The Boundary Layer Method 
In order to calculate the friction drag of an airfoil for a given flow condition (angle of attack, Reynolds number), an analysis of the viscous boundary layer is necessary. From the momentum loss in this small layer on the surface of the airfoil the drag can be derived. As the velocity distribution changes with angle of attack, the drag changes too. Also, the thickness of the boundary layer changes with Reynolds number.
The boundary layer module uses the velocity distribution derived by
the panel method and
performs its calculations based on the formulas presented in [14,
15, 16].
The method is a so called integral boundary layer method, which does
not handle laminar separation bubbles or large scale
separation (stall). The boundary layer module works best in the Reynolds number
regime between 500'000 and 20'000'000.
The results of the boundary layer module are also used to correct lift, drag and
moment coefficients empirically, if separation occurs. Additionally, a blending
to separated, flat plate coefficients is performed for very high angles of
attack.
The procedure starts at the stagnation point and marches along each surface, integrating simplified boundary layer equations. The integration follows a 2nd order RungeKutta scheme with stabilization by automatic step reduction. This can be a bit slow some times, but works more reliable than the simple Newton method used before. During the way towards the trailing edge, the method checks, whether transition from laminar to turbulent or separation occurs.
The following empirical transition criteria have been implemented and can be selected by the user:
Method  Transition assumed when  Recommendation  

Eppler 1[14]  Re > 1x10^{5}  
Eppler 2 [17]  Re > 1x10^{5}


Michel 1 [35]  Re > 2x10^{6}  
Michel 2  Re > 2x10^{6}  
Granville  Here, an additional local pressure gradient
parameter K is used ("Pohlhausen parameter")
Instability is assumed when K > K_{instability} In regions of instability, transition is assumed when K > K_{transition} 
Re > 5x10^{6}  
Drela e^{n} approximation (Xfoil pre 1991) 


Drela e^{n} approximation (Xfoil post 1991) [36] 
Note: 

Arnal e^{n} approximation by Würz 
Note: 
If laminar separation is detected, the method switches to turbulent flow and continues. When turbulent separation is found, the boundary layer integration is stopped and an empirical drag penalty depending on the length of the separated region is added to the result.
Flow State  Separation assumed when 

laminar  
turbulent 
The drag is applied by examining the boundary layer parameters at the trailing edge, using the so called SquireYoung formula.
The tables produced on the BoundaryLayer card contain the following columns:
symbol  description 

x/l  normalized xcoordinate 
y/l  normalized ycoordinate 
v/V  normalized surface velocity 
d_{1}  displacement thickness 
d_{2}  momentum loss thickness 
d_{3}  energy loss thickness 
C_{f}  local friction coefficient 
H_{12}  shape factor d_{1}/d_{2} 
H_{32}  shape factor d_{3}/d_{2} 
flow state  laminar, turbulent, separated 
y_{1}  the first cell height required for y+=1 (multiplied
by 100 resp. in %) This value can be useful for grid generation for NavierStokes solvers 
For abbreviations see the quick reference page.
Last modification of this page: 29.08.06
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