Second Moment Closure Modeling of Stratified Shear Layers and Wakes
Open Access
- Author:
- Jain, Naman
- Graduate Program:
- Mechanical Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- December 09, 2022
- Committee Members:
- Laura Pauley, Major Field Member
Robert Kunz, Chair & Dissertation Advisor
Michael Krane, Outside Unit & Field Member
Xiang Yang, Major Field Member
Robert Francis Kunz, Professor in Charge/Director of Graduate Studies - Keywords:
- Turbulence Modeling
Second Moment Closure Modeling
RANS
DNS
Stratified Flow
Shear Layers
Mixing Layers
Wake
Anisotropic Turbulence Dissipation Rate
Turbulence Dissipation Modeling - Abstract:
- Buoyant shear layers and wakes are encountered in many engineering and environmental applications and have been studied by researchers in the context of experiments and modeling for decades. These flows are typically characterized by high Reynolds and Froude numbers, leading to significant/intractable space-time resolution requirements for turbulence-resolving CFD models of such flows, i.e., Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES). Therefore, Reynolds-Averaged Navier-Stokes (RANS) based models are attractive for these configurations, but their accuracy hinges on numerous modeling assumptions. The inherently complex physical mechanisms observed in stratified flows render eddy viscosity-based RANS modeling inappropriate. RANS Second-Moment Closure (SMC) based modeling is more suitable for such complex systems because they account for flow anisotropy by solving the transport equations of important second-moment terms. Also, turbulent density fluctuations and their auto- and velocity cross-correlations are dynamically important in stratified systems, and their dynamics must be adequately captured. Accordingly, in this thesis, Second-Moment Closure is pursued for stratified flows. An eleven-equation SMC model is adopted and improved. Specifically, transport equations for the Reynolds stresses, density fluxes, density/temperature variance, and dissipation transport equations are solved. A range of sub-models for diffusion, pressure strain/scrambling, and dissipation are incorporated, assessed, and improved upon. Although many researchers have pursued SMC over the years, these works have primarily focused on bulk and important second-order statistics. By contrast, in this work, DNS data, produced by the author and his colleagues at Penn State, is used for SMC sub-model assessment and improvement, as these turbulence-resolving simulations provide the exact form of all turbulence statistics and their corresponding SMC models. Also, these data are used to assess the performance of the full RANS closure. This study results in several important recommendations for SMC model improvement. Also, this study has led to the development of a new anisotropic dissipation model, derived and assessed through comparison to DNS data. For the shear layers, the SMC model accurately predicts the growth rate and Reynolds shear stress profiles. In contrast, the stress anisotropy and budgets are captured only qualitatively. Comparing DNS of exact and modeled terms, inconsistencies in model performance and assumptions are observed, including inaccurate prediction of individual statistics, non-negligible pressure diffusion, and dissipation anisotropy. For the stratified shear layer, gradient Richardson number, shear layer growth rates, and stress, flux, and variance decay rates are captured with less accuracy than corresponding flow parameters in the non-stratified shear layer. Detailed analysis of the Reynolds stress budget terms identifies the need to improve turbulence dissipation rate modeling. For the stratified wakes, the SMC models were compared with non-stratified and stratified wake DNS results. A self-consistent RANS-based procedure to initialize SMC simulations is presented to capture the near-wake DNS peak mean defect velocity decay rate. However, over-prediction of wake height and under-prediction of defect velocity, wake width, and turbulent kinetic and potential energies are observed. Also, SMC predicts a near isotropic decay of normal Reynolds stresses in contrast to the anisotropic decay returned by DNS. The DNS data also provide essential physics and modeling insights related to the inaccuracy of the dissipation rate isotropy assumption and the non-negligible size of pressure-diffusion terms. In order to account for the anisotropy in the turbulence dissipation rate tensor induced by stratification, a novel DNS-informed RANS-consistent algebraic model is derived in this work. A generalizable anisotropic dissipation rate model was obtained by invoking tensor representation theory to enrich the model form based on local flow quantities. This is followed by a DNS-informed supervised linear regression algorithm. Finally, a reinforcement machine learning-based strategy was adopted to calibrate the model coefficients to obtain a RANS-consistent model for stratified flows. The proposed model form is shown to considerably improve the Reynolds stress evolution and, consequently, the mean defect velocity decay rate.