Course syllabus for Turbulence modeling

MTF072 Computational fluid dynamics (CFD) or Mechanics of Fluids or any corresponding course

The object of the course is to give the students a thorough knowledge and understanding of modern,
advanced turbulence models for unsteady fluid flow simulations.

• Describe different RANS turbulence models such as Reyonlds stess models, algebraic Reynolds stress models, k-els, k-omega, V2F, k-omega SST
  
• Understand and outline the difference between LES, RANS, URANS, DES and hybrid LES-RANS

• Derive the exact transport turbulence equations using tensor notation
  

• Describe the modeling assumptions, using tensor notation, in turbulence models

• Identify and interpret the different terms in the turbulence models presented in the course.

• Describe the difference between resolved and modeled Reynolds stresses

• Describe different approaches to handle the near-wall problem in LES

• Describe the advantages of second-moment closures compared to eddy-viscosity models

• Derive the V2F model

• Reproduce the different spatial filtering approaches in LES

• Derive the SGS models using tensor notation

• Understand and describe the concept of modeled (for example SGS) dissipation between resolved and modeled scales

• Describe the method how to prescribe unsteady, fluctuating inlet boundary conditions

• Be able to carry out an simulation with a commercial CFD code

Today, most CFD simulations are carried out with traditional RANS (Reynolds-Averaged Navier-Stokes). In RANS, we split the flow variables into one time-averaged (mean) part and one turbulent part. The latter is modelled with a turbulence model such as k-eps or Reynolds Stress Model. For many flows it is not appropriate to use RANS, since the turbulent part can be very large and of the same order as the mean. Examples are unsteady flow in general, wake flows or flows with large separation. For this type of flows, it is more appropriate to use Large Eddy Simulation (LES).  In order to extend LES to high Reynolds number flows new methods have been developed. These are called DES (Detached Eddy Simulation), URANS (Unsteady RANS) or Hybrid LES-RANS.  They are all unsteady methods and they are a mixture of LES and RANS. In aero-acoustics the noise is generated by turbulence. The best way to accurately predict large-scale turbulence is to carry out an unsteady simulation of the flow field (i.e. LES, DES, hybrid LES-RANS or URANS). After that the noise is predicted separately in CAA (Computational Aero-Acoustics).

In LES, DES, URANS  and  Hybrid LES-RANS the large-scale part of the turbulence is solved for by the discretized equations whereas the small-scale turbulence is modeled. The definition of ''large-scale'' varies in the different methods. Furthermore, the limit between ''large-scale'' and ''small-scale' is often not well defined. Since turbulence is three-dimensional and unsteady, it means that in all the methods the simulations must always be carried out as  three-dimensional, unsteady simulations.

We will address questions like:

• How should I make my mesh?

• why should I in LES use a non-dissipative discretization scheme?

• is it necessary to used central differencing in DES and URANS?
  
• what is the different between LES and unsteady RANS?
•  what turbulence models can I use in DES and unsteady RANS?
• to enhance numerical stability, can a turbulence model with high dissipation be used?
  
• how do I prescribe inlet boundary conditions?
• inlet boundary conditions: can I use steady inlet boundary conditions? which is best, synthesized turbulence or a pre-cursor DNS?

In the first project, we will learn how to interpretat results from an unsteady simulation. We will also use a commercial CFD package to evaluate different RANS turbulence models.

When doing LES-URANS/DES, you have to ask yourself similar questions as when doing measurements:

• when is the flow fully developed so that I can start time-averaging?
• for how long time do I need to time-average?
• is it enough if I get accurate mean flow or do I also need accurate resolved turbulent stresses?
• how do I estimate the quality of my LES or hybrid LES-RANS? Spectra?   2-point correlations? SGS dissipation?
  

The most important drawback/bottleneck of LES is the requirement to use very fine grid near walls. The grid must be fine in all directions, not only the wall-normal direction. Much of the research on LES is today focused in getting around this bottleneck. One approach is hybrid LES-RANS. In this method  RANS is used near walls and LES is used in the remaining part of the domain.


.For more information

.Lecturer's homepage

Two projects should be carried out by the students.

1. The students will be given data from a numerical simulation (LES or DNS). The data will be two-dimensional, time-averaged velocity (recirculating flow) and pressure fields, the Reynolds stresses. The data will be analyzed. First we will study the velocity fields and find out how large are the forces (per unit volume) due to pressure gradient, turbulent Reynolds and viscous stresses. The forces ska balance the acceleration term on the left-hand side.

Next we analyze the transport equations of the turbulent
Reynolds stresses, u_iu_j. We identifiy regions of large production terms, which should correspond to regions of large Reynolds stresses. Reynolds stresses will be computed using the eddy-viscosity assumption, and these will be compared to their exact counter-parts.

In the second part of this assignment, the students will use a commercial CFD package to compute flows using RANS. Different turbulence models will be evaluated.