# Numerical prediction of ventilation patterns and thermal processes in ice rinks

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Building and Environment 40

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latent, convective and radiative heat ux into the ice are presented and analyzed.

concerted effort has been undertaken to develop designprocedures and specify operational guidelines which

between the surfaces, pollutant and water vapour

Such numerical studies have been undertaken in 2Dand 3D congurations by Chen et al. [1], Yang [2],

evaluated systematically the effect of different ventila-tion and heating systems on energy consumption andthermal comfort.

ARTICLE IN PRESS

Corresponding author. Tel.: +1-819-821-7144; fax: +1-819-821-

In view of this situation, the present project aims to

develop a model for ice rinks which takes into account

0360-1323/$ - see front matter r 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.buildenv.2004.08.004

7163.

E-mail address: Nicolas.Galanis@USherbrooke.ca (N. Galanis).would reduce energy consumption and gas emissionswhile maintaining the quality of the indoor air and ice aswell as the comfort of skaters and spectators. Thechallenge is great because of the diversity of size andconguration of the buildings, and the differences inheating and ventilation systems in use. This complexityand the coupling between air movement, heat transferthrough the building envelope, heat and mass transferbetween the air and ice surface, radiation exchanges

Nielsen et al. [3], Jones and Whittle [4]. However,these studies do not generally take into account theinteraction between convection, radiation, vapour diffu-sion and mass transfer between the ice surface and theair. They do not include the inuence of thesephenomena on heat losses through the envelope.Furthermore, previous studies have not evaluated theeffect of these heat and mass transfer processes onthe refrigeration load. Finally, no CFD study hasKeywords: Numerical simulation; Turbulent mixed convection; Ice rinks; Ventilation; Heating; Thermal comfort; Humidity; Radiation;

Refrigeration load; Heat losses

1. Introduction

Canadian ice rinks use approximately 3500GWh ofelectricity annually and generate 5 105 tons of gasescontributing to the greenhouse effect. The potential forimprovement in both areas is substantial. However, no

dispersion in a large irregular domain, explain the lackof design and operation norms.The development of reliable CFD codes offers the

potential for systematic analysis of the velocity, tem-perature, pollutant and/or vapour concentration dis-tributions in ice rinks and other large buildings.r 2004 Elsevier Ltd. All rights reserved.Numerical prediction of venprocesses

O. Bellachea, M. OaCANMET Energy Technology C

bTHERMAUS, Faculte de genie, Universite

Abstract

A numerical simulation of the heat and mass transfer phenom

k2e turbulence model. The complexity of the geometry has bprotection panels which have a signicant effect on the ow e

ow pattern, the isotherms and the lines of constant absolute

presented for several positions in the zone occupied by the spe(2005) 417426

ation patterns and thermalice rinks

nea, N. Galanisb,

Varennes QC Canada J3X 1S6

erbrooke, Sherbrooke QC, Canada J1K 2R1

in a ventilated ice rink has been carried out using the standard

aken into account by considering elements such as the plastic

he results calculated for four different congurations show the

elative humidity. Values of the effective draft temperature are

rs. The heat losses through the walls and ceiling as well as the

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P static pressure (Pa)

y vertical coordinate (m)bT coefcient of thermal expansion K1bc coefcient of mass expansionGf diffusion coefciente dissipation rate of turbulent kinetic energy

m2=s3k turbulent kinetic energy m2=s2m dynamic viscosity (kg/m s)n kinematic viscosity m2=sr density kg=m3st; se;sk turbulence model constantsf general eld variable

nd Enall of the above phenomena and predicts energyconsumption as well as ice and comfort conditions.For this purpose, we have calculated results for winterconditions and a particular ice rink in Montreal,Canada using the standard k2e model to simulate theow eld and taking into account radiation exchangesbetween the inside surfaces of the envelope and the ice.

Prt turbulent Prandtl numberqi heat ux for each element i of the envelope

(W)qci convective ux between the air and inside

surface of the element i (W)qri net radiative heat ux (W)qli heat latent (W)T temperature CTc average (control) space dry bulb temperature

CNomenclature

C absolute humidity (kg/kg)Ce1;Ce2;Ce3;Cm;Cd turbulence model constantsDin characteristic length (m)g acceleration of gravity m=s2GB buoyancy production of kG stress production of kH in height of the inlet (m)Lin width of the inlet (m)

O. Bellache et al. / Building a418In an earlier paper [5], we have presented numericalpredictions for the velocity and temperature elds aswell as comfort conditions and heat uxes through thebuilding envelope for four different combinations ofinlet air conditions (temperature and direction of theventilation air). In the present paper, we extendthe formulation by including mass transfer betweenthe ice surface and the air. Four different congurationsof the ventilation system are considered and results withand without vapour diffusion and condensation arepresented and compared in each case.

2. Modeling and calculation procedure

A schematic representation of a cross-section of theice rink is shown in Fig. 1. Since the length of thebuilding is considerable (64m) the ow eld far fromthe end walls is considered to be two-dimensional (novelocities perpendicular to the shown cross-section). Asshown in Fig. 1, three rows of stands run the wholelength of the building on one side. A narrow corridorencircles the ice surface. Protective transparent barriersseparate the corridor and stands from the skatingsurface. Heating and ventilation for the spectators ist time (s)U in inlet velocity (m/s)

V*

velocity vectoru,v components of velocity (m/s)Sf source termx horizontal coordinate (m)

vironment 40 (2005) 417426provided by blowing Qin 6:75m3=s of air througheight regularly spaced inlets (0:3m 1m; each at aheight of 6m, above the ice surface). Air is extractedthrough a single outlet on the ceiling but for thepurposes of this study we have considered that there areeight smaller openings at the same Z coordinate as theinlets. Therefore, the ow eld in the XY plane midwaythrough each set of inlets and outlets can be considered

Fig. 1. (a,b) Cross section of the ice rink under consideration.

to be two-dimensional (no velocity component in the Zdirection) and the numerical calculations in that planecan be considerably simplied.Fig. 1a with the air outlet to the right of the inlet

represents the actual conguration of the ventilationsystem. Fig. 1b with the air outlet to the left of the inletrepresents the conguration originally proposed in thearchitectural plans. In both cases the ventilation airenters through a 0.3m opening at x 27:25m; y 6mand leaves through a 1m wide opening in the ceilingy 8m; respectively, at x 30m in the rst cong-uration (Fig. 1a) and at x 17:63m in the second

The appropriate values or expressions forf; Gf and Sfare dened in Table 1.The boundary conditions for this problem are as

follows:

The ventilation air enters through the inlet at 30 Cand 45% relative humidity with horizontal andvertical velocities equal to 2.435m/s and 1:406m=srespectively. The turbulence kinetic energy kin anddissipation rate ein are

kin 0:05U in2; ein CmCd3=4k3=2in ;

ex

inthab

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f

mt mt=Pr mt=Prt STm mt=skt=se

O. Bellache et al. / Building and Environment 40 (2005) 417426 419conguration (Fig. 1b). The origin of the Cartesiancoordinate system is at the bottom left corner of thecross-section.Several turbulence models for the simulation of

indoor air motion have been compared during thepresent project, although their results are not presentedhere. It was found that the standard k2e model byLaunder and Spalding [6] performed quite well and wasvery stable. Chen [7] also has compared the performanceof ve turbulence models in predicting natural convec-tion, forced convection, and mixed convection in rooms,and used experimental data for their validation. Hefound that the prediction of the mean velocity is moreaccurate than that of the turbulent velocity and statedthat the performance of the standard ke model is good.Therefore, this model was selected for the presentinvestigation.The air is considered to have constant properties

except for its density in the expression of the bodyforces, which is assumed to vary linearly with bothtemperature and concentration (Boussinesq hypothesis).Its absorptivity is set equal to zero (totally transparentto radiation of all wavelengths). The ow is assumed tobe turbulent with mean values independent of time.The partial differential equations modeling the air

movement, heat transfer and mass diffusion can bewritten in the following general form:

@rf@t

divrV*f Gfrf Sf: (1)

Table 1

Values of f; Gf and Sf

Equation f GMass 1 0

X-momentum U mY-momentum V mEnergy T mAbsolute humidity C Turbulent kinetic Energy k mDissipation rate e m

mt rCmCdk2=e; Prt 1GB gbmt=Prt@T=@xi; G mt@Ui=@xj @Uj=@xi:@Ui=@xj

Ce1 1:44; Ce2 1:92; Ce3 1; Cm 0:5478; Cd 0:1643; sk 1; se 1t=sc ScG re GBeCe1G Ce2re=k Ce3GBe=k:3;the ice rinks are elliptic, non-linear and coupled sincee air density depends on both the temperature and thesolute humidity.

Sf0

@P=@x@P=@y rgbTT T r rgbcC Crequations modeling the heat and mass transfer processesThe last term of Eq. (3) denotes the latent heatchanged between the air and the ice.It should be noted that the seven partial differentialqi0:1DinDin 2HL=H L: 2

At the outlet the relative pressure is set equal to zero. A uniform temperature T ice 5:5 C is imposedunder the ice at Y 0; for the calculation withvapour diffusion, the air layer in contact with the iceis assumed to be saturated.

On all the other solid surfaces (walls, ceiling, stands)the velocity components, concentration gradient andturbulent kinetic energy are equal to zero. Thecorresponding temperature is related to that of theair within the ow domain and to the externaltemperature by an energy balance which takes intoaccount conduction through the solid, convection tothe inside and outside as well as net radiation uxesbetween the inside surfaces. Thus, the heat ux qi foreach element i of the inside surfaces is equal to thefollowing algebraic sum [8]:

qci qri qli: (3)sc 1:

the solution is obtained iteratively starting from an

less than 1%. Four cases were studied for each of thetwo congurations shown in Fig. 1:

Case 1: the vertical duct providing the ventilation andheating air is supposed to constitute a physical barrier tothe airow extending from Y 6m to the ceiling. Air isextracted through a single outlet on the right of the inlet(Fig. 1a).

Case 2: the inlet duct constitutes a physical barrier butthe outlet is situated on the left of the inlet (Fig. 1b).

Case 3: inlet without vertical duct and air is extractedthrough a single outlet on the right of the inlet as incase 1.

Case 4: inlet without vertical duct and the outlet issituated on the left of the inlet as in case 2.Calculations were performed twice for each of those

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Fig. 2. Validation of the model and numerical code (a) Prole of

vertical component of velocity near the hot wall in section z 65mm;(b) Prole of vertical component of velocity near the hot wall in section

z 125mm:

nd Enarbitrary initial condition. The calculation domain wassubdivided into zones corresponding to the existingphysical discontinuities appearing in Fig. 1. In thepresent case, there are 15 zones in the x direction and 11in the y direction. The number of grid points, or nitevolume, within each resulting subdivision of the domainhas been selected based on a preliminary analysis toensure that the results are independent of their number.The discretisation grid was non-uniform with highernode density near the inlet and the solid surfaces wheregradients are high. Numerical tests have also beencarried out to ensure that the results are independent ofthe number of iterations. Under-relaxation was oftennecessary to achieve convergence which was declaredwhen the cumulative residuals for each of the conserva-tion equations was less than 106:The experimental data by Cheesewright et al. [11] was

used to validate the predictions of the model. Thatexperiment was carried out using air in a squareenclosure 0:25m 0:25m with adiabatic horizontalwalls and isothermal vertical walls. The temperaturedifference between the hot and cold walls was 43:4 C:Fig. 2a shows the measured velocity vectors while thecorresponding results computed by the present modeland code are shown in Fig. 2b. The agreement betweenour predictions and the measured values is well withinthe uncertainty of the latter. Similarly, calculatedvelocities and temperatures for mixed convection of airin a rectangular enclosure with isothermal horizontalwalls and diabatic vertical walls were found to agreeclosely [5] with corresponding measurements by Bra-connier et al. [12]. Finally, the predicted air, ice and walltemperatures were successfully compared with corre-sponding values measured in the actual ice rink [5]. Inview of these successful validations, we consider that theselected model and calculation procedure are reliableand accurate. They can therefore be used for theparametric studies.

4. Results and discussion

The results presented here were obtained using morethan 100 40 grid points and over 15 103 iterations.The external temperature and the corresponding con-vection coefcient were considered constant and equalto 10 C and 7W=m2K; respectively. The total error3. Numerical solution and validation

The simulations have been carried out with thenumerical code PHOENICS [9] which uses the nitevolume method and a staggered grid. The hybrid schemewas used for the numerical solution. The SIMPLEalgorithm [10] was used for the pressure correction and

O. Bellache et al. / Building a420for mass, momentum and energy is, in all reported cases,vironment 40 (2005) 417426four cases. At rst, vapour diffusion was neglected as in

duct. Fig. 3d shows the absolute humidity in the ice rink.The absolute humidity is generally low on the left side ofthe inlet and high in the zone occupied by the spectators.Its variation is signicant over the ice, while it does notvary much near the stands. This is consistent with theow eld since ventilation air does not enter in the leftside of the inlet. Finally, Fig. 3e shows that the relativehumidity is quite high above the ice but rather lowabove the stands. This is a direct consequence of theow pattern which results in relatively high tempera-tures in the well-ventilated region above the stands andin low temperatures above the ice.The results of case 2 are shown in Fig. 4. The

ventilation air forms a fairly narrow jet which owsfrom the inlet towards the stands, turns downw...

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