An approximate theoretical analysis and experimental verification of turbulent entrance region flow of drag reducing fluids

Mathematical model of the entry length in the flow of suspensions of solid particles in a gas

“…On the other hand, the calculated entry length in the turbulent region decreases when the Reynolds number is increased or the relative mass fraction of solid particles is reduced. This conclusion, which contradicts the results of Shintre et al [6], is found to be in agreement with experimental results, which show an inverse relation between the entry length and Reynolds number in turbulent flow. In contrast, Shintre et al [6] used a simplified procedure for estimating the exponent and found an increase in the entry length with increases in the Reynolds number over the whole region of turbulent flow.…”

“…In estimating the values of these coefficients Shintre et al [6] used the integrated form of the equation for the velocity field in the turbulent flow of non-Newtonian fluids. They did not consider the dependence of these coefficients on the Reynolds number or the rheological characteristics of the flow.…”

“…Due to the fact that the flow of a suspension of solid particles in gas has non-Newtonian properties, we used the same set o f equations as the above-mentioned authors [6]. The solution was required to satisfy the equation for the velocity field in steady turbulent and laminar flow, and hence a power-law relation [8] and the Ostwald-De Waele equation were used [7].…”

“…A mathematical simulation of the entry length of flow of a non-Newtonian fluid with a flat velocity profile at the entrance was published by Shintre, Mashelkar and Ulbrecht [6]. These authors made use of the time-smoothed equation of continuity and the momentum balance for axisymmetric flow [7].…”

Developing and fully developed turbulent flow of drag reducing fluids in an annular duct

“…The simplest limiting case of annular flow is a cylindrical pipe obtained by taking F, = 1. In this case, it is seen that the theoretical predictions are akin to those of Shintre et al (1977) and hence an experimental verification would only be duplication of information, as this has already been done quite carefully by Shintre et al (1977) for drag reducing fluids. Darby and Chang (1984) have presented experimental values of tube flow friction factors for several polymer solutions.…”