.Buildings.Fluid.HydronicConfigurations.UsersGuide.ControlValves .Buildings.Fluid.HydronicConfigurations.UsersGuide.ControlValvesTo define the concept of the valve authority one may start with a reminder of the definition of the valve flow characteristic. The valve flow characteristic is the function that relates the volume flow rate (expressed as the ratio to the flow rate at fully open conditions) to the valve opening for a constant pressure differential: 1 bar in SI units and 1 psi in IP units (refer to Modelica.Fluid.UsersGuide.ComponentDefinition.ValveCharacteristics for further details). However, in a real system the pressure differential at the valve boundaries increases as the valve closes. Indeed, the pressure drop across the other fixed flow resistances in series with the valve (for instance a heat exchanger) tends towards zero with the decreasing flow rate. So the pressure differential available at the circuit boundaries shifts entirely towards the valve. This yields a shift of the "inherent" characteristic of the valve towards higher pressure drop values, hence higher flow rate values. With respect to the control loop this means an increased process gain which may be detrimental to the control loop stability.
The valve authority β is introduced as a metric of this disturbance of the inherent valve characteristic when the valve is integrated into a hydronic circuit. See Buildings.Fluid.HydronicConfigurations.Examples.TwoWayOpenLoop for a numerical illustration. The authority is defined as the ratio between the pressure differential at the valve boundaries when the valve is fully open and the pressure differential at the valve boundaries when the valve is fully closed.
β = Δp(y=100%) / Δp(y=0%)
The above equation is directly tractable in a numerical model and can effectively be used to compute the valve authority.
As mentioned previously, Δp(y=0%) may also be apprehended as the pressure differential at the boundaries of the circuit where the flow rate is modulated by the control valve.
A general design rule for stable controls of hydronic systems is to ensure a control valve authority greater or equal to 0.5.
Some authors such as R. Petitjean (1994) claim that the valve authority should be corrected to account for flow imbalance in real systems. Indeed, even for a perfectly balanced system at design conditions, some level of flow imbalance is inevitable at other operating points. Some circuits may therefore be exposed to a pressure differential higher than at design conditions. Such high pressure differential affects Δpmin = Δp(y=100%) and Δpmax = Δp(y=0%) with the same factor. Therefore, the valve authority β remains the same. However, the rate of change of the flow rate with respect to the valve opening is increased and the controllability is potentially degraded, which is not captured by the conventional definition of the authority. The concept of "practical authority" is introduced to overcome that limitation. It is defined as the ratio of the pressure differential at fully open conditions and at design flow rate to the maximum pressure differential corresponding to fully closed conditions.
β' = (Δp valve fully open and design flow) / (Δp valve fully closed)
The two definitions of the authority are related by the square of the ratio of the actual flow rate to the design flow rate.
β' = β / (V̇actual / V̇design)2
Particularly, when the valve is fully open, if the flow rate is equal to the design value then β' = β. In most of the simulation models developed during the design phase, we use theoretical values of pressure drops and consider perfectly balanced systems at design conditions. We will therefore use the conventional authority β for our analysis.
Three-way valves are typically designed to perform a mixing function, i.e., with two inlet ports and one outlet port. Therefore, all configurations that include three-way valves integrate them in a mixing arrangement, even when they perfom a diverting function such as Buildings.Fluid.HydronicConfigurations.ActiveNetworks.Diversion.
The definition of the authority for a three-way valve is based on the equivalence with a pair of two-way valves actuated in opposition, as illustrated in the figure below.
Using the nomenclature from the right-hand side figure with the pair of two-way valves, we have: β = ΔpA-B(y=100%) / ΔpA-B(y=0%).
The same caveat as in the case of two-way valves holds for the flow rate at which the pressure drop ΔpA-B(y=100%) is evaluated. There is some additional intricacy for evaluating ΔpA-B(y=0%) = ΔpJ-M(y=0%) because that pressure drop depends on the flow rate in the bypass branch. If the bypass branch is not balanced, the authority given by the above formula can virtually take any value and is no more representative of the valve installed characteristic. Contrary to the pressure drop ΔpA-B(y=100%) that can be corrected to account for a given amount of overflow (see the definition of the practical authority) there is no straightforward correction term that can be formulated for the pressure drop ΔpA-B(y=0%). So, contrary to the case of two-way valves, there is no generic formulation directly tractable in a simulation model to compute the authority of a three-way valve. The above equation requires to "conceptually" consider a balanced bypass when assessing ΔpA-B(y=0%).
For the common case where the valve is used to modulate the flow rate through a coil with a design pressure drop Δpcoil the generic definition of the authority can be rewritten as β = ΔpA-AB(y=100%) / (ΔpA-AB(y=100%) + Δpcoil).
Although this seems as a sound requirement to ensure an actual constant flow with a constant speed pump, the answer actually depends on the application.
The models
Buildings.Fluid.Actuators.Valves.ThreeWayEqualPercentageLinear
and
Buildings.Fluid.Actuators.Valves.ThreeWayLinear
both use a default value of fraK=0.7 for the ratio of
the Kvs coefficient between the bypass branch and the
direct branch.
This default setting yields a pressure drop in the
bypass branch ΔpL-M(y=0%) that is
1 / 0.72 ≈ 2 times higher at design flow rate
than the pressure drop in the
direct branch ΔpA-B(y=100%).
If the valve is used in a diversion arrangement to modulate the flow
rate through a heat exchanger, and if the valve is
sized with an authority of β = 0.5
this default setting implies that the bypass is balanced.
However,
fraK=1.0 appears more consistent,
fraK=0.7 may cause sizing issues.
For those reasons the default setting for all three-way valve components
within this package is fraK=1.0 unless specified otherwise.
Petitjean, R., 1994. Total hydronic balancing. Tour & Andersson AB, Ljung, Sweden.