Development and Application of a Novel Non-Iterative Balancing Method for Hydronic Systems

Abstract

The improvement of efficiency in new and existing buildings is one of the key aspects in achieving the climate change targets promoted by international regulatory and technical bodies, and among the measures that deserve renewed attention is the balancing of hydronic systems. However, the balancing procedures currently applied have not been updated for decades and are still largely unimplemented, as they are mainly based on cumbersome and iterative procedures. This paper deals with the proposal and advanced adaptation of a non-iterative balancing method previously developed for air systems, known as the progressive flow method (PFM). The application to water systems of the PFM’s concepts includes some aspects of an existing empirical method called the compensated method (CM) and overcomes its main limitations; moreover, the original PFM has been radically rethought in its implementation aspects, taking advantage of the tightness of water distribution systems, minimising instrumentation and the number of measurement operations, to definitively overcome the iterative nature of the currently applied methods. Experimental validation was carried out. Compared with a standard method, the enhanced PFM reduced the number of measurements by 48% and the number of balancing operations by 41%, achieving final flow rates within tolerances and the same configuration of balancing devices.

1. Introduction

The European Directive published on April 2024 [1] reiterates the importance of the energy performance of buildings (EPBD) as one of the key aspects in achieving the greenhouse gas emission reduction and carbon neutrality targets of the European Green Deal. The directive includes among the required interventions the balancing of hydronic systems in new and existing buildings, also in accordance with the most recently issued technical standards on the same topic, such as ISO EN 52120-1:2022 [2]. The EN 52120-1 Standard deals with the evaluation of control and management of building systems and in particular indicates the balancing of hydronic systems characterized by more than 10 terminals as one of the requirements for obtaining any energy class above the worst (Class D), for both residential and non-residential buildings.

The subject of balancing in HVAC is an issue of confirmed interest since performances and consumption are closely affected by proper control of flow rate values; this topic is usually associated with constant flow systems, which are gradually being reduced due to the increased use of variable flow systems in all areas of HVAC. Nevertheless, not only are many constant-flow systems built in the past still maintained in operation, but this type of system remains essential for a number of applications such as those based on radiators, fan coil units, and underfloor heating/cooling systems, as well as in many industrial applications where local users require flow rates to be kept within close tolerances.

While the most advanced types of variable volume systems (such as those based on pressure-independent electronic valves with flow meters or with mechanical compensators) do not generally require balancing (S.T. Taylor et al. 2002 [3]), many applications still need balancing; radiators systems equipped with thermostatic valves need pre-balancing to handle start-up transients (T. Cholewa et al. 2017 [4], L. Zhang et al. 2017 [5]), while a number of systems serving on/off zones designed to operate at constant flow rates need balancing of local terminals. In addition, even in situations where the desired performance is achieved, balancing hydronic systems is also a viable solution for pursuing significant reductions in consumption. A study by L. Sarran et al. 2022 [6] concerning underfloor heating systems for low-energy apartments in Copenhagen, Denmark, presented the development and application of gray-box modelling aimed at continuous commissioning and highlighted how poor balancing and set-up were the decisive causes of gaps between assumed and actual consumption.

In cases of retrofitting existing multi-unit residential buildings, a more economically viable strategy than installing individual thermostatic radiators valves (TRV) is to define grouping strategies whereby a variable number of suites can be controlled through a single valve. These strategies were investigated by J.P. Fine et al. in 2020 [7] and applied to post-war buildings in Toronto, Canada; in the case study, 14% reduction in space-heating energy consumption and 10 years payback time were achieved, compared with 17,8 years for the solution with individual TRV. In any case, the possibility of control for large groups of apartments is based on the premise of hydronic balancing between all radiators belonging to the same group.

In 2024 S. Khamesi et al. [8] reported numerical evaluations supplemented by case studies regarding the lifecycle cost of plants evaluated over periods as long as 50 years. The evaluation also confirmed the importance of balancing to maximize the benefits of an optimized distribution layout (direct vs. reverse return). In all cases, balancing was indicated as fundamental, indicating LCC variations between unbalanced and balanced systems that could reach values between 30% and 50%.

Among the most recent applications, the issue of balancing is strategic in the field of district heating systems (DHSs), where it has been verified that the problem of poor flow control is one of the main causes of high temperature returns and degradation of the energy performance of distribution systems and thermal generation units (G.P. Henze et al. 2011 [9], Averfalk et al. 2017 [10]).

In particular, L. Zhang et al. showed in a 2016 [11] paper how demand-driven heat-delivery logic made possible through good balancing at the user level, introduced in the form of pre-set thermostatic valves combined with automatic balancing valves, was able to stabilize the temperatures of the dwellings served and optimize the operation of the primary distribution network with a reduction in pumping consumption (42.8% in the case analyzed) and a substantial reduction in thermal losses (17%). A similar analysis conducted by H. Wang et al. in 2017 [12] showed that energy consumption could be reduced by up to 30% through balancing. Ashfaq et al. in 2018 [13] determined how balancing was a crucial requirement for low-temperature DHSs, by analyzing the effects of imbalance in four different control scenarios. The results showed that energy consumption was significant in all cases analyzed. Z. Che et al. in 2023 [14] reported on the problems of poor balancing in DHSs and the difficulty of performing balancing via traditional methods; they proposed a method to regulate the hydraulic balance of the network by managing the opening of automatic valves with an NSGA-II (non-dominated sorting genetic algorithm II) as a function of heat demand.

In the field of solar thermal collectors, the issue of balancing water circuits is of great importance; Bava et al. in 2016 [15] produced a model for studying the flow distribution within collectors, reiterating that good balancing is especially important with regard to the optimized management of low-flow operation achievable by applying variable speed pump technology (Plaza Gomariz et al. 2019 [16]).

In addition, flow rate control has been found to be critical in a number of emerging applications linked to new technologies promoted by energy transition policies, such as battery power systems used in the hybrid powertrain sector; these storage systems need thermal uniformity guaranteed by water cooling circuits whose balancing requirements are often affected by the presence of invasive flow meters characterized by non-negligible drop losses (R. De Rosa et al. 2023 [17]).

While on the one hand, the need for balancing continues to exist, on the other hand, HVAC systems balancing is an often-neglected issue because of its inherent difficulties and time-consuming procedures; this frequently leads to badly balanced or completely unbalanced systems. This is also due to the fact that for heating terminals, the change in flow rate does not equate to an equivalent change in power output. This is due to the typical behaviour of any exchanger, where a reduction/increase of the flow rate is always associated with an increase/reduction of ∆$T$; S. Hámori et al. (2014) [18] modelled the dependence between the deviation of the user flow rate from the design value and variations in room temperature for different types of radiators, showing, for example, that for some terminal types, a variation of flow rate in the range between −15% and +25% resulted in room temperature variations of less than 1 °C. Since poor balancing does not directly impact performance, in these cases, it is often disregarded.

In other types of application, such as in cases of radiant floor heating and cooling systems mostly characterized by a number of parallel circuits working under constant flow conditions, Seong-Ryong Ryu et al. (2008) [19] showed that such systems are very sensitive to flow variations and highlighted the need for a proper balancing of user sub-systems based on TRNSYS simulations.

In 2020 H.-I. Cho et al. [20] investigated the relationship between issues related to maintaining comfortable environmental conditions and energy consumption in existing buildings and identified how balancing could be considered the most cost-effective and most decisive intervention; they analyzed a series of buildings in Geneva, Switzerland, and verified possible savings between 2% and 14%. The same authors in 2022 [21] indicated the evaluation of the mean square deviation of indoor temperatures as a valuable criterion for the selection of buildings for which water system balancing would result in high potential energy savings.

Cholewa et al. in 2018 [22] presented the results of a long-term study on the energy benefits of introducing balancing among different control systems in a set of buildings for a period of six years, resulting in energy savings of between 14.6% and 23.8% and payback time between 1.4 and 4.9 seasons of heating. This can sometimes also be obtained by the transformation of constant flow-borne systems into variable rate flow systems; however, automatic balancing devices such as thermostatic valves, differential pressure control valves, and pressure-independent flow controllers result in increased pump work and significant installation costs.

The methods traditionally proposed by network balancing associations such as the Testing, Advancing and Balancing Bureau (TABB) and National Environmental Balancing Bureau (NEBB) are iterative methods. The first proposal of a non-iterative method was made in the 1990s by R. Petitjan, who presented the compensated method (CM) [23] based on the use of calibrated balancing valves.

Many applications of the CM are available; among these, in 2001 Magyar [24] reported the application of the CM in six buildings in Hungary (each characterized by a number of flats from 20 to 354), showing experimentally that only a correct balancing procedure made it possible to achieve the required performance at the lowest consumption.

In 2010 [25], CIBSE (the Chartered Institution of Building Services Engineers) included the CM among the suggested methods for hydronic systems balancing.

Research and interesting insights about balancing have also come from the field of air systems balancing; the proposal by F. Pedranzini et al. in 2013 [26] of a non-iterative method called the progressive flow method (PFM) presented an approach for air systems similar to the one considered via the CM for water systems. The method was based on combined operations on dampers, fan velocity control, and proper flow measurements at the terminals. In addition to that, the PFM included some conceptual enhancements derived from a more general and theory-based approach.

J. Tamminen et al. in 2016 [27] proposed a non-iterative fan pressure-based method for air systems balancing which also partly used the procedures adopted by the PFM. This method suffered from some declared limitations related to the uncertainty of the flow rate estimation carried out by the fan curves and did not consider the extent of air leakages in airducts. However, the interest in this method lies in the fact that it made use of an assessment of the flow rate to the fan, introducing the possibility of drastically reducing the number of local measures; this concept is largely adopted in the proposal presented here.

2. Material and Methods

2.1. Traditional Balancing Methods

The purpose of every testing, adjusting, and balancing (TAB) procedure is to reach the only single configuration of the balancing devices and setting of the pump at which two main conditions are fulfilled: (i) flow rates are measured at the design value (within the tolerances), (ii) consumption is the minimum achievable. The latter condition can be referred to as the “minimum-energy or minimum-pressure balancing requirement” and is satisfied when at least one path (namely the most disadvantaged—MD) sees all valves completely open and the pressure provided by the pump is that required for the flow at the MD terminal to reach its nominal value. All balancing methods, to be satisfactory, must be able to identify this unique configuration.

In current practice, the most applied procedures are the ones proposed by ASHRAE (American Society of Heating, Refrigerating and Air-Conditioning Engineers) [28] and/or NEBB (U.S. National Environmental Balancing Bureau) [29], both basically refer to the same methods: the ratio method (RM), also referred to as the proportional method, and the stepwise method (SM), both iterative in nature. The same technical arrangement is required for the application of both methods in terms of balancing devices (typically calibrated balancing valves), requested accessibility, measurement techniques of terminal/branch flow rates, as well as total flow rate. Whatever the procedure followed, flow meters’ accuracy must fit the required tolerance.

Considering the NEBB reference, in Appendix A are summarized the operational steps for the TAB activity of a constant water volume (CWV) system according to the two methods mentioned.

2.2. Non-Iterative Methods

The compensated method (CM) for water systems and the progressive flow method (PFM) for air ductwork were proposed in order to overcome iterativity and were based on assimilable conceptual assumptions. The CM is a practical method with clear procedures developed for constant water volume systems whose balancing devices are calibrated balancing valves (CBVs), and the PFM was developed for air systems and was presented with a theoretical background and experimental validation; moreover, the PFM’s theoretical approach allows a more comprehensive exploration of a number of situations that the CM (by its authors’ own admission) does not fully address. In addition to that, PFM can be applied to systems equipped with terminal sensors other than CBVs (i.e., differential pressure probes across the terminal).

In the following, a description of the CM as presented in the literature [23,24] is reported and some critical aspects are highlighted. Then, the theory developed for the PFM is presented to highlight how the informed application of the latter makes it possible to overcome these operational limitations.

2.2.1. Description of the Compensated Method

The method is based on (i) the availability of calibrated balancing valves (CBVs) at each terminal and (ii) the presence of a branch CBV, named “partner valve”. Specifically, the method has been developed exploiting the features of CBVs: these devices are manual modulating valves provided with pressure taps and whose flow coefficient value at every knob position can be obtained from the manufacturer’s data sheets. Such devices offer the advantage of acting as a flow rate meter and as a balancing device at the same time. The CM procedure requires the availability of two pressure gauges to obtain simultaneous flow-rate measurements at specific CBVs.

The basic idea is that it is possible to balance the terminals sequentially and one at a time by acting on its valve, without affecting the flow conditions of the previously balanced terminals: this requires following a specific order and at the same time acting on a branch valve named the “partner valve” to supply the circuit with a compensation flow.

With reference to Figure 1, a branch with multiple users to be balanced can be considered and the following steps carried out:

Terminal 1 is considered the farthest terminal (on the right in the upper figure). A manometer is connected to the CBV valve BV-1 for flow measurement, and the valve is then opened to the maximum (consistent with the minimum pressure drop required for reliable measurement; 3 kPa at nominal flow rate is the value recommended by the authors of the method). The nominal flow rate value at this terminal is reached through adjusting the partner valve. From this point on, that value is considered as the ‘reference’, and it is constantly monitored and kept constant via continuous adjustment of the partner valve.

The operator moves to the very next terminal (Terminal 2 on the lower figure), connects the second manometer to the pressure taps of the valve BV-2, and acts on that valve to obtain the nominal flow rate. Any action causes a flow change in the reference valve, which has to be continuously compensated by modulating the partner valve. The balancing of Terminal 2 is completed when both the design flow rates occur simultaneously. The method continues with the third user BV-3 (still keeping the reference value on the farthest BV-1), and so on until all users have been balanced to each other.

The method does not show any criticalities if the farthest terminal is also the unfavored terminal (referred to as the “index” in the CM procedure), but this may not always be true: when it happens that, even having fully opened the valve of the new terminal, its design flow rate value is not reached (while the reference flow rate is maintained at its nominal value), this means that the new terminal just considered is disadvantaged compared to the reference one, and it will therefore be necessary to go back and act on the terminals already considered.

In this case, the enforcement of an iterative sub-procedure can be avoided thanks only to the full exploitation of the specific features of the calibrated balancing devices, and the method indicates a series of additional operations involving measurements, calculation, and full re-balancing of the whole branch from the beginning. Any time a newly considered terminal behaves as the new most disadvantaged, the whole sub-procedure must be repeated for each of them.

In the case of systems consisting of multiple branches, each branch can be balanced independently and, lastly, the branches are balanced among themselves; this requires only a main partner valve (or providing the same feature by acting on the pump velocity) and the consideration of the branches in the same sequence as before for the terminals. Even in this case, the procedure proceeds cleanly only if the farthest branch turns out to be the most disadvantaged one.

Critical issues related to the use of the compensated method can be summarized as follows:

-

CBVs have to be installed on every single terminal;

-

The procedure requires flow rate measurements at every terminal, with the re-location of the manometer at every step, which is time consuming;

-

The use of CBVs as flow meters requires reaching the minimum pressure at which detection is possible, adding this drop to the drop in every path (the MD path included), thereby increasing the required head pressure of the pump.

-

In cases where the most disadvantaged (index) terminal is not also the farthest, an alternative procedure is imposed, the reference terminal has to be properly throttled and the entire branch have to be re-balanced.

To overcome these critical issues, the application of the PFM to water systems is proposed. In the following, the theory developed for the validation of the progressive flow method is introduced and applied to water systems.

3. Theory and Calculations

3.1. Progressive Flow Method Theory

The studied method was originally developed for air systems in order to overcome the iterative nature of classical methods, in the form of application of the same methods previously mentioned for water systems TAB: the ratio method and step-wise method.

The assumptions that led to its validation in air systems are considered still valid in water systems; these consist of constant density and a quadratic relationship between velocity and pressure drop under the assumption of a fully turbulent flow regime (ASHRAE [30]).

The lumped-parameters representation of a supply air system (Figure 2) is formally the same as that of a close-loop water system, with the notable difference that in an air system, the return path through the atmosphere has no pressure losses, whereas the hydronic piping is affected by pressure drops due to friction in the return path. In the transposition of the method from air to water, the air diffusers have been replaced by the terminal users’ exchangers, the fan replaced by a pump, and the dampers replaced by balancing valves. The main physical parameter considered in the model is the loss factor R due to friction in pipes and fittings, the overall value of which can be suitably increased by throttling the balancing devices. The relevant quantities considered by the equations are flow rate $\dot{Q}$ [m³ s⁻¹], pressure drop $∆P$ [Pa], and the head pressure provided by the pump $∆H$ [Pa].

In addition to the shared characteristics, the two systems also have differences in actual installations, the most significant of which for the purposes of this research is the tightness. One of the consequences is that while the performance validation of an air systems requires the measurement of the flow rate exactly at the terminals because of air leakages along the ducts, the tightness in the case of water systems allows cumulative measurements to be carried out; according to mass conservation, the branch flow rate is equal to the sum of the flow rates of terminals belonging to that branch, and the flow rate at the pump is equal to the sum of the branches’ flow rates.

This fact does not lead to any optimization in balancing procedures when using the standard iterative methods or CM, which require flow meters at each terminal. In contrast, in the case of the PFM, the tightness is fully exploited in order to obtain a significant improvement: as described below, flow measurements can be carried out at a single point (e.g., at the pump) while measurements at the terminals can be replaced with an easier to do acquisition of the pressure difference across the user or, in some cases, with the measurement of temperature difference (S. C. Sugarman 2014) [31].

In any case, the analysis of the theory behind the method does not distinguish the way in which the flow rate is measured. This distinction is addressed in terms of further optimization, when the application procedure of the method is presented.

The theorical framework of the method was developed considering the lumped-parameters model previously shown in the lower part of Figure 2.

The relationship between the pressure drop ∆P [Pa] on a straight section (major/distributed losses) as well as across fittings (minor/local losses) and the volume flow rate $\dot{Q}$ [m³ s⁻¹] is assumed to be

$$∆P=R·{\dot{Q}}^2$$

(1)

where R [Pa·s²·m⁻⁶] is the loss factor, whose overall value for major losses depends on piping geometry, (length and diameter), fluid properties (density), and friction factor f; for minor losses, R depends on the geometry of fittings and components (i.e., curves, tees, exchangers, balancing valves) and can be expressed by means of density, average fluid velocity, and the geometry- and size-dependent loss coefficient k [30].

In the following, the value of f is considered constant within the typical operating range characterized by a fully turbulent flow, so R is assumed to be non-dependent on the flow rate value and dependent only on the actual setting of the balancing devices.

In case of series and/or parallel arrangement of the components, the relationship (1) can be used appropriately to describe any portion of a system by means of an equivalent loss factor.

-

For the series configuration of two components or paths whose loss factors are indicated respectively as R_a and R_b, the following applies:

$$R_{S\left(a,b\right)}=R_a+R_b$$

(2)

-

For the parallel configuration, the following applies:

$$R_{P(a,b)}={\displaystyle \frac{1}{\left(\frac{1}{R_a}+\frac{1}{R_b}\right)+\frac{2}{\sqrt{R_a·R_b}}}}$$

(3)

These relationships can be combined to create a model through which balancing methods can be tested and subsequently verified experimentally.

From the perspective of how to identify the final balanced configuration, a method is proven to be non-iterative when the parameters whose values are to be assigned are introduced progressively one by one so that the value of every new considered parameter depends only on (i) the design values and (ii) values already determined as a result of a previous calculation or measurement. In this way, at each step, an unknown quantity can be calculated immediately by means of an explicit relation or, in the case of application to a practical procedure, by means of a single calibration/measurement operation that does not involve any further modification of what has been set previously.

On a procedural level, this means that the system is operated in such a way that in each current operation, a measured flow rate depends on the position of a single valve, so that its correct position can be easily found by adjusting it until the desired flow rate value is reached.

This requires a logic of bottom-to-top engagement of the circuits and the observance at each step of a system flow condition that maintains unchanged the flow rates and settings adjusted in previous steps. So, in order to guarantee the progressive involvement of the parameters to be regulated and avoid any back effect of the new balancing actions, the following conditions are necessary:

-

the procedure starts from the farthest terminal by giving a clear criterion to set the adjustment of its valve position;

-

the operator moves backwards and just one terminal at a time is involved;

-

a specific control is introduced in order to keep downward (already adjusted) quantities (flow rates and valve positions) unchanged.

The introduction of such a control is shared by the CM and PFM, with the difference that the PFM provides that the mentioned control can also take place in real time by means of a control loop acting on the portion of the system upstream of the point currently being balanced, in order to keep the downstream flow conditions automatically unchanged.

Returning to the consideration of the representation of a generic branch (Figure 2), each terminal path (i.e., a radiator, a fancoil unit, or an air-handling unit’s coil) is represented as a parallel i^th shunt from the main path, whose $R_i$ value can vary from a minimum value (at valve fully open) to an infinite value according to the throttle position of the balancing valve. As it is shown in Figure 3, and referring to the split i-point, three sections can be identified: the upstream part of the system on the left, the i-terminal path, and the downstream D part on the right.

The upstream part of the system can be conceptually replaced by an equivalent pump providing the required flow rate $\left({\dot{Q}}_D+{\dot{Q}}_i\right)$ at the given head pressure ($H_P$).

The downstream part can also be represented by a single equivalent circuit in parallel with the i^th path, characterized by the loss factor $R_D$ and supplied at the same pressure ($H_P$); at the very start of the procedure, the i^th terminal itself is the farthest and so, the downward loss factor $R_D$ value is assumed to be infinite.

The i^th parallel path is characterized by the loss factor $R_i$, which is univocally related to the valve position and whose value can be analytically determined by knowing both pressure and flow rate:

$$R_i={\displaystyle \frac{\begin{array}{c}{H}_P\end{array}}{{{\dot{Q}}^2}_i}}$$

(4)

When the i^th terminal is not the farthest, $H_P$ depends on downstream conditions:

$$\begin{array}{c}{H}_P\end{array}=R_D·{\dot{Q}}_D^2$$

(5)

where ${\dot{Q}}_D$ is the sum of all the flow rates at the terminals in the downstream portion.

So,

$$R_i=R_D{\displaystyle \frac{{\dot{Q}}_D^2}{{\dot{Q}}_i^2}}$$

(6)

The procedure has been developed in such a way that $R_i$ has to be defined only when the downstream resistance values are already defined, so that $R_D$ is known and $R_i$ can easily be calculated.

The analytical step of calculating the value of $R_i$ corresponds, in the practical procedure, to the adjustment of the balancing device which allows the flow rate value ${\dot{Q}}_i$ to be reached while the simultaneous maintenance of the flow rate value ${\dot{Q}}_D$ is kept.

According to the previous description, the procedure to be followed when $R_D$ is known is clear; however, the first step still needs to be defined. At the very start of the procedure, and referring to the last terminal $(i=n)$, the situation is quite different (Figure 4), and Equation (6) can be written as

$$R_{\mathrm{n}}={\displaystyle \frac{\begin{array}{c}{\mathrm{H}}_P\end{array}}{{\dot{Q}}_n^2}}$$

(7)

$H_P$ cannot be calculated using (5) because there is no downstream section already calculated, and for any value of $H_P$ there is a correspondent value of $R_n$ giving the designed ${\dot{Q}}_n$ flow rate value; so, one additional criterion has to be considered. This criterion can be found via applying the minimum energy requirement; at the design flow rate, the loss factor has to be as low as possible, so the additional information needed is given by consideration of the maximum opening of the valve as the first step of the PFM procedure.

Back to the general case in procedure, notice that the calculation of $R_D$ and $H_P$ must be updated at each step by simply by adding the new branch in parallel to the pre-existing downstream equivalent branch as well as the additional line resistance $R_{i-1,i}$ (Figure 5).

Referring for generality to the (i − 1)^th node, as shown in Figure 5 and according to (2) and (3), the following applies:

$$R_{D(i-1)}={2R}_{i-1,i}+{\displaystyle \frac{1}{\left(\frac{1}{R_{D\left(i\right)}}+\frac{1}{R_i}\right)+\frac{2}{\sqrt{R_{D\left(i\right)}·R_i}}}}$$

(8)

Then, applying Equation (6) with updated values, it is possible to calculate the balancing value as

$$R_{i-1}=R_{D(i-1)}{\displaystyle \frac{{\dot{Q}}_D^2}{{\dot{Q}}_i^2}}$$

(9)

Every time the operator moves to the next branch, the setting of only one new valve position is involved. The action required is the adjusting of the (i − 1)^th valve in order to obtain the desired flow rate value ${\dot{Q}}_{i-1}$, and the measurement-driven adjustment allows detection of its final value without any iteration. In the meantime, it is necessary to increase the upstream flow rate to flush the new opening path, keeping unchanged all flow rates on the downstream side as well as the pressure at the i^th shunt nodes.

If this is the case, it makes no difference whether the ${\dot{Q}}_{i-1}$ value is measured directly at the terminal or deduced in terms of the increased flow rate provided by the pump.

While the CM involves modulating the position of the partner valve to keep unchanged the flow rate measured at the CBV installed on the index (reference) path, the PFM allows the invariance of the downstream flow rates to be granted by means of simply keeping constant the pressure across the terminal itself, without introducing additional CBV pressure drops. In addition, control of the reference flushing condition can be obtained by alternative ways other than adjusting the branch (partner) valve only, e.g., by varying the pump speed, by opening or closing other upstream branches, or by a combination of all these actions.

If the procedure starts with all the terminals belonging to a specific branch in a closed position, the branch flow rate grows step by step, where each step counts the nominal flow rate of the newly activated terminal, according to the denomination of “progressive flow method”.

As already pointed out in Section 2.2.1, the procedure described in this way allows any branch to be balanced, provided that the farthest terminal is also the disadvantaged one. If this is not the case, the compensated method proposes a subroutine involving measurements and the re-balancing of all terminals.

Considering the most common hydronic system architectures, there are situations in which the position of the disadvantaged terminal is not decisive and an adapted version of the procedure can still be applied without the need to retroactive sub-routines; manifold-based systems and reverse return systems belong to this category. Appendix B examines these systems and shows how the procedure can be adapted and applied.

All other cases (i.e., direct return water systems) point to a situation that is rather common in air systems, which the PFM has had to deal with since its very first formulation.

This critical issue has been addressed from a conceptual perspective and the conclusion is that, given the presence of valves in the proper positions, the general balancing theory can be applied in a more extensive manner and an extended procedure can be applied without the enforcement of any retroactive subroutines.

3.2. Management of Cases Where the Farthest Terminal Is Not the Most Disadvantaged

The configuration can be examined with reference to Figure 6, where two different paths are represented branching off from (i − 1) points: the first corresponds to the (i − 1)^th branch which has to be activated; the second, on the right in Figure 6, consists of the downstream part of the system, represented by the equivalent loss factor ($R_{D(i-1)}$), which is assumed to have already been balanced.

According to the general theory of balancing in case of ramification, a choking action in the favored path is required, and this implies the availability of a balancing device on it. In cases where the favored circuit is downstream, the requirement can be satisfied by the presence of an adjustable line loss ($R_{Line i-(i-1)}$) whose throttling action affects all downstream terminals equally and does not affect their pre-existing mutual balancing.

Analytically, in cases where the (i − 1)^th path is disadvantaged, the proper value of the additional line resistance $R_{Line i-(i-1)}$ depends on the new path loss $R_{(i-1)100}$ (the resistance of the (i − 1)^th path with the valve BV_i−1 in 100% open condition), on the equivalent resistance of the downstream part already balanced $R_{D(i-1)}$, and on the flow rate values $Q_{i-1}$ and $Q_D$:

$$H_P=R_{(i-1)100}\times {Q_{i-1}}^2=\left(R_{Line i-(i-1)}+R_{D(i-1)}\right)\times {Q_D}^2$$

$$R_{Line i-(i-1)}=R_{(i-1)100}{\left({\displaystyle \frac{Q_{i-1}}{Q_{Di}}}\right)}^2{-R}_{D(i-1)}$$

(10)

In terms of system equipment, the requirements are shown in Figure 7.

In practice, while the automatic control loop (or an assistant operator) acts on the system (i.e., on the pump), maintaining unchanged the downstream quantities, the operator starts to open the valve BV_i−1 and the (i − 1)^th terminal begins to be flushed, causing a decrease in the downstream flow rate, which is assumed to be immediately compensated by the upstream control. When the terminal valve is fully open, if the flow rate $Q_{i-1}$ still does not reach the nominal value, this means that the (i − 1)^th terminal is actually the MD. Then, the operator moves to act on the line valve BV_{liIe i;(i−1)} and begins to close it, and the flow deviation combined with the loop compensation increases $Q_{i-1}$ up to the desired value.

As mentioned before, the flow rate measurement required for this operation can be performed directly on the (i − 1)^th terminal if a local flow meter is available; in case it is not, it is possible to measure the total flow rate coming from the pump, whose target value corresponds to the value of the previous downstream flow rate (unchanged) increased by the nominal value of the newly added terminal.

In any case, the line resistance can be introduced by installing a simple device capable of introducing a modulable pressure drop without any measuring features. Since it is assumed that the pipeline designer knows which terminal will be disadvantaged with respect to the part of the system that remains downstream, the design can provide for the presence of appropriate line balancing valves, allowing the complete PFM procedure to be carried out.

3.3. Optimization of the Number of Flow Meters and Measurements

A second significant implementation can be achieved by reducing the number of flow meters, resulting in lower installation costs and easier application of the method to existing systems in need of balancing; moreover, the centralisation of measurements saves the time needed to move instruments during the TAB procedure. As previously mentioned, due to the tightness of water systems, flow measurement at the terminals can be avoided and replaced by centralized flow rate measurement combined with simpler reference pressure measurements on only one terminal per branch, whose position depends on the branch configuration type, as follows:

-

on the farthest terminal in direct return configurations (provided that the line valves are installed where needed);

-

on the most disadvantaged terminal in reverse return configurations (see Appendix B);

-

on the manifold itself in manifold-based configurations (see Appendix B).

If balancing starts with all the terminals in closed position, their progressive activation results in step-by-step increasing of the total flow rate, whose magnitude is given by the volume of water flowing into the newly activated terminal. With the right procedure, this allows measurements to be centralized without any problems of distance between the flow meter and the device being adjusted.

The choice of the control point and of the flow rate measuring system must comply with the following specifications:

(1)

Consistency: the variation in flow rate resulting from the activation of any terminal can be detected at the considered measuring point;

(2)

Resolution: the range and the resolution of the instrument installed at the control point are suitable for the acquisition of the total flow rate supplied to the portion of the system under balancing and for the correct detection of each increasing step, respectively.

If both conditions (1) and (2) are met, it will be possible to proceed with balancing via properly instrumenting a smaller number of flow-meters (or even only one, at the pump).

As far as consistency is concerned, it is important to emphasize that this condition must only be met during the balancing phase and not during normal operation. One way of achieving this may be, for example, to shut off branches other than those currently under balancing. As for compliance with the condition of resolution, with an increasing number of terminals, the flow meter is required to provide a wider measuring range and at the same time a finer resolution. This can be fulfilled by installing two or more instruments with different ranges and resolution placed in parallel and activated as required.

3.4. PFM Balancing Procedure

On the basis of the theoretical elements outlined above, a procedure was developed and is here proposed as a PFM procedure.

Figure 8 shows the case of a system in direct return configuration, with a single branch and n terminals, each with a balancing device. If the designer has determined that the most disadvantaged terminal is not the farthest (e.g., the MD terminal is Terminal 2 as shown in Figure 8), a line valve may be provided (shown in grey), as discussed above. The balancing procedure involves the monitoring of the pressure across the last terminal on the right (the farthest) and the flow rate measurements at the control point placed after the pump, represented by a rotameter. The pump is driven at variable speed and is suitable for inclusion in an automatic control loop when required.

The procedure has been designed as follows:

Preliminary Setup. All the balancing valves shall be closed with only the exception of the one serving the farthest, which has to be fully open. In case of presence of line valves, they must be fully opened as well. For stability of pump operating at low flow rates, it may be appropriate to provide a modulating bypass across the circulator.

First step. (Figure 9). Measuring the flow rate at the control point (represented by the ‘watching eye’ icon), the pump velocity is varied until the flow rate measured by the rotameter reaches the design value of the n-terminal ${\dot{Q}}_n$.

Second step. (Figure 10). An automatic control loop is implemented to keep unchanged the flow rate at the n-terminal acting on the pump velocity. In order to do that, a probe is connected to the pressure taps across the terminal and the actual value is taken as reference. Then, a controller is electrically connected to the probe and to the inverter. The set on the loop controller is ${\mathsf{\Delta }P}_{set}={\mathsf{\Delta }P}_{reference}$.

Third step (balancing). The operator acts on terminal balancing devices or on line valves. Each user is balanced, starting from (n − 1) and moving backwards (Figure 10) to the first terminal of the branch. At each new path considered, the gradual opening of the valve causes a reduction in the reference pressure, which is immediately compensated by the loop control. In most cases, the terminal that has just been opened, compared with that previously activated, is not disadvantaged; the valve is throttled to a opening position lower than 100% and the correct balancing position is detected. When a disadvantaged terminal (e.g., Terminal 2 in Figure 10) is encountered, the total opening of the terminal is not sufficient to guarantee the desired flow rate through the user, so the operator moves to act on the line valve according to the theory. Then, the procedure continues as planned to the next terminal.

If the system is multi-branch, each branch is assumed to be equipped with a balancing device. After balancing the terminals belonging to each branch, the next step is to achieve balance between different branches, following the same strategy as before: starting with all branches closed, first open the reference branch completely, bring it to nominal flow rate conditions acting on upstream components (e.g., on the pump), set the reference pressure loop control, and progressively open all the other branches in sequence, as described previously.

Again, the application of the PFM in direct return systems requires the presence of line valves downstream of the disadvantaged branch if this is not also the farthest.

Fourth step (adjustment). According to the procedure, the pump speed is continuously adjusted through the reference pressure control following the previous steps, so that each terminal is brought to and maintained at its nominal flow rate. The adjustment phase requires only the following actions to be performed:

-

take note of the final speed reached with the setting of the last terminal/branch;

-

remove the reference pressure control loop;

-

set the registered speed as the operating speed of the pump;

-

check that the power consumption and the working point are consistent with the pump manufacturer’s specifications.

At the end of the procedure, it can be verified that at least one path is clear (with no valves even partially closed); that path is the most disadvantaged one. The pump provides the pressure needed for that path and the minimum energy/pressure requirement is fulfilled.

In cases of manifold-based systems, the procedure is the same with the only difference that the reference pressure probe can be installed on the manifold itself; such a case is examined and illustrated in Appendix C.

Cases with systems composed of a main manifold connected to a number of risers each supplying local manifolds with several terminals are also very frequent. This type of case is also described in detail in Appendix C.

Finally, a case where several direct return distribution sub-systems branch off from a single manifold can be considered as a more general case. For this reason, this model was used as a case study for the experimental validation of the method.

3.5. Experimental Validation

3.5.1. Test Rig Description

In order to validate the proposed procedure, it was decided to compare the PFM with the standard ratio method (RM), on a real water system of enough complexity to highlight the specificities of the two procedures. The implemented circuit consisted of a significant number of terminals (eight in total) distributed two-by-two over four branches derived from a main collector, as shown in Figure 11.

The adopted configuration made it possible to verify the balancing procedures applied firstly at the terminal level (in pairs) and then at the branch level, combining the manifold-based architecture and four double-user sub-systems. Flow measurement at terminals was conducted using ultrasonic probes embedded in electronically controlled Belimo EP015R flow valves, differential pressure measurement across the users was acquired via Thermokon mod. DPL1V differential pressure probes, while central flow measurement at the pump was carried out using Frank M350 rotameters. A detailed description of the circuit, the type of control and the measuring instruments used can be found in Appendix D. Figure 12 shows a picture of the realized test rig and

Table 1. Measurement Equipment, Models, Ranges, and Accuracies.

Instrument	Model	Measuring Range	Accuracy
Ultrasonic flow meters at terminals	Belimo electronic valves mod. EP015R	0–1200 L/h	6% of the reading value ranging from 25% to 100% of the measuring range.
Rotameter flow meters at the pump	Frank mod. M350	50 ÷ 500 L/h	8% of measured value for flow rates between 20% and 100% of measuring range according to VDE/DIN 3531.
		300 ÷ 3000 L/h
Pressure probes	Thermokon mod. DPL1V	0 ÷ 1 Bar	Declared accuracy 1%, resolution 0.2 kPa.

shows the main information about the measurement equipment used.

3.5.2. Comparison between Ratio Method and PFM

First, a set of target flow rates was defined as well as a balancing tolerance value of ±10% for individual flow rates, according to the standard requirement (ASHRAE and NEBB [28,29,32]) and international commissioning associations such as the Building Services Research and Information Association (BSRIA) [33].

Nominal pressure drop values of the simulated terminals were defined with reference to typical hydronic terminals, and the determined values were obtained by adjusting the calibrated balancing valves positioned for that purpose.

This configuration applies to a real case of seven fan coil units (from A2 to D2) characterized by head losses of about 5 kPa with quite different nominal values of flow rate, and one different type (A1) representing a manifold serving an underfloor heating/cooling system whose loss is estimated at 30 kPa. The established flow rates, referring to a working $\mathsf{\Delta }T=5 °\mathrm{C}$, led to heating capacities values consistent with the defined types.

Table 2. Design flow rates and drop simulation valves setup.

Branch	Terminal Unit	H/C Capacity	User ΔP	Flow Rate		TU Valve Position
		[W]	[kPa]	l/h	l/s	Reference
A	A1	1149	29.21	200	0.06	0.6
	A2	1724	5.01	300	0.08	3
B	B1	1724	5.01	300	0.08	3
	B2	2011	6.82	350	0.10	3
C	C1	1437	6.51	250	0.07	2.5
	C2	2299	5.54	400	0.11	3.5
D	D1	1724	5.01	300	0.08	3
	D2	2874	5.95	500	0.14	4

shows the system design configuration and lists the assumed thermal powers, design flow rates, pressure losses, and handwheel position of the drop simulation valve for each thermal unit (TU).

As the two methods refer to different flow meter readings, the comparison of the results required an initial consistency check of the measuring instruments. The full test carried out is described in Appendix E. The main result was that in the range of flow values to be considered for comparison, rotameters overestimated the measurement by an average of 4.9% compared with ultrasonic probes (Appendix E 

Table A1. comparison of measured values at 100%, 66%, 33% of 1200 L/h (full scale of the MBV ultrasonic probes).

Branch	Terminal Unit	Flow Rate 33% (400 L/h)		Δ		Flow Rate 66% (800 L/h)		Δ		Flow Rate 100% (1200 L/h)		Δ
		Rotameter	MBV	[%]	K	Rotameter	MBV	[%}	K	Rotameter	MBV	[%]	K
A	A1	400	373	6.8	0.93	800	715	10.6	0.89	1200	1050	12.5	0.88
	A2	400	383	4.3	0.96	800	730	8.8	0.91	1200	1085	9.6	0.90
B	B1	400	377	5.8	0.94	800	715	10.6	0.89	1200	1085	9.6	0.90
	B2	400	380	5.0	0.95	800	730	8.8	0.91	1200	1088	9.3	0.91
C	C1	400	384	4.0	0.96	800	728	9.0	0.91	1200	1097	8.6	0.91
	C2	400	382	4.5	0.96	800	719	10.1	0.90	1200	1071	10.8	0.89
D	D1	400	381	4.8	0.95	800	725	9.4	0.91	1200	1083	9.8	0.90
	D2	400	383	4.3	0.96	800	732	8.5	0.92	1200	1093	8.9	0.91
Average		400	380	4.9	0.95	800	724.2	9.5	0.91	1200	1082	9.9	0.901
Asameter: Frank M350 (300–3000 L/h)
MBV: Belimo EPIV DN 15 (300–1200 L/h)

).

After the adjustment step, the PFM (higher measuring rotameter-referred) is expected to lead to a pump speed that is lower than the velocity obtained after the final adjustment step required by the ratio method procedure (lower measuring MBV-referred). According to the consistency check, the expected difference for pump velocity was about 5%.

However, although at different final speeds, both methods were expected to reach the same proportion of flow rate values according to the design data; so, the most significant validation resulted from the comparison of final valve positions.

After conducting the preliminary set-up activities, the two methods were applied in succession. The step-by-step execution of the two procedures is reported in Appendix F.

At the end of both procedures, the flow values and the positions of all balancing devices as well as the final speed of the pump were registered. It was also verified that both methods led to an effective minimum energy/pressure configuration, with at least one clear path.

Finally, for each method applied, the number of balancing actions N_bal required as well as the number of measurements N_meas (including the repositioning of the probe instruments) was determined.

4. Results

The results in terms of final flow rate show how the RM led to a balanced situation within tolerances: the terminal with the greatest deviation was terminal C1, which had a flow rate difference of 8.8% from the nominal value. As far as the progressive flow method is concerned, its operation did not involve the measurement of flow rate at individual terminals other than in terms of the increase in the overall flow rate at the time of its activation. In any case, the method proceeded to sequentially activate the terminals only when the updated total flow rate was at the desired value, so the value at the end of the procedure could be precisely adjusted to the nominal value (2600 l/h), within the accuracy limits of the rotameter. After considering this, the equivalence of the two different procedures was assessed by comparing, in addition to the total flow rate just discussed, (i) the final positions of the balancing devices and (ii) the final pump speed. Useful values for comparison referring to both methods are presented in

Table 3. Comparison of results between RM and PFM procedures.

Design Data		Ratio Method			Progressive Flow Method
Terminal Unit	Design Flow Rate [l/h]	Valve Opening [%]	Final Pump Speed	Flow Rate Sum of MBV [l/h]	Valve Opening [%]	Final Pump Speed	Flow Rate Rotameter [l/h]
A1	200	100%	85%	2622	100%	80%	2600
A2	300	55%			60%
B1	300	100%			100%
B2	350	56%			70%
C1	250	100%			100%
C2	400	75%			92%
D1	300	73%			70%
D2	500	100%			100%
Total	2600	-			-

.

Regarding the final valve configurations and referring to the values reported in Table 3, a radar graph (Figure 13) has been provided to compare the positions reached after the application of each procedure.

The chart highlights some local differences; it may be noticed that the B2 and C2 terminals differed significantly (respectively, 56% to 70% for B2 and 75% vs. 92% for C2).

Application of the PFM did not require direct measurements at the B2 and C2 terminals and so, direct comparison in terms of flow rate values was not possible.

5. Discussion

Regarding the terminal valve positions, the fact that B2 and C2 showed positions that differed by 14% and 17%, respectively, at the ends of the two procedures deserves further investigation: the assessment that needs to be made is firstly whether the difference in flow rate is expected to be greater or less than the difference in valve stroke. Since the valves used in the balancing test rig were control valves, the factors that must be considered for this analysis derive from the theory describing the flow rate/position relationship for this type of valve. These factors are represented by (i) the inherent characteristics of the valves used, (ii) the degree of openness of the valves in which the behavior is to be analyzed, and (iii) the value of the Authority parameter assumed by the valves with respect to the controlled circuit. These valves are designed to maintain equipercentage behavior in the upper half of the opening and the authority calculation gives a value for both in the range of 0.2–0.3. In accordance with ASHRAE [30] and as shown in Figure 14; considering an Authority value within the range [0.2–0.3] (or, in percentage, [20–30%]), the flow rate variations related to the difference in the opening respectively between 92% and 75% and between 70% and 54%, were expected to be lower than 10%, as highlighted by the red and green reference quotas.

As for the speed rotation of the pump and referring to the previously expressed considerations, the difference must be consistent with the difference in measurements obtained by the instruments taken as the reference instruments for each method; the value obtained by applying the PFM method based on rotameters led to a rotation speed of (80 − 85)/80 × 100= −6.25% lower than that obtained with the terminal ultrasonic probe-based ratio method, in good agreement with the 4.9% difference verified by carrying out preliminary consistency tests between the two measuring instruments (Appendix E, Table A1).

After discussing the PFM from the theoretical point of view and its experimental validation, it is considered useful to investigate its practical advantages.

A first evaluation was made by simply comparing the overall N_meas and N_bal required by the application on the test rig; the values were compared with the ones obtained through application of the PFM, see

Table 4. Comparison between Ratio Method and Progressive Flow Method applied on the test rig.

N	Ratio Method	PFM	Difference
Nmeas	27	14	−48%
Nbal	22	13	−41%

.

The PFM proved to be more efficient, both in terms of the actions required for balancing and in terms of movement of the measurement probes; the advantage would increase with greater numbers of users per local manifold. The proposed method turns out to be entirely non-iterative and performs balancing directly at the nominal flow rate without requiring iterations or a final adjusting step. In addition, with presence of the appropriate line valves, the PFM overcomes the critical limitations shown by the other non-iterative method, i.e., the CM.

Lastly, the listed advantages are characteristic of a method that can be applied regardless of the presence of flow meters on all terminals; pressure taps can more easily be provided across the terminals to be used as a reference control and this can be a key factor in balancing existing buildings that are difficult to work on. The simplifications on which the evolution of the PFM originally developed for air systems has been based have essentially been made possible by the opportunity to adopt methods of adjusting the compensation flow rate by means of real-time control, which replaces the time-consuming adjustment phases of iterative methods.

The assumption, which is always verifiable, of perfect tightness of the hydronic piping has a great influence on the method’s operating mode because it allows all flow rate measurements to be reported to a single measuring station located at the pump. However, the full applicability of the method requires specific attention on the part of the designer and, in particular, the ability to determine at the design stage which positions will require the presence of line-balancing valves.

6. Conclusions

The proposed method was investigated, taking into account that there are many existing and new applications for which balancing is required. Traditional methods present the problems of being iterative and requiring direct or indirect terminal flow measurement systems.

The compensated method, which was proposed in the 1990s to overcome the problem of iterativity, also has some drawbacks such as the need to install calibrated balancing valves with flow measurement features on all terminals, and it does not fully address some situations that can be faced during balancing and that require going back in operations.

The proposed method, referred to as PFM and derived from previous studies on the balancing of air systems, is presented from a theoretical perspective and declined for application with reference to the main architectures of water systems; the method has been optimized by appropriately exploiting the tightness characteristic of hydronic networks, making it possible to propose a procedure that does not involve terminal flow measurements but only $∆P$ measurements across the farthest terminals, which are used as a reference, and a single centralized flow measurement point.

The flow rate detection equipment, consisting of multiple instruments placed in parallel and activated as required, can be used to apply the procedure to all sections of even complex plants according to a logic of scalability that guarantees adequate resolution and measuring range. The measuring tool can be placed in series with the pump during TAB operations and removed after finishing, to be reused on similar installations.

The procedure was tested experimentally in comparison with a standard method (ratio method). The results were validated and both applied methods led to a result within the accepted tolerance of 10% in terms of flow rate and to a comparable configuration of the balancing device.

Finally, savings were quantified not only in terms of the number of flow meters required, but also the numbers of measuring and balancing operations required, which in the case analyzed were reduced by 48% and 41%, respectively.

The research developed in the field of balancing water systems offers interesting insights. In particular, these include developments in the application of general balancing concepts to the field of flow control in variable flow systems and a possible rethinking of the dynamic control modes currently adopted.