Energy and Buildings 41 (2009) 500–511
Prediction of yearly energy requirements of indoor ice rinks
Lotfi Seghouani, Ahmed Daoud, Nicolas Galanis *
Departement de Genie Mecanique, Universite de Sherbrooke, Sherbrooke, Qc, Canada J1K 2R1
A R T I C L E I N F O
Article history:
Received 24 April 2008
Received in revised form 20 October 2008
Accepted 22 November 2008
Keywords:
Zonal method
Ground conduction
Radiation exchanges
Convection
Condensation
Refrigeration load
A B S T R A C T
A model of the transient heat transfer between the ground under and around the foundations of an
indoor ice rink and the brine circulating in pipes embedded in the concrete slab under the ice has been
coupled with a previously developed model calculating heat fluxes towards the ice by convection,
radiation and phase changes. Subroutines calculating the energy consumption for heating and
humidifying (or cooling and reheating) the ventilation air have also been added to the model. The
resulting simulation tool has been used to calculate monthly refrigeration loads and energy
consumption by the ventilation system, the lights, the brine pump, the radiant heating system of the
stands and the underground electric heating used to prevent freezing and heaving for four North
American cities with very different climates. Correlations expressing the energy consumption of the
ventilation air stream in terms of the sol-air temperature are formulated.
� 2008 Elsevier B.V. All rights reserved.
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1. Introduction
Indoor ice rinks are large buildings without internal partitionsand with high-energy consumption. They have a complex energysystem in which a large ice sheet is cooled and maintained at a lowtemperature by a refrigeration system, while the stands are heated(or cooled) to ensure comfortable conditions for the spectators.Also, the building is ventilated to ensure good air quality. Themovement of the ventilation air through these wide-open areasand the simultaneous operation of heating and cooling equipmentsincrease energy consumption and greenhouse gas (GHG) emis-sions.
A study by Lavoie et al. [1] shows that the potential for energysavings in a typical ice rink in Quebec is roughly 620 MWh/yearand the potential GHG emission reduction is 146 tons-equivalentCO2/year. Since there are 435 indoor ice rinks in Quebec andseveral thousand in North America, it would be interesting toimprove their energy efficiency while preserving good ice qualityand comfort for the spectators. To achieve this objective precisemethods for the calculation of the corresponding loads arenecessary.
Three different methods are commonly used for the thermalmodeling of buildings: the nodal method, computational fluiddynamics (CFD) and the zonal method. The first one is the simplest
* Corresponding author.
E-mail address: [email protected] (N. Galanis).
Abbreviations: AIM, above ice model; BIM, below ice model; IST, ice surface
temperature.
0378-7788/$ – see front matter � 2008 Elsevier B.V. All rights reserved.
doi:10.1016/j.enbuild.2008.11.014
and is implemented by representing the inside volume of the entirebuilding, or of large parts thereof, by a single node. Therefore thenodal method does not necessitate an important computingcapacity but, on the other hand, it does not provide a detaileddescription of the indoor conditions. The application of such amodel to ice rinks (or other large buildings without internalpartitions such as supermarkets or gymnasia) can lead to veryimprecise results because the mass fluxes between different partsof the inside volume are extremely difficult to estimate.
On the other hand, the modeling of an ice rink for CFDcalculations is very complex due firstly to their size and geometry,and secondly to the variety of the heat and mass transfermechanisms which take place therein. Thus, the model must takeinto account heat transfer through the envelope and heat gains fromthe ground, air motion within the building due to forced and naturalconvection, vapour diffusion and condensation on the ice sheet, heattransfer by radiation between all internal surfaces, conduction in theice and floor as well as heat generation by the lights, the resurfacingoperations, the refrigeration system, etc. Hence, the literaturereview revealed few CFD studies for large buildings such as ice rinks.Jones and Whittle [2] described the status and capabilities of CFD forbuilding air flow prediction while Jian and Chen [3] as well as Yanget al. [4] used a CFD code to evaluate air quality in large ventilatedenclosures. However, these studies did not calculate heating andrefrigeration loads and ignored the interaction between the indoorand outdoor environments.
More recently Bellache et al. [5,6] have carried out numericalsimulations in 2D and steady state conditions using a CFD codewhich predicts velocity, temperature and absolute humiditydistributions in an indoor ice rink with ventilation and heating.
Nomenclature
A area (m2)
Cp specific heat (J/kg K)
Cd discharge coefficient
g acceleration of gravity (m/s2)
h height (m)
k thermal conductivity (W/(m K)
mi; j airflow between zones i and j (kg/s)
mB brine flow rate (kg/s)
M mass (kg)
P static pressure (Pa)
qcd conductive flux (W/m2)
qcv convective flux (W/m2)
qrd radiative flux (W/m2)
qcond condensation flux (W/m2)
qrs heat flux due to resurfacing (W/m2)
QCool cooling rate (W)
QHeat heating rate (W)
QHumid energy rate due to humidification (W)
QRe heat energy rate due to reheating (W)
QH electrical power in sand layer (W)
QIce heat rate into node 1 calculated by AIM (W)
Qnode lateral heat transfer to node n (W)
R thermal resistance (m2 K/W)
Snode surface for lateral heat transfer at node n (m2)
t time (h)
T temperature (K)
Tb brine temperature (K)
Tgr temperature of ground surface (K)
Tnode temperature at node n (K)
Tsol-air sol-air temperature (8C)
Unode average conductance for lateral heat transfer at
node n (W/m2 K)
Wg moisture source term (kg/s)
z1, z2 top and bottom depths of ground segment (m)
Subscripts and superscriptsi cell i or surface i
i, j between surface or cell i and j
o outside
p present time step
p + 1 next time step
Greek symbolsDt time step (s)
eij constant depending on flow direction (�1)
r air density (kg/m3)
v absolute humidity (kgmoisture/kgdry air)
L. Seghouani et al. / Energy and Buildings 41 (2009) 500–511 501
The CFD code also calculates the heat fluxes toward the ice due toconvection from the air, to condensation of vapour and to radiationfrom the walls and ceiling. However, these calculations did nottake into account the contributions of ice resurfacing, systempump work and ground heat to the refrigeration load.
This 2D CFD model was later improved by Bellache et al. [7] byincluding transient phenomena, heat transfer through the groundand energy gains from lights as well as the effects of resurfacingand dissipation of pump work in the coolant pipes. The ground at a
depth of 2 m was assumed to have a constant temperature whilethe horizontal plane through the centers of the brine pipes wasassumed to be an isothermal surface with temperature equal to theaverage of the supply and return brine temperatures.
Ouzzane et al. [8] contributed preliminary experimentalmeasurements for a Canadian indoor ice rink which provide abetter understanding of its thermal and energy behaviour. Thesemeasured values were also used for the verification and calibrationof the numerical model developed by Bellache et al. [7]. The maindrawback of the CFD approach is that it requires considerablecomputer memory and CPU time for the simulations. Thus, thetransient 2D model by Bellache et al. [7] requires approximately24 h of calculations on a modern desktop computer to simulate theresponse of an ice rink over a period of 1 day.
An alternative method to CFD, which requires less calculationtime and computer memory, was developed by Daoud et al. [9–11].It combines a zonal airflow model, a radiation model, a humiditytransport and condensation model and takes into account resurfa-cing and occupation. This above ice model (AIM) predicts the heatfluxes through the envelope as well as the temperature and absolutehumidity distributions for a 3D transient regime during an entiretypical meteorological year. In particular it calculates the heat fluxesinto the ice sheet by convection, radiation and condensation. Thetemperature below the ice sheet was assumed uniform andconstant. The results show a satisfactory agreement with corre-sponding measurements and CFD calculations.
The present article describes a second part in the developmentof a global 3D transient model of an ice rink. The below ice model(BIM) was developed using an implicit unidirectional electricalanalogy, taking into account the secondary loop and brinemovement and the heat gain from the ground (with changingmeteorological conditions). The BIM was coupled successfully withthe previously mentioned AIM. The combined model eliminatesthe assumption of constant temperature below the ice sheet usedin AIM. Instead the temperature of the brine entering the pipesbelow the ice sheet must be specified. The combined modelevaluates the return brine temperature, the total refrigeration load,the ice surface temperature (IST), the heat gain from ground, aswell as the energy consumption of the ventilation system and ofthe radiant heaters. Parametric studies were undertaken in orderto evaluate the impact of the climate, brine inlet temperature, icethickness and other parameters on the calculated results and theirresults are presented in the last part of the present paper.
2. Description and modeling
2.1. Ice rink description
Figs. 1 and 2 show a schematic representation of the studied icerink ‘‘Camilien Houde’’ located in Montreal (Canada). The buildingis 64.2-m long, 41.5-m wide and its height is 9.2 m. The ice surfaceis 61-m long, 25.9-m wide and is surrounded by a narrow corridor.The space above the stands is heated by eight radiant heaters(22 kW � 8) which are controlled by a thermostat. Seven inletssupply a stream of ventilation air. Its flow rate is 4270 L/s exceptduring resurfacing of the ice when it is increased to 10,384 L/s toevacuate the combustion gases of the resurfacing vehicle. The airexits through four outlets on the walls. Heat gains from lighting are10 W/m2 above the ice and 5 W/m2 above the stands; those due tothe presence of the audience are also taken into account while thenumber of spectators is specified according to a weekly schedule[7,11]. The ice resurfacing takes place several times per day, lasts12 min and is modeled as a 1 mm film of hot water at 60 8C. Itsfrequency, specified in the schedule mentioned above, is higher inthe evenings and weekends. The stands, corridors and boards arealso modeled in the AIM.
Fig. 1. Schematic section of the ice rink and the different layers under the ice (not to scale).
Fig. 2. Top view of the ice showing the different zones and the flow of the brine.
L. Seghouani et al. / Energy and Buildings 41 (2009) 500–511502
The ground structure beneath the ice rink is represented inFig. 1 and comprises horizontal layers of ice (50 mm), concrete(150 mm), thermal insulation (100 mm), sand (200 mm) and,finally, soil. The total depth of this structure included in thecalculation domain is 4 m.
The secondary coolant used to maintain the ice at the desiredtemperature is calcium chloride brine. It is supplied from aheader located at the west end of the ice sheet and circulates inthe concrete slab at a depth 57.5 mm below the ice surfacewithin 74 uniformly distributed, four-pass polyethylene tubes(25 mm ID). The spacing between tubes is 87.5 mm. The maincollector has an internal diameter of 150 mm. The flow rate ofthe pump is 28.5 L/s.
An electrical heater of 8 kW is activated in the sand layer whenthe ground temperature at a depth of 4 m is below 4 8C to preventfreezing under the concrete slab which can cause damage to theunderground structure and ice.
2.2. Model of air movement and heat exchanges above the ice (AIM)
The air movement and heat exchanges occurring in the rinkabove the ice surface are simulated using a 3D transient modelwith 64 zones [9–11]. It consists of six coupled submodels solvedwith the ‘‘onion’’ method. The first submodel is the energy modelwhich uses the Multizone Building Model (type 56) of TRNSYS [12].It is based on two relations. The first one expresses energy
conservation inside each thermal zone i:
ðM CpÞidTi
dt¼ ðqcvAÞi þ
Xj
m j! iCpT j (1)
while the second expresses energy conservation for each internalsurface in contact with the air in the building:
qcd ¼ qcv þ qrd þ qcond þ qrs (2)
The conductive flux through the wall is evaluated using thetransfer functions method while the convection flux between thewall surface and the air inside the building is calculated using aconstant heat transfer coefficient (3 W/m2 K). The radiation fluxbetween internal surfaces of the building is provided by asubmodel (radiative transfer submodel) based on the Gebhartmethod [13]. The condensation flux is attributed to the ice surfacewhen its temperature is below the dew point of the air above it. It isprovided by a submodel (humidity transport submodel) whichcalculates the absolute humidity of the air in every thermal zoneinside the building using the following conservation equation:
Mair;idvi
dt¼X
i; j
mi; jðv j �viÞ þ Wg;i (3)
Finally, qrs corresponds to the heat flux occurring when theresurfacing operation deposits approximately 0.5 m3 of water at
Fig. 3. Schematic representation of the ventilation system.
L. Seghouani et al. / Energy and Buildings 41 (2009) 500–511 503
60 8C on the ice surface. It is calculated using the equationrecommended by ASHRAE [14].
The airflow mi,j between thermal zones used in Eq. (1) isprovided by the zonal airflow submodel. The formulation usedexpresses the mass flow crossing the common surface betweentwo zones i and j in terms of their pressure difference. Thus, in thecase of a vertical interface
mi; j ¼ ei; jCd
ffiffiffiffiffiffiffiffi2ri
pAi; jjP j � Pij1=2 (4)
While in the case of a horizontal interface
mi; j ¼ ei; jCd
ffiffiffiffiffiffiffiffi2ri
pAi; j P j � Pi �
1
2ðrighi þ r jgh jÞ
��������1=2
(5)
The coefficient eij is equal to +1 when flow is from zone i to zonej and equal to �1 for flow from zone j to zone i.
A new submodel not described in our previous publications[9,10] is used to simulate the behaviour of the ventilationsystem. It consists of two units (see Fig. 3). The first one is usedfor cooling, dehumidifying and reheating the external air whenits temperature is above 23 8C while the second unit is forheating and humidifying it when its temperature is below 15 8C.When the temperature of the entering air is between 23 8C and15 8C none of the units is in operation unless the humidity levelis too high or too low. The humidity controls are such that therelative humidity of the air entering the ice rink is maintainedbetween 20% and 33%. The equations modeling the operation ofthese two units are the mass and energy conservation equationsfor a gas–vapour mixture in a steady state, steady flow process.It should be noted that the results presented here assume thatonly outdoor air is handled by the ventilation system (norecirculation).
The final submodel evaluates the ventilation effectiveness bycalculating the age of the air in every zone of the ice rink.
The data exchange between these six submodels is representedin Fig. 4. It takes place several times at every timestep until theoutputs of each submodel vary by less than 10�3.
Fig. 4. Information flow in the above-ice model (AIM).
2.3. Below ice modeling (BIM)
The modeling of the ice rink ground structure shown in Figs. 1and 2 is of a substantial nature. Indeed, the concrete slab is one ofthe most important parts of an ice rink. It forms and maintains theice by removing heat from it, using a secondary coolant (brine)circulating in the embedded network of pipes.
The BIM is based on the transient one-dimensional conductionequation and the electrical circuit analogy. For that, the ice surfaceis divided in eight equal square surfaces (one to eight) shown inFig. 2, which correspond to those used by the zonal submodel of theAIM. Each of these surfaces is subdivided into two parts (A and B).The brine flows from west to east under part A of the eight surfacesand in the opposite direction under part B (see Fig. 2). Thus, thebrine enters at 1A or 2A with a constant temperature Tb,in and exitsat 1B or 2B with a temperature Tb,out which is not the same for theNorth and South brine loops.
Heat transfer between the tubes is neglected since the brinetemperature increases by less than 2 8C between inlet and outlet.This justifies the hypothesis of one-dimensional vertical heattransfer between the different layers of the ground structure.However, the BIM takes into consideration heat exchangesbetween the horizontal layers and the outdoor or the indoorappropriate ground surface as explained below. Therefore, it takesinto account three-dimensional phenomena.
Fig. 5 shows the equivalent electrical circuit under one-half of theice. At each of the 16 subdivisions of the ice surface shown in Fig. 2the heat flux calculated by AIM enters the ice at node 1. The electricalheating in the sand layer is added to nodes 5 and 6. The temperatureof node 7 is considered as given by the following correlation based onthe deep soil (4 m) temperature data for Montreal [15]
T7 ¼ 3:34� 4:78� 10�3 t � 1:97� 10�7 t2 þ 1:15� 10�9 t3
� 2:66� 10�13 t4 þ 2:15� 10�17 t5 � 5:91� 10�22 t6
þ 273:15 (6)
where t is in h and T7 in K.The heat exchanges between the horizontal layers and the
outdoor or indoor ground surface are added at nodes 2–6. They areevaluated using the ASHRAE method [16] and are divided in twohalves attributed to the circuits under parts A and B. This methoduses the formula:
Qnode ¼ UnodeSnodeðTo � TnodeÞ (7)
where the below-grade average U-factor is given by:
Unode ¼2ksoil
pðz2 � z1Þ� ln z2 þ
2ksoilR
p
� �� ln z1 þ
2ksoilR
p
� �� �(8)
For nodes 4, 5 and 6 on the north, east and west sides of the icerink To is the temperature of the ground surface outside the icerink. It is calculated at each time step by the following correlationbased on the surface soil temperature data for Montreal [15]
Tgr ¼ �2:56� 1:31� 10�2 t � 6:88� 10�6 t2 � 1:79
� 10�10 t3 � 2:02� 10�13 t4 þ 2:42� 10�17 t5 � 7:93
� 10�22 t6 þ 273:15 (9)
where t is in h and Tgr in K.
Fig. 5. Thermal circuit model for below ice structure (1A, 1B. . . etc. identify zones in Fig. 2).
L. Seghouani et al. / Energy and Buildings 41 (2009) 500–511504
On the south side To is taken as constant (equal to thetemperature in the changing rooms). On the three other sides, fornodes 2, 3 and 4, To is taken as the temperature of the concretesurface in the corridors surrounding the ice surface which iscalculated by the AIM.
The brine enters each subdivision and absorbs the heat comingfrom nodes 2 and 4. Its temperature therefore increases and itenters the next subdivision where the process is repeated. Each ofthe 16 subdivisions (parts A and B of surfaces 1–8 in Fig. 2) ismodeled in the same manner and only the entering brinetemperature and the lateral heat exchanges calculated by Eq. (7)vary from one to another. Thus there are 7 unknown temperaturesunder each of the 16 subdivisions (at nodes 1–6 and at the brineoutlet) or 118 unknown temperatures altogether.
The implicit discretisation of the transient energy balance foreach node under each subdivision leads to a system of linearequations which can be represented by the matrix equation
A T ¼ B (10)
where T is the vector of the seven unknown temperatures. Theexpressions of the 7 � 7 matrix A and of the vector B are given inthe appendix.
This system of linear equations is solved by inversing matrix A
since this direct method is suitable for small-size systems. Thesolution starts under surface 1A and then continues to 3A, 5A, etc.
following the direction of flow. The temperature of all the nodes isthus obtained for each of the 16 subdivisions. Then, thetemperature of each level below the ice is obtained by averagingthe 16 corresponding node temperatures. The final outlettemperature of the brine is calculated by assuming that the twostreams from 1B and 2B are mixed adiabatically. The heat ratesfrom the ice to the brine and from the soil to the brine are alsoevaluated and therefore the total refrigeration load is calculated. AFORTRAN subroutine of this model was incorporated as a new typein TRNSYS [12].
2.4. Coupling of the AIM and BIM
The coupling of the BIM with the AIM was realised using the‘‘Onion’’ method. Fig. 6 shows a schematic representation of thecoupling method. During one time step, the BIM calculates thetemperature T2 between the ice and the concrete for each of theeight zones. It provides them as inputs to the AIM in which they areused as boundary conditions. This model calculates the eight totalheat fluxes towards the ice and returns them as inputs to the BIM.Several such data exchanges take place until outputs of each modelvary by less than 10�3. Then time is incremented and thisprocedure is repeated.
For the simulations performed in the present project hourlyaverage weather data for a typical meteorological year (tempera-tures of the air and the ground at 0 m and 4 m depth as well as solar
Fig. 6. Schematic representation of the onion coupling between AIM and BIM.
Table 2Comparison of climatic conditions in the cities under consideration.
L. Seghouani et al. / Energy and Buildings 41 (2009) 500–511 505
radiation [15]) is used. In order to ensure the periodicity of theresults (values at the end of the 365th day must be identical tothose at the beginning of the first one) we carried out simulationsover 17 months by repeating the meteorological data for January toMay and did not consider the results of the initial 5 months to besure that the effects of the arbitrary initial values are eliminated.
The choice of time step is based on four considerations. The firstis that TRNSYS accepts only time steps of the form 1/N where N isan integer. The second is the duration of resurfacing (12 min)which means that the time step should not exceed 0.2 h. The thirdis the need to minimize the time required for the calculation of theresults over the 17-month period which implies that the time stepmust be large. Finally, a small time step is necessary to capturemore transient details. As a compromise between these con-siderations we have opted for a time step equal to 0.1 h. With thischoice the entire yearly simulation requires about 80 h on apersonal computer (with an Intel Core 2 Duo 6400 2.13 GHzprocessor and 2 Go of RAM). This is a considerable improvementover an equivalent CFD two-dimensional simulation whichrequires 24 h to calculate the results for a single day [7].
2.5. Model validation
The AIM was successfully validated in previous studies [9–11].The predictions of the more complete numerical model presentedhere are validated by comparison with measurements recorded inthe Camilien Houde ice rink over relatively short periods in 2005and 2006 [8]. Table 1 presents such a comparison of the measuredand calculated brine outlet temperature and ice surface tempera-ture. Measured values are the averages of recorded temperatureswhile calculated values are monthly averages for the typicalmeteorological year. Although these conditions are not identical,the small seasonal variation of these results makes this comparisonacceptable. The agreement between measured and calculatedvalues of these temperatures shows that the proposed modelpredicts satisfactorily these values. The maximum relativedifference is less than 10%, which is acceptable since thesimulations did not take into account the refrigeration systemwhich regulates the inlet brine temperature. This difference isprincipally due to the boundary condition used for the simulation(constant brine inlet temperature Tb,in = �9 8C) and to imprecisionof the measurements.
Similar agreement has also been established between themeasured and calculated values of the heat flux into the ice. Theformer was obtained by integrating the readings of four heat fluxsensors installed under the ice sheet. The corresponding dailymean values for 1 October 2005 are: 94.9 W/m2, 56.6 W/m2,
Table 1Comparison between measured and calculated temperatures.
Measured Calculated
Return brine temperature (8C) �7.3 From �7.8 to �8.0
Ice surface temperature (8C) From �5.5 to �6.3 From �5.2 to �6.0
90.6 W/m2 and 113.0 W/m2 [8]. Disregarding the second sensorwhich gives significantly lower values than the other three, themean value of the experimentally measured heat flux is 99.5 W/m2. On the other hand, the model predicts an average total heatflux of 108 W/m2 for October which is about 8% higher than themeasurements. In view of the fact that these values do notcorrespond to identical climate conditions, their agreement isjudged to be acceptable.
In view of these results we consider that the proposed modelcan be used with confidence for the calculation of typical yearlyrefrigeration loads and for parametric studies which aim toestablish the effect of design and operation conditions on theseloads.
3. Parametric analysis
The analysis in this section starts from a ‘‘base case scenario’’which corresponds to meteorological conditions for a typical yearin Montreal (latitude N 458470, longitude W 738750), a constantbrine inlet temperature to the slab equal to �9 8C, an ice thicknessof 5.08 cm, an under slab insulation thickness equal to 10 cm, asetpoint of 15 8C with a nocturnal set back of 7 8C and an hysteresisof �0.2 8C for the electronic thermostat, while the undergroundheating (8 kW) is in operation when the ground temperature at adepth of a 4 m is below 4 8C. The results of this transient simulationare compared with corresponding results obtained by varying theparameters defining the base case scenario one at a time.
3.1. Effects of the climate
Results have been calculated for typical meteorological yearsfor the cities of Edmonton (latitude N 538310, longitude W 114850),Houston (latitude N 298580, longitude W 958220) and Pittsburgh(latitude N 408300, longitude W 808130) for which correlationssimilar to those for Montreal (Eqs. (6) and (9)) have been obtainedfrom the meteorological data [15]. These results are comparedwith those for the base case at Montreal. As indicated by the valuesin Table 2 these climatic conditions vary from very warm andhumid during the summer in Houston to very cold and dry inwinter in Edmonton.
Figs. 7 and 8 illustrate the effects of the climate on the averagedaily energy consumption of the ventilation system which, asmentioned before, is constituted of two units (cf. Fig. 3). Inparticular, Fig. 7 shows that the energy consumption of the firstunit, which dehumidifies the ventilation air by cooling andreheating it, is greatest for Houston where it is significantthroughout the year. On the other hand, for the other three citiesthis quantity is essentially zero during the winter months butbecomes important during the summer. The seasonal variation ofthis quantity as well as its relative magnitude between the fourcities under consideration is consistent with the meteorologicaldata of Table 2. The same is true for the results in Fig. 8 whichshows the energy consumption of the second unit of theventilation system. This one heats and humidifies the incomingventilation air and is therefore high in winter and essentially zeroin summer, largest for Edmonton and lowest for Houston. It is
Heating dry
bulb (99%)
Cooling dry
bulb (2%)
Mean coincident
wet bulb
Edmonton �30.5 8C 24.0 8C 15.7 8CHouston �0.4 8C 33.5 8C 24.9 8CMontreal �21.8 8C 25.8 8C 19.5 8CPittsburgh �14.1 8C 28.7 8C 20.6 8C
Fig. 7. Effect of the climate on the cooling and reheating energy consumption of the
ventilation system.
Fig. 8. Effect of the climate on the heating and humidification energy consumption
of the ventilation system.
L. Seghouani et al. / Energy and Buildings 41 (2009) 500–511506
interesting to note that the peak energy consumption for cooling–reheating is for every city higher than the one for heating–humidification.
The predicted total annual energy consumption of theventilation system for Edmonton, Houston, Montreal and Pitts-burgh is 1278 MWh, 4033 MWh, 1435 MWh and 2228 MWh,respectively. The distribution of this total among the fourprocesses is shown in Fig. 9. Cooling uses the largest part inHouston, Pittsburgh and, surprisingly, Montreal while in Edmon-ton the largest part is used for heating. Humidification requires avery small part of the total energy consumption in all cases.
The impact of the climate on the temperature of the ice surfaceis quite small (�1 8C) since this variable is essentially determinedby the temperature of the brine which for these simulations is thesame throughout the year for all four cities. Therefore the values ofIST are not presented here. However, it should be noted that thesevalues are somewhat influenced by the temperature of the airabove the ice which depends on whether the radiant heating is on
Fig. 9. Effect of the climate on the annual ener
and whether the ventilation air is heated or cooled. Thus the IST forall cities is slightly higher in winter, when heating is required, thanin summer, when the ventilation air requires cooling. Similarly, theIST during the summer is a little bit higher in Edmonton than inHouston since the former city requires much less cooling of theventilation air and necessitates heating of the stands as shown inFig. 10. This last figure also shows that the radiant heating of thestands exhibits the expected seasonal behaviour, that it issignificantly smaller in Houston and quite important in Edmontoneven during the summer. It should be noted that the daily energyconsumption of the radiant heaters is for all cities significantlylower than the corresponding values of the ventilation system(sum of consumption shown in Figs. 7 and 8).
Fig. 11 shows the influence of the climate on the refrigerationload, i.e. on the sum of the heat reaching the brine from the ice andfrom the ground. This quantity is greatest for Houston where theseasonal variation is also the least pronounced. This result isconsistent with the climatic conditions which signify that the
gy consumption of the ventilation system.
Fig. 10. Effect of the climate on the energy consumption of the radiant heating. Fig. 11. Effect of the climate on the refrigeration load.
L. Seghouani et al. / Energy and Buildings 41 (2009) 500–511 507
envelope and indoor air are warmer in Houston and that, therefore,heat fluxes towards the ice by both radiation and convection arealso higher in this city. Furthermore, because the humidity ishigher in Houston the corresponding heat flux due to condensationof water vapour on the ice is also higher in this city. Thecombination of all these effects explains the results shown in thisfigure.
Table 3 compares the annual refrigeration load and thecorresponding energy consumption of the different systems foreach city. It confirms the fact that the refrigeration load is greatestfor Houston and shows that this quantity is always smaller thanthe energy consumption by the ventilation system. It is importantto note that the refrigeration load does not vary significantly (lessthan 7.5% of the average value) between these four locationsdespite their very different climates. This is attributed to the factthat the indoor conditions are quite similar due to the controls onthe ventilation system and the radiant heaters. However, it isexpected that the energy consumption of the refrigeration systemwill be higher in locations with warm climates since thecondensation temperature and pressure will be higher than inlocations with cold climates.
Table 3 also shows that the energy consumed by the lights andthe brine pump does not depend on the climate in accordance withthe modeling assumptions. Lighting consumes more energy than
Table 3Annual energy consumption of different systems and annual refrigeration load for eac
Annual refrigeration load Annual energy consumption of differ
Ventilation system Radiant he
Edmonton 1023 1278 133
Houston 1110 4033 30
Montreal 979 1435 86
Pittsburgh 1018 2228 74
Table 4Monthly underground electrical heating for each city (MWh).
the radiant heaters for each of the four locations underconsideration while the same is true for the energy used by thebrine pump in three of the four cities. The greatest and smallestcontributors to the total energy consumption are the ventilationsystem and the underground heater respectively for each of thefour cities under consideration. Finally, the total annual energyconsumption is highest, by a considerable margin, in Houston(where summer operation requires considerable quantities ofenergy for cooling and dehumidification) and lowest in Edmonton.
Table 4 shows the energy consumption by the undergroundheater which is activated to avoid freezing and heaving of theground under the concrete slab. Its operation is not at all necessaryin the case of the warmer climates (Houston and Pittsburgh) whilein Edmonton and Montreal it is in operation for approximately 7and 5 months, respectively.
3.2. Effects of the hysteresis of the thermostat
The influence of this parameter is established by comparing theresults for an electronic thermostat with a hysteresis of �0.2 8Cwith those for a conventional bimetallic thermostat with a hysteresisof �1.5 8C. The set point is 15 8C in both cases.
Fig. 12 shows that the refrigeration load is always higher in thecase of the electronic thermostat. The difference varies from
h city (MWh).
ent systems
ating Underground heating Lighting Brine pump Total
40.5 148.7 98.1 1698.3
0 148.7 98.1 4309.8
30.1 148.7 98.1 1797.9
0 148.7 98.1 2548.8
Fig. 12. Effect of the thermostat hysteresis on the refrigeration load.Fig. 14. Effect of the brine inlet temperature on the refrigeration load.
L. Seghouani et al. / Energy and Buildings 41 (2009) 500–511508
approximately 125 kWh/day in summer to 200 kWh/day in winter.This result can be explained by the fact that the radiant heating isturned on more frequently with an electronic thermostat in orderto maintain the temperature in the zone occupied by the spectatorsat (15 � 0.2) 8C; therefore the corresponding average air andenvelope temperatures are slightly higher and result in increasedconvective and radiative fluxes towards the ice. However, the energysavings associated with the conventional thermostat are achieved atthe expense of the spectators comfort since in that case the airtemperature above the stands oscillates between 13.5 8C and 16.5 8C.The smaller difference in summer energy consumption between thetwo cases under consideration is due to the fact that the radiantheating load is greatly reduced during these warm months.
It should also be noted that the type of thermostat influencesthe ice temperature, i.e. its quality. Thus the temperature of the icesurface is higher for the base case (electronic thermostat) byapproximately 0.25 8C in winter and 0.15 8C in summer.
3.3. Effect of the nocturnal set back
Two cases are compared in this section. The first one is the basecase in which the thermostat controlling the radiant heating
Fig. 13. Effect of the nocturnal set back on the refrigeration load.
elements is set to 15 8C during the day and 7 8C during theunoccupied night hours, while in second case the thermostat is setto 15 8C throughout the day.
Fig. 13 shows that the use of a thermostat with nocturnal setback (base case) reduces the refrigeration load. However, thisreduction is very small (it varies from 25 kWh/day during thewinter to 50 kWh/day during the summer). It is due to the decreaseof the operation time of the radiant heating elements and thecorresponding reduction of the air and envelope temperatureswhich in turn lower the convective and radiative fluxes towardsthe ice. The corresponding effect on the IST is insignificant(reduction of 0.1 8C when nocturnal set back is used) since theseflux reductions are small compared to their respective values.Finally, it is important to note that the heat flux from the ground tothe brine is totally unaffected by the use, or not, of the nocturnal setback since the conditions below the concrete slab are independentof those prevailing within the ice rink.
3.4. Effect of the brine inlet temperature
Three different constant brine inlet temperature were used forthis study (Tb,in = �8 8C, �9 8C and �10 8C). Fig. 14 shows that the
Fig. 15. Effect of the ice thickness on the refrigeration load.
Table 5Effect of the ice thickness on the January temperatures of the ice and the brine.
Ice thickness (cm) Temperatures (8C) (January)
Ice surface Brine (inlet) Difference
2.54 �6.20 �9.0 2.8
5.08 �5.97 �9.0 3.03
7.62 �5.74 �9.0 3.26
Table 6Effect of the ice thickness on the July temperatures of the ice and the brine.
Ice thickness (cm) Temperatures (8C) (July)
Ice surface Brine (inlet) Difference
2.54 �5.46 �9.0 3.54
5.08 �5.13 �9.0 3.87
7.62 �4.83 �9.0 4.17
Fig. 16. Effect of the insulation thickness on the heating rate from the soil.
Fig. 17. Effect of the insulation thickness on the temperature of the insulation–sand
interface.
L. Seghouani et al. / Energy and Buildings 41 (2009) 500–511 509
refrigeration load increases when the inlet brine temperaturedecreases. The increase is about 100 kWh/day for each decrease ofTb,in by 1 8C. This behaviour is qualitatively logical since the brineacts as a heat sink while the conditions of the heat sources aboveand below the concrete slab remain the same for these threesimulations.
A�1 8C increase or decrease of the inlet brine temperature causes,respectively, an augmentation or diminution of �0.8 8C of the icesurface temperature, for all months of the year. An analogousobservation can be made for the outlet brine temperature whichincreases or decreases by the same amount as the inlet brinetemperature.
3.5. Effect of the ice thickness
Fig. 15 shows that the refrigeration load decreases slightly withthe increase of the ice thickness. It is reduced by 8–10% when the icethickness triples (from 2.54 cm to 7.62 cm). This is due to thecorresponding increase of the thermal resistance of the ice sheetwhich also causes a small increase of the IST. The increase of thelatter is greater in summer due to the augmentation of theconvection and radiation fluxes during this warm season. Further-more, Tables 5 and 6 show that, when the ice thickness is increasedby 5 cm, the temperature difference between the ice surface and thebrine increases by 14% (from 2.8 8C to 3.26 8C) for the month ofJanuary and by 18% (from 3.54 8C to 4.17 8C) for the month of July.
These results should not be generalised. They have beencalculated by fixing the brine inlet temperature and do notnecessarily apply to other control strategies (such as, for example,cases where the ice surface temperature is kept constant).
3.6. Effect of the insulation thickness
Fig. 16 shows that an increase of the underground insulationthickness from 10 cm to 30 cm reduces the heat rate transferred tothe brine pipes from the soil by approximately 25% for all months ofthe year. It should also be noted that the change of insulationthickness has an insignificant effect on the heat rate from the ice tothe brine pipes. However, the effect of this reduction of the heat ratefrom the soil on the total refrigeration load is not significant sincethe former is less than 10% of the latter (cf. Fig. 15). The mostimportant impact of added underground insulation is to reduce therisk of freezing under the concrete slab which can cause heavingand damage to the ice. Fig. 17 which shows the average temperatureof node 5 situated at the sand–insulation interface clearly illustratesthis effect. Furthermore, as this insulation thickness is increased theenergy consumption of the electrical element in the sand can bereduced without increasing the danger of freezing.
4. Non-linear correlations of energy loads
This section presents four correlations between the monthlymean value of the energy consumption (in kWh/day) of thedifferent processes taking place in the ventilation system and thecorresponding sol-air temperature (in 8C) calculated with theexpression and parameters proposed by ASHRAE [17]. They arebased on numerous simulations carried out at the four selectedcities (Montreal, Edmonton, Houston and Pittsburgh).
Cooling load correlation:
QCool ¼ 283:96þ 189:1 Tsol-air þ 4:85 T2sol-air (14a)
Reheating load correlation:
QRe heat ¼ 8:63þ 192:58 Tsol-air � 2:217 T2sol-air (14b)
Heating load correlation:
QHeat ¼ 1943:1� 140:23 Tsol-air þ 1:89 T2sol-air (14c)
Humidification load correlation:
QHumid ¼ 44:9� 10:95 Tsol-air þ 0:79 T2sol-air (14d)
Figs. 18 and 19 show that these fairly simple correlations agreequite well with the calculated values. These results also show that
Fig. 18. Energy consumption of ventilation system (cooling/reheat) vs. sol-air
temperature.
Fig. 19. Energy consumption of the ventilation system (heating/humidification) vs.
sol-air temperature.
L. Seghouani et al. / Energy and Buildings 41 (2009) 500–511510
the energy consumption by the heating and cooling processesdepend heavily on Tsol-air while those by the reheat and, inparticular, humidification processes are less dependent on thisparameter.
5. Conclusion
A transient model which calculates heat transfer through theground towards the brine pipes imbedded in the concrete slabunder the ice of an indoor ice rink has been formulated and coupledwith a previously developed one which calculates heat fluxes in thebuilding by convection, radiation and phase changes. The resultingsimulation tool has been enriched with subroutines whichcalculate the energy consumption for heating and humidifying,or cooling and reheating, the ventilation air. After validation withexperimental results, this tool was used to evaluate the refrigera-tion load as well as the energy consumed by the radiant heaters ofthe stands, each process of the ventilation system, the lights, thebrine pump and the underground electric heater over a typical yearat four North American locations (Edmonton, Houston, Montreal,Pittsburgh) with very different meteorological conditions. Theresults of this analysis show that:
� T
he annual refrigeration load does not vary significantly (lessthan �7.5% from the mean value) between these four locationsdespite their very different climates. � T he annual energy consumption by the ventilation system issignificantly influenced by the meteorological conditions; it ishighest in hot and humid locations and is always greater than thecorresponding refrigeration load.
� T he annual energy consumptions by the radiant heaters and bythe underground electric heater are very small compared to therefrigeration load even in the coldest of the four cities underconsideration.
The main results of the other parametric studies are thefollowing:
� T
he use of an electronic thermostat with a low hysterisis(�0.2 8C) rather than a bimetallic one with a high hysteresis(�1.5 8C) increases the refrigeration load by more than 10% if thesame set point is used in both cases; however the energy savingsassociated with the bimetallic thermostat are achieved at theexpense of the spectator’s comfort. � T he use of a thermostat with nocturnal set back results in a smallreduction of the refrigeration load.
� A reduction of the brine temperature causes an increase of therefrigeration load and an almost equal reduction of the icesurface temperature.
� A n increase of the ice thickness causes a decrease of both therefrigeration load and the ice surface temperature.
� A n increase of the underground insulation thickness causes aslight decrease of the refrigeration load and reduces significantlythe danger of ground freezing and heaving.
Finally, four correlations expressing the energy consumptionsfor heating and humidifying, or cooling and reheating, theventilation air in terms of the sol-air temperature have beenproposed.
Acknowledgements
This study was financed by the Natural Sciences andEngineering Research Council (NSERC) of Canada through theStrategic Project Grant STPGP 306792 (Title: Development ofdesign tools and of operation guidelines for the heating,ventilation, air conditioning and refrigeration systems of icerinks).
Appendix A
The expressions of the 7 T 7 matrix A and of the vectors B and T in
Eq. (10) are:
A¼
Að1;1Þ � 1
RIce0 0 0 0 0
1
RIceAð2;2Þ 1
Rc10 0 0 0
01
Rc1Að3;3Þ 1
Rc20 0 �mBCPB
0 01
Rc2Að4;4Þ 1
RIns0 0
0 0 01
RInsAð5;5Þ 1
RSand0
0 0 0 01
RSandAð6;6Þ 0
0 0 2 0 0 0 �1
0BBBBBBBBBBBBBBBBBBBB@
1CCCCCCCCCCCCCCCCCCCCA
(A.1)
nd Buildings 41 (2009) 500–511 511
B ¼
Q Ice þðM CpÞeq1
DtT p
1
�1
2U2S2Tgr �
ðM CpÞeq2
DtT p
2
�mBC pBT In �
1
2U3S3Tgr �
ðM CpÞeq3
DtT p
3
�1
2U4S4Tgr �
ðM CpÞeq4
DtT p
4
�QH �1
2U5S5Tgr �
ðM CpÞeq5
DtT p
5
�QH �1
2U6S6Tgr �
ðM CpÞeq6
DtT p
6 �1
RSoilT7
T in
0BBBBBBBBBBBBBBBBBBBBB@
1CCCCCCCCCCCCCCCCCCCCCA
(A.2)
and
T ¼ T pþ11 T pþ1
2 T pþ13 T pþ1
4 T pþ15 T pþ1
6 TPþ1Out (A.3)
Here the coefficients in Eq. (A.1) are
Að1;1Þ ¼ðM CpÞeq1
Dtþ 1
RIce
Að2;2Þ ¼ � 1
RIceþ 1
Rc1þ1
2U2 S2 þ
ðM CpÞeq2
Dt
!
Að3;3Þ ¼ � 1
Rc1þ 1
Rc2þ1
2U3 S3 þ
ðM CpÞeq3
Dt
!
Að4;4Þ ¼ � 1
RInsþ 1
Rc2þ1
2U4 S4 þ
ðM CpÞeq4
Dt
!
Að5;5Þ ¼ � 1
RSandþ 1
RInsþ1
2U5 S5 þ
ðM CpÞeq5
Dt
!
Að6;6Þ ¼ � 1
RSoilþ 1
RSandþ1
2U6 S6 þ
ðM CpÞeq6
Dt
!
(A.4)
And the equivalent thermal capacity in Eqs. (A.2) and (A.4) is
calculated as follows:
ðM CpÞeq1 ¼1
2MIceCPIce
(A.5a)
ðM CpÞeq2 ¼1
2MIceCPIce
þ 1
2Mc1CPC
(A.5b)
ðM CpÞeq3 ¼1
2MBCPB (A.5c)
ðM CpÞeq4 ¼1
2Mc2CPC
þ 1
2MInsCPIns
(A.5d)
L. Seghouani et al. / Energy a
1 1
ðM CpÞeq5 ¼ 2MInsCPInsþ2
MSandCPSand(A.5e)
ðM CpÞeq6 ¼1
2MSandCPSand
þ 1
2MSoilCPSoil
(A.5f)
References
[1] M. Lavoie, R. Sunye, D. Giguere, Potentiel d’economies d’energie en refrigerationdans les arenas du Quebec, Report prepared by the CANMET Energy TechnologyCenter, 2000.
[2] P.J. Jones, G.E. Whittle, Computational fluid dynamics for building air flowprediction—current status and capabilities, Building and Environment 27 (3)(1992) 321–338.
[3] Z. Jian, Q. Chen, Airflow and air quality in a large enclosure, ASME Journal of SolarEnergy Engineering 117 (2) (1995) 114–122.
[4] C. Yang, P. Demokritou, Q. Chen, J.D. Spengler, A. Parsons, Ventilation and airquality in indoor ice skating arenas, ASHRAE Transactions 106 (2) (2000) 338–346.
[5] O. Bellache, M. Ouzzane, N. Galanis, Coupled conduction, convection, radiationheat transfer with simultaneous mass transfer in ice rinks, Numerical HeatTransfer Part A 48 (2005) 219–238.
[6] O. Bellache, M. Ouzzane, N. Galanis, Numerical prediction of ventilation andthermal processes in ice rinks, Building and Environment 40 (3) (2005) 417–426.
[7] O. Bellache, N. Galanis, M. Ouzzane, R. Sunye, D. Giguere, Two-dimensionaltransient model of airflow and heat transfer in ice rinks (1289-RP), ASHRAETransactions 112 (2) (2006) 706–716.
[8] M. Ouzzane, R. Sunye, R. Zmeureanu, D. Giguere, J. Scott, O. Bellache, Cooling loadand environmental measurements in a Canadian indoor ice rink (1289-RP),ASHRAE Transactions 112 (2) (2006) 538–545.
[9] A. Daoud, N. Galanis, Calculation of the thermal loads of an ice rink using zonalmodel and building energy simulation software, ASHRAE Transactions 112 (2)(2006) 526–537.
[10] A. Daoud, N. Galanis, O. Bellache, Calculation of refrigeration loads by convection,radiation and condensation in ice rinks using a transient 3D zonal model, AppliedThermal Engineering (2007), http://dx.doi.org/10.1016/j.applthermaleng.2007.11.011.
[11] A. Daoud, Analyse des transferts de chaleur et de masse transitoires dans un arenaa l’aide de la methode zonale, These de doctorat en sciences appliquee, Universitede Sherbrooke (Quebec), Canada, 2007.
[12] TRNSYS, A transient system simulation program, Software Manual, Solar EnergyLaboratory, University of Wisconsin-Madison, 2000.
[13] B. Gebhart, Heat Transfer, Second edition, McGraw-Hill, 1971.[14] ASHRAE, Ice Rinks, ASHRAE Handbook-Refrigeration, American Society
of Heating, Refrigeration, and Air-Conditioning Engineers, Inc., Atlanta,2002.
[15] ENERGYPLUS, http://www.eere.energy.gov/buildings/energyplus/.[16] ASHRAE, Residential cooling and Heating load Calculations ASHRAE Handbook-
fundamentals, American Society of Heating, Refrigeration, and Air-ConditioningEngineers, Inc., Atlanta, 2005, pp. 29.11–29.12.
[17] ASHRAE, Non-residential cooling and Heating load Calculations ASHRAE Hand-book-fundamentals, American Society of Heating, Refrigeration, and Air-Condi-tioning Engineers, Inc., Atlanta, 2001, pp. 29.14–29.17.
