modelDiversionOpenLoop

Information

This model represents a heating system where the configuration Buildings.Fluid.HydronicConfigurations.ActiveNetworks.Diversion is used to modulate the heat flow rate transmitted to a constant load. Two identical secondary circuits are connected to a primary circuit with a constant speed pump. The main assumptions are enumerated below.

• The model is configured in steady-state.
• The design conditions at time=0 are defined without considering any load diversity.
• Each circuit is balanced at design conditions.
• The bypass of the diversion circuit is balanced at design conditions if the parameter is_bal is set to true. Otherwise no fixed flow resistance is considered in the bypass branch, only the variable flow resistance corresponding to the bypass port of the three-way valve.

When simulated with the default parameter values, this example shows the following points.

• The overflow caused by the unbalanced bypass when the valve is fully closed in the first circuit (see plot #2 at time=100) creates a concomitant flow shortage in the second circuit with the valve fully open. However, the flow shortage (4%) is of a much lower amplitude than the overflow (30%). Indeed the equivalent flow resistance seen by the pump is lower than at design conditions, leading a shift of the operating point of the pump towards a flow rate value higher than design, which partly compensates for the overflow.
• The impact on the heat flow rate transferred to the load (see plot #4) is of an even lower amplitude (2%). This is dependent on the emission characteristic of the terminal unit that would theoretically be steeper with a higher effectiveness at design conditions, although the order of magnitude would remain the same. For reference, the terminal unit in this example represents a recirculating air terminal such as a fan coil unit in heating mode with a water ΔT of 10 °C at design conditions, so an effectiveness ε = ΔT_liq / (T_{liq, inl} - T_{air, inl}) = 0.25.
• The equal-percentage / linear characteristic of the control valve yields a relationship between the heat flow rate transferred to the load and the valve opening that is close to linear (see plot #4), with a Pearson correlation coefficient equal to 0.99.

Sensitivity analysis

Those observations are confirmed by a sensitivity study to the following parameters.

• Ratio of the terminal unit pressure drop to the pump head at design conditions (refer to the schematic in the documentation of Buildings.Fluid.HydronicConfigurations.ActiveNetworks.Diversion for the nomenclature): ψ = Δp_J-A / Δp_pump varying from 0.1 to 0.4
• Ratio of the control valve authority: β = Δp_A-AB / Δp_J-AB varying from 0.1 to 0.7
• Balanced bypass branch: is_bal switched from false to true
• Valve characteristic: ThreeWayValve switched from equal percentage-linear (EL) to linear-linear (LL).

Direct and bypass mass flow rate

The overflow in the bypass branch when the valve is fully closed increases with ψ and decreases with β. It is close to 70% for ψ = 40% and β = 10%. However, the concomitant flow shortage in the other terminal unit with a valve fully open (see Figure 2) is limited to 12%. For a valve authority of β = 50% one may note that the flow shortage is below 5%, indicating that selecting the control valve with a suitable authority largely dampens the impact of an unbalanced bypass.

Figure 1. Bypass mass flow rate (ratio to design value) at fully closed conditions as a function of ψ for various valve authorities β (color scale), and a bypass branch either balanced (right plot) or not (left plot).

Figure 2. Direct mass flow rate (ratio to design value) at fully open conditions as a function of ψ for various valve authorities β (color scale), and a bypass branch either balanced (right plot) or not (left plot).

Primary mass flow rate

The total primary mass flow rate (or pump mass flow rate) is plotted on Figure 3. This helps assess the actual flow variation in "constant flow circuits", i.e., constant speed pump distribution systems with terminal units equipped with three-way control valves. The total pump flow can vary up to 50% when the bypass of the three-way valves is not balanced, whereas the flow variation is limited to about 20% when the bypass of the three-way valves is balanced. If the characteristic of the valves is equal percentage and linear, this variation is rather by higher values for an unbalanced bypass and by lower values for a balanced bypass. If the characteristic of the valves is linear and linear, this variation is always by higher values. Eventually, when the control valve authority is higher than 0.5 the flow variation is limited to about ±20% in all cases.

Figure 3. Pump mass flow rate (ratio to design value) as a function of ψ for various valve authorities β (color scale), a bypass branch either balanced (right plots) or not (left plots) and either an equal-percentage / linear valve characteristic (top plots) or a linear / linear valve characteristic (bottom plots).

Heat flow rate transferred to the load

The heat flow rate transferred to the load is presented

• on Figure 4 at full opening to illustrate the impact on the coil capacity of the flow shortage previously discussed,
• on Figure 5 at 10% opening to illustrate the linearity of the relationship between the transmitted heat flow rate and the valve opening at low load in the case of an equal percentage valve (where values of the heat flow rate close to 10% of the coil capacity indicate a good linearity).

The impact on the coil capacity of the flow shortage due to an unbalanced bypass is limited to about 5% and is less than 2% for an authority higher or equal to 0.5. A balanced bypass tends to disturb the linearity of the heat flow rate with the valve opening. But again, if the valve is selected with an authority higher or equal to 0.5 that disturbance is highly reduced.

Figure 4. Heat flow rate (ratio to design value) at fully open conditions as a function of ψ for various valve authorities β (color scale), and a bypass branch either balanced (right plot) or not (left plot).

Figure 5. Heat flow rate (ratio to design value) at 10% open conditions as a function of ψ for various valve authorities β (color scale), and a bypass branch either balanced (right plot) or not (left plot).

Parameters

Components

Revisions

• June 30, 2022, by Antoine Gautier:
  First implementation.