Flow of Newtonian and Power-Law Fluids Past an Elliptical Cylinder: A Numerical Study

Abstract

Extensive numerical simulations of the 2-D laminar flow of power-law fluids over elliptical cylinders with different aspect ratios have been carried out to establish the conditions for the onset of wake formation and the onset of vortex shedding. The continuity and momentum equations were solved numerically using FLUENT (version 6.3.26). The influence of the power-law index (0.3 ≤ n ≤ 1.8) and the aspect ratio (E = b/a; 0.2 ≤ E ≤ 5) of the cylinder on the critical values of the Reynolds number denoting the onsets of flow separation and vortex shedding are presented. For shear-thinning (n < 1) fluid behavior, the onsets of wake formation and vortex shedding are both seen to be postponed to higher Reynolds numbers as compared to those in shear-thickening fluids (n > 1). Also, the values of the Strouhal number (St c) and the time-average drag coefficient (C̅ D) corresponding to the cessation of the steady-flow regime are presented. Velocity vector plots denoting the flow separation and vorticity profiles showing the vortex shedding are also included. The delineation of different flow regimes also helps identify the range of validity of some of the results on flow and heat transfer available in the literature.

Effect of power-law fluid behavior on momentum and heat transfer characteristics of an inclined square cylinder in steady flow regime

“…All else being equal, wakes tend to be shorter in power-law fluids than that in Newtonian media. This finding is also consistent with that reported for a circular cylinder [41,43], a square cylinder at a = 0 [13,49] and an elliptic cylinder [12,58]. The variation of the wake length with Reynolds number, Re and power-law index, n is shown in Fig.…”

“…Similarly, reliable results for a square cylinder (a = 0) are also available over the similar ranges of conditions [49][50][51][52][53][54][55][56][57]. Somewhat less extensive results are available for elliptic and rectangular cylinders [12,13,[58][59][60] and these are limited to the so-called steady flow regime. Broadly, all else being equal, shear-thinning viscosity facilitates heat transfer under all regimes, i.e., forced, free and mixed convection regimes by varying amounts depending upon the shape of the bluff body and the values of the pertinent dimensionless numbers like Richardson number, direction of gravity, etc.…”

“…Irrespective of the type of cross-section, similar transitions have been observed for elliptic, square and rectangular, triangular and semi-circular cylinders under appropriate conditions. As expected, the transitional values of the Reynolds number not only vary from one shape to another but even for a given shape are influenced by the orientation of the bluff body with respect to the incident fluid stream [10][11][12][13], blockage, etc. For instance, the flow regime in the vicinity of a square cylinder is much more influenced by the angle of incidence than that by the value of the Reynolds number.…”

“…(12) gives the local values of the Nusselt number, it is customary to introduce the surface averaged value of the Nusselt number Nu avg which is evaluated as:…”

Two-dimensional steady flow over a semi-circular cylinder: drag coefficient and Nusselt number

“…This flow regime persists up to about Re % 180 and the flow transits to three-dimensional regime beyond this Reynolds number. Similar transitions are known to occur for elliptic [8] and square cross-section [6,7] cylinders, though the critical Reynolds number separating any two flow regimes are not very well understood and undoubtedly, as expected, tend to be geometry dependent. Intuitively, one can therefore expect similar flow regimes to occur in the case of a semi-circular cylinder, albeit there has been no systematic study to delineate the value of the critical Reynolds number.…”