Modeling and Analysis of Stably Stratified Wall-Bounded Turbulent Flows
Date
2022-10
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Abstract
Stably stratified wall-bounded turbulent flows have been drawing a great deal of research interest. The profound driver is the underlying physics in the topic that concerns many problems in industry as well as the natural environment, e.g., stratified mixing efficiency in topographically complex boundary regions and closure parameterization in operational atmospheric models. In this dissertation, stratified turbulence in wall-bounded flows is studied and modeled via a series of numerical simulations. Under sufficiently strong stratification, fully developed wall-bounded turbulence could transition to intermittent flows in which laminar and turbulent patches coexist. Using direct numerical simulations (DNS), I explore the boundary at which such a transition occurs in the parameter space for stably stratified channel flow (SCF). A range of friction Reynolds (Reτ ) and Richardson (Riτ ) numbers, parameters that are observed to control the dynamics, are covered by the numerical simulations. For each Reτ investigated, the stratification level is varied incrementally from moderate to relatively strong, leading the fully turbulent flows to transition to intermittently turbulent. My results show that depending on Riτ and Riτ , SCF could exhibit intermittency in the near-wall and/or the channel core. At low-Reτ -high-Riτ , intermittency spans the entire channel depth, whereas at high-Reτ -low-Riτ , intermittency is confined in the channel core. Within the tested range, I identify the near-wall intermittency boundary by quantifying the volume fraction of turbulent patches in each simulation. The applicability of various dimensionless parameters for predicting the onset of near-wall intermittency is examined. My results suggest that near-wall intermittency in SCF occurs for Nusselt number, N u ≲ 3. A first-order closure model based on a K-profile type parameterization is developed for SCF. The model is shown to have good agreement with predicted mean profiles of velocity and potential temperature closely matching their DNS counterparts. The boundary at which near-wall intermittency occurs in SCF is delineated using the developed model based on the critical value N u = 3. The second topic of this dissertation concerns with the development of a computational framework for modeling stably stratified turbulent flows over flat boundaries. I examine the performance of a turbulence modeling framework consisting of residual-based variational multiscale method (RBVMS) and isogeometric analysis (IGA) applied to two canonical numerical experiments, namely stably stratified channel flows at Reτ = 180, 550, and a stable boundary layer (SBL). In the SCF cases, the framework is implemented with two augmentation companion features, namely weak imposition of Dirichlet boundary conditions (WD) and a new subgrid-scale (SGS) model. The performance of the modeling framework, as well as its interaction with the two companion features, are assessed in both weakly and strongly stratified regimes. In comparison to existing direct numerical simulation (DNS) data, my study reveals that RBVMS–IGA framework is able to faithfully capture the flow structures and one-point statistics in SCF simulation with relatively coarse grid resolution. The framework also demonstrates its capability of replicating intermittent flow dynamics under strong stratification. Such dynamics are reproduced robustly when the modeling framework is enhanced with WD and the new SGS model, features that are shown to generally improve numerical accuracy of simulations for the cases tested. My results confirm the computational efficiency as well as the robustness of RBVMS–IGA framework in modeling stratified wall-bounded flows. In addition, we develop a wall-function-based weak imposition of Dirichlet boundary condition (WFWD) for stably stratified flows. The performance of WFWD is validated with SCF at Reτ = 550 and in a stable atmospheric boundary layer, demonstrating its effectiveness and potential in mitigating the effects of under-resolved boundary layer on stratified wall-bounded flow modeling. Comparisons are made against results of the original formulation of WD, as well as direct or large-eddy simulations whenever available. My results show that WFWD with a smooth wall function offers improved accuracy over its WD counterpart in predicting one-point statistics of SCF at various degrees of stratification. Furthermore, on account of adopting a rough wall function WFWD successfully predicts the occurrence of super-geostrophic jet as well as statistics that are in good agreement with highly-resolved large-eddy simulations. My findings suggest that formulating the weak imposition of Dirichlet boundary condition based on wall functions could mitigate shortcomings of WD when factors like roughness play a significant role. The final portion of the dissertation focuses on modeling stably stratified wall-bounded turbulent flows over complex boundaries. The performance of the developed computational framework is validated against observations in a laboratory experiment on strongly stratified flow past a three-dimensional bell-shaped hill. Good agreement is observed for qualitative flow physics, with the predicted occurrences of flow separation, recirculation, and hydraulic jump closely matching those in the experiment. In addition, the dividing-streamline height and the wavelength of lee wave computed from the present framework compare well to theoretical predictions. I show that the present framework is able to tackle various degrees of stratification in wall-bounded flows. The effect of weak imposition of Dirichlet boundary condition on the performance of the framework is also examined. The dissertation is concluded with an outlook toward applying the present framework to modeling stratified flow past real-world terrains at microscale (∼10 m) by simulating stratified flow past a two-dimensional environmental terrain.
Description
Keywords
Wall-bounded turbulence, Intermittent turbulence, Variational multiscale method, Isogeometric analysis, Computational fluid dynamics, Weak imposition of Dirichlet boundary condition, Stratified channel flow, Stable boundary layer
Citation
Cen, H. (2022). Modeling and analysis of stably stratified wall-bounded turbulent flows (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.