3d graph of control valve dynamic (flow vs pressure/valve travel)

surface3d_valve_flow.py

#!/usr/bin/env python3
# play with cv ( coefficient of flow) of control valve

from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from matplotlib import cm
import numpy as np

# some const (see http://www.idealvalve.com/pdf/Flow-Calculation-for-Gases.pdf)
SG = 0.554
T_DEG_C = 21.0
P_DOWNSTREAM = 44.0
VALVE_CV = 0.1

# convert °C to Rankine
deg_r = T_DEG_C * 1.8 + 32 + 459.67

# build data
x_ouv = np.linspace(0.0, 100.0, 1000)
y_p_upstream = np.linspace(50.0, 60.0, 1000)
x_ouv, y_p_upstream = np.meshgrid(x_ouv, y_p_upstream)

# sub critical flow (when: P up < 2 x P down)
z_qi = (962 * VALVE_CV * x_ouv) / np.sqrt((SG * deg_r) / (y_p_upstream ** 2 - P_DOWNSTREAM ** 2))

# plot surface
fig = plt.figure()
ax = fig.gca(projection='3d')
surf = ax.plot_surface(x_ouv, y_p_upstream, z_qi, cmap=cm.coolwarm, linewidth=0, antialiased=False)

# custom label for axis
ax.set_xlabel("Valve position (%)")
ax.set_ylabel("P upstream (barA)")
ax.set_zlabel("Q (Nm3/h)")

# add color bar
fig.colorbar(surf, shrink=0.5, aspect=5)

plt.show()