Boundary Layer Flow 15 - Boundary Layer Flow Transition

Question 1

Laminar-turbulent transition

Answer 1

As Re increases (i.e. further from start of boundary layer), ratio between the inertial and viscous forces increases, so small perturbations become unstable, grow into vortices and eventually turbulence
Transition to turbulence -> higher rate of momentum transfer -> boundary layer thicker -> flow losses (e.g. in a gas turbine or aircraft wing)

Question 2

Define stability

Answer 2

Immunity to (small) disturbances (Criminale 1967)

Question 3

Factors affecting transition

Answer 3

Free stream disturbances (kinematic, acoustic, thermal) can cause earlier transition
Roughness will generally cause earlier transition
Adverse pressure gradient causes earlier transition
Mach number
Wall cooling/heating
Suction/blowing

Question 4

Morkovin’s transition roadmap (1984)

Answer 4

Natural transition - Tu < 1% via Tollmien-Schlichting (TS) waves
Bypass transition - Tu > 1%, TS waves ‘bypassed’ (e.g. turbo machinery)

Question 5

What is Tu?

Answer 5

Free stream turbulence intensity

Question 6

Natural transition process over a smooth surface

Answer 6

Starts with unstable 2D waves, TS waves, convected downstream slower than outer velocity
Their amplitude is amplified exponentially downstream, and develops 3D waves and eddies
Vortex breakdowns at regions of high shear
Formation of turbulence spots (i.e. localised turbulent regions)
Coalescence of spots leads to an ‘explosion’ to turbulence

Question 7

Bypass transition process

Answer 7

Development of streaks (span wise modulation of BL), bypassing first three stages of natural transition
Streak breakdown, incipient spots
Formation, interaction and merging of turbulent spots

Question 8

Consequences of BL transition

Answer 8

More efficient transfer of momentum/energy/heat in BL to/from wall region
Sudden increase in BL thickness
More uniform velocity profile in the BL
More resilient to the adverse pressure gradients
Increased friction drag

Question 9

General properties of turbulence

Answer 9

Irregular, diffusive, dissipative
Rotational and 3D
Comprising vortex tubes (eddies) of different sizes or scales superimposed on each other in a highly complex manner
Range of eddies depends on Re of mean flow

Question 10

Points about turbulent flows being irregular

Answer 10

Velocity taken at fixed point in space
Irregular fluctuation both with time and space, but not statistically random

Question 11

Points about turbulent flows being diffusive

Answer 11

Fluctuation leads to enhanced diffusivity which results in much greater mixing of properties
Rate of mass/heat transfer can be several orders of magnitudes larger than that in laminar flow

Question 12

Points about turbulent flows being dissipative

Answer 12

Within vortices, viscous shear stresses perform work which converts kinetic energy of turbulence into internal energy of the fluid
Rate of energy dissipation is much greater than corresponding viscous dissipation in laminar flow
If there is no continuous external energy source for the continuous generation of turbulent motions, the turbulent motion will decay
In most cases, turbulence comes from high strain rate region (e.g. wall BL)

Question 13

Turbulence control

Answer 13

Delay/promote transition
Reduce friction drag
Vanish turbulence

Question 14

Suppressing turbulence in a pipe

Answer 14

Vanish turbulence by momentarily making flow even more turbulent