《空气动力学》（双语版）chapter11 SUBSONIC COMPRESSIBLE FLOW OVER AIRFOILS：LINEAR THEORY（2/2）

CHAPTER 11 SUBSONIC COMPRESSIBLE FLOW OVER AIRFOILS LINEAR THEORY 11. 4 PRANDTL-GLAUERT COMPRESSIBILITY CORRECTION The methods that approximately take into account of the effects of compressibility by correct the incompressible flow results is called compressible corrections

CHAPTER 11 SUBSONIC COMPRESSIBLE FLOW OVER AIRFOILS: LINEAR THEORY 11.4 PRANDTL-GLAUERT COMPRESSIBILITY CORRECTION The methods that approximately take into account of the effects of compressibility by correct the incompressible flow results is called compressible corrections

We will derive the most widely known correction of Prandtl-Glauert compressibility correction in this section Since the prandtl-glauert method is based on the linearized perturbation velocity potential equation (1-M2) 3×∞2 0 So it has restrictions: thin airfoil at small angle of attack purely subsonIC give inappropriate results at M。≥0.7

We will derive the most widely known correction of Prandtl-Glauert compressibility correction in this section. Since the Prandtl-Glauert method is based on the linearized perturbation velocity potential equation: 0 ˆ ˆ (1 ) 2 2 2 2 2 =   +   −  x y M   So it has restrictions: thin airfoil at small angle of attack; purely subsonic; give inappropriate results at M  0.7

B2=(1-M2) 02a2 0 7= (5,)=B0(x,y)

0 ˆ ˆ 2 2 2 2 2 =   +   x y    (1 ) 2 2  = − M  = x  = y ( , ) ˆ  ( ,) =  x y

ax as ax an ax Ba5 oOo on n ao ay as ay an Oy 00(1a)05_102 Ox2 a5( ox Ba5 00(00ma0 Oy2an(n丿ay =P0m1

            =     +     =   1 ˆ ˆ ˆ x x x            =     +     =   y y y ˆ ˆ ˆ 2 2 2 2 1 1 ˆ            =               =   x x 2 2 2 2 ˆ           =               =   y y

B B 00+P0m O 0o Ba5 0 0202=0

0 1 ˆ ˆ 2 2 2 2 2 2 2 2 2 2 =   +   =   +             x y 0 2 2 2 2 =   +      