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1 #!/usr/bin/env python3

2 # Desc: Humidity conversion functions from EVA-2020-02-2

3 # Ref/Attrib: https://gitlab.com/baltakatei/ninfacyzga-01

 def rel_to_abs(T,P,RH):

6 """Returns absolute humidity given relative humidity.

8 Inputs:

9 --------

10 T : float

11 Absolute temperature in units Kelvin (K).

12 P : float

13 Total pressure in units Pascals (Pa).

14 RH : float

15 Relative humidity in units percent (%).

17 Output:

18 --------

19 absolute_humidity : float

20 Absolute humidity in units [kg water vapor / kg dry air].

22 References:

23 --------

24 1. Sonntag, D. "Advancements in the field of hygrometry". 1994. https://doi.org/10.1127/metz/3/1994/51

25 2. Green, D. "Perry's Chemical Engineers' Handbook" (8th Edition). Page "12-4". McGraw-Hill Professional Publishing. 2007.

27 Version: 0.0.1

28 Author: Steven Baltakatei Sandoval

29 License: GPLv3+

30 """

32 import math;

34 # Check input types

35 T = float(T);

36 P = float(P);

37 RH = float(RH);

39 #debug

40 # print('DEBUG:Input Temperature (K) :' + str(T));

41 # print('DEBUG:Input Pressure (Pa) :' + str(P));

42 # print('DEBUG:Input Rel. Humidity (%) :' + str(RH));

44 # Set constants and initial conversions

45 epsilon = 0.62198 # (molar mass of water vapor) / (molar mass of dry air)

     t = T - 273.15; # Celsius from Kelvin

     P_hpa = P / 100; # hectoPascals (hPa) from Pascals (Pa)

49 # Calculate e_w(T), saturation vapor pressure of water in a pure phase, in Pascals

     ln_e_w = -6096*T**-1 + 21.2409642 - 2.711193*10**-2*T + 1.673952*10**-5*T**2 + 2.433502*math.log(T); # Sonntag-1994 eq 7; e_w in Pascals

     e_w = math.exp(ln_e_w);

     e_w_hpa = e_w / 100; # also save e_w in hectoPascals (hPa)

53 # print('DEBUG:ln_e_w:' + str(ln_e_w)); # debug

54 # print('DEBUG:e_w:' + str(e_w)); # debug

56 # Calculate f_w(P,T), enhancement factor for water

     f_w = 1 + (10**-4*e_w_hpa)/(273 + t)*(((38 + 173*math.exp(-t/43))*(1 - (e_w_hpa / P_hpa))) + ((6.39 + 4.28*math.exp(-t / 107))*((P_hpa / e_w_hpa) - 1))); # Sonntag-1994 eq 22.

58 # print('DEBUG:f_w:' + str(f_w)); # debug

60 # Calculate e_prime_w(P,T), saturation vapor pressure of water in air-water mixture, in Pascals

61 e_prime_w = f_w * e_w; # Sonntag-1994 eq 18

62 # print('DEBUG:e_prime_w:' + str(e_prime_w)); # debug

64 # Calculate e_prime, vapor pressure of water in air, in Pascals

     e_prime = (RH / 100) * e_prime_w;

66 # print('DEBUG:e_prime:' + str(e_prime)); # debug

68 # Calculate r, the absolute humidity, in [kg water vapor / kg dry air]

     r = (epsilon * e_prime) / (P - e_prime);

70 # print('DEBUG:r:' + str(r)); # debug

72 return float(r);

 def rel_to_dpt(T,P,RH):

75 """Returns dew point temperature given relative humidity.

77 Inputs:

78 --------

79 T : float

80 Absolute temperature in units Kelvin (K).

81 P : float

82 Total pressure in units Pascals (Pa).

83 RH : float

84 Relative humidity in units percent (%).

86 Output:

87 --------

88 T_d : float

89 Dew point temperature in units Kelvin (K).

91 References:

92 --------

93 1. Sonntag, D. "Advancements in the field of hygrometry". 1994. https://doi.org/10.1127/metz/3/1994/51

94 2. Green, D. "Perry's Chemical Engineers' Handbook" (8th Edition). Page "12-4". McGraw-Hill Professional Publishing. 2007.

96 Version: 0.0.1

97 Author: Steven Baltakatei Sandoval

98 License: GPLv3+

99 """

100

101 import math;

102

103 # Check input types

104 T = float(T);

105 P = float(P);

106 RH = float(RH);

107

108 #debug

109 # print('DEBUG:Input Temperature (K) :' + str(T));

110 # print('DEBUG:Input Pressure (Pa) :' + str(P));

111 # print('DEBUG:Input Rel. Humidity (%) :' + str(RH));

112

113 # Set constants and initial conversions

114 epsilon = 0.62198 # (molar mass of water vapor) / (molar mass of dry air)

     t = T - 273.15; # Celsius from Kelvin

     P_hpa = P / 100; # hectoPascals (hPa) from Pascals (Pa)

117

118 # Calculate e_w(T), saturation vapor pressure of water in a pure phase, in Pascals

     ln_e_w = -6096*T**-1 + 21.2409642 - 2.711193*10**-2*T + 1.673952*10**-5*T**2 + 2.433502*math.log(T); # Sonntag-1994 eq 7; e_w in Pascals

     e_w = math.exp(ln_e_w);

     e_w_hpa = e_w / 100; # also save e_w in hectoPascals (hPa)

122 # print('DEBUG:ln_e_w:' + str(ln_e_w)); # debug

123 # print('DEBUG:e_w:' + str(e_w)); # debug

124

125 # Calculate f_w(P,T), enhancement factor for water

     f_w = 1 + (10**-4*e_w_hpa)/(273 + t)*(((38 + 173*math.exp(-t/43))*(1 - (e_w_hpa / P_hpa))) + ((6.39 + 4.28*math.exp(-t / 107))*((P_hpa / e_w_hpa) - 1))); # Sonntag-1994 eq 22.

127 # print('DEBUG:f_w:' + str(f_w)); # debug

128

129 # Calculate e_prime_w(P,T), saturation vapor pressure of water in air-water mixture, in Pascals

130 e_prime_w = f_w * e_w; # Sonntag-1994 eq 18

131 # print('DEBUG:e_prime_w:' + str(e_prime_w)); # debug

132

133 # Calculate e_prime, vapor pressure of water in air, in Pascals

     e_prime = (RH / 100) * e_prime_w;

135 # print('DEBUG:e_prime:' + str(e_prime)); # debug

136

     n = 0; repeat_flag = True;

138 while repeat_flag == True:

139 # print('DEBUG:n:' + str(n)); # debug

140

141 # Calculate f_w_td, the enhancement factor for water at dew point temperature.

142 if n == 0:

             f = 1.0016 + 3.15*10**-6*P_hpa - (0.074 / P_hpa); # Sonntag-1994 eq 24

144 f_w_td = f; # initial approximation

145 elif n > 0:

             t_d_prev = float(t_d); # save previous t_d value for later comparison

             f_w_td = 1 + (10**-4*e_w_hpa)/(273 + t_d)*(((38 + 173*math.exp(-t_d/43))*(1 - (e_w_hpa / P_hpa))) + ((6.39 + 4.28*math.exp(-t_d / 107))*((P_hpa / e_w_hpa) - 1))); # Sonntag-1994 eq 22.

148 # print('DEBUG:f_w_td:' + str(f_w_td)); # debug

149

150 # Calculate e, the vapor pressure of water in the pure phase, in Pascals

151 e = (e_prime / f_w_td); # Sonntag-1994 eq 9 and 20

152 # print('DEBUG:e:' + str(e)); # debug

153

154 # Calculate y, an intermediate dew point calculation variable

         y = math.log(e / 611.213);

156 # print('DEBUG:y:' + str(y)); # debug

157

158 # Calculate t_d, the dew point temperature in degrees Celsius

         t_d = 13.715*y + 8.4262*10**-1*y**2 + 1.9048*10**-2*y**3 + 7.8158*10**-3*y**4;# Sonntag-1994 eq 10

160 # print('DEBUG:t_d:' + str(t_d)); # debug

161

162 if n == 0:

163 # First run

164 repeat_flag = True;

165 else:

166 # Test t_d accuracy

             t_d_diff = math.fabs(t_d - t_d_prev);

168 # print('DEBUG:t_d :' + str(t_d)); # debug

169 # print('DEBUG:t_d_prev:' + str(t_d_prev)); # debug

170 # print('DEBUG:t_d_diff:' + str(t_d_diff)); # debug

171 if t_d_diff < 0.01:

172 repeat_flag = False;

173 else:

174 repeat_flag = True;

175

176 # Calculate T_d, the dew point temperature in Kelvin

177 T_d = 273.15 + t_d;

178 # print('DEBUG:T_d:' + str(T_d)); # debug

179

180 if n > 100:

181 return T_d; # good enough

182

183 # update loop counter

184 n += 1;

185 return T_d;