CFD - Modelling Turbulent Flows

Question 1

Reynolds Number (Re)

Answer 1

A dimensionless number used to indicate whether a fluid flow is either laminar or turbulent

Question 2

Critical Reynolds Number

Answer 2

The onset of turbulence/transition occurs at a critical value of Re = 2300.

Question 3

General Definition of Re

Answer 3

The ratio of inertia forces to friction forces.

Question 4

Common features in transition processes

Answer 4

• Amplification of initially small disturbances
• Development of areas with concentrated rotational structures
• Formation of intense small-scale motions
• Growth and merging of these areas into full turbulent flows

Question 5

What affects the transition processes

Answer 5

• Pressure Gradient
• Disturbance Levels
• Wall Roughness
• Heat Transfer

Question 6

Characteristics of Turbulence

Answer 6

• Irregularity (random and chaotic): treated statistically rather than deterministically
• Three-dimensional rotation, unsteady
• Diffusivity: enhanced mixing and increased rates of mass, momentum, and energy transports in a flow
• Dissipation of energy (Kinetic Energy to Internal Energy)
• Multi-scale vortex structures in the turbulent fields
• Energy cascades from large-scale to smaller scale structures
• Mixing: turbulence increases the mixing of momentum and heat

Question 7

Energy Cascade

Answer 7

Large-scale structures cascade down to small-scale structures

Question 8

Kolmogorov Length Scale

Answer 8

Structures that are small enough that molecular diffusion becomes important and viscous dissipation of energy finally takes place.

Question 9

Spectral Energy E(K). Units: (m^3/s^2)

Answer 9

Kinetic energy per unit mass per unit wave number of fluctuations around the wave number K.

Question 10

Kolmogorov Microscales

Answer 10

The smallest scales presented in a turbulent flow where viscosity dominates and the turbulent kinetic energy is dissipated into heat.

Question 11

Reynolds Decomposition

Answer 11

Defines flow property phi(t) at this point as the sum of a steady mean component “phi bar” and a time-varying fluctuating component phi ‘ (t).

phi(t) = “phi bar” + phi ‘ (t)

Question 12

Kinetic Energy per unit mass of the turbulence at a given location

Answer 12

k = 1/2 x ui’ x ui’ = 1/2 x (u’^2 + v’^2 + w’^2

ui’ - time-averaged fluctuation in velocity

Question 13

Turbulence Intensity Ti

Answer 13

The average r.m.s velocity divided by a reference mean flow velocity

Ti = sqrt(2k/3)/Vref

Question 14

Reynolds Averaged Navier-Stokes (RANS)

Answer 14

Average the Navier-Stokes Equations in time and use a model to predict the extra terms that appear. Models all turbulent scales.

Question 15

Large Eddy Simulation (LES)

Answer 15

Solve the Navier-Stokes Equations only for large turbulent scales and use a model to account for the small turbulent scales

Question 16

Direct Numerical Simulation (DNS)

Answer 16

Solve the Navier-Stokes Equations for all turbulent scales.

Question 17

Number of Extra Transport Equations

Answer 17

Algebraic Turbulence Model (Mixing Length Model) - 0

Spalart-Allmaras Model/1 Eq Differential Turbulence Model - 1

K-Epsilon Model/K-Omega Model/Algebraic Stress Model - 2

Reynolds Stress Model/Second Moment Closure - 7

Question 18

Near-Wall Flows

Answer 18

For turbulent flows, the boundary layer can be divided into inner and outer regions:

Inner Region:
Wall
- Viscous Sublayer
- Buffer Layer
- Log-Law Layer
——————————
Outer Region

Question 19

Viscous Sublayer

Answer 19

A thin layer in contact with the wall, dominated by viscous effects, almost laminar.

0 < y+ < 5~8

u+ = y+

Question 20

Buffer Layer

Answer 20

A transitional layer between the other two.

5~8 < y+ < 30~70

Question 21

Log-Law Layer

Answer 21

Dominated by viscous and turbulent effects.

u+ = 1/k ln(y+) + B

30~70 < y+ < 500

Question 22

Non-Slip Condition

Answer 22

On the wall, the velocity is zero.

Question 23

y+

Answer 23

Non-dimensional wall coordinate

Question 24

u+

Answer 24

Wall parallel velocity non-dimensionalised with friction velocity