纳米流体流动与传热问题的高精度紧致差分格式和数值模拟研究

Using the governing model equation of fluid flow to simulate the flow and heat transfer of nanofluids efficiently and accurately has always been a challenging research in the field of numerical heat transfer and hydrodynamics. This research will help to develop an efficient heat exchange system, which has important scientific value and practical significance for alleviating energy problems. The existing numerical simulation studies mainly focus on the influence of volume fraction of nanoparticles, size of nanoparticles, aspect ratio of the cavity, Rayleigh number (Ra) or Richardson number (Ri). However, some experimental data and theoretical analysis results are inconsistent, even contrary conclusions. The understanding of mechanism is not deep enough. In view of the fact that the current numerical simulation studies mainly adopt low-order accuracy schemes on uniform grids, the present research will focus on constructing an exponential compact difference scheme with high accuracy and high resolution on non-uniform grids for solving viscous incompressible flow based on the vorticity-velocity formulations and developing an efficient and accurate adaptive numerical simulation algorithm for the flow and heat transfer of nanofluids in enclosure. Thus, the flow field structure can be captured accurately, the flow and heat transfer characteristics of nanofluids can be studied, and the internal mechanism of heat transfer enhancement by nanofluids can be deeply revealed.

采用流体流动的控制方程，进行高效精确地数值模拟纳米流体流动与传热问题的研究一直是数值传热领域和流体力学领域一个富有挑战性的研究课题，其研究成果将有助于研制开发高效的热交换系统，对于缓和能源问题具有重要的科学价值和现实意义。已有的数值模拟研究主要集中在纳米颗粒体积分数、纳米颗粒尺寸、腔体纵横比、Rayleigh数或Richardson数的影响，某些实验数据和理论分析产生了一定的偏差，甚至得到了相悖的结论，机理性认识还不够深入。针对目前的数值模拟研究在数值方法上主要采用均匀网格上的低阶精度格式的缺陷，本申请项目将采用涡量-速度方法，构造非均匀网格上高精度和高分辨率的指数型紧致差分格式，发展数值模拟封闭腔体内纳米流体流动与传热问题精确高效的网格自适应算法，精确捕捉流场结构，研究纳米流体的流动特性和传热特性，深入揭示纳米流体强化传热的内在机理。

本项目采用单相直接方法对封闭腔内纳米流体对流与传热问题进行了精确高效地数值模拟，主要从差分格式构造和数值模拟两方面开展了研究。发展了数值求解控制方程组的高精度紧致差分格式及边界条件的同阶离散格式，通过直接数值模拟，重点分析了纳米流体粘度模型、纳米颗粒类型、纳米颗粒形状、纳米颗粒体积分数、瑞利数和雷诺数对纳米流体强化传热性能的影响。数值模拟研究表明：（1）添加了金属纳米颗粒的纳米流体的强化传热效果高于添加了金属氧化物纳米颗粒的纳米流体；（2）Brinkman粘度模型倾向于低估纳米流体的有效粘度，Chandrasekara粘度模型当体积分数小于3%时,添加 Al2O3纳米颗粒可以通过提高导热系数来改善换热, 但是当体积分数大于等于3%时,由添加Al2O3纳米颗粒引起的粘度的增加导致对流换热恶化；（3）在低瑞利数(Ra=10^3)下, 对任一雷诺数, 添加球形纳米颗粒和棒状纳米颗粒的纳米流体热壁面上的平均纽塞特数均随着纳米颗粒体积分数的增大而增大, 而且添加了棒状纳米颗粒的纳米流体的强化传热效果强于添加了球形纳米颗粒的纳米流体。在高瑞利数(Ra>10^3)下, 添加了球形纳米颗粒的纳米流体,对任一雷诺数,其热壁面上的平均纽塞特数随着纳米颗粒的体积分数的增大而增大,而且瑞利数越大,纳米流体的强化传热效果越好。而添加了棒状纳米颗粒的纳米流体,只有在高雷诺数下,其热壁面上的平均纽塞特数随着体积分数的增加而增大,而且随着瑞利数的增大强化传热效果减弱。基于以上研究，本项目还进行了混合纳米流体的数值模拟：采用文献实验数据拟合修正了数值模拟控制方程组中的粘度系数模型和导热模型，进行了混合纳米流体（氧化物粒子和金属粒子比例为9:1）的数值模拟，研究结果表明随着瑞利数的增加腔体热壁面上平均纽塞特数均增大，当添加的纳米颗粒体积分数为3%时,纳米流体强化传热性能最强。