Study of wall-bounded turbulent heat transfer and flow dynamics at transcritical conditions
Keywords: Engineering.
Mechanical Engineering.

Transcritical fluid conditions, at pressures above the thermodynamic critical pressure, present a thermodynamic regime with fluid behaviors that differ significantly from those at more commonly-encountered subcritical pressures. In engineering settings, increasing societal demands for higher power and energy efficiencies necessitate the increasing relevance of transcritical operating conditions. In the context of these current trends, a wide range of technological sectors such as energy generation, propulsion, and chemical processing are increasingly utilizing turbulent fluid flows at transcritical conditions. Despite the relevance and prevalence of transcritical flows at turbulent conditions in the presence of walls, the details of the flow and heat transfer have not been thoroughly investigated. For such flows, enhanced fluctuations, steep gradients, and intensified heat transfer are key characteristics -- the combination of these features create a challenging physical environment to be studied. Particularly, the structure of the turbulent thermal boundary layer under realistic density gradients and heating conditions remains poorly understood. Statistical descriptions of the temperature field in such flows are inconsistently provided using existing models; because an accurate description of the temperature statistics are crucial towards understanding the heat transfer, this lack of understanding and the associated inability to predict the near-wall temperature present a critical gap in knowledge. To address this issue, this thesis discusses the design, computational generation, results, and analysis of a set of direct numerical simulations of fully developed transcritical turbulent channel flow cases. Six cases are chosen to sample the parameter space, ranging from the symmetric wall temperatures case (without significant convective wall heat flux) up to several strongly heated cases (with significant convective wall heat flux). The pressure and temperature conditions in the current study cause density changes of a factor of up to order 20 between the hot and cold walls. The resulting transcritical turbulent flow displays a number of distinguishing characteristics when compared to flows at classical (constant-property + ideal gas) thermodynamic conditions. Many fundamental results from classical turbulence theory (specifically scalings and quantitative predictions of engineering parameters) have been shown to be invalid or have become points of contention in the community. Because of this, we present and discuss flow features of the turbulent cases in the current investigation. As a consequence of the proximity of the Widom line to the hot wall, a central theme that is observed is the presence of significant asymmetries in the momentum and thermal field features when comparing regions near the cold wall and near the hot wall. These observations serve to inform general insights into the understanding and modeling of transcritical wall-bounded turbulence. Previous transformations that attempt to collapse the near-wall mean temperature profiles are examined. By addressing model deficiencies in capturing the transcritical thermal boundary layer by these past works, we formulate and propose an improved mean temperature transformation. The viscous sublayer behavior of the mean temperature has been well characterized and collapsed in the literature; however, the behavior further from the wall in the logarithmic region has not. Because computational cost limitations for practical engineering applications necessitate a wall model from the wall up through a portion of the log region, accurate predictive understanding of the temperature behavior is critical to correctly capture the wall heat transfer in such computations (as a thermal analogy to the log-layer mismatch problem). Our proposed transformation is shown to perform well in collapsing the slope of the logarithmic region to a single universal value with reduced uncertainty. Appropriate considerations for real fluid effects that involve strong variations in thermodynamic quantities are included; as a result, the transformation handles well the steep gradients and large relative fluctuation magnitudes presented by cases with strong wall heat transfer. We borrow from the established procedure of past transformations by separating the transformed profile into the Prandtl-number-dependent and non-Prandtl-number-dependent components. As an extension to improve the utility of our transformation, we then propose a predictive framework that models each component analytically, such that the entire near-wall mean temperature profile can be predicted using only input parameters. The final combination of the transformation and the extended framework thus provides a tool towards the development of more accurate reduced-order models for wall-bounded transcritical turbulence