《燃烧流体力学》（英文版）Chapter 2 Turbulent Flow

煤烧圆家重点实验宝 So, Eq (2-7)becomes (po)+(m)=()+S(2-10 where generalized transport coefficient opt turbulent Prandtl number μe=μ+pt=p(V+v)- effective viscous coefficient National Lab, of Coal Combustion. HUST Wuhan 430074 P R CHINA E-mail:pcbnlcc@hust.edu.cn

NL CC National Lab. of Coal Combustion, HUST Wuhan 430074, P. R. CHINA E-mail: pcbnlcc@hust.edu.cn So, Eq. (2-7) becomes       S x x v t x j j j j +      =   +   ( ) ( ) ( ) (2-10) where t t t        = + - generalized transport coefficient  t - turbulent Prandtl number e =  + t = (n + nt ) - effective viscous coefficient

煤烧圆家重点实验宝 Note: Turbulent viscous coefficient is only a assumption, its reliability and applicability should be proved Discussion molecular transport:)s-termed movement Average free movement distance Turbulent transportation: k National Lab, of Coal Combustion. HUST Wuhan 430074 P R CHINA E-mail:pcbnlcc@hust.edu.cn

NL CC National Lab. of Coal Combustion, HUST Wuhan 430074, P. R. CHINA E-mail: pcbnlcc@hust.edu.cn Note: Turbulent viscous coefficient is only a assumption, its reliability and applicability should be proved. Discussion: molecular transport: '2 v - termed movement Average free movement distance Turbulent transportation: k l

煤量甏圆家重点实验宝 From dimensional analysis A=C21 For turbulent boundary layer, from similarity of laminar and turbulent flows Prandtl(1925) assumed = Lm: mixing z length National Lab, of Coal Combustion. HUST Wuhan 430074 P R CHINA E-mail:pcbnlcc@hust.edu.cn

NL CC National Lab. of Coal Combustion, HUST Wuhan 430074, P. R. CHINA E-mail: pcbnlcc@hust.edu.cn From dimensional analysis C k l t 1/ 2  =   (2-10) For turbulent boundary layer, from similarity of laminar and turbulent flows, Prandtl (1925) assumed y u u l l u m t m   = = '   ' Lm: mixing length

煤量甏圆家重点实验宝 2 2-12) In general u,=p12 2-13) x or pvy,=p/2,oy,, Ov, l a x: OX pl2., ad (2-14) Ox: ax. a National Lab, of Coal Combustion. HUST Wuhan 430074 P R CHINA E-mail:pcbnlcc@hust.edu.cn

NL CC National Lab. of Coal Combustion, HUST Wuhan 430074, P. R. CHINA E-mail: pcbnlcc@hust.edu.cn So, y u t l m   = 2   (2-12) In general, j i i j t m x v x v l   +   = 2   (2-13) or j j i i m j i j i i j j i i j i j m x x v x l v v x v x v x v x v v v l     +   − =   +     +   − =         2 ' ' ' ' 2 ( ) (2-14) ( = Ys , h)

煤量甏圆家重点实验宝 1)Free shear flow m(x)=4(x)215) 2)Developed turbulent tube flow n/R=014-0.08(1-y/R)2-006(1-y/R) (2-16) National Lab, of Coal Combustion. HUST Wuhan 430074 P R CHINA E-mail:pcbnlcc@hust.edu.cn

NL CC National Lab. of Coal Combustion, HUST Wuhan 430074, P. R. CHINA E-mail: pcbnlcc@hust.edu.cn 1) Free shear flow l (x) y (x) m =  E (2-15) 2) Developed turbulent tube flow 2 4 l / R 0.14 0.08(1 y / R) 0.06(1 y / R) m = − − − − (2-16)