Data-Augmented Resolvent Analysis of Wall-Bounded High-Pressure Transcritical Flow

TL;DR

This work extends resolvent-analysis methods to wall-bounded flows in high-pressure transcritical regimes by incorporating real-fluid thermodynamics and data-driven base states. It combines operator-based linearization with spatio-temporal FFT and POD to identify dominant forcings, responses, and coherent structures tied to the pseudo-boiling region. Key findings show maximum amplification at spanwise wavenumbers of order one, with forcing dominated by thermodynamic fluctuations near pseudo-boiling and phase-speed-filtered structures revealing slow-moving modes not present in classical turbulence; POD highlights energy localization near the hot wall and pseudo-boiling layer. The approach enables improved reduced-order modeling and flow-control insights for transcritical devices, informing strategies to optimize mixing and heat transfer in micro-confined and propulsion-relevant flows.

Abstract

High-pressure transcritical fluid flows are central to modern energy and propulsion systems. A key challenge lies in confined configurations, where optimizing performance requires a deep understanding of the coupled hydrodynamic and thermodynamic nonlinearities that govern such flows. In this regard, low-order decomposition techniques offer an interpretable framework to quantify how nonlinear forcings drive coherent responses and amplify key flow structures. This work, thus, pursues two main objectives: establish a resolvent-based framework tailored to high-pressure transcritical fluid flows, and characterize the spatio-temporal sensitivity of the resolvent operator using data-driven turbulent base flows. These analyses identify the flow responses and forcings that optimally enhance mixing and heat transfer, along with their characteristic scales. The results of the resolvent framework reveals that amplification is dominated by streamwise-elongated structures with spanwise periodicity, associated with peak singular values near spanwise wavenumbers of order unity. Unlike ideal-gas or incompressible/isothermal flows, the dominant forcings arise from thermodynamic fluctuations in the pseudo-boiling region. Moreover, when the turbulent mean flow is used as input, this results in intensified responses manifesting as coherent counter-rotating vortex pairs. The energetic scale motions are constrained by the nature of the low-Reynolds-number regime considered, with a single dominant spectral mode reaching streamwise lengths comparable to those in the instantaneous fields. Data-driven analyses further reveal coherent structures propagating at phase speeds absent from classical incompressible wall-bounded turbulence. These structures are intensified near the pseudo-boiling region and constrained toward the hot wall, in strong agreement with resolvent-mode predictions of near-wall scale motions.

Figures (23)

• Figure 1: Comparison of base flows at high-pressure (HP) and ideal-gas (IG) conditions, including laminar Poiseuille solutions and ensemble-averaged turbulent mean flow from DNS, for (a) streamwise velocity, (b) temperature, and (c) isobaric specific heat capacity, all normalized using bulk scaling parameters.
• Figure 2: Schematic of the DNS channel flow showing isosurfaces of normalized Q-criterion at $Q = 2 \cdot 10^9$, colored by reduced density, on an $x$–$y$ plane view.
• Figure 3: Normalized wall-normal profiles of (a) mean streamwise velocity and (b) TKE for the cold and hot walls.
• Figure 4: Map of the maximum singular values ($\sigma_1$) at phase speed $c = 1$ (normalized by bulk velocity) for the turbulent mean flow.
• Figure 5: Responses (a) and forcing (b) along wall-normal direction at the wavenumbers parameter-space of maximum amplification for data-driven turbulent mean flow.