Upscaling drag reduction of rotational rheometer to linear pipe flow

Drag reduction (DR) is a phenomenon associated with adding small amounts of drag-reducing agents to reduce friction causing a reduction in the pressure gradient needed for pumping a solution under turbulent conditions. Traditionally, DR has been measured with linear flow devices, such as flow loops. Recent developments in rheological measurement techniques have enabled the evaluation of DR using rotational rheometers. However, due to differences in flow nature and length scale, direct comparison between outcomes is not possible. This study introduces nondimensional quantities, namely dimensionless pressure difference for pipe flow and dimensionless torque for rheometers, as the basis for comparing the DR results of linear and rotational flow. Theoretically, the DR expressions derived from these dimensionless quantities showed similar structures, featuring a factor with quadratic viscosity and linear density terms. Experimentally, DR tests were carried out using an industrial-scale pipe flow and a laboratory-scale rotational rheometer, using solutions of tap water with high-viscosity partially hydrolyzed polyacrylamide at two molecular weights. Samples tested with the rheometer were collected from flow loop experiments, ensuring the same polymer solutions were tested with both devices. Results showed that DR, expressed as a function of Reynolds number using nondimensional measurements, follows similar behavior for both instruments. The experimental DR results from the rheometer were extrapolated to the pipe flow scale, showing overall agreement between extrapolated and experimental results. These findings suggest that rotational rheometers could effectively replace linear flow instruments for screening polymer solutions in DR applications.