CAE 331/513 Building Science Fall 2017

Transcription

1 CAE 331/513 Building Science Fall 2017 October 5, 2017 Psychrometrics (equations) Advancing energy, environmental, and sustainability research within the built environment Dr. Brent Stephens, Ph.D. Civil, Architectural and Environmental Engineering Illinois Institute of Technology

2 Graduate student projects (CAE 513 only) Expectations document on BB now Individual projects Literature review Some modeling and/or measurement Conference-type paper submission Due dates for deliverables: Tuesday, October 17: Project topic via Thursday, November 30: Final report submission 2

3 Graduate student projects: Topic suggestions Energy questions Efficiency of radiant vs. central forced air heating/cooling? Efficiency of different air distribution systems (e.g., overhead/ufad) Net zero energy/carbon design/operation Electrical metering and power draw signatures HVAC systems Heat pumps, geothermal, energy recovery, absorption chillers, cogeneration Green building rating systems LEED, Green Globes, EnergyStar, Living Building, BREEAM, Moisture Dampness, fungal growth, remediation, buffering capacity IAQ/IEQ Thermal comfort, aerosols, ventilation, VOCs Other Electrical, lighting, plumbing, acoustics Tools you can use: Energy simulation, MATLAB modeling, measurements in BERG Lab 3

4 Last time Introduced Psychrometrics and several key terms: 1. Dry bulb temperature 2. Vapor pressure 3. Saturation 4. Relative humidity 5. Absolute humidity (or humidity ratio) 6. Dew point temperature 7. Wet bulb temperature 8. Enthalpy 9. Density 10. Specific volume 4

5 d SI chart 5

6 d Relative Humidity φ 50% Enthalpy h 44 kj/kg da Dew Point Temp T dew 11.7 C Specific Volume v m 3 /kg da Dry Air Density ρ 1/v 1.18 kg da /m 3 Wet Bulb Temp T wb 15.5 C Dry Bulb Temp T = 22 C Humidity Ratio W 8.2 g/kg da (i.e., kg/kg) 6

7 IP chart

8 Enthalpy h 30 Btu/lb Specific Volume v ft 3 /lbm Dew Point Temp T dew 40 F Wet Bulb Temp T wb 65 F Humidity Ratio W 5.8 lb/lb da Relative Humidity φ 13% Dry Bulb Temp T 100 F

9 grains/lb: 1 lb = 7000 grains Alternate IP chart (Wang) 9

10 PSYCHROMETRIC EQUATIONS 10

11 Specifying the state of moist air In order to specify the state of moist air, we need total atmospheric pressure, p, the air temperature, T, and at least one other property W, φ, h, p w, or T dew We can use the psychrometric chart We can also use the underlying equations for greater accuracy and automation All equations are in ASHRAE 2013 Handbook of Fundamentals Chapter 1 11

12 Remember: Vapor pressure and Saturation Air can hold moisture (i.e., water vapor) Vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases p w *Units of pressure, Pa or kpa (aka partial pressure ) The amount of moisture air can hold in vapor form before condensation occurs is dependent on temperature We call the limit saturation p ws *Units of pressure, Pa or kpa (aka saturation vapor pressure ) 12

13 Relative humidity, φ (RH) The relative humidity ratio, φ, is the mole fraction of water vapor (x w ) relative to the water vapor that would be in the mixture if it were saturated at the given T and P (x ws ) We can also describe RH by partial pressures (ideal gas) Relative humidity is a common measure that relates well to how we perceive moisture in air φ = x w x ws T,P = p w / p tot p ws / p tot = p w p ws 13

14 p ws for 0 C< T <200 C (SI units) For p ws, the saturation pressure over liquid water: ln p ws = C 8 T +C 9 +C 10 T +C 11 T 2 +C 12 T 3 +C 13 lnt Note: These constants are only for SI units IP units are different Units: *We will use this equation for most conditions in building science (above 0 C) 14

15 p ws for -100 C< T <0 C (SI units) For p ws, the saturation pressure over ice: ln p ws = C 1 T +C 2 +C 3 T +C 4 T 2 +C 5 T 3 +C 6 T 4 +C 7 lnt Note: These constants are only for SI units IP units are different Units: 15

16 Humidity ratio, W (SI units) The humidity ratio, W, is ratio of the mass of water vapor to mass of dry air in a given volume We use W when finding other mixture properties Note 1: W is small (W < 0.03 for most real building conditions) Note 2: W is sometimes expressed in grains/lb where 1 lb = 7000 grains (I don t use this but you will in CAE 464 HVAC Design) Units: W = m w m da = MW w x w MW da x da = x w x da [ kg w kg da ] x da = p da p da + p w = p da p tot x w = p w p da + p w = p w p tot 16

17 Humidity ratio, W (SI units) The humidity ratio, W, is ratio of the mass of water vapor to mass of dry air in a given volume We use W when finding other mixture properties Note 1: W is small (W < 0.03 for most real building conditions) Note 2: W is sometimes expressed in grains/lb where 1 lb = 7000 grains (I don t use this but you will in CAE 464 HVAC Design) W = x w x da = p w / p tot p da / p tot = p w p da = p w p tot p w where: p tot = p da + p w =101,325 sea level 17

18 Saturation humidity ratio, W s (SI units) At a given temperature T and pressure P there is a maximum W that can be obtained If we try to add any more moisture, it will just condense out It is when the partial pressure of vapor has reached the saturation pressure This maximum humidity ratio is called the saturation humidity ratio, W s From our previous equation we can write: W s = p ws p da = p ws p tot p ws UNITS [ kg w kg da ] 18

19 Degree of saturation, µ (SI units) The degree of saturation, µ (dimensionless), is the ratio of the humidity ratio W to that of a saturated mixture W s at the same T and P Note that µ and φ are not quite the same Their values are very similar at lower temperatures but may differ a lot at higher temperatures! µ = W $ # & " W s % T,P µ = φ 1+ (1 φ)w s / (0.6295) µ φ = 1 (1 µ) p ws / p tot 19

20 Specific volume, ν, and density, ρ (SI units) The specific volume of moist air (or the volume per unit mass of air, m 3 /kg) can be expressed as: v = R da T p da = R da T p tot p w = R da T ( W ) p tot v (T )( W ) / p tot If we have ν we can also find moist air density, ρ (kg/m 3 ): ρ = m da + m w V = 1 ( v 1+W ) 20

21 Enthalpy, h (SI units) The enthalpy of a mixture of perfect gases equals the sum of the individual partial enthalpies of the components Therefore, the enthalpy (h) for moist air is: h = h da +Wh g h = enthalpy for moist air [kj/kg] h g = specific enthalpy for saturated water vapor (i.e., h ws ) [kj/kg w ] h da = specific enthalpy for dry air (i.e., h ws ) [kj/kg da ] Some approximations: h da 1.006T h g T h 1.006T +W ( T ) *where T is in C and h is in kj/kg 21

22 Remember: 3 different temperatures T, T dew, and T wb The standard temperature, T, we are all familiar with is called the dry-bulb temperature, or T d It is a measure of internal energy We can also define: Dew-point temperature, T dew Temperature at which water vapor changes into liquid (condensation) Air is maximally saturated with water vapor Wet-bulb temperature, T wb The temperature that a parcel of air would have if it were cooled to saturation (100% relative humidity) by the evaporation of water into it Units of Celsius, Fahrenheit, or Kelvin ü The energy needed to evaporate liquid water (heat of vaporization) is taken from the air in the form of sensible heat and converted to latent heat, which lowers the temperature at constant enthalpy 22

23 Dew-point temperature, T dew The dew point temperature, T dew, is the air temperature at which the current humidity ratio (W) is equal to the saturation humidity ratio (W s ) at the same temperature i.e., W s (p, T dew ) =W When the air temperature is lowered to the dewpoint at constant pressure, the relative humidity rises to 100% and condensation occurs T dew is a direct measure of the humidity ratio W since W = W s at T = T dew 23

24 d Dew Point Temp T dew 11.7 C W = W s at T = T dew 24

25 Dew-point temperature, T dew (SI units) Dew-point temperature, T dew Note: These constants are only for SI units IP units are different 25

26 Wet-bulb temperature, T wb (SI units) Wet-bulb temperature, T wb Requires iterative solving find the T wb that satisfies the following equation (above freezing): W = ( T wb )W s@t wb 1.006(T T wb ) T 4.186T wb = actual W And for T below freezing: W = ( T wb )W s@t wb 1.006(T T wb ) T 2.1T wb = actual W *Where T wb and T are in Celsius 26

27 Obtaining these data from ASHRAE Tables ASHRAE HoF Ch. 1 (2013) Table 2 gives us W s, v da, v s, h da, and h s directly at different temperatures: 27

28 Obtaining these data from ASHRAE Tables ASHRAE HoF Ch. 1 (2013) Table 3 gives us p ws at different temperatures: 28

29 Revisit example from last class Moist air exists at 22 C dry-bulb temperature with 50% RH at sea level Find the following: (a) the humidity ratio, W (b) dew point temperature, T dew (c) wet-bulb temperature, T wb (d) enthalpy, h (e) specific volume, ν (f) density, ρ Also: (g) degree of saturation, µ 29

30 Psychrometric equations summary (SI units) pv = nrt p = p da + p w p w W m w = MW p w w = p w [ kg w = [ kg w ] ρ = m + m da w = 1 ] m da MW p da p w p da kg da p da V p pv 1+W w kg da p w ( ) φ = p w p ws pv = p ρ = RT R i = R MW i Dew point temperature: ln p ws = C 8 T +C 9 +C 10 T +C 11 T 2 +C 12 T 3 +C 13 lnt 30

31 Psychrometric equations summary (SI units) Wet bulb temperature (iterative solver): W = ( T )W 1.006(T T wb s@t wb wb ) T 4.186T wb Specific volume: v = R T da = R T ( W ) da p p w p v (T )( W ) / p Specific enthalpy: h 1.006T +W ( T ) *where T is in C = actual W *Where T wb and T are in Celsius 31

32 d Relative Humidity φ 50% Enthalpy h 44 kj/kg da Dew Point Temp T dew 11.7 C Specific Volume v m 3 /kg da Density ρ 1/v 1.18 kg da /m 3 Wet Bulb Temp T wb 15.5 C Dry Bulb Temp T = 22 C Humidity Ratio W 8.2 g/kg da (i.e., kg/kg) 32

33 Revisit another example from last class Moist air exists at 30 C dry-bulb temperature with a 15 C dew point temperature Find the following: (a) the humidity ratio, W (b) degree of saturation, µ (c) relative humidity, ϕ (d) enthalpy, h (e) specific volume, ν (f) density, ρ (g) wet bulb temperature, T wb 33

34 Humidity ratio W = p w p p C For a known T dew = 15 C, we know that the actual humidity ratio in the air, W, is by definition the same as the saturation humidity ratio, W s, at an air temperature of 15 C C =W s@t=15 C = p ws@15c = kpa Assume p = kpa (sea level) p ws p p C C =W s@t=15 C = = kg w kg da

35 Degree of saturation Need the saturation humidity T = 30 C: W s@t=30 C = p ws p p C! µ = W $ # & " W s =30 C p ws@15c = kpa W s@t=30 C = = kg w µ = W W s = = 0.39 kg da 35

36 From previous: Relative humidity φ = p w p ws p w@t=30 C = p ws@t=15 C =1.7057kPa p ws@t=30 C = kPa φ = = 0.40 = 40% 36

37 Enthalpy h 1.006T +W ( T ) *where T is in C h 1.006(30) + ( )( (30)) = 57.4 kj kg 37

38 Specific volume and density v (T )( W ) / p v ( )( ( )) / ( ) ρ = 1 ( v 1+W ) = v m3 kg da ( ) =1.157 kg m 3 38

39 Wet-bulb temperature Wet-bulb temperature is the T wb that fits this equation: W = ( T wb )W s@t wb 1.006(T T wb ) T 4.186T wb = Procedure: where: T = 30 C T wb =? C W s@twb =? = Guess T wb, calculate pws for that T, calculate W s for that T Repeat until W calculated based on those values (and original T) in equation above is equal to actual W ( in our case) T wb = 20.1 C p ws p p wb =? *Where T wb and T are in Celsius 39

40 d Enthalpy h 58 kj/kg da Specific Volume v m 3 /kg da Saturation W W s 0.27 kg w /kg da Relative Humidity φ 40% Dew Point Temp T dew 15 C Dry Bulb Temp T = 30 C Wet Bulb Temp t b 20 C Humidity Ratio W 10.7 g/kg da (i.e., ) 40

41 IP units example Moist air exists at 68 F dry-bulb temperature with 50% RH at sea level Find the following using psychrometric equations (IP units): (a) the humidity ratio, W (b) the saturation humidity ratio, W s (c) degree of saturation, µ (d) specific volume, ν (e) density, ρ (f) enthalpy, h 41

42 HW 3 assigned HW 3 assigned on Blackboard last time Building an Excel-based psychrometric calculator Due Tuesday October 10 Next time: psychrometric processes 42