MTF271 Turbulence Modeling (7.5 hec)

Aim of the course

The object of the course is to give the students a thorough knowledge and understanding of modern, advanced turbulence models such as RSM and turbulence-resolving methods such as LES, DES, PANS, SAS etc (see below)

Course content

Reynolds stress models (RSM) will be discussed in some detail. The pressure-strain term is an important part in these models which must be modeled. Different modeling approaches for modeling this term will be discussed.

We will also discuss non-linear eddy-viscosity models. This type of models is often a good compromise between modeling accuracy and numerical stability.

Approximately half of the course will be devoted to turbulence-resolving methods such as

  • LES (Large Eddy Simulations).
  • URANS (Unsteady Reynolds-Averaged Navier-Stokes)
  • DES (Detached-Eddy Simulations)
  • PANS (Partially-Averaged Navier-Stokes)
  • Hybrid LES-RANS
In LES the Navier-Stokes equations are filtered over a small volume (usually the computational cell). Thereby the dependent variables are split into one subgrid part (turbulent fluctuations smaller than the cell) and one resolved part (turbulent scales which are resolved by our numerical method). The big advantage of LES is that only a small part of the turbulence is modeled (the subgrid scales) and thus dependence of the turbulence modeling is weak, and the accuracy of LES is consequently high. The disadvantage with LES is that since a large part of the turbulence is resolved, we must solve the unsteady equations: this is one of the main reason why LES is very expensive.

Organization

11 pre-recorded lectures are uploaded to Canvas.

There will be six discussion seminars during lecures on Campus.

  • The students are distributed (randomly) in three groups (approximately 12 in each).
  • Each discussion seminar will last 45 minutes.
Two assignments (Assignment 1 and Assignment 2a & 2b) should be carried out by the students. The assignments will supervised on Campus. Students can use Python (recommended), Matlab or Octave. Both Octave and Python are open-source software. Many large Swedish industries prefer engineers to use Python instead of Matlab due to Matlab's high license fees. For Assignment 2b, only Python scripts are available.

Assignment 1

  • In the first part of Assignment 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 and the (SGS) dissipation. The data will be analyzed.
    We will start analyzing 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 Assignment 1, the students will use Machine Learning and try to improve turbulence models. An example can be found here

    Assignment 2

  • In Assignment 2, the students will be given flowfields of channel flow at high Reynolds number and the flow over a hump. Both flows have been obtained using PANS/DES/IDDES. These flows will be analysed using different modeling assumptions such as DES, DDES, PANS and SAS.

Course literature

  • eBook (can be downloaded for free).

Examination

  • Grades. failed, 3, 4 or 5
  • Part 1: Two assignments including written presentations. This part is mandatory. Written presentations are part of the examination.
  • Part 2: Discussion seminars. This part is not mandatory.
  • Part 3: oral exam is mandatory (but strongly recommended).
  • Oral exam based on the questions in the Discussion seminars and the Assignments. The teachers will also ask follow-up questions. There we try to test if the student has understood the topic or if he/she has memorized it. A good understanding gives grade 4 or 5.
  • Two students at the time during 60 minutes.
  • Each students will be given 7 random questions taken from the Discussion seminars
  • The oral exams will be given in the period 23 Maj -- 5 June
  • To get grade 'passed', you must pass the Oral exam and getting grade 'passed' on the two assignment reports.
  • When you write the reports, you should consider:
    1. Language. Is the report clear and well-written and is the English understandable?
    2. Figures. Are the figures clear and understandable. Are all lines explained? Does the figure give any valuable information?
    3. Analysis. How well are the results analyzed?

    Prerequisites

    Recommended pre-requisites:

    TME226 Mechanics of fluids
    OR
    any corresponding course

    We recommend students with insuffient prerequisites to study part of the eBook (Chapter 1, 2, 5, 6, 8, and 9 and Appendix B [tensor notation]); the easiest way is probably to watch the recorded lectures of the course TME226 Mechanics of fluids or read relevant Lecture Notes in Appendix A in the eBook L. Davidson, Fluid mechanics, turbulent flow and turbulence modeling

    This www page can be found on

    www.tfd.chalmers.se/~lada/comp_turb_model/

    Examinator: Professor Lars Davidson, tel 772 1404
    E-mail: lada@chalmers.se



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