What is Prandtl Hypothesis for Boundary Layers?
Flow around profile can be divided into boundary layer and potential flow. In boundary layer the flow is rotational due to shear between no-slip wall and outer flow.
What are the possibilities and limitations for potential flow with regard to effects of friction?
- Potential flow cannot represent direct effects of friction ie. explicit Force terms in momentum equation
- Potential flow can represent indirect effects of friction such as through Kutta condition
- Pressure distribution along profiles can be well predicted by potential flows, as long as Prandtl’s hypothesis applies
What is boundary layer edge delta(x)?
It is the distance from the wall to the edge of the boundary layer at a given coordinate x.
What is the pressure gradient in wall normal direction for boundary layers?
It is 0
How do flow properties change in wall-normal and in flow direction for boundary layer flow?
- Change quickly in wall normal direction
- Change very slowly in flow direction
What is the formula for characteristic scale of wall normal velocity V in boundary layer?
V ~ (delta / l) * U_infinity
What are the key properties of wall normal and streamwise velocity in boundary layer flow?
- Streamwise velocity u is dominant
- Wall normal velocity v is small but essential for mass conservation
What is the most important method we use to simplify NS equations for boundary layer flow?
Boundary layer scaling through the introduction of characteristic scales.
What are some key points for viscosity in boundary layer?
- Viscous Term in streamwise direction is negligible
- Viscous term in wall normal direction is dominant
What are the boundary conditions for 2D, incompressible, steady boundary layer flow?
- u(x,y = 0) = 0
- v(x,y = 0) = 0
- u(x,y -> infinity) = U_infinity
What is a point where the boundary layer equations do not formally apply and why?
At the leading edge as the flow there develops equally fast in all directions
How does boundary layer thickness grow as a function of distance from leading edge?
- with the square root of distance from leading edge up to a certain point after which it decreases with the square root of increasing Reynolds number
What are the properties of length scales in streamwise and wall normal directions?
Are small in wall normal direction and large in streamwise direction
What is the main idea behind the similarity solution approach for boundary equations?
The main idea is to reduce the problem from a system of partial differential equations (PDEs) with two independent variables, x and y, into one equation with a single independent variable, called the similarity variable.
Why is delta_99 used?
Because u(x,y = delta) = U_infinity is impractical
What is the friction coefficient for boundary layer flow?
Wall sheer stress divided by dynamic free stream pressure.
What is the momentum thickness?
The momentum thickness provides a measure of the loss of momentum due to the viscous effects in the boundary layer. It gives the equivalent distance by which the wall would need to be moved (upshifted) to make the momentum flux across the boundary-layer section equal to the momentum flux in an inviscid flow.
How can momentum deficit be captured using momentum thickness?
For a flat-plate ZPG boundary layer, the momentum thickness can be integrated across the boundary layer thickness, and the momentum deficit can be captured by the integral.
What is Pohlhausen boundary layer profile?
The Pohlhausen boundary layer profile provides an efficient method to approximate the velocity profile in a zero-pressure-gradient flat-plate boundary layer.
What are the Falkner Skan Equations?
The Falkner-Skan boundary layer equations extend the classical Blasius solution to account for non-zero pressure gradients. This is done by generalizing the similarity variable and modifying the stream function.
What is boundary layer seperation?
Whenever inertia is relevant in comparison to friction (non-small Reynolds number) a flow may not be able to follow sudden contour-shape changes
What is accelerated boundary layer?
In case of favorable pressure gradient near the wall, boundary layer thickens as flow speeds up
What are the properties of ZPG boundary laye?
Monotonically increasing velocity profile.
Inflection point at the wall.
Local shear stress maximum at the wall.
Zero pressure gradient (i.e., no acceleration or deceleration).
What are properties of decelerated boundary layer?
Convex curvature of u(y) near the wall.
Local shear stress maximum at the wall, but the flow is decelerating.
Adverse pressure gradient (pressure increases along the flow direction).
