PSYCHROMETRY AND CALCULATIONS FOR AIR CONDITIONING DESIGN

INTRODUCTION

Comfort air conditioning is the process of keeping a giving space within specified conditions of temperature, relative humidity, etc. Maintaining these specified conditions become necessary as a result of the unpleasantly high temperatures from solar heat gains and heat gains from lighting and other equipment in the confined space. The process is quite a complex one requiring an understanding of the properties of air in its different conditions as it passes through the process. Air primarily is a mixture of two major component gases (oxygen and nitrogen), traces of a number of other gases and water vapour. The water vapour in the air is condensable (under right conditions of temperature and pressure) and where all vapour in the air is condensed out, the air is referred to as “Dry air”. The typical percentage proportion of the various components of dry air is given below:

Gas	Proportion (%)
Nitrogen	78.048
Oxygen	20.9476
Carbon dioxide	0.0314
Hydrogen	0.00005
Argon	0.9347

It should be noted that the composition varies slightly at different geographic locations and from time to time.

The natural means of introducing water vapour into air is through evapo-transpiration (from plants) and evaporation (from humans in form of sweat or from water bodies). As the conditions of temperature, pressure vary, water molecules drop out or are added to the surrounding air. The rate at which these occur is dependent on temperature, pressure and wind velocity.  Also the water vapour holding capacity of the air is temperature and pressure dependent. It is therefore vital for any one studying air conditioning to understand that the air under study is a mixture of two different gaseous substances. One of these is the dry air with composition as outlined above and the other, water vapour. The amount of water vapour contained in moist air within the temperature range of -18 ⁰C to 37 ⁰C varies from 0.05 to 3% by mass. This variation has a critical influence on the characteristics of moist air.

BASIC AIR-CONDITIONING TERMINOLOGIES

Dry bulb temperature, DB (⁰C or ⁰F): this is the ambient air temperature as measured by a standard temperature measuring device.

Wet bulb temperature, WB (⁰C or ⁰F): this is the temperature recorded by a thermometer that has its bulb wrapped in moist cloth and rotated rapidly in the air to cause evaporation of its moisture. A fast evaporation from the cloth indicates low moisture content of the surrounding air while a slow evaporation indicates that the surrounding air is already moisture-laden. In dry air, moisture rapidly evaporates from the cloth drawing heat from the thermometer and producing a lower temperature reading usually called the wet-bulb depression (the difference between the DB and WB temperatures)

Relative humidity, RH (%): As mentioned earlier, the moisture (water vapour) holding capacity of air varies with temperature. This therefore means that for any given temperature, there is an amount of moisture that will bring the air to saturation (i.e. to 100% of its water vapour holding capacity). This water vapour contained in the air exerts its own pressure (termed vapour pressure). Relative humidity is the ratio of the vapour pressure of the moist air (the air being considered) to the vapour pressure of the same air if it were to be at 100% saturation at the same temperature.

Dew point temperature,  T_dew (⁰C or ⁰F): this is the temperature of saturated air which has the same vapour pressure as the air under consideration. Note that saturated air has the same WB and DB temperatures. Because the air has reached saturation, condensation begins at this temperature and will continue if lowered further.

Sensible heat Q_S : addition or extraction of heat from a substance results in changes in the temperature of the substance. The sensible heat is a measure of the thermal energy associated with a change in the temperature of a substance. It is termed sensible because, this form of heat can be felt by the sense of touch.

Latent heat Q_L : this is a measure of the thermal energy associated with a change of state or phase of a substance. Take as an example the heating of a kettle of water. As heat of added, the temperature of the water is felt to rise (sensible heat). At a point, say about 100 ⁰C, the temperature stays the same even as more heat is added. The additional heat is used up in changing the state of the water from the liquid state to the vapour state. This added heat used up is the latent heat.

Enthalpy: this is the measure of the total heat (sensible and latent heat) in a substance and is a measure of its internal energy and capacity to do work  

PSYCHROMETRY

Water vapour, air, temperature and pressure interact with each other with consequences which can be exploited for heating processes or cooling processes. For example, as air temperature rises, its capacity to hold water vapour rises also and the warmer air becomes less dense. Psychrometry is the study of the behavior of air and water vapour and a sound knowledge of Psychrometrics is necessary to carry out air-conditioning calculations. The terminologies discussed above are particularly relevant in Psychrometry.  The psychrometric chart is a graphical representation of the thermodynamic properties of moist air and various air-conditioning processes and cycles.  The figure below shows the variables shown in a typical psychrometric chart for any given point.

The chart helps the designer to calculate and analyze the work and energy transfer during various air-conditioning processes and cycles. Typical arrangement of the coordinates on the chart is shown below: It should be noted that psychrometric charts in use today have two kinds of basic coordinates. Those published by the American Society of Heating Refrigeration and Air-conditioning Engineers (ASHRAE) and the Charted Institution of Building Services Engineering (CIBSE) use the h-w coordinates, where enthalpy h and humidity ration w are the coordinates. Charts published by Carrier Corporation and the Trane Company use the  T-w coordinates. An abridged ASHRAE psychrometric chart is shown below.

To understand the use of the chart above, let’s assume an air-conditioned room at sea level has an indoor design temperature of 75 ⁰F and a relative humidity Ф of 50% and we want to determine the humidity ratio, enthalpy h, dew point T_dew  of the indoor air. To do this, we shall follow these steps

1.      Establish the room condition of T = 75 ⁰F and a relative humidity Ф of 50% on the chart (point r). This is the point where the temperature line at 75 ⁰F meets the 50% Ф-line.

2.      Draw a horizontal line toward the humidity ratio scale w-line, w lb/lb. This line cuts the humidity ratio scale at w_r = 0.0093 lb/lb.

3.      To get the enthalpy, draw a line through point r parallel to the enthalpy h-line. This gives the enthalpy of the room air as h_r = 28.1 Btu/lb.

4.      Draw a horizontal line left ward from point r to meet the saturation curve. This cuts the curve at 55 ⁰F. This is the dew point temperature, T_dew.

By using the chart, we can also determine the specific volume and the wet bulb temperature of the room air by simply drawing lines parallel to these coordinates from the room state point, r. To determine these two values draw a line from the room point r, parallel to the specific volume line (v-line) to get the specific volume and another line parallel to the wet bulb temperature line (T^*-line). These give the room air specific volume and wet bulb temperatures as v_r = 13.67 ft³/lb and T^* = 62.5 ⁰F respectively.

With our room air considered as state 1, now let us assume that a quantity of air of different temperature and relative humidity (in state 2) is brought into the room. What happens? Both streams of air will mix to form a third state point (state 3). From the principles of conservation of mass and conservation of energy (both well dealt with in many thermodynamics textbooks), the three state points lie on a straight line in a mass-energy coordinate system as in psychrometric charts published by the CIBSE and ASHRAE.  It shows clearly that when two air streams mix adiabatically, the mixture state (state 3) lies on the straight line which joins state point 1 and state point 2. Also the position of state point 3 is such that the line is divided inversely as the ratio of the masses of dry air in the constituent airstreams. This is shown below.

Since air conditioning is the treatment or conditioning of air to alter its temperature and moisture content to suit specific requirements, the psychrometric chart is vital in tracing, analyzing and predicting the changes occurring in the air as it is subjected to cooling, heating, humidification, dehumidification etc. Using the chart we can determine the amount of heat to be removed from (or added to) a space or the amount of moisture to be removed from (or added) to change the condition of the air in the room.

AIR-CONDITIONING LOADS

The main purpose of the air conditioning system is to provide suitable thermal conditions of comfort to the occupants or to provide suitable conditions for process or manufacturing applications. It is therefore vital to carry out cooling (or heating) load calculations to ensure that the cooling (or heating) equipment designed or selected serves the intended purpose of maintaining the required conditions in the conditioned space. For human comfort, it is required to keep the dry bulb temperature, the relative humidity and air velocity within control limits.

Principal sources of heat transfer to a conditioned space are:

·         Direct or indirect transmission of solar radiation from the sun. This accounts for a major part of the building heat gain. By proper design and orientation of the building, selection of suitable materials and landscaping, the overall energy cost (initial and operational) can be reduced.

·         Conduction through building elements (roofs, walls, windows etc.)

·         Infiltration of air into conditioned space through cracks

·         Heat emission by building occupants

·         Ventilation. This normally quoted in terms of volume is the quantity of outside air required to dilute contamination from all sources to an acceptable level. This is different from the conditioned air being supplied to the room. The later is usually quoted in terms of mass of air required to absorb any surplus heat or moisture within the conditioned space or conversely, to supply heat or moisture to keep the space within specified conditions.

·         Electrical load due to lighting

·         Load due to office equipment and or process machinery.

Design challenges

I choose to discuss the design challenges now before I go any further so as to give the reader an understanding of the shortcomings being encountered in the design of air conditioning systems for a location as mine, Nigeria. Some of these challenges are:

First, in the design of the space to be air-conditioned most architects do not take into consideration solar geometry for the location being considered as an energy consideration for the building’s orientation. This accounts for high energy requirements of the air conditioning equipment.

Second, we do not have proper documentation and standards for the properties of the materials used in our building construction industry. This is vital as the mechanism of heat transfer is a function of the thermal transmittance coefficient (U) and the temperature difference across the material under consideration.

Third, for any given location the variations in temperature, humidity and wind integrate to provide the climate experience. A study of these interrelationships, their hourly and daily variations, the seasonal changes in climatic conditions give rise to design guides for each geographical location. These design guides as published in developed countries such as USA, Canada, UK etc. provide valuable data for calculating air conditioning loads. They provide information such as design outdoor and indoor conditions for various locations and building use. They also provide peak solar gain times, peak solar cooling load in watt per building area exposed to sunlight etc.

With these challenges, variations will surely exist in our air conditioning load calculation and therefore a lot of experience is needed in applying data from imported standards and guides.

CALCULATIONS FOR AIR CONDITIONING DESIGN

Having outlined the various sources of heat gain above, it should be borne in mind that when designing air conditioning systems, the principal concern is directed towards heat gains, especially during the summer months. The reason for this approach is because heat gains present more searching demands than heat losses. The heat gain in any air conditioning process can be considered in two main parts – sensible heat gains and latent heat gains.

Sensible heat gains: as discussed earlier, this refers to that part of the heat which changes the temperature of the conditioned space. The quantity of air required to combat this heat gain is directly proportional to the difference in temperature between the supply air and the air in the conditioned space. This temperature difference is usually limited to a maximum of 20⁰ in order to avoid draft within the space. The sensible heat gain is calculated using:

H = M _*c _*∆T

Where H = sensible heat gain (kW)

            M = mass of supply air (kg/s)

            C = specific heat capacity of air (kJ/kg K)

            ∆T = design temperature rise (K)

Latent heat gain: these do not cause any increase in temperature but affect the moisture content of the air in the conditioned space. If the air in the room is not saturated, then it has the capacity to absorb water vapour from the room thereby causing the moisture content to rise. As we know, it is necessary to provide heat for any form of evaporation to take place. It is therefore customary to consider the addition of moisture to the air in the room in terms of kW of latent heat rather than kg/s of water evaporated.

From the above, the conditioned air supplied to the room has dual function: it is cool enough initially to suffer a temperature rise up to the room dry-bulb temperature in order to offset the sensible heat gains, and its initial moisture content is low enough to permit a rise to the value of the room moisture content as latent heat gains are offset. This is shown below where S is the supply state point and R is the return state point.

Heat Gain Equations

Having determined design outdoor and indoor conditions from necessary design guides, the formulae given below are employed for single space heat load considerations.

S/N	Quantity	Formula	Contributes to
1.	Heat gain for roof	Qr = Ur * Ar * CLTDr	Sensible Heat
2.	Heat gain for walls	Qw = Uw * Aw * CLTDw	Sensible Heat
3.	Heat gain for glass (unshaded)	Qg = Ug * Ag * CLTDg	Sensible Heat
4.	Heat gain for glass (Shaded)	Qgs = Ags * SC * SHGF * CLF	Sensible Heat
5.	Heat gain for partitions (walls, ceilings, floors)	Qp = Up * Ap * TDp	Sensible Heat
6.	Heat gain due to internal lights	QSL = (3.41 * W *CLF *zone% *P)/100	Sensible Heat
7.	Sensible Heat gain from occupants	Qsp = NP *SHP * CLFP * P	Sensible Heat
8.	Latent Heat gain from occupants	QLP = NP * LHP * P	Latent Heat
9.	Sensible Heat gain from equipment	QSEQ = 3.41 * WEQ * CLFEQ * P	Sensible Heat
10.	Latent Heat gain from equipment	QLEQ = Lat.Equip	Latent Heat
11.	Sensible heat due to outside air (ventilation or infiltration)	Q SOA = 1.1 * CFM * TDOA * AF	Sensible Heat
12.	Latent Heat gain due to outside air (ventilation or infiltration)	QLOA = 0.68 * CFM * ∆g * AF	Latent Heat

Q = Heat gain, Btuh

U = Design coefficient of thermal transmission, Btuh/ft²-F

A = Net area, ft²

CLTD = Cooling load temperature difference, F

SC = Shading coefficient

SHGF = Maximum solar heat gain factor for north facing glass, Btuh/ft²

CLF = Cooling load factor for north facing glass, dimensionless

TD = Design temperature difference across the partition, floor, or ceiling, F

W = Total wattage of lighting fixtures including ballast effects for fluorescent lights, Watts

Zone % = Percentage of lighting load to zone (100% if no plenum)

P = Profile i.e. the internal operating loads profile at given hour, fraction

SH_P = Sensible heat gain per person, Btuh/person

NP = Number of people in space considered

CLF_P = Cooling load factor to account for cooling system running 24 hours/day (equals to 1 since cooling system does not run 24 hours/day)

P = Internal operating profile percent at given hour, fraction

W_EQ = Recommended rate of heat gain, Btuh/ft² _* ft² or Watts

CLF_EQ = Cooling load factor to account for hours of operation of equipment

 Lat.Equip = Latent heat gain per piece of equipment, Btuh

CFM = Infiltration or ventilation rate, CFM

TD_OA = Inside – outside temperature difference at peak time, F

AF = Altitude factor, dimensionless

∆g = Inside – outside humidity ratio difference at peak time, grains of moisture.

In considering the cooling load for a whole building, the load from the single spaces obtained from the above formulae are summed up and further calculations are done to determine the following:

·         Supply fan power, Q_SF

·         Supply duct heat load, Q_SD

·         Return air load (recirculation fan power and heat gain through extract ventilated luminaires), Q_RA

·         Reheat load, Q_RH

In that case, the design refrigeration load will be given by:

            Q_R =(Q + Q_SF + Q_SD + Q_RA + Q_RH) _* f_P

Where Q_R = design refrigeration load and

             f_P = factor to cover chilled water pump power and heat gain to pipes.

APPLICATION OF PSYCHROMETRICS TO AIR CONDITIONING DESIGN

Let us now look at a practical application of the psychrometric chart in the design of an air conditioning system. As the figure below shows, the design conditions are as follows:

·         Room is to be maintained at 24 ⁰C (75.2 ⁰F) and a relative humidity of 50% RH

·         Outdoor condition is 34 ⁰C (93.2 ⁰F) and 40% RH

·         Total room sensible heat Q_SR  = 135 kW

·         Total room latent  heat Q_LR = 30 kW

·         Ventilation requirement is 1outdoor air to 3 re-circulated air (by mass)

·         Outside fresh air first flows over coil 1 where it is cooled to 10 ⁰C DBT and 85% RH.

·         The air is now mixed with the re-circulated air and through the fan, passed through coil 2 and sensibly cooled to 12 ⁰C DBT to be delivered to the room.

We want to find the mass flow rates of the supply air at the grill and the outside air required for ventilation.  Also, we would like to find the dry bulb temperature and enthalpy of the air handled by the fan, and the required cooling capacity of the cooling unit.

Mass flow rate of supply air.

From the room conditions, using the chart below, locate the point at which the dry bulb temperature of 24 ⁰C meets the 50% RH curve.  For clarity, you can copy the chart and print it out in A3 sized paper. From the point located follow the horizontal line rightward to hit the humidity ratio axis. This cuts the axis at w_i  =  0.0093 kg/kg. This is the humidity ratio of the room air.

Assuming a difference of 12⁰ between temperature of air supplied to the room and that to be maintained in the room, then the supply air temperature would then be 12 ⁰C.

The mass flow rate of air supplied is obtained from sensible energy balance,         

                                                             m_SA = Q_SR / (c _*∆T)

                                                                    = 135 / (1.021 _* 12)

                                                                    = 11 kg/s

The moisture content of the supply air can be obtained from latent energy balance,

                                                             w_S = w_i – (Q_LR /( m_{SA *} h_fg))

where h_fg = latent heat of vaporization of water, 2501 J/kg. Therefore,

                                                             w_S = 0.0093 – (30 / (11 _* 2501) = 0.0089 kg/kg

Back to the chart, taking a horizontal line from the humidity ratio axis at 0.0089 kg/kg to cut the 12 ⁰C DBT line, gives the supply air RH to be 100%.  

Ventilation

As noted earlier, ventilation is required to dilute contamination from all sources to an acceptable level. The volume of this air is usually related to the type of activity with the space and the number of persons in the space.  Since 25% of the supply air is fresh air,

Mass flow rate of fresh air,               m_o  = 0.25 _* 11 = 2.75 kg/s

Mass flow rate of re-circulated air, m_rc = 0.75 _* 11 = 8.25 kg/s

Condition of mixed air (handled by fan)

Using the sensible energy balance equation, the conditions of the mixed air can be found as follows:

Temperature of mixed air:

                        t_m = (m_o*t_o + m_{rc *} t_i) / (m_o + m_rc)

                            = (2.75 _* 34 + 8.25 _* 24) / (2.75 + 8.25)

                            = 26.5 ⁰C

Humidity ratio of mixed air:

                     w_m = (m_{o *} w_o + m_{rc *}  w_i) / (m_o + m_rc)

                           = (2.75 _* 0.0134 + 8.25 _* 0.0093) / (2.75 + 8.25)

                          = 0.0103 kg/kg

Enthalpy of mixed air:

                    h_m = (m_{o *} h_o + m_{rc *}  h_i) / (m_o + m_rc)

                         = (2.75 _* 68 + 8.25 _* 48) / (2.75 + 8.25)

                        = 53 kJ/kg

Required cooling capacity of coil

From the psychrometric chart, the enthalpy of air at the exit of the coil, h_c = 34 kJ/kg

Therefore required coil capacity, Q_c = m_{S *} (h_m – h_c)

                                                           = 11 _*  (53 – 34)

                                                          = 209 kW

If you have not yet printed a large copy of the psychrometric chart above do so now. Then on the chart, try locating the state points discussed in this example. You should be able to locate the following state points on the chart.

·         Inside design condition (t_i = 24 ⁰C, 50% RH, and w_i = 0.0093 kg/kg). What is the enthalpy of this state point from the chart?

·         Outdoor design condition (t_o = 34 ⁰C, 40% RH). Find w_o and h_o

·         Condition of the mixed outdoor and re-circulated air streams (t_m = 26.5 ⁰C, w_m = 0.0103 kg/kg)

·         Supply air condition (t_s = 12 ⁰C, w_s = 0.0089 kg/kg). Can you find the enthalpy of this state point?

Plotting these points on the chart will help you visualize the processes involved in air conditioning design.

It is not possible to cover completely all the necessary issues of psychrometrics and air conditioning design in any one post. Feel free to contact me should the need arise for clarity on any item discussed in this post or if you need assistance on your design.

Thanks for reading through and hope you find this post useful.

FURTHER READING:

1.      Walter T. Grondzik et al, Mechanical and Electrical Equipment for Buildings, 11^th Ed., John Wiley & Sons Inc.

2.      Jones, W. P., Air Conditioning Engineering, 5^th Ed., Butterworth Heinemann Publishers, 2001.

3.      Refrigeration and Air Conditioning, Kharagpur, India, 2008.