7 annex - upcommons

7 Annex

7.1 Single plume class (SinglePlume)

1

2

3

4 ””” Contains the S i n g l e Plume c l a s s . ”””

5 from sc ipy . opt imize import f s o l v e

6 import numpy as np

7 import matp lo t l i b . pyplot as p l t

8 from psychrochart . chart import PsychroChart

9 from sc ipy . i n t e g r a t e import ode int

10 from c o o l i t . Mate r i a l s import AirVapour

11 from c o o l i t . Plume import GovernEq

12

13 c l a s s SinglePlume ( ob j e c t ) :

14 ””” Contains the a t r i b u t e s and methods f o r the plume s o l u t i o n .

15

16 On i n i t i a l i z a t i o n , the ob j e c t c a l c u l a t e s i t s ob j e c t v a r i a b l e s immediately .

17

18 The ob j e c t v a r i a b l e s i n c lude :

19

20 Input v a r i a b l e s :

21

22 ∗ s e l f . zetamax Maximum length to

i n t e g r a t e (m)

23 ∗ s e l f . a lpha p The axisymmetric

entrainment c o e f f i c i e n t f o r a point−source plume

24 ∗ s e l f . i n t e r v a l s t e p s Number o f s t ep s o f

i n t e g r a t i o n f o r s i n g l e plume

25 ∗ s e l f . P amb Ambient p r e s su r e (Pa)

26 ∗ s e l f . temp amb Ambient temperature (C)

27 ∗ s e l f . re l amb humidity Ambient r e l a t i v e humidity

(%)

28 ∗ s e l f . temp source Source temperature (C)

55

29 ∗ s e l f . r e l h u m i d i t y s o u r c e Re la t i v e humidity at the

source (%)

30 ∗ s e l f . v e l o c i t y s o u r c e Stack e x i t v e l o c i t y (m/ s )

31 ∗ s e l f . a r e a sou r c e Stack e x i t area (mˆ2)

32 ∗ s e l f . s p e c mo i s tu r e s ou r c e Source s p e c i f i c l i q u i d

moisture (Kg/Kg)

33

34 I n i c i a l i z a t i o n o f v a r i a b l e s / f i r s t c a l c u l a t i o n s :

35

36 ∗ s e l f .Ma Air molar mass ( kg/mole )

37 ∗ s e l f .Mv Water vapor molar mass (

kg/mole )

38 ∗ s e l f . Cpa S p e c i f i c heat o f ( dry )

a i r at constant p r e s su r e ( kJ/kg K)

39 ∗ s e l f .R Gas constant f o r dry a i r

( J /(Kg∗K) )

40 ∗ s e l f . g Grav i t a t i ona l

a c c e l e r a t i o n (m/ s ˆ2)

41 ∗ s e l f . P r e s su r e s ou r c e Source ’ s p r e s su r e (Pa)

42 ∗ s e l f . vap pressure amb Ambient vapor p r e s su r e at

the source (Pa)

43 ∗ s e l f . spec amb humidity Ambient s p e c i f i c humidity

at the source

44 ∗ s e l f . v irtual temp amb Vi r tua l temperature o f

the ambient

45 ∗ s e l f . v ap p r e s su r e s ou r c e Source vapor p r e s su r e (Pa

)

46 ∗ s e l f . spec humid i ty source S p e c i f i c humidity

47 ∗ s e l f . Volume source Source ’ s volume f l u x (m

ˆ3/ s )

48 ∗ s e l f . Momentum source Source ’ s momentum f l u x (m

ˆ4/ s ˆ2)

49 ∗ s e l f . t e m p e x c e s s f l u x s o u r c e Source ’ s temperature

exce s s f l u x

50 ∗ s e l f . s p e c h u m i d i t y e x c e s s f l u x s o u r c e Source ’ s s p e c i f i c

humidity exce s s f l u x

56

51 ∗ s e l f . s p e c m o i s t u r e f l u x s o u r c e Source ’ s s p e c i f i c l i q u i d

moisture f l u x

52 ∗ s e l f . t o t a l m o i s t u r e f l u x s o u r c e Total moisture f l u x at

the source

53 ∗ s e l f . t o t a l s e n s h e a t f l u x s o u r c e Total s e n s i b l e heat f l u x

at the source

54

55

56 ”””

57

58 de f i n i t ( s e l f , zetamax , alpha p , i n t e r v a l s t e p s , P amb , temp amb ,

\

59 re l amb humidity , temp source , r e l humid i ty sou r c e ,

\

60 v e l o c i t y s o u r c e , a r ea source , sp e c mo i s tu r e s ou r c e ) :

61 r ”””

62 I n i t i a l i z e the c l a s s and s e t i t s pe r sona l v a r i a b l e s .

63

64 Does a l l the c a l c u l a t i o n s at once , so v a r i a b l e s are immediately usab le

.

65


67 ∗ s e l f . zetamax

68 ∗ s e l f . a lpha p

69 ∗ s e l f . i n t e r v a l s t e p s

70 ∗ s e l f . P amb

71 ∗ s e l f . temp amb

72 ∗ s e l f . re l amb humidity

73 ∗ s e l f . temp source

74 ∗ s e l f . r e l h u m i d i t y s o u r c e

75 ∗ s e l f . v e l o c i t y s o u r c e

76 ∗ s e l f . a r e a sou r c e

77 ∗ s e l f . s p e c mo i s tu r e s ou r c e

78

79 ∗ s e l f .Ma

80 ∗ s e l f .Mv

57

81 ∗ s e l f . Cpa

82 ∗ s e l f .R

83 ∗ s e l f . g

84 ∗ s e l f . P r e s su r e s ou r c e

85 ∗ s e l f . vap pressure amb

86 ∗ s e l f . spec amb humidity

87 ∗ s e l f . v irtual temp amb

88 ∗ s e l f . v ap p r e s su r e s ou r c e

89 ∗ s e l f . spec humid i ty source

90 ∗ s e l f . Volume source

91 ∗ s e l f . Momentum source

92 ∗ s e l f . t e m p e x c e s s f l u x s o u r c e

93 ∗ s e l f . s p e c h u m i d i t y e x c e s s f l u x s o u r c e

94 ∗ s e l f . s p e c m o i s t u r e f l u x s o u r c e

95 ∗ s e l f . t o t a l m o i s t u r e f l u x s o u r c e

96 ∗ s e l f . t o t a l s e n s h e a t f l u x s o u r c e

97

98 ”””

99 s e l f . zetamax = zetamax

100 s e l f . a lpha p = alpha p

101 s e l f . i n t e r v a l s t e p s = i n t e r v a l s t e p s

102 s e l f . P amb = P amb

103 s e l f . temp amb = temp amb

104 s e l f . re l amb humidity = rel amb humidity

105 s e l f . temp source = temp source

106 s e l f . r e l h u m i d i t y s o u r c e = r e l h u m i d i t y s o u r c e

107 s e l f . v e l o c i t y s o u r c e = v e l o c i t y s o u r c e

108 s e l f . a r e a sou r c e = ar ea sou r c e

109 s e l f . s p e c mo i s tu r e s ou r c e = spe c mo i s tu r e s ou r c e

110

111 s e l f .Ma = AirVapour ( temp source , temp source , P amb) .Ma

112 s e l f .Mv = AirVapour ( temp source , temp source , P amb) .Mv

113 s e l f . Cpa = AirVapour ( temp source , temp source ,

\

114 P amb) . s p e c i f i c h e a t [ 0 ] /1000

115 s e l f .R = AirVapour ( temp source , temp source , P amb) .R/ s e l f .Ma

58

116 s e l f . g = 9 .81

117 s e l f . P r e s su r e s ou r c e = P amb

118 s e l f . vap pressure amb = rel amb humidity ∗1e−2∗AirVapour ( temp amb ,

\

119 0 , 0) . s a t p r e s s u r e

120 s e l f . spec amb humidity = s e l f . vap pressure amb ∗ s e l f .Mv/( ( P amb−

\

121 s e l f . vap pressure amb ) ∗ s e l f .Ma

\

122 + s e l f . vap pressure amb ∗ s e l f .Mv)

123 s e l f . v irtual temp amb = s e l f . temp amb∗(1+0.608∗ s e l f . spec amb humidity )

124 s e l f . v ap p r e s su r e s ou r c e = r e l h u m i d i t y s o u r c e ∗1e−2∗

\

125 AirVapour ( temp source ,

\

126 temp source , P amb) . s a t p r e s s u r e

127 s e l f . spec humid i ty source = s e l f . v ap p r e s su r e s ou r c e ∗

\

128 s e l f .Mv/( ( s e l f . P r e s su r e s ou r c e −

\

129 s e l f . v ap p r e s su r e s ou r c e ) ∗ s e l f .Ma

\

130 + s e l f . v ap p r e s su r e s ou r c e ∗ s e l f .Mv)

131 s e l f . Volume source = v e l o c i t y s o u r c e ∗ a r ea sou r c e

132 s e l f . Momentum source = v e l o c i t y s o u r c e ∗∗2∗ a r ea sou r c e

133 s e l f . t e m p e x c e s s f l u x s o u r c e = ( temp source−temp amb ) ∗

\

134 s e l f . Volume source

135 s e l f . s p e c h u m i d i t y e x c e s s f l u x s o u r c e = ( s e l f . spec humid i ty source−

\

136 s e l f . spec amb humidity ) ∗

\


138 s e l f . s p e c m o i s t u r e f l u x s o u r c e = s e l f . s p e c mo i s tu r e s ou r c e ∗

\


59

140 s e l f . t o t a l m o i s t u r e f l u x s o u r c e=s e l f . s p e c h u m i d i t y e x c e s s f l u x s o u r c e

\

141 + s e l f . s p e c m o i s t u r e f l u x s o u r c e

142 s e l f . t o t a l s e n s h e a t f l u x s o u r c e = s e l f . t e m p e x c e s s f l u x s o u r c e

\

143 − AirVapour ( temp source , temp source , P amb) . l a t e n t h e a t /

\

144 s e l f . Cpa∗ s e l f . s p e c m o i s t u r e f l u x s o u r c e

145 s e l f . yy = [ s e l f . Volume source , s e l f . Momentum source ,

\

146 s e l f . P r e s su r e s ou r c e ]

147

148

149

150 de f s o l v e g o v e q ( s e l f ) :

151 ”””

152 Method that s o l v e s the governing equat ions ( volume , momentum and

153 pre s su r e ) and re tu rn s t h e i r va lue . The i n t e g r a t i o n i s c a r r i e d out by

154 ode int Python package from Scipy .

155

156 ”””

157 zetamin = 0 # I n i t i a l he ight (m)

158 i n i t = [ s e l f . Volume source , s e l f . Momentum source , s e l f . P r e s su r e s ou r c e

] # Source va lue s f o r odes in func t i on QM ICT Pressure Point

159 zeta span = np . l i n s p a c e ( zetamin , s e l f . zetamax , s e l f . i n t e r v a l s t e p s ) #

Range o f he ight va lue s

160 i n t e g r a t i o n = GovernEq ( s e l f . g , s e l f . alpha p , s e l f . Cpa , \

161 s e l f . t o t a l m o i s t u r e f l u x s o u r c e ,

\

162 s e l f . t o t a l s e n s h e a t f l u x s o u r c e , s e l f . temp amb ,

\

163 s e l f . spec amb humidity , s e l f .R,

\

164 s e l f . virtual temp amb , s e l f .Ma, s e l f .Mv, s e l f . yy )

165 QM = ode int ( i n t e g r a t i o n . govern eq , i n i t , z e ta span )

166 s e l f . z e ta = zeta span

60

167 s e l f . Volume = QM[ : , 0 ] # Volume f l u x o f the plume at d i f f e r e n t

e l e v a t i o n

168 s e l f .Momentum = QM[ : , 1 ] # Momentum f l u x o f the plume at d i f f e r e n t

e l e v a t i o n

169 s e l f . Pres sure = QM[ : , 2 ] # Ambient p r e s su r e ( which i s equal to the

p r e s su r e o f the plume at the same e l e v a t i o n )

170

171 re turn s e l f . Volume , s e l f .Momentum, s e l f . Pres sure

172

173

174 de f s o l v e v a r ( s e l f ) :

175 ”””

176 Method that c a l c u l a t e s a l l the v a r i a b l e s that c a r a c t e i z e s the plume

177 at the d i f f e r e n t he ight po in t s .

178

179 ”””

180

181 s e l f . Volume , s e l f .Momentum, s e l f . Pres sure = s e l f . s o l v e g o v e q ( )

182

183 # I n i z i a l i z e l i s t o f v a r i a b l e s a long the he ight ( ze ta )

184

185 TT = s e l f . t o t a l s e n s h e a t f l u x s o u r c e # Plume ’ s temperature exce s s

f l u x

186 s e l f . s p e c m o i s t u r e f l u x = np . z e ro s ( l en ( s e l f . z e ta ) ) # Plume ’ s s p e c i f i c

l i q u i d moisture f l u x

187 s e l f . s p e c humid i ty f l ux = np . z e r o s ( l en ( s e l f . z e ta ) ) # Plume ’ s s p e c i f i c

spec humid i ty f luxumid i ty f l u x

188 s e l f . plume temp = np . z e ro s ( l en ( s e l f . z e ta ) ) # Plume ’ s temperature (C)

189 s e l f . spec humidity = np . z e r o s ( l en ( s e l f . z e ta ) ) # Plume ’ s s p e c i f i c

humidity (Kg/Kg

190 s e l f . vap pre s sure = np . z e ro s ( l en ( s e l f . z e ta ) ) # Vapor p r e s su r e in the

plume (Pa)

191 s e l f . r e l humid i ty = np . z e ro s ( l en ( s e l f . z e ta ) ) # Re la t i v e humidity o f

the plume

192 # The r e s u l t s with vapour pressure wet bulb temp in s t ead o f

s a t p r e s s u r e change , high s e n s i b i l i t y to s a t p r e s s u r e

61

193

194 s e l f . spec mo i s ture = np . z e ro s ( l en ( s e l f . z e ta ) ) # The s p e c i f i c l i q u i d

moisture o f the plume

195 s e l f . dens i ty moi s t p lume = np . z e r o s ( l en ( s e l f . z e ta ) ) # The dens i ty o f

moist plume

196 s e l f . dens i ty amb a i r = np . z e r o s ( l en ( s e l f . z e ta ) ) # The dens i ty o f

ambient a i r

197 s e l f . abso lute humid i ty = np . z e ro s ( l en ( s e l f . z e ta ) ) # The humidity

r a t i o ( or abso lu t e humidity ) o f the plume

198 s e l f . humid i ty ra t i o = np . z e r o s ( l en ( s e l f . z e ta ) ) # This l i n e d e v i a t e s

from o r i g i n a l MATLAB CODE:

199 # In MATLAB code , y−ax i s o f psychometr ic chart i s s p e c i f i c humidy , but

the

200 # module in Python from MIT uses humidity r a t i o as the y−ax i s

201

202

203 f o r i in range (0 , l en ( s e l f . z e ta ) ) :

204 # Calcu la te v a r i a b l e s assuming there i s no condensat ion . T RH, to

see i f the re i s condensat ion

205 W = 0

206 s e l f . s p e c m o i s t u r e f l u x [ i ] = W

207 s e l f . s p e c humid i ty f l ux [ i ] = s e l f . t o t a l m o i s t u r e f l u x s o u r c e − W

208 s e l f . plume temp [ i ] = s e l f . temp amb + TT / s e l f . Volume [ i ]

209 s e l f . spec humidity [ i ] = s e l f . spec amb humidity +

\

210 s e l f . s p e c humid i ty f l ux [ i ] / s e l f . Volume [ i ]

211 s e l f . vap pre s sure [ i ] = s e l f . spec humidity [ i ] ∗

\

212 s e l f . Pres sure [ i ] / ( s e l f .Mv / s e l f .Ma

\

213 ∗ (1 − s e l f . spec humidity [ i ] ) +

\

214 s e l f . spec humidity [ i ] )

215 s e l f . r e l humid i ty [ i ] = s e l f . vap pre s sure [ i ] /

\

62

216 AirVapour ( s e l f . plume temp [ i ] , 0 ,

\

217 0) . s a t p r e s s u r e

218

219 i f s e l f . r e l humid i ty [ i ] >= 1 or s e l f . s p e c m o i s t u r e f l u x [ i ] > 1e

−10: # I f , a c tua l l y , the re i s condensat ion , modify the v a r i a b l e s ’ va lue

accord ing to that

220 s e l f . yy = np . array ( [ s e l f . Volume [ i ] , s e l f .Momentum[ i ] ,

\

221 s e l f . Pres sure [ i ] ] )

222 water = GovernEq ( s e l f . g , s e l f . alpha p , s e l f . Cpa , \

223 s e l f . t o t a l m o i s t u r e f l u x s o u r c e ,

\

224 s e l f . t o t a l s e n s h e a t f l u x s o u r c e , s e l f . temp amb ,

\

225 s e l f . spec amb humidity , s e l f .R,

\

226 s e l f . virtual temp amb , s e l f .Ma, s e l f .Mv, s e l f . yy )

227 W = f s o l v e ( water . condensat ion ,

\

228 s e l f . t o t a l m o i s t u r e f l u x s o u r c e /10)

229

230 s e l f . s p e c m o i s t u r e f l u x [ i ] = W

231 s e l f . s p e c humid i ty f l ux [ i ] = s e l f . t o t a l m o i s t u r e f l u x s o u r c e

\

232 − W

233 s e l f . plume temp [ i ] = ( s e l f . temp amb − 273 .15 +

\

234 s e l f . t o t a l s e n s h e a t f l u x s o u r c e /

\

235 s e l f . Volume [ i ]

\

236 + 597 .31∗4 .1868∗W/ s e l f . Volume [ i ] /

\

237 s e l f . Cpa) /(1 + 0 .57∗4 .1868∗W/

\

63

238 s e l f . Volume [ i ] / s e l f . Cpa) + 273.15

239 s e l f . spec humidity [ i ] = s e l f . spec amb humidity +

\

240 s e l f . s p e c humid i ty f l ux [ i ] /

\

241 s e l f . Volume [ i ]

242 s e l f . vap pre s sure [ i ] = s e l f . spec humidity [ i ] ∗

\

243 s e l f . Pres sure [ i ] / ( s e l f .Mv / s e l f .Ma

\

244 ∗ (1 − s e l f . spec humidity [ i ] ) +

\


246 s e l f . r e l humid i ty [ i ] = s e l f . vap pre s sure [ i ] /

\

247 AirVapour ( s e l f . plume temp [ i ] , 0 ,

\

248 0) . s a t p r e s s u r e

249

250 Pre s su r e s ou r c e = s e l f . Pres sure [ i ]

251 s e l f . spec mo i s ture [ i ] = s e l f . s p e c m o i s t u r e f l u x [ i ] / s e l f . Volume [ i ]

252 s e l f . dens i ty amb a i r [ i ] = Pre s su r e s ou r c e / s e l f .R/

\

253 s e l f . v irtual temp amb

254 s e l f . dens i ty moi s t p lume [ i ] = Pre s su r e s ou r c e / s e l f .R/

\

255 ( s e l f . plume temp [ i ] ) /(1+0.608∗

\

256 s e l f . spec humidity [ i ]

\

257 − s e l f . spec mo i s ture [ i ] )

258 s e l f . abso lute humid i ty [ i ] = s e l f . vap pre s sure [ i ] ∗ s e l f .Mv/

\

259 ( Pre s sure source−

\

260 s e l f . vap pre s sure [ i ] ) / s e l f .Ma

64

261 s e l f . humid i ty ra t i o [ i ] = s e l f . spec humidity [ i ]/(1−

\


263

264 re turn s e l f . r e l humid i ty , s e l f . s p e c mo i s tu r e f l ux ,

\

265 s e l f . spec humid i ty f lux , s e l f . plume temp ,

\

266 s e l f . spec humidity , s e l f . vap pressure , s e l f . humid i ty rat io ,

\

267 s e l f . spec mois ture , s e l f . dens i ty amb ai r ,

\

268 s e l f . dens i ty moist p lume , s e l f . abso lute humid i ty

269

270

271 de f p l o t r h ( s e l f ) :

272 ”””

273 Method that p l o t s the r e l a t i v e humidity in func t i on o f the he ight .

274

275 ”””

276 s e l f . r e l humid i ty , , , , , , , , , , = s e l f . s o l v e v a r ( )

277 # RH vs zeta

278 p l t . f i g u r e (1 )

279 p l t . p l o t ( s e l f . r e l humid i ty ∗100 , s e l f . zeta , ’ r−− ’ ,

\

280 l a b e l = ’ S i n g l e Plume ’ )

281 p l t . x l a b e l ( ”$RH p$” )

282 p l t . y l a b e l ( ’ z (m) ’ )

283 p l t . l egend ( )

284 p l t . show ( )

285

286 de f p l o t t d ( s e l f ) :

287 ”””

288 Method that p l o t s the temperature d i f f e r e n c e between the plume and

289 the ambient in func t i on o f the he ight .

290

65

291 ”””

292 , , , s e l f . plume temp , , , , , , , = s e l f . s o l v e v a r ( )

293 # ( t plume − t ambient ) vs ze ta

294 p l t . f i g u r e (2 )

295 p l t . p l o t ( s e l f . plume temp−s e l f . temp amb , s e l f . zeta , ’ r−− ’ ,

\


297 p l t . x l a b e l ( ” $t p$ − $ t a$ ( $ˆ\ c i rc$C ) ” )

298 p l t . y l a b e l ( ’ z (m) ’ )

299 p l t . l egend ( )

300 p l t . show ( )

301

302 de f p l o t h r ( s e l f ) :

303 ”””

304 Method that p l o t s the temperature o f the plume in func t i on o f

305 the humidity r a t i o .

306

307 ”””

308 , , , , , , s e l f . humid i ty rat io , , , , = s e l f . s o l v e v a r ( )

309 # HR vs zeta

310 p l t . f i g u r e (3 )

311 p l t . p l o t ( s e l f . plume temp , s e l f . humid i ty ra t i o ∗1000 , ’ r−− ’ ,

\


313 p l t . x l a b e l ( ” $t p$ (K) ” )

314 p l t . y l a b e l ( ”$HR p$” )

315 p l t . show ( )

316

317

318 de f p l o t p sych romet r i c ( s e l f ) :

319 ”””

320 Method that p l o t s the psychrometr ic chart o f the plume .

321

322 ”””

323

66

324 s e l f . r e l humid i ty , s e l f . s p e c mo i s tu r e f l ux , s e l f . spec humid i ty f lux ,

\

325 s e l f . plume temp , s e l f . spec humidity , s e l f . vap pressure ,

\

326 s e l f . humid i ty rat io , , , , = s e l f . s o l v e v a r ( )

327 p l t . f i g u r e (4 )

328

329 # Add the e l e v a t i o n s on the psychrometr ic chart and change

temperatures to C

330 zp = s e l f . zetamax/5

331 ip = np . z e r o s (5 )

332 f o r i in range (0 , l en ( s e l f . z e ta ) ) :

333 i f s e l f . z e ta [ i ] <= zp and s e l f . z e ta [ i +1] > zp :

334 ip [ 0 ] = i

335 e l i f s e l f . z e ta [ i ] <= zp∗2 and s e l f . z e ta [ i +1] > zp ∗2 :

336 ip [ 1 ] = i ;


338 ip [ 2 ] = i


340 ip [ 3 ] = i

341

342 s e l f . plume temp [ i ] = s e l f . plume temp [ i ] − 273 .15

343

344

345 ip [ 4 ] = l en ( s e l f . z e ta )

346 s t r 1 = s t r ( zp ) + ’ (m) ’

347 s t r 2 = s t r ( zp ∗2) + ’ (m) ’

348 s t r 3 = s t r ( zp ∗3) + ’ (m) ’

349 s t r 4 = s t r ( zp ∗4) + ’ (m) ’

350 s t r 5 = s t r ( zp ∗5) + ’ (m) ’

351

352 cus tom sty l e = {

353 ” l i m i t s ” : {

354

355 ” range temp c ” : [ 1 0 , 40 ] ,

356 ” range humid i ty g kg ” : [ 0 , 3 0 ] ,

67

357 ” pre s sure kpa ” : s e l f . Pres sure [ 0 ] / 1 0 0 0 ,

358 } ,

359 # ” s a t u ra t i o n ” : {” l i n ew id th ” : 10} , # i n c r e a s e s red l i n e

t h i c k n e s s

360 ” chart params ” : {

361 ” with zones ” : Fa l se # Removes Summer/Winter zones

362 }

363 }

364

365 axes = PsychroChart ( cus tom sty l e ) . p l o t ( ax=p l t . gca ( ) ) # ’ d e f a u l t ’ f o r

de fau l t , ’ ashrae ’ f o r b lack and white , ’ minimal ’ f o r minimal , ’ cu s tom sty l e

’ f o r custom l i m i t s

366 axes . t ex t (0 , 25 , ’ $P {amb}$ = %s (Pa) \ n$ t {amb}$ = %s (\ u2103 ) , $RH {

amb}$ = %s %% \ n$ t {0}$ = %s (\ u2103 ) , $RH 0$ = %s %%’ % ( s e l f . Pressure [ 0 ] ,

s e l f . temp amb − 273 .15 , s e l f . re l amb humidity , s e l f . temp source − 273 .15 ,

s e l f . r e l h u m i d i t y s o u r c e ) , f o n t s i z e =12)

367 axes . p l o t ( s e l f . plume temp , s e l f . humid i ty ra t i o ∗1000 , ’b− ’ , l a b e l = ’

S i n g l e Plume ’ )

368 axes . l egend ( )

369

370 axes . t ex t ( s e l f . plume temp [ i n t ( ip [0 ]−1) ] , s e l f . spec humidity [ i n t ( ip

[0 ]−1) ]∗1000 , s t r1 , ho r i zon ta l a l i gnment=’ r i g h t ’ , v e r t i c a l a l i g n m e n t=’ bottom ’ )









375

376 p l t . show ( )

377

378

379 de f f i nd condensa t i on ( s e l f ) :

380 ”””

68

381 Method that p r i n t s the i n t e r v a l o f he i gh t s where the re i s condensat ion

382 or , i f the re i s n ’ t condensat ion , the value and he ight where maximum

383 r e l a t i v e humidity i s achieved .

384

385 ”””

386 s e l f . r e l humid i ty , , , , , , , , , , = s e l f . s o l v e v a r ( )

387 RH max = max( s e l f . r e l humid i ty ) # Get the maximum r e l a t i v e humidity

with in the d i l u t i o n proce s s

388 i max = np . argmax ( s e l f . r e l humid i ty )

389 f lag RH = 0

390 EPS = 1e−6 # Margin e r r o r that s e t s when s t a r t s and f i n i s h e s

condensat ion

391 i f RH max >= 1 and s e l f . r e l humid i ty [−1] < 1 :

392 f o r i in range (0 , l en ( s e l f . r e l humid i ty ) ) :

393 i f abs ( s e l f . r e l humid i ty [ i ]−1) < EPS and flag RH == 0 :

394 zeta1 = s e l f . z e ta [ i ]

395 f lag RH = 1

396 i f abs ( s e l f . r e l humid i ty [ i ]−1) < EPS:

397 zeta2 = s e l f . z e ta [ i ]

398 re turn ’ Plume i s v i s i b l e between ’ + s t r ( round ( zeta1 , 2 ) ) + ’ (m)

and ’ + s t r ( round ( zeta2 , 2 ) ) + ’ (m) ( S i n g l e Plume) . ’ + ”\n\n”

399

400 e l s e :

401 re turn ’The maximum r e l a t i v e humidity i s ’ + s t r ( round (RH max , 2 )

∗100) + ’ % which i s reached at ’ + s t r ( round ( s e l f . z e ta [ i max ] , 2 ) ) + ’ (m)

( S i n g l e Plume) . ’ + ”\n\n”

Listing 1: SinglePlume.py

69

7.2 Governing equations class (GovernEq)

1

2

3

4 ””” Contains the Govern EQ c l a s s . ”””

5 from math import pi , s q r t

6 from sc ipy . opt imize import f s o l v e

7 from c o o l i t . Mate r i a l s import AirVapour

8

9 c l a s s GovernEq ( ob j e c t ) :

10 ”””

11 Contains the plume ’ s governing equt ions o f volume , momentum

12 and pre s su r e .

13

14 ”””

15

16 de f i n i t ( s e l f , g , alpha p , Cpa , t o t a l m o i s t u r e f l u x s o u r c e ,

\

17 t o t a l s e n s h e a t f l u x s o u r c e , temp amb , spec amb humidity ,

\

18 R, virtual temp amb , Ma, Mv, yy ) :

19 s e l f . g = g

20 s e l f . a lpha p = alpha p

21 s e l f . Cpa = Cpa

22 s e l f . t o t a l m o i s t u r e f l u x s o u r c e = t o t a l m o i s t u r e f l u x s o u r c e

23 s e l f . t o t a l s e n s h e a t f l u x s o u r c e = t o t a l s e n s h e a t f l u x s o u r c e

24 s e l f . temp amb = temp amb

25 s e l f . spec amb humidity = spec amb humidity

26 s e l f .R = R

27 s e l f . v irtual temp amb = virtual temp amb

28 s e l f .Ma = Ma

29 s e l f .Mv = Mv

30 s e l f . yy = yy

31

32

70

33 de f govern eq ( s e l f , Y, plume temp ) :

34 ”””

35 Function that eva lua t e s at each d i f f e r e n t i a l he igh ( zeta ) the

36 d i f f e r e n t a i l va lue s o f Volume , Momentum and Pressure , tak ing

37 i n t o account the e f f e c t s o f condensat ion ( s epa ra t ing wet and

38 dry plumes )

39

40 ”””

41 s e l f . yy = Y

42 y1 , y2 , y3 = Y # Var iab l e s o f the s o l u t i o n (Volume , Momentum,

Pressure )

43

44 # Calcu la te RH to see i f the re i s condensat ion

45 water content = 0

46 t emp exce s s f l ux = s e l f . t o t a l s e n s h e a t f l u x s o u r c e

47 spe c humid i ty f l ux = s e l f . t o t a l m o i s t u r e f l u x s o u r c e − water content

48 plume temp = s e l f . temp amb + temp exce s s f l ux / y1

49 spec humidity = s e l f . spec amb humidity + spec humid i ty f l ux /y1

50 vap pre s sure = spec humidity ∗ y3 / ( s e l f .Mv / s e l f .Ma ∗ (1 −

\

51 spec humidity ) + spec humidity )

52 r e l humid i ty = vap pre s sure / AirVapour ( plume temp , 0 , 0) . s a t p r e s s u r e

53

54 i f r e l humid i ty >= 1 or water content > 1e−10: # I f the re i s

condensat ion

55 water content = f s o l v e ( s e l f . condensat ion ,

56 s e l f . t o t a l m o i s t u r e f l u x s o u r c e /10) # Water

content because o f condensat ion

57 t p i = ( s e l f . temp amb − 273 .15 +

\

58 s e l f . t o t a l s e n s h e a t f l u x s o u r c e / y1 + 597.31 ∗ 4 .1868

\

59 ∗ water content / y1 / s e l f . Cpa) / (1 + 0.57 ∗ 4 .1868

\

60 ∗ water content / y1 / s e l f . Cpa) + 273.15

71

61 SHi = ( s e l f . t o t a l m o i s t u r e f l u x s o u r c e −

\

62 water content ) / y1 + s e l f . spec amb humidity

63 Tvi = t p i ∗ (1 + 0.608 ∗ SHi − water content / y1 )

64

65 e l s e : # I f the re i s NO condensat ion

66 SHi = s e l f . t o t a l m o i s t u r e f l u x s o u r c e /y1 +

\

67 s e l f . spec amb humidity

68 Tvi = ( s e l f . temp amb + s e l f . t o t a l s e n s h e a t f l u x s o u r c e /y1 ) ∗

\

69 (1 + 0.608∗ SHi − water content /y1 )

70

71 dy1dz = 2 ∗ s e l f . a lpha p ∗ s q r t ( p i ∗ y2 )

72 dy2dz = s e l f . g ∗ (1 − s e l f . v irtual temp amb / Tvi ) ∗ y1 ∗∗ 2 / y2

73 dy3dz = − s e l f . g ∗ y3 / s e l f .R / s e l f . v irtual temp amb

74

75 re turn [ dy1dz , dy2dz , dy3dz ]

76

77

78 de f condensat ion ( s e l f , water content ) :

79 ”””

80 Function that eva lua t e s the water content o f the plume

81

82 ”””

83 tp = ( s e l f . temp amb − 273 .15 + s e l f . t o t a l s e n s h e a t f l u x s o u r c e /

\

84 s e l f . yy [ 0 ] + 597.31 ∗ 4 .1868 \

85 ∗ water content / s e l f . yy [ 0 ] / s e l f . Cpa) / (1 + 0.57 ∗ 4 .1868

\

86 ∗ water content / s e l f . yy [ 0 ] / s e l f . Cpa) + 273.15

87 pl = AirVapour ( tp , 0 , 0)

88 SH sp = pl . s a t p r e s s u r e ∗ s e l f .Mv / ( ( s e l f . yy [ 2 ] −

\

89 pl . s a t p r e s s u r e ) ∗ s e l f .Ma + pl . s a t p r e s s u r e ∗ s e l f .Mv)

72

90 out = s e l f . t o t a l m o i s t u r e f l u x s o u r c e − ( SH sp −

\

91 s e l f . spec amb humidity ) ∗ s e l f . yy [ 0 ] − water content

92 re turn out

Listing 2: GovernEq.py

7.3 Air and vapour properties class (AirVapour)

1 # −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

2 #

3 # CoolIT : A c o o l i n g tower s imu la t i on and des ign so f tware

4 #

5 # Copyright (C) 2017 by Energy Systems Design Laboratory , Un ive r s i ty o f

Alberta

6 #

7 # This so f tware i s d i s t r i b u t e d under the MIT License .

8 # For more in format ion , s ee LICENSE. txt f i l e

9 #

10 # − Class : AirVapour

11 # − Desc r ip t i on : Contains f u n c t i o n s f o r the AirVapour Class .

12 # − Developers : J . Cook

13 #

14 # −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

15 ””” Contains the AirVapour c l a s s . ”””

16 import math

17

18

19 c l a s s AirVapour ( ob j e c t ) :

20 ””” Contains the f u n c t i o n s f o r the a i r vapour mixtures .

21

22 On i n i t i a l i z a t i o n , the ob j e c t c a l c u l a t e s i t s ob j e c t v a r i a b l e s immediately .

23


25 ∗ s e l f . l a t e n t h e a t o f e v a p o r a t i o n

73

26 ∗ s e l f . vapour pressure wet bulb temp

27 ∗ s e l f . s a t p r e s s u r e

28 ∗ s e l f . humidity

29 ∗ s e l f . d ens i ty

30 ∗ s e l f . v i s c o s i t y

31 ∗ s e l f . s p e c i f i c h e a t

32 ∗ s e l f . l a t e n t h e a t

33 ∗ s e l f . enthalpy

34

35 ”””

36

37 de f i n i t ( s e l f , T wb , T av , P av ) :

38 r ”””

39 I n i t i a l i z e the c l a s s and s e t i t s pe r sona l v a r i a b l e s .

40

41 Does a l l the c a l c u l a t i o n s at once , so v a r i a b l e s are immediately usab le

.

42











53

54 ”””

55 s e l f . T wb = T wb

56 s e l f . T av = T av

57 s e l f . P av = P av

58

59 s e l f . l a t e n t h e a t o f e v a p o r a t i o n = 2501598.53344643

60 s e l f .Ma = 28.966 e−3 # Air molar mass ( kg/mole )

74

61 s e l f .Mv = 18.02 e−3 # Water vapor molar mass ( kg/mole )

62 s e l f .R = 8.3144598 # I d e a l gas constant ( J /( mole∗K) )

63 s e l f . s e t vapour pre s sure wet bu lb temp (T wb)

64 s e l f . s e t s a t p r e s s u r e (T wb)

65 s e l f . s e t humid i ty (T wb , T av , P av )

66 s e l f . s e t d e n s i t y (T wb , T av , P av )

67 s e l f . s e t v i s c o s i t y (T wb , T av , P av )

68 s e l f . s e t s p e c i f i c h e a t ( T av )

69 s e l f . s e t l a t e n t h e a t ( T av )

70 s e l f . s e t en tha lpy (T wb , T av , P av )

71

72 de f s t r ( s e l f ) :

73 ”””

74 The s t r i n g method f o r the c l a s s .

75

76 This w i l l p r i n t a l l the ob j e c t v a r i a b l e s in the c l a s s .

77



80 ∗ s e l f .Ma

81 ∗ s e l f .Mv

82 ∗ s e l f .R









91 ”””

92 strName = ”<%s in s t ance at %s>” % ( s e l f . c l a s s . name , id ( s e l f ) )

\

93 + ”\n”

94 strT wb = ”Wet bulb temperature : ”

\

75

95 + s t r ( s e l f . T wb)

\

96 + ”\n”

97 strT av = ” Air vapour temperature : ”

\

98 + s t r ( s e l f . T av )

\

99 + ”\n”

100 s t rP av = ” Pressure o f the a i r vapour : ”

\

101 + s t r ( s e l f . P av )

\

102 + ”\n”

103 strLatentHeat = ” Latent heat o f evaporat ion : ”

\

104 + s t r ( s e l f . l a t e n t h e a t o f e v a p o r a t i o n )

\

105 + ”\n”

106 strMa = ” Air molar mass : ”

\

107 + s t r ( s e l f .Ma)

\

108 + ”\n”

109 strMv = ”Water vapor molar mass : ”

\

110 + s t r ( s e l f .Mv)

\

111 + ”\n”

112 strR = ” I d e a l gas constant : ”

\

113 + s t r ( s e l f .R)

\

114 + ”\n”

115 strVapourPress = ”Vapour p r e s su r e at wet bulb temp : ”

\

76

116 + s t r ( s e l f . vapour pressure wet bulb temp )

\

117 + ”\n”

118 s t rSa tPr e s s = ” Saturat ion pr e s su r e : ”

\

119 + s t r ( s e l f . s a t p r e s s u r e )

\

120 + ”\n”

121 strHumidity = ”Humidity : ”

\

122 + s t r ( s e l f . humidity )

\

123 + ”\n”

124 s t rDens i ty = ” Density : ”

\

125 + s t r ( s e l f . d ens i ty )

\

126 + ”\n”

127 s t r V i s c o s i t y = ” V i s c o s i t y : ”

\

128 + s t r ( s e l f . v i s c o s i t y )

\

129 + ”\n”

130 s t r S p e c i f i c H e a t = ” S p e c i f i c Heat : ”

\

131 + s t r ( s e l f . s p e c i f i c h e a t )

\

132 + ”\n”

133 strLatentHeatVap = ” Latent heat o f vapo r i z a t i on : ”

\

134 + s t r ( s e l f . l a t e n t h e a t )

\

135 + ”\n”

136 strEnthalpy = ” Enthalpy : ”

\

77

137 + s t r ( s e l f . enthalpy )

\

138 + ”\n”

139 re turn strName + strT wb + strT av + strP av + strLatentHeat + strMa

\

140 + strMv + strR + strVapourPress + s t rSa tPr e s s + strHumidity

\

141 + st rDens i ty + s t r V i s c o s i t y + s t r S p e c i f i c H e a t + strLatentHeatVap

\

142 + strEnthalpy

143

144 de f k e l v i n t o c e l c i u s ( s e l f , T k ) :

145 r ”””

146 Convert from degree s ∗K∗ to degree s ∗C∗ .

147

148 Args :

149 T k ( f l o a t ) : Temperature in degree s K

150

151 Returns :

152 T c ( f l o a t ) : Temperature in degree s C

153

154 ”””

155 re turn T k − 273 .15

156

157 de f s e t vapour pre s sure wet bu lb temp ( s e l f , T wb) :

158 r ”””

159 Calcu la te and s e t the vapour p r e s su r e at wet bulb temperature .

160

161 Function uses the WMO, Goff method to f i n d the vapour p r e s su r e at wet

162 bulb temperature .

163

164 Args :

165 T wb ( f l o a t ) : Wet Bulb Temperature in degree s K.

166

167 . . math : : P {av , sa t } = 10ˆ z

168

78

169 | where

170

171 . . math : :

172 z = &10.79574(1−273.16/T {wb}) \\

173 &− 5 .028 ∗ l o g {10}( T {wb}/273 .16) \\

174 &+ 1.50475 ∗ 10 − 4(1−10ˆ{−8.2969 ∗ ( T {wb}/273.16−1) }) \\

175 &+ 0.42873 ∗ 10 − 3(10ˆ(+4.76955 ∗ (1 − 273.16/ T {wb}) ) − 1) \\

176 &+ 2.78614

177

178 | and : math : ‘ T {wb} ‘ i s the wet bulb temperature in degree s ∗K∗ .

179

180 ”””

181

182 z = 10.79574 ∗ (1 − 273 .16/(T wb+1e−14) ) \

183 − 5 .028 ∗ math . log10 (T wb/273 .16) \

184 + 1.50475 ∗ math . pow(10 , −4) \

185 ∗ (1 − math . pow(10 , −8.2969 ∗ (T wb / 273 .16 − 1) ) ) \

186 + 0.42873 ∗ math . pow(10 , −3) \

187 ∗ (math . pow(10 , 4 .76955 ∗ (1 − 273 .16 / (T wb+1e−14) ) ) − 1) \

188 + 2.78614

189

190 s e l f . vapour pressure wet bulb temp = math . pow(10 , z )

191

192

193 de f s e t s a t p r e s s u r e ( s e l f , T wb) :

194 r ”””

195 Calculateand s e t the s a t u r a t i o n pr e s su r e at a g iven T ( a l t e r n a t i v e

method to vapour pressure wet bulb temp )

196

197 Args :

198 T wb : Temperature in degree s K

199

200 Output :

201 P sv : Saturated pr e s su r e (Pa)

202

203 ”””

79

204 P sv = math . exp (−5.8002206 e3/T wb+1.3914993−4.8640239e−2∗T wb +

\

205 4.1764768 e−5∗(T wb∗∗2) − 1.4452093 e−8∗(T wb∗∗3) +

\

206 6.5459673∗math . l og (T wb) )

207 s e l f . s a t p r e s s u r e = P sv

208

209

210

211

212

213 de f se t humid i ty ( s e l f , T wb k , T av k , P av ) :

214 r ”””

215 Calcu la te and s e t the humidity r a t i o .

216

217 Args :

218 T wb k ( f l o a t ) : Wet Bulb Temperature in degree s K.

219 T av k ( f l o a t ) : Air Vapour Temperature in degree s K.

220 P av ( f l o a t ) : Pressure o f the a i r−vapour mixture in Pa .

221

222 Equations are from the 1997 ASHRAE HANDBOOK − FUNDAMENTALS,

223 SI Edit ion , Chapter 6 (26) and (35)

224

225 . . math : : w { sa t } = 0.62198 \ f r a c {P {v , sa t }}{P {av} − P {v , sa t }}

226

227 where : math : ‘ P {av } ‘ i s the t o t a l mixture p r e s su r e in Pa .

228

229 . . math : :

230

231 w = \ f r a c {(2501−2.381T {wb, c e l }) w { sa t }−(T {av , c e l}−T {wb, c e l }) }

232 {2501+1.805T {av , c e l }−4.186T {wb, c e l }}

233

234 where : math : ‘ T {av , c e l } ‘ i s temperature in degree s Ce l s ius , w i s

235 humidity ra t i o , and the s u b s c r i p t ∗wb∗ i n d i c a t e s wet bulb co n d i t i o n s .

236

237 ”””

80

238 T wb cel = s e l f . k e l v i n t o c e l c i u s ( T wb k )

239 T av ce l = s e l f . k e l v i n t o c e l c i u s ( T av k )

240

241 P v sat = s e l f . vapour pressure wet bulb temp

242

243 w sat = 0.62198 ∗ P v sat / ( P av − P v sat + 1e−14)

244 w = ((2501 − 2 .381 ∗ T wb cel ) ∗ w sat − ( T av ce l − T wb cel ) )

\

245 / (2501 + 1.805 ∗ T av ce l − 4 .186 ∗ T wb cel )

246

247 s e l f . humidity = w sat , w

248

249 de f s e t d e n s i t y ( s e l f , T wb , T av , P av ) :

250 r ”””

251 Calcu la te and s e t the dens i ty o f the a i r vapour mixture .

252

253 Args :

254 T wb ( f l o a t ) : Wet bulb temperature in K

255 T av ( f l o a t ) : Temperature o f the a i r−vapour mixture in degree s K

256 P av ( f l o a t ) : Pressure o f the a i r−vapour mixture in Pa

257

258 Equation i s

259

260 . . math : :

261

262 \ rho {av}=(1+w)(1−w/(w+0.62198) ) P {av }/(287 .1 T {av })

263

264 where : math : ‘\ rho {av } ‘ i s the moist a i r dens i ty in : math : ‘ kg/mˆ3 ‘ ,

265 w i s humidity ra t i o ,

266 P i s the t o t a l mixture p r e s su r e in ∗Pa∗ , and

267 T i s the temperature in degree s ∗K∗ .

268

269 ”””

270 w = s e l f . humidity [ 1 ]

271 s e l f . d ens i ty = (1 + w) \

272 ∗ (1 − w / (w + 0.62198 + 1e−14) ) ∗ P av / (287 . 1 ∗ T av + 1e−14)

81

273

274 de f s e t v i s c o s i t y ( s e l f , T wb , T av , P av ) :

275 r ”””

276 Calcu la te and s e t the v i s c o s i t y o f the a i r vapour mixture .

277

278 Args :

279 T wb ( f l o a t ) : Wet bulb temperature in ∗K∗

280 T av ( f l o a t ) : Temperature o f the a i r−vapour mixture in ∗K∗

281 P av ( f l o a t ) : Pressure o f the a i r−vapour mixture in ∗Pa∗

282

283 Equations used are

284

285 . . math : :

286

287 X a = 1/(1+1.608w)

288

289 . . math : :

290

291 X v = w/(w+0.622)

292

293 . . math : :

294

295 \mu {a} = 2.287973 ∗ 10ˆ{−6}+6.259793 ∗ 10ˆ{−8}T {av}−3.131956

296 ∗ 10ˆ{−11}T {av}ˆ2 + 8.15038 ∗ 10ˆ{−15}T {av}ˆ3

297

298 . . math : :

299

300 \mu {v} = 2.562435 ∗ 10ˆ{−6}+1.816683 ∗ 10ˆ{−8}T {av}+2.579066

301 ∗ 10ˆ{−11}T {av}ˆ2 − 1.067299 ∗ 10ˆ{−14}T {av}ˆ3

302

303 . . math : :

304

305 \mu {av} = ( X a\mu aM aˆ{0.5}+X v\mu vM v ˆ{0 .5} ) /( X a M aˆ{0 .5}

306 + X vM v ˆ{0 .5} )

307

308 where

82

309 : math : ‘ M a = 28.97 kg/mol ‘ ,

310 : math : ‘ M v = 18.016 kg/mol ‘ ,

311 : math : ‘ T {av } ‘ i s temperature in degree s K,

312 : math : ‘\mu‘ i s dynamic v i s c o s i t y in ∗kg/ms∗

313

314 ”””


316 M a = 28.97

317 M v = 18.016

318 X a = 1 / (1 + 1.608 ∗ w)

319 X v = w / (w + 0 .622 )

320

321 u a = 2.287973 ∗ math . pow(10 , −6) \

322 + 6.259793 ∗ math . pow(10 , −8) ∗ T av \

323 − 3.131956 ∗ math . pow(10 , −11) ∗ math . pow( T av , 2) \

324 + 8.150380 ∗ math . pow(10 , −15) ∗ math . pow( T av , 3)

325

326 u v = 2.562435 ∗ math . pow(10 , −6) \

327 + 1.816683 ∗ math . pow(10 , −8) ∗ T av \

328 + 2.579066 ∗ math . pow(10 , −11) ∗ math . pow( T av , 2) \

329 − 1.067299 ∗ math . pow(10 , −14) ∗ math . pow( T av , 3)

330

331 s e l f . v i s c o s i t y = ( X a ∗ u a ∗ math . pow(M a , 0 . 5 )

332 + X v ∗ u v ∗ math . pow(M v , 0 . 5 ) ) \

333 / ( X a ∗ math . pow(M a , 0 . 5 ) + X v ∗ math . pow(M v , 0 . 5 ) )

334

335 de f s e t s p e c i f i c h e a t ( s e l f , T) :

336 r ”””

337 Calcu la te and s e t the s p e c i f i c heats o f the a i r and the vapour .

338

339 Args :

340 T ( f l o a t ) : Temperature in degree s K

341


343

344 . . math : :

83

345

346 c {pa} = 1.045356∗10ˆ3 − 3.161783∗10ˆ{−1}

347 T 0+7.083814∗10ˆ{−4}T 0ˆ2+8.15038∗10ˆ{−15}T 0ˆ3

348

349 . . math : :

350

351 c {pv} = 1.3605∗10ˆ3 + 2.31334 T 0−2.46784∗10ˆ{−10}T 0ˆ5+5.91332

352 ∗ 10ˆ{−13}T 0ˆ6

353

354 | where

355 | : math : ‘ T 0 ‘ i s : math : ‘ (T+273.15) /2 ‘

356 ( where T i s temperature in degree s ∗K∗) ,

357 | : math : ‘ c p ‘ i s s p e c i f i c heat at constant p r e s su r e in ∗J/kgK∗ .

358

359 ”””

360 T 0 = (T + 273 .15) / 2

361

362 c pa = 1.045356 ∗ math . pow(10 , 3) \

363 − 3.161783 ∗ math . pow(10 , −1) ∗ T 0 \

364 + 7.083814 ∗ math . pow(10 , −4) ∗ math . pow( T 0 , 2) \

365 − 2.705209 ∗ math . pow(10 , −7) ∗ math . pow( T 0 , 3)

366

367 c pv = 1.36050 ∗ math . pow(10 , 3) \

368 + 2.31334 ∗ T 0 \

369 − 2.46784 ∗ math . pow(10 , −10) ∗ math . pow( T 0 , 5) \

370 + 5.91332 ∗ math . pow(10 , −13) ∗ math . pow( T 0 , 6)

371

372 s e l f . s p e c i f i c h e a t = c pa , c pv

373

374

375 de f s e t l a t e n t h e a t ( s e l f , T) :

376 r ”””

377 Calcu la te and s e t the l a t e n t heat at a g iven temperature (T > 0

378 degree s c e l s i u s ) .

379

380 Args :

84

381 T ( f l o a t ) : Temperature in degree s K

382

383 Equations used i s

384

385 . . math : :

386

387 l v = (597.31−0.57∗T) ∗4.1868

388

389 | where

390 | : math : ‘ lv ‘ i s Latent heat o f evaporat ion in ∗J/g∗ (T > 0

391 degree s c e l s i u s ) .

392

393 ”””

394 T ce l = s e l f . k e l v i n t o c e l c i u s (T)

395

396 l v = (597.31−0.57∗ T ce l ) ∗4.1868 \

397

398 s e l f . l a t e n t h e a t = lv

399

400

401 de f s e t en tha lpy ( s e l f , T wb , T av , P av ) :

402 r ”””

403 Calcu la te and s e t the enthalpy o f the a i r vapour mixture .

404

405 . . todo : :

406

407 Fin i sh Documentation ( d e f i n i t i o n o f v a r i a b l e s )

408

409 Args :

410 T wb ( f l o a t ) : Wet Bulb Temperature in degree s K.

411 T av ( f l o a t ) : Air Vapour Temperature in degree s K.

412 P av ( f l o a t ) : Pressure o f the a i r−vapour mixture in Pa .

413


415

416 . . math : :

85

417

418 i {av} = c {pa }(T−273.15) + w( i { fgwo} + c {pv}(T−273.15) )

419

420 | where

421 | : math : ‘ i {av } ‘ i s enthalpy o f the damp a i r in ∗J/kg∗ dry a i r ,

422 | : math : ‘ i { fgwo } ‘ i s l a t e n t heat o f evaporat ion o f water

423 at 273 .15 ∗K∗

424 | T i s temperature in degree s ∗K∗ ,

425 | : math : ’ c {pa } ’ and : math : ‘ c {pv} ‘ are the s p e c i f i c heats o f water

426 and a i r at constant p r e s su r e in : math : ’ J/kgK ’

427 | w i s the humidity o f the a i r vapour mix

428

429 ”””

430 c pa , c pv = s e l f . s p e c i f i c h e a t


432

433 s e l f . enthalpy = c pa ∗ ( T av − 273 .15)

\

434 + w ∗ ( s e l f . l a t e n t h e a t o f e v a p o r a t i o n + c pv ∗ ( T av − 273 .15) )

435

436

437 i f name == ” main ” :

438 pass

Listing 3: AirVapour.py

86

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