arXiv subjects

Wei-Tao Bi

Publications and source records attributed to Wei-Tao Bi.

4 recordsLinked to original sources

arXiv2025

Quantifying non-equilibrium pressure-gradient turbulent boundary layers through a symmetry-based framework

This study establishes a symmetry-based framework to quantify non-equilibrium processes in complex pressure gradient (PG) turbulent boundary layers (TBLs), using a Lie-group-informed dilation-symmetry-breaking formalism. We derive a universal multilayer defect scaling law for the evolution of total shear stress (TSS). The law shows that gradually varying adverse pressure gradients (APGs) break the dilation symmetry in the two-layer defect scaling of equilibrium TSS, leading to three-layer TSS structures. For abrupt PG transitions, we identify boundary-layer decoupling into: 1) an equilibrium internal boundary layer, and 2) a history-dependent outer flow, arising from disparate adaptation timescales. The framework introduces a unified velocity scale mapping non-equilibrium TSS to canonical zero-PG scaling. Validation spans different aerodynamic systems, including developing APG on airfoils, APG-to-favorable-PG transition on a Gaussian bump, and favorable PG to rapidly amplifying APG in a converging-diverging channel. The work enables improved prediction of non-equilibrium PG TBL behavior through unified characterization of stress evolution dynamics, providing new physics-based parameterizations that could promote machine learning of complex wall-bounded turbulent flows.

physics.flu-dyn↗

arXiv2024

Quantifying equilibrium pressure-gradient turbulent boundary layers via a symmetry approach

We propose a theory for predicting the mean velocity and Reynolds shear and normal stresses profiles in the wake region of equilibrium adverse pressure-gradient (PG, APG) turbulent boundary layers (TBLs). Firstly, we explore the PG-induced dilation-symmetry-breaking of the total stress $τ^+$ to construct a modified defect power law for $τ^+$. Crucially, a PG stress $P_0^+$ is identified, which quantifies the APG-induced total-stress overshoot and is proportional to the Clauser PG parameter $β$. The wall-normal location with peak stress is predicted. The total stress profiles with arbitrary $β$ are transformed into an invariant profile, which is the ultimate state of the total stress at infinite $β$. This transformation is equivalent to the outer scaling of the Reynolds shear stress recently-proposed by Wei & Knopp (JFM, 2023). The Reynolds normal stresses are predicted accordingly based on the similarity of the Reynolds shear and normal stresses in the wake region. Secondly, a defect power law is proposed for the stress and kinetic energy lengths in the wake region. Two critical parameters in the defect power law are identified to depend on $β$ and determine the length profiles. With the total stress and stress length models, the streamwise mean-velocity profile is predicted. Especially, an invariant mean velocity profile is derived, which describes the ultimate state of the mean velocity in the wake region at infinite $β$. This invariant profile is also equivalent to the outer scaling of Wei & Knopp. The theory also predicts the variation of the Coles' wake parameter $Π$ with $β$, in close agreement with the empirical relation that correlates hundreds of experimental data. The predictions are validated with five published DNS, LES, and experimental databases on the equilibrium APG TBLs.

physics.flu-dyn↗

arXiv2023

Multi-layer analytic solution for k-ω model equations via a symmetry approach

Despite being one of the oldest and most widely-used turbulence models in engineering CFD, the k-ω model has not been fully understood theoretically because of its high non-linearity and complex model parameter setting. Here, a multi-layer analytic expression is postulated for two lengths (stress and kinetic energy lengths), yielding an analytic solution for the k-ω model equations in pipe flow. Approximate local balance equations are analyzed to determine key parameters in the solution, which are shown to be rather close to the empirically-measured values from numerical solution of the Wilcox k-ω model, hence the analytic construction is fully validated. Furthermore, the predictions of three critical locations in the model's three transition functions are validated, which enables an in-depth understanding of the parameter setting of the model. These results provide clear evidence that the k-ω model sets in it a multi-layer structure, which is similar to but different, in some insignificant details, from the Navier-Stokes turbulence. This finding explains why the k-ω model is so popular, especially in computing the near-wall flow. Finally, the analysis is extended to a newly-refined k-ω model called SED k-ω, showing that the SED k-ω model has improved the multi-layer structure in the outer flow but preserved the setting of the k-ω model in the inner region.

physics.flu-dyn↗

arXiv2023

A symmetry-based theory for the mean velocity profiles of turbulent boundary layers subjected to pressure gradient and historical turbulence effects

The pressure gradient has a significant influence on the mean-flow properties of turbulent boundary layers. Conventional analytical studies on PG turbulent boundary layers are conducted separately for the viscous sub-layer and overlap layer only, with the remaining large portion of the boundary layers less described theoretically. Here a symmetry approach is proposed for modeling whole mean velocity profiles of turbulent boundary layers with both PG and historical turbulence effects. First, a modified defect law is constructed for the total stress profile to capture the Reynolds stress overshoot owing to the PG and historical turbulence effects. Second, the multi-layered power-law formulation of the stress length function in the structural ensemble dynamics theory of the canonical zero-PG turbulent boundary layer (J. Fluid Mechanics, 2017, Vol. 827, pp. 322-35) is extended to describe the PG turbulent boundary layer. Comparing with that of the zero-PG turbulent boundary layers, the stress length of the PG turbulent boundary layer possesses a variable (in magnitude and extension) plateau in the defect layer, which are characterized by three parameters: the buffer layer thickness, the (nominal) K'arm'an constant, and the defect-law exponent. In the case of intense turbulence from upstream flow, a newly-identified "bulk turbulent layer" replaces the conventional buffer layer and overlap layer. With the above formulations, the entire mean velocity profile is predicted analytically, and validated to accurately describe the published direct numerical simulation data on a two-dimensional separation bubble. The study provides a novel method to parameterize PG turbulent boundary layers with high accuracy and sound physics, and paves a way for quantifying complicated boundary-layer flows.

physics.flu-dyn↗