turbulens – teori och modellering · turbulens – teori och modellering. introduction. two...
TRANSCRIPT
Turbulens – Teori ochmodellering
Introduction
Two questions:• Why did you chose this course?• What are your expectations?
Turbulence – Theory and modelling
•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
Goals
Turbulence – Theory and modelling
•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
Goals
Turbulence – Theory and modelling
•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
Goals (continued)
Turbulence – Theory and modelling
•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.
Examination and requirements
Turbulence
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.
Turbulence
• Random• 3D• Diffusive• Dissipative• Property of the flow• High Reynolds number• Continuum
Turbulence
Big whirls have little whirlsWhich feed on their velocityLittle whirls have lesser whirlsAnd so on to viscosity – in the molecular sense
L F Richardson
outflow
Heating/Cooling
Impingement wall
nozzleMean Sherwood number Sherwood number fluctuation
0=i
i
xu∂∂
ij
ij
j
i
jij
jii Fxx
uxx
pxuu
tu
+−+−=+∂∂τ
∂∂
∂∂ν
∂∂
ρ∂∂
∂∂ 1
Models for turbulence,
combustion etc.
Geometry
Mathematical description Results
For example velocity, pressure,
temperatureNumerical methods
Question
• Why do we need to model turbulence?
Turbulence modelling
Example:
Pipe flow, turbulent Reynolds number, Re = 10000
Relation between largest and smallest scales ~ Re3/4
⇒ No. of nodes ~ Re9/4 ≈2⋅109 ⇒ ca. 30 gigabyte RAM
Conclusion: Model needed
Turbulence modelling
Isotropic turbulence in a box
Turbulence modelling
Direct simulation of isotropic turbulenceRequired time at a computing rate of 82 Gflop
Re N N3 M N3M CPU time Memory
94 104 1.1E06 1.2E03 1.3E09 14s 18 Mb
375 214 1.0E07 3.3E03 3.2E10 6.6 min 150 Mb
1500 498 1.2E08 9.2E03 1.1E12 3.8 h 2 Gb
6000 1260 2.0E09 2.6E04 5.2E13 7.3 days 30 Gb
24000 3360 3.8E10 7.4E04 2.8E15 1.1 years 565 Gb
96000 9218 7.8E11 2.1E05 1.6E17 61 years 11 Tb
N3= number of grid pointsM= number of time stepsN3M= total work required
TurbulenceInstantaneous velocity field of a round jet
Turbulence
Mean velocity
Turbulent kinetic energy
Turbulence data have meaning only in a statistical sense
Turbulence modelling
RANS models
A.Abdon och B. Sundén, Värmeöverföring, LTH
Discussion:
Are these flows laminar or turbulent? Motivate.
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
Turbulence
Leonardo da Vinci
Turbulence
Laminar
Turbulent
Osborne Reynolds (1883)
νUL
=ReReynolds number: