摘要
圆筒内开缝圆筒自然对流换热的工业应用背景是发电厂采用的大电流离相封闭电流母线。由于热效应可能引起母线局部过热等问题，会严重影响母线的安全运行，需对封闭电流母线采取可靠而有效的散热措施，其所抽象出的理论研究模型就是圆筒内开缝圆筒的自然对流换热。本文关注圆筒内开缝圆筒自然对流换热的另一原因是其所表现出丰富的非线性特性。在某些参数范围内，这种圆筒内开缝圆筒的自热对流换热会出现自维持振荡，分岔及混沌等非线性现象。研究及预测这些奇妙而复杂的非线性现象对于发展传热学理论体系和加深人类对自然界的理解，具有重要意义。
本文针对水平放置的圆筒内开缝圆筒自然对流换热展开工作。
首先对水平圆筒内开缝圆筒自然对流换热的二维模型进行了数值模拟，探讨了其中基本的流动和换热规律及非线性特性，并与前人已存在的实验结果进行了比较；然后，通过激光干涉实验，得到了不同物理参数和几何结构下的温度分布；进一步采用三维模型对水平圆筒内开缝圆筒自然对流换热进行模拟，并比较分析二维模型、实验、三维模型结果间的异同和所表现出的三维流动和传热规律及其中的非线性特性。为了能够更精准地预测圆筒内开缝圆筒自然对流换热规律及其中的非线性特性，同时也为了研究问题多一种途径和参照，还发展了紧致差分方法。
本文获得了如下研究成果：
1)采用具有QUICK格式的SIMPLE算法对水平圆筒内开缝圆筒自然对流换热的二维模型进行了数值计算，给出了圆筒内开缝圆筒自然对流换热二维模型的基本流型及对应温度场，揭示了这种流动和换热具有对称和非对称的两涡流型及四涡流型流场、T字和2T字型温度场，并给出了系统的静态分岔解、自维持振荡解及从稳态到混沌的发展过程。
2)在本文研究参数范围内，开缝位置不同的圆筒内开缝圆筒自然对流换热的实验和二维数值结果表明：对于水平开缝圆筒((?)=(?)/2)，温度场是稳态的，相同参数下经过多次实验和数值计算，会获得两种不同的温度分布，实验与数值结果一致，从实验和数值计算两个方面证明该系统存在静态分岔现象；对于圆筒内竖直((?)=0)和偏斜((?)=(?)/4)开缝圆筒，尽管实验边界条件是稳态的，但实验温度场表现出了非对称的自维持振荡现象。但二维模型的数值结果是稳态的，未能反映实验发现的温度场自维持振荡现象。
3)采用三维模型，对水平圆筒内开缝圆筒自然对流换热问题进行了数值模拟。数值结果表明，当Ra数较小时，系统为稳态的，二维和三维数值模拟获得的平均当量导热系数均与已有文献的实验结果相一致。当Ra数较大时，这种自然对流换热随时间振荡，流场和温度场呈现出三维特性，二维模型的数值结果与文献中的换热实验结果的差异趋于增大，但是三维模型的数值结果与实验结果吻合良好。
4)本文的研究表明，对于水平放置的圆筒内竖直开缝圆筒自然对流换热问题，当流动和换热为稳态时，呈现二维流动与换热，但存在一个临界Rac，当超过这个临界值Rac时，流动和换热随时间振荡，呈现三维特性。临界Rac与开缝度S c相关。
5)当圆筒内开缝圆筒水平开缝时，在本文实验参数范围内，温度场是稳态的，具有对称和非对称两种不同的温度场，且三维数值结果、二维数值结果及实验结果均一致。
6)采用三维模型对本文实验中圆筒内竖直开缝圆筒自然对流换热的模拟结果表明：实验参数下，尽管边界条件稳态且对称，三维数值温度场随时间振荡，与实验结果一致，获得了二维数值结果所未能获得的自维持振荡现象。
7)发展了求解泊松方程和对流扩散方程的紧致修正法，对几类典型的偏微分方程进行求解，获得较高精度。采用延时修正方法，将紧致格式与SIMPLE算法相结合，构造了求解流动与换热问题的基于SIMPLE的紧致方法。通过底部加热的方腔内自然对流换热问题验证了该方法的准确性，高精度以及对分岔现象的预测能力。
8)采用本文所发展的紧致方法对圆筒内开缝圆筒自然对流换热问题进行数值模拟。随着Ra数的增加，系统从稳态，经历周期性振荡状态，最终发展为混沌，与具有QUICK格式的SIMPLE算法表现的系统从稳态到混沌的发展过程一致。
The engineering background of natural convection heat transfer in a horizontalannulus with an internal slotted circle is natural cooling of enclosed isolated-phasebuses used in power plants. The local overheated of enclosed isolated-phase busesinduced by thermal effective can affect the normal running of machine seriously. So itis necessary to make some effective measure for heat dissipating. The theoreticalmodel for those above is natural convection heat transfer in a horizontal annulus withan internal slotted circle. The other reason for focusing on those problems is abundantand complex phenomenon induced by non-linear characteristics. In the scope of somecertain parameters, some non-linear phenomenon such as self-sustained oscillation,bifurcation, and chaos will appear during the investigation of natural convection heattransfer in a horizontal annulus with an internal slotted circle. Study on thosewonderful and complex dynamic characters is necessary and worth for thedevelopment of heat transfer theory and cognition of natural law.
Firstly, two-dimensional model is applied for natural convection heat transfer ina horizontal annulus with an internal slotted circle. The based regulars of flow andheat transfer are discussed and compared with some existed experimental results.Secondly, the laser interferometer experiment platform had been constructed to studythe natural convection heat transfer of cylindrical envelope with different internalstructure and analysis the non-linear phenomenon. Thirdly, three-dimensional modelis applied for natural convection heat transfer in a horizontal annulus with an internalslotted circle. Two-dimensional, three-dimensional, and experimental results arecompared and analyzed for investigating three-dimensional flow and heat transfer andnon-linear characteristics. Finally, compact finite difference schemes are developedfor predicting non-linear characteristics accurately. Based on those objects above, themain content in this paper is as follows:
1) Natural convection heat transfer in cylindrical envelope with an internalconcentric cylinder with slots is solved by two dimensional SIMPLE algorithms withQUICK scheme. The based flow and temperature field is obtained, includingsymmetric and non-symmetric two-vortex flow pattern and temperature with theshape of T, four vortex flow pattern and temperature with the shape of double T.Typical non-linear phenomenon is obtained by two-dimensional model, includingstatic bifurcation, self-sustained oscillation, and the route from steady to chaos.
2) Experimental and two-dimensional numerical methods are applied for solving natural convection heat transfer in cylindrical envelope with an internal slottedconcentric cylinder with different site. The results indicate that for vertical slottedstructure, temperature field of both experiment and numerical solution is steady, andtwo different temperature fields are obtained under the same boundary conditions.The phenomenon of static bifurcation is verified by both experimental and numericalmethod; for level slotted structure, experimental boundary conditions are steady andsymmetric, but the non-symmetric unsteady experimental temperature fields areobtained, the oscillated phenomenon is obvious on the top of internal slottedconcentric cylinder, the amplitude of oscillation increases with the increasingRayleigh numbers, the numerical solution of two-dimensional model is steady, and itcan not reflect the oscillation phenomenon in experimental temperature.
3) Three-dimensional mathematical model was established, and it is applied forsolving natural convection heat transfer in cylindrical envelope with an internalslotted concentric cylinder. The numerical results of Wang’s experimental parametersindicate that when the Rayleigh number is lower, the system is steady, three and twodimensional numerical solutions are consistent with experimental solutions. When theRayleigh number is higher, the system is unsteady with steady and symmetricboundary condition. Those oscillated solution shows three characteristics of flow andheat transfer. The discrepancy between two-dimensional numerical and experimentalresults increases gradually with the increasing Ra numbers, but the three-dimensionalnumerical results is continent with experimental results.
4) For cylindrical envelope with an internal vertical slotted concentric cylinder, theflow and heat transfer of this system is steady and two-dimensional. There exists acritical Rayleigh number Racor slotted degree Sc. When the value of parameters ishigher than the critical value, the flow and heat transfer is oscillating with time andthree-dimensional with steady and symmetric boundary conditions.
5) Three-dimensional model is applied for solving natural convection heat transferin cylindrical envelope with an internal level slotted concentric cylinder in this paper.The results indicate that the temperature is steady, and two different temperature fieldsare obtained under the same boundary conditions. Both three-dimensional anddimensional numerical solution can reflect experimental temperature field.Three-dimensional numerical method can predict the experimental temperature fieldand static bifurcation phenomenon.
6) Three-dimensional model is applied for solving natural convection heat transfer in cylindrical envelope with an internal vertical slotted concentric cylinder in thispaper. When Rayleigh number is equal to6.46×104, three-dimensional numericaltemperature field is oscillating with time, and it can predict experimental temperaturefield. The oscillated temperature lines are obvious on the top of internal slottedconcentric cylinder, the amplitude of oscillation increases with the increasingRayleigh numbers. Three-dimensional numerical method can reflect the oscillatedtemperature, which can not be obtained by two-dimensional numerical scheme. Theoscillated system induced by non-linear characteristic can be verified by experimentaland numerical method.
7) Compact correction methods are developed firstly for solving two typical partialdifference equations. The compact method based on SIMPLE is developed bydeferred correction method, and it can obtain the high order accurate solutions. Theproblem of natural convection heat transfer of cavity heated from below is calculatedby this method. Numerical results show that the compact scheme has higher accuracythan classical scheme and predict static bifurcation phenomenon.
8) Compact finite difference scheme based on SIMPLE algorithm by author isapplied for solving natural convection heat transfer in cylindrical envelope with aninternal slotted concentric cylinder. The numerical results indicate that with theincreasing Rayleigh numbers, the system evolve from steady, periodic oscillating, tochaos. Different numerical method can predict the route from steady to chaos and beconsistent with SIMPLE algorithm with QUICK scheme..
引文
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