MHD Flow Regimes in Annular Channel

TL;DR

This paper develops a semi-analytic spectral method to analyze MHD laminar flow in annular channels, revealing flow patterns and inertial perturbation laws across different magnetic field strengths.

Contribution

It introduces a computationally efficient semi-analytic algorithm and provides new insights into flow regimes and suppression laws in MHD annular flows.

Findings

Established average velocity map and flow pattern delimitation in $ ext{η}$-$M$ space.

Identified three regimes of inertial perturbation suppression with distinct laws.

Mapped flow pattern transitions and vortex behavior at high Hartmann numbers.

Abstract

One method and two results are contributed to the complete understanding about MHD laminar flow in annular channel with transverse magnetic field in this paper. In terms of the method, a computationally cheap semi-analytic algorithm is developed based on spectral method and perturbation expansion. By virtue of the fast computation, dense cases with almost continuous varying Hartmann number $M$, Reynolds number $Re$ and cross-section ratio $\eta$ are calculated to explore the flow patterns that are missed in previous research. In terms of the results of inertialess regime, we establish the average velocity map and electric-flow coupling delimitation in $\eta$-$M$ space. Seven phenomenological flow patterns and their analytical approaches are identified. In terms of the results of inertial regime, we examine the law of decreasing order-of-magnitude of inertial perturbation on primary flow with increasing Hartmann number. The proposed semi-analytic solution coincides with the $Re^2/M^{4}$ suppression theory of Baylis & Hunt (J. Fluid Mech., vol. 43, 1971, pp. 423-428) in the case of $M<40$. When $M>40$, the pair of trapezoid vortices of secondary flow begins to crack and there is therefore a faster drop in inertial perturbation as $Re^2/M^{5}$, which is a new suppression theory. When $M>80$, the anomalous reverse vortices are fully developed near Shercliff layers resulting in the slower suppression mode of $Re^2/M^{2.5}$, which confirms the prediction of Tabeling & Chabrerie (J. Fluid Mech., vol. 103, 1981, pp. 225-239).