Boundary Layer Flow 13 - Boundary Layer Flow Separation Flashcards
How does boundary layer separation affect the ideal flow past a sphere?
Makes model incorrect - flow is correct at the front of the sphere, not at the back as it misses BL flow development and separation
Properties of BL on a curved surface
Attached flow until maximum flow speed at top of curve
Separation point, after which flow separation is possible
Creates separation streamline, under which is reverse flow, causing eddies
Near to the wall under adverse pressure gradient
Inertia term is small/negligible, diffusion balances pressure gradient
2nd derivative of velocity is positive
Away from the wall under adverse pressure gradient
2nd derivative of velocity becomes negative to meet the free stream velocity
BL velocity profile under adverse pressure gradient
S-shape with a point of inflection
Velocity profile under favourable pressure gradient
2nd derivative of velocity is negative all the way from the wall to outer BL edge
Velocity profile is very rounded with no point of inflection
More energy can be supplied to near wall region from high speed region, so flow is more stable and there can be no flow separation
When does flow separation occur?
Boundary layer will separate if there is an excessive momentum loss near the wall in fighting against the adverse pressure gradient
Stronger adverse pressure gradient, higher point of inflection within flow
Flow separation starts from when shear stress and du/dy are zero (separation point)
What does it mean if the velocity profile is thin?
Less energy available
Weak adverse gradient
dU/dx < 0
dp/dx > 0
No separation
Point of inflection in the flow
Critical adverse gradient
Zero slope at wall
Separation point
Excessive adverse gradient
Backflow at the wall
Separated flow region
Experimental observations
When dp/dx < 0, flow is smooth and stable
When dp/dx > 0, BL thickness grows quickly and separation occurs
Other definitions of BL thickness
Low velocity region, due to viscosity and no slip wall
Flow displacement, due to low velocity in BL (displacement thickness)
Momentum loss due to existence of BL (momentum thickness)
These parameters are often used to build flow loss models (e.g. in gas turbine)
Define displacement thickness
Distance by which the external inviscid flow is effectively displaced outwards in the y-direction due to the decrease in velocity in the BL
Define momentum thickness
Thickness that accounts for the momentum loss in the flow because of the formation of the BL
