《燃烧流体力学》（英文版）Chapter 3 Jet Flow Theor

煤烧圆家重点实验宝 Chapter 3 Jet Flow Theory 8 1 Theory of Isothermal Free Jet Free jet: Jet without the limitation of solid boundary 1. General Properties 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 Chapter 3 Jet Flow Theory §1 Theory of Isothermal Free Jet Free jet: Jet without the limitation of solid boundary 1. General Properties

煤量甏圆家重点实验宝 Ce 开始区域 转捩载面 基本区域一 气流核心 内边界 S S S 外边界 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

煤量甏圆家重点实验宝 1)turning section O 2)beginning region and basic region 3)core with velocity of beginning one 4)turbulent boundary layer-the part between inner boundary (v=vo) and outer boundary (v=0) 5)polar point: cross point of outer boundary surface 6) Similarity 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) turning section SH dO 2 1  4 2) beginning region and basic region 3) core with velocity of beginning one 4) turbulent boundary layer - the part between inner boundary (v=vo ) and outer boundary (v=0) 5) polar point: cross point of outer boundary surface 6) Similarity

煤量甏圆家重点实验宝 In basic region, the distribution of non-dimensional velocity is complete similar 1. e at corresponding points y Where vm-velocity at x axis yc -distance of points with velocity(1/2)vm with x axis 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 In basic region, the distribution of non-dimensional velocity is complete similar i. e. at corresponding points 1 2 1 2         =                 =         m x m x c c v v v v y y y y Where vm - velocity at x axis yc - distance of points with velocity (1/2)vm with x axis

煤烧圆家重点实验宝 b- half of jet width In beginning region, the velocity distribution in boundary layer is similar at different sections f(c=f (3-2) Where:Ayo=y-y 0.lv-0.9 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 ( ) ( ) b y f y y f v v m c x = = (3-1) b - half of jet width In beginning region, the velocity distribution in boundary layer is similar at different sections ( ) ( ) 0 b y f y y f v v b x c =   = Where: 0 9 0 0.1 0. 0 b v v c y y y y y  = −  = − (3-2)

煤量甏圆家重点实验宝 7) Attenuation of v S 0.67,=f v (3-3) 2. Turbulent properties 1) In core region,y个↑,x个,vt↑ 2)in basic region, Vtmax >3 vt 3)vx>> Vaz,VX≈vy≈vz 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 7) Attenuation of vm 0.67, ( ) 0.67, 0 0 0 0 0 r as f v v r as v v r as x m  =  = (3-3) 2. Turbulent properties 1) in core region, y↑, x↑, nt↑ 2) in basic region, ntmax > 3 nto 3) vx >> vy ≈vz , v’x ≈ v’y ≈ v’z

煤烧圆家重点实验宝 In core region f(2) 3-4 f2 b 4)mixing length l/b=0.11 /b=0.10 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 In core region, ( ) ' ' ( ) ' ' 2 1 b y f v v b y f v v ym y xm x = = (3-4) 4) mixing length l tx/b = 0.11 l ty/b = 0.10 (3-5)

煤量甏圆家重点实验宝 3. Outer boundary and iso-velocity line In basic region b <0.y.∞ 2 ∝C1 db dy 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 3. Outer boundary and iso-velocity line In basic region dy dv l dt db dy dv v l v v v v dy dv v dt db x t x x t y x y x x y        ' 0, ' ' ( ' ' ) ' 2 2

煤量甏圆家重点实验宝 From the similarity of velocity const db Also dt COnSt of Coal Combustion. HUST COST 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 the similarity of velocity m t t x m v dt db const b l b l b v dy dv    = =       =       ... 1 2 Also, b const x const dx db dx db v dt db v dt dx dt dx dx db dt db m m =  = = = =  (3-6)

煤量甏圆家重点实验宝 For const b (3-7) const = const (3-8) const 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 For . . const v v const b y m x =  =      (3-7) i. e. . . const v v const x y m x = = (3-8)