Ventilation
3 Psychrometrics
Vladimír Zmrhal (room no. 814)
http://users.fs.cvut.cz/~zmrhavla/index.htm
Dpt.
Dpt. of
Environmental
Engineering
1
Dry air
Components in
Dry Air
Volume Ratio
compared to Dry Air
Molecular Mass
M [kg/kmol]
Molecular Mass in
Air
Oxygen
0.2095
32.00
6.704
Nitrogen
0.7809
28.02
21.88
Carbon Dioxide
0.0003
44.01
0.013
Hydrogen
0.0000005
2.02
0
Argon
0.00933
39.94
0.373
Neon
0.000018
20.18
0
Helium
0.000005
4.00
0
Krypton
0.000001
83.8
0
131.29
0
Xenon
0.09
Total Molecular Mass of Air
10-6
28.97
2
1
Water vapor
is almost always presence in the air
the amount of water vapor varies from zero (dry air) to a maximum
that depends on temperature and pressure
water vapor in air will replace other gases and reduce the total
density of the mixture
dry air is more dense than moist air !
3
Moist air
the mixture (two-component) of dry air and water vapour
compared to the other gases in the air water may condense
Saturation
is a state of neutral equilibrium between moist air and the
condensed water phase (liquid or solid)
the maximum vapor pressure possible before the vapor start to
condense at an actual temperature - is called the saturation
pressure – p‘‘v
4
2
Thermodynamic properties
Dry air and water vapor
• gas constant for dry air
ra = 287.1 [J/kgK]
• gas constant for water vapor
rv = 461.5 [J/kgK]
• latent heat vaporization of water
l = 2500 [kJ/kg]
(for 0 °C)
• specific heat capacity of dry air
ca = 1010 [J/kgK]
• specific heat capacity of water vapor
cv = 1860 [J/kgK]
Subscripts: a = dry air, v = water vapor, w = water
5
Dalton‘s law
Moist air
Dalton‘s law (1801) of parcial pressures
p = ∑ pi = pa + pv
i
where
pa
… partial pressure of dry air [Pa]
pv
… partial pressure of water vapor [Pa]
equation of state (ideal gas law)
pv = rT
v=
1
ρ
6
3
Humidity of moist air
relative humidity
ϕ=
pv
pv′′
[%]
humidity ratio
x=
mv ra pv
p
ϕ pv′′
=
= 0.622 v = 0.622
ma rv pa
pa
p − ϕ pv′′
[kgv/kgda]
absolute humidity (water vapor density)
a = ρv =
mv pv
=
V rvT
[kg/m3]
7
Density of moist air
from Dalton´s law …
ρ = ρ a + ρv =
=
ma mv pa pv p − pv pv
+
=
+
=
+
V
V raT rvT
raT
rvT
 ra
1 
 p − pv  1 −
raT 
 rv
ρ=



1
( p − 0.378ϕ pv′′ )
ra T
the moist air is lighter than dry air !!!
8
4
Enthalpy of moist air
the sum of the individual partial enthalpies of the components
1 kg of dry air + x kg/kgda of saturated water vapor
h = ha + xhv
[kJ/kgda]
h = ca t + x ( l + cv t ) = 1,01t + x ( 2500 + 1.86t )
enthalpy relate to 0 °C
h(t = 0 °C; x = 0 kgv/kgda) = 0
[kJ/kgda]
9
Water vapor saturation pressure
for t = -20 to 0°C
ln pv′′ = 28.926 −
6148
273.1 + t
for t = 0 to 80 °C
ln pv′′ = 23.58 −
4044,2
235.6 + t
Example 1: Calculate air
state
t = 20 °C
ϕ = 40 %
p = 100 kPa
h=?
x=?
a=?
ρ=?
10
5
Water vapor saturation pressure
according to ASHRAE Handbook
ln pv′′ =
C1
+ C2 + C3 ⋅T + C4 ⋅ T 2 + C5 ⋅T 3 + C6 ⋅ T 4 + C7 ⋅ ln (T )
T
for t = -100 to 0 °C
C1 = -5.6745359.103
C2 = 6.3925247
C3 = -9.6778430.10-3
C4 = 6.2215701.10-7
C5 = 2.0747825.10-9
C6 = -9.484024.10-13
C7 = 4.1635019
for t = 0 to 200 °C
C1 = -5.8002206.103
C2 = 1.3914993
C3 = -4.8640239.10-2
C4 = 4.1764768.10-5
C5 = -1.4452093.10-8
C6 = 0
C7 = 6.5459673
11
Molliere h-x diagram
graphic representation of the
relationship between air
temperature, moisture content and
enthalpy
basic design tool for building
engineers
Example 2: Find out air state
in h-x diagram
t = 34 °C
h = 60 kJ/kg
x=?
ϕ=?
pv = ?
12
6
Molliere vs. Psychrometric chart
13
ASHRAE Psychrometric chart
14
7
Molliere h-x diagram
Direction of the air-conditioning process δ
is used to establish the direction of a condition on the
psychrometric chart
δ=
∆h h2 − h1
=
∆x x 2 − x1
Room sensible heat factor (RSHF) ϑ
expresses the ratio between sensible heat load and total heat
load in the room
ϑ=
Qsen
Qsen
c ∆t
=
=
Qtotal Qsen + Qlat ∆h
15
Molliere h-x diagram
Dry bulb temperature t
usually referred to as air temperature, is the air property that is
most common used tdb = t
Dew-point temperature tdp
is the temperature at which water vapor starts to condense out
of the air (the temperature at which air becomes completely
saturated)
Wet bulb temperature twb
this is the temperature indicated by a moistened thermometer
bulb exposed to the air flow
the temperature of adiabatic saturation
16
8
Molliere h-x diagram
Psychrometric equation
pv = pv′′,wb − Ap(t − twb )
A = 662 ⋅ 10−6
[K-1]
Example 3:
t = 30 °C
h = 56 kJ/kg
twb = ?
tdp = ?
17
Molliere h-x diagram
Assman psychrometer
twb
tdb
Example 4: tdb = 34 °C, twb = 18 °C, ϕ = ?
18
9
Mixing of two moist airstreams
Moisture balance
M1x1 + M 2 x 2 = (M1 + M 2 ) x m
xm =
M1x1 + M 2 x 2
( M1 + M 2 )
Enthalpy balance
M1h1 + M 2h2 = (M1 + M 2 )hm
hm =
MIX´ - when hot air 2´ is
mixed with cold air 1´ it
results in fog if the mixing
point is below the
saturation line of the air.
M1h1 + M 2h2
( M1 + M 2 )
19
Mixing of three moist airstreams
Example 5:
Mixing of 3 airstreams.
Draw the mixing into the h-x diagram
M1 = 2 kg/s
M2 = 5 kg/s
M3 = 3 kg/s
t1 = -15 °C
t2 = 21 °C
t3 = 30 °C
x1 = 0,6 °C
x2 = 6 °C
x3 = 7 °C
tmix = ?
xmix = ?
20
10
Mixing of two moist airstreams
⇒
M 1 ( x1 − x m ) = M 2 ( x m − x 2 )
Mass flow rate
M = V.ρ [kg/s]
M1 ( h1 − hm ) = M 2 ( hm − h2 )
δ=
∆h hm − h2 h1 − hm
=
=
∆x x m − x 2 x 1 − x m
M1 ( x m − x 2 )
=
M 2 ( x1 − x m )
M1 ( hm − h2 )
=
M 2 ( h1 − hm )
21
Thank you for your
attention
22
11