双筒粘度计中牛顿流体的振荡解*
Solution for the Oscillation of a Newtonian Fluid in a Co-Axial Viscometer
-
摘要: 当双筒粘度计的一筒振摆时,静止的另一筒上所测得的力矩表现出相位滞后,一个重要的原因是两筒间狭隙中的流体有惯性效应.本文提出一种化为常微分方程两点边值问题的方案,得到Navier-Stokes方程的一个新的精确解,可以说明这一效应.计算结果表明,随着Womersley数α和无量纲隙宽δ的增大,隙中流体速度剖面逐渐偏离线性而过渡到边界层型,从而使所测得力矩量值变小且相位滞后加大.本文所提出的计算方案具有数值精度高、稳定性好的优点,很容易推广到求解其它线性周期性问题.Abstract: When one cup of a co-axial viscometer oscillates, the measured moment on the other(stationary) cup.shown a phase lag, partly due to the inertial effect of the fluid within the gap between the cups. In this paper such an effect is illustrated by a new exact solution of the Navier-Stokes equation, which is derived herein by a scheme of reducing it to a two-point boundary value problem for ODEs. Our numerical results indicate that, as the Womersley number a or the dimensionless gap width increases, the fluid velocity profile within the gap gradually deviates from the linear one and transits to that of the boundary layer type, with the result that the moment decreases in the magnitude and lags behind in the phase. With the advantage of high accuracy and excellent stability, the scheme proposed herein can readily be extended to solve other linear periodic problems.
-
[1] 翁维良、廖福龙、吴云鹏等编著.《血液流变学研究方法及其应用》,科学出版社(1989),260-273. [2] 吴望一编著.《流体力学》,下册,北京大学出版社(1983),252-255. [3] 张捷迁、章光华、陈允文著,《真实流体力学》.上册,清华大学出版社(1986),130-141. [4] AbraAnow itz,M.and I.A,Sieguneds.,Handbook of Mathematical Functions with Formulas,Graphs,and Mathematical Tables,National Bureau of Standards(1964).360-364. [5] 凌复华、殷学纲、何治奇编著,《常微分方程数值方法及其在力学中的应用》.重庆大学出版社(1990),55-92. -
点击查看大图
计量
- 文章访问数: 2191
- HTML全文浏览量: 69
- PDF下载量: 622
- 被引次数: 0
下载:
