Effect of Polymer Additives on the Hydraulic Resistance of Flow
Abstract Generated abstract
This paper examines how small polyethylene oxide additions affect hydraulic resistance in turbulent water flow through the annular channel of a tube-in-tube heat exchanger. Pressure drop, flow rate, and temperature were measured in a stabilized section over Reynolds numbers of about 10,000 to 40,000 while varying polymer concentration and molecular weight. The experiments show that polymer additives reduce the hydraulic friction coefficient, with the reduction increasing at higher flow velocity, higher polymer concentration, and greater molecular weight. The authors interpret the molecular-weight dependence as consistent with a mechanism in which longer polymer chains damp large turbulent vortices.
Full Text
EFFECT OF POLYMER ADDITIVES
ON THE HYDRAULIC RESISTANCE OF FLOW
I. P. CHASHCHIN; N. T. SHALAVIN, Yu. N. SUKHUSHIN
(Presented by the scientific seminar of the Department of Processes, Apparatuses, and Cybernetics of Chemical Production)
It is known from the literature that, when high-molecular substances with concentrations of \(10^{-2}\)—\(10^{-6}\%\) are introduced into a flow, a reduction in hydraulic resistance occurs [1—4].
For the purpose of a more thorough study and clarification of the mechanism of the influence of polymer additives, we carried out investigations on a “tube-in-tube” type heat exchanger operating in cooler mode. Distilled water with an added polymer, circulating in a closed circuit, was passed through the annular section of the heat exchanger. In order to reduce the influence of inlet and outlet conditions on the hydrodynamics of the flow, the entire length of the heat exchanger was conventionally divided into sections.
For greater accuracy, the pressure drop in the stabilized section \((L/d_e > 60)\) was measured with a U-shaped two-liquid manometer with an accuracy of \(\pm 0.5\ \mathrm{N/m^2}\). The working liquids in the manometer were isobutyl iodide \((\rho = 1613\ \mathrm{kg/m^3})\) and distilled water \((\rho = 1000\ \mathrm{kg/m^3})\). The flow rate of the heat-transfer medium was measured by a volumetric method with an accuracy of \(\pm 0.01\) liter.
Measurements of the wall and flow temperatures in this section were made with chromel–copel thermocouples connected to a millivolt microammeter with an accuracy of \(\pm 0.2^\circ \mathrm{C}\). The experiments were conducted at Reynolds-number values of \((1—4)\cdot 10^4\) and differed from one another in the flow rate of the heat-transfer medium and the amount of polymer additive. Polyethylene oxide was used as the polymer additive in the experiments. When a polyethylene oxide additive is introduced into the flow, a reduction in the coefficient of hydraulic resistance \((\lambda_{\mathrm{tr}})\) is observed. The reduction effect depends on the flow velocity and the concentration of the polymer additive.
The experimental results show that the reduction in the coefficient of hydraulic friction resistance in the presence of a polymer additive increases with increasing velocity of the heat-transfer-medium flow. Thus, at a Reynolds number \(Re\) equal to \(3 \cdot 10^4\), the coefficient of hydraulic resistance decreases by approximately a factor of 2 in comparison with the heat-transfer medium without an additive. It was also established that, with an increase in the concentration \((3 \cdot 10^{-5} : 3 \cdot 10^{-2})\) of polymer, the effect of reducing hydraulic resistance increases. The data obtained by us agree satisfactorily with the literature [1—4].
We also investigated the influence of a polyethylene oxide additive on the magnitude of the coefficient of hydraulic resistance as a function of the molecular weight of the polymer at its constant concentration in the flow of \(3 \cdot 10^{-3}\%\). The investigations were carried out using poly-
polyethylene oxide with molecular weights \((3.647;\ 5.0;\ 6.093;\ 9.333)\cdot 10^6\) l.
From the results of the studies presented in Fig. 1, it is evident that, as the molecular weight of the polymer increases, the reduction in hydraulic resistance is greater, the greater its molecular weight. The effect of reducing the coefficient of hydraulic resistance can be explained by the fact that, with increasing molecular weight of the polymer (taking into account its linear structure), the length of its chain increases. This, in turn, leads to the damping of large turbulent vortices on the polymer molecule, which also confirms the hypothesis of Barenblatt [4] on the mechanism of the influence of polymer additives.
Fig. 1. Dependence of the reduction in the coefficient of hydraulic resistance on the molecular weight of the polymer: 1 — heat-transfer medium without additive; 2 — heat-transfer medium with a polymer additive, mol. wt. \(=3.647\cdot 10^6\); 3 — heat-transfer medium with a polymer additive, mol. wt. \(=5.0\cdot 10^6\); 4 — heat-transfer medium with a polymer additive, mol. wt. \(=6.093\cdot 10^6\); 5 — heat-transfer medium with a polymer additive, mol. wt. \(=3.333\cdot 10^6\).
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