Suppression of turbulence and travelling waves in a vertical heated pipe

TL;DR

This paper investigates how buoyancy forces in a heated vertical pipe can suppress turbulence, leading to laminar or convection-driven flow states, with implications for heat transfer efficiency.

Contribution

It demonstrates that buoyancy can suppress turbulence and traveling waves in pipe flow, revealing the mechanisms behind laminarisation and the role of weakened rolls in this process.

Findings

Buoyancy causes flattening of the base flow profile.

Laminarisation occurs when buoyancy exceeds a critical parameter.

Weakened rolls are critical for flow laminarisation.

Abstract

Turbulence in the flow of fluid through a pipe can be suppressed by buoyancy forces. As the suppression of turbulence leads to severe heat transfer deterioration, this is an important and undesirable phenomenon in both heating and cooling applications. Vertical flow is often considered, as the axial buoyancy force can help drive the flow. With heating measured by the buoyancy parameter $C$, our DNS show that shear-driven turbulence may either be completely laminarised or transitions to a relatively quiescent convection-driven state. Buoyancy forces cause a flattening of the base flow profile, which in isothermal pipe flow has recently been linked to complete suppression of turbulence (K\"{u}hnen et al. Nat. Phys., 2018), and the flattened laminar base profile has enhanced nonlinear stability (Marensi et al. JFM, 2019). In agreement with these findings, the nonlinear lower-branch travelling-wave solution analysed here, which is believed to mediate transition to turbulence in isothermal pipe flow, is shown to be suppressed by buoyancy. A linear instability of the laminar base flow is responsible for the appearance of the relatively quiescent convection driven state for $C\gtrsim 4$ across the range of Reynolds numbers considered. In the suppression of turbulence, however, i.e. in the transition from turbulence, we find clearer association with the analysis of He et al. (JFM, 2016) than with the above dynamical systems approach, which describes better the transition to turbulence. The laminarisation criterion He et al. propose, based on an apparent Reynolds number of the flow as measured by its driving pressure gradient, is found to capture the critical $C=C_{cr}(Re)$ above which the flow will be laminarised or switch to the convection-driven type. Our analysis suggests that it is the weakened rolls, rather than the streaks, which appear to be critical for laminarisation.