VL V - Transport equation turbulent flows

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Last updated 5:59 PM on 5/21/26
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19 Terms

1
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Which terms can be identified in the teansport equation and where are they active

Production:

  • energy containing range

Transport:

  • transfers energy from energy containing to dissipation range

Dissipation:

  • Dissipation range

2
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explain wave triade

it indicates that the entire wave-numbers influence energy exchange

Interdependencies of the wave numbers

3
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Difference between Reynolds averaging and decomposition

  • Averaging: Averaging entire term xD

  • Decomposition: Splitting in mean average and fluctuation

4
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explain closure problem of RANS

Contains 10 unknowns:

  • 6 Reynolds Stress Tensor

  • 3 velocity

  • 1 pressure

Only 4 equations:

  • three momentum

  • Pressure poisson equation

» system not closed

5
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Accuracy of RANS in regards to rare flows

Rare flows cant be predicted in normal operation, since only average states are computed

6
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Pros and Cons of additional transport equations for Reynold stresses

Pros:

  • smaller modeling errors of RST

  • Additional information of anisotropy of RST

  • more accurate results

Cons:

  • More expensive

  • RST equation numerically unstable

    • Better grids required

7
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what does RST mean

Reynolds Stress Tensor

8
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What does the viscous diffusion term describe Transport equation

  • Spreading of Reynolds stress tensor

  • Symbol Sij

<ul><li><p>Spreading of Reynolds stress tensor</p></li><li><p>Symbol S<sub>ij</sub></p></li></ul><p></p>
9
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Whats the Production term and whats needed

  • RST * Derivative of mean velocity field

  • Velocity gradient in mean field needed

  • Symbol {PI}ij

<ul><li><p>RST * Derivative of mean velocity field</p></li><li><p>Velocity gradient in mean field needed</p></li><li><p>Symbol {PI}<sub>ij</sub></p></li></ul><p></p>
10
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Whats the turbulent convection term + symbol

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11
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Whats the “Pressure diffusion“ term

  • correlation between velocity and pressure fluctuation

  • only named diffusion because of the way its modeled

  • Symbol: Pij

<ul><li><p>correlation between velocity and pressure fluctuation</p></li><li><p>only named diffusion because of the way its modeled</p></li><li><p>Symbol: P<sub><sup>ij</sup></sub></p></li></ul><p></p>
12
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Whats the pressure-rate-of-strain tensor term

  • Symbol: Xij

  • gradient part is strainrate

<ul><li><p>Symbol: X<sub>ij</sub></p></li><li><p>gradient part is strainrate</p></li></ul><p></p>
13
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Whats the dissipation tensor term

  • Symbol: {Epsilon}ij

<ul><li><p>Symbol: {Epsilon}<sub>ij</sub></p></li></ul><p></p>
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15
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16
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Whats the Material Derivative Term and how can it be split

  • Left: local [variable] change

  • Right: convective Term

<ul><li><p>Left: local [variable] change</p></li><li><p>Right: convective Term </p></li></ul><p></p>
17
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Is the RST a stress force

Only in a Mathematical sense

18
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Whats the RST

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19
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When to use Reynolds Averaging and when decomposition

  • Averaging in general

  • Decomposition only for non-linear terms