VL VI - Transition laminar to turbulent

Important instabilities

• Kelvin-Helmholtz instability (KHI)

• Rayleigh-Taylor Instability (RTI)

• Richtmyer-Meshkov Instability (RMI)

Preliminaries KHI

• Inviscid (approximately)

• Rotationless

• Potential Flow

Recipe For Linear Stability Theory

• Governing Equations

• Reynolds Decomposition

• Perturbation equation

• Linearization of perturbation equation

• Wave-mode

• Eigenvalues

• Interpretation of EVs

• Stability diagram

How does KHI happen

Fluid Layers with different velocity layers

Steps laminar to turbulent flow

1. Stable, laminar flow

2. Primary instability: (unstable Tollmien Schlichting waves)

3. Secondary instability

4. Breakup vortices

5. Turbulent spots

6. Turbulent flow

Rayleigh Inflection point theorem for inviscid vs. viscid

inviscid:

• can only be potentially unstable with an inflection point in the surface

• otherwise stable for infinite reynolds number

viscid:

• can get unstable with high reynolds numbers

When to use temporal ansatz

• if we want to know when something occurs

• driven by convection

When to use convective ansatz

• if we want to know where sth occurs

• driven by temporal perturbation

Name the four possible stability states of dynamical systems regarding small disturbances

• stable

• unstable

• neutrally stable

• nonlinearly stable

Name three physical parameters influencing the transition mechanism

• surface roughness

• wall geometry

• disturbance spectrum of flow field

What is canonical flow

• Representative flow configuration with isolated characteristic feature

• Represents section of more complec realisitc flow

• Describes isolated phenomenon

Benefits of numerical with Canonical flow

• Calibration and validation of turbulence models

• Phenomenological investigation

Whats x₀ in a round jet

virtual origin of the stream

Properties of Round jet

• Statistically stationary with axial symmetry

Whats q’

Indication of fluctuation

Whats U_J

Nozzle exit velocity

How does the RST change for a Round Jet canonical flow

• Axisymmetric mean flow

• Invariant under rotation

so every rotational part is 0 cross form

How has the round jet velocity plot be nondimensionalized

• Using core velocity

• half width velocity

whats r_0,5

Half width velocity

Radius r where velocity is half

Are the velocity profiles of round jet self similar

yes

Whats independant of Reynolds number for turbulent flows

• non dimensional spreading

• half width velocity

Explain the advantage of using canonical flow configurations for the development of turbulence models compared to more complex configurations.

Canonical Flows are simple test cases, which can be thoroughly investigated both experimentally and via direct numerical simulations. Hence, they are well-suited for the development and calibration of turbulence models and their validation.

Explain the concept of self-similarity in the context of turbulence modeling. 

Self-similarity means that by normalizing the flow configuration with suitably chosen reference parameters, the results are identical. The results can be represented with the help of a similarity function. They thus allow a generally valid representation of the flow field of the respective flow configuration and are thus particularly suitable for modeling approaches.