Numerical investigation of the convective heat transfer coefficient for a concentric annulus with rotating inner cylinder with application in the deep geothermal drilling process

Abstract

We present a numerical analysis of the convective heat transfer coefficient for the turbulent Taylor–Couette–Poiseuille flow in a concentric annular gap. The study utilizes rotational speeds defined by the Taylor number (Ta) ranging from 2×104 to 1×108, each combined with the axial flow defined by Reynolds number Re=4485, resulting in eight distinct simulation cases in addition to one base case where no rotation is involved. The transient k−ω model available with ANSYS FLUENT for computational fluid dynamics is used for turbulence modelling. The hydrodynamic and thermal fields of the model are validated by comparison with experimental and numerical results from the literature, with an overall qualitatively good agreement. Moreover, the resultant velocity fields exhibit an improvement over the LES results from the literature in comparison with the experimental data. The influence of the flow on the thermal fields is investigated by the swirl parameter N, which compares the rotation speed of the inner cylinder and the mean axial speed. There is no noticeable effect on the thermal fields for the magnitudes of N<1.19. Coherent structures are present for N≥1.19, confirming a direct effect of the temperature and the velocity profiles. The convective heat transfer coefficients (CHTC) are examined by their non dimensional form, the Nusselt number Nu, across the inner rotating wall and the outer static wall. The rotation of the inner wall shows a positive effect on the CHTC for both inner and outer walls. The correlation between the Nu and Ta delivers the exponents of 0.334 and 0.266 for the inner and the outer wall, respectively.