Measurements and CFD Modeling of Drag-Reduction Effects

Summary

Computational-fluid-dynamics (CFD) modeling of drag reduction (DR) by polymer additives dissolved in hydrocarbon was carried out in pipe flows and in a rotating shear viscometer. A two-layer turbulence model was applied that described turbulence damping by the molecules of drag-reducing additives (DRAs) in the near-wall regions. The von Karman constant in the near-wall region was used as the model parameter. Extensive measurements of the DR effect for a rotating viscometer were performed at different Reynolds numbers, apparent molar masses, and DRA concentrations. The model with only one fit parameter was able to reproduce the experimental results in both pipe flows and the rotating viscometer. Experimental results were used in relating the model parameter to the relevant physical properties.

Introduction

The phenomenon of DR by low concentrations of long-chain polymers has been widely studied since Toms discovered the effect more than 50 years ago. In long oil pipelines, the pumping capacity can be significantly increased and pumping costs decreased by applying small amounts of DRA. A reduction of up to 70% in pressure loss in pipe flow has been achieved.

The DR effect has mostly been studied in pipe flow because it is the most important application.1–3 With pipe diameters larger than 40 mm, DR effects can also be measured accurately at high Reynolds numbers for high-viscosity (3·10–5 m2/s) oil. How- ever, pipeline construction may be rather expensive and the measurements time-consuming. The advantage of pipe-flow measurements is the large amount of general knowledge about turbulent flow in pipes.

In a spinning wheel consisting of a ring-shaped pipe and equipped with torque-measurement devices, pressure loss can be measured accurately with a small amount of fluid and without degradation losses. One possible drawback of this method is the short liquid-volume length that provides only partial DR effects.

Measurements in a rotating-viscometer-type apparatus have been carried out by, for example, Tong et al.,4 Cadot et al.,5 and Choi et al.6 It is easy to control the turbulent flow conditions in this type of experiment by varying the diameter of the rotating cylinder and the rotational speed.

We have carried out extensive measurements of DR effects in a viscometer equipped with a rotating cylinder in a baffled vessel. DR efficiency was measured with varying polymer molar masses and concentrations as well as rotational speed. The experimental setup is relatively easy to model with CFD.

Although a vast amount of research on DR has been done, the mechanism of the phenomenon is still poorly understood. Lumley,7 Thirumalai and Bhattacharjee,8 and Ryskin9 have presented possible explanations and theoretical analysis.

The commonly approved theory of DR is based on polymer molecules stretching outside the viscous sublayer because of shear forces and the subsequent enhanced damping of the transverse turbulent fluctuations close to the pipe wall.

The polymer chain elongates in an extensional flow if the strain rate exceeds a critical value. The DR effects are related to the polymers' elongation and relaxation properties and depend on polymer characteristics, such as apparent molar mass, molar mass distribution, and chain structure, as well as polymer concentration and shear stresses. Furthermore, fully stretched polymer chains can be degraded by high shear stresses, leading to losses in DR effects.

CFD modeling of the DR effect in turbulent flow is challenging. Attempts to model the DR effect have been made by Hassid and Poreh10 with a one-equation turbulence model, Poreh and Hassid 11 and Patterson et al.12 with a modified k-e model, and Sureshkumar et al.13 with direct numerical simulation.

Turbulence damping should be based on anisotropic turbulence models in which the damping effects are described, in each direction, by polymer DR properties. These models, however, are computationally expensive and, therefore, not suitable for engineering applications.

In this paper, the effect of drag reducers on turbulence has been modeled with an isotropic two-layer turbulence model that employs the one-equation model of Hassid and Poreh10 in the near-wall region and the standard k -e model in the fully turbulent regions. The results of measurements with the rotating viscometer were used to fit the model parameters, and the validity of the model was tested in pipe flows. The developed DR model was incorporated into the commercial CFD code STAR-CD14 for simulating local DR effects in arbitrary flow conditions.

Measurements of DR and Degradation Effects in Hydrocarbon Solvent

Description of Measuring Device.

In this study, the flow conditions necessary to elongate the polymer, the DR efficiency of polymers of various apparent molar masses, and their degradation kinetics have been measured with the rotating shear viscometer shown in Fig. 1.

The vessel is equipped with a rotating cylinder 99 mm in diameter and baffles around the vessel and near the bottom. The rotation speed of the cylinder can be adjusted within the 0- to 3,200-rpm range. The vessel stands on two bottom discs with an annular ball bearing in between, allowing frictionless movement of the upper disc. DR effects can be exactly measured under turbulent conditions by measuring the torque force of the bottom plate against the balance sensor.