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CFD > Turbulent modelling > Flashcards

Turbulent modelling Flashcards

1
Q

Mixing length model

A
  • zero equation model (no transport equations)
  • Lm is mixing length, representing the region in which turbulent mixing is expected to act
  • main advantage is speed and simplicity of the model
  • no transport effects in this model, which are needed to account for CONVECTION and DIFFUSION of patches of turbulence away from site or moment of generation
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2
Q

Eddy viscosity

A
  • turbulence is a viscous phenomena

- analogous to laminar viscosity

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3
Q

Reynolds stresses

A
  • uiuj

- tensor of non-zero correlations that result from the averaging process

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4
Q

RANS +/-

A
  • needs extensive closure modelling
  • no information about instantaneous flow, cheap for engineering applications
  • generally only models a single scale, the integral scales
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5
Q

LES +/-

A
  • needs closure modelling only at small isotropic scales
  • enables instantaneous information to be obtained
  • remains expensive and relatively uncertain, not predictive
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6
Q

Hybrid RANS-LES +/-

A
  • RANS used near to a wall, LES used far from a wall
  • can provide limited information about instantaneous flow
  • a useful compromise which is increasing popularity with industry
  • split between GLOBAL and NON-GLOBAL methods
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7
Q

Detached Eddy Simulation

A
  • GLOBAL method, adapts automatically between RANS and LES
  • used within an existing RANS framework, with improvements for numerical aspects where the model switches to LES
  • the switch is based on the length scale equation, which returns the minimum of the grid scale and the turbulence length scale from which the RANS model its based on
  • main problem is grid-induced separation, over refinement of the boundary layers results in undesirable switching to LES in the near wall region, can spontaneously induce unphysical flow separation
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8
Q

Embedded Large Eddy Simulation

A
  • NON-GLOBAL method, requires the user to pre-define regions of the domain where the model will act in RANS and LES
  • main challenge is generation of unsteady inlet velocity at the interface from RANS to LES
  • generally achieved via introduction of synthetic turbulence at interface
  • superimpose unsteady fluctuations on top of a mean flow field from the RANS domain, must be correlated such that they represent coherent turbulent eddies
  • white noise is uncorrelated in time and space and therefore doesnt work
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9
Q

Energy Cascade definition

A
  • the transfer of energy, originating from the mean flow with scales of that order, to progressively smaller and smaller eddies my means of the non-linear interaction; dissipated as heat by viscous forces
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10
Q

Characteristics of turbulence

A
  1. Strong vorticity
  2. Irregularity
    • chaotic and stochastic
  3. Three dimensionality
  4. Unsteadiness
  5. Broad spectrum of scales
  6. Dissipative
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11
Q

3 important things about energy spectrum

A
  • midsection of the cascade, ‘inertial subrange’, becomes broader as the Reynolds number increases
  • as the turbulent eddies become smaller, directional information is lost
  • the gradient of the inertial subrange is a constant value E(k) ~ k^(-5/3)
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12
Q

Newtonian fluid

A
  • viscous stresses vanish when the fluid is at a rest
  • viscous stresses are linearly proportional to the strain rate
  • there are no preferred directions in the fluid
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13
Q

Turbulence modelling vs simulation

A

Modelling - reconstruction of bulk effects of turbulent scales without resorting to direct representation of their dynamics

Simulation - more complete resolution of the time and spatial variation of turbulent scales, without resorting to semi-empirical modelling

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14
Q

Length scales

A

Integral - associated with the bulk of the energy

Taylor - associated with isotropic motion

Kolmogorov - associated with viscous dissipation

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15
Q

Eddy viscosity disadvantages

A
  • modelling is based on local information only (one closure point)
  • constants calibrated from simple (equilibrium) flows
  • turbulence kinetic energy production is usually over predicted in regions of high strain
  • Reynolds stresses are assumed to be isotropic
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16
Q

Bandwidth EQ

A

integral length scale/kolmogorov length scale

17
Q

VLES +/-

A
  • lies between URANS and fully resolved LES

- conceptual objective is to resolve flow up to a corresponding wave number

18
Q

DNS +/-

A
  • best representation of the full Navier-Stokes; no modelling required
  • all scales of motion are captured
  • extremely expensive, a research tool for low Reynolds numbers only
19
Q

DES +/-

A
  • apply URANS to attached boundary layers in their entirety
  • apply LES to strongly separated flow regions
  • particularly relevant to external aerodynamics
20
Q

Role of Reynolds stresses/turbulence model

A
  • RANS represents time-averaged flow
  • Reynolds stresses are the tensor of non-zero correlations that result from the averaging process
  • in order to solve the RANS equations, approximations to these terms are required
21
Q

Low & high Re distinction

A
  • low Re models operate in the viscous sub layer when viscous stress dominate
  • they need: terms sensitive to viscous stress, sufficient resolution in this region
  • high Re models operate in the log layer where turbulent shear stress dominates
  • a coarser mesh is acceptable, though near wall model ‘wall functions’ are required
22
Q

General benefit

A

DNS - detailed instantaneous information about turbulence
LES - instantaneous nature retained, with some loss of accuracy and insight
RANS-LES - instantaneous nature retained, significant approximations near to wall
RANS - speed & means for efficient production of mean flow field without need for instantaneous turbulence resolution

23
Q

General requirement

A

DNS - extremely high computational resource, knowledge of boundary and initial conditions
LES - retains prohibitively large requirements for practical cases, best practice guidelines exist but are case dependant
RANS-LES - more practical than LES but require time averaging, significantly increases cost
RANS - computational requirements are lower but knowledge of basic modelling limitations is needed

24
Q

Log layer

A
  • a universal law for turbulent flows which can be derived by applying the assumptions listen in the question to the N-S equations
  • U+ is proportional to log y+
25
Q

RANS suitability

A
  • statistically steady flows, or at close to energetic equilibrium
  • attached boundary layer flows with a single predominant velocity gradient can be well approximated by RANS
26
Q

LES suitability

A
  • provides instantaneous info about flow, useful for prediction of unsteady events such as noise, flutter, thermal fatigue
  • additional physical content of LES also infers greater predictive capability for high Reynolds number flows
27
Q

Lm term and uses

A
  • ‘mixing length’ , represents the region throughout which turbulent mixing are expected to act
  • used as a ‘wall function’ to approximate near wall turbulent physics
  • a close analogue is also commonly used as the sub-grid-scale model in large eddy simulation
28
Q

Integral lengthscale

A

(k^3/2)/epsilon

CFD (4 decks)

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