Module 14: The psychrometrics of air conditioning systems

The CPD articles in the April, August, November and December 2009 editions of the CIBSE Journal have set out the principles of the Psychrometric Chart and how to use the chart to plot individual processes, determine the respective component loads and combine these into commonly employed sub-systems

This article will further develop the use of the chart to combine the processes to develop a basic constant volume, full fresh air system – this technique may then be used to determine the required components of an air conditioning system and may also provide the basis for comparisons of the performance of different systems or operating regimes. Symbols are defined in the box at the end of the article – you may also find it useful to be able to refer to those earlier articles (they are all available online at www.cibsejournal. com). To help understand the example in this article you are recommended to build up the process on a psychrometric chart.

Fig. 1: Summer psychrometric processes

Combining the processes

The psychrometry for the complete air conditioning system can be developed from the combination of the individual components and sub-systems that have been previously described. It is the function of the individual processes that determine the plant requirements although, of course, the final components are normally restricted to those commercially available. To provide an example a system will be developed to satisfy the room loads for a 8m wide by 5m deep by 3m high single room that have been determined as:-

  • summer (cooling) room load of 5kW (sensible gain) 1.2kW (latent gain)
  • winter (heating) load of 1.9kW (sensible loss) and 0.8kW (latent gain).

The design conditions for the room are 20ºC to 24ºC operative temperature and 35% to 50% saturation (ie a range of acceptable conditions that can vary season to season). The room is of medium thermal weight (medium to fast response) and has a moderate amount of glazing, and so at this stage it would be reasonable to assume that values of air temperatures equivalent to values of operative temperatures be used.

Establishing the supply air mass flow rate

As a design decision (based on the strategy being used to distribute air in the room) the minimum supply air temperature will be 16ºC (8K lower than the room temperature). If, alternatively, a low level supply system was to be used, the supply air temperature may well have been limited to being no more than 5K cooler than the room temperature. (See CIBSE Guide Section B2.4.2 [1] for more details.) It is normally the requirements of room cooling as opposed to heating (in air conditioning applications) that will determine the air supply rate in a constant volume system. Hence the mass flow rate, , of the supply air can be calculated from the room sensible cooling load, ΦSC = CpRS – θSC) where Cp is the air specific heat capacity of air that can be taken as 1.012 kJ·kg-1·K-1. So = ΦSC / [CpRS – θSC)] = 5.0 / [1.012 x (24 – 16)] = 0.62 kg·s-1.

Fig. 2: Winter psychrometric processes

The summer system

The summer room sensible/total heat ratio will be 5.0/(5.0+1.2) = 0.81 and since this is a coincident sensible cooling and latent cooling load, the gradient of the room ratio line (RRL) is taken from the bottom quadrant of the protractor on the psychrometric chart and is drawn through summer room point RS. The intersection of this line with the specified value of θSC (ie 16ºC) provides the summer supply air point SC. As an alternative to using the RRL to determine the supply air point, the room latent load may be used to calculate the supply air moisture content from ΦL = hfg (gR – gS) and so reading the value of gR from the chart as 8.8g·kg-1da or 0.0088 kg·kg-1 da the value of gS = gR– (ΦL/hfg) = 0.0088- [1.2/(0.62 x 2450)] = 0.0080kg·kg-1da or 8.0g·kg-1da. Looking at the chart (Figure 1) these two methods provide the same supply air point – the simple calculation method is probably the most reliable. However, the use of the RRL allows the designer to look at the range of supply air conditions that could be used if there was flexibility in the design supply air temperature.

To develop the ‘summer cycle’ the outdoor air, OS, is plotted (the values identifying OS having been established from climate data such as Table A2.6 of CIBSE Guide [2]). In a full fresh air system, air at OS must be finally conditioned to produce air at SC. Looking at the chart OS has a higher temperature and moisture content than SC, where (from the chart) hO= 57kJ·kg-1 and hS= 35kJ·kg-1. Hence there is a need to reduce the enthalpy of the air by (57 – 35)kJ·kg-1 = 22kJ·kg-1.

Fig. 3: Basic system component schematic

In this simple system (and in many installed systems) a cooling coil will be used to both cool and dehumidify the air. The air condition leaving the coil will be determined primarily by the dehumidifying requirement and the contact factor, β, of the coil. From the manufacturer a contact factor of 0.85 has been obtained (based on the flowrate of the air passing through the coil, and the coil size) and from this the coil temperature, (the coil ‘ADP’) indicated by point X on the chart may be determined.

So β = 0.85 = (gO – gS) / (gO – gX) so gX= gO – (gO – gS) / 0.85 = 11.4 – (11.4 – 8.0) / 0.85 = 7.4g·kg-1da and hence the point X may be plotted where the saturation curve intersects with a moisture content of 7.4g·kg-1da. The cooling coil process line is then OS→C where C is the intersection of the line OS to X with the supply air moisture content, gS and has an enthalpy, hC, of 32.5kJ·kg-1.

The air now has an appropriate moisture content to supply the room but, as a result of the need to dehumidify the air, the dry bulb temperature is below the required value of θS. An afterheater is used to increase the temperature from θC to θS. (The fan will also act as a sensible air heater).

The winter process

To outdoor condition, OW is plotted (on Figure 2) based on a knowledge of local climatic data (that can, for example come from Table A2.4 of CIBSE Guide [2]). To determine the supply air point (at winter design), SH the supply air temperature, θSH must be established. θSH will be determined either from a knowledge of the supply air mass flowrate ṁ in combination with the room sensible heating load, φSH, the supply air mass flowrate having previously been established from the cooling requirement, φSC; or the supply air temperature may be determined from a requirement of the particular supply regime (eg low level or high level supply).

In this case, having already determined the air mass flowrate from the cooling load as 0.62kg·s-1 the heating supply air temperature will be θSH= θR + (ΦSH/Cp) = 19 + [1.9/(0.62 x 1.012)] = 22ºC. The winter room sensible/total heat ratio will be 1.9/(1.9 + 0.8) = 0.70 and since this is a coincident sensible heating and latent cooling load, the gradient of the room ratio line (RRL) is taken from the top quadrant of the protractor and is drawn through winter room point RW. The intersection of this line with the calculated value of θSH (ie 22ºC) provides the winter supply air point SH (and of course a similar calculation to that used for the summer design may be undertaken using the winter latent load to confirm the supply air moisture content). The supply air enthalpy hSH can be read off as 33.0kJ·kg-1.

Point SH is clearly both at a higher temperature and moisture content than the winter outdoor air condition, OW, and so a sensible heater and a humidifier is required; in this example a steam humidifier has been used. To increase the temperature typically a water or electric coil (or frequently two coils – a preheater or frost coil, and an afterheater) may be used. In this example one heating process will be shown from OW→P→AH, where θAH is the supply temperature (or maybe just slightly cooler as the subsequent steam humidifier will also add a small degree of sensible heat to the air) where hAH is 27.0kJ·kg-1. A steam humidifier is then used to increase the moisture content (with potentially a small increase in air dry bulb temperature) from gP (the same as gOW) to gSH with the process P→SH.

By examining the psychrometric requirements determined for summer and winter operation, the initial schematic of a basic full fresh air, constant volume conditioning system can be sketched out as in Figure 3.

Calculating the loads

The loads may be readily established from the chart where Power (kW) = mass flow rate (kg·s-1) x enthalpy change (kJ·kg-1) = ṁΔh and so, for example, the summer cooling coil design load is 0.62 x (57.0-32.5) = 15.2kW.

The summer afterheater load = 0.62 x (35.0- 32.5) = 1.55kW, and so the total plant load is thus 15.2 + 1.55 = 16.8kW. This compares with the room cooling load of 5.2kW sensible + 1.2kW latent = 6.4kW! However, it is not correct to simply compare the two values as the plant load includes:

  • The power to cool the outdoor air (that will be providing necessary ventilation fresh air to the room) down to the room condition;
  • The power to ‘overcool’ the air dry bulb temperature so that condensation takes place to dehumidify the air; and
  • Reheat power to bring the air dry bulb temperature from the lower dehumidifying temperature back up to the supply air temperature.

The load in winter will comprise the heater load, 0.62 x (27.0 -1.0) = 16.1kW and the humidifier load, 0.62 x (33.0-27.0) = 3.7kW giving a total plant load of 19.8kW. The significant difference between the plant and the room loads is by virtue of the need to increase the temperature and moisture content of the cold, dry outdoor air before it can be heated to provide any useful room conditioning.

Fig. 4: All-year-round operating regime based on outdoor conditions

Year round operation

The modes of operation for this simple system are shown in Figure 4. This diagram (after Legg [3]) indicates the operating modes for the system for the annual range of outdoor conditions.


The preheater is likely to be controlled using feedback from a downstream duct sensor and is set to maintain a minimum temperature (likely to be between 5ºC and 8ºC) when the system is in operation – this will only operate in winter. The humidifier should only operate when the outdoor air has a low moisture content – this is predominantly when the outdoor air is cooler (tables of percentage frequencies of occurrence of outdoor conditions may be used to determine the actual periods).

For this simple example system a room dry bulb temperature sensor could provide the information to the controller to modulate both the afterheater and the cooling coil in sequence. However the cooling coil will also be controlled from the feedback from a room humidity sensor – if the room humidity rises the cooling coil will be actuated. This will override the requirement for dry bulb temperature control and so, if the resulting room temperature is too cool, the afterheater will also be actuated to reheat the air. This is, alongside the humidification load, a potential profligate use of energy that, with appropriate system design, may be substantially reduced – this will be discussed in later articles.

A graphical interpretation of operating regimes (preferably combined with frequency based climate data) provides an accessible tool to assist the designer in examining and optimising the all-year system operation.