heat distribution

Research Article

Building Systems and

Components

E-mail: [email protected]

A simulation methodology for heat and cold distribution in thermo-hydronic networks

Roel Vandenbulcke (), Luc Mertens, Eddy Janssen

Karel de Grote University College, Department of Applied Engineering, Salesianenlaan 30, B-2660 Antwerp, Belgium Abstract This paper presents a simulation methodology to analyze hydronic heat distribution systems in a fast and user friendly way. As suggested in its name, the “Base Circuit Methodology” (BCM) is based on the observation that thermo-hydronic networks can be built up as a modular composition of elementary “Base Circuits” (BCs). Once the hydronic and thermodynamic behavior of such basic components is described in a set of dedicated equations, complex thermal distribution networks can easily be modeled by connecting the basic sub models. In addition to control performance simulations (accuracy, stability, speed) the BCM puts extra effort into energy efficiency analysis. In fact, every BC is a local sub unit in which heat flows are gathered, divided or changed in terms of temperature and/or flow. Therefore the BCM model setup yields the opportunity to analyze the net heat transport and its adaptations while crossing the network. Doing so, system designers get the efficiency variables more structured, leading to straightforward abilities to optimize heat and cold distribution. Practical examples prove the benefits of the methodology. Moreover, a test installation was built in which flows, pressures, and temperatures are confronted with the simulation results. The simulations are processed by means of the iterative equation solver EES (Engineering Equation Solver; ©F-chart) which has been experienced as a very compliant software package. As a result the methodology is delivered as a validated and open source library.

Keywords hydronic system,

heating system,

HVAC simulation,

Engineering Equation Solver (EES),

open header Article History Received: 30 October 2011

Revised: 26 January 2012

Accepted: 30 January 2012 © Tsinghua University Press and

Springer-Verlag Berlin Heidelberg

2012

1 Introduction

Rational considerations and the anxiety for the Global Warming Up are the main drivers to minimize the overall energy consumption meanwhile optimizing the feeling of thermal comfort in buildings. Concerning these aspects, engineers are forced to find the better solutions for heat and cold production and distribution considered from the point of view of ecology, economy and energy resources. The challenge consists of developing design principals suitable for both small and complex thermo-hydronic circuits.

Heat pumps, condensing boilers, variable speed chillers, etc. are generally known and wide spread technologies to reduce thermal energy consumption and are often governmentally stimulated. In practice, however, their performance is rather saddening because of sub optimal plant design. In fact, important heat and cold distribution aspects are frequently overlooked and therefore destroy the

overall and real plant efficiency. In the specific case of central heating systems with condensing boilers one can verify that the level of condensation stays far away from the promised conditions while the opportunities to recover latent heat are potentially present. Thermo-hydronic networks are typically designed for full load conditions based on static calculations and rules of thumb. In partial load, however, temperatures and flows change drastically, resulting in less efficient working conditions for the heat and cold production units. Moreover, this unknown partial load behavior covers over 90% of time.

The lack of practical hydronic engineering tools strongly contrasts with the high degree of freedom during the network design and the actual innovative possibilities of recent control strategies and software skills: e.g., today, pumps have variable speed control and higher order programmable logic facilities to deal with head loss compensation, constant head, differential pressure control or other sophisticated and adaptive control techniques. One by one they bear

BUILD SIMUL (2012) 5: 203–217 DOI 10.1007/s12273-012-0066-7

Vandenbulcke et al. / Building Simulation / Vol. 5, No. 3

204

List of symbols

BWL bottom winding limit c specific heat (J/(kg·K)) ck polynomial coefficients D diameter (m) Δp pressure difference (Pa) Δpump pump head (Pa) e wall roughness (m) E exergy (J) E exergy power (W) f Darcy friction factor h/h100 dimensionless valve displacement (0..1) IOUT integral term controller output KI integral gain (1/(K·s)) KP proportional gain (1/K) Kv hydraulic conductivity ((m3/h)/ bar ) Kvs Kv value for fully opened valve ((m3/h)/ bar ) L length (m) m mass flow (kg/s) MV manipulated value NTU number of transfer units P power (W) POUT proportional term controller output Q heat (J)

Re Reynolds number RR relative roughness T temperature (K,℃) TWL top winding limit UA overall conductance (W/K) v velocity (m/s) V volumetric flow (m3/h) ζ factor for local flow resistance μ dynamic viscosity (Pa·s) ρ density (kg/m3) τintegration controller integration time constant (s)

Subscripts

α, β, γ base circuit gateway index amb ambient BV balance valve CV control valve R hydraulic resistance ref reference SP set point su, ex supply, exhaust x, y node index 100 full load reference

optimization opportunities which must be fine tuned in the total design concept. Otherwise, and this is too often the case, energy is lost. Due to the enormous hydronic alternatives, system designers lose the overview in practical cases. Even for new buildings a “copy/paste” driven approach instead of a customized design can be observed.

Considering the above mentioned problems, an overall scientific supervision on the hydronic design process can result in increasing the overall energy efficiency and the cost- effectiveness of the granted resources. As thermo-hydronic installations can grow out to complex and multivariate systems the best way to consider and to investigate on new installation concepts is to simulate them before they are set up in real live. Such simulations, however, are rather complicated due to the non-linear behavior of heat and mass transfer. Interactions between the thermal and hydraulic part of the problem further increase this complexity. Therefore a common and appropriate practice is to split the model into two parts. One part concentrates on the thermal effect and deals with the heat carrier temperatures and heat flows while the other describes the hydraulic aspects like fluid flows and pressures. Doing so, several investigators have succeeded in dealing with both the hydraulic and

thermal problems in their simulations, leading to interesting insights in thermo-hydronic interactions and control strategies. Gamberi et al. (2009) built up a Simulink© simulator for building hydronic heating systems using the Newton-Raphson algorithm. Werdin (2004) proposed diverse component models applicable for both hydronic and thermal simulations. Xu et al. (2008) analyzed the effect of thermostatic radiator valves by means of a combined thermal and hydraulic model. Other dedicated component models can be found in the ECBCS Annex 10 report (1982- 1987) which gathers the contributions of different authors.

In the aforesaid models it is common practice to consider the network as a multi connected system of hydronic components. The hydronic equation set is more or less approached as an electric network analogy. For each pipe node the sum of flows must equal zero (continuity principle) to obey the conservation of mass while for each closed loop the sum of pressure differences must be zero. Once all flows are known, the thermal energy conservation is applied for each pipe node to calculate the respective fluid temperatures.

This general approach, however, is time consuming since each single component must be provided with the necessary


205

parameters and linked with its adjacent component models, by equating the corresponding variables. For big central heating systems with an enormous amount of components, this becomes an almost discouraging job. Therefore, the usage of dedicated simulations in big thermo-hydronic networks is rather scarce. System designers do not take time to invest in such extensive analysis method and therefore hang onto the more static calculations. Even for research purposes, investigators limit their analysis to small hydronic networks or parts of it (e.g., only the hydronic loops of an air handling unit).

Also in typical building simulation programs such as TRNSYS, DOE2, EnergyPlus,… the hydronic network is mostly reduced to a strictly thermal problem, disregarding the hydraulic consequences and assuming perfect hydronic behavior. In fact, to calculate the fluid flows in complex hydronic networks, an overall hydronic equation set must be constructed by means of equation based models in which input and output variables should not be distinguished from each other beforehand. For example, a pipe inlet and outlet cannot be specified since the flow direction is not known. Most models used in the typical building simulation programs are based on functions in which input and output variables must be explicitly stated. This way, water flows are usually considered as known input instead of hydronic calculation results.

This paper presents an innovative methodology to improve the usability of thermo-hydronic simulation in big central heating and cooling systems. With this contribution, we hope to bring hydronic simulation to a real application level for system designers and engineers. As suggested in its name the “Base Circuit Methodology” (BCM) is based on the observation that thermo-hydronic networks can be built up as a modular composition of elementary “Base Circuits” (BCs). For every BC encountered in the network, the appropriate BC model (subset of several embedded component models) can be loaded from the BCM library and subsequently connected with the adjacent BCs. For a convenient linking of BCs, the model is constructed in such a way that the number of variables to be exchanged with neighbor BCs is minimized. Moreover, since every BC can be considered as a “thermal power node”, the BCM yields some additional tools to analyze all net heat flows and their transformations while crossing the thermo-hydronic network. While the method can be used in more general circumstances its description will be strictly formulated from a point of view of HVAC.

Figure 1 illustrates how the overall network model is built up as a composition of BCs by means of the BCM library, how the BCs can be connected and how they interact with existing models of boilers, condensing boilers, chillers, radiators, etc. as can be found in the literature mentioned.

Fig. 1 Schematic illustration of the BCM library

2 The base circuit methodology (BCM)

Figure 2 illustrates the typical hydraulic representation of the BC in its most general form. Net heat flows (the difference between supply and exhaust pipe) can enter or exit the BC at the so called gateways α, β and γ. A net heat flow entering the circuit is conventionally positive; an outgoing heat flow carries a negative sign. At the perimeter of the BC, every gateway has an x-connection and a y-connection which can be linked to other BCs. Internally the x-node connects all x-connections and the y-node connects all y-connections. A sign convention for the mass flows is included and indicated by the flow arrows. Mass flows entering the gateways at the x-connection are positive. Mass flows entering the gateway at the y-connection are negative. The pressure differences over the gateways are conventionally positive when the absolute pressure at the x-connection is higher than the absolute pressure at the y-connection. All temperatures, pumps and

Fig. 2 The base circuit and nomenclature


206

hydraulic resistors (R) are indicated by the respective gateway index (α,β,γ) and a node index (x,y).

2.1 Model validity constraint

At this stage, attention should be paid to the fact that the BCM model setup is only valid under the constraint that for every mass flow entering or leaving the x-connection of the respective gateway, the mass flow at the y-connection is equal in size but opposite in sign. This special feature is the key to create dense BC models and minimize data exchange with neighboring BCs. In central heating and indirect cooling systems, characterized by a branched and tree shaped heat distribution this requirement is mostly fulfilled. Exceptions, however, can be encountered in industrial ring shaped networks. How to deal with the BCM in these exceptional cases will be illustrated for an industrial cooling system in Section 3.2.

2.2 Hydronic model of the BC

The hydronic equation set of the base circuit consists of four equations. The first three equations describe the pressure difference Δpxy between the x and y node according to the three different gateways. This in respect with the flow direction as stated in Fig. 2. Since the hydraulic resistances are passive elements creating head loss, the sign of the pressure differences depends on the flow direction incorporated by the SIGN function:

, ,

R, , R, ,

Δ Δ Δpump Δpump

SIGN( ) (Δ Δ )xy α α x α y

α α x α y

p p

V p p

= + -

- ⋅ + (1)

, ,

R, , R, ,

Δ Δ Δpump Δpump

SIGN( ) (Δ Δ )xy β β x β y

β β x β y

p p

V p p

= + -

- ⋅ + (2)

, ,

R, , R, ,

Δ Δ Δpump Δpump

SIGN( ) (Δ Δ )xy γ γ x γ y

γ γ x γ y

p p

V p p

= + -

- ⋅ + (3)

with Δpump= pump head; ΔpR= head loss. The fourth equation in the hydronic model describes the continuity principle. Since the heat carrier is assumed to be incom- pressible, no mass is accumulated and the sum of the ingoing and outgoing mass flows is zero. As the flows at the x and y nodes are equal in size and opposite in sign the same continuity holds for both, resulting in one single equation:

0α β γm m m+ + = (4)

Depending on the kind of hydraulic resistances encountered different formulas are used to model the resulting

pressure differences in the above hydronic equation set: The head losses caused by pipe friction can be calculated

according to a diversity of formulas as can be found in Potter and Wiggert (2002), e.g., Hazen-Williams, Chezy- Manning, Darcy-Weisbach. All of them might be used in the BCM. However, in this paper the Darcy-Weisbach equation is preferred as it is the most accurate one:

2

Δ2

L vp f ρD

= ⋅ ⋅ ⋅ (5)

with ρ= fluid density; L= pipe length; D= internal pipe diameter; v= average flow velocity. The flow velocity is calculated based on the volumetric flow and the internal pipe diameter. Within EES (Engineering Equation Solver; ©F-Chart, Klein 2008) the friction factor f can be retrieved very conveniently from the Moody chart by means of the built in “Moodychart” function. This function has the Reynolds number Re and the relative roughness RR as variables:

MoodyChart( ,RR); ; RRD ef Re Re ρ v μ D= = ⋅ ⋅ = (6)

This internal MoodyChart function spans all flow regimes very well and provides a smooth transition from the laminar to the turbulent flow regime. The relative roughness RR is the dimensionless ratio of the average wall roughness e and the internal pipe diameter D. The dimensionless Reynolds number is calculated given the fluid density ρ, the average flow velocity v, the internal pipe diameter D and the dynamic viscosity μ. EES can deliver the dynamic viscosity μ as function of the fluid temperature and pressure in the respective pipe. However, to avoid recurrent crosslinks in the models, a constant average system pressure and average system temperature is used. For HVAC simulations this is a reasonable approximation.

Pressure differences due to local resistances such as bends, T-pieces, pipe reductions, etc. are calculated by means of their ζ values which can be retrieved from tables.

2

Δ2vp ζ ρ= ⋅ ⋅ (7)

Head losses in balance valves and control valves are calculated by means of their Kv values which is a commonly used engineer’s method to express the hydraulic conductivity:

2

refΔ

KvρVp

ρ= ⋅)(

(8)

with ρ= actual fluid density during the simulations; ρref = fluid density during the manufacturer’s Kv measurements (typically 1000 kg/m3).


207

Once the system is hydraulically balanced, the Kv values for balance valves are fixed model parameters. For control valves, the Kv value is function of the valve stroke and modeled according to the valve characteristic as prescribed by the valve manufacturer. The following equations illustrate a linear 2-way valve characteristic (e.g., used for loading the domestic water heater) and an equal percentage 2-way valve characteristic (e.g., used for power or temperature control) according to ISSO publication 44 (1998):

0 0

100

Kv Kv Kv1Kvs Kvs Kvs

hh

= - ⋅ +( ) (linear valve) (9)

1001

0

Kv Kvs1Kvs Kv

hh

-= - ( )( ) (equal percentage valve) (10)

with h/h100= dimensionless valve displacement; Kv= actual Kv value; Kvs= Kv value for the completely opened valve; Kv0= Kv value at that point of the basic shape of the valve characteristic which intersects the y-axis. Typical values for the Kvs/Kv0 ratio are situated between 25 and 50. Mostly, these characteristic parameters are available in manufacturer data according to VDI/VDE 2173 (2007, “Fluid characteristic quantities of control valves and their determination”). Similarly all kinds of valve characteristics as well as 3-way valves are modeled in the BCM.

For control stability analysis with a small simulation step size, it might be necessary to take the inertia of the valve actuator into account. In central heating applications, the action time from a closed to a completely opened valve can range from 35 sec up till 180 sec. The closing time might even be longer. In the BC models, this inertia is supposed to be linear and applied according to the procedure proposed by Latinen and Vartinen (IEA ECBCS Annex 10). For thermostatic radiator valves, the model proposed by

H. Ast (IEA ECBCS Annex 10) is applied. For equipment (e.g., filters, dirt separators, boilers,…) for

which a pressure loss diagram is more commonly specified instead of a Kv value, ζ value or similar, the BC model must be provided with an equivalent Kv value based on the pressure loss diagram. However, during model validation we experienced the need to pay attention to the accuracy of pressure loss diagrams provided by manufacturers as they are often based on extrapolations.

The pump heads Δpump in the hydronic equation set are function of the volumetric flow as defined by the pump curves. Using manufacturing data, the pump curves could be implemented in a parameterized model using a polynomial law:

pump 0Δ ( )n k

kkp c ω V

== ⋅å (11)

with ω [rpm]= pump speed. Yet, the BCM focuses on modern variable speed pumps with internal control logics such as constant head control and pipe loss compensated head control, as illustrated in Fig. 3. Assuming ideal internal control loops, these pump curves are linear which makes them very easy to model. Of course improved pump models taking into account the efficiency and the electric energy consumption can also be applied and will be added to the BCM library hereafter.

Note that gravity head caused by the density difference between supply and return water in the rise pipes, is not taken into account to keep things straightforward. Moreover, in modern hydronic networks with forced pump circulation this is a reasonable approximation.

Fig. 3 (a) constant head pump curve, (b) pipe loss compensated pump curve

2.3 Thermal model of the BC

When the water temperatures across the pipe-nodes are analyzed, one can notice that two specific situations will occur, respectively a mixing and dividing situation (Fig. 4). One must realize that for dividing situations two equations must be defined while for a mixing node one equation suffices. In networks with several pumps the flow situation (dividing, mixing) is not predefined. For example, the open header is a typical network component in which the flow situation often changes, as illustrated in Fig. 5. Since the primary and secondary flow continuously change the open

Fig. 4 Temperatures across a pipe-node for (a) dividing situation and (b) mixing situation


208

header will keep the mass balance at its equilibrium point, resulting in a swapping flow direction. When the secondary flow is bigger than the primary flow, the open header flow is directed upwards what leads to a mixing point at the top. In the opposite case the mixing point will be at the bottom. The latter situation is typical for partial load regimes and leads to an increased boiler supply temperature and therefore a decreased efficiency in condensing boilers. This energy destructing condition is illustrated in Fig. 5 by means of an IR-image. Another example of changing flow directions will be found in ring configured networks as encountered in industrial cooling applications (see e.g., Fig. 17). In such networks several flow paths exist to reach a thermal unit. As the hydraulic resistances of these paths change, changing flow directions must be expected.

Consequently, as the flow situation across the pipe-nodes can change, the BCM deals with this by using two conditional equation sets. A first set is used when in the x-node a mass flow is divided and as a result two mass flows are mixing in the y-node. The used set of equations is called the “DM” set (x Dividing; y Mixing):

, ,α x β xT T= (dividing x-node)

, ,α x γ xT T= (dividing x-node) (12)

, , , 0α y α β y β γ y γT m T m T m⋅ + ⋅ + ⋅ = (mixing y-node)

In the opposite case, when the x-node is in mixing mode and the y-node is in dividing mode, the “MD” equation set is used (x Mixing; y Dividing):

, , , 0α x α β x β γ x γT m T m T m⋅ + ⋅ + ⋅ = (mixing x-node)

, ,α y β yT T= (dividing y-node) (13)

, ,α y γ yT T= (dividing y-node)

To call the right set of equations the base circuit model first analyzes whether the circuit is in a DM- or in an MD-mode.

To explain this analysis all possible flow situations are illustrated in Fig. 6. Regarding the flows at the gateways six different situations occur. With respect to the mass flow convention the sign combinations are listed in Table 1. From there the product P of these signs can be considered. A plus sign makes x dividing while a minus sign corresponds to x mixing. Conform to the model validity constraint the y-node reacts complementary: this means x dividing corresponds to y mixing and vice versa. In conclusion it should be clear that the product of the flow signs P is a straightforward variable used to select the proper equation set automatically. Since the flow sign convention is in- trinsically covered by the methodology no confusion will occur when linking neighbor BCs.

Fig. 6 Six possible flow situations inside the base circuit

Table 1 Analysis of the flow situations in order to find the proper equation set

Mass flow signs Flow situation α β γ

Product sign P

Equation set

1 + – – + DM

2 + + – – MD

3 + – + – MD

4 – + + – MD

5 – – + + DM

6 – + – + DM

Fig. 5 Changing mixing point in the open header, IR-picture


209

Thermal pipe losses can be included in the thermal BC model. Doing so, the fluid temperatures at the end of the pipes differ from the temperatures at the beginning. The heat losses Ploss over a pipe can be macroscopically expressed by

loss su ex( )P m c T T= ⋅ ⋅ - (14)

with Tsu= supply temperature at the beginning of the pipe, Tex= water temperature at the end of the pipe, m = mass flow, c= thermal fluid capacity. Moreover, the heat transfer between the pipe and its environment can be written as

loss su ambUA( ) (1 exp( NTU)); NTUP m c T Tm c

= ⋅ ⋅ - ⋅ - - =⋅

(15)

with Tamb= ambient temperature; NTU= number of transfer units. The heat transfer coefficient and area UA is calculated given as input the pipe dimensions and insulation materials. By combining Eqs. (14) and (15), an expression for the fluid temperature at the end of the pipe is found, as it is applied in the non-adiabatic BC model:

ex su su amb(( ) (1 exp( NTU)))T T T T= - - ⋅ - - (16)

The ambient temperature Tamb can be provided with a constant value (e.g., 20℃). However, a more accurate approach is to exchange Tamb between the BC model and the building model.

2.4 Pre-modeled circuits and the BCM library

Although the BC might look a little strange at this stage, it forms a basis upon which all kinds of thermal distribution systems can be modeled. As an example, in this section a typical hydronic mixing circuit (Fig. 7, on the left) is modeled as a BC (Fig. 7, on the right).

From the general BC representation in Fig. 2, only the necessary components remain in Fig. 7. The redundant pumps are erased and respectively removed from the hydronic equation set. All hydraulic head losses in pipes, balance valves and control valves are ascribed to the respective hydraulic

Fig. 7 Typical mixing circuit and its BC representation

resistors. The bypass pipe of the mixing circuit is represented in the BC by shortcutting the β-gateway hydraulically and thermally. Correspondingly, both the temperature and pressure difference over the β-gateway equals zero in the equation set; Δpβ = 0 and Tβ;x= Tβ;y.

The same approach is applied to pre-model other frequently used hydronic circuits, such as those listed by Petitjean (1994), ISSO publication 44 (1998) and ISSO publication 47 (2005). Such BC models are gathered in the BCM library (Fig. 1). Note that some BCs in the BCM library are a composition of several single BCs as they are often used in combination. Doing so the model setup time is further decreased. For example, the library include BCs with four pipe nodes although the BC is actually defined having only two nodes.

2.5 Stepwise application of the BCM

The BCM model setup is stepwise explained for a simplified central heating system, as illustrated in Fig. 8. The heat exchangers HX1 and HX2 can be considered as networks of radiators which also may be implemented in the BCM. In this case they are simplified to maintain the overview. The room temperatures Tr,1 and Tr,2 are controlled by means of active mixing circuits which control the supply water temperature of the radiators. An open header disconnects the primary boiler flow and the secondary flow in the collectors to ensure a minimum boiler flow (typical requirement for a boiler with small water content).

Step 1: Recognizing the BCs

Since a thermo-hydronic network can be built up as a modular composition of BCs, they need to be recognized in the system scheme first. In this rather small network, this recognition is very straightforward as illustrated in Fig. 8. Even for more complex networks, this identification step remains rather easy since the different hydraulic BC configurations are graphically suggested in the BCM library. The knowledge that a BC always includes two pipe nodes and can be considered as a power node (see Introduction) might be helpful as well. At the end an index number must be assigned to every BC on the scheme.

Step 2: Loading the sub models from the BCM library

For every BC indicated on the system scheme, the right thermo-hydronic BC model must be loaded from the BCM library and appended to the overall equation set. Accordingly the model code of the respective BCs can be copied into the main equation window within the EES software. Subsequently all BC variables and parameters must be given the same index as their respective BC number.


210

However EES provides a more convenient way to call the necessary BC sub models. In fact all BC models can be called from the BCM library by means of EES “MODULES”. When EES encounters a CALL statement to a “MODULE”, it automatically grafts the equations of the respective BC model into the equations of the main program, without displaying them. This way a very compact and synoptic model structure is obtained. Figure 9 illustrates the CALL statement for BC3 (active mixing circuit) in the current example (Fig. 8).

The argument list of the CALL statement consists of a first set of exchange variables to be connected with the adjacent BCs (flows, pressure differences and temperatures at the BC gateways) and a second set of parameters regarding the pipes, balance valves, control valves, etc. Since BC3 includes an actuator (3-way valve), the manipulated value MV from the controller model is passed to the BC model. If a non-adiabatic thermal BC model is used, the ambient temperature Tamb is exchanged with the building model to calculate the real thermal pipe losses. For the current example, consisting of four BCs and three heat exchangers in total seven similar CALL statements are inserted in the equation window. This compact way of dealing with the model setup supports the problem transparency.

Note that heat exchangers like radiators, fan coil units, boilers, chillers, etc. are not really BCs as defined above. However, they are present in the library to sustain the overall setup. Dedicated models of these heat exchangers are retrieved from literature but are not in the scope of the current paper.

Step 3: Interconnecting the adjacent BCs

Once all necessary BC models are loaded from the BCM library into the EES software, all embedded BCs are hydraulically and thermally coupled by equating the flows, pressure differences and temperatures at the linked gateways, as illustrated in Fig. 10. This way the number of unknowns equals the number of equations, and so the composed overall thermo-hydronic model can be solved. With respect to the sign conventions (Fig. 2), for xx/yy connections the pressure differences over the gateways will have equal signs and the mass flows will have opposite signs. For xy/yx connections the flows have equal signs but the pressure differences have opposite signs. Note that the physical location where two gateways of adjacent BCs are connected with each other, can be chosen arbitrarily. However, when a non-adiabatic thermal BC model is used, it is advisable to make sure that a BC does not overlap multiple building zones. Doing so, only one ambient temperature (room temperature) needs to be exchanged with the zone model leading to a more convenient model setup. Therefore, the cut location of the gateways is often situated underneath the zone bounds (i.e., walls, ceiling,...).

Step 4: Connecting the BC models with the heat load models

For dynamic network simulations, dynamic heat load models must be provided and connected with the BC models. In the present example, the dynamic heat demands of zones 1 and 2 are modeled according to the commonly used RC- equivalent network approach as proposed by Laret (1981)

Fig. 8 Scheme of the central heating system (left) and its BC representation (right)

Fig. 9 CALL statement and argument list to load the BC model into the main program


211

Fig. 10 Connection of adjacent BCs

and extensively studied and further optimized by several investigators, e.g., Fraisse et al. (2002), Masy (2008). In some cases it might be beneficial to combine the BCM library and the extensive building model capabilities of TRNSYS. Therefore, a connection between TRNSYS and EES can be made by means of the TRNSYS type66 and the EES-supported DDE (dynamic data exchange). Neither the accuracy nor the applicability of dynamic load models are part of the present research. However, while comparing alternative thermo-hydronic configurations it should be noted that the real load model accuracy is often of minor importance as long as the load is representative.

Step 5: Adding control techniques

To obtain the desired room temperatures, control techniques and control strategies are obviously required. In Fig. 8 three control loops can be observed, one boiler controller and two room temperature controllers. In the current example the boiler temperature controller is considered to work perfectly and can be set to a constant or variable temperature like in external temperature compensation algorithms. For the two room controllers, closed loop control is applied. The displacements of the 3-way valves are PI-controlled. The actions taken by such controllers are based on two aspects: the actual value of the error between temperature set points and the real measured values for it, as well as the time integrated error values.

The proportional component POUT of the control action depends on the current error and the proportional gain factor KP. For the control loop in zone 1 one gets:

OUT p p

r,1,SP r,1

100error; ;ProportionalBanderror

P K K

T T

= ⋅ =

= -

(17)

with Tr,1,SP= set point temperature of the respective zone; Tr,1 = current room temperature. The set point room temperature can be varied to take night setback into account. In modern DDC controllers (direct digital control) the proportional band is often specified instead of the proportional gain.

The integral component of the control action IOUT is found by adding the product of the current error and the integral gain KI to the preceding integral term. In Eq. (18), the preceding integral term is supplied to the current calculation with the “INTEGRALVALUE” command within EES (note that this command does not refer to an integral calculation command). To avoid so called “winding up” of the controller, the integral term must be limited. For this reason a Top Winding Limit (TWL) and a Bottom Winding Limit (BWL) are used:

OUT

OUT I

min(TWL; max(BWL;INTEGRALVALUE(stepsize; ) error stepsize))

I tI K

= -

+ ⋅ ⋅

(18)

with: IOUT= integral term of the respective zone controller; stepsize= time interval between the current and the previous iterative calculations. The integral gain KI is calculated as the ratio of the proportional gain and the controller integration time constant τintegration:

PI

integration

KK τ= (19)

The addition of the proportional and integral terms finally result in the overall control action or manipulated value MV which is limited between 0 and 100.

OUT OUTMV min(100; max(0; ))P I= + (20)

Note that PI-controlled actuators can be useful for control performance analysis in terms of accuracy, speed and stability. However, for energy efficiency analysis with a larger time frame and a larger simulation step size (e.g., hourly based), P-control is mostly more than satisfying.

For control performance analysis with a small step size (e.g., 1 sec) the BCM library provides additional control models including first order temperature sensor models according to McGee (1988).

Step 6: Analysis

Once the thermo-hydronic network model is built up as a modular composition of BCs, all thermal and hydraulic variables can be retrieved from the simulation. In combination with the EES plotting tools, this yields profound analysis possibilities. As an example, some typical analysis plots will be shown.

In Fig. 11 the room temperatures Tr,1 and Tr,2 and their set point temperature Tr,SP (day: 20℃; night set back: 15℃) are shown for a simulation scope of 100 hours with a 0.01 hour step size. The external temperature Te is represented by the dotted line.


212

The room temperatures Tr,1 and Tr,2 are respectively controlled by acting on the 3-way valves in BC3 and BC4. The valve lifts of these 3-way valves in BC3 (hlift,3) and BC4 (hlift,4) are plotted on the right ordinate. It is clear that during the morning warming up, both 3-way valves are completely opened to overcome the thermal capacitance of the rooms. Once the day set point temperature is reached the valve lifts decrease again as only the static heat losses are to be compensated.

Another interesting result is the manifestation of the “on-off behavior” for small valve lifts in BC4. The reason for this phenomenon can be found in the control rangeability of the 3-way valve. In fact, in case of low thermal load the valve will be almost closed. For these very small valve lifts the flow becomes unpredictable, leading to an oscillating valve behavior.

Beside transient analyses other correlations can be analyzed as well. For example Fig. 12 illustrates the heating characteristics of the mixing circuits BC3 and BC4. For every simulation step the actual heat emitted in the zones is dot-plotted as a function of the corresponding valve lifts. From a control technical point of view, these heating characteristics should return smooth and preferentially linear curves to assure a good overall performance. In the current example, it is clear that the equal percentage valve in BC3 (control PHEAT,1) bears a much more linear behavior compared to the linear valve in BC4 (control PHEAT,2). But also the influence of valve authority, the Kvs/Kv0 ratio and hydraulic interactivity can be analyzed in these heating curve representations.

In addition, several system variables can be plotted as function of the thermal load, allowing the system designer

Fig. 12 Heat characteristics for an equal percentage (PHEAT,1) and linear (PHEAT,2) valve characteristic

to broaden his view from a strictly full load calculation to partial load analysis. In fact in real cases, big discrepancies between full and partial load conditions result in energy efficiency loss. For example, Fig. 13 illustrates the partial load effect of a mixing point at the bottom of the open header in case of a constant boiler temperature (75℃). As the system is designed at 75/65/20℃, the return water temperature Tα,y,1 coming from the collector is logically equal to 65℃ in full load (right site on the curve). However, in partial load the return water temperature in the collector Tα,y,1 decreases, giving opportunity to recover latent heat from the condensing boilers exhaust gasses. Unfortunately, in partial load, hot boiler water (75℃) is short cut in the open header as the secondary flow gets smaller than the primary flow. As a result, the water temperature Tγ,y,1 increases drastically and thus destroys the condensing opportunities. Fortunately, boiler controllers with external temperature compensation have become common practice and reduce this problem drastically as will be illustrated in Section 3.1.

Fig. 11 Simulation results of room temperatures and valve lifts


213

Fig. 13 Water temperature increase towards the boiler due to a mixing point at the bottom of the open header

3 Simulation examples

In this section, two real test cases in which the practical usability of the BCM was studied, are presented. The first example illustrates how the methodology yields insight in the dynamic behavior of a central heating system in both full and partial load conditions. The second example shows how the BCM can be used as a design tool in a more static and industrial application.

3.1 Dynamic behavior of a central heating system

In this first test case, the BCM is applied to model the thermo-hydronic behavior of the central heating system in a school building (SIBSO2, Antwerp, Fig. 14). Two condensing boilers (2´160 kW) provide the necessary heat to the building. In total 44 different zones (classrooms, office rooms, refectory,…) are heated by means of 79 radiators spread over the zones. According to the orientation of the rooms, respectively situated at the east or west facade of the building, a different water supply temperature is provided by means of two active mixing circuits controlled by a pre-set weather depending heating curve (“pre-control”). On each radiator a thermostatic radiator valve (TRV) further refines the room temperature control (“after control”). The gymnasium is heated with two fan coil units which are manually controlled by the fan speed. An open header is used to ensure a minimum boiler flow and to avoid hydraulic interactivity between the 3-way valves. Regarding the hydronics, one can observe a typically branched and tree shaped design. This way the BCM model validity requirement (as defined under Section 2.1) is met.

Fig. 14 Scheme central heating system, SIBSO2, Antwerp

To build up the overall thermo-hydronic model of this heating system, 166 BCs are loaded from the BCM library. Subsequently, the adjacent BCs are connected. The 44 zones are modeled by means of RC equivalent networks.

In accordance with the open header problem explained in Fig. 13, the ingoing boiler water temperature for this school building is analyzed in case of a constant boiler temperature and a weather depending boiler temperature, as illustrated in Fig. 15.

3.2 Optimal network design for an industrial cooling system

In this practical case (Procap Hoboken NV, Antwerp) the mold dies of 24 injection molding machines needed to be cooled to a precise temperature to obtain correct process conditions. To achieve the desired die temperature, the cold water flows in the die heat exchangers are controlled


214

Fig. 15 Ingoing boiler water temperature in case of constant boiler temperature and external temperature compensation

by manual flow valves based on the operators’ experience (automatic control is not allowed). However, as there is no real feedback control in such practice, the thermal performance of the heat exchangers becomes sensitive to disturbances due to fluctuating network pressures. Therefore, the objective was to design a thermo-hydronic network in which pressure fluctuations are minimized to an acceptable level. A ring shaped network (Fig. 16) was recommended as the pressure fluctuations due to variable loads are smaller in such configuration.

The BCM was used to design this network and to define its pipe dimensions. However, it should be noted that the BCM model validity requirement (as explained in Section 2) is actually not met in this ring shaped network. In fact, while building up the network as a composition of BCs, one will observe that flows entering a BC gateway at the x-connection are not necessarily equal in size at the y-connection, which is typical for ring shaped networks. To overcome this rather exceptional model constraint, a customized hydronic BC model was developed. Although this customized model implies a greater number of variables to link the adjacent BCs, the basic BCM idea is still usable this way.

To model the network, in total 25 BCs are used of which only one BC contains a pump. All other BCs are equal and as

Fig. 16 Ring shaped network with 24 injection molding machines

such very straightforward to implement. Once familiar with the BCM, the set-up of this model takes less than 15 minutes by using the BCM library. The implementation of all hydronic parameters (pump curve, pipe sizes and lengths) and the actual analysis of the different load conditions are, of course, more time consuming but inevitable for all simulation methodologies, BCM included.

Once modeled, all flows, temperatures and differential pressures inside the network could be calculated for a random set of active molding machines. To keep an interactive overview while experimenting with different pipe sizes, the variables were graphically presented in a three dimensional drawing as illustrated in Fig. 17. In fact, all calculated EES-variables can be automatically exported into a “csv-file” and can subsequently be imported into the 3D drawing software.

The flows and differential pressures are shown for a full load situation, i.e., all machines in action. By means of the flow arrows it is made clear that in this loop configured network the flow has two possible flow paths to reach the respective machines. The pressure graph shows the pressure differences at the cold/hot plug-in positions of the different machines. To avoid interactivity in the real installation these pressure differences should more or less be independent of the load. Using our BCM approach, pipe sizes for which an acceptable level of pressure fluctuations is reached, could be found by experiment.

Fig. 17 3D graphical representation of the flow and the differential pressure in the network


215

4 Model validation

As explained before, the BCM is a handsome trick to arrange the hydronic and thermal equation sets in a more structured and dense manner. Therefore, the expected accuracy is in accordance with the embedded models retrieved from the literature. In order to check the resulting accuracy of the BC models, the behaviour of different heat distribution BCs is analyzed in the BCM test installation (Fig. 18) and

Fig. 18 Left: BCM test installation; right: control and data acquisition cabinet

compared with the simulation results. Flow and pressure measurements allow hydronic model tuning. Water temperatures are measured to refine the thermal models.

In the validation procedure, the BC is approached as an isolated entity. Accordingly, temperature measurements of incoming water flows, as well as the pressure differences over the external gateways are considered as environmental variables and therefore used as input in the simulations. Doing so there is no need to provide a steady environment during the measurements. Especially for variables which are difficult to control at a constant value during the measurements, e.g., the boiler water temperature, this validation approach is very convenient and allows to concentrate the analysis on the unitary BC.

The validation scheme and simulation results of a BC, in this case a PI controlled active mixing circuit, are illustrated in Fig. 19. The simulated water temperature Tγ,x,1 (supply water temperature towards the end units) appears to represent the experimental measurements rather well.

Fig. 19 BC model validation scheme and simulation vs. experiment comparison


216

5 Energy efficiency analysis in the BCM

Since BCs are typical “power nodes” where net heat flows (difference between supply and exhaust pipe) are collecting, dividing or changed in terms of temperature and/or flow, the BCM model setup yields the opportunity to analyze all net heat flows and their adaptations while crossing the thermo-hydronic network. In particular two types of heat flow observation tools are worked out, offering the engineer additional information while optimizing the energy efficiency of the system.

5.1 Thermodynamic efficiency of the net heat flows

Analogous with the formulation for heat exchangers, the thermodynamic efficiency at a BC gateway is defined as the ratio of the actual temperature difference and the thermodynamic maximal achievable temperature difference. Considering an ingoing net heat flow at the α-gateway, the thermodynamic efficiency is calculated as follows:

, ,

, sink

α x α yα

α x

T Tε T T

-=

- (21)

The sink temperature Tsink is the lowest temperature the net heat flow will encounter at the emission site. Although the net heat flows crossing the network are finally emitted at different room temperatures, it is more practical to assume a general sink temperature (e.g., 20℃).

In common practice the efficiency focus is located at production and emission site. However with this analysis efficiency losses can be located in the intermediate distribution network too.

5.2 Exergy loss calculation in the BC

Beside energy analysis the BCM can also deal with exergy calculations. Since for all embedded BCs the exergy powers can be automatically calculated, all exergy losses in the thermo-hydronic network can be visualized in a very synoptic way. Especially for low temperature heating and cooling applications, exergy analysis has been formerly used for optimization purposes as documented in the IEA ECBCS Annex49 report and Babiak et al. (2007). This paper does not intend to discuss exergy loss analysis; however, it illustrates how BC exergy losses can be calculated.

The exergy loss inside the BC is calculated by observation of the ingoing and outgoing exergy powers at the BC gateways. As the temperature of the heat Q in the heat carrier fluid decreases when heat is emitted to the environment with temperature Tref , the exergy E must be calculated according to the “body” approach. This way the exergy factor can be

written as follows:

ref

ref ref1 lnE T T

Q T T T= - ⋅-( ) ( ) (22)

Accordingly, the exergy power of the water flow entering the x-connection of the α-gateway can be written as follows:

,ref, , ref

, ref ref( ) 1 ln α x

α x α α xα x

TTE m c T T T T T= ⋅ ⋅ - ⋅ - ⋅-( ( ) ( ))

(23)

On a same basis, the outgoing exergy power at the y-connection of the respective gateway can be calculated. However, to get the net exergy power at the BC gateway, the outgoing exergy power at the y-connection must be sub- tracted from the ingoing exergy power at the x-connection:

,ref

, , ,1 ln α x

α αα x α y α y

TTE P T T T= ⋅ - ⋅-( ( ) ( )) (24)

With the same sign convention as the mass flows, the total exergy power loss is calculated straightforward as the sum of the respective gateway exergy powers:

loss α β γE E E E= + + (25)

As an example, Fig. 20 illustrates the exergy losses in the intermediate distribution network between production and emission site. Because of water flows with different temperatures are mixed together inside the two BCs, Exergy power is lost.

By using the above mentioned analysis tools, it becomes clear how the hydronic network can affect the total plant efficiency. This way, energy loss on the heat production site can be assigned to locatable parts of the heat distribution network. In particular mixing points must be avoided as much as possible. A mixing point in a return pipe decreases the heat production efficiency (e.g., “open header problem”, Fig. 13) while mixing points in the supply pipes (e.g., BC3 and BC4 in Fig. 8) decrease the thermodynamic efficiency of the end units, which finally also leads to an increased energy consumption. By means of example we (Vandenbulcke and Merten 2011) recently illustrated a fuel consumption

Fig. 20 Sankey diagram of the net exergy flows and exergy losses


217

decrease of 7.1% only by optimizing the hydronic network configuration and control. Yet, a more extensive study on hydronic system optimization incorporating the above mentioned analysis tools, is still to be done in the future work.

The computing time to run the simulations depends on the step size, time horizon and the size of the hydronic system. A detailed thermo-hydronic simulation of the heating system as illustrated in Fig. 14, takes approximately 44 minutes for a one year time horizon using a 15 minutes step size. However, for hydronic design optimization, a more restricted simulation horizon of one week for each season already reveals the most important optimization opportunities. This way, computational costs remain acceptable.

6 Conclusions

The aim of our study was to get scientific insight in the set of thermo-hydronic equations that arises during the design of huge heating and cooling networks. Step by step it was realized that such equations can be considered as sub groups that cover local “Basic Circuits” (BCs). They accept net flows of mass, energy and exergy and distribute them to neighbor BCs. Six basic flow types are identified and form the basis for an automated equations setup. From a thermodynamic point of view the sub units behave as independent entities. In the design phase the BCs can be taken from a library and combined almost without limitation. The performance and controllability of a specific installation can then more easily be analyzed and optimized. The EES-software turned out to be a very good candidate to solve the systems.

At this stage the Base Circuit Methodology (BCM) is a useful tool for experienced EES users. However, a graphical user interface (GUI) might enlarge the usability and bring simulation into the daily practice of system designers. Since EES provides dynamic data exchange (DDE), the GUI could be developed in an independent application to build up a Simulink or LabView alike approach. The necessary BCs would be dragged from the library into the workspace and linked simply by moving the mouse cursor from gateway to gateway. For example, by double clicking on a BC icon, a popup window would appear in which all BC parameters can be entered. Further investigations in this direction are foreseen.

It is the authors’ ambition to develop and sustain the BCM library as an open source library of pre-modeled BCs which will be made available on the internet. To provide reliable models, further validation efforts are planned. At the end, the BCM will be a practical tool used by scientists and designers.

Acknowledgements

The BCM test installation was built in the frame of the VALID project (Variable Flow Validation, project number: IWT-TETRA070106 ), financially supported by the Agency for Innovation by Science and Technology of the Flemish Government.

References

Babiak J, Olesen BW, Pétráš D (2007). Low temperature heating and high temperature cooling, REHVA Guidebook 7.

Fraisse G, Viardot C, Lafabrie O, Achard G (2002). Development of a simplified and accurate building model based on electrical analogy. Energy and Buildings, 34: 1017 1031.

Gamberi M, Manzini R, Regattieri A (2009). Simulink© simulator for building hydronic heating systems using the Newton-Raphson algorithm. Energy and Buildings, 41: 848 855.

IEA ECBCS, Annex 10 (1982 1987). International Energy Agency, System Simulation.

IEA ECBCS, Annex 49 (2006 2009). International Energy Agency, Midterm Report, Low Exergy Systems for High-Performance Buildings and Communities, Germany.

ISSO publicatie 44 (1998). Ontwerp van hydraulische schakelingen voor verwarmen, Instituut voor studie en stimulering van onderzoek op het gebied van gebouwinstallaties, Nederland. (in Dutch)

ISSO publication 47 (2005). Ontwerp van hydraulische schakelingen voor koelen, Instituut voor studie en stimulering van onderzoek op het gebied van gebouwinstallaties, Nederland. (in Dutch)

Klein SA (2008). EES: Engineering Equation Solver, User manual. USAF-chart software. Madison, WI: University of Wisconsin.

Laret L (1981). Contribution au développement des modèles mathématiques du comportement thermique transitoire de structures d’habitation. PhD thesis, University of Liège. (in French)

Masy G (2008). Definition and validation of a simplified multizone dynamic building model connected to heating system and HVAC unit. PhD thesis, University of Liège.

McGee TD (1988). Principles and Methods of Temperature Measurement. New York: John Wiley & Sons.

Petitjean R (1994). L’équilibrage hydraulique global, Un manuel pour la conception des circuits hydrauliques et la détection des anomalies dans les installations de chauffage et de conditionnement d’air, Tour & Andersson AB. (in French)

Potter MC, Wiggert DC (2002). Mechanics of Fluids, 3rd edn. Pacific Grove, CA: Brooks Cole & Wadsworth Group.

Vandenbulcke R, Mertens L (2011). A simulation assisted design tool for boiler room hydronics. In: Proceedings of Building Simulation 2011, IBPSA (pp. 2140 2147), Sydney, Australia.

VDI/VDE2173 (2007). Strömungstechnische Kenngrössen von Stellventilen und deren Bestimmung, Verein Deutscher Ingenieure. (in German)

Werdin H (2004). Ein Beitrag zur modellbasierten Inbetriebnahme und Fehlererkennung von heizungs- und raumlufttechnischen Anlagen. PhD thesis, University of Dresden, Der Andere Verlag Osnabrück. (in German)

Xu B, Fu L, Di H (2008). Dynamic simulation of space heating systems with radiators controlled by TRVs in buildings. Energy and Buildings, 40: 1755 1764.

heat distribution

Documents

simulation methodology

important heat

heat pumps

cold distribution aspects

keywords hydronic system

net heat transport

thermal energy consumption

base circuit methodology