Supercritical carbon dioxide Taylor–Couette–Poiseuille flow heat transfer

Abstract

Taylor–Couette–Poiseuille flow commonly occurs in rotating machinery in the annulus between the outer casing and rotating shaft as part of lubrication or thermal management systems. To improve efficiency of these machines, industry is beginning to work with low viscosity, high density fluids operating at high pressures, such as supercritical carbon dioxide turbines. Within existing literature, vast high quality heat transfer data exists for air under Taylor–Couette–Poiseuille flow regimes. However, for other fluids, these data are limited in their experimental coverage, especially at high Taylor numbers (i.e. >1×1010). This paper presents first of its kind experimental data for supercritical carbon dioxide. The data are analysed to provide insight into the heat transfer processes and to provide a Taylor–Couette–Poiseuille flow heat transfer correlation. Operating conditions of the experimental campaign cover pressures of 7 and 10 MPa, a temperature range of 315 to 333 K, and rotational speeds of 10 to 25 kRPM. This equates to Taylor number and axial Reynolds number ranges of 9.52×1010 to 8.73×1011 and 3.41×104 to 5.4×104, respectively. The range of conditions tested covers the operational envelope of those found in thermal management systems for supercritical carbon dioxide turbine designs. It is found that heat transfer of supercritical carbon dioxide is significantly higher than that of ideal gases (e.g. air) for the same Taylor number range. Further findings show that change in fluid properties near the critical point (i.e. heat capacity and density) increase the Nusselt number from 1.5×103 at 10 MPa to 3.1×103 at 7 MPa at an effective Reynolds number of 2.5×106. A dimensional analysis shows the importance of capturing the change in fluid properties when near the critical point and to account for tangential energy transport. To capture this we introduce a non-dimensional parameter, Ψ, being the ratio of tangential energy flux to inertial energy flux. Including Ψ in heat transfer correlations improves their validity by capturing additional mechanisms that influence heat transfer. The suitability of correlations including Ψ are demonstrated using air and supercritical carbon dioxide data sets. Finally, analysing heat transfer trends across the range of Ψ tested provides insight on how heat transfer mechanisms vary with operating condition. This work provides a vital step forward for the unification of Taylor–Couette–Poiseuille flow heat transfer correlations across multiple experimental data sets.