《空气动力学》（双语版）chapter11 SUBSONIC COMPRESSIBLE FLOW OVER AIRFOILS：LINEAR THEORY（1/2）

02,0 2a Ox SO a ox Pa(0+ 2a ayl a P( 83,2、oOp,Op=0 ax Ox Ox ay ay

        +   = − 2 2 2 ( ) ( ) 2 x y d a d             +     = −   2 2 2 ( ) ( ) x 2a x x y     so         +     = −   2 2 2 ( ) ( ) y 2a y x y     ( ) 0 2 2 2 2 =     +     +   +   x y x x y y       

We get the velocity potential equation 102|0 2 X 200、O =0 a ox In this equation, the speed of sound is also the function ofφ y

( )( ) 0 2 ( ) 1 ( ) 1 1 1 2 2 2 2 2 2 2 2 2 2 =        −           + −           − a x y x y a x x a y y        We get the velocity potential equation: In this equation , the speed of sound is also the function of :          +  −  = − 2 2 2 0 2 ( ) ( ) 2 1 x y a a    (11.12)

For subsonic flow, Eq. 11 12 is an elliptic partial differential equation. For supersonic flow, Eq 11 12 is a hyperbolic partial differential equation. For transonic flow, Eq 11 12 is mixed type equation

For subsonic flow, Eq. 11.12 is an elliptic partial differential equation. For supersonic flow, Eq.11.12 is a hyperbolic partial differential equation. For transonic flow, Eq.11.12 is mixed type equation