倾斜偏心环空中宾汉流体层流流动

LAMINAR FLOW OF BINGAM'S FLUID IN INCLINED ECCENTRIC ANNULUS

本文应用流体力学中的运动微分方程,建立了宾汉流体在倾斜偏心环空中的层流流动模型。通过求解微分方程得出了宾汉流体在该流动条件下的精确流速分布公式,并由此分析了倾斜偏心环空宾汉层流流动特征;然后证明了当环空流速较高时,也就是当宾汉流体的屈服值τ_0与单位长度压降丨dp′/dz丨的比值较小时,宾汉流体层流最大流速“半径”ρ近似等于相同条件下的牛顿流体最大流速“半径”ρ_1。文中也分析了由此产生的误差,结果表明当屈服值τ_0与单位长度压降丨dp′/dz丨的比值小于或等于0.01米时,相对误差不超过1.27％;最后进一步提出了精确计算该流动条件下的宾汉层流流量公式及压降公式。

Using the differential motion equation in fluid mechanics, this paper developed the flow models of the laminar flow of Bingham's fluid in an inclined eccentric annulus. By solving the differential equation, it presented the accurate flow velocity distribution, formulas of Bingham's fluid under flow conditions and analyzed the flow features of Bingham's fluid laminar in an inclined eccentric annulus. It has been proved that when flow velocity in the annulus is higher, i. e. when the rate between Bingham's fluid yield value and the gradient of pressure are less, the maximum velocity 'radius' of Bingham's fluid laminar flow approximates to that of Newton's. This paper also analyzed the error produced therefrom. The results showed that when the ratio between the yield value and the gradient of pressure is not larger than 0.01m, the relative error is less than 1.27％; and lastly the paper also proposed the accurate flow rate and pressure fall formulas of Bingham's laminar flow under flow conditions.