Computational transport processes for micromixers* - Micromixers Fundamentals Design and Fabrication - page 90

FIGURE 3.7
Comparisons of the predicted f against the exact solution.

3.5.2 Validation - solution procedure of the Navier-Stokes equations
Figure 3.8 shows a fluid within a square cavity. There is a lid at the top of the cavity. The lid is driven
at a constant velocity of u o . The motion of the lid transfers momentum to the fluid through the effect
of viscosity. This leads to a circulatory motion of the fluid in the cavity. The flow is governed by one
dimensionless number, i.e., the Reynolds number ð Re ¼ ru o L =mÞ .The u -velocity and v -velocity

profiles along the dotted lines of y L/2 , respectively, are compared to the two-

dimensional solution of [23] . Figures 3.9 and 3.10 show the comparisons for Re

¼ L/2 and x ¼

¼ 100 and

Re 1000, respectively. The predicted velocity profiles agree well with those of [23] for both

Reynolds numbers. With these comparisons, the present solution procedure of the Navier-Stokes
equations is validated.

¼

FIGURE 3.8
Schematic of a lid-driven cavity flow.