Introduction

An expansion vessel (also called an expansion tank) is a key component in any closed-loop hydronic system. It accommodates changes in the fluid volume resulting from thermal expansion of the system’s volume during operation, thereby preventing excessive pressure in the system. Without an expansion vessel, the heated fluid would have nowhere to expand to leading to dangerously high pressures and system damage.

Hysopt focuses on a diaphragm expansion vessels of which the internally topology is depicted below for a system using water as heat transfer medium:

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Conceptual representation of a diaphragm expansion vessel

It is important to adequately design the expansion vessels in order to avoid air infiltration, evaporation of the liquid, pump cavitation and excessive pressures anywhere in the system under all, valid operating conditions. Practically, in the Hysopt software, the expansion vessel base circuit is also used to adapt the type of fluid used in the system. (e.g. glycol or ethanol mixtures)

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Expansion vessel Base Circuit in Hysopt

Expansion vessel Base Circuit

Below is a screenshot of Hysopt’s Expansion Vessel with parameter list. The expansion vessel can be found in the heating library and cooling library under “System peripherals”.

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Expansion Vessel Base Circuit with parameter list

Parameter list

General

• Mixture and Brine

  • Brine: Define the fluid mixture (e.g., water or water+glycol). If none, water is used as fluid type.

  • Mixture: define the concentration of mixture as part of the water+glycol mixture.

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Changing the fluid type in an hydronic loop

• System Volume

  • The total volume of fluid in the system (pipes, equipment, etc.).

• Minimal System Temperature / Maximal System Temperature

  • Defaulted to 4 °C and 90 °C, respectively. Used to determine the fluid’s density extremes.

• Expansion Coefficient

  • Calculated from the fluid densities at the minimal and maximal temperatures. Shown as 0 % by default and can be overridden by the user if needed.

• Maximal Static Height above Vessel

  • The static head of water/mixture above the expansion vessel. Used to determine the minimum required pre-charge pressure.

• Safety Valve Height above Vessel

  • The relative height of the safety valve compared to the vessel. Affects the maximal allowable pressure at the vessel’s location, which influences the final pressure during design.

Safety Valve Parameters

• Design Discharge Pressure
  The design discharge pressure at which the safety valve is expected to open.

• Effective Discharge Pressure
  Only relevant if using the part catalogue: The effective discharge pressure of the part-selected safety relief valve.

Expansion Vessel Parameters

• Design Pre-Charge Pressure
  The theoretically calculated pre-charge pressure that is necessary to ensure the minimum pressure in the system to avoid issues like evaporation and cavitation.

• Final Pressure
  The maximum allowed gauge pressure at the vessel location (often derived from the safety valve setting). If the vessel is oversized, the final pressure is recalculated and will be lower than the maximal allowable pressure as derived from the safety valve.

• Acceptance Factor
  The fraction of the gross vessel volume actually usable to accommodate expansion (calculated from pre-charge and final pressures).

• Design Volume
  The theoretically calculated volume needed (gross size) for the vessel to handle the net expansion volume.

• Installed Volume
  If a manufacturer’s part or catalog selection is made, the actual installed tank volume is displayed here.

• Installed Pre-Charge Pressure

Expansion vessel sizing

The expansion vessel needs to be adequately sized to avoid harmful situations at any location in the hydronic loop. Properly sized and properly pre-charged expansion vessels will:

• Avoid air infiltration at any point in the system

• Avoid evaporation of the fluid at any point in the system

• Avoid pump cavitation

• Keep the pressure below the maximal allowed pressure at all locations in the loop (at components, at piping, …)

Below is a step-by-step procedure to size the expansion vessel for your situation

Step 1: Determine the inputs

Brine and Mixture

As the thermal expansion properties depends on the type of medium used, enter the properties of the heat transfer medium used in the system.

If the heat transfer medium is water, you can ignore this step.

System Volume

The system volume is the sum of all internal volumes of production units, end units, low loss headers, piping, storage tanks and all other system components that are part of the corresponding hydronic loop.

The total system volume must be determined upfront. To assist in the determination of the pipework volume and the storage tank volume, you can consult the “info message” after running optimise components , as shown below.

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Design Discharge Pressure

The design discharge pressure represents the pressure setting at which the system’s safety valve would open. This pressure is seen as the maximal allowable pressure in the system at the location of the safety valve.

The safety valve’s setting itself can be determined by investigating the maximal operating pressure of all system components (pipework PN, production unit maximal pressure, …). Hysopt does not support (yet) this determination so it is advised to consult a professional guideline or standard to determine the safety relief valve sizing and setting.

Maximal static height above the vessel

The maximal static height above the vessel represents the height difference between the expansion vessel (= reference height) and the highest point of the particular hydronic loop. The used convention is shown in the picture:

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Definition of maximal static height above vessel

The maximal static height matters because the fluid’s pressure declines the higher the fluid climbs. Therefore, the highest system location will be the critical point when the system is at rest at which evaporation and underpressure must be avoided.

Safety Valve Height above vessel

The safety valve height above vessel is the height difference between the expansion vessel (=reference height) and the system’s safety valve. If the safety relief valve is installed at a different height than the expansion vessel, its setting must be recalculated to reflect the pressure at the expansion vessel’s location.

The applied convention is shown in the picture:

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Positive is safety valve above the vessel. Negative if safety valve is below vessel

Step 2: Net volume: T_min, T_max, the expansion coefficient

Minimal system temperature

The minimal system temperature is typically equal to 4°C as the temperature at which water is the most dense. If another minimal system temperature is preferred, you can always override the value and lock the parameter.

Maximal system temperature

The maximal system temperature is chosen to be the maximum design temperature + 5°C. As an example, a system that is designed at 70/50°C will get a maximal system temperature of 75°C.

It is advised that the maximal system temperature is no lower than 35°C, even for cooling installation, to take into account a resting installation at warm outdoor conditions.

If you prefer to build in additional safety or use another rule-of-thumb to determine the maximal system temperature, you can again override the value and lock the parameter.

Expansion coefficient

The expansion coefficient e describes the relative volume expansion of a medium if heated from the minimal system temperature to the maximal system temperature. The expansion coefficient can be calculated as:

with:

• ρ_Tmax: The medium’s density at the maximal system temperature

• ρ_Tmin: The medium’s density at the minimal system temperature

If the volume of a medium at the initial condition (T = T_min) is represented by V_init, than the volume at the maximal system temperature will be V_init * (1+e).

For the expansion vessel situation, this initial volume equals the system volume. We can subsequently calculate the extra amount of volume by increasing the temperature from Tmin to Tmax as:

For practical reasons, it is advised to always have some fluid in the expansion vessel, called the water reserve. Therefore, we add a fixed water reserve percentage wr% of 0.5% of the system’s volume to the volume that we expect in the expansion vessel. The total volume of fluid that the expansion vessel would need to accomodate for, defined as the net volume V_net, can now be calculated as:

with:

• V_net : The volume of fluid in the expansion vessel at the maximal system temperature

• V_expansion : The thermal expansion volume by heating the system volume from Tmin to Tmax

• V_{water_reserve} : A fixed percentage (0.5%) of the system volume to avoid the expansion vessel to be empty

• V_system : The system volume

• e : The expansion coefficient

• wr% : Fixed water reserve percentage of 0.5%

Step 3: Pressure limitations of the system

To go from the net volume to the gross volume of the expansion vessel, we must take into account the pressure limitations of the system. Typically, we have the following pressure limitations:

1. Minimal allowable pressure: Necessary to avoid evaporation, underpressure and pump cavitation anywhere in the system

2. Maximal allowable pressure: Governed by the system’s safety valve setting and location

Design pre-charge pressure

The design pre-charge pressure represents the pressure that is put on the expansion vessel when leaving the factory. It is the gas pressure before system filling and is defined as a gauge pressure.

The design pre-charge pressure is chosen in such a way that evaporation, pump cavitation and underpressure are avoided at all times at any location in the system. Hysopt calculates the pre-charge pressure based on the maximal static height above vessel, plus an additional safety margin.

Final pressure

The final pressure represents the pressure (gauge pressure) at the expansion vessel when the complete system volume is heated to the maximal temperature.

During design, we choose the final pressure to be equal to the maximal allowable pressure at the expansion vessel location to minimise the required expansion vessel volume. However, the final pressure can also be chosen lower than the maximal allowable pressure, which will result in an oversized expansion vessel.

If the user overwrites the design volume, we will recalculate the final pressure following its definition, namely the pressure when the complete system is at the maximal temperature. This value will deviate from the maximal allowable pressure at the vessel location, which arises from the safety valve properties.

The acceptance factor

The acceptance factor represents the percentage of the expansion vessel that can effectively be used to take in any fluid. The acceptance factor is not 100% due to the minimal and maximal pressure limitations of the system, and is thus derived from the pre-charge and final pressure.

Step 4: Calculation output - Vessel size/pre-charge pressure

The design volume of the expansion vessel is one of the outputs of the calculation and represents the theoretically, minimal required volume of the expansion vessel to satisfy proper system operation, if the expansion vessel is pre-charged at the shown design pre-charge pressure.

Example Sizing Scenarios

Example 1: Standard Sizing (No Special Conditions)

On default the Hysopt software will calculate the design volume and pressures of the expansion vessel based on ideal design conditions. These are:

• The expansion vessel is on the pump(s) suction side.

• The pump differential pressure is negligible compared to the safety relief valve setting.

• Pump is not located between the expansion vessel and the safety relief valve.

Additional pressure from the pump is considered in the “Pre-charge” OR “Final pressure” calculation depending on the location of the pump(s) and/or the expansion vessel.

Example model

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Parameter tab of the Hysopt software - Expansion vessel

Calculations

1. Determination of the system volume

Currently, the user has to determine the system volume himself. The Hysopt software can determine the total water volume of the pipes and thermal storage. These values can be found on the information label when hovering over the expansion vessel. These calculated values must be manually added to the total water volume of the other components (e.g. Radiators, Boilers, etc.). The other parameters of the expansion vessel are calculated by the Hysopt software.

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Information label - expansion vessel

• Total water volume of the pipes = 0.25 m³

• Total water volume of thermal storage = 1 m³

• Total water volume of radiators = 1 m³

• Total water volume of boiler = 0.2 m³

2. Determination of the max/min system temperatures for expansion coefficient

By default, the minimal system temperature is 4°C. If the system has a lower minimal temperature, it is advised to switch to a glycol mixture.

By default, the maximal system temperature is based on the supply temperature in the model + 5°C. In this example the supply temperature of the system is 70°C, therefore the software will use 75 °C as the maximum system temperature.

• Minimal system temperature = 4°C

• Maximal system temperature = 75°C

The expansion coefficient e is subsequently calculated with the formula below:

The density of water at the minimal and maximal system temperature can be determined by using density tables. A density table is shown as example below:

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Source: https://www.engineeringtoolbox.com/water-density-specific-weight-d_595.html

• Density at minimal system temperature = 999.97 kg/m³

• Density at maximal system temperature = 974.84 kg/m³

• Expansion coefficient e = 2.51%.

4. Determination of the maximal static height and safety valve height above the expansion vessel

The user needs to fill in these value depending on the configuration of the system. In this example, the values of these parameters are:

• Maximal static height above expansion vessel = 15 meter

• Safety valve height above expansion vessel = 3 meter

5. Determination of Design discharge pressure, Design pre-charge pressure and Final pressure

The pre-charge pressure is calculated with the formula below:

Where:

• p_0,gauge = Pre-charge pressure

• p_st = Static height pressure

• p_d = Vapour pressure, this factor is negligible at full liquid phase state.

• M_pre = 30 kPa = Pre-charge pressure margin.

• ρ_{min_temp} = density of the water at the lowest system temperature

• g = gravitational constant

• H_max,static = Maximal static height of the system above the expansion vessel

By default, the software uses a pre-charge pressure margin of 30 kPa. If you want to apply another pre-charge pressure margin, you can manually calculate the pre-charge pressure and lock the value.

• Pre-charge pressure = 177.15 kPa

The final pressure in the design situation is calculated with the formula below:

where:

• p_final = Final pressure

• p_max,sv = Design discharge temperature

• M_sv = Safety valve setting margin

• ρ_max = Density of the water at the highest system temperature

• H_sv,vessel = Static height of the safety valve above the expansion vessel

By default, the Design discharge pressure of the safety valve is set to 350 kPa (=3.5 bar). If this valus is different for your situation, you can adjust the value of the “Design discharge pressure” at the safety valve component. The default safety valve setting margin is 0.9. If you want to change this pressure margin, you need to manually calculate your desired final pressure, fill in that value and lock the final pressure.

5. Determination of the Design volume of the expansion vessel

At last, the design volume of the expansion vessel is calculated with the formula below:

where:

• V_system = Total water volume of the system

• e = Expansion coefficient

• wr% = water reserve factor

• η_g = Acceptance factor

The default water reserve factor is 0.5%. If the user want to change this parameter, Design volume of the expansion vessel needs to be manually calculated and filled in.

Example 2: Expansion vessel at discharge side of pump

If the expansion vessel is at the discharge side of the pump, additional pressure from the pump must be considered in the “Pre-charge pressure” calculation. The additional pump pressure will have an impact on the calculations of the “Design volume” of the expansion vessel.

Example model

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In this example, the same system configuration is used except for the location of the expansion vessel. This means that most of calculated parameters will not be affected. Only the pre-charge pressure, acceptance factor and design volume of the expansion vessel will be affected by having the vessel at a different location, more specifically at the discharge side of the pump. To take into account the pump influence correctly, you need to manually add the pressure from the pump(s) to the calculated “Pre-charge pressure” in order to calculate the correct design volume of the expansion vessel.

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Parameter tab of the Hysopt software - Expansion vessel

Calculations

• Pre-charge pressure

The pre-charge pressure can be calculated with the formula below, if the vessel stands at the discharge side oof the pump:

Where:

ΔP_pump= Pump pressure in kPa, in this example the pump pressure is 14.41 kPa

It is possible that the “Design pre-charge pressure” exceeds the “Final pressure” and/or the “Design discharge pressure”. In this cases you must manually fill in a higher value for the “Design discharge pressure”.

• Design volume of the expansion vessel

The design volume of the expansion vessel is calculated with the formula below:

In this situation the acceptance factor η_g differs than with the standard sizing due to the change in Pre-charge pressure, therefore increasing the required volume of the expansion vessel.

Example 3: Pump Between Vessel & Safety Valve

If the pump is located in between the expansion vessel and the safety relief valve, the final pressure is limited by the pump pressure. The pump pressure will certainly have an impact on the calculations of the “Design volume” of the expansion vessel.

Example model

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Example of a circulation pump inbetween the expansion vessel and safety relief valve

In this example the same system configuration is used, only the location of the pump is changed. This means that most of calculated parameters will not be affected. Only the final pressure, acceptance factor and design volume of the expansion vessel will be affected. Currently, the user has to manually subtract the pressure from the pump(s) with the calculated “Final pressure”, to calculate the correct design volume of the expansion vessel.

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Parameter tab of the Hysopt software - Expansion vessel

Calculations

• Final pressure

The final pressure is calculated with the formula below:

where:

• ΔP_pump= Pump pressure in kPa, in this example the pump pressure is 14.41 kPa

It is possible that the “Design pre-charge pressure” exceeds the “Final pressure” and/or the “Design discharge pressure”. In this cases you must manually fill in a higher value for the “Design discharge pressure”.

• Design volume of the expansion vessel

The design volume of the expansion vessel is calculated with the formula below:

In this situation the acceptance factor η_g differs than with the standard sizing due to the change of Final pressure, therefore the volume of the expansion vessel differs.

Example 4: Expansion automat (Constant pressure vessels)

When using an expansion automat, the required design volume of the expansion vessel can be lowered due to the higher efficiency of the expansion vessel. In this case the acceptance factor of the expansion vessel is significantly higher, depending on the maximal efficiency of the expansion automat. Currently, the user needs to manually fill in the acceptance factor in the Hysopt software.

Example model

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Parameter tab of the Hysopt software - Expansion vessel

Calculations

• Design volume of the expansion vessel

The design volume of the expansion vessel is calculated with the formula below:

In this situation the acceptance factor η_g depends on the maximal efficiency of the expansion automat. In this example an acceptance factor of 95% is used.

Overview design volume expansion vessel

Warnings and Errors

Warnings

1. The final pressure and the acceptance factor are recalculated due to part selection or a locked design volume. The recalculated final pressure is x bar. The safety valve setting would allow a maximal pressure at the vessel location of x bar.

The design volume of the expansion vessel is overwritten, therefore the calculations of the final pressure and maximal pressure at the vessel are recalculated based on the locked volume of the expansion vessel.

2. Acceptance factor and design pre-charge OR final pressure OR design volume are locked simultaneously, causing inconsistent results. Please unlock one the parameters.

The acceptance factor and pre-charge OR final pressure OR design volume are locked simultaneously, this will cause inconsistent calculations. Therefore it is advised to unlock one of the parameters.

3. Pre-charge pressure (x kPa) opens safety valve (x kPa)

The “Pre-charge pressure” is higher than the “Design discharge pressure”, therefore the safety valve will open at the “Pre-charge pressure”. This is not a good design, because the safety valve will always be open. Check the input parameters and make sure that the “Design discharge pressure” is higher than the “Design pre-charge pressure”.

Errors

1. Expansion vessel too small (expected x l but installed x l): The recalculated acceptance factor (100%) and final pressure (infinity) are invalid due to insufficient vessel size

The design volume of the expansion vessel is overwritten, therefore the calculations of the final pressure and maximal pressure at the vessel are recalculated based on the locked volume of the expansion vessel. In this case the locked design volume of the expansion vessel is to low, therefore resulting in invalid calculations.

To solve this error: Unlock the design volume of the expansion vessel or fill in a volume that is higher than the expected value.

2. The final pressure (x kPa) cannot be lower than the pre-charge pressure (x kPa) in practical situations. Please verify the inputs, increase the maximal allowable pressure if possible or consider other design configurations (see wiki).

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This error can occur in the following situations:

1. The “Design discharge pressure” parameter being too low, therefore the calculation of the “Final pressure” is not sufficient.

2. The “Final pressure” is locked with a value that is lower than the “Pre-charge pressure”.

3. The “Design pre-charge pressure” is locked with a value that is higher than the “Final pressure”.

To solve this error (based on the situations above):

1. Increase the “Design discharge pressure” so that the final pressure is sufficient.

2. Unlock the “Final pressure”

3. Unlock the “Design pre-charge pressure”