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首页> 外文期刊>Applied Mathematical Modelling >Clausius-Duhem inequality for quasi-1D transient flows in variable cross-section area deformable pipes
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Clausius-Duhem inequality for quasi-1D transient flows in variable cross-section area deformable pipes

机译：可变横截面区域变形管中的准1D瞬态流动的Clausius-Duemem不等式

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This paper presents the derivation of the Clausius-Duhem inequality for quasi-lD transient flows of compressible fluids in radially deformable pipes of varying cross-section area. To do so, a decomposition of the normal stress in spherical and deviatoric components was considered, so that the power expended to radially deform the fluid could be properly accounted for in the first law of thermodynamics, generating a coherent Clausius-Duhem inequality. Based on the derived inequality for Newtonian-Fourier fluids, we focus on their implications and applications. As implications we show that the restrictions imposed on the dynamic and bulk viscosities are different from those retrieved from the 1D and 3D contexts. As applications, we present two distinct studies concerning pipe flows. The first shows by appealing to numerical simulations that the weighting-function and local-balance unsteady friction models violate the second law of thermodynamics since they present negative local rate of energy dissipation. The second presents an analysis to estimate upper bounds of the local rate of energy dissipation associated with shear, and volumetric and axial deformations for laminar and turbulent transient regimes, under flow conditions characterized by the Ghidaoui's dimensionless parameter P, for liquids with different bulk to shear viscosity ratios. Although the dissipation is dominated by shear, that one due to volumetric deformation may become more relevant for laminar flows, when small numbers P and high bulk viscosities liquids are considered.
机译：本文介绍了径向可变形管的压缩流体中的Quasi-LD瞬态流量的克劳斯 - Duemem不等式的推导。为此，考虑了球形和脱极组件中的正常应力的分解，使得在热力学的第一定律中，可以适当地占流体的径向变形的功率，从而产生连贯的克劳斯 - Duhem不平等。基于牛顿傅立叶液的衍生不等式，我们专注于他们的影响和应用。作为含义，我们表明，对动态和批量粘度的限制不同于从1D和3D上下文检索的那些。作为应用，我们提出了两个关于管道流动的不同研究。首先通过吸引权重函数和局部平衡不稳定的摩擦模型侵犯了第二种热力学定律，因为它们呈现负局部能量耗散率。第二次提出了一种分析，以估计与剪切相关的剪切相关的局部能量耗散速率的上限，以及用于层流和湍流瞬态瞬变的体积和轴向变形，其流动条件是GHIDAOUI的无量纲参数P的流动条件，用于剪切的液体。粘度比。虽然散射由剪切支配，但是当考虑少量P和高堆积粘度液体时，由于少量变形而导致的，对于液体的流动可能变得更加相关。

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