屈服假塑性流体轴向同心环空中速度及温度分布研究

Study of the velocity and temperature profiles for the annulus pipe flow of H-B fluid

赫谢尔-巴尔克莱(Herschel Bulkley)流变模式是一个三参数模式,因其精度较高,近几年国内多采用其描述钻井液的流变性。本文将非牛顿流体动量方程、能量方程与H B流体的本构方程相结合,推导出了流体在轴向同心环空中的速度及温度分布公式。数值研究结果表明,由于H B屈服应力的作用,轴向同心环空内存在柱塞流动,柱塞的大小与H B屈服应力τ0成正比,与单位管长压力降Δp L成反比。在其它相同条件下,柱塞速度随环空尺寸的增大而增大。随着流变指数的增大,流核速度变小。柱塞内温度呈对数曲线变化,柱塞外侧温度与内侧温度不相同,从柱塞边界到管壁,温度逐渐减小。越靠近管壁,温度降低幅度越大。

Herschel-Bulkley equation which includes three parameters is often used in drilling to describe the rheology of drilling fluid, for its high precision. Combining the constitutive equation of Herschel-Bulkley fluid with the momentum equation and the energy equations of non-Newtonian fluid, the velocity and the temperature profiles for the annulus pipe flow of Herschel-Bulkley fluid are obtained. The numerical results show that there is a slug flow in the annulus pipe due to the action of Herschel-Bulkley yield stress τ_0 . The size of the slug is in direct proportion to τ_0 and inverse proportion to ΔP~*L . The velocity of the slug flow increases as the size of the annular space increases, and decreases as the rheology exponent increases. The temperature in the slus flow is in logarithmic form in which the outside temperature is not identical with the inside. And from the boundary of the slug flow to the pipe wall the temperature graduallly decreases. Furthermore, the nearer to the pipe wall, the faster the temperature decreases.