Air conditioning design on the h-x diagram: a step-by-step guide

Every air conditioning design starts with two questions: what are the input conditions (outdoor air, indoor loads) and what are the required output conditions (temperature and humidity in the room). The h-x diagram visualizes these conditions, lets you choose the right sequence of processes (cooling, mixing, heating, humidification) and calculate the capacities of the individual components. This article walks through the procedure in simplified form, on one example: an office for 100 people in Prague, summer operation without heat recovery (HRV).

Step 1: Establishing the design conditions

Outdoor air — summer design conditions

Design conditions are drawn from climate data, not from intuition. ASHRAE Climatic Design Data gives, for each location, values corresponding to 0.4%, 1% or 2% annual exceedance. For Prague, the summer design conditions are roughly 32 °C (dry-bulb temperature) at φ = 40% — on the h-x diagram this corresponds to the state $h = 63\ \text{kJ/kg}$, $x = 11.9\ \text{g/kg}$, wet-bulb temperature about 21 °C.

Indoor design conditions

The required conditions follow from the standards for thermal comfort. ASHRAE Standard 55 and EN 16798-1 (European standard) typically define 24–26 °C / φ 40–60% for offices. We choose 25 °C / φ = 50% — enthalpy about $50\ \text{kJ/kg}$, humidity ratio $10\ \text{g/kg}$.

Step 2: Calculating the indoor thermal and moisture load

• Sensible heat: people (100 × 65 W = 6.5 kW) + lighting + IT equipment + solar gains. For the example, a total of 30–40 kW.
• Latent heat: evaporation of sweat (100 × 55 W = 5.5 kW) + moisture from building structures. For the example, a total of 6–8 kW.

The ratio of sensible to total load (SHR, sensible heat ratio) indicates how steeply the room-state line rises on the diagram. For our office, $\text{SHR}=0.82$.

Step 3: Plotting the room state and the supply air

The indoor air state (25 °C / 50% RH) is the starting point. From it we draw a load line in the direction set by the SHR ratio — it shows how the air state changes as it absorbs the thermal and moisture load. The supply air must lie on this line, usually at a temperature of 14–16 °C. A lower supply temperature means a smaller flow rate but a higher risk of draught; a higher temperature, conversely, requires a larger flow rate.

Step 4: Mixing outdoor and recirculated air

The system supplies a portion of fresh outdoor air (the hygienic minimum per EN 16798-1, or Czech Government Regulation No. 361/2007 Coll.) and recirculates the rest. Let us assume 30% outdoor and 70% recirculated air. The resulting mixed state lies on the line connecting the outdoor and indoor states, 30% of the way from the indoor point (that is, 70% from the outdoor point — closer to the larger mass fraction, the recirculation) — roughly 27 °C / φ = 47%, $h = 54\ \text{kJ/kg}$.

Step 5: Cooling and dehumidification to the supply-air state

We cool the mixture to the required supply-air state (14–16 °C). In doing so, the air condenses out the excess moisture. In a simplified view (the ideal case, without a bypass factor) the line first goes vertically down (sensible cooling) to the dew point, then down and to the left along the saturation curve (dehumidification) — a real coil in fact heads toward the so-called apparatus dew point (ADP), and the supply air never fully reaches the saturation curve; the degree of deviation is expressed by the bypass factor.

$$\Phi_{\text{cool}} = \dot{m} \cdot (h_{\text{mix}} - h_{\text{supply}})$$

The enthalpy difference is about $54 - 34 = 20\ \text{kJ/kg}$. At a flow rate of $4\ \text{kg/s}$ we get $\Phi_{\text{cool}} = 80\ \text{kW}$ (part of which is the load from the fresh outdoor air, beyond the room’s own load from Step 2).

Step 6: Reheating and component selection

If the supply air is too cold or too humid after cooling (φ > 95%), we add reheating — a vertical line upward on the diagram (constant x, rising t). Based on the enthalpy differences and flow rates, we then select the capacity of the cooling coil, the heaters, the flow rate of the heat-transfer medium and the humidification capacity for winter operation. Every value has a direct visual equivalent on the h-x diagram.

Winter operation: a different diagram, the same logic

In winter the outdoor air is cold and dry and the room needs to be heated and humidified. The design conditions for Prague are roughly −12 °C / φ = 80% (in line with EN 12831-1). The outdoor air has an extremely low humidity ratio ($x \approx 1.1\text{–}1.2\ \text{g/kg}$), and its relative humidity after heating to 22 °C drops to a mere 7%. Heat recovery with moisture transfer (an enthalpy exchanger) can partly address this. Even so, humidification is practically indispensable for achieving ideal winter conditions in any building with mechanical ventilation.

Iterating the design by hand is tedious. In PsychroView you enter the outdoor and indoor air states, set the recirculation ratio, and immediately see the mixed state, the course of cooling and the resulting capacities — a change in one parameter is instantly reflected across the whole scheme.

Frequently asked questions

Why is the cooling capacity calculated from enthalpy, not temperature? A cooling coil removes both sensible and latent heat. The temperature difference captures only the sensible component; the heat of the condensing vapor is captured only by the enthalpy difference. Sizing on temperature alone leads to a permanently undersized coil.

Where on the diagram is the mixed state of outdoor and recirculated air? On the segment between the two states, at the position set by the flow ratio — closer to the state with the larger mass fraction. With 30% outdoor air and 70% recirculation, the mixture is 30% of the way from the indoor point (70% from the outdoor point).

Where do I get the outdoor-air design conditions for my location? From climate databases (ASHRAE Climatic Design Data, national standards or national climate-data databases), usually as the value with a 0.4% annual probability of exceedance.