Turbulence Modeling – The SlideShare Alert Series

Introduction

The SlideShare Alert Series is decomposed from a information excerpts which I have found to be most effective in the qualitative appreciation of specific frequently in-use turbulence modeling routes.

For each of the slideshares one may find at least one corresponding “All About CFD” post elaborating on the specific turbulence modeling subject matter.

More information about turbulence models is found easily in abundance in: All About CFD – Mapping the Territory – where all blog posts and site resources are found with a very short explanation about their content.


The Turbulence Modeling Guide

The Turbulence Modeling Guide is an all-encompassing turbulence modeling guide which contains the information about all the turbulence models from The SlideShare Alert Series and then some other turbulence models which are less frequently or seldom in-use. The Turbulence Modeling Guide builds gradually in an intentionally set order.


The SlideShare Alert Series

(1) The law of the wall is associated with wall-bounded shear flows, and depending upon just how one counts, these might be viewed as having two, three or even four different length scales represented in their physical behaviors.

(2) The linear Boussinesq hypothesis major claim is that the principal axis of the Reynolds stresses coincide with those of the average strain. As it where the Boussinseq hypothesis is the basis for eddy-viscosity models.

The following slideshare packs the motivational and theoretical basis for two of modern industrial CFD modeling pillars.

The slideshare is based upon two blog posts from “All About CFD” blog:

(1) The Law Of The Wall

(2) The Boussinesq Hypothesis

(1) In fluid dynamics and turbulence theory, Reynolds decomposition is a mathematical technique used to separate the expectation of a (any variable) quantity from its fluctuations.
For example we may perform the Reynolds Decomposition on the physical quantity of the instantaneous velocity:

In the above the average (time, but it may also be applied to spatial or ensemble averages) quantity is denoted with an overbar while the fluctuating part of the decomposition is denote by the apostrophe sign.

(2) The expected value is often found from an ensemble average which is an average taken over multiple experiments under identical conditions.

(3) Direct numerical simulation (DNS) for the complete Navier–Stokes equations in is only possible on very small computational grids and small time steps when and even then for only but the modest Reynolds numbers due to computational constraints.

(4) Although the Reynolds Decomposition and the Decomposition for Large Eddy Simulation look the same in first glance, the Reynolds Decomposition leads to Reynolds Averaged Navier-Stokes equations (RANS), a simplifications of the Navier-Stokes equations such that all turbulence is contained in a model allowing the prediction of flow patterns in larger computational domains of industrial and engineering importance.

The Reynolds Decomposition (scroll to 7:04 min of the video)

  • SlideShare 3: Turbulence Modeling – Spalart-Allmaras Turbulence Model

Full disclosure first, I am a huge fan of philippe spalart and his work. As a Senior Technical Fellow, Boeing Commercial Airplanes, Spalart directed his contribution in turbulence modeling through a methodology I know well from the time working for the Israeli Aerospace Industry (IAI) – Tailoring.
For example: the ,model as an eddy viscosity model fails in good prediction of rotating flows?… Let us know explore a phenomenology to express such a rotation in our turbulence model!!

(1) The Spalart-Allmaras turbulence model is a 1-equation closure model which is actually an equivalent to 2-equation closure model (and in this sense “complete”) since its turbulence equation is for the eddy-viscosity itself.

(2) As written in my opening full-disclosure, the Spalart-Allmaras model is a special one since it was neatly and specifically tailored for external aerodynamic applications.

(3) Spalart-Allmaras turbulence model evolved to include many corrections to capture certain phenomena whilst still also keeping weak wall sensitivity (a very favorable trait).

(4) The model served in a remarkable way as the basis for the development of Spalart’s DES family of hybrid RANS/LES monolithic turbulence models.

The slideshare is based upon two blog posts from “All About CFD” blog:

(1) Understanding The Spalart-Allmaras Turbulence Model

(1) The family of k-ε turbulence models still remains among the most popular turbulence models for industrial applications.

(2) Most known and recognized among this family of turbulence models is the Jones-Launder k-ε turbulence model.

(3) The model supplies the flow equations with two additional partial differential turbulence equations. One for the turbulence kinetic energy and the other for its dissipation for the modeling of the entire turbulent flow field.

(4) The model is in this sense closed (i.e. no flow parameters are specified a priori besides calibration constants).

The following slideshare is based upon the following “All About CFD” blog posts:

(1) Understanding The k-ε Turbulence Model
(2) Turbulence Modeling – Near Wall Treatment

(1) The first k-ω turbulence model for computational purposes presented here is the original David D. Wilcox model. In contrast to what we learned about the near wall dependency in models such as k-ε model, the model of Wilcox is wall insensitive, yet tends to have on arbitrary freestream values.

(2) Designed to give results similar to those the original k-ω Florian Menter’s Base-Line (BSL) k- ω Turbulence Model is identical to the Wilcox model in the inner 50 percent of the boundary-layer but changes gradually to the high Reynolds number Jones-Launder k-ε model (in a k-ω formulation) towards the boundary-layer edge. The new model is also virtually identical to the Jones-Lauder model for free shear layers.

(3) A second major drawback is evident in almost all eddy-viscosity models relating the Reynolds stress to the mean flow strain and is one of the salient differences between such a modeling approach and a full Reynolds-stress model (RSM) as the RSM approach accounts for the important effect principal turbulent shear-stress transport.
The ingenious idea by Menter, is related to an observed success in implementing the Bradshaw’s assumption, thus deriving the well-known and popular Shear-Stress Transport (SST) k- ω Turbulence Model.

(4) We finalize by effectively describing Finally The GEKO k- ω Turbulence Model somewhat of a new paradigm than a new version of model.

The slideshare is based upon two blog posts from “All About CFD” blog:
(1) From Kolmogorov to Wilcox to BSL to SST – The k-ω Family of Turbulence Models… Then we’re going to slide on ANSYS paradigm – GEKO
(2) GEKO – And Then There Were Six…

  • SlideShare 6: Turbulence Modeling – Hybrid Methods

(1) One of the most popular hybrid RANS-LES models is Detached Eddy Simulation (DES) devised originally by Philippe Spalart.

(2) The term DES is based on the Idea of covering the boundary layer by RANS model and switching the model to LES mode in detached regions thereby cutting the computational cost significantly yet still offering some of the advantages of an LES method in separated regions.

(3) A problem with the original (or “natural”) DES is that an incorrect behavior may be encountered for flows with thick boundary layers or shallow separations.

(4) It was found that when the stream-wise grid spacing becomes less than the boundary layer
thickness the grid may be fine enough for the DES length scale to switch the DES to its LES mode without proper “LES content”, i.e. resolved stresses are too weak (“Modeled Stress Depletion” or MSD”), which in turn shall reduce the skin friction and by that may cause early separation.

(4) This described problem in the reduction of skin friction may cause early separation. The phenomenon is a non-physical phenomenon induced by the reciprocity relations between the grid size and the switching between RANS and LES, thus it is is termed Grid Induced Separation (GIS).

(5) As a consequence of the original DES deficiencies an advancement to the model was devised, termed Delayed-DES (DDES). In actuality, DES limiter is added to DES formulation as if to “shield” and maintain RANS behavior in the boundary layer without grid dependency.

(6) It also shown that the concept of DES (along with its formulation improvements) is also possible to be formulated using k-ω formulation.

(7) Not only that, the conceptual independency on the formulation shall lead us to behold another new general paradigm – Stress-Blended Eddy Simulation (SBES in short). Again, by calling it a new paradigm it is meant that SBES is not a new hybrid RANS-LES model, but a modular approach to blend existing models, allowing CFD practitioner to use a pre-selected (perhaps most convenient to him) RANS and another pre-selected LES model.

(8) We then move to some excerpts about the concept of Embedded (or Zonal) LES. Again, not quite a new model but a new modeling approach. An infrastructure for the incorporation by choice of one of many non-dynamic LES models with most RANS models in predefined regions.

The slideshare is based the following blog posts from “All About CFD” blog:
(1) Scale-Resolving Simulation (SRS) as Part of Daily Engineering Routine
(2) Understanding The Detached Eddy Simulation From DES to IDDES
(3) “The Grey Area” – Interfacing RANS and LES and Hybrid Subtleties
(4) Predictions for CFD in 2030





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