! Toolbox to build a composite turbulent velocity profile ! out of interpolations of the universal law of the wall ! and of the particular laws of the wake of various parallel geometries. ! Ref.: P. Luchini, Eur. J. Mech. B/Fluids 71, 15-34 (2018). ! Ref.: P. Luchini, arXiv preprint arXiv:2310.11542 submitted to the Journal of Fluid Mechanics (2023). ! The wake functions exhibit a linear leading term with coefficient 0, 1, 2 ! which equals the dimensionless pressure gradient, ! in accordance with P. Luchini, Phys. Rev. Letters 118, 224501 (2017). ! ! TurbMeanFlow.cpl -- Copyright 2018-2023 Paolo Luchini ! http://CPLcode.net/Applications/FluidMechanics/TurbMeanFlow !( Permission is hereby granted, free of charge, to use and copy this software provided the above comments and citations are kept intact. !) REAL FUNCTION wall(REAL z)=LOG(z+3.109)/0.392+4.48-(7.3736+(0.4930-0.02450∗z)∗z)/(1+(0.05736+0.01101∗z)∗z)∗EXP(-0.03385∗z) ! Law of the wall REAL FUNCTION cwake(REAL Z)=(Z-0.5)/(EXP(-25∗(Z-0.5))-1) ! planar Couette wake function REAL FUNCTION dwake(REAL Z)=Z-0.57∗Z^7 ! planar duct wake function REAL FUNCTION pwake(REAL Z)=2∗Z-0.67∗Z^7 ! cylindrical pipe wake function REAL FUNCTION ocwake(REAL Z)=Z-0.71∗Z^3 ! open channel wake function ! Friction laws. ! 2018 coefficients from Sec. 6 of P. Luchini, Eur. J. Mech. B/Fluids 71, 15-34 ! with Colebrook (1939) correction for relative roughness=k/D REAL FUNCTION planeductfriction(REAL Retau)=8/[2.55∗LOG(Retau)+2.36]^2 REAL FUNCTION pipefriction(REAL Retau)=8/[2.55∗LOG(Retau)+1.3]^2 REAL FUNCTION Prandtlpipefriction(REAL Retau)={2/LOG(10)∗LOG[SQRT(32)∗Retau]-0.8}^-2 REAL FUNCTION Moody[REAL Re,roughness; OPTIONAL REAL FUNCTION(REAL) friction=pipefriction] RESULT=0.02 DO RESULT=friction{1/[SQRT(32/RESULT)/Re+roughness/1.64]} FOR 5 TIMES END Moody !( ! Example: plot pipe velocity profile in plus units at Retau=1000 USE gnuplot USE TurbMeanFlow Retau=1000 plot [0:Retau] wall(x)+pwake(x/Retau) with lines !) !( ! Example: draw Moody's chart USE gnuplot USE TurbMeanFlow set logscale xy set grid plot [1000:1E6] Moody(logx,0) w l, Moody(logx,0.001) w l, Moody(logx,0.002) w l, Moody(logx,0.005) w l, Moody(logx,0.01) w l, Moody(logx,0.02) w l, Moody(logx,0.05) w l !)