Expansion in closed heating systems

Water expands when it is heated. In a closed system the water cannot escape, so the expansion has to be absorbed somewhere — otherwise the pressure rises uncontrollably.

A closed diaphragm expansion vessel absorbs the expansion: as the water expands, the diaphragm is pressed against an air/gas cushion, keeping the pressure rise within the system's limits.

The expansion factor e is not a fixed constant — it depends on the temperatures and is looked up in a table of the volumetric expansion of water. The nominal vessel size also depends on the pre-charge and system pressure (Boyle's law) and is sized according to the vessel manufacturer's instructions.

• 01The safety valve is the last line of protection against overpressure and discharges at its set opening pressure.
• 02It does not replace the expansion vessel — the valve must not operate under normal running conditions.
• 03The discharge from the valve must be routed safely and visibly in accordance with the applicable rules.

The expansion volume ΔV tells how much water the vessel must take up — but the vessel's nominal size V_n is larger, because the air cushion behind the membrane is compressed according to Boyle's law (p · V = constant), and because there must be a small water reserve so the membrane is never fully emptied. The relationship is the vessel manufacturers' standard formula:

• 01Pre-charge p_0: set after the system's static height — as a rule of thumb the height in metres from tank to the system's highest point divided by 10 (+ approx. 0.2 bar in practice), but at least approx. 1.0 bar.
• 02Charge pressure: the system is filled to slightly above the pre-pressure so there is a water reserve on the membrane from the start.
• 03Max. pressure p_e: chosen below the safety valve opening pressure with margin so the valve does not blow during normal heating.
• 04Water reserve V_v: a small buffer (manufacturers typically specify a minimum value) so the membrane is not completely empty in cold conditions.

The expansion volume is calculated as ΔV = V · (e / 100), where e is water's relative volume expansion between the filling and max. operating temperature. e is not a constant, but follows from water's density, which falls with rising temperature. The table is calculated from standard density data with a filling temperature of approx. 10 °C:

The values are calculated as (ρ_fill / ρ_max − 1) · 100 based on water density at the two temperatures (e.g. 999.7 kg/m³ at 10 °C and 977.8 kg/m³ at 70 °C gives 2.24 %). If the fill temperature is different, the values change accordingly. (Source: physical substance data for water; VDI 2035.)