AHH Software (Mollier-hx-Diagram)

Design concerning Mollier and Carrier. Languages: Danish, Dutch, English, French, German, Italian, Russian.

Diagram range -100 < t < 300 °C and 0 < x < 1000 g/kg. Height -5000 < h < 15000 m or air pressure 0.1 < p < 16 bar.

150 locations for meteorological data. 3 different ranges of thermal comfort, process range, all processes with air humid.

1.32 kg/m3

1.30 kg/m3

1.28 kg/m3

1.26 kg/m3

1.24 kg/m3

1.22 kg/m3

1.20 kg/m3

1.18 kg/m3

1.16 kg/m3

1.14 kg/m3

20 kJ/kg

40 kJ/kg

Ent

halp

y

100%

50%

90%

80%

70%

60%

40% 30% 20% 15% 10% 5%

Re

l. h

um

idity

-0 g

/kg

2 g

/kg

4 g

/kg

6 g

/kg

8 g

/kg

10

g/k

g

12

g/k

g

14

g/k

g

16

g/k

g

18

g/k

g

Water

-12 °

-10 °

-8 °

-6 °

-4 °

-2 °

0 °

2 °

4 °

6 °

8 °

10 °

12 °

14 °

16 °

18 °

20 °

22 °

24 °

26 °

28 °

30 °

32 °

34 °

36 °

Te

mp

era

ture

1

1

2

3

4 5 5

6

7

Zeller Consulting Suisse, HVAC solutions, Jurastrasse 35, CH-3063 IttigenTelefon: +41 79 222 66 42, info@zcs.ch, www.zcs.ch

Process range

1) Winter: Sorption rotor2) Winter: Humidifier3) Winter: Heater4) Summer: Humidifier5) Summer: Sorption rotor6) Summer: Cooler7) Summer: Heater

Meteorological datafor Dusseldorfconcerning Meteonorm

Range of thermal comfortaccording to DIN 1946

Mollier-h-x-Diagram for air humid - Pressure 1.008 bar (45.000 m / 10.000 °C / 80.000 % rH)

Meteorological data Based on the software from www.meteonorm.com. Average values between 1995 to 2005. The following locations we deliver with the soft-ware AHH. Further 7000 locations worldwide one can generate with the software from www.meteonorm.com. With the software MDI one can select the service hours. Austria Height (m) Wet bulb (°C) Graz 424 24.4 Innsbruck 580 22.1 Klagenfurt 452 23.2 Linz 250 23.5 Salzburg 432 22.9 Villach 495 23.3 Wien 179 24.6 France Height (m) Wet bulb (°C) Lyon 299 23.1 Marseille 0 25.3 Nantes 27 23.6 Nice 5 24.8 Paris 42 24.2 Strasbourg 140 23.8 Toulouse 150 23.9 Germany Height (m) Wet bulb (°C)

Aachen 180 24.0 Augsburg 485 21.5 Berlin 44 24.3 Bielefeld 109 22.8 Bochum 100 23.8 Bonn 104 22.5 Braunschweig 88 22.5 Bremen 3 23.1 Chemnitz 406 21.9 Dortmund 80 23.8 Dresden 154 22.6 Duisburg 25 23.9 Düsseldorf 45 22.9 Essen 69 23.3 Frankfurt 125 23.5 Gelsenkirchen 75 24.0 Halle 90 23.3 Hamburg 1 22.7 Hannover 88 23.7 Karlsruhe 123 23.9 Kiel 22 22.3 Köln 61 23.2 Krefeld 48 23.9 Leipzig 143 24.4 Magdeburg 61 23.0 Mannheim 95 23.5 Mönchengladb. 75 23.1 München 536 21.9 Münster 59 22.7 Nürnberg 281 22.6 Stuttgart 297 23.0 Wiesbaden 119 22.1 Wuppertal 238 23.9 Italy Height (m) Wet bulb (°C) Bari 0 26.5 Bologna 158 25.8 Catania 3 28.3 Firenze 153 25.1 Genova 0 28.0 Milano 98 28.1 Napoli 0 27.4 Palermo 1 27.8 Roma 1 27.2 Torino 378 24.7 Venezia 1 27.0 Netherland Height (m) Wet bulb (°C) Almere 0 22.9 Amsterdam 0 23.6 Apeldoorn 21 23.9 Breda 7 23.1 Den Haag 0 23.6 Eindhoven 16 23.3 Enschede 46 23.4 Groningen 0 23.2 Haarlem 0 22.9 Nijmegen 30 23.7 Rotterdam 0 23.3 Tilburg 15 23.8 Utrecht 0 23.1

Switzerland Height (m) Wet bulb (°C) Aarau 385 22.4 Altdorf 459 23.0 Appenzell 780 21.0 Basel 270 23.8 Bellinzona 227 24.3 Bern 568 22.7 Biel 435 22.8 Chur 590 22.2 Delémont 431 23.4 Dietikon 385 23.1 Dübendorf 434 22.8 Emmen 427 23.0 Frauenfeld 411 23.2 Fribourg 588 22.6 Genève 379 22.1 Glarus 478 22.9 Hersiau 775 21.1 Jungfraujoch 580 4.5 Köniz 582 22.5 Kriens 499 22.4 Chaux-Fonds 994 20.1 Lancy 398 23.2 Lausanne 526 22.0 Liestal 322 24.1 Lugano 273 24.4 Luzern 436 22.6 Montreux 400 22.1 Neuchâtel 438 22.9 Sarnen 468 22.4 Schaffhausen 402 22.6 Schwyz 516 22.9 Sion 518 21.8 Solothurn 437 22.8 St.Gallen 670 21.7 Stans 457 23.1 Thun 562 22.4 Uster 464 22.8 Vernier 445 22.3 Winterthur 440 22.9 Yverdon 433 22.9 Zug 425 22.8 Zürich 413 22.5 Diverse Height (m) Wet bulb (°C) Ankara 872 22.8 Athinai 0 26.3 Beograd 200 25.8 Bratislava 144 24.5 Bruxelles 100 23.9 Bucuresti 79 25.9 Budapest 130 24.0 Dublin 0 19.1 Gibraltar 5 23.8 Helsinki 12 22.1 Kiev 108 23.3 Kobenhavn 19 22.2 Lisboa 0 24.4 Ljubljana 309 24.3 London 36 22.0 Luxembourg 380 22.1 Madrid 608 21.1 Minsk 214 23.2 Moskva 152 23.0 Nicosia 5 28.5 Oslo 154 20.8 Podgorica 198 27.5 Praha 256 23.0 Reykjavik 0 14.5 Riga 14 24.7 Sarajevo 841 21.5 Skopie 325 24.6 Sofia 573 23.1 Stockholm 15 22.5 Tallinn 40 22.8 Tirana 227 24.6 Vilnius 121 21.8 Warszawa 90 23.1 Zagreb 146 25.4

Mollier-hx-Diagram 1. Definition The Mollier-hx-diagram represents the air water mixture. It is in such a way developed that the 0 °C iso-therm is horizontal in the range of unsaturated air. The nebula isotherm of over saturated air by 0 °C go parallel to the enthalpy. On t = 0 °C and x = 0 kg/kg the enthalpy h = 0 J/kg, which leads to ranges with negative enthalpies. By exchange of the centerlines one receives the Carrier-xh-Diagram (Psychrometric chart) within the software AHH to be alternatively worked can. 2. Area Usually the Mollier-hx-Diagram is based on a pressure of 1.013 bar according to sea level and exhibits a range, which permits not all applications. The software AHH permits the desired range for each application and supports the good clarity because of each stretching of the axes of coordinates. Temperature -100 to 300 °C Absolute humidity 0 to 1000 g/kg Pressure absolute 0.1 to 16 bar Height -5000 to 15000 m 3. Thermodynamics In specialized books one usually finds the specific temperature-referred thermal capacity. This value points out, how much energy must be spent, in order to warm up the medium with appropriate temperature around 1°C. If one wants to know, which energy is needed, in order the medium of t1 to t2 to warm up, the means of the specific temperature-referred thermal capacity must be determined. Below the average val-ues were formed of 0 °C to t °C and combined into tables and approximation polynomials, which make a fast processing possible on computers. 3.1. Air, Water and Steam

𝑡 𝑐𝑝𝑙 𝑐𝑝𝑑 𝑝𝑑 ℎ𝑤 ℎ𝑑 𝑟 °C J/kgK J/kgK Pa J/kg J/kg J/kg -100 1007.20 1815.40 0.00160 -90 1006.90 1817.50 0.00933 -80 1006.63 1819.60 0.05333 -70 1006.40 1821.70 0.258 -60 1006.20 1823.80 1.076

-50 1006.07 1826.00 3.939

-40 1006.00 1828.10 12.870 -30 1005.97 1830.30 38.101 -20 1006.00 1832.50 103.450 -10 1006.08 1834.70 259.980

0 1006.18 1836.90 610.480 0 2500500 2500500 10 1006.31 1839.10 1230 42000 2518900 2476900 20 1006.45 1841.40 2340 83900 2537300 2453400 30 1006.60 1843.70 4240 125600 2555500 2429900 40 1006.81 1846.00 7370 167300 2573500 2406200 50 1007.03 1848.30 12300 209100 2591300 2382200 60 1007.30 1850.60 19900 250900 2608800 2357900 70 1007.60 1852.90 31100 292800 2625900 2333100 80 1007.90 1855.30 47300 334700 2642500 2307800 90 1008.30 1857.70 70100 376800 2658700 2281900 100 1008.70 1860.10 101300 418900 2674400 2255500 110 1009.00 1862.50 143300 461100 2689600 2228500 120 1009.50 1864.90 198500 503500 2704200 2200700 130 1009.90 1867.30 270100 546100 2718300 2172200 140 1010.30 1869.80 361400 588900 2731800 2142900 150 1010.80 1872.30 476000 631900 2744500 2112600 160 1011.30 1874.80 618000 675200 2756500 2081300 170 1011.80 1877.30 792000 718800 2767600 2048800 180 1012.40 1879.80 1002700 762700 2777600 2014900 190 1013.00 1882.40 1255200 807000 2786300 1979300 200 1013.60 1884.90 1555100 851800 2793700 1941900 210 1014.20 1887.50 1908000 897100 2799400 1902300 220 1014.80 1890.10 2320100 943000 2803400 1860400 230 1015.50 1892.70 2797900 989600 2805400 1815800 240 1016.20 1895.30 3348000 1036900 2805100 1768200 250 1016.90 1898.00 3978000 1085100 2802500 1717400 260 1017.60 1900.60 4694000 1134300 2797400 1663100 270 1018.40 1903.30 5505000 1184500 2789500 1605000 280 1019.20 1906.00 6419000 1236100 2778700 1542600 290 1020.10 1908.70 7445000 1289300 2764900 1475600 300 1021.00 1911.40 8592000 1344200 2748000 1403800

Richard Mollier (1863-1935)

W. H. Carrier (1876-1950)

Stable,

non saturatedhumid air

Non stable,

meta stable,over saturated

humid air

En

tha

lpy (

kJ/k

g)

Abs. hym

idity (g/kg)

0°CSeparation

0°C

rh = 100 %

𝑐𝑝 =∫ 𝑐𝑝𝑡𝑑𝑡

𝑡2

𝑡1

𝑡2−𝑡1

𝑡1 = 0

𝑡2 = 𝑡

𝑐𝑝 =∫ 𝑐𝑝𝑡𝑑𝑡

𝑡

0

𝑡

3.2. Approximation polynomials (-100 < t < 300 °C) Specific heat capacity of dry air (J/kgK)

𝑐𝑝𝑙 = (𝑎 + 𝑐𝑡 + 𝑒𝑡2) (1 + 𝑏𝑡 + 𝑑𝑡2 + 𝑓𝑡3)⁄

Specific capacity of water-steam (J/kgK)

𝑐𝑝𝑑 = (𝑎 + 𝑐𝑡) (1 + 𝑏𝑡 + 𝑑𝑡2)⁄

Pressure absolute of water-steam (Pa)

(−100 < 𝑡 ≤ 0°𝐶)

𝑙𝑛(𝑝𝑑) = (𝑎 + 𝑐𝑡 + 𝑒𝑡2) (1 + 𝑏𝑡 + 𝑑𝑡2 + 𝑓𝑡3)⁄

(0 > 𝑡 ≤ 300°𝐶)

𝑙𝑛(𝑝𝑑) = (𝑎 + 𝑐𝑡 + 𝑒𝑡2 + 𝑔𝑡3 + 𝑖𝑡4) (1 + 𝑏𝑡 + 𝑑𝑡2 + 𝑓𝑡3 + ℎ𝑡4)⁄ Enthalpy of water on Liquidus (J/kg)

ℎ𝑤 = (𝑎 + 𝑐𝑡 + 𝑒𝑡2) (1 + 𝑏𝑡 + 𝑑𝑡2 + 𝑓𝑡3)⁄ Enthalpy of water-steam on Solidus (J/kg)

ℎ𝑑 = (𝑎 + 𝑐𝑡 + 𝑒𝑡2 + 𝑔𝑡3 + 𝑖𝑡4) (1 + 𝑏𝑡 + 𝑑𝑡2 + 𝑓𝑡3 + ℎ𝑡4)⁄ Latent heat of vaporization of water-steam (J/kg)

𝑟 = ℎ𝑑 − ℎ𝑤 Enthalpy of water-steam on the area of wet steam (J/kg)

ℎ𝑑 = ℎ𝑤 + 𝑥𝑑𝑟 4. Equations for wet air The air pressure depends on the height, the temperature and the humidity. As basis for Mollier-hx-Diagram and Carrier-xh-Diagram the air pressure is to determine by the height, the middle yearly tempera-ture and the middle yearly humidity (average 80%). 4.1. Pressure absolute

𝑧 =𝑀𝑙𝑔𝐻

𝑅𝑇

1 + 𝑥

1 + 𝑥𝑀𝑙

𝑀𝑤

; 𝑝 = 1.01325𝑒−𝑧

4.2. Density humid

𝜌 =𝑀𝑙𝑝

𝑅𝑇

1 + 𝑥

1 + 𝑥𝑀𝑙

𝑀𝑤

4.3. Maximal absolute humidity and absolute humidity

𝑥𝑠 =𝑀𝑤

𝑀𝑙

𝑝𝑑

𝑝−𝑝𝑑 ; 𝑥 =

𝑀𝑤

𝑀𝑙

𝜑𝑝𝑑

𝑝−𝜑𝑝𝑑

4.4. Relative humidity

𝜑 = (𝑝𝑥𝑀𝑙

𝑀𝑤) [𝑝𝑑 (1 + 𝑥

𝑀𝑙

𝑀𝑤)]⁄

4.5. Enthalpy humid

ℎ = 𝑐𝑝𝑙𝑡 + 𝑥(𝑟0 + 𝑐𝑝𝑑𝑡)

a = 1.00617203411816E+03 b = -5.14584155927084E-04 c = -5.07744861271335E-01 d = -4.08693984761444E-06 e = -3.94830238325583E-03 f = 3.86998536082132E-10 a = 1.83690225155577E+03 b = 2.96850242760703E-04 c = 7.68576185706328E-01 d = -8.23605125618347E-08 a = 6.41424538282508E+00 b = 1.34952974449424E-02 c = 1.68771989526873E-01 d = 3.60425763984253E-05 e = 1.03764255356861E-03 f = -2.54470285416322E-09 a = 6.41425292688508E+00 b = -1.17398221741019E-02 c = -2.31391504282494E-03 d = 5.85324578180939E-05 e = -7.97076080224934E-04 f = 3.14129016158240E-07 g = 1.13870924045918E-05 h = -1.05815083120807E-09 i = -2.45705078974294E-08 a = 3.63051146855678E+00 b = -2.04547872985726E-03 c = 4.19231841629432E+03 d = -8.10031771231269E-07 e = -8.90297066641696E+00 f = 9.66233360384174E-10 a = 2.50049979241906E+06 b = -1.09042949248609E-02 c = -2.54218801181540E+04 d = 6.03477944019292E-05 e = 1.30688801015895E+02 f = -1.24219636812250E-07 g = -2.06485565012501E-01 h = 1.15773454895717E-10 i = 1.21390880909374E-04

Ml = 28.96 kg/kMol Mw = 18.02 kg/kMol g = 9.81 m/s2 r0 = 2500500 J/kg s0 = 333100 J/kg R = 8314.41 J/kMolK

4.6. Temperature of humid air

𝑡 =ℎ−𝑥𝑟0

𝑐𝑝𝑙+𝑥𝑐𝑝𝑑 ; 𝑇 = 273.16 + 𝑡

4.7. Mass flow dry, volume flow wet, capacity humid

�̇�𝑙 =�̇�𝑙𝜌

1+𝑥 ; 𝑉�̇� =

�̇�𝑙(1+𝑥)

𝜌 ; �̇� =

�̇�𝑙∆ℎ

3600

5. Direction of humidification For point A the direction of humidification go in the conventional Mollier-hx-Diagram, due to an edge yard-

stick, which has its origin in the coordinate-zero point B. One must thus the humidification direction (°) which on depends of the enthalpy hb of the humidification medium, to shift // from B to A. The humidifica-

tion is possible with prepared water, unsaturated or saturated steam. The abscissa tilting angle (°) caus-es that the zero-degree isotherm in the area of unsaturated air is horizontal. Scale h = 2500500 J/kg = 50 mm Scale x = 1 kg/kg = 50 mm

𝑡𝑎𝑛𝛽 =ℎ

𝑥=

2500500

1=

50𝑚𝑚

50𝑚𝑚= 1.00 → 𝛽 = 45.00°

Humidification with water, t = 30 °C

ℎ𝑏 = ℎ𝑤 = 125600 𝐽/𝑘𝑔

ℎ = 𝑥(𝑟0 − ℎ𝑏) = 1(2500500 − 125600) = 2374900 𝐽/𝑘𝑔

𝑡𝑎𝑛𝛿 =ℎ

𝑥=

2374900

1=

47.49𝑚𝑚

50.00𝑚𝑚= 0.95 → 𝛿 = 43.52°

Humidification with unsaturated steam, xd = 70 %, t =110 °C

ℎ𝑏 = ℎ𝑤 + 𝑥𝑑𝑟 = 461100 + 0.7 × 2500500 = 2211450 𝐽/𝑘𝑔

ℎ = 𝑥(𝑟0 − ℎ𝑏) = 1(2500500 − 2211450) = 289050 𝐽/𝑘𝑔

𝑡𝑎𝑛𝛿 =ℎ

𝑥=

289050

1=

5.78𝑚𝑚

50.00𝑚𝑚= 0.116 → 𝛿 = 6.59°

Humidification with saturated steam, t = 160 °C

ℎ𝑏 = ℎ𝑑 = 2756500 𝐽/𝑘𝑔

ℎ = 𝑥(𝑟0 − ℎ𝑏) = 1(2500500 − 2756500) = −256000 𝐽/𝑘𝑔

𝑡𝑎𝑛𝛿 =ℎ

𝑥=

−256000

1=

−5.12𝑚𝑚

50.00𝑚𝑚= −0.102 → 𝛿 = −5.85°

6. Cooling process In the software the cooling process in the heat exchanger is divided in 15 cells in air direction.

Here, it is assumed that a high degree of cross-counter-flow.

The surface temperature trx plays in each cell a crucial role.

When this is less than the dew point ttx, condensate forms.

For small ttx-trx, the droplets of condensate are small too.

These can be separated in a 1st demister only, which produce bigger droplets.

A 2nd demister can separate this big droplets.

Demisters with less than 100 Pa pressure drop have a bad separation.

This play the big rule, when the dehumidification during the cooling process is important.

En

tha

lpy (

kJ/k

g)

t = 0 °C

Abs. hum

idity (kg/kg)

x r

0

x=0.01

En

tha

lpy (

kJ/k

g)

t = 0 °C

Abs. hum

idity (kg/kg)

t = 100 °C

x r

0cp

l t

x cpd t

x=0.01

En

tha

lpy (

kJ/k

g)

t = 0°C

Abs. humidity (kg/kg)

x=0.01

Humidification

Isotherm

A

B

x hb

x(r0-hb)

Humidification

twx

trx

tkx

tw1

tk1

tr1

tw0

tr0

tk0

1

x

tw0

trx

twx

tw1

tt x

tr1

tto

7. Climate change For the meteorological data would you consult the German standard DIN 4710 [1] and the software from www.meteonorm.com [2] please. There you can produce world-wide data files to include it in the application AHH. The necessary cooling requirements in sweltering mid-summer results from the maximum outside air enthalpy versus meteorological data. Who calculated by default with 32°C / 40%, do not be surprised, if the cooler at the beginning is 42% and after 15 years even 60% is too small, see the following page please.

[1] The German standard DIN 4710 recorded 87’600 events à 0.1 hours per year as average values of the period from 1961 to 1990 and therefore forms a large area in the Mollier-HX-Diagram; see red curve in the diagram above.

[2] The software Meteonorm recorded 8’760 events à 1.0 hours per year, and therefore forms a smaller area in the Mollier-HX-Diagram than the German standard DIN 4710 what is a risk in the design of coolers in sweltering midsummer.