《燃烧流体力学》（英文版）Chapter 6 Radiation Heat Transfer

煤量甏圆家重点实验宝 Chapter 6 Radiation Heat Transfer 8 1 The Equation of Radiation Transfer 1. Attenuation by Absorption and Scattering 1)Absorption (6-1) n/abs 77-7 Where Kn- linear absorption coefficient Over a geometric path s 040g0(c 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 6 Radiation Heat Transfer §1 The Equation of Radiation Transfer 1. Attenuation by Absorption and Scattering 1) Absorption (dI ) I ds  abs = −  (6-1) Where Kη - linear absorption coefficient Over a geometric path s ( ) ( ) ( )        −  =      =  I s I ds I e s 0 exp 0 0 (6-2)

煤量甏圆家重点实验宝 aral. Scattered phe 八∧ Photons Absorbed photons √A产 Transmitted photons ds FIGURE 8-2 Attenuation of radiative intensity by absorption and scattering National Lab, of Coal Combustion, HUST Wuhan 430074P 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 Where ,x,ds Is optical thickness Absorbtivity (6-3) 7 2)Scattering difference between absorption and scattering n /sca (6-4) 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 Where ds s  = 0    Is optical thickness Absorbtivity: ( ) ( ) ( )       − = − −  e I I I s 1 0 0 (6-3) 2) Scattering difference between absorption and scattering (dI ) I ds s  sca = −   (6-4)

煤烧圆家重点实验宝 3)Total attenuation extinction coefficient =K +O 77 7 Optical distance based on extinction B,ds (6-6) 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) Total attenuation extinction coefficient  =   + s Optical distance based on extinction (6-5)  = s ds 0    (6-6)

煤烧圆家重点实验宝 2. Augmentation by Emission and Scattering ) Emission nvem Kni bn (6-7) Combined eqs(6-1)and(6-7) for an absorbing emitting medium n bn (6-8) 7 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 2. Augmentation by Emission and Scattering 1) Emission (dI ) I ds b  em =   (6-7) Combined eqs (6-1) and (6-7) for an absorbing - emitting medium ( )      I I ds dI = b − (6-8)

煤烧圆家重点实验宝 For an isothermal gas layer of thickness s is ()=10)x+,0-c)(69 If only emission is considered, the emissivity is defined as S/Ib (6-10) 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 For an isothermal gas layer of thickness s is ( ) ( ) ( )        − − I s = I e + I − e 0 b 1 (6-9) If only emission is considered, the emissivity is defined as ( )       − = I s I = − e / b 1 (6-10)

煤量甏圆家重点实验宝 2)Scattering The total spectral radiative heat flux impinging on da from solid angle dA; as (d45·)2dn This flux travels through dV for a distance ds/S.s The total amount of energy scattered away from si is ,(,(M8)2d)24。=an()Bdm 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 2) Scattering The total spectral radiative heat flux impinging on dA from solid angle di as I  (s ˆ i )(dAs ˆ i s ˆ)di d. This flux travels through dV for a distance ds s s i / ˆ  ˆ The total amount of energy scattered away from si is ( ( )( ) ) I (s )dAd d ds s s ds I s dAs s d d s i i i  s  i i i  =                ˆ ˆ ˆ ˆ ˆ ˆ

煤烧圆家重点实验宝 THE EQUATION OF RADIATIVE TRANSFER IN PARTICIPATING MEDIA 5u⊥ ds dQ2 -ds+---- 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

煤量烧圆家重点实验宝 The fraction D(S, S)dQ/4 T is scattered into the cone de around the direction s dn-scattering phase function The amount of energy flux from dQ2, scattered into dQ2 an1(42d14:g2 4兀 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 The fraction  (s ˆ i ,s ˆ)d / 4 is scatteried into the cone d around the direction s η - scattering phase function The amount of energy flux from di scattered into d ( ) ( )    d d s s I s dAd d ds i s i i       4 ˆ , ˆ ˆ

煤烧圆家重点实验宝 The energy flux scattered into the direction s from all Incoming direction Si I(s.MAc2dndsΦ(s n/sca (sdAdQdn 4 sn n n。214x or dI,(s) snL I,(S, ) P(S, S)s2 (6-10 sca 4丌J4z Which is valid anywhere inside an arbitrary volume 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 The energy flux scattered into the direction s from all incoming direction si ( ) ( ) ( ) ( )          4 ˆ ˆ ˆ , ˆ 4   =    d dI s dAd d I s dAd d ds s s s i i i sca or ( ) ( ) ( ) ( ) i i i s sca dI s = ds  I s  s s d       4 ˆ ˆ , ˆ 4 ˆ (6-10) Which is valid anywhere inside an arbitrary volume