2018/3/11 Skin Friction Drag:Laminar flow Laminar,Transitional,and Turbulent over a smooth flat plate 图上清大华 Flow 圈上清文大华 laminar transitional turbulent X=0 X=1 9=0.064.06 10 Turbulent Local skin friction 1 Re, coefficient -0.74Rex6 1000C4 Average,or C= 1.328 Transitional friction coefficient Rer Laminar C=1.328Rex12 Re=pV1/u where,is characteristic length,fuselage length 1 or winglean aerodynamic chord 104 105 106 107 Rex ong 26 Skin Friction Drag in Turbulent Flow 国上活大蜂 Wave Drag 国上活支大峰 Drag increases due to compressibility effects for airspeeds higher DI=CFASq 0.0045 than critical Mach number Mcr,due to the appearance of shock waves. ·This increase has a moderate slope 05 until reachina Cris small but the 0.0035 drag divergence dynamic pressure and Mach Mdd wetted area are large ·Drag diverge Mach is defined 0.0025 02 as 70- 106107 nt ge or 0.455 CFhrb (l0gR)s1+0.144M2p65 106<Re<109 Fig.8 Wave drag inerease at transonie airxpeeds. M。 Drag Build-up for the Wing 国上清大学 Drag build-Up with Component Form Factors 园上清天大学 Dw.o=Dwr+Dw.p zero-lift drag CD.or= wg Sq Dwo=CEnurbswet q+k CEnurbswet q Cooe -KyCrah SeZer- coefficient for the wing Dwo=(1+k)CEnirbSwet q Dw.o=KwCrsuet q CD.o= KC S Zero-lift drag The drag estimate is based on a multiple of the friction drag.K,the coefficient for the form factor for the wing -1 airplane erslty-Dr.V(enbin Song 52018/3/11 5 © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Skin Friction Drag: Laminar flow over a smooth flat plate tw   , 2 , 0 0.664 0.664 1 Re 2 f lam x x c Vx V        , 0 , 0 1.328 Re l f lam F lam l l c dx C dx     Local skin friction coefficient Average, or integrated, skin friction coefficient X=0 X=l Re  Vl /  where , is characteristic length, fuselage length or wing mean aerodynamic chord l © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Laminar, Transitional, and Turbulent Flow •26 laminar transitional turbulent 104 105 106 107 Rex 10 4 1 1000cf Turbulent cf=0.74Rex -1/5 Laminar cf=1.328Rex -1/2 Transitional 0 X © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Skin Friction Drag in Turbulent Flow D C S q f turb F turb wet , ,  106<Rel<109 CF is small but the dynamic pressure and wetted area are large    0.65 2.58 2 10 , log 1 0.144 0.455 R M CF turb   106 107 108 109 Rel 0.0045 0.0035 0.0025 CF © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Wave Drag • Drag increases due to compressibility effects for airspeeds higher than critical Mach number Mcr, due to the appearance of shock waves. • This increase has a moderate slope until reaching drag divergence Mach Mdd • Drag divergence Mach is defined as – 20-drag-count increase, or – drag-increase slope of 0.1 Mcr Mdd © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Drag Build-up for the Wing DW,0 = DW,f + DW,p = zero-lift drag DW,0 = CF,turbSwet q + k CF,turbSwet q DW,0 = (1 + k) CF,turbSwet q DW,0 = KWCFSwet q The drag estimate is based on a multiple of the friction drag, KW, the form factor for the wing © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Drag build-Up with Component Form Factors ,0 ,0W W D D C Sq  ,0 , W W wet D W F turb S C K C S  ,0 , 1 i i n wet D i F turb i S C K C  S   Zero-lift drag coefficient for the wing Zero-lift drag coefficient for the airplane