Precise measurements of torque in von Karman swirling flow driven by a bladed disk

TL;DR

This study accurately measured torque in a swirling turbulent flow driven by a bladed disk, revealing that previous anomalies were due to experimental misalignments rather than fundamental physics, and confirmed the similarity law across various viscosities.

Contribution

The paper demonstrates that careful experimental redesign can eliminate background errors, confirming the similarity law in turbulent swirling flows with high precision.

Findings

Misalignments caused apparent similarity law breakdown

Redesigned setup reduced errors to near torque meter resolution

Confirmed the similarity law across different viscosities

Abstract

Scrupulous measurements and detailed data analysis of the torque in a swirling turbulent flow driven by counter-rotating bladed disks reveals an apparent breaking of the law of similarity. Potentially, such breakdown could arise from several possible factors, including dependence on dimensionless numbers other that $Re$ or velocity coupling to other fields such as temperature. However, careful redesign and calibration of the experiment showed that this unexpected result was due to background errorscaused by minute misalignments which lead to a noisy and irreproducible torque signal at low rotation speeds and prevented correct background subtraction normally ascribed to frictional losses. An important lesson to be learnt is that multiple minute misalignments can nonlinearly couple to the torque signal and provide a dc offset that cannot be removed by averaging. That offset can cause the observed divergence of the friction coefficient C_f from its constant value observed in the turbulent regime. To minimize the friction and misalignments, we significantly modified the experimental setup and carried out the experiment with one bladed disk where the disk, torque meter and motor shaft axes can be aligned with significantly smaller error, close to the torque meter resolution. As a result we made precise measurements with high resolution and sensitivity of the small torques produced for low rotation speeds for several water-glycerin solutions of different viscosities and confirmed the similarity law in a wide range of Re in particular in low viscosity fluids.