Structure of the thermal boundary layer in turbulent channel flows at transcritical conditions

Abstract

Enhanced fluctuations, steep gradients, and intensified heat transfer are characteristics of wall-bounded turbulence at transcritical conditions. Although such conditions are prevalent in numerous technical applications, the structure of the thermal boundary layer under realistic density gradients and heating conditions remains poorly understood. Specifically, statistical descriptions of the temperature field in such flows are provided inconsistently using existing models. To address this issue, direct numerical simulations are performed by considering fully developed transcritical turbulent channel flow at pressure and temperature conditions that cause density changes of a factor of up to $O(20)$ between the hot and cold walls. As a consequence of the proximity of the Widom line to the hot wall, significant asymmetries are observed when comparing regions near the cold wall and near the hot wall. Previous transformations that attempt to collapse the near-wall mean temperature profiles among different cases to a single curve are examined. By addressing model deficiencies of these transformations, a formulation for an improved mean temperature transformation is proposed, with appropriate considerations for real fluid effects that involve strong variations in thermodynamic quantities. Our proposed transformation is shown to perform well in collapsing the slope of the logarithmic region to a single universal value with reduced uncertainty. Coupled with a predictive framework to estimate the non-universal shift parameter of the logarithmic region using a priori information, our transformation provides an analytic profile to model the near-wall mean temperature. These results thus provide a framework to guide the development of models for wall-bounded transcritical turbulence.

Small-scale turbulent characteristics in transcritical wall-bounded flows

“…In particular, at supercritical pressures, the transitioning from the liquid-like phase to gas-like phase as the temperature increases, which is called 'transcritical conditions', can occur without the formation of the interface (Simeoni et al 2010;Bolmatov, Brazhkin & Trachenko 2013;Simeski & Ihme 2023). Thermodynamic and transport properties, including density, viscosity, specific heat capacity and thermal conductivity, vary significantly across the Widom line as the increasing temperature, thereby introducing significant real-fluid thermodynamic effects (Simeoni et al 2010;Bolmatov et al 2013;Ma, Yang & Ihme 2018;Guo, Yang & Ihme 2022;Li et al 2023). It has been confirmed that real-fluid thermodynamic effects which are induced by strong variations in thermal properties considerably change the large-scale structures of wall-bounded turbulence (Patel et al 2015;Ma et al 2018;Kawai 2019;Kim, Hickey & Scalo 2019;Guo et al 2022;Li et al 2023).…”

“…The database used for the present analysis was obtained from DNS of a straight turbulent channel of transcritical nitrogen (Ma et al 2018;Guo et al 2022;Li et al 2023). For the broader use of the transcritical DNS database by the turbulence and combustion community, we have made this database open-access on https://blastnet.…”

“…The Peng-Robinson (PR) equation of state (EoS) (Peng & Robinson 1976) and Chung's transport-property model (Chung et al 1988) are employed to describe the thermodynamics of the working fluid. These models have been used in past DNS studies on turbulence of transcritical fluids (Miller, Harstad & Bellan 2001;Ma et al 2018;Kim et al 2019;Toki, Teramoto & Okamoto 2020;Guo et al 2022;Li et al 2023). In Appendix A, we discuss the EoS and the transport-property model in more detail.…”

“…Thermodynamic and transport properties, including density, viscosity, specific heat capacity and thermal conductivity, vary significantly across the Widom line as the increasing temperature, thereby introducing significant real-fluid thermodynamic effects (Simeoni et al 2010;Bolmatov et al 2013;Ma, Yang & Ihme 2018;Guo, Yang & Ihme 2022;Li et al 2023). It has been confirmed that real-fluid thermodynamic effects which are induced by strong variations in thermal properties considerably change the large-scale structures of wall-bounded turbulence (Patel et al 2015;Ma et al 2018;Kawai 2019;Kim, Hickey & Scalo 2019;Guo et al 2022;Li et al 2023). Sciacovelli, Cinnella & Grasso (2017) carried out systematic DNS investigations to study small-scale structures of isotropic turbulence of high-pressure dense fluids which have similar physical properties to transcritical fluids, their analysis showed a weakening of compressive structures and an enhancement of expanding ones.…”

Effects of thermophoresis on high-pressure binary-species boundary layers with uniform and non-uniform compositions

“…Toki, Teramoto & Okamoto (2020) also simulated a planar turbulent channel flow of supercritical nitrogen and introduced a temperature transformation in the logarithmic region that accounts for the temperature variations of the mean density and of the isobaric specific heat in that region. Guo, Yang & Ihme (2022) performed a planar turbulent channel flow of supercritical nitrogen with increasing a density change ratio in the channel to approximately 20, and provided a framework to guide the development of models for wall-bounded transcritical turbulence.…”