Turbulens Teori och modellering

Transcription

1 Turbulens Teori och modellering

2 Introduction Two questions: Why did you chose this course? What are your expectations?

3 Turbulence Theory and modelling Goals Understanding the phenomena that affects the transition from laminar to turbulent flow Knowledge about the theory for describing turbulent flow Knowledge about turbulence models applicability and limitations Ability to analyse a flow situation and chose a propper modelling approach accordingly

4 Turbulence Theory and modelling Goals Be able to describe the physical mechanisms of the transition from laminar to turbulent flow for a simple flow case Be able to explain Kolmogorov s theory, including the basic assumptions and the validity of the theory Be able to, from a phenomenological perspective, assess if a flow is turbulent Be able to explain some of the important and basic terms of the subject Be able to describe the character of the turbulence in different flow situations with respect to the properties and development of the turbulence, and explain how the differences between these flow situations are reflected in the modelling

5 Turbulence Theory and modelling Goals (continued) Be able to analyse a flow case and suggest a method for numerical simulation with respect to governing equations, possible simplifications and choice of turbulence model, and also to compare with alternative methods. Be able to scrutinise and from given criteria estimate the credibility of results from turbulent flow simulations Be able to actively participate in discussion of problems relevant for the subject Be able to present, both orally and in writing, a technical report containing analyses and choice of turbulence model

6 Turbulence Theory and modelling Examination and requirements To pass (grade 3) the following is required: Approved home works, lab-report and group study (GS) Participation in the computer exercises Oral exam for higher grade (grades 4 and 5) Participation in the laboratory exercise, computer exercises and the guest lecture is mandatory. The home works are handed in individially. However, you are alowed, even encouraged, to work in groups discussing the problems. The groups study is to be presented both in writing as well as orally. One report per group.

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8 Turbulence

9 Two questions 1. How would you describe turbulence? Think about key-words to characterise it. 2. Think about situations where turbulent flow is better than laminar and vice versa.

10 Turbulence Random 3D Diffusive Dissipative Property of the flow High Reynolds number Continuum

11 Turbulence Big whirls have little whirls Which feed on their velocity Little whirls have lesser whirls And so on to viscosity in the molecular sense L F Richardson

12 Turbulence I am an old man now, and when I die and go to Heaven there are two matters on which I hope enlightenment. One is quantum electro-dynamics and the other is turbulence of fluids. About the former, I am really rather optimistic. Sir Horace Lamb

13 Heating/Cooling Impingement wall outflow Mean Sherwood number Sherwood number fluctuation nozzle

14 Numerical methods ui 0 x i ui uiu j 1 t Mathematical description x j p ui ij Fi x x x x i j j j Results For example velocity, pressure, temperature Geometry Models for turbulence, combustion etc.

15 Question Why do we need to model turbulence?

16 Turbulence modelling Example: Pipe flow, turbulent Reynolds number, Re = Relation between largest and smallest scales ~ Re 3/4 No. of nodes ~ Re 9/ ca. 30 gigabyte RAM Conclusion: Model needed

17 Turbulence modelling Isotropic turbulence in a box

18 Turbulence modelling Direct simulation of isotropic turbulence Required time at a computing rate of 82 Gflop Re N N 3 M N 3 M CPU time Memory E06 1.2E03 1.3E09 14s 18 Mb E07 3.3E03 3.2E min 150 Mb E08 9.2E03 1.1E h 2 Gb E09 2.6E04 5.2E days 30 Gb E10 7.4E04 2.8E years 565 Gb E11 2.1E05 1.6E17 61 years 11 Tb N 3 = number of grid points M= number of time steps N 3 M= total work required

19 Turbulence Instantaneous velocity field of a round jet

20 Turbulence Turbulence data have meaning only in a statistical sense Mean velocity Turbulent kinetic energy

21 Turbulence modelling RANS models A.Abdon och B. Sundén, Värmeöverföring, LTH

22 Turbulence Backward facing step From

23 Discussion: Are these flows laminar or turbulent? Motivate.

24 Turbulence Brief history: 15th century, da Vinci, observations of turbulence 18th century, Euler, equations for inviscid flow Early 19th century, Navier and Stokes, the N-S equations 1883, Reynolds, flow instability in pipe flow 1904, Prandtl, boundary layer theory 1941, Kolmogorov, theory on turbulent scales 1963, Smagorinsky, first sub-grid scale model for LES 1970, Launder et al., two-equation model for turbulence

25 Turbulence Leonardo da Vinci

26 Turbulence Osborne Reynolds (1883) Laminar Turbulent Reynolds number: Re UL