software: Gnuplot
input: area_averaged_axial_mean_velocity_TI_1.txt
# One Rotor, front, eldad blade # TSR 5, TI =15% #X/D X half width, Ux U Ux/U 0.5 0.23 0.275 0.363 0.6 0.605 1 0.46 0.93 0.353 0.6 0.588333333 2 0.92 0.316 0.383 0.6 0.638333333 3 1.38 0.334 0.41 0.6 0.683333333 4 1.84 0.349 0.441 0.6 0.735 5 2.3 0.365 0.462 0.6 0.77 6 2.76 0.379 0.48 0.6 0.8 7 3.22 0.39 0.497 0.6 0.828333333 8 3.68 0.405 0.509 0.6 0.848333333 9 4.14 0.42 0.52 0.6 0.866666667 10 4.6 0.431 0.529 0.6 0.881666667
gnuplot code
a = 0.6*(1-sqrt(1-0.7133))
d=0.46
f(x) = (0.6-a*d*d/((d+2*k*x)*(d+2*k*x)))/0.6
fit f(x) 'area_averaged_axial_mean_velocity_TI_1.txt' using 1:6 via k
# plotting
set terminal postscript eps font 24
set out 'k_fit_ti_1_tsr5.eps'
set autoscale
unset log
unset label
unset pm3d
set xtic auto
set ytic auto
unset grid
# set title 'Normalized velocity recover in the wake'
set xlabel "Normalized axial distance, X/D"
set xrange [*:12]
# r0 initial pulse
set yrange [0.5:1]
set ylabel "Normalized mean axial velocity, ~U{0.8-} / U{/Symbol \245}"
set style line 1 lt 1 lc rgb "black" lw 4 pt 1 ps 2
set style line 2 lt 2 lc rgb "black" lw 4 pt 3 ps 2
set style line 3 lt 3 lc rgb "black" lw 4 pt 5 ps 2
set style line 4 lt 4 lc rgb "black" lw 4 pt 7 ps 2
set style line 5 lt 5 lc rgb "black" lw 4
set style line 6 lt 6 lc rgb "brown" lw 4
k_value = sprintf("k = %.3f", k)
set label 1 at 1, 0.85 k_value
set key at graph 0.9, 0.3
set key spacing 1
plot 'area_averaged_axial_mean_velocity_TI_1.txt' using 1:6 ls 1 with points title 'RANS', f(x) lw 3 title "best fitted"
output:
