Variation of fiber orientation in turbulent flow inside a planar contraction with different shapes

In this study, we have investigated the influence of shape of planar contractions on the orientation distribution of stiff fibers suspended in turbulent flow. To do this, we have employed a model for the orientational diffusion coefficient based on the data obtained by high-speed imaging of suspension flow at the centerline of a contraction with flat walls. This orientational diffusion coefficient depends only on the contraction ratio and turbulence intensity. Our measurements show that the turbulence intensity decays exponentially independent of the contraction angle. This implies that the turbulence variation in the contraction is independent of the shape, consistent with the results by the rapid distortion theory and the experimental results of axisymmetric contractions. In order to determine the orientation anisotropy, we have solved a Fokker–Planck type equation governing the orientation distribution of fibers in turbulent flow. Although the turbulence variation and the orientational diffusion are independent of the contraction shape, the results show that the variation of the orientation anisotropy is dependent on shape. This can be explained by the variation of the rotational Péclet number, Pe_r, inside the contractions. This quantity is a measure of the importance of the mean rate of the strain relative to the orientational diffusion. We have shown that when Pe_r < 10 turbulence can significantly influence the evolution of the orientation anisotropy. Since in contractions with identical inlet conditions the streamwise position where Pe_r = 10 depends on the shape, the orientation anisotropy is dependent on the variation of rate of strain in a given contraction. We demonstrate the shape effect by considering contraction with flat walls as well as three contractions with different mean rate of strain variation.