Stabilizing Taylor-Couette Flow via Temperature Gradients: Critical Thresholds and Heat Transfer Behavior at Various Radius Ratios

Charmiyan, Mahmoud; Hashemi, Amir Mohammad; Joodaki, Ali; Aloui, Fethi

doi:10.22075/jhmtr.2026.39808.1885

Stabilizing Taylor-Couette Flow via Temperature Gradients: Critical Thresholds and Heat Transfer Behavior at Various Radius Ratios

Document Type : Full Length Research Article

Authors

Mahmoud Charmiyan ¹^{, 2}

Amir Mohammad Hashemi ¹^{, 3}

Ali Joodaki ¹^{, 2}

Fethi Aloui ⁴

¹ Department of Mechanical Engineering, Energy and Environment Research Group, Ayatollah Boroujerdi University, Boroujerd, Iran

² Center for International Scientific Studies and Collaborations (CISSC), Ministry of Science, Research and Technology of Iran, Iran

³ School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran

⁴ LAMIH, CNRS UMR 8201, INSA Hauts-de-France, Université Polytechnique Hauts-de-France, Campus Mont Houy, Building Gromaire, F-59313 Valenciennes Cedex 9, France

10.22075/jhmtr.2026.39808.1885

Abstract

This numerical analysis examines how a radial temperature gradient influences the stabilization threshold of Taylor-Couette flow across a range of radius ratios (0.77 ≤ η ≤ 0.95). Numerical simulations were conducted for seven radius ratios, with a constant temperature gradient applied between the inner and outer cylinders. Three-dimensional unsteady simulations were performed using the finite-volume method implemented in OpenFOAM to accurately resolve the temporal evolution and spatial structure of Taylor vortices under the imposed temperature gradients; pressure–velocity coupling was handled via the PISO algorithm, with second-order spatial discretization on a structured O-grid to ensure accurate capture of flow instabilities. The primary objective was to determine the temperature gradient required to stabilize the flow at the threshold of transition from laminar to vortex flow. Velocity contours, vorticity, skin friction coefficient, velocity profiles, and streamlines were analyzed to assess flow stability. The results reveal that the minimum stabilizing temperature gradient occurs at a radius ratio of 0.877, beyond which the required temperature gradient increases significantly. For a radius ratio of 0.77, the Richardson number exceeds 10, leading to flow destabilization due to buoyancy forces. A predictive relationship for the stabilizing temperature gradient as a function of the radius ratio was derived. Additionally, the Nusselt number at the stabilizing temperature gradient was examined, and empirical correlations were provided. The findings highlight the critical role of temperature gradients in controlling flow stability and vortex suppression in Taylor-Couette systems, offering valuable insights for engineering applications.

Keywords

CFD

Taylor-Couette instabilities

OpenFOAM

Flow patterns

Heat transfer

Subjects

Computational Heat transfer

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