Details of viscous flow around an airfoilBoundary Layer
Concept
Boundary layer thickness definitionsBoundary layer on a flat
plateDisplacement ThicknessMomentum Thickness
Boundary layer thickness definitions
Displacement Thickness (d *)Displacement Thickness and Momentum
Thickness
Method of AnalysisExact solution - Only for laminar BL- Using
Blasius (1908) solution
General Form of Momentum Integral Equation
Alternative Form of Momentum Integral EquationThis equation is
valid for: Steady flow Incompressible flow 2-D flow No body
force
Can be applied for LAMINAR and TURBULENT boundary layers.
where H = d*/q Velocity-profile "shape factor". Alternative Form
of Momentum Integral Equation
Zero Pressure Gradient BLwhere u/U = velocity distribution and
usually is expressed as u/U = f (y/d), also d = d (x).
AssumptionsDimensional AnalysisDarcy-Weisbach equation The above
equation is valid for laminar and turbulent BL, with assumptions:
1. Steady flow 2. Incompressible flow 3. 2-D flow 4. No body forces
5. dp/dx = 0.
How to solve the BL equation? Assume a velocity profile: u/U = f
(y/d), with B.Cs:at y = 0, u = 0, at y = d, u = U, at y = d, u/y =
0.
How to solve the BL equation?
The MIE becomes:
Finally:tw = f(d), and d = d (x).
The rate of growth of the BL For laminar BL flow:For turbulent
BL flow:The turbulent BL develops more rapidly than the laminar
BL.
Skin Friction Coefficient (Cf)Cf is defined as:
For laminar BL flow:For turbulent BL flow:tw in the turbulent BL
is much higher than in the laminar BL
