Refrigeration and Air-conditioning (MEng 4711)

Lecture 6

Psychrometry

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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 study of the properties of mixtures of air and water vapor.

• Atmospheric air is a mixture of many gases plus water vapor and a number of pollutants (Fig. 6.1). The amount of water vapor and pollutants vary from place to place.

• The concentration of water vapor and pollutants decrease with altitude, and above an altitude of about 10 km, atmospheric air consists of only dry air. The pollutants have to be filtered out before processing the air. Hence, what we process is essentially a mixture of various gases that constitute air and water vapor. This mixture is known as moist air.

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Fig. 6.1 Atmospheric air

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• 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. The composition of dry air is given table below.

• Based on the above composition the molecular weight of dry air is found to be 28.966 and the gas constant R is 287.035 J/kg.K.

Introduction

• As mentioned before the air to be processed in air conditioning systems is a mixture of dry air and water vapor.

• While the composition of dry air is constant, the amount of water vapor present in the air may vary from zero to a maximum depending upon the temperature and pressure of the mixture (dry air + water vapor).

• 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 18.015 and its gas constant is 461.52 J/kg.K.

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Introduction

Methods for estimating properties of moist air

• In order to perform air conditioning calculations, it is essential first to estimate various properties of air.

• It is difficult to estimate the exact property values of moist air as it is a mixture of several permanent gases and water vapor.

• However, moist air up to 3 atm. pressure is found to obey perfect gas law with accuracy sufficient for engineering calculations.

• Since in most cases the pressures involved are low, one can apply the perfect gas model to estimate psychometric properties.

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Basic gas laws for moist air:

• According to the Gibbs-Dalton law for a mixture of perfect gases, the total pressure exerted by the mixture is equal to the sum of partial pressures of the constituent gases.

• According to this law, for a homogeneous perfect gas mixture occupying a volume V and at temperature T, each constituent gas behaves as though the other gases are not present (i.e., there is no interaction between the gases). Each gas obeys perfect gas equation. Hence, the partial pressures exerted by each gas, p1,p2,p3

… and the total pressure pt are given by:

• where n1,n2,n3,… are the number of moles of gases 1,2,3,…7

• Applying this equation to moist air.

where

p = pt = total barometric pressure

pa = partial pressure of dry air

pv = partial pressure of water

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Basic gas laws for moist air:

Important psychrometric properties:

• Dry bulb temperature (DBT) is the temperature of the moist air as measured by a standard thermometer or other temperature measuring instruments.

• Saturated vapor pressure (psat) is the saturated partial pressure of water vapor at the dry bulb temperature. This is readily available in thermodynamic tables and charts.

• ASHRAE suggests the following regression equation for saturated vapor pressure of water, which is valid for 0 to 100oC

• where psat = saturated vapor pressure of water in kiloPascals

• T = temperature in K

• The regression coefficients c1 to c6

are given by:

• c1 = -5.80022006E+03, c2

= -5.516256E+00, c3 = -4.8640239E-02

• c4 = 4.1764768E-05, c5

= -1.4452093E-08, c6 = 6.5459673E+00

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• Relative humidity (Φ) is defined as the ratio of the mole fraction of water vapor in moist air to mole fraction of water vapor in saturated air at the same temperature and pressure. Using perfect gas equation we can show that:

• Relative humidity is normally expressed as a percentage. When Φ is 100 percent, the air is saturated.

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Important psychrometric properties:

• Humidity ratio (W): The humidity ratio (or specific humidity) W is the mass of water associated with each kilogram of dry air. Assuming both water vapor and dry air to be perfect gases, the humidity ratio is given by:

• Substituting the values of gas constants of water vapor and air Rv and Ra

in the above equation; the humidity ratio is given by:

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Important psychrometric properties:

• For a given barometric pressure pt, given the DBT, we can find the saturated vapor pressure psat from the thermodynamic property tables on steam.

• Then using the above equation, we can find the humidity ratio at saturated conditions, Wsat.

• It is to be noted that, W is a function of both total barometric pressure and vapor pressure of water.

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Important psychrometric properties:

• Dew-point temperature: If unsaturated moist air is cooled at constant pressure, then the temperature at which the moisture in the air begins to condense is known as dew-point temperature (DPT) of air. An approximate equation for dew-point temperature is given by:

• where Φ is the relative humidity (in fraction). DBT & DPT are in oC.

• Of course, since from its definition, the dew point temperature is the saturation temperature corresponding to the vapor pressure of water vapor, it can be obtained from steam tables or using Eqn. above.

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Important psychrometric properties:

• Properties such as humidity ratio, enthalpy and specific volume are based on 1 kg of dry air.

• This is useful as the total mass of moist air in a process varies by the addition/removal of water vapor, but the mass of dry air remains constant.

• Degree of saturation μ: 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, i.e.,

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Important psychrometric properties:

• Enthalpy: The enthalpy of moist air is the sum of the enthalpy of the dry air and the enthalpy of the water vapor.

• Enthalpy values are always based on some reference value. For moist air, the enthalpy of dry air is given a zero value at 0oC, and for water vapor the enthalpy of saturated water is taken as zero at 0oC.

• The enthalpy of moist air is given by:

where – cp

= specific heat of dry air at constant pressure, kJ/kg.K

– cpw = specific heat of water vapor, kJ/kg.K

– t = Dry-bulb temperature of air-vapor mixture, oC

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Important psychrometric properties:

• where

W = Humidity ratio, kg of water vapor/kg of dry air

ha = enthalpy of dry air at temperature t, kJ/kg

hg = enthalpy of water vapor at temperature t, kJ/kg

hfg = latent heat of vaporization at 0oC, kJ/kg

• The unit of h is kJ/kg of dry air. Substituting the approximate values of cp

and hg, we obtain:

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Important psychrometric properties:

• Humid specific heat: From the equation for enthalpy of moist air, the humid specific heat of moist air can be written as:

• where

cpm = humid specific heat, kJ/kg.K

cp = specific heat of dry air, kJ/kg.K

cpw = specific heat of water vapor, kJ/kg

W = humidity ratio, kg of water vapor/kg of dry air

• Since the second term in the above equation (w.cpw) is very small compared to the first term, for all practical purposes, the humid specific heat of moist air, cpm

can be taken as 1.0216 kJ/kg dry air.K

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Important psychrometric properties:

• Specific volume: The specific volume is defined as the number of cubic meters of moist air per kilogram of dry air.

• From perfect gas equation since the volumes occupied by the individual substances are the same, the specific volume is also equal to the number of cubic meters of dry air per kilogram of dry air, i.e.,

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Important psychrometric properties:

Psychrometric chart

• A Psychrometric chart graphically represents the thermodynamic properties of moist air.

• Standard psychrometric charts are bounded by the dry-bulb temperature line (abscissa) and the vapor pressure or humidity ratio (ordinate). The Left Hand Side of the psychrometric chart is bounded by the saturation line.

• Psychrometric charts are readily available for standard barometric pressure of 101.325 kPa at sea level and for normal temperatures (0-50oC).

• ASHRAE has also developed psychrometric charts for other temperatures and barometric pressures (for low temperatures: -40 to 10oC, high temperatures 10 to 120oC and very high temperatures 100 to 120oC).

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Psychrometric chart

• The basic features of the psychrometric chart are illustrated in Fig. shown below.

• The dry-bulb temperatures are shown on the horizontal axis, and the specific humidity is shown on the vertical axis.

• Some charts also show the vapor pressure on the vertical axis since at a fixed total pressure P there is a one-to-one correspondence between the specific humidity v and the vapor pressure Pv.

• On the left end of the chart, there is a curve (called the saturation line) instead of a straight line.

• All the saturated air states are located on this curve. Therefore, it is also the curve of 100 percent relative humidity. Other constant relative-humidity curves have the same general shape.

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Psychrometric chart

Psychrometric chart

• Lines of constant wet-bulb temperature have a downhill appearance to the right.

• Lines of constant specific volume (in m3/kg dry air) look similar, except they are steeper.

• Lines of constant enthalpy (in kJ/kg dry air) lie very nearly parallel to the lines of constant wet-bulb temperature. Therefore, the constant wet-bulb-temperature lines are used as constant-enthalpy lines in some charts.

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• For saturated air, the dry-bulb, wet-bulb, and dew-point temperatures are identical (Fig. 14–15).

• Therefore, the dew-point temperature of atmospheric air at any point on the chart can be determined by drawing a horizontal line (a line of ω = constant) from the point to the saturated curve.

• The temperature value at the intersection point is the dew-point temperature.

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Psychrometric chart

EXAMPLE: The Use of the Psychrometric Chart

• Consider a room that contains air at 1 atm, 35°C, and 40 percent relative humidity. Using the psychrometric chart, determine

a) the specific humidity,

b) the enthalpy,

c) the wet-bulb temperature,

d) the dew-point temperature, and

e) the specific volume of the air.

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a) The specific humidity is determined by drawing a horizontal line from the specified state to the right until it intersects with the ω axis. At the intersection point we read

ω = 0.0142 kg H2O/kg dry air

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EXAMPLE: The Use of the Psychrometric Chart

b) The enthalpy of air per unit mass of dry air is determined by drawing a line parallel to the h constant lines from the specific state until it intersects the enthalpy scale, giving h =71.5 kJ/kg dry air

c) The wet-bulb temperature is determined by drawing a line parallel to the Twb = constant lines from the specified state until it intersects the saturation line, giving Twb = 24°C

d) The dew-point temperature is determined by drawing a horizontal line from the specified state to the left until it intersects the saturation line, giving Tdp = 19.4°C

e) The specific volume per unit mass of dry air is determined by noting the distances between the specified state and the v = constant lines on both sides of the point. The specific volume is determined by visual interpolation to be v = 0.893 m3/kg dry air

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Measurement of psychrometric properties:

• Based on Gibbs’ phase rule, the thermodynamic state of moist air is uniquely fixed if the barometric pressure and two other independent properties are known.

• This means that at a given barometric pressure, the state of moist air can be determined by measuring any two independent properties.

• One of them could be the dry-bulb temperature (DBT), as the measurement of this temperature is fairly simple and accurate.

• The accurate measurement of other independent parameters such as humidity ratio is very difficult in practice.

• Since measurement of temperatures is easier, it would be convenient if the other independent parameter is also a temperature.

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• Of course, this could be the dew-point temperature (DPT), but it is observed that accurate measurement of dew-point temperature is difficult.

• In this context, a new independent temperature parameter called the wet-bulb temperature (WBT) is defined.

• Compared to DPT, it is easier to measure the wet-bulb temperature of moist air.

• Thus knowing the dry-bulb and wet-bulb temperatures from measurements, it is possible to find the other properties of moist air.

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Measurement of psychrometric properties:

AIR-CONDITIONING PROCESSES• Maintaining a living space or an

industrial facility at the desired temperature and humidity requires some processes called air-conditioning processes.

• These processes include simple heating (raising the temperature), simple cooling (lowering the temperature), humidifying (adding moisture), and dehumidifying (removing moisture). Sometimes two or more of these processes are needed to bring the air to a desired temperature and humidity level.

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Simple Heating and Cooling (ω = constant)

• The amount of moisture in the air remains constant during this process since no moisture is added to or removed from the air.

• That is, the specific humidity of the air remains constant (ω = constant) during a heating (or cooling) process with no humidification or dehumidification.

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• Notice that the relative humidity of air decreases during a heating process even if the specific humidity ω remains constant.

• This is because the relative humidity is the ratio of the moisture content to the moisture capacity of air at the same temperature, and moisture capacity increases with temperature.

• Therefore, the relative humidity of heated air may be well below comfortable levels, causing dry skin, respiratory difficulties, and an increase in static electricity.

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Simple Heating and Cooling (ω = constant)

• A cooling process at constant specific humidity is similar to the heating process, except the dry-bulb temperature decreases and the relative humidity increases during such a process.

• Cooling can be accomplished by passing the air over some coils through which a refrigerant or chilled water flows.

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Simple Heating and Cooling (ω = constant)

Sensible cooling:

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• Figure below shows the sensible cooling process O-A on a psychrometric chart.

• The heat transfer rate during this process is given by:

• Sensible heating (Process O-B): During this process, the moisture content of air remains constant and its temperature increases as it flows over a heating coil. The heat transfer rate during this process is given by:

• where cpm is the humid specific heat (≈1.0216 kJ/kg dry air) and ma

is the mass flow rate of dry air (kg/s).

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Sensible heating:

Heating with Humidification

• Problems associated with the low relative humidity resulting from simple heating can be eliminated by humidifying the heated air.

• This is accomplished by passing the air first through a heating section (process 1-2) and then through a humidifying section (process 2-3), as shown in the Fig.

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• The location of state 3 depends on how the humidification is accomplished.

• If steam is introduced in the humidification section, this will result in humidification with additional heating (T3 > T2).

• If humidification is accomplished by spraying water into the airstream instead, part of the latent heat of vaporization comes from the air, which results in the cooling of the heated airstream (T3 < T2).

• Air should be heated to a higher temperature in the heating section in this case to make up for the cooling effect during the humidification process.

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Heating with Humidification

Example: Heating with Humidification of Air

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Cooling with Dehumidification

• The specific humidity of air remains constant during a simple cooling process, but its relative humidity increases.

• If the relative humidity reaches undesirably high levels, it may be necessary to remove some moisture from the air, that is, to dehumidify it. This requires cooling the air below its dew point temperature.

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Example: Cooling and Dehumidification

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Adiabatic Mixing of Airstreams

• Many air-conditioning applications require the mixing of two airstreams.

• This is particularly true for large buildings, most production and process plants, and hospitals, which require that the conditioned air be mixed with a certain fraction of fresh outside air before it is routed into the living space.

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• The heat transfer with the surroundings is usually small, and thus the mixing processes can be assumed to be adiabatic. Mixing processes normally involve no work interactions, and the changes in kinetic and potential energies, if any, are negligible.

• Then the mass and energy balances for the adiabatic mixing of two airstreams reduce to

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Adiabatic Mixing of Airstreams

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Adiabatic Mixing of Airstreams

Example 3: Adiabatic mixing

• Saturated air leaving the cooling section of an air-conditioning system at 14°C at a rate of 50 m3/min is mixed adiabatically with the outside air at 32°C and 60 percent relative humidity at a rate of 20 m3/min. Assuming that the mixing process occurs at a pressure of 1 atm, determine the specific humidity, the relative humidity, the dry-bulb temperature, and the volume flow rate of the mixture.

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Solution

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Cooling Towers

• Power plants, large air-conditioning systems, and some industries generate large quantities of waste heat that is often rejected to cooling water from nearby lakes or rivers.

• In some cases, however, the cooling water supply is limited or thermal pollution is a serious concern. In such cases, the waste heat must be rejected to the atmosphere, with cooling water recirculating and serving as a transport medium for heat transfer between the source and the sink (the atmosphere).

• One way of achieving this is through the use of wet cooling towers.

• Cooling towers also are frequently employed to provide chilled water for applications other than those involving power plants.

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Cooling Tower

• A schematic diagram of a forced-convection, counterflow cooling tower is shown in Fig. below. The warm water to be cooled enters at 1 and is sprayed from the top of the tower.

• The falling water usually passes through a series of baffles intended to keep it broken up into fine drops to promote evaporation.

• Atmospheric air drawn in at 3 by the fan flows upward, counter to the direction of the falling water droplets.

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• As the two streams interact, a small fraction of the water stream evaporates into the moist air, which exits at 4 with a greater humidity ratio than the incoming moist air at 3.

• The energy required for evaporation is provided mainly by the portion of the incoming water stream that does not evaporate, with the result that the water exiting at 2 is at a lower temperature than the water entering at 1.

• Since some of the incoming water is evaporated into the moist air stream, an equivalent amount of makeup water is added at 5 so that the return mass flow rate of the cool water equals the mass flow rate of the warm water entering at 1.

• For operation at steady state, mass balances for the dry air and water and an energy balance on the overall cooling tower provide information about cooling tower performance.

• In applying the energy balance, heat transfer with the surroundings is usually neglected. The power input to the fan of forced-convection towers also may be negligible relative to other energy rates involved.

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Cooling Towers

Example: Cooling of a Power Plant by a Cooling Tower

• Cooling water leaves the condenser of a power plant and enters a wet cooling tower at 35°C at a rate of 100 kg/s. Water is cooled to 22°C in the cooling tower by air that enters the tower at 1 atm, 20°C, and 60 percent relative humidity and leaves saturated at 30°C. Neglecting the power input to the fan, determine (a) the volume flow rate of air into the cooling tower and (b) the mass flow rate of the required makeup water. 56

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