煤量甏圆家重点实验宝 Chapter 2 Turbulent Flow 8 1 Basic Concept of Turbulence 1. Classification wall turbulence- friction of wall free turbulence -interaction of fluid layers homogeneous turbulence ∫h isotropic turbulence 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 2 Turbulent Flow §1 Basic Concept of Turbulence 1. Classification wall turbulence - friction of wall free turbulence - interaction of fluid layers homogeneous turbulence isotropic turbulence
煤烧圆家重点实验宝 2. Turbulence average 1)time average 0 T→> 2-1) 2)space average ()=lim-(x,10)d 2-2) X→0 X 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. Turbulence average 1) time average → = = T T t x t dt T x 0 0 0 ( , ) 1 ( ) lim (2-1) 2) space average → = x x s x t dx x t 0 0 0 ( , ) 1 ( ) lim (2-2)
煤烧圆家重点实验宝 3)Probability density Function (x2)=「叭(x4)P()dp(2-3) 4)Reynolds average for turbulent quantity p 三-y whereφ— transient value φ— average value National Lab, of Coal Combustion. HUST pulsing value 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) Probability Density Function − e (x0 ,t 0 ) = (x0 ,t 0 )P()d 4) Reynolds average for turbulent quantity − ' where ⎯ transient value ⎯ average value ’⎯ pulsing value (2-4) (2-3)
煤量甏圆家重点实验宝 =(如-)=p-=025 Assume A=A+A' b=b+B A+b=A+a++b=atB AB=AB=0 AB=(A+A B+B)=AB+A'B OA OAOA aA + axax a 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 = ( − ) = − = 0 (2-5) Assume x A x A x A x A AB A A B B AB A B AB AB A B A A B B A B B B B A A A = + = = + + = + = = + = + + + = + = + = + ' ( ')( ') ' ' ' ' 0 ' ' '
煤烧圆家重点实验宝 In general,0+'an Correlation quantity of turbulence The above formulae indicate that the average of linear calculation of turbulent quantity equals linear calculation of corresponding average of turbulent values, the average of non-linear calculation of turbulent quantity equals the sum of non-linear calculation of corresponding average of turbulent values and pulsing correlation of these quantities 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, 0 ' B' A Correlation quantity of turbulence The above formulae indicate that the average of linear calculation of turbulent quantity equals linear calculation of corresponding average of turbulent values, the average of non-linear calculation of turbulent quantity equals the sum of non-linear calculation of corresponding average of turbulent values and pulsing correlation of these quantities