Advanced Turbulence Modeling Strategies Within the Hybrid RANS-LES Framework

Abstract

Reynolds Averaged Navier-Stokes (RANS) models still represent the most common turbulence modeling technique used in Computational Fluid Dynamics (CFD) today. RANS models are preferred primarily due to their relatively low computational demand and ease of use. The general RANS framework utilizes the ensemble averaged form of the Navier Stokes equations in which all turbulent scales are modelled, and hence requires reduced computational effort compared to scale resolving methods. Despite their popularity, RANS models have been found to perform poorly in flows with separated shear layers, unsteady wakes, and temporally evolving flows. There has been ongoing progress towards high-fidelity methods such as Large Eddy Simulation (LES) to more accurately represent these flow features. LES models apply filters to the equations of fluid motion to resolve the large turbulent structures that are responsible for energy transfer. The smaller scales however, are represented using a sub-grid scale (SGS) model. LES models perform well in separated shear layers where large eddies dictate the energy and momentum transfer, due to the small time and length scales associated with near wall flow. The costs associated with LES are a major limiting factor in their adoption in industrial and academic research. This has led to the development of Hybrid RANS-LES (HRL) models which offer improved performance over RANS models while being relatively inexpensive compared to LES models. The hybrid modeling approach aims to provide the best of both worlds. In hybrid models, LES models are used far away from the wall to resolve large scale structures primarily responsible for the transfer of momentum and energy, while the wall bounded turbulence is treated using a RANS model. However, HRL models suffer from inherent drawbacks associated with their handling of RANS to LES transition in addition to a high degree of grid sensitivity. The present study proposes advanced turbulence modeling strategies within the hybrid RANS-LES class of models. Major contributions include: (i) evaluation of RANS and hybrid RANS-LES models for separated and non-stationary flows, (ii) development of time-filtering techniques for the dynamic Hybrid RANS-LES (DHRL) model to improve predictive capabilities for non-stationary periodic and non-periodic flows, and (iii) a new variant of the DHRL model for complex turbulent flows to address a known weakness in the DHRL formulation. First, the performance of the DHRL model is evaluated against popular RANS and HRL models for flow over a three-dimensional axisymmetric hill. DHRL model results indicate superior prediction of mean flow statistics and turbulent stresses. However, some discrepancy in Reynolds stress prediction and the lack of a smooth LES-mode away from the wall is observed. Second, static and dynamic time filters are implemented to extend the DHRL model from an ensemble averaged framework to a non-stationary framework. Results once again indicate superior model performance when compared to other models investigated. The model consistently reproduces results similar to pseudo-spectral LES and DNS data for mean flow and second moment statistics. Some underprediction in the outer layer is observed due to the model remaining partially in RANS mode, a known potential source of error for the DHRL model. Third, the dynamic time filtering (DTF) proposed in the previous study is extended via the incorporation of double exponential filtering for applications in flows with non-periodic and/or monotonically time-varying statistics. Results indicate an improvement in performance for high frequency oscillations in a pulsating channel and a good agreement with DNS data for temporally varying mixing layer. Discrepancies in temporal evolution of flow statistics is observed due to the imposed initial fluctuation, however the results indicate that it is able to accurately simulate the appropriate flow physics, and fine tuning of the initial fluctuations would significantly improve predictive capabilities. Additionally, benchmark DNS data for medium and low frequency oscillation is added to supplement the existing DNS for high frequency oscillations. Finally, the performance of a new variant of the DHRL model with an improved blending parameter is investigated for the test cases of fully developed channel, three-dimensional axisymmetric hill, and pulsating channel. The new model variant introduces a blending parameter that smoothly transitions the model from RANS-to-LES in regions where RANS tends to significant overpredict turbulent stresses. Results indicate an improvement over the baseline model for all the cases previously investigated.