Shear Stress

Question 1

Define the velocity of a particle in turbulent flow

Answer 1

v_instantaneous = v_mean + v_fluctuation
v = v_bar + v’

Question 2

Define the shear stress due to turbulence for 2D flow

Answer 2

tau = - rho * mean(v_x’ * v_y’)

Question 3

How does turbulence affect viscosity?

Answer 3

The effect of turbulence can be represented as an increased viscosity.

Question 4

Define total shear stress.

Answer 4

tau = (mew + epsilon) * dv_bar / dy
total shear stress = (coeff. of visc. + eddy visc.) * mean velocity gradient

Question 5

Define shear stress for fully laminar flow, and explain it

Answer 5

tau = mew * dv / dy
epsilon = 0

Question 6

Define shear stress for fully turbulent flow, and explain it

Answer 6

tau = epsilon * dv_bar / dy
epsilon is much larger than mew, so can approximate mew as 0

Question 7

In a laminar boundary layer, what creates the shear stress?

Answer 7

Layers sliding over each other at speeds which vary with distance to the solid boundary. A faster layer will pull the adjacent, slower layer forward, and the slower layer will act equally and oppositely.

Question 8

In a turbulent boundary layer, what creates the shear stress?

Answer 8

The particles move between layers due to turbulent eddies. This causes extra shear stress in different directions.

Question 9

Where can air flow be assumed to be ideal?

Answer 9

In freestream flow, because the velocity gradient is negligible, so there is no shear stress/viscosity. The velocity gradient only exists in the boundary layer, due to the no-slip condition.