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

TL;DR

The study analyzes flow past a cylindrically rotated body at a high rotation rate in a compressible regime by varying $Re_{\infty}$ over $[1000,6000]$ with $M_{\infty}=0.1$ and fixed $U_s/U_{\infty}=10$, solving the 2D compressible Navier–Stokes equations to produce a high-fidelity dataset for benchmarking and ML development. A detailed bifurcation analysis reveals a critical $Re_{\infty}=5650$ where the Magnus–Robins wake transitions from steady to unsteady, including sub-, critical, and super-critical regimes characterized by Hopf bifurcations and multi-frequency shedding. The work links vorticity dynamics, temporal scales, and force distributions to wake transition, showing how compressibility and rotation modulate enstrophy production via a CETE framework. Additionally, an artificial neural network is trained on the simulation data to rapidly predict onset time, lift, and drag, achieving up to 99% accuracy and offering a 99.9% reduction in computation time for dense parameter sweeps, thereby providing a practical surrogate for design and solver benchmarking.

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.

Figures (17)

• Figure 1: Schematic of uniform flow past a rotating cylinder with surface speed, $U^*_s$.
• Figure 2: Comparison of computed and experimental tokumaru1991rotary normalized transverse velocity upstream of cylinder with steady rotation at $Re_{\infty}$ = 3800 and $U^*_s = 10 U_{\infty}$. The free-stream Mach number, $M_{\infty}$ of the simulation is fixed at 0.1 to mimic the experimental setup.
• Figure 3: Time variation of spanwise vorticity for $U^*_s = 10U_{\infty}$ and (a)-(c)$Re_{\infty} = 1000$, (d)-(f)$Re_{\infty} = 1500$, (g)-(i) $Re_{\infty} = 2000$, (j)-(l) $Re_{\infty} = 2500$. The vorticity is plotted at indicated times starting from the onset of instability in frames (a), (d), (g), and (j).
• Figure 4: Time variation of spanwise vorticity for $U^*_s = 10U_{\infty}$ and (a)-(c)$Re_{\infty} = 3000$, (d)-(f)$Re_{\infty} = 3500$, (g)-(i) $Re_{\infty} = 4000$, (j)-(l) $Re_{\infty} = 4500$. The vorticity is plotted at indicated times starting from the onset of instability in frames (a), (d), (g), and (j).
• Figure 5: Time variation of spanwise vorticity for $U^*_s = 10U_{\infty}$ and (a)-(c)$Re_{\infty} = 5000$, (d)-(f)$Re_{\infty} = 5500$, (g)-(i) $Re_{\infty} = 6000$. The vorticity is plotted at indicated times starting from the onset of instability in frames (a), (d), and (g).