【作者】 刘玉泉；

【导师】 朱克勤；

【作者基本信息】 清华大学 ， 力学， 2013， 博士

【摘要】 非牛顿流体在平面槽道、环形管道等结构中的二维流动的稳定性问题，无论在理论研究方面还是实际应用方面都有重要价值。而在众多非牛顿特性中，剪切稀化特性作为最基础特性之一，近年来是非牛顿流体力学的一个研究热点。此外，横流作用下的稳定性研究对于理解多孔壁面吹吸在流动控制方面的作用有重要意义。本文研究的流动包括横流下平面槽道中的流动，以及环形管道中的轴向流动，流动由壁面运动和压力梯度共同驱使。流体模型包括广泛使用的幂律流体模型、宾汉流体模型，也采用了更接近真实流体特性的Carreau流体模型。推导了均匀横流下幂律流体平面Couette-Poiseuille流动、环形管道中宾汉流体轴向Couette-Poiseuille流动的精确解。平面槽道流动情况下对幂律流体和Carreau流体分别建立稳定性方程，利用模态和非模态的稳定性方法，研究了扰动的长期发展与短期瞬态增长，讨论了剪切稀化效应和横流对模态和非模态稳定性的影响。均匀横流下幂律流体平面Couette-Poiseuille流动的精确解表明，当横流与压力梯度满足一定关系时，基本流可保持Couette速度剖面的直线分布，不随横流和剪切稀化效应而改变，此时它们仅作为稳定性方程中的附加惯性项和粘性项产生影响。模态稳定性分析显示，剪切稀化使流动趋向失稳，横流使流动先趋向失稳再趋向稳定，流动由稳定变为不稳定的临界横流雷诺数在流向雷诺数增大时趋于一定值，且幂律流体和牛顿流体的这一定值之间存在线性关系式。非模态稳定性分析显示，剪切稀化和横流对瞬态增长分别起到增强和削弱的效果。当横流与压力梯度之间的限制得到解除，对均匀横流下Carreau流体平面Couette-Poiseuille流动的稳定性研究表明，横流使流动先趋向稳定再趋向失稳最终趋向稳定，基本流的改变催生了一个流动由不稳定变为稳定的临界横流雷诺数，且有长波和短波两种失稳机制。流动由不稳定变为稳定的临界横流雷诺数的失稳机制仍仅为长波，发现剪切稀化改变基本流的稳定作用和附加粘性项的失稳作用在这里产生了竞争。非模态稳定性分析显示，剪切稀化仍使瞬态增长得到增强，而横流使瞬态增长先增强后减弱，这一增强作用源于改变基本流。环形管道中宾汉流体轴向Couette-Poiseuille流动的精确解表明，有两种平面槽道结构下不存在的流动型态存在于环形管道结构下，并阐释了它们的物理机制。更多还原

【Abstract】 The stability of two-dimensional flows of non-Newtonian fluids in plane or annular channelshas important value in both theoretical studies and practical applications. As one of the basic featuresof non-Newtonian fluids, the shear-thinning property has drawn lots of research focus during the lastdecades. In addition, studies on the flow stability under crossflow are significantly meaningful tounderstand the effects of blowing and suction through porous walls as an efficient flow controlmethod.In the present work, flows in plane channels under crosslfow as well as axial flows throughconcentric annuli are considered, which are driven by both the wall motion and the pressure gradient.Applied fluid models include widely used power-law fluids and Bingham fluids. Carreau fluids,which present characteristics closer to real fluids, are also taken into consideration. Exact solutionsfor plane Couette-Poiseuille flow of power-law fluids under uniform crossflow, as well as axialCouette-Poiseuille flow of Bingham fluids through concentric annuli, are derived. With the stabilityequations established for power-law fluids and Carreau fluids in plane channel flow situation, studieson the long-term development and short-term transient growth of flow disturbances are performedusing modal and non-modal approaches. Effects of the shear-thinning property and crossflow onmodal and non-modal stability are analyzed.As the exact solution for plane Couette-Poiseuille flow of power-law fluids under uniformcrossflow shows, the basic flow can maintain Couette velocity profile as long as a relation betweencrossflow and pressure gradient is satisfied. Therefore, the basic flow is not influenced by crossflowand shear-thinning property, which affect the flow stability only by additional inertial and viscousterms in the stability equation. Modal stability analyses demonstrate that the shear-thinning propertydestabilizes the flow, while crossflow destabilizes the flow first and then stabilizes it. The criticalcrossflow Reynolds number that makes the stable flow unstable tends towards a constant as thestreamwise Reynolds number increases. A linear relation between the constant for a power-law fluidand that for a Newtonian fluid is discovered. Non-modal stability analyses demonstrate that theshear-thinning property enhances transient growth, while crossflow weakens it.When the restriction between crossflow and pressure gradient is removed, the basic flow is nolonger uninfluenced by crossflow and shear-thinning property. As studies on the stability of planeCouette-Poiseuille flow of Carreau fluids under uniform crossflow shows, crossflow stabilizes theflow first, and then destabilizes it, and stabilizes it eventually. The alteration of the basic flow induces an extra lower critical crossflow Reynolds number that makes the unstable flow stable,which contains both long-wave and short-wave instability mechanism. The critical crossflowReynolds number that makes the stable flow unstable contains long-wave instability mechanism only.The competition between stabilization of altering the basic flow and destabilization of an additionalviscous term in the stability equation is discovered, both of which originate from the shear-thinningproperty. Non-modal stability analyses demonstrate that the shear-thinning property still enhancestransient growth, while crossflow enhances it first and then weakens it. The enhancement effect ofcrossflow comes from the alteration of the basic flow.As the exact solution for axial Couette-Poiseuille flow of Bingham fluids through concentricannuli shows, there are two flow cases existing in annular geometry, which vanish in plane geometry.The physical mechanism of these two flow cases is illustrated.更多还原