Homotopy and adomian semi-numerical solutions for oscillatory flow of partially ionized dielectric hydrogen gas in a rotating MHD energy generator duct

Beg, OA; Beg, TA; Munjam, SR; Jangili, S

Abstract

Hydrogen-based MHD power generators offer significant advantages over conventional designs. The optimization of these energy devices
benefits from both laboratory scale testing and computational simulation. Motivated by this, in the current work, a mathematical model is
developed for MHD pumping of partially ionized hydrogen in a rotating duct with oscillatory, Maxwell displacement and magnetic induction
effects under an inclined static magnetic field. Perfectly electrically conducting duct walls are assumed. The non-dimensional conservation
equations are solved using the power-series based Homotopy Analysis Method (HAM) with an appropriate embedding parameter. Detailed
graphical visualization of the impact of emerging parameters on the non-dimensional primary and secondary velocity components (u, v)
and magnetic induction components ( , ) x y b b
across the duct is presented. Average squared residual errors for all key variables
, , , ( and ) u v bx by     with associated CPU times at various orders of the HAM iteration are also included. Validation with an Adomian
Decomposition Method (ADM) is also conducted, and excellent agreement is obtained (tabulated). The computations have shown that with
increasing inverse Ekman number strong damping is observed in the primary flow whereas the secondary flow is accelerated, in particular in
the core region of the duct. With elevation in Maxwell displacement effect (for the case of a 45 degrees inclined magnetic field i.e.  = /4)
there is a strong decrease in primary magnetic induction at the lower wall of the duct and elevation in magnitudes at the upper duct wall;
however, in the core region no tangible modification is computed. The opposite trend is observed for the secondary magnetic induction. With
increasing magnetic Prandtl number (i.e. ratio of magnetic Reynolds number to ordinary Reynolds number) in the presence of strong Maxwell
displacement current, strong magnetic field and high inverse Ekman number, the primary velocity is accelerated in both the left and right half
space of the duct with a dip in magnitude at the centreline. However, the secondary velocity exhibits a much lower enhancement in both zones
with only weak acceleration near the duct walls. Both velocity components achieve symmetrical distributions about the duct centreline. A
significant depletion in primary magnetic induction is computed near the lower duct wall with enhancement near the upper duct wall; the
contrary behaviour is exhibited by the secondary induced magnetic field. Applications of the study arise in hybrid rotating hydrogen based
MHD energy generators and furthermore the computations provide a good basis for generalization to 3-dimensional flows with commercial
multi-physical fluid dynamic codes e.g. ADINA-F, COMSOL, ANSYS FLUENT-Maxwell wherein further phenomena may be explored
including Alfven wave effects and dielectric losses.

Citation

Beg, O., Beg, T., Munjam, S., & Jangili, S. (2021). Homotopy and adomian semi-numerical solutions for oscillatory flow of partially ionized dielectric hydrogen gas in a rotating MHD energy generator duct. International Journal of Hydrogen Energy, 46(34), 17677-17696. https://doi.org/10.1016/j.ijhydene.2021.02.189

• Journal Article Type: Article
• Acceptance Date: Feb 24, 2021
• Online Publication Date: Apr 3, 2021
• Publication Date: May 17, 2021
• Deposit Date: Feb 26, 2021
• Publicly Available Date: Apr 3, 2022
• Journal: International Journal of Hydrogen Energy
• Print ISSN: 0360-3199
• Publisher: Elsevier
• Volume: 46
• Issue: 34
• Pages: 17677-17696
• DOI: https://doi.org/10.1016/j.ijhydene.2021.02.189
• Publisher URL: https://doi.org/10.1016/j.ijhydene.2021.02.189
• Related Public URLs: http://www.journals.elsevier.com/international-journal-of-hydrogen-energy/