k fit in Park Model

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: