《燃烧流体力学》（英文版）Chapter 4 Gas- Solid Two-Phase Flow

煤烧圆家重点实验宝 Chapter 4 Gas-Solid Two-Phase Flow Examples: pulverized coal dust as 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 4 Gas - Solid Two-Phase Flow Examples: pulverized coal soot dust ash

煤烧圆家重点实验宝 8 1 Characteristics of GaS-solid Two Phase Flow RoSin-Pammler formula K4)=c×1 (4-1) R(dk)-weight percent of particle with d > dk n-index of non-evenness d- characteristic diameter dR exp 4-2) 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 Characteristics of Gas-solid Two Phase Flow Rosin-Pammler Formula ( )  ( )  n R dk = exp − dk / d (4-1) R(dk ) - weight percent of particle with d > dk n - index of non-evenness d - characteristic diameter ( ) ( )  ( )  n k n n k k d d d d n d d dR exp / ( ) ( 1) = − − (4-2)

煤烧圆家重点实验宝 Particle average dimension radii average dlo=∑nkdkΣn 4-3) area average d20=(∑nkdk2△>nk)12(4-4) volume average d30=(2nkd /2nk)3(4-5) Sauter average d32=Enk dk/(2nydk2)(4-6 Typical particle size coal in fluidized beds 0-10 mm pulverized coal 1-100um National Lab, of Coal Combustion. HUST 1-10um 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 Particle average dimension: radii average d10 = Snkdk /Snk (4-3) area average d20 = (Snkdk 2 /Snk ) 1/2 (4-4) volume average d30 = (Snkdk 3 /Snk ) 1/3 (4-5) Sauter average d32 = Snkdk 3 /(Snkdk 2 ) (4-6) Typical particle size: coal in fluidized beds 0 - 10 mm pulverized coal 1 - 100mm soot 1 - 10 mm

煤量甏圆家重点实验宝 2. Density Pm -combined density, Pm= Mm/Vm=(M+ Me)/V pr- superficial density of fluid, Pf=M/v Po, Pk -superficial density of particle, P,=M/V Pp-real density of particle relation +n=P+∑=p1+②∑nml/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 2. Density rm - combined density, rm = Mm/Vm = (Mp + Mf )/Vm rf - superficial density of fluid, rf = Mf /Vm rp , rk - superficial density of particle, rp = Mp / Vm rp - real density of particle relation: = + = + = + ( ) m f p f k f k k p r r r r r r n d / 6 r 3 (4-7)

煤量甏圆家重点实验宝 3. Concentration Volume concentration P (4-8) Mass concentration M+M P M 4-9) 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 3. Concentration Volume concentration f p v f p p v V V C V V V C = + = (4-8) Mass concentration f p w f p p w M M C M M M C = + = (4-9)

煤烧圆家重点实验宝 In general P C<C In pulverized coal transportation Cm≈05C=103 (4-10) E=0.26=0.38 mn ran 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 general, v w m p C  C  r  r In pulverized coal transportation 0.26, 0.38 1 0.5, 10 min 3 = = = = −  = − ran v m f w v C V V C C    (4-10)

煤烧圆家重点实验宝 4. Viscosity A. Einstein n1+2.5C When Cv is not high 1+25C C=10-20%. F Guth 1+2.5C.+14.1C2 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 4. Viscosity A. Einstein: 2 (1 ) 1 2.5 v v f m C C − + = m m (4-11) When Cv is not high v f m =1+ 2.5C m m Cv = 10 -20%, F. Guth 2 1 2.5 v 14.1 v f m = + C + C m m

煤量甏圆家重点实验宝 C>20%.DG. Thomas lm =1+2.5C.+1005C2+0.0275e 166C 5. Specific heat and conductivity Cm=CC+C(1-C pm pp M m) (4-20) c Cy C+Cx(1-Cw) F. J. Wasp 2C p100p (4-21) 2x+n+10(x-p) 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 Cv >20%, D. G. Thomas, Cv v v f m C C e 2 1 6.6 =1+ 2.5 +10.05 + 0.0275 m m 5. Specific heat and conductivity (1 ) (1 ) cm vp w vf w pm pp w pf w C C C C C C C C C C = + − = + − (4-20) F. J. Wasp             + + − + − − = ) ( 100 2 ( ) 100 2 2 f p v f p f p v f p m f C C           (4-21)

煤量甏圆家重点实验宝 6. Heat and Mass Transfer Ranz- Marshell N=2+0.6Re5Pr03 sh=2+06Re503(4-2) 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 6. Heat and Mass Transfer Ranz- Marshell: 0.5 0.33 0.5 0.33 2 0.6Re 2 0.6Re Pr Sh Sc Nu p p = + = + (4-22)

煤量烧圆家重点实验宝 82 Forces Acted on Particles 1. Friction 2pdpv P (4-23) Stokes,Cd=(1+Re23).24Re(11000(4-25) where Re =v-vid/v when T>tf, v=(1/3)Vp +(2/3)Vf (4-26) when mass of particles change Cd=doiN(1+byB In(1+B)=m /(d NuDpe National lab. of coal combustion -27 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. Forces Acted on Particles 1. Friction ( ) r p d p p F = r C r v − v v − v  2 2 (4-23) Stokes, Cd = (1 + Rep 2/3).24/Rep (1 1000) (4-25) where Rep = v - vp dp / n when Tp > Tf , n = (1/3)np +(2/3)nf (4-26) when mass of particles change, Cd = Cd0ln(1 + B)/B ln(1 + B) = m / (dpNuDrf ) (4-27)