cae 331/513 building science - built envibuilt-envi.com/...lecture13_psychrometric-processes... ·...
TRANSCRIPT
![Page 1: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/1.jpg)
CAE 331/513 Building Science Fall 2017 October 10, 2017 Psychrometric processes (part 1)
Dr. Brent Stephens, Ph.D. Civil, Architectural and Environmental Engineering
Illinois Institute of Technology [email protected]
Advancing energy, environmental, and sustainability research within the built environment www.built-envi.com Twitter: @built_envi
![Page 2: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/2.jpg)
2 http://illinoisashrae.org
![Page 3: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/3.jpg)
3 https://www.ashrae.org/membership--conferences/student-zone/scholarships-and-grants/ashrae-scholarship-program-and-stem
Deadline: December 1st
![Page 4: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/4.jpg)
HW 3
• Due today – psychrometric state calculations
4
![Page 5: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/5.jpg)
Psychrometric equations summary (SI units)
5
φ =pwpws Dew point temperature:
W =mwmda
=MWwpwMWda pda
= 0.622pwpda
= 0.622pwp− pw
[ kgw
kgda
]W =mwmda
=MWwpwMWda pda
= 0.622pwpda
= 0.622pwp− pw
[ kgw
kgda
] ρ =mda +mwV
=1v1+W( )
ln pws =C8T+C9 +C10T +C11T
2 +C12T3 +C13 lnT
pV = nRT
p = pda + pw
Ri =RMWi
pv = pρ= RT
![Page 6: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/6.jpg)
Psychrometric equations summary (SI units)
6
W =(2501− 2.326Twb )Ws@Twb
−1.006(T −Twb )2501+1.86T − 4.186Twb
= actual W
Wet bulb temperature (iterative solver):
v = RdaTp− pw
=RdaT (1+1.6078W )
pv ≈ 0.287042(T + 273.15)(1+1.6078W ) / p
*where T is in °C
h ≈1.006T +W (2501+1.86T )
*Where Twb and T are in Celsius Specific volume:
Specific enthalpy:
![Page 7: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/7.jpg)
Obtaining these data from ASHRAE Tables
7
ASHRAE HoF Ch. 1 (2013) Table 2 gives us Ws, vda , vs , hda, and hs directly at different temperatures:
![Page 8: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/8.jpg)
Obtaining these data from ASHRAE Tables
8
ASHRAE HoF Ch. 1 (2013) Table 3 gives us pws at different temperatures:
![Page 9: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/9.jpg)
Why is this stuff helpful?
9
![Page 10: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/10.jpg)
PSYCHROMETRIC PROCESSES Using the psychrometric chart
10
![Page 11: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/11.jpg)
Use of the psychrometric chart for processes
We can use the psychrometric chart (and equations) not only to describe states of moist air, but for a number of processes that are important for building science and HVAC applications
Examples: • Sensible cooling or heating • Warming and humidification of cold, dry air • Cooling and dehumidification of warm, humid air
– Sensible + latent cooling
• Evaporative cooling • Mixing of airstreams
11
![Page 12: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/12.jpg)
Typical components of an HVAC system
12
Primary components
Secondary components
![Page 13: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/13.jpg)
Typical HVAC processes
13
Some common psychrometric processes:
Air mixing Heating
Cooling and dehumidification
Humidification
Refrigeration
Heat generation
Common primary processes:
![Page 14: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/14.jpg)
Definitions: Sensible and latent heat
14
• Sensible heat transfer – Increase or decrease in temperature of
a substance without undergoing a phase change
• Latent heat transfer – Heat transfer required to change the
phase of a substance (e.g., heat required to change liquid to vapor)
Qtotal
=Qsensible
+Qlatent
Units of [W], [BTU/hr], or [ton]
![Page 15: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/15.jpg)
Sensible and latent heat transfer equation
15
Q1à2 = total rate of heat transfer from state 1 to state 2 (W or BTU/hr or ton) mda = mass flow rate of dry air (kgda/s or lbda/hr) hexit,2 = enthalpy at the exit (J/kgda or BTU/lbda) hinlet,1 = enthalpy at the inlet (J/kgda or BTU/lbda)
Generic equations for both heating and cooling processes:
.
Q1→2 = !mda (h2 − h1) Qtotal = !mda (hexit − hinlet )
![Page 16: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/16.jpg)
Sensible heat transfer equation
16
Qsensible = rate of sensible heat transfer (W or BTU/hr or ton) Cp = specific heat of air (J/kgK or BTU/lb°F) ρda = dry air density (kg/m3 or lb/ft3) Tinlet = inlet temperature (K or °F) Texit = exit temperature (K or °F)
For heating: For cooling:
Qsensible = !mdaCp (Texit −Tinlet ) = ρda !VdaCp (Texit −Tinlet )
Qsensible > 0
Qsensible < 0
![Page 17: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/17.jpg)
Latent heat transfer equation
17
Qlatent = rate of latent heat transfer (W or BTU/hr or ton) mw = mass flow rate of water vapor (kgw/s or lbw/hr) hfg = enthalpy, or latent heat, of vaporization (J/kg or BTU/lb) * hfg = 2260 kJ/kg or 970 BTU/lb for water Winlet = inlet humidity ratio (kgw/kgda or lbw/lbda) Wexit = exit humidity ratio (kgw/kgda or lbw/lbda)
For humidification: For dehumidification:
.
Qlatent = !mdahfg (Wexit −Winlet ) = ρda !Vdahfg (Wexit −Winlet )
Qlatent > 0
Qlatent < 0
![Page 18: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/18.jpg)
Heating and humidification of cold, dry air
• Example: Heating and humidification of air – Process: Adding moisture and heat (sensible + latent heating)
18
8°C 40% RH 35°C
30% RH
Q1: What is the enthalpy change required? Q2: What is the total rate of heat transfer if the airflow rate is 10 m3/s? Q3: What is the split between sensible and latent transfer?
![Page 19: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/19.jpg)
• d
19
2
1
Heating and humidification of cold, dry air
8°C 40% RH
35°C 30% RH
![Page 20: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/20.jpg)
• d
20
2
1
Heating and humidification of cold, dry air
ΔW
Δhtotal
ΔT
Δhsensible = 44 - 16 = 28 kJ/kgda Δhtotal = 64 - 16 = 48 kJ/kgda
Δhsensible
SHR = 28/48 = ~0.58
![Page 21: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/21.jpg)
Sensible heat ratio (SHR)
• The sensible heat ratio is defined as:
• Allows for understanding sensible load relative to latent load
21
SHR =!qsens!qtotal
=!qsens
!qsens + !qlatent=ΔhsensΔhtotal
Here is a process with an SHR ≈ 0.4
![Page 22: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/22.jpg)
Enthalpy protractor (Δh/ΔW)
• The other side of the enthalpy protractor tells us: – What is the enthalpy change relative to the change in humidity ratio
22
ΔhtotalΔW
Here is a process with Δh/ΔW ≈ 1850 BTU/lbw SI units: kJ/kgw
![Page 23: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/23.jpg)
Cooling and dehumidification of warm, humid air
23
38°C 34% RH
13°C 90% RH
• Example: Air flowing over a cooling coil • Removing both moisture and heat
– Sensible + latent cooling
![Page 24: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/24.jpg)
• d
24
1
2
Cooling and dehumidification of warm, humid air
ΔW
Δh SHR ~ 0.61
The red line is actually impossible… no moisture removal The blue lines show what really happens
ΔT
38°C 34% RH
13°C 90% RH
![Page 25: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/25.jpg)
Example: Sensible cooling
• Moist air is cooled from 40°C and 30% RH to 30°C without condensation – What is the RH at W at the process end point?
25
![Page 26: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/26.jpg)
• d
26
1
Sensible cooling
![Page 27: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/27.jpg)
• d
27
1 2
Dew point is ~19°C New T = 30°C • No condensation New RH is ~53% W does not change W1 = W2 = 0.014 kgw/kgda
Sensible cooling
![Page 28: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/28.jpg)
• d
28
1 2
h1 ≈ 76 kJ/kg h2 ≈ 66 kJ/kg Δh ≈ -10 kJ/kg SHR = 1.0
Dew point is ~19°C New T = 30°C • No condensation New RH is ~53% W does not change W1 = W2 = 0.014 kgw/kgda
Sensible cooling
![Page 29: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/29.jpg)
Example: Sensible + latent cooling
• Moist air is cooled from 40°C and 30% RH to 15°C – Q1: Does the water vapor condense? – Q2: What is RH at W at the process end point?
29
![Page 30: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/30.jpg)
• d
30
1
Sensible + latent cooling
![Page 31: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/31.jpg)
• d
31
1
2 Dew point is ~19°C New T = 15°C • There is condensation New RH is 100% W decreases to ~0.010
Two part cooling process: 1. Constant humidity ratio cooling until saturation 2. Constant RH cooling w/ moisture condensation
Δh = 42 – 76 = -34 kJ/kg
Sensible + latent cooling
SHR ~ 0.75
![Page 32: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/32.jpg)
Real data: ASHRAE RP-1299 Energy implications of filters
32
0.008
0.010
0.012
0.014
Hum
idity
ratio
, kg/
kg
0
10
20
30Te
mpe
ratu
re, C
6 PM 7 PM 8 PMHour
Temp - before coil Temp - after coilW - before coil W - after coil
AC on AC off
Temperature and humidity ratio differences across AC coils in homes
T before coil
T after coil
W before
coil W
after coil
![Page 33: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/33.jpg)
Real data: ASHRAE RP-1299 Energy implications of filters
33
What are we looking at?
Before coil
After coil
AC on/off
![Page 34: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/34.jpg)
• d
34
1
Sensible + latent cooling
2
Δh = 34 – 51 = -17 kJ/kg SHR ~ 0.78
![Page 35: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/35.jpg)
Evaporative cooling example • Hot, dry outdoor air is cooled with an evaporative cooler, or “swamp
cooler” – Q1: What is the T, RH, and W of the supply air? – Q2: Why would we choose this system?
35
32°C 20% RH
T = ? RH = ?
![Page 36: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/36.jpg)
• d
36
OA
Evaporative cooling
![Page 37: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/37.jpg)
• d
37
OA
Evaporative cooling
Cooling occurs along constant wet bulb
![Page 38: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/38.jpg)
• d
38
OA
Evaporative cooling
Cooling occurs along constant wet bulb SA
![Page 39: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/39.jpg)
• d
39
Evaporative cooling
RH near 100% W = ~12.2 gw/kgda Δh = 0
OA
SA
![Page 40: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/40.jpg)
• d
40
Evaporative cooling
RH near 100% W = ~12.2 gw/kgda Δh = 0
Δh = 0 means no energy is required other than for fans (for air) and pumps (for water)
OA
SA
![Page 41: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/41.jpg)
PSYCHROMETRIC PROCESSES Using energy and mass balance equations
41
![Page 42: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/42.jpg)
Energy/mass balances for psychrometric processes
42
!mda,1h1 +Q1→2 = !mda,2h2!mda,1 = !mda,2 = !mda!mda,1W1 = !mda,2W2
Q1→2 = !mda (h2 − h1)
Heating air
Q
Energy balance:
Mass balance on air:
Mass balance on water vapor:
Therefore:
![Page 43: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/43.jpg)
Energy/mass balances for psychrometric processes
43
Cooling and dehumidifying
!mda,1h1 +Q1→2 = !mda,2h2 + !mwhw,2!mda,1 = !mda,2 = !mda!mda,1W1 = !mda,2W2 + !mw!mw = !mda (W1 −W2 )Q1→2 = !mda[(h2 − h1)− (W1 −W2 )hw,2 ]
Energy balance:
Mass balance on air:
Mass balance on water vapor:
Therefore:
And: (Q is negative for cooling)
*Note that hw = hg for steam/vapor and hw = hf for water
![Page 44: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/44.jpg)
Energy/mass balances for psychrometric processes
44
Humidifying
!mda,1h1 + !mwhw = !mda,2h2!mda,1 = !mda,2 = !mda!mda,1W1 + !mw = !mda,2W2
!mw = !mda (W2 −W1)!mwhw = !mda (h2 − h1)h2 − h1W2 −W1
=ΔhΔW
= hw
Energy balance:
Mass balance on air:
Mass balance on water vapor:
Therefore:
And:
And: *Note that hw = hg for steam/vapor and hw = hf for water
![Page 45: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/45.jpg)
Energy/mass balances for psychrometric processes
• Mixing: Often in HVAC systems we mix airstreams adiabatically – Adiabatically = Without the addition or extraction of heat – e.g. outdoor air mixed with a portion of return/recirculated air
45
!mda,1h1 + !mda,2h2 = !mda,3h3!mda,1 + !mda,2 = !mda,3!mda,1W1 + !mda,2W2 = !mda,3W3
Energy:
Mass (air):
Mass (water):
![Page 46: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/46.jpg)
Energy/mass balances for psychrometric processes
• Mixing: For most parameters, the outlet conditions end up being the weighted averages of the input conditions based on their mass flow rates – Dry bulb temperature – Humidity ratio – Enthalpy – (not RH!)
46
T3 =mda1T1 + mda2T2mda1 + mda2
W3 =mda1W1 + mda2W2
mda1 + mda2
h3 =mda1h1 + mda2h2mda1 + mda2
![Page 47: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/47.jpg)
Energy/mass balances for psychrometric processes
47
Space heat and moisture gains
!mdah1 +Qgains + !mwhw∑ = !mdah2!mdaW1 + !mw∑ = !mdaW2
!mw∑ = !mda (W2 −W1)
!mwhw∑ +Qgains = !mda (h2 − h1)
ΔhΔW
=!mwhw∑ +Qgains!mw∑
Energy balance:
Mass balance on water vapor:
Therefore:
Therefore:
And: *Note that hw = hg for steam/vapor and hw = hf for water
![Page 48: CAE 331/513 Building Science - Built Envibuilt-envi.com/...lecture13_psychrometric-processes... · CAE 331/513 Building Science ... Psychrometric equations summary (SI units) 5 φ=](https://reader031.vdocument.in/reader031/viewer/2022022602/5b5741847f8b9a8f128d7caf/html5/thumbnails/48.jpg)
Next time
• Psychrometric processes: example problems
48