VLIII - Channel Flows

How can turbulence be modelled

as additional viscosity

how is turbulent viscosity calculated

q’*l
q magnification of fluctuation

Reynolds averages kinetic energy Production term importance

Production taken from mean flow and taken to fluctuations

Has HIT Production explain why

No, due to it being a dissipating flow (isotropic)

Different way of writing production term and significance of it

Subtraction of isotropic part of RST => only anisotropic flow states can have production in incompressible flows

Through what can production occur

Through the symmetric velocity-gradient tensor

Where is energy produced (production highest) round jet?

In the macro scale and at 0,6*r0,5, energy traveling downstream while staying in the middle

Where has the mean flow convection the highest energy round jet

In the middle

Which stress is dominant along the walls Channel flow

Viscous stress

why do Reynolds stresses disappear at the wall

due to no-slip condition (fluctuations are zero)

Where do Reynolds stresses dominate channel flow

In the middle of the channel

What does a higher Re Number lead to channel flow stresses

• Viscous stresses fall of steeper

• Reynolds stresses get larger in near wall region

Dominating parameters in near wall region channel flow

• Viscosity

• Wall shear stress

Whats the Friction reynolds number

Ratio between channel width and l+

What are wall units

• y+

• Ratio out of Wall distance and l+

whats l+

• viscous lengthscale

• ration out viscosity and friction velocity

Whats the friction velocity

sqrt(wall shear stress / density)

Explain eddy viscosity approach for turbulent jets

Simplified relation between Reynolds stress and mean velocity. Which are connected via eddy viscosity (turbulence viscosity)

Name two differences and similarities of laminar and turbulent channel flows

differences:

• no Reynolds stress in laminar flow

• lower maximum velocity for turbulence

similarities:

• same control parameters

• pressure gradient in x direction to drive flow

• linear dependence of total stress on channel height

Name parameters necessary to fully describe turbulent channel flow. Explain universal parameters derived

Describe:

• density

• viscosity

• channel height

• wall shear stress or pressure gradient

Universal parameters:

• friction velocity ut

• viscous length scale l+

• Friction Reynolds number Ret

• dimensionless wall unit y+

Explain the concept of the universal law of the wall. Discuss which layers are introduced, their limits, and - if applicable - universal laws for the velocity.

1. Viscous sublayer: y+<5, universally computable dimensionless velocity u+=y+.

2. Buffer layer: 5<y+<30, dimensionless velocity not universally computable.

3. Logarithmic layer: y+>30, y/δ<0.3, universally computable dimensionless velocity u+=1/κlog(y+)+A.

4. Velocity-defect layer: y/δ>0.3, dimensionless velocity not universally computable.

Explain the behavior of the velocity fluctuations with decreasing wall distance. Discuss why wall modeling is in general a challenge for turbulence modeling. 

Near the wall, u′ and w′ ∝ y, while v′ ∝ y². so fluctuations are mainly parallel to the wall (quasi-2D flow). Wall modeling is challenging because the wall strongly influences the Reynolds stresses, which turbulence models must capture accurately.

What is the criterion for the smallest cell size in a DNS of a turbulent boundary layer, and what is the criterion in a RANS simulation?

• DNS: Kolmogorov scale must be resolved with a given number of cells (between 3 and 10)

• RANS: y+=1 must hold at the center of the first cell at the wall, i.e., Δx=2y+.