunate channel of the thermosiphon elevation tube and the second generator. In this way, the two-phase solution is elevated continuously without pumps with a low driving temperature. The structure of the overflow-type spray system is optimized to make the aqueous solution of LiBr be absorbed and to make the condensate be evaporated in a once-through spray. Therefore, the aqueous solution in the refrigeration system can be in steady continuous absorption and evaporation without the absorber pump and the evaporator pump. In a cross-flow horizontal falling film heat exchanger, the staggered coil is wrapped with the mesh screen to hold up more liquid film. The performance of the heat and mass transfer is improved due to an increase in the wet ratio of the surface. Based on the heat and mass transfer theory of falling film absorption, an experimental study is carried out to analyze the performance of the refrigeration system. An experimental investigation is undertaken to characterize the effects of the absorption pressure, the inlet temperature of the solution, and the inlet temperature of the cooling water on the heat and mass transfer in the absorption process. The implications of the data are discussed in detail.

关键词： Refrigerating machinery

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Simulation of microstructure and rheological properties of surfactant solution

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Transactions of Nanjing University of Aeronautics and Astronautics 2007年第3期24卷 232-238页

作者： Xiong, Xianpeng Liu, Weihua Ang, Haisong Gao, Xiufeng Wei, Jinjia College of Aerospace Engineering NUAA 29 Yudao Street Nanjing 210016 China State Key Laboratory of Multiphase Flow in Power Engineering Xi'an Jiaotong University Xi'an 710049 China

The Brownian dynamics (BD) simulation of a dilute surfactant solution is conducted in a steady shear flow. The rodlike micelle is assumed as a rigid rod composed of lined-up beads. A novel intercluster potential model is introduced for describing the interactions between, micelles. In the model, the Lennard-Jones and the soft-sphere potentials are used as inter-bead potentials for end-end and interior-interior beads, respectively. The micelles are combined at their ends to form a network structure at lower shear rates and are disconnected to become more and more parallel to the shear flow direction with increasing shear rate. The change of micellar microstructures with the variation of the shear rate results in shear thinning characteristics of the computed shear viscosities and first normal stress difference coefficients. The effects of surfactant solution concentration on the micellar structures and rheological properties are also investigated. Results show that the shear viscosities and the first normal stress difference coefficients increase with increasing the viscosity of the surfactant solution.

关键词： Surface active agents

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Effects of geometric parameters on steady laminar heal transfer in wavy channels

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Jisuan Wuli/Chinese Journal of Computational Physics 2007年第2期24卷 192-196页

作者： Xie, Gongnan Wang, Qiuwang Zeng, Min Luo, Laiqin State Key Laboratory of Multiphase Flow in Power Engineering Xi'an Jiaotong University Xi'an 110049 China

Periodically fully developed convective heat transfer characteristics in a two-dimensional wavy channel are investigated numerically with a constant wall temperature. The calculations are performed with Pr=0.7, Re=20-500 on non-orthogonal non-staggered grids generated by an elliptic equation system. A semi-implicit method for pressure linked equations revised (SIMPLER) algorithm in curvilinear body-fitted coordinates is employed. Effects of Reynolds number and geometric parameters, such as aspect ratio φ and shape ratio γ, on heat transfer and friction factor are studied. It shows that no recirculation region occurs through the whole channel at low Reynolds numbers, small aspect ratio or small shape ratio. With the increase of Reynolds number, aspect ratio or shape ratio, heat transfer is enhanced due to flow recirculation. Corresponding friction factor increases simultaneously.

关键词： Heat convection

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Method for liquid viscosity coefficient measurement using inclined tube

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Kung Cheng Je Wu Li Hsueh Pao/Journal of engineering Thermophysics 2007年第3期28卷 382-384页

作者： He, Mao-Gang Zhang, Ying Wang, Xiao-Fei Zhong, Qiu Li, Hui-Zhen State Key Laboratory of Multiphase Flow in Power Engineering Xi'an Jiaotong University Xi'an 710049 China

In this paper, we provide a method which can be used to measure the viscosity coefficient of the liquid under high-pressure condition and low-boil substances using inclined tube, and measurement system was designed and constructed. The kinematic viscosity coefficients of pure water which is the standard substance to calibrate viscosity measurement system were measured to verify the accuracy and reliability of the experimental system. The measurement results show that the absolute average of relative deviations is 0.65%. Then the kinematic viscosity coefficients of the saturated liquid of the low-boil substance, R134a were also measured to detect the measurement system.

关键词： Viscosity

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Application of high resolution finite difference scheme in direct numerical simulation of turbulent flow

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Kung Cheng Je Wu Li Hsueh Pao/Journal of engineering Thermophysics 2007年第5期28卷 859-861页

作者： Ma, Liang-Dong Li, Zeng-Yao Tao, Wen-Quan State Key Laboratory of Multiphase Flow in Power Engineering School of Energy and Power Engineering Xi'an Jiaotong University Xi'an 710049 China

A direct numerical simulation of a fully developed turbulent flow and heat transfer in a square duct is studied based on high resolution finite difference scheme. The flow and temperature fields are obtained at a turbulent Reynolds number of 400 based on the mean friction velocity and the hydraulic diameter, and the Prandtl number (Pr) of 0.71. Two kinds of point-stencil method are used for the spatial derivatives of the pressure Poisson equation, i.e. the second-order and fourth-order central difference, respectively. The results show that satisfactory solutions can be obtained in the present DNS simulation with coarse grids compared with the method of second-order central difference. And the solutions from the two kinds of point-stencil method for pressure Poisson equation are consistent with the second-order central difference being more economical in saving computation time.

关键词： Pipe flow

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Gas‐Liquid Two‐Phase flows Inverse Analysis in An Aeration Tank

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AIP Conference Proceedings 2007年第1期914卷 877-882页

作者： Wen Cheng Zhang‐bin Wang Yuichi Murai Fujio Yamamoto 1State Key Laboratory of Multiphase Flow in Power Engineerig Xi’ann Jiaotong University Xi’an 710049 China 2Environment Research Institute Xian University of Technology Xian 710048 China 3Div. of Mec. Science Graduate School of Engineering Hokkaido University Japan 4Graduate School of Engineering University of Fukui Bunkyo 3‐9‐1 Fukui 910‐8507 Japan

In bubbly two‐phase flow, the gas phase and liquid phase have different flow fields. The mathematical expression for the motion of a small bubble at low Re number has been already established, the liquid velocity along the trajectory of the bubble is calculated inversely by using the motion equation. Whole field liquid flow structure has also estimated using a spatial and/or temporal interpolation method. This paper proposes an algorithm for estimating the liquid phase flow field based on measurement data on bubble data on bubble motion. The applicability of the algorithm is examined with Taylor‐Green vortex flow as an analytical test case. Meanwhile, The result, based on the theory, has been applied to reconstruct liquid phase velocity field by using the data of bubble velocity in an aeration tank.

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