# Coupled Conduction, Convection, Radiation Heat Transfer with Simultaneous Mass Transfer in Ice Rinks

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This article was downloaded by: [Moskow State Univ Bibliote]On: 10 February 2014, At: 08:57Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registeredoffice: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK

Numerical Heat Transfer, Part A:Applications: An International Journal ofComputation and MethodologyPublication details, including instructions for authors andsubscription information:http://www.tandfonline.com/loi/unht20

Coupled Conduction, Convection,Radiation Heat Transfer withSimultaneous Mass Transfer in Ice RinksO. Bellache a , M. Ouzzane a & N. Galanis ba CANMET Energy Technology Center , Varennes, QC, Canadab THERMAUS, Facult de gnie, Universit de Sherbrooke ,Sherbrooke, QC, CanadaPublished online: 02 Sep 2006.

To cite this article: O. Bellache , M. Ouzzane & N. Galanis (2005) Coupled Conduction, Convection,Radiation Heat Transfer with Simultaneous Mass Transfer in Ice Rinks, Numerical Heat Transfer, PartA: Applications: An International Journal of Computation and Methodology, 48:3, 219-238, DOI:10.1080/10407780590945588

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COUPLED CONDUCTION, CONVECTION, RADIATIONHEAT TRANSFER WITH SIMULTANEOUS MASSTRANSFER IN ICE RINKS

O. Bellache and M. OuzzaneCANMET Energy Technology Center, Varennes QC, Canada

N. GalanisTHERMAUS, Faculte de genie, Universite de Sherbrooke,Sherbrooke QC, Canada

This article presents numerical predictions of velocity, temperature, and absolute humidity

distributions in an indoor ice rink with ventilation and heating. The computational fluid

dynamics (CFD) simulation includes the effects of radiation between all inside surfaces

of the building envelope, turbulent mixed convection, and vapor diffusion, as well as conduc-

tion through the walls and condensation on the ice. The net radiative fluxes for each element

of the envelopes inside surfaces are calculated with a modified version of Gebharts method.

This modification reduces the calculation time and the memory required to store the radi-

ation view factors for the discretized elements of the inside surfaces of the envelope. The

predicted temperatures show very good agreement with measured data. The CFD code also

calculates the heat fluxes toward the ice due to convection from the air, to condensation of

vapor, and to radiation from the walls and ceiling. It is shown that a low emissivity ceiling

reduces the sum of these fluxes and the risk of vapor condensation on the ceiling.

INTRODUCTION

Air flow velocities as well as temperature and absolute humidity distributionswithin buildings are essential for the calculation of heating and cooling loads as wellas for the design of efficient HVAC systems. However, their prediction is difficult asa result of complicated flow patterns, the coexistence of zones in which forced con-vection predominates with others in which natural convection is more important,different turbulence structures near and far from the walls, as well as the interactionbetween the indoor and outdoor environments. During the last few decades, predic-tion methods for indoor air flow have increasingly relied on numerical analysis basedon different turbulent models and the time-averaged form of the NavierStokesequations. To this date, however, no study has undertaken the simultaneous deter-mination of all these variables for complex geometries such as ice rinks, in which

Received 18 March 2004; accepted 30 December 2004.

Address correspondence to Nicolas Galanis, THERMAUS, Faculte de genie, Universite de

Sherbrooke, 2500, Boul. Universite, Sherbrooke, Quebec J1K 2R1, Canada. E-mail: nicolas.galanis@

usherbrooke.ca

219

Numerical Heat Transfer, Part A, 48: 219238, 2005

Copyright # Taylor & Francis Inc.ISSN: 1040-7782 print=1521-0634 online

DOI: 10.1080/10407780590945588

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mechanical ventilation, mass transfer, and all modes of heat transfer play a signifi-cant role.

Nielsen [1] was among the first to apply computational fluid dynamics (CFD)methods for indoor air flow studies. He solved the steady-state two-dimensionalequations for the conservation of mass, momentum, temperature, turbulence energy,and dissipation rate for a rectangular ventilated room with adiabatic surfaces exceptfor the bottom one, where a uniform heat flux was prescribed. The reported velocityand temperature distributions were deemed to be in reasonable agreement withexperimental data [2]. This study quantified the effects of buoyancy and their depen-dence on the room and inlet slot geometries.

Davidson [3] performed a similar numerical study using a 3-D transient formu-lation for a ventilated room with an internal heat source and adiabatic walls. Thepredicted flow pattern was shown to agree reasonably well with experiments usingwater. However, the agreement between calculated and measured temperature pro-files was not always satisfactory.

All these studies ignored the interaction between the indoor and outdoor envir-onments and neglected heat transfer by radiation between the interior surfaces of theroom. Chen Qingyan [4] and Chen and Van der Kooi [5] proposed a methodology

NOMENCLATURE

ce1; ce2; ce3; cm; cd turbulence model constants

C absolute humidity (=kg

water=kg dry air)

df distance from the surface to

the first grid point in the

adjacent fluid

Din characteristic length (m)

F view factor

g acceleration of gravity

(m=s2)

G stress production of k

GB buoyancy production of k

Gij Gebharts absorption factor

for surface element j

hig specific enthalpy of

sublimation (J=kg)

Hin height of the air inlet (m)

Lin width of the air inlet (m)_mm ventilation mass flow rate

(kg=s)

P static pressure (Pa)

Prt turbulent Prandtl number

qcd conduction heat flux in solid

envelope (W)

qcv convective flux between the

air and the inside surface of

the envelope (W)

q latent heat flux toward the

ice (W)

qr net radiative heat flux (W)

S area of surface element i

(m2)

S/ source term

t time (s)

T temperature (C)Td dew-point temperature (

C)u, v velocity components (m=s)

Uin, Vin inlet velocity components

(m=s)

V velocity vector

X horizontal coordinate (m)

Y vertical coordinate (m)

b expansion coefficient (K1)b coefficient of mass expansionC/ diffusion coefficientei emissivity of surface element

i

e dissipation rate of turbulentkinetic energy (m2=s3)

k turbulent kinetic energy

(m2=s2)

k thermal conductivity(W=mK)

m; mt molecular, turbulentviscosity (kg=ms)

q density (kg=m3)rt; re; rj turbulence model constants/ general field variable

220 O. BELLACHE ET AL.

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for the solution of combined problems of energy analysis and indoor flow whichtakes into account these effects. They used time-independent air flow patterns calcu-lated by a CFD code with the ke turbulence model for typical situations. They thensolved the algebraic room energy balance equation with a load calculation codewhich used transient temperature differences between the air near the inside surfacesand the middle point of the room. This temperature difference was evaluated fromthe solution of the transient differential energy equation obtained by the CFD codewith the predetermined time-independent velocity distribution. Iterations betweenthese two equations were necessary to achieve convergent results.

Li [6] extended the application of CFD codes in the field of HVAC by includ-ing heat conduction through walls and radiation transfer between their internal sur-faces. This formulation was then applied [7] to study the radiative effects on flow andtemperature fields in a room ventilated by displacement. The calculated results wereshown to be in good agreement with measured data. This approach is conceptuallysimpler than the one proposed by Chen [4], since it eliminates the need to interfacethe load calculation and CFD codes. However, the inclusion of radiation signifi-cantly increases the size of the coefficient matrix of the discretized conservationequations. To prevent this, Li et al. [7] applied a decoupling technique using a coar-ser grid for radiation calculations which were not performed at every iteration.

Recently, Singh and Sharif [8] studied two-dimensional mixed-convection cool-ing of a rectangular enclosure with isothermal or adiabatic thermal conditions appliedat the interface between the fluid and solid boundaries. Cold fluid is blown into thecavity from an inlet in one side wall and exits through an outlet in the opposite sidewall. They assumed that the flow is laminar, did not include radiation exchanges, anddid not take into account the presence and effects of humidity gradients.

In the present study, a formulation similar to the one developed by Li [6, 7] isused to calculate the velocity, temperature, and absolute humidity distribution in anindoor ice rink with ventilation and heating. The geometric configuration of this icerink is more complex than the simple parallelipipedic form adopted in all previousstudies, due to the presence of spectator stands and the transparent protective bar-riers which separate them from the ice surface. Another particularity of indoor rinksis due to the importance of radiative exchanges between the ice and the ceiling, whichcontributes significantly to the refrigeration load [9]. The model includes the effectsof radiation between all inside surfaces of the building envelope, turbulent mixedconvection, and vapor diffusion, as well as conduction through the walls and con-densation on the ice. A new approach is proposed to simplify radiation calculations.The CFD code used to calculate the flow field also evaluates the heat fluxes towardthe ice due to convection from the air, to vapor condensation, and to radiation fromthe walls and ceiling. The combination of a complex geometry, thermal boundaryconditions applied outside the envelope, and turbulent mixed convection due toboth thermal and concentration gradients distinguish the present study from allprevious ones.

MODELING OF THE PROBLEM

A schematic representation of a cross section of the ice rink under considera-tions is shown in Figure 1. Three rows of stands run the whole length of the building

SIMULTANEOUS HEAT AND MASS TRANSFER IN ICE RINKS 221

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on one side, and a narrow corridor encircles the ice surface. Protective transparentbarriers separate the corridor and stands from the ice surface. Heating and venti-lation for the spectators is provided by blowing 6.75 m3=s of air through eight regu-larly spaced inlets (0:3m 1m, each at a height of 6m above the ice surface). Air isextracted through a single outlet on the ceiling, but for the purposes of this study wehave considered that there are eight smaller openings at the same Z coordinates asthe inlets. Since the length of the building is considerable (64m), the flow field inthe XY plane midway through a set of inlets and outlets situated near the mid-planeat Z 32m can be considered to be two-dimensional (no velocity component andno heatmass transfer in the Z direction). The numerical calculations in such a planecan be considerably simplified.

Several turbulence models for the simulation of indoor air motion have beencompared during the present project, although their results are not presented here.It was found that the standard ke model by Launder and Spalding [10] performedquite well and was very stable. Chen [11] has also compared the performance of fiveturbulence models in predicting natural convection, forced convection, and mixedconvection in rooms and used experimental data for his validation. He found thatthe prediction of the mean velocity is more accurate than that of the turbulentvelocity and stated that the performance of the standard kemodel is good. Therefore,this model was selected for the present investigation.

The partial differential equations modeling the air motion, heat transfer, andvapor diffusion for steady-state conditions can be written in the following generalform:

qq/qt

div qV/ C/r/ S/ 1a

The appropriate values or expressions for /, C/, and S/ in the region occupied by airare defined in Table 1. It should be noted that in this region these seven partial dif-ferential equations are elliptic, nonlinear, and coupled, since the air density is

Figure 1. Cross section of the ice rink under consideration.

222 O. BELLACHE ET AL.

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considered to vary with both the temperature and the absolute humidity:

q q0 bT T0 bC C0 1bOn the other hand, within the solids in the calculation domain (ceiling, walls,

ice, stands, protective barriers), the velocity is zero. For the purposes of this study wealso assume that these solids are impermeable to vapor and do not include any heatsources. Therefore their temperature is the only unknown quantity and can be calcu-lated from the two-dimensional conduction equation.

The boundary conditions for this problem are as follows.

The ventilation air enters through the inlet at 30C and 45% relative humidity withhorizontal and vertical velocities equal to 2.435 and 1.406m=s, respectively.The turbulence kinetic energy kin and dissipation rate ein are [12]

kin 0:05Uin2 ein CmCd0:75k1:5in

0:1DinDin 2HL

H L 2

At the outlet, the relative pressure is set equal to zero.A uniform temperature, Tice 5:5C, is imposed under the ice at Y 0; for the

calculation with vapor diffusion, the air layer in contact with the ice is assumedto be saturated.

On all the ot...

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