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首页> 外文期刊>International Journal of Heat and Mass Transfer >Laminar flow of non-linear viscoelastic fluids in straight tubes of arbitrary contour
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Laminar flow of non-linear viscoelastic fluids in straight tubes of arbitrary contour

机译：非线性粘弹性流体在任意轮廓的直管中的层流

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摘要

The fully developed steady velocity field in pressure gradient driven laminar flow of non-linear viscoelastic fluids with instantaneous elasticity constitutively represented by a class of single mode, non-affine quasilinear constitutive equations is investigated in straight pipes of arbitrary contour (e)D. A continuous one-to-one mapping is used to obtain arbitrary tube contours from a base tube contour (e)D_0. The analytical method presented is capable of predicting the velocity field in tubes with arbitrary cross-section. The base flow is the Newtonian field and is obtained at 0(1). Field variables are expanded in asymptotic series in terms of the Weissenberg number Wi. The analysis does not place any restrictions on the smallness of the driving pressure gradients which can be large and applies to dilute and weakly elastic non-linear viscoelastic fluids. The velocity field is investigated up to and including the third order in Wi. The Newtonian field in general arbitrary contours is obtained and longitudinal velocity field components due to shear-thinning and to non-linear viscoelastic effects are identified. Third order analysis shows a further contribution to the longitudinal field driven by first normal stress differences. Secondary flows driven by unbalanced second normal stresses in the cross-section manifest themselves as well at this order. Longitudinal equal velocity contours, the secondary flow field structure, the first and the second normal stress differences as well as wall shear stress variations are discussed for several non-circular contours some for the first time.
机译：在任意轮廓（e）D的直管中，研究了压力梯度驱动的非线性弹性粘弹性流体的层流中充分发展的稳态速度场，该流体由一类单模非仿射拟线性本构方程表示。连续的一对一映射用于从基础管轮廓（e）D_0获得任意管轮廓。提出的分析方法能够预测具有任意横截面的管中的速度场。基本流是牛顿场，在0（1）处获得。字段变量根据Weissenberg数Wi以渐近级数展开。该分析对驱动压力梯度的较小性没有任何限制，该较小的驱动压力梯度可能很大，并且适用于稀和弱弹性非线性粘弹性流体。对速度场进行研究，直到并包括Wi中的三阶。获得了一般任意轮廓的牛顿场，并确定了由于剪切稀化和非线性粘弹性效应而产生的纵向速度场分量。三阶分析显示了由第一法向应力差驱动的纵向场的进一步贡献。横截面中由不平衡的第二法向应力驱动的二次流也按此顺序显示。讨论了一些非圆形轮廓的纵向等速轮廓线，次级流场结构，第一和第二法向应力差以及壁切应力变化。

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