A turbulent model of torque in von Karman swirling flow

TL;DR

This paper introduces a stochastic Langevin-based model to predict turbulent torque fluctuations in von Karman swirling flow, validated with experiments and providing insights into power fluctuation behaviors under different forcing conditions.

Contribution

It presents a novel analytical stochastic model for turbulent torque in swirling flows, validated against experimental data, and offers a physical interpretation using turbulence theory.

Findings

Power fluctuations are half in constant torque compared to constant velocity.

The model accurately predicts the PDF of power fluctuations without adjustable parameters.

Experimental validation confirms the model's applicability in real turbulent flows.

Abstract

A stochastic model is derived to predict the turbulent torque produced by a swirling flow. It is a simple Langevin process, with a colored noise. Using the unified colored noise approximation, we derive analytically the PDF of the fluctuations of injected power in two forcing regimes: constant angular velocity or constant applied torque. In the limit of small velocity fluctuations and vanishing inertia, we predict that the injected power fluctuates twice less in the case of constant torque than in the case of constant angular velocity forcing. The model is further tested against experimental data in a von Karman device filled with water. It is shown to allow for a parameter-free prediction of the PDF of power fluctuations in the case where the forcing is made at constant torque. A physical interpretation of our model is finally given, using a quasi-linear model of turbulence.