Role of varying Reynolds number for flow past a rotating cylinder at high rotation rate

TL;DR

This study investigates how varying Reynolds number affects flow dynamics past a rotating cylinder at high rotation rates, revealing bifurcations, flow instabilities, and developing an ANN surrogate model for rapid predictions.

Contribution

It provides a comprehensive bifurcation analysis over a wide Reynolds number range and introduces an ANN model for fast, accurate force and instability predictions.

Findings

Critical Reynolds number identified at 5650 for flow behavior change.

Flow separation reduces with increasing Reynolds number, saturating at high values.

ANN model achieves 90-99% accuracy, reducing computation time by 99.9%.

Abstract

The present study reports comprehensive bifurcation analysis of flow past a rotating cylinder at a fixed rotation rate by varying free-stream Reynolds number ($Re_{\infty}$) from 1000-6000 in intervals of 50. Two-dimensional compressible Navier-Stokes equations are solved using dispersion relation preserving numerical methods over 101 test cases, amounting to $10^6$ core hours of computing. The dataset produced from high-fidelity simulations serve as useful benchmarking tools for testing compressible flow solvers, estimating unsteady force distribution and vorticity dynamics. For moderate $Re_{\infty}$, rotation induces circulation that reduces pressure drag with increasing $Re_{\infty}$. For higher $Re_{\infty}$, boundary layer becomes thinner with suppressed flow separation, but effect of rotation saturates. Thus, benefits of increasing $Re_{\infty}$ taper off and pressure recovery stalls. The bifurcation analysis reveals a critical $Re_{\infty}$ of 5650 beyond which global behavior of Magnus-Robins effect changes significantly. Supercritical flow is receptive to time-dependent instabilities and structures in wake of the cylinder become dynamically unstable. Even small changes in $Re_{\infty}$ leads to different instantaneous force distributions and sharp fluctuations in lift and drag calculations. Stronger, coherent vortices in the wake generate consistent, high-energy periodic signals, contributing to strong Fourier amplitudes in spectra. An artificial neural network (ANN) is trained using simulation datasets to serve as fast, inexpensive alternatives for calculating lift, drag, and onset time of instability. The ANN reduces time required for simulation by 99.9\%, enabling dense parametric sweeps. Maximum accuracy achieved for the ANN is between 90-99\% for the parameters examined.