PSYCHROMETRY AND AIR CONDITIONING PDF

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Psychrometry And Air Conditioning By: ENGR. YURI G. MELLIZA Psychrometry The specific objectives of this lecture are to: 1. Define psychrometry and the composition of moist air 2. Discuss the methods used for estimating properties of moist air 3. Present perfect gas law model for moist air 4. Define...

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Psychrometry And Air Conditioning By: ENGR. YURI G. MELLIZA

Psychrometry

The specific objectives of this lecture are to: 1. Define psychrometry and the composition of moist air 2. Discuss the methods used for estimating properties of moist air 3. Present perfect gas law model for moist air 4. Define important psychrometric properties 5. Present graphical representation of psychrometric properties on a psychrometric chart 6. Discuss measurement of psychrometric properties 7. Discuss straight-line law as applied to air-water mixtures 8. Discuss the concept of adiabatic saturation and thermodynamic wet bulb temperature 9. Describe a wet-bulb thermometer 10. Discuss the procedure for calculating psychrometric properties from measured values of barometric pressure, dry bulb and wet bulb temperatures 11. Describe a psychrometer and the precautions to be taken while using psychrometers (Section 27.5)

At the end of the lecture, the student should be able to: 1. Define psychrometry and atmospheric air 2. Use perfect gas law model and find the total pressure of air from partial pressures of dry air and water vapour 3. Define and estimate psychrometric properties 4. Draw the schematic of a psychrometric chart 5. Discuss the straight-line law and its usefulness in psychrometry 6. Explain the concepts of adiabatic saturation and thermodynamic wet bulb temperature 7. Differentiate between thermodynamic WBT and WBT as measured by a wet bulb thermometer 8. Estimate various psychrometric properties given any three independent properties 9. Describe a psychrometer

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Introduction: Atmospheric air makes up the environment in almost every type of air conditioning system. Hence a thorough understanding of the properties of atmospheric air and the ability to analyze various processes involving air is fundamental to air conditioning design. Psychrometry is the science of study of various properties of air, method of controlling its temperature and moisture content or humidity and its effect on various materials and human beings. Studying Psychrometry helps understanding different constituents of air and how they affect each other, which in turn unravels various mysteries of the atmosphere and the nature. Some of the psychrometric properties of air that we are going to study are: dry bulb temperature, wet bulb temperature, dew point temperature, relative humidity etc. Composition of Air Air comprises of mixture of various gases and water vapor or moisture. The air without any water vapor is called as dry air, thus the ordinary air is the mixture of dry air and water vapor. As such the air always contains some amount of water vapor so the pure dry air doesn’t really exists, however its concept is very important in understanding the properties of the air and how various changes occur in the air conditioning process. The dry air and water vapor mixture is merely physical one as there is no chemical reaction between the two. The dry air is composed of various gases, chiefly nitrogen (78%), and oxygen (21%). The remaining 1% of the gases includes carbon dioxide, and very small quantities of inert gases like hydrogen, helium, neon, and argon. The water vapor is also small part of the air included among remaining 1% of the gases. The amount of moisture in air by its mass keeps on varying from place to place and depending on the atmospheric conditions at a particular place. The places located close to the sea areas contain more moisture while the desert areas contain less moisture. Similarly, during the raining seasons the moisture content of the air is high while during summers and winters its low. The air contains usually 1% to 3% of moisture by mass. At the normal atmospheric temperature conditions oxygen gas exists in superheated conditions as gas since its boiling point is -182.7 C (-297F). By nature oxygen is highly active agent causing rusting and corrosion of metals. Nitrogen too exists in superheated condition as gas in the atmosphere since its boiling point is -195 C (319F) . However, nitrogen is an inert gas and does not cause any chemical reactions in the atmosphere. Since the chief constituents of the air are oxygen and nitrogen and they both exist in superheated condition, the air also exists in the superheated conditions as the gas. It is important to note here that small changes in the temperature of the dry air during the air conditioning process cause very small changes in its volume and density. It is also important to note that all the heat that is added or removed from the air during air conditioning process is the sensible heat and no latent heat is involved since the boiling point temperatures of oxygen and nitrogen are very low. Another important point to note is that the water vapor exists in the superheated condition, but when it is cooled or heated there is change in its phases, hence it absorbs or liberates sensible heat as well as the latent heat due to changes in its phases. This is what makes the whole process of air conditioning highly complicated. Cooling of water vapor results in its condensation, whiles its heating leads to superheating.

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Gas Mixture One of the properties of gases is that they mix with each other. When they do so, they become a solution—a homogeneous mixture. Some of the properties of gas mixtures are easy to determine if we know the composition of the gases in the mix. In gas mixtures, each component in the gas phase can be treated separately. Each component of the mixture shares the same temperature and volume. (Remember that gases expand to fill the volume of their container; gases in a mixture do that as well.) However, each gas has its own pressure. The partial pressure of a gas, Pi, is the pressure that an individual gas in a mixture has. Partial pressures are expressed in KPa (Absolute); however, we use the term pressure when talking about pure gases and the term partial pressure when we are talking about the individual gas components in a mixture.

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Principles of Gas Mixture 1.

Total mass of a mixture

m 2.

m

Mass fraction

xi 

3.

n

i

Mole fraction

yi  5.

mi m

Total moles of a mixture

n 4.

i

ni n

Equation of state Mass Basis For the Mixture

PV  mRT Fort the Components Pi Vi  mi R i Ti

Mole Basis For the Mixture PV  n RT

Fort the Components

Pi Vi  n i RTi 6.

Amagat’s Law The total volume of a mixture of gases is equal to the sum of the volume occupied by each component at the mixture pressure P and temperature T.

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P = P1 = P2 = P3 T = T1 = T2 = T3

n  n1  n 2  n 3 PV PV PV2 PV3 ; n1  1 ; n 2  ; n3  RT RT RT RT

n

PV PV1 PV2 PV3    RT RT RT RT  PV PV1 PV2 PV3  RT   RT  RT  RT  RT  P     V  V1  V2  V3 V   Vi yi 

7.

n i Vi  n V

Dalton’s Law The total pressure of a mixture of gases P is equal to the sum of the partial pressure that each gas would exert at the mixture volume V and temperature T.

V  V1  V2  V3 T  T1  T2  T3 n  n1  n 2  n 3 PV PV PV PV ; n1  1 ; n 2  2 ; n 3  3 RT RT RT RT PV P1V P2 V P3V    RT RT RT RT  PV P1V P2 V P3V  RT        RT RT RT RT  V  P  P1  P2  P3

n

P

P

yi 

8.

i

n i Pi  n P

Molecular Weight Of A Mixture (M)

M

y M

M

R 8.3143 KJ  R R kg - K

i

i

5

9.

Gas Constant (R)

R

x R

R

R 8.3143 KJ  M M kg - K

i

i

10. Specific Heat Of A Mixture At Constant Volume

Cv  At Constant Pressure

CP 

x C i

x C i

vi

Pi

Cp  Cv  R 11. Ratio Of Specific Heat C k P CV Rk k 1 R CV  k 1 12. Gravimetric And Volumetric Analysis CP 

Gravimetric analysis gives the mass fractions of the components in the mixture. Volumetric analysis gives the volumetric or molal fractions of the components in the mixture. CONVERSION

xi 

yi M i

y M i

yi 

 i

yi M i M

xi Mi xi Mi



Where m – mass in kg n – number of moles, kgm x – masss fraction y – mole fraction P – absolute pressure in KPa V – volume in m3 R – Gas constant in KJ/kg-K R - universal gas constant in KJ/kgm-K T – absolute temperature in K M – molecular weight in kg/kgm Cp – specific heat at constant pressure in KJ/kg-C or KJ/kg-K Cv – specific heat at constant volume KJ/kg-C or KJ/kg-K Subscript i – refers to the components

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Moist Air The moist air can be thought of as a mixture of dry air and moisture. For all practical purposes, the composition of dry air can be considered as constant. In 1949, a standard composition of dry air was fixed by the International Joint Committee on Psychrometric data.

Composition of Dry Air

Constituents

Molecular Weight

Volumetric Fraction

Oxygen (O2)

32

0.2095

Nitrogen (N2)

28

0.7809

Argon (Ar)

39.944

0.0093

Carbon Dioxide (CO2)

44

0.0003

Based on the above composition the molecular weight of dry air is found to be 29.00 and the gas constant R is 0.287 KJ/kg.K. As mentioned before the air to be processed in air conditioning systems is a mixture of dry air and water vapour. While the composition of dry air is constant, the amount of water vapour present in the air may vary from zero to a maximum depending upon the temperature and pressure of the mixture (dry air + water vapour). At a given temperature and pressure the dry air can only hold a certain maximum amount of moisture. When the moisture content is maximum, then the air is known as saturated air, which is established by a neutral equilibrium between the moist air and the liquid or solid phases of water. For calculation purposes, the molecular weight of water vapor is taken as 18.0 and its gas constant is 0.462 KJ/kg - K.

FUNDAMENTAL PARAMETERS  Total Pressure(P): The total pressure of moist air is equal to the sum of the partial pressure of dry air and water vapor. P  Pa  Pv KPa

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 Vapor Pressure (Pv): The vapor pressure (Pv) is the partial of water vapor n the mixture (Moist air). Pv  Pw  P(A)t d  t w  KPa Where A  6.66 x 10 - 4  For tw  0C A  5.94 x 10 - 4

 For tw  0C

td - dry bulb temperatu re, C tw - wet bulb temperatu re, C

 Saturation pressure at wet bulb temperature (Pw): Pw is the saturation pressure corresponding the wet bulb temperature of the mixture, and can be determined from steam table.  Dry Bulb temperature (td): The dry-bulb temperature is the temperature of air measured by a thermometer freely exposed to the air, but shielded from radiation and moisture. It is the temperature that is usually thought of as air temperature, and it is the true thermodynamic temperature.

 Wet Bulb temperature (tw): The wet-bulb temperatur is the temperature read by a thermometer covered in water-soaked cloth (wet-bulb thermometer) over which air is passed.

Psychrometry Apparatus for measuring td and tw

 Humidity Ratio (W): The humidity ratio W is the ratio of the mass of the water vapor mv to the mass of the dry air ma in the mixture.

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W

mv ma

From Amagat' s Law mv 

Pv V R vT

ma 

Pa V R aT

Pv V R v T R a Pv 0.287 Pv 0.622 Pv W    Pa V R v Pa 0.462 Pa Pa R aT W

0.622 Pv P  Pv

 Relative Humidity (): The relative humidity is the ratio of the mole fraction of the water vapor yv in a mixture to the mole fraction yd of the water vapor in a saturated mixture at the same temperature and pressure: Pv yv  P y d Pd P Pv  x 100% Pd 

Where: Pd – saturation pressure corresponding the dry bulb temperature from steam table

 Enthalpy (h): The enthalpy of a mixture of ideal gases is equal to the sum of the enthalpies of each component: h  h a  Wh v ha  1.0045 ( td ) h v  2501 .3  1.86( t d ) h  1.0045 ( t d )  W2501 .3  1.86( t d )

KJ kgda

Specific Volume (): Specific volume is the ratio of the volume of dry air in the mixture.



0.287 t d  273  m3 P  Pv kgda

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Degree of Saturation (): The degree of saturation is the ratio of the humidity ratio W to the humidity ratio of a saturated mixture Ws at the same temperature and pressure, W  P  Pv           Ws   P  Pd 

The Psychrometric Chart A psychrometric chart is a graphical representation of the psychrometric processes of air. Psychrometric processes include physical and thermodynamic properties such as dry bulb temperature, wet bulb temperature, humidity, enthalpy, and air density. A psychrometric chart can be used in two different ways. A psychrometric chart can be used in two different ways. The first is done by plotting multiple data points, that represent the air conditions at a specific time, on the chart. Then, overlaying an area that identifies the ―comfort zone.‖ The comfort zone is defined as the range within occupants are satisfied with the surrounding thermal conditions. After plotting the air conditions and overlaying the comfort zone, it becomes possible to see how passive design strategies can extend the comfort zone.

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Sensible Heat and Latent Heat of Moist air The sensible heat of moist air (Qs) is the thermal energy associated with the change of air temperature between two state points without a change in phase. The sensible depends on its temperature T above the reference temperature of 0C. Latent heat of moist air, often represented by (QL) is the thermal energy associated with the change of phase of water vapor. Both of them are in KJ/kg. Sensible Heat Qs  mC p ( t 2  t1 )

KJ sec

KJ kg - C For air conditioni ng calculatio ns

C p  1.0045  1.86 W

Cp  1.02

KJ kg - C

Latent Heat Q L  m( W2  W1 )h fg

KJ sec

Where hfg  2500

KJ kg

m - mass flow rate of dry air in

kg sec

Sensible Heat Ratio or Sensible Heat Factor The sensible heat ratio or sensible heat factor (SHR or SHF) of an air-conditioning process is defined as the ratio of the change in absolute value of sensible heat to the change in absolute value of total heat, both in KJ/sec.

SHF 

Qs Qs  Q Qs  Q L

Example No. 1 The design indoor air temperature and relative humidity of an air conditioned space at sea level are 75°F (23.9°C) and 50 percent. Find the humidity ratio, the enthalpy, and the density of the indoor moist air

Example No. 2 For a sample of air having 22ºC DBT, relative humidity 30 percent at barometric pressure of 760 mm of Hg, Calculate: a. Pv b. W c. H d.  Example No. 3 Wet and dry bulb temperature measurements made outside on a cold day reveal that td = 5.0°C and tw = 4.0°C. If P = 100 KPa, determine a. Pv in KPa b. W c. H d.  e. The RH, tw and Q if the mixture is heated at constant pressure to 25C

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Psychrometric Processes The basic psychrometric processes involved in air conditioning to vary psychrometric properties of air according to the requirement are as follows: 1. Sensible heating 2. Sensible cooling 3. Cooling and Dehumidifying 4. Heating and Humidifying 5. Humidifying 6. Adiabatic mixing of air streams Sensible Heating Sensible heating is the addition of heat tp moist air, without the addition of moisture. The process follows a constant specific humidity line. Let air at temperature t d1 passes over a heating coil of temperature t d3 , as shown in Figure. It may be noted that the temperature of air leaving the heating coil (t d2 ) will be less than t d3 . The process of sensible heating, on the psychrometric chart, is shown by a horizontal line 1-2 extending from left to right as shown in Figure. The point 3 represents the surface temperature of the heating coil. The heat absorbed by the air during sensible heating may be obtained from the psychrometric chart by the enthalpy difference (h2 – h1) as shown in Figure. It may be noted that the specific humidity during the sensible heating remains constant W1 = W2. The dry bulb temperature increases from t d1 to td2 and relative humidity reduces from 1 to 2.

Notes: 1. For sensible heating, steam or hot water is passed through the heating coil. The heating coil may be electric resistance coil. 2. The sensible heating of moist air can be done to any desired temperature. By Energy Balance Qs  m(h 2 - h1 ) Qs  mC p (t d2 - t d1 ) Cp  1.0045  1.86W W  W1  W2

Sensible Cooling A sensible cooling process removes heat from the moist air, resulting in a drop of its temperature; its humidity ratio remains constant, as in the figure below. The sensible cooling process occurs when moist air flows through a cooling coil containing chilled water at a temperature equal to or greater than the dew point of the entering moist air. The temperature of moist air reduces from t d1 to td2, with W1 = W2 which results an increased in relative humidity.

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Q s  m ( h1  h 2 ) Q s  mC p ( td1  td 2) C p  1.0045  1.86 W KJ kg - C W  W1  W2

C p  1.02

Cooling and Dehumidifying Process A cooling and Dehumidifying process is the removal of heat and moisture from moist air. Both the humidity ratio and temperature decreases. It involves both sensible heat and latent heat transfer because some water vapor is condensed in the form of liquid water, called the condensate.

By energy balance

Q s  mC p t d1  t d 2   6

mh 1  Q c  mh 2  m w h w

C p  1.0045  1.86 Wa

Q c  m(h 1 - h 2 ) - m w h w  1

Wa  W2

By moisture balance

Q L  m( h1  h a )  7

mW1  mW2  m w

Q L  m( W1  Wa )h fg  8

m w  m( W1  W2 )  2

h fg  h fg at t d2  (From steam table)

Equation 2 to equation 1

KJ kg Qs SHF  Qs  Q L

Q c  m(h1 - h 2 ) - ( W1  W2 )h w   3

h fg  2500

Qc  Qs  Q L  4 Q s  m(h a  h 2 )  5

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Heating and Humidifying Process Heating and humidifying process is the addition of heat and moisture to moist air. This process is generally required during the cold months of the year. It involves both sensible and latent heat transfer because water is evaporated resulting an increase in humidity ratio. The sensible heat transfer is associated with an increase in dry bulb temperature and the latent heat transfer is associated with an increase in specific humidity (or humidity ratio).

By energy balance

Q s  mC p t d 2  t d1   6

mh 1  Q H  m w h w  mh 2

C p  1.0045  1.86 Wa

Q H  m(h 2 - h1 ) - m w h w  1

Wa  W1

By moisture balance

Q L  m( h 2  h a )  7

mW1  m w  mW2

Q L  m( W2  Wa )h fg  8

m w  m( W2  W1 )  2

h fg  h fg at t d2  (From steam table)

Equation 2 to equation 1

KJ kg Qs SHF  Qs  Q L h fg  2500

Q H  m(h 2 - h1 ) - ( W2  W1 )h w   3 Q H  Qs  Q L ...