Wood humidity

wood.py

#!/usr/bin/env python
# coding: utf-8


import numpy as np
from scipy import constants, optimize
import matplotlib.pyplot as plt


plt.rcParams.update({'figure.autolayout': True})
def switch_mpl_style(latex=True):
    import matplotlib
    if latex:
        plt.rcParams['figure.figsize'] = (7 * 1.61, 7)
        matplotlib.rcParams['text.usetex'] = True

        plt.rc('axes', labelsize=22)    # fontsize of the x and y labels
        plt.rc('xtick', labelsize=20)   # fontsize of the tick labels
        plt.rc('ytick', labelsize=20)   # fontsize of the tick labels
        plt.rc('legend', fontsize=15)   # legend fontsize
    else:
        matplotlib.rcParams['text.usetex'] = False
        plt.rc('axes', labelsize=10)    # fontsize of the x and y labels
        plt.rc('xtick', labelsize=10)   # fontsize of the tick labels
        plt.rc('ytick', labelsize=10)   # fontsize of the tick labels
        plt.rc('legend', fontsize=10)   # legend fontsize



switch_mpl_style()


# $$ w_{eq} = \frac{1800}{W} (  \frac{K H}{1 - KH} + \frac{K_1 K H + 2 K_1K_2K^2 H^2}{1 + K_1 K H + K_1K_2K^2H^2}   ) $$
# 
# 
# * $w_{eq}$ teneur en eau %
# * $H$ : humidité relative de l'air
# * T : temperature en °C
# * $W = 349 + 1.29T + 0.0135T^2$
# * $K = 0.805 + 0.000736T - 0.00000273T^2$
# * $K_1 = 6.27 - 0.00938 T -  0.000303 T^2$
# * $K_2 = 1.91 + 0.0407 T - 0.000293 T^2$






def get_weq(T, humidity):
    Tf = constants.convert_temperature(T, 'C', 'F')
    
    W = 330 + 0.452 * Tf + 0.00415 * Tf**2
    K = 0.791 + 0.000463 * Tf - 0.000000844 * Tf**2
    K_1 = 6.34 + 0.000775 * Tf - 0.0000935 * Tf**2
    K_2 = 1.09 + 0.0284 * Tf - 0.0000904 * Tf**2

    
    term_1 = K * humidity / (1 - K * humidity)
    term_2 = K_1 * K * humidity + 2 * K_1 * K_2 * K**2 * humidity**2
    term_2 /= 1 + K_1 * K * humidity + K_1 * K_2 * K**2 * humidity**2
    
    weq = 1800 * (term_1 + term_2) / W
    
    return weq

RH = np.linspace(0, 100, 100)
temperatures = np.linspace(-10, 40, 3)

for T in temperatures:

    weq = get_weq(T, RH/100)
    plt.plot(RH, weq, label=f'$T={T}' + r'~^\circ {\rm C}$')

plt.xlabel(r'${\cal R}_{\rm H}~(\%)$')
plt.ylabel(r'$w_{\rm eq}~(\%)$')
plt.grid()
plt.legend()
plt.tight_layout()
plt.savefig('RH-0-100.pdf')




RH = np.linspace(30, 70, 100)
temperatures = np.linspace(10, 30, 3)

for T in temperatures:

    weq = get_weq(T, RH/100)
    plt.plot(RH, weq, label=f'$T={T}' + r'~^\circ {\rm C}$')

plt.xlabel(r'${\cal R}_{\rm H}~(\%)$')
plt.ylabel(r'$w_{\rm eq}~(\%)$')
plt.grid()
plt.legend()
plt.tight_layout()
plt.savefig('RH-30-70.pdf')