Two-dimensional transient model of airflow and heat transfer in ice rinks.ABSTRACT
A two-dimensional transient model of air movement as well as heat and mass transfer in an ice rink was developed and tested by comparing its predictions with measured values in a Montreal municipal ice rink. The model was then used to predict the daily heat flux flux
In metallurgy, any substance introduced in the smelting of ores to promote fluidity and to remove objectionable impurities in the form of slag. Limestone is commonly used for this purpose in smelting iron ores. profiles into the ice by convection, radiation, condensation, and resurfacing operations for a representative configuration and for average, steady, and periodic meteorological conditions Noun 1. meteorological conditions - the prevailing environmental conditions as they influence the prediction of weather
environmental condition - the state of the environment . The heat loads from the ground and dissipation Dissipation
See also Debauchery.
lax indulger. [Am. Lit.: Hans Breitmann’s Ballads]
wasteful ne’er-do-well. [Br. Lit. in the floor pipes were also calculated. The effects of climate and some design parameters or operating conditions (ceiling emissivity Emissivity
The ratio of the radiation intensity of a nonblack body to the radiation intensity of a blackbody. This ratio, which is usually designated by the Greek letter ε, is always less than or just equal to one. , below-floor insulation thickness, and average brine brine
a salt solution used in the curing of meat. Standard ingredients are sodium chloride (15 to 30%) and sodium nitrate (0.15 to 1.50%) but many other ingredients may be added for special effects.
see artemia. temperature) on the daily loads were evaluated and analyzed an·a·lyze
tr.v. an·a·lyzed, an·a·lyz·ing, an·a·lyz·es
1. To examine methodically by separating into parts and studying their interrelations.
2. Chemistry To make a chemical analysis of.
The several thousand indoor ice rinks of North America North America, third largest continent (1990 est. pop. 365,000,000), c.9,400,000 sq mi (24,346,000 sq km), the northern of the two continents of the Western Hemisphere. are used for spectator Spectator, English daily periodical published jointly by Joseph Addison and Richard Steele with occasional contributions from other writers. It succeeded the Tatler, a periodical begun by Steele on Apr. 12, 1709, under the pseudonym Isaac Bickerstaff. events such as ice sports and ice shows. They are different sizes (ASHRAE ASHRAE American Society of Heating, Refrigerating & Air Conditioning Engineers 2002) but are characterized by the following common features: large dimensions with few or no dividing walls; significant refrigeration refrigeration, process for drawing heat from substances to lower their temperature, often for purposes of preservation. Refrigeration in its modern, portable form also depends on insulating materials that are thin yet effective. load; simultaneous need of heating (or air conditioning air conditioning, mechanical process for controlling the humidity, temperature, cleanliness, and circulation of air in buildings and rooms. Indoor air is conditioned and regulated to maintain the temperature-humidity ratio that is most comfortable and healthful. ), refrigeration, and ventilation; high energy consumption; and, finally, considerable emissions of greenhouse gases greenhouse gas
Any of the atmospheric gases that contribute to the greenhouse effect.
greenhouse gas (GHG GHG Greenhouse Gas
GHG Governor's Horse Guard (various locations) ) due to energy consumption and synthetic refrigerant re·frig·er·ant
1. Cooling or freezing; refrigerating.
2. Reducing fever.
1. A substance, such as air, ammonia, water, or carbon dioxide, used to provide cooling either as the working substance of losses. The state (temperature, humidity humidity, moisture content of the atmosphere, a primary element of climate. Humidity measurements include absolute humidity, the mass of water vapor per unit volume of natural air; relative humidity (usually meant when the term humidity , etc.) and motion of the ventilation air through these large buildings often lead to uncomfortable thermal conditions for the spectators and possible formation of fog as well as an increase of the refrigeration load and a deterioration de·te·ri·o·ra·tion
The process or condition of becoming worse. of ice conditions. A recent study (Lavoie et al. 2000) indicates that in Quebec alone ice rinks offer a potential energy conservation of 1300 GWh (4436 x [10.sup.6] Btu) annually and a possible GHG reduction of 0.5 MTons of C[O.sub.2] equivalent per year. According to according to
1. As stated or indicated by; on the authority of: according to historians.
2. In keeping with: according to instructions.
3. the study's authors, the current performance of ice rinks is poor due to the lack of design and operational guidelines guidelines,
n.pl a set of standards, criteria, or specifications to be used or followed in the performance of certain tasks. taking into consideration the interaction between the ice-making, ventilation, and heating systems.
For its part, ASHRAE Technical Committee 10.2, Automatic Icemaking Plants and Skating skating: see ice skating; ice dancing; roller skating.
Sport in which bladelike runners or sets of wheels attached to shoes are used for gliding on ice or on surfaces other than ice. Rinks, in a work statement (MacCracken and Scott 2003) stated that "the available information from ASHRAE is of limited usefulness for the design and operation of ice sheet cooling systems cooling systems
for housed animals include spraying of roofs with water, evaporative pads with fans, foggers and misters; for pastured animals shelter from the sun by trees or artificial shade devices and cooling ponds are used. by the general HVAC (Heating Ventilation Air Conditioning) In the home or small office with a handful of computers, HVAC is more for human comfort than the machines. In large datacenters, a humidity-free room with a steady, cool temperature is essential for the trouble-free & R design community or arena owner/operators." It therefore issued a request for proposals to "develop and verify methods for determining ice sheet cooling loads," which was eventually awarded to the CANMET CANMET Canada Centre for Mineral and Energy Technology Energy Technology Centre-Varennes. This paper presents the adopted methodology and initial results obtained while performing task 1 ("Develop a two-dimensional transient numerical model of ice sheet heat transfer") and task 2 ("Numerical model validation") of the project.
General Description of the Adopted Approach
The adopted model uses a detailed description of the skating rink and typical steady-periodic ambient Surrounding. For example, ambient temperature and humidity are atmospheric conditions that exist at the moment. See ambient lighting. conditions (ASHRAE 2005) to calculate the corresponding profiles of the heat loads (conductive conductive
having the quality of readily conducting electric current.
flooring or floor covering made specially conductive to electrical current, usually by the inclusion of copper wiring that is earthed , convective, and radiant) over a 24-hour period. A major difficulty in modeling the phenomena occurring in such buildings is due to their complexity: the model must take into account heat transfer through the envelope and heat gain from the ground, air motion within the building due to forced and natural convection, vapor diffusion diffusion, in chemistry, the spontaneous migration of substances from regions where their concentration is high to regions where their concentration is low. Diffusion is important in many life processes. and condensation on the ice sheet, heat transfer by radiation between all internal surfaces, heat transfer by convection between the indoor air and all internal surfaces, sensible and latent heat latent heat, heat change associated with a change of state or phase (see states of matter). Latent heat, also called heat of transformation, is the heat given up or absorbed by a unit mass of a substance as it changes from a solid to a liquid, from a liquid to a gas, gains from the spectators, conduction conduction, transfer of heat or electricity through a substance, resulting from a difference in temperature between different parts of the substance, in the case of heat, or from a difference in electric potential, in the case of electricity. in the ice and floor as well as heat generation by the lights, the resurfacing operations, and the secondary coolant coolant (kōō´lnt),
n pump work. A second difficulty in modeling the interrelated in·ter·re·late
tr. & intr.v. in·ter·re·lat·ed, in·ter·re·lat·ing, in·ter·re·lates
To place in or come into mutual relationship.
in phenomena occurring in this type of building is due to their size, irregular form, and lack of internal partitions. These buildings cannot be readily subdivided into distinct, well-mixed zones surrounded by surfaces of uniform temperature and uniform long- and shortwave radiation Shortwave radiation (SW) is a term used to describe the radiant energy in the visible (VIS), near-ultraviolet (UV), and near-infrared (NIR) wavelengths. The wavelength range is not always exactly defined, as there is no standard cut-off for the NIR. (these are the major assumptions of the heat balance and radiant time series methods described in chapter 30 of the 2005 ASHRAE Handbook--Fundamentals). Furthermore, such zonal methods require values of the heat and mass transfer coefficients In engineering, the mass transfer coefficient is a diffusion rate constant that relates the mass transfer rate, mass transfer area, and concentration gradient as driving force: that are not easy to specify accurately, especially for zones that are not separated by solid partitions. The use of a computational fluid dynamics Computational fluid dynamics
The numerical approximation to the solution of mathematical models of fluid flow and heat transfer. Computational fluid dynamics is one of the tools (in addition to experimental and theoretical methods) available to solve (CFD CFD - Computational Fluid Dynamics ) code (Chen and Srebric 2002) for the simultaneous calculation of all unknown variables eliminates the uncertainty resulting from the assumptions necessary for the application of zonal methods. Such code does not require values of the heat and mass transfer coefficients and provides more detailed descriptions of the flow field. Specifically, CFD codes determine the spatial distribution of air velocity, air temperature, and absolute humidity absolute humidity
The weight of water vapor present per unit volume of a gas or a mixture of gases. over the ice sheet. They also provide the spatial distribution of the ice, wall, and ceiling temperatures as well as the corresponding distributions of the heat fluxes into the ice sheet and into the secondary coolant.
Nielsen et al. (1979) and Davidson (1989) were among the first to apply CFD methods for airflow studies in ventilated ven·ti·late
tr.v. ven·ti·lat·ed, ven·ti·lat·ing, ven·ti·lates
1. To admit fresh air into (a mine, for example) to replace stale or noxious air.
2. rooms. However, they ignored the interaction between the indoor and outdoor environments and neglected heat transfer by radiation between the interior surfaces of the room. Chen and Van der Kooi (1988) proposed a methodology using a CFD code to calculate time-independent airflow patterns and a separate load calculation code, which solved the algebraic 1. (language) ALGEBRAIC - An early system on MIT's Whirlwind.
[CACM 2(5):16 (May 1959)].
2. (theory) algebraic - In domain theory, a complete partial order is algebraic if every element is the least upper bound of some chain of compact elements. room energy balance equation using transient temperature differences. Li (1992) extended the application of CFD codes in the field of HVAC by including heat conduction Heat conduction or thermal conduction is the spontaneous transfer of thermal energy through matter, from a region of higher temperature to a region of lower temperature, and hence acts to even out temperature differences. through the walls and radiation transfer between their internal surfaces. This formulation was then applied (Li et al, 1993) to study the radiative effects on flow and temperature fields in a room ventilated by displacement displacement, in psychology: see defense mechanism.
Same as offset. See base/displacement. . Yuan Yuan (yüän), river, 540 mi (869 km) long, rising in S Guizhou prov. and flowing generally NE to Donting lake, Hunan prov., SE China. Navigation above Changde is limited by rapids to small craft. et al. (1992) and Yang yang (yang) [Chinese] in Chinese philosophy, the active, positive, masculine principle that is complementary to yin; see yin, under principle. et al. (2000) used a commercial CFD code to study ventilation and air quality in gymnasia and skating rinks, respectively. Very recently, Bellache et al. (2005a) used the same commercial CFD code to analyze steady-state simultaneous heat and mass transfer in ice rinks. Their model was improved for this study by including transient phenomena, heat transfer through the ground, and energy gains from lights as well as the effects of resurfacing and dissipation of pump work in the pipes under the ice.
[FIGURE 1 OMITTED]
MODELING OF THE PROBLEM
The characteristics of eight ice rinks in the Montreal area were analyzed in order to select one that would serve as the basis for the project. Among the criteria used for this selection were the following: closeness to the two-dimensional configuration requested by ASHRAE; agreement with the owner/operator for the installation of the instrumentation necessary for the validation of the model; representativeness of the ice rink architecture and its HVAC & R systems and operation/occupation schedule.
This analysis led to the selection of the Camilien Houde ice rink, which is approximately 64 m (210 ft) long. A schematic A graphical representation of a system. It often refers to electronic circuits on a printed circuit board or in an integrated circuit (chip). See logic gate and HDL. representation of its cross section is shown in Figure 1. Seven rows of stands run the length of the building on one side, and a narrow corridor encircles the ice surface. The dasher dash·er
1. One that dashes, especially the plunger of an ice-cream freezer.
2. Sports The ledge along the top of the boards of an ice rink. boards are extended with protective transparent barriers separating the corridor and stands from the ice surface. Natural gas infrared heaters An infrared heater is a body with a higher temperature which transfers energy to a body with a lower temperature through electromagnetic radiation. Depending on the temperature of the emitting body, the wavelength of the infrared radiation ranges from 780 nm to 1 mm. provide spot heating of the players' and scorekeepers' benches, which are situated on the west side of the building symmetrically sym·met·ri·cal also sym·met·ric
Of or exhibiting symmetry.
Adv. 1. with respect to the plane at Z = 32 m (105 ft). The spectator area's infrared heaters are distributed regularly over the length of the building. They are activated by motion sensors and deactivated by a thermostatic control thermostatic control
a control system for the maintenance of a fixed temperature. when the air temperature over the stands reaches 15[degrees]C (59[degrees]F). As the heaters are direct-fired, the combustion products are expelled through roof-mounted exhaust fans interlocked with the burner A drive that writes write-once optical discs such as CD-Rs and DVD-Rs. A "burner" implies a one-time recording, but the term is erroneously used to refer to drives that "write" to re-recordable CD-RW and DVD-RW/+RW media as well. See burn, CD-R and DVD-R. controls. Outside air mixed with return air provides ventilation through regularly spaced diffusers above the spectator stands when the propane-fueled resurfacing machine is operating. Return air grilles are situated at the north and south ends of the stands. Humidity control Humidity control
Regulation of the degree of saturation (relative humidity) or quantity (absolute humidity) of water vapor in a mixture of air and water vapor. Humidity is commonly mistaken as a quality of air. is provided by two mechanical dehumidifiers located in the roof-truss spaces at each end of the building. A 24-hour operating schedule, which specifies occupancy, lighting, and resurfacing as well as possible stoppages of the refrigeration and heating operations during unoccupied periods (e.g., between midnight and 5 a.m. depending on the next morning's activities), is selected and contributes to the transient character of the conditions in the building (see appendix). Calcium chloride calcium chloride, CaCl2, chemical compound that is crystalline, lumpy, or flaky, is usually white, and is very soluble in water. The anhydrous compound is hygroscopic; it rapidly absorbs water and is used to dry gases by passing them through it. brine is used as the secondary coolant to maintain the ice surface temperature at the desired value. It is supplied from a header located at the west end of the ice sheet and circulates in the concrete floor under the ice in 146 two-pass polyethylene polyethylene (pŏl'ēĕth`əlēn), widely used plastic. It is a polymer of ethylene, CH2=CH2, having the formula (-CH2-CH2-)n 32 mm (1.25 in.) tubes on 89 mm (3.5 in.) spacing.
It follows from this description that the building and its heating, cooling, and ventilation systems ventilation system Public health An air system designed to maintain negative pressure and exhaust air properly, to minimize the spread of TB and other respiratory pathogens in a health care facility are symmetrical symmetrical
equally on both sides.
symmetrical multifocal encephalopathy
inherited disease in two forms: Limousin form appears at about a month old with blindness, forelimb hypermetria, hyperesthesia, nystagmus, aggression, weight with respect to the mid-plane at Z = 32 m (105 ft). Assuming that spectators are uniformly distributed throughout the length of the stands and that the differences of outdoor conditions due to solar radiation solar radiation,
n the emission and diffusion of actinic rays from the sun. Overexposure may result in sunburn, keratosis, skin cancer, or lesions associated with photosensitivity. and wind direction on the north/south walls are negligible, it follows that in the x-y plane midway through the length of the building (Z = 32 m [105 ft]) there will be no velocity components and no heat or mass transfer in the Z direction. Therefore, the conditions in this plane approximate very closely the two-dimensionality required by ASHRAE.
The airflow within ice-rink buildings is turbulent, as evidenced by the studies mentioned earlier. Several turbulence turbulence, state of violent or agitated behavior in a fluid. Turbulent behavior is characteristic of systems of large numbers of particles, and its unpredictability and randomness has long thwarted attempts to fully understand it, even with such powerful tools as models exist and several were tested during an early phase of the project. The detailed results of these tests are not presented here due to lack of space. The principal conclusion is that the standard k-[epsilon] model (Launder Launder
To move illegally acquired cash through financial systems so that it appears to be legally acquired. and Spalding 1974) was very stable and gave satisfactory predictions compared to experimental and numerical results from the literature. Chen (1995) has also compared the performance of five turbulence models in predicting natural, forced, and mixed convection in rooms. He used experimental data for their validation and concluded that the performance of the standard k-[epsilon] model is good. Therefore, this model was selected for the present investigation.
The partial differential equations partial differential equation
In mathematics, an equation that contains partial derivatives, expressing a process of change that depends on more than one independent variable. modeling the air movement, heat transfer, and vapor diffusion for transient conditions can be written in the following general form:
[[partial derivative partial derivative
In differential calculus, the derivative of a function of several variables with respect to change in just one of its variables. Partial derivatives are useful in analyzing surfaces for maximum and minimum points and give rise to partial differential ]([rho][phi])/[partial derivative]t] + div([rho][[??].V][phi] - [[GAMMA].sub.[phi]][nable][phi]) = [S.sub.[phi]] (1)
The appropriate values or expressions for [phi], [[GAMMA].sub.[phi]], and [S.sub.[phi]] in the region occupied by air are defined in Table 1. It should be noted that in this region, these seven partial differential equations are elliptic el·lip·tic or el·lip·ti·cal
1. Of, relating to, or having the shape of an ellipse.
2. Containing or characterized by ellipsis.
a. , nonlinear A system in which the output is not a uniform relationship to the input.
nonlinear - (Scientific computation) A property of a system whose output is not proportional to its input. , and coupled, since the air density varies with both the temperature and the absolute humidity:
[rho] = [[rho].sub.o][??]1 + [beta](T - [T.sub.o]) + [beta]*(C - [C.sub.o])[??] (2)
On the other hand, within the solids in the calculation domain (ceiling, walls, protective barriers, ice, concrete floor, insulation, and ground) the velocity is zero. For the purpose of this study, it is also assumed that these solids are impermeable impermeable /im·per·me·a·ble/ (-per´me-ah-b'l) not permitting passage, as of fluid.
Impossible to permeate; not permitting passage. to vapor and do not include any heat sources. Therefore, the temperature is the only unknown quantity and can be calculated from the two-dimensional transient conduction equation.
The boundary conditions boundary condition
The set of conditions specified for behavior of the solution to a set of differential equations at the boundary of its domain. for this problem are as follows.
The external surfaces of the building are subject to variable, site-dependant meteorological conditions. Since the objective of the project is to obtain "typical" daily profiles of refrigeration load components rather than corresponding maximum values, it was decided to use average meteorological conditions. The hourly data for three North American North American
named after North America.
North American blastomycosis
see North American blastomycosis.
North American cattle tick
see boophilusannulatus. sites with very different climatic conditions (Edmonton, Houston, and Pittsburgh) provided by the US Department of Energy (DOE 2005) were used to calculate average daily profiles of sol-air temperatures Sol-air temperature (Tsol-air) is a variable used to calculate cooling load of a building and determine the total heat gain through exterior surfaces. It is an improvement over
[q.sub.cd, o] = [h.sub.o]A([T.sub.sol-air] - [T.sub.s]). (3)
For the purposes of this study, the value of [h.sub.o] was considered constant and equal to 17 W/[m.sup.2] x K (3 Btu/h x [ft.sup.2] x [degrees]F), as recommended by ASHRAE (2005).
The dry-bulb temperature The dry-bulb temperature is the temperature of air measured by a thermometer freely exposed to the air but shielded from radiation and moisture. In construction, it is an important consideration when designing a building for a certain climate. and humidity of the ventilation air entering the building when resurfacing takes place are the corresponding outdoor values calculated as explained in the previous paragraph. The horizontal and vertical components of the ventilation air velocity at the supply diffusers are both equal to 0.27 m/s. The relative pressure at the return air grilles is assumed to be zero.
[FIGURE 2 OMITTED]
The ground at a depth of 2 m (6.5 ft) is assumed to have a constant temperature (4.9[degrees]C [40.8[degrees]F] for the base case). Heat fluxes across the underground surfaces of the computational domain are evaluated as proposed by ASHRAE (2005).
On the inside surfaces of the ice rink (walls, ceiling, stands, and ice) the velocity components, concentration gradient concentration gradient
The graduated difference in concentration of a solute per unit distance through a solution.
Noun 1. , and turbulent kinetic energy Turbulent Kinetic Energy (TKE) is the mean kinetic energy per unit mass associated with eddies in turbulent flow. It is a concept used to assess what contribution to buoyancy is brought by turbulence. are equal to zero. The corresponding temperature is related to that of the air within the flow domain by an energy balance that takes into account conduction through the solid, convection to the inside air, and net radiation fluxes This article only describes one highly specialized aspect of its associated subject.
Please help [ improve this article] by adding more general information. between the inside surfaces. Thus, the conductive heat conductive heat
Heat transmitted to the body by direct contact, as by an electric pad. flux for each element of the inside surfaces is
[q.sub.cd, i] = [q.sub.cv, i] + [q.sub.r, i] + [q.sub.s, i] + [q.sub.l, i]. (4)
The last two terms denote de·note
tr.v. de·not·ed, de·not·ing, de·notes
1. To mark; indicate: a frown that denoted increasing impatience.
2. the heat flux due to resurfacing operations and the latent heat due to vapor condensation (mass transfer to ice sheet) and are only taken into account for the ice surface. The conductive and convective heat con·vec·tive heat
Heat conveyed to the body by a moving warm medium, such as air or water. fluxes [q.sub.cd] and [q.sub.cv] are calculated by the CFD code, while the net radiative heat flux [q.sub.r] between surface j and all the N inside surfaces of the envelope is calculated using Gebhart's method. Its implementation in the CFD code has been described in a paper by Bellache et al. (2005b).
The total loads due to vapor condensation, resurfacing, and brine pump (Marine Engin.) a pump for changing the water in the boilers, so as to clear them of the brine which collects at the bottom.
See also: Brine work dissipation are calculated assuming quasi-steady conditions. In particular, we have used the formulation from ASHRAE (2002) to calculate the resurfacing heat flow on the ice surface. Thus,
[q.sub.l, i] = [dot.m.sub.in]([C.sub.in] - [C.sub.out])[h.sub.ig] (5)
[q.sub.s, i] = [rho][V.sub.f][4.2([T.sub.f] - 0) + 334 + 2(0 - [T.sub.ice])] (6)
[q.sub.p, i] = [rho]gQ[H.sub.sys] (7)
[q.sub.l, i] and [q.sub.s, i] are attributed to the ice surface (cf. Equation 4), while [q.sub.p, i] is attributed to the brine. The heat produced by a resting occupant occupant n. 1) someone living in a residence or using premises, as a tenant or owner. 2) a person who takes possession of real property or a thing which has no known owner, intending to gain ownership. (See: occupancy) is about 100 W (ASHRAE 2005).
The numerical solution of the system of coupled partial differential equations has been carried out using the finite volume method The finite volume method is a method for representing and evaluating partial differential equations as algebraic equations. Similar to the finite difference method, values are calculated at discrete places on a meshed geometry. , a staggered grid, and the hybrid scheme for discretization dis·cret·i·za·tion
The act of making mathematically discrete. of the convection terms. The SIMPLE algorithm was used for the pressure correction, and the solution was obtained iteratively using the numerical code PHOENICS PHOENICS Parabolic Hyperbolic Or Elliptic Numerical Integrated Code Series (fluid dynamics software from CHAM, Wimbledon, UK) .
The calculation domain was first subdivided into zones corresponding to the physical discontinuities shown in Figure 1. In the present case there are 27 zones in the X direction and 30 zones in the Y direction. The number of grid points, or finite volumes, within each of the resulting 810 subdivisions of the domain has been varied to ensure that the results are independent of their number. The discretization grid was always non-uniform with higher density near the air inlets and the solid surfaces where gradients are higher. Numerical tests were carried out with 100 x 50 and 200 x 100 grid points in the X and Y directions, respectively. The number of iterations was also varied. Table 2 shows that all the results are essentially identical. Therefore, the results reported in the present paper were calculated with 100 x 50 grid points and 10,000 iterations. Analogous tests were conducted with different timesteps. The results presented here were all calculated with a timestep of 600 s. Finally, the simulation was run for two days with identical 24-hour meteorological conditions in order to ensure that the calculated "typical" daily profiles of the refrigeration loads were periodic. Under-relaxation was often necessary to achieve convergence, which was declared when the cumulative residuals for each of the conservation equations were less than [10.sup.-6].
The horizontal surface Noun 1. horizontal surface - a flat surface at right angles to a plumb line; "park the car on the level"
floor, flooring - the inside lower horizontal surface (as of a room, hallway, tent, or other structure); "they needed rugs to cover the bare through the centerlines of the floor pipes is assumed to be isothermal i·so·ther·mal
Of, relating to, or indicating equal or constant temperatures.
having the same temperature. . This assumption is based on the small center-to-center spacing of the floor pipes as well as on the small increase of brine temperature (~1[degrees]C [2[degrees]F]) between the supply and return headers. For the purposes of the present study, the temperature of this surface is assumed to be equal to the average brine temperature in the floor pipes.
When resurfacing takes place, the total heat reaching the brine generally exceeds the capacity of the refrigeration plant A refrigeration plant uses gas, liquid, and mechanical energy to move heat from one place to another. A liquid, such as ammonia, which has a low boiling temperature is allowed to pass into a space via tubing. . During these time intervals, the energy balance for the brine can be approximated as follows:
M[C.sub.p][d[bar.T]/dt] = [summation summation n. the final argument of an attorney at the close of a trial in which he/she attempts to convince the judge and/or jury of the virtues of the client's case. (See: closing argument) over i]([q.sub.cd, i] + [q.sub.p, i] (8a)
The summation on the right-hand side right-hand side n → derecha
right-hand side right n → rechte Seite f
right-hand side n → lato destro includes all the conductive fluxes reaching the isothermal surface from above (ice side) and below (ground side). The heat capacity term on the left-hand side left-hand side n → izquierda
left-hand side left n → linke Seite f
left-hand side n → lato or includes contributions from the brine and the concrete in the appropriate finite volumes.
When resurfacing is not taking place, the capacity of the refrigeration plant is greater than the total heat transferred to the brine. During these time intervals, the space average of the brine temperature is assumed to be constant. Therefore, the corresponding energy balance is
[dot.m][C.sub.p][DELTA]T = [summation over i]([q.sub.cd, i] + [q.sub.p, i]). (8b)
The adopted model and calculation procedure have been validated in several steps. Initially, the selected k-[epsilon] two-equation model was successfully validated for turbulent natural and mixed convection in small enclosures by comparing steady-state velocity and temperature profiles with corresponding measured values (Bellache et al. 2005a). Secondly, predicted air, ice, and wall temperatures for an ice rink were successfully compared with corresponding measured values in a previous project (Bellache et al. 2005b). For the purposes of the present project, long-term transient measurements that serve for the validation of the prediction model and for the better understanding of physical processes affecting the cooling load of the ice sheet and of occupant comfort are being conducted in the selected ice rink. The details of this experimental project are presented in a separate paper (Ouzzane et al. 2006). Furthermore, additional measurements of air and surface temperatures have been collected using RTD RTD returned to duty (US DoD)
RTD Ready to Drink
RTD Richmond Times-Dispatch
RTD Regional Transportation District
RTD Research, Technological Development
RTD Research and Technology Development
RTD Real-Time Data sensors and an infrared temperature sensor. In the following paragraphs we compare the experimental values for February 24, 2005, corresponding to the weekday schedule of the operating system operating system (OS)
Software that controls the operation of a computer, directs the input and output of data, keeps track of files, and controls the processing of computer programs. , with the corresponding numerical predictions.
Figure 3 shows the outdoor temperature evolution over this 24-hour period and compares measured and calculated air temperature evolutions at two positions in the ice rink. The predicted time evolution of the air temperatures for each position follows very closely the corresponding measured profile. This is a first indication that the model satisfactorily represents the transient behavior of the phenomena taking place in the rink. The small, systematic underestimation of these temperatures is attributed to the inaccuracy in·ac·cu·ra·cy
n. pl. in·ac·cu·ra·cies
1. The quality or condition of being inaccurate.
2. An instance of being inaccurate; an error. of the assumed initial conditions used for the simulation. Indeed, since a complete three-dimensional map of air temperatures is not available, the simulation was executed with a uniform initial air temperature throughout the rink. Second, the model correctly predicts that the air temperature over the stands (X = 28.2 m) is approximately 4[degrees]C (7[degrees]F) warmer than the corresponding value near the west wall (X = 0.6 m) due to the operation of the radiant heaters. However, it is worth noting that the measured temperature over the stands rarely reaches the setpoint (15[degrees]C or 59[degrees]F) at Y = 7.7 m.
Figure 4 shows the vertical profiles of calculated and measured air temperatures near the center of the ice surface (X = 14 m, Y < 5 m [10 ft]) at 10 a.m. Hot wire measurements indicate that hardly any air movement takes place in this zone. In the first 20 cm (8 in.) above the ice, the agreement between measured and calculated temperatures is excellent. In this region, the temperature increases linearly with height and the corresponding gradient gradient
In mathematics, a differential operator applied to a three-dimensional vector-valued function to yield a vector whose three components are the partial derivatives of the function with respect to its three variables. The symbol for gradient is ∇. is quite high. This first linear region is followed by an anomalous a·nom·a·lous
1. Deviating from the normal or common order, form, or rule.
2. Equivocal, as in classification or nature. behavior (for Y between 0.2 and 0.5 m) and a second region of linear increase. The predictions underestimate both the extent of this second region of linear increase and the corresponding gradient. This discrepancy DISCREPANCY. A difference between one thing and another, between one writing and another; a variance. (q.v.)
2. Discrepancies are material and immaterial. may be due to the initial conditions or to the assumption of a two-dimensional flow field for the calculations. Above this second linear region, the air temperature is independent of the height. These constant values are in good agreement with the corresponding temperatures in Figure 3. This is significant since the values in Figure 3 were measured with the instrumentation used to establish the long-term transient performance, while those in Figure 4 where obtained with the RTD sensors. Finally, it is important to note that temperature profiles exhibiting the same characteristics as those in Figure 4 have also been measured by Pennanen et al. (1997).
[FIGURE 3 OMITTED]
[FIGURE 4 OMITTED]
Calculated and measured ice surface temperature evolutions for this same winter day are shown in Figure 5. These measurements were performed with an infrared temperature sensor. Again the transient response In electrical engineering and Mechanical Engineering, a transient response or natural response is the response of a system to a change from equilibrium. Specifically, transient response in Mechanical Engineering is the portion of the response that approaches zero after a is very well predicted by the simulation. The systematic small difference between predicted and measured values is again attributed to the assumed initial conditions used for the simulation. The time evolution of this variable can be easily explained based on the prevailing conditions in the rink. Between midnight and 3 a.m. the lights are off while the refrigeration system is operating; therefore, the temperature of the ice surface decreases. Then the compressors are turned off from 3 a.m. to 5:30 a.m. and the ice surface temperature increases. After 5:30 a.m., the compressors and some lights are turned on and the ice temperature decreases steadily until 9:30 a.m. The peak temperatures occurring at more or less regular intervals between 10 a.m. and 10 p.m. are due to the resurfacing operation. During this operation, the refrigeration system is operated at maximum capacity to meet the peak load conditions. The difference between the measured and calculated peak temperatures is due to the fact that the measurement does not always coincide with the application of the hot water used for resurfacing purposes.
Further transient measurements and comparisons of calculated and measured values will become available during the second year (2005-06) of the project. However, since the comparisons in Figures 3, 4, and 5 (as well as other comparisons not presented here for lack of space) are quite encouraging, we have started using the model and the numerical code to calculate heat fluxes into the ice and the brine. Some preliminary results are presented in the next section of the paper.
[FIGURE 5 OMITTED]
RESULTS AND DISCUSSION
The ASHRAE request for proposals specified that the two-dimensional transient numerical model simulating ice sheet heat transfer should be used to determine how the cooling load is affected by climatic conditions as well as by changes in design and operating characteristics. After consultation with the members of ASHRAE TC 10.2, the three site/season combinations previously specified were selected to analyze the effects of the climate. The chosen design characteristics include two subfloor insulation thicknesses (0 and 7.6 cm [3 in.]), subfloor heating (yes or no), and three ceiling emissivities (0.9, 0.5, and 0.1). The operating characteristics include three ice thicknesses (2.5, 5.1, and 7.6 cm [1, 2, and 3 in.]), two operating schedules (see appendix), and three average brine temperatures (-7[degrees]C, -9[degrees]C, and -11[degrees]C [19.4[degrees]F, 15.8[degrees]F, and 12.2[degrees]F). The following paragraphs present calculated results for several different combinations of these parameters.
The base case corresponds to the configuration of Figure 1 and the meteorological conditions of Figure 2 (spring in Pittsburgh). For this case there is no subfloor heating, the ice and subfloor insulation thicknesses are, respectively, 5.1 cm (2 in.) and 7.6 cm (3 in.), the average brine temperature in the floor pipes is -9[degrees]C (15.8[degrees]F), the ceiling emissivity is 0.9, and the weekend operating schedule (see appendix) applies.
Figure 6 shows the evolution of the temperature at different positions in the calculation domain over two 24-hour periods with identical meteorological conditions (see Figure 2). The first few hours must be disregarded because of the influence of the arbitrary initial conditions. Steady periodic conditions prevail for the second 24-hour period and, therefore, all subsequent discussion refers to the time interval between t = 24 hours and t = 48 hours. During that period, the temperature of the ground-insulation interface is constant. This is due to the large thermal inertia inertia (ĭnûr`shə), in physics, the resistance of a body to any alteration in its state of motion, i.e., the resistance of a body at rest to being set in motion or of a body in motion to any change of speed or change in direction of of the ground and the fact that the ground temperature at a depth of 2 m (6.5 ft) was assumed to be constant. Since its predicted value is just below the freezing point freezing point
Temperature at which a liquid becomes a solid. When the pressure surrounding the liquid is increased, the freezing point is raised. The addition of some solids can lower the freezing point of a liquid, a principle used when salt is applied to melt ice on , it is probably advisable ad·vis·a·ble
Worthy of being recommended or suggested; prudent.
ad·visa·bil to install ground heating in this case to avoid freezing and heaving.
[FIGURE 6 OMITTED]
On the other hand, the temperature of the ice surface decreases slightly between midnight and approximately 8 a.m. since occupation, lights, and resurfacing are nonexistent non·ex·is·tence
1. The condition of not existing.
2. Something that does not exist.
non during that period (c.f. appendix) while the brine temperature is constant. After 8 a.m., however, when activities pick up, the temperature of the ice surface varies considerably. Its peaks, which reach the freezing point, coincide with the resurfacing operations (c.f. appendix), which are assumed to last ten minutes each. After each of the morning resurfacing operations, the temperature of the ice surface returns to a more or less constant value of approximately -4[degrees]C (24.8[degrees]F). During the afternoon, however, when the frequency of the resurfacing operations increases, the temperature of the ice surface after each resurfacing tends to increase. Thus, at 9 p.m. (t = 45 hours), this temperature is approximately -2.5[degrees]C (27.5[degrees]F). This is due to the cumulative effect of the resurfacing operations and the approximately constant cooling capacity of the brine. The effect of resurfacing also influences the average peaks. The dew point dew point: see dew. of the air near the ceiling remains constant, and it is important to note that it is considerably lower than the ceiling temperature. Thus, there is no danger of condensation on the ceiling for the conditions under consideration. Finally, the ceiling temperature follows fairly closely the variation of the outside temperature (c.f. Figure 2).
Figure 7 shows the corresponding heating load profiles over the same period. Curve #1 shows that the heat flux from the ground to the brine is time independent. This is consistent with the results of the previous figure regarding the temperatures of the brine and the interface between the ground and the insulation. Curve #2 corresponds to the heat flux into the ice due to condensation. It is constant since the ice temperature and the state of the ventilation air change little during a typical day. Curve #3 shows the heat flux into the ice due to convection from the air in the ice rink. This quantity is nearly constant most of the time, except when resurfacing takes place. During these time intervals, the ice temperature increases (c.f. Figure 6); therefore, the convective heat flux decreases. Curve #4 depicts the radiation flux into the ice. It is lower during the night since the lights are off and the ceiling temperature is relatively low (see Figure 6). It becomes more important during the day when the effect of these two sources increases. The short-duration, steep decreases of this flux occurring between 8 a.m. (t = 32) and 11 p.m. (t = 47) coincide with resurfacing operations and are due to the corresponding increase of the ice temperature (c.f. Figure 6). Curve #5 shows the total heat flux into the ice from above (convection + condensation + radiation + resurfacing). The pronounced peaks coincide with the resurfacing operations (c.f. appendix). The maximum heat flux into the ice occurs around 2 p.m. (t = 38) and is approximately equal to 300 W/[m.sup.2] (95.13 Btu/h x [ft.sup.2]). Finally, curve #6 shows the total heat flux into the brine from above. For the entire day, the integral of this quantity is the same as the corresponding integral for curve #5. However, the inertia of the ice sheet and the concrete floor are such that the peaks of curve #6 are considerably lower than those of curve #5. For the same reason, they occur slightly later and last longer than those on the ice surface, which is directly exposed to the hot water applied during resurfacing. Thus, the maximum heat flux into the brine from above (this quantity does not include the heat flux from the ground) occurs at about 10 p.m. (t = 46) and is approximately equal to 150 W/[m.sup.2] (47.56 Btu/h x [ft.sup.2]), i.e., half the corresponding value for the ice.
[FIGURE 7 OMITTED]
Table 3 shows the daily loads into the ice (integral of the quantities in Figure 7 from t = 24 to t = 48) and the corresponding average fluxes for the base case defined previously. For these conditions, radiation is the largest contributor to the total refrigeration load, followed by approximately equal contributions from convection and resurfacing operations. It should be noted that the daily load into the ice (integral of curve #6) differs by only 0.5% from the corresponding value for the ice (line 6 of Table 3). This excellent result is a good indicator of the precision of the numerical calculations. The total pump work corresponds to 0.248 kWh/[m.sup.2] (78.62 Btu/[ft.sup.2]), while the friction dissipation in the floor pipes represents 0.076 kWh/[m.sup.2] (24.09 Btu/[ft.sup.2]) on a daily basis. The former is approximately the same as the contribution of condensation, while the latter is very close to the energy transmitted to the brine from the ground (0.082 kWh/[m.sup.2] [25.99 Btu/[ft.sup.2]]). Depending on the fraction of the total pump work that is lost to the surroundings, the total refrigeration load transmitted to the chillers is between 2.41 and 2.58 kWh/[m.sup.2] (763.97 and 817.86 Btu/[ft.sup.2]). The corresponding average fluxes are, respectively, 101 and 108 W/[m.sup.2] (32.02 and 34.25 Btu/h x [ft.sup.2]).
Figures 8 through 11 show the effects of different parameters on the daily loads into the ice (by convection, radiation, condensation, and resurfacing operations) and into the brine (from the ground and due to dissipation in the floor pipes) as well as on their sum. In each case, one clearly identified parameter is varied while the others all retain the values specified in the description of the base case.
Figure 8 shows that the differences between weekends and weekdays are essentially due to the lower number of resurfacing operations in the latter case. The corresponding load is significantly lower (0.352 kWh/[m.sup.2] [111.58 Btu/[ft.sup.2]]) and compensates for the small increases of the convection and radiation loads, which are due to a slight decrease of the average ice temperature. The latter is a direct result of the reduction in the daily number of resurfacing operations (9 on weekdays, 12 on weekends). The total is 2.41kWh/[m.sup.2] (763.97 Btu/[ft.sup.2]) on weekends and 2.34 kWh/[m.sup.2] (741.78 Btu/[ft.sup.2]) on weekdays. It is important to note that the load into the brine from the ground is totally unaffected by the operation schedule.
Figure 9 illustrates the effects of the climate by comparing the base case (spring in Pittsburgh) with winter conditions in Edmonton and summer conditions in Pittsburgh. Three of the four daily loads into the ice are lowest in winter and highest in summer, due to the corresponding changes of the outdoor dry-bulb temperature and absolute humidity. The influence of the climate on ground gains is very small, while daily loads from resurfacing and dissipation are independent of climatic conditions. The total is 1.98 kWh/[m.sup.2] (627.66 Btu/[ft.sup.2]) for winter in Edmonton, 2.41 kWh/[m.sup.2] (763.97 Btu/[ft.sup.2]) for spring in Pittsburgh, and 2.89 kWh/[m.sup.2] (916.13 Btu/[ft.sup.2]) for summer in Pittsburgh.
Figure 10 shows the effects of ceiling emissivity. The daily radiation load into the ice decreases considerably as the ceiling emissivity decreases. On the other hand, the corresponding load due to convection increases slightly due to a small decrease of the temperature of the ice surface. However, the effect on the total is very positive: this value is 2.41, 2.13, and 1.80 kWh/[m.sup.2] (763.97, 675.21, and 570.60 Btu/[ft.sup.2]), respectively, for [[epsilon].sub.c] = 0.9, 0.5, and 0.1. It is important to note that the load into the brine from the ground is totally unaffected by the ceiling emissivity.
Finally, Figure 11 shows that, as expected, the convective, radiative, and ground loads increase significantly as the average brine temperature decreases. The condensation load varies very slightly, while resurfacing and dissipation loads are not dependent on this parameter. The total is 2.25, 2.41, and 2.53 kWh/[m.sup.2] (713.25, 763.97, and 802.01 Btu/[ft.sup.2]), respectively, for average brine temperatures of -7[degrees]C, -9[degrees]C, and -11[degrees]C (19.4[degrees]F, 15.8[degrees]F, and 12.2[degrees]F).
[FIGURE 8 OMITTED]
[FIGURE 10 OMITTED]
Turbulent flow with simultaneous mass diffusion in a ventilated ice rink coupled to conduction through its envelope and radiation between the inside surfaces of the latter has been modeled using the standard k-[epsilon] model and a modified version of Gebhart's method.
The model and numerical code used for the solution of the coupled partial differential equations were validated by comparing their predictions with measured values in a municipal ice rink situated in Montreal. They were then used to evaluate the daily profiles of heat fluxes into the ice and the brine for a representative ice rink and steady periodic meteorological conditions. The results for the base case (spring conditions in Pittsburgh) show that the maximum heat flux into the ice occurs during resurfacing and is approximately equal to 300 W/[m.sup.2] (95.13 Btu/h x [ft.sup.2]). The corresponding value for the brine is approximately 150 W/[m.sup.2] (47.56 Btu/h x [ft.sup.2]). The daily loads into the ice were also calculated: for the base case, approximately 43% of the total is due to radiation, while convection and resurfacing each contribute approximately 19.6% of the total.
[FIGURE 9 OMITTED]
[FIGURE 11 OMITTED]
The effects of the operation schedule, climate, ceiling emissivity, and average brine temperature on the daily refrigeration loads were also evaluated and presented.
For the conditions under investigation, the results show that a decrease in the ceiling emissivity from 0.9 to 0.1 reduces the radiation energy portion of the total refrigeration load from 43% to 21.7%. This results in a reduction of 25% of the total ice load.
The authors acknowledge the financial support received from ASHRAE for the research project and the technical support of ASHRAE TC 10.2, Automatic Ice Making Plants/ Skating Rinks.
NOMENCLATURE nomenclature /no·men·cla·ture/ (no´men-kla?cher) a classified system of names, as of anatomical structures, organisms, etc.
A = area, [m.sup.2] ([ft.sup.2])
C = absolute humidity, kg water/kg dry air (lb/lb)
[C.sub.p] = specific heat, kJ/kg x K (Btu/lb x [degrees]F)
[h.sub.ig] = specific enthalpy enthalpy (ĕn`thălpē), measure of the heat content of a chemical or physical system; it is a quantity derived from the heat and work relations studied in thermodynamics. of sublimation sublimation, in chemistry
sublimation (sŭblĭmā`shən), change of a solid substance directly to a vapor without first passing through the liquid state. , J/kg (Btu/lb)
[H.sub.sys] = hydraulic head Hydraulic head is a specific measurement of water pressure or total energy per unit weight above a datum. It is usually measured as a water surface elevation, expressed in units of length, but represents the energy at the entrance (or bottom) of a piezometer. , m (ft)
k = turbulent kinetic energy, [m.sup.2]/[s.sup.2] ([ft.sup.2]/[h.sup.2])
m = mass flow rate, kg/s (lb/h)
M = mass, kg (lb)
[q.sub.cd] = conductive heat flow rate, W (Btu/h)
[q.sub.cv] = convective heat flow rate, W (Btu/h)
q = heat flow rate due to condensation, W (Btu/h)
[q.sub.r] = radiant heat heat proceeding in right lines, or directly from the heated body, after the manner of light, in distinction from heat conducted or carried by intervening media.
See also: Radiant flow rate, W (Btu/h)
[q.sub.s] = heat flow rate due to resurfacing, W (Btu/h)
[q.sub.p] = heat flow rate due to pumping, W (Btu/h)
Q = volume flow, L/s (cfm)
[S.sub.[phi]] = source term in Equation 1
T = temperature, [degrees]C ([degrees]F)
t = time, s (h)
[bar.V]= velocity vector, m/s (ft/h)
V = volume, [m.sup.3] ([ft.sup.3])
X, Y = Cartesian coordinates Cartesian coordinates (kärtē`zhən) [for René Descartes], system for representing the relative positions of points in a plane or in space. , m (ft)
[beta] = thermal expansion thermal expansion
Increase in volume of a material as its temperature is increased, usually expressed as a fractional change in dimensions per unit temperature change. coefficient coefficient /co·ef·fi·cient/ (ko?ah-fish´int)
1. an expression of the change or effect produced by variation in certain factors, or of the ratio between two different quantities.
2. , [K.sup.-1] ([R.sup.-1])
[beta]* = coefficient of mass expansion
[[GAMMA].sub.[phi]] = diffusion coefficient in Equation 1
[DELTA]T = temperature difference, K (R)
[epsilon] = dissipation rate of turbulent kinetic energy, [m.sup.2]/[s.sup.3] ([ft.sup.2]/[h.sup.3])
[[epsilon].sub.c] = ceiling emissivity
[lambda] = thermal conductivity thermal conductivity
A measure of the ability of a material to transfer heat. Given two surfaces on either side of the material with a temperature difference between them, the thermal conductivity is the heat energy transferred per unit time and per unit , W/m x K (Btu/h x ft x [degrees]F)
[rho] = density, kg/[m.sup.3] (lb/[ft.sup.3])
[phi] = field variable in Equation 1
i = inside
o = outside
b = brine
f = flood water
gr = ground
p = pump
ASHRAE. 2002. 2002 ASHRAE Handbook--Refrigeration, chapter 34. Atlanta: American Society of Heating, Refrigerating re·frig·er·ate
tr.v. re·frig·er·at·ed, re·frig·er·at·ing, re·frig·er·ates
1. To cool or chill (a substance).
2. To preserve (food) by chilling. and Air-Conditioning Engineers, Inc.
ASHRAE. 2005. 2005 ASHRAE Handbook--Fundamentals. Atlanta: American Society of Heating, Refrigerating, and Air-Conditioning Engineers, Inc.
Bellache, O., M. Ouzzane, and N. Galanis. 2005a. Numerical prediction of ventilation patterns and thermal processes in ice rinks. Building and Environment 40:417-26.
Bellache, O., M. Ouzzane, and N. Galanis. 2005b. Coupled conduction, convection, radiation heat transfer with simultaneous mass transfer in ice rinks. Numerical Heat Transfer, Part A 48:219-38.
Chen, Q. 1995. Comparison of different k-[epsilon] models for indoor air flow computations. Numerical Heat Transfer, Part B 28:353-69.
Chen, Q., and J. Srebric. 2002. A procedure for verification, validation, and reporting of indoor environment CFD analyses. HVAC & R Research 8(2):201-16.
Chen, Q., and J. Van der Kooi. 1988. Accuracy--A program for combined problems of energy analysis, indoor airflow and air quality. ASHRAE Transactions 94(2):196-214.
Davidson, L. 1989. Ventilation by displacement in a three-dimensional room: A numerical study. Building and Environment 24(4):363-72.
DOE. 2005. ENERGYPLUS. Washington, DC: US Department of Energy. www.eere.energygov/buildings.
Launder, B.E., and D.B. Spalding. 1974. The numerical computation of turbulent flows. Computer Methods in Applied Mechanics the principles of abstract mechanics applied to human art; also, the practical application of the laws of matter and motion to the construction of machines and structures of all kinds.
See also: Mechanics and Energy 3:269-89.
Lavoie, M., R. Sunye, and D. Giguere. 2000. Potentiel d'economies d'energie en refrigeration dans les arenas du Quebec. Report prepared by the CANMET Energy Technology Center, Varennes, Canada.
Li, Y. 1992. Simulation of flow and heat transfer in ventilated rooms. Transactions of the Dept. of Mechanics/ Applied Comp. Fluid Dynamics fluid dynamics
n. (used with a sing. verb)
The branch of applied science that is concerned with the movement of gases and liquids. , Royal Institute of Technology, Stockholm, Sweden.
Li, Y., L. Fuchs, and M. Sandberg. 1993. Numerical prediction of airflow and heat radiation interaction in a room with displacement ventilation. Energy and Buildings 20(1):27-43.
MacCracken, M.M., and J.P. Scott. 2003. Work statement: Develop and verify methods for determining ice sheet cooling loads. ASHRAE TC 10.2. Atlanta: American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc.
Nielsen, P.V., A. Restivo, and J.H. Whitelow. 1979. Buoyancy buoyancy (boi`ənsē, b`yən–), upward force exerted by a fluid on any body immersed in it. Buoyant force can be explained in terms of Archimedes' principle. affected flows in ventilated rooms. Numerical Heat Transfer 2:115-27.
Ouzzane, M., R. Sunye, R. Zmeureanu, D. Giguere, J.P. Scott, and O. Bellache. 2006. Cooling load and environmental measurements in a Canadian indoor ice rink (RP-1289). ASHRAE Annual Meeting, Quebec City, Quebec, June 24-28.
Pennanen, A.S., R.O. Salonen, S. Alm, M.J. Jantunen, and P. Pasanen. 1997. Characterization of air quality problems in five Finnish indoor ice arenas. J. of the Air & Waste Management Association 47(10):1079-86.
Yang, C., P. Demokritou, and Q. Chen. 2000. Ventilation and air quality in indoor ice skating ice skating, gliding along an ice surface on keellike runners known as ice skates. Skating as a Sport
Skating, besides being an important form of winter recreation and the essential skill in the game of ice hockey (see hockey, ice) has developed arenas. ASHRAE Transactions 160(2):339-46.
Yuan, X., Q. Chen, A. Moser, and P. Suter. 1992. Numerical simulation of air flows in gymnasia. Indoor Environment 1:224-33.
Operating Schedule Lighting Lighting Resurfacing Time (hour) Weekday Weekend Weekday 1 10% 10% 0% 2 10% 10% 0% 3 10% 10% 0% 4 10% 10% 0% 5 10% 10% 0% 6 10% 10% 0% 7 10% 100% 0% 8 10% 100% 0% 9 10% 100% 0% 10 10% 100% 0% 11 10% 100% 0% 12 10% 100% 100% 13 10% 100% 0% 14 100% 100% 100% 15 100% 100% 0% 16 100% 100% 100% 17 100% 100% 0% 18 100% 100% 100% 19 100% 100% 100% 20 100% 100% 100% 21 100% 100% 100% 22 100% 100% 100% 23 100% 100% 0% 24 100% 100% 100% Resurfacing Occupancy Occupancy Time (hour) Weekend Weekday Weekend 1 0% 0% 0% 2 0% 0% 0% 3 0% 0% 0% 4 0% 0% 0% 5 0% 0% 0% 6 0% 0% 0% 7 0% 0% 0% 8 100% 10% 20% 9 100% 10% 20% 10 0% 10% 20% 11 100% 10% 20% 12 100% 10% 20% 13 0% 10% 20% 14 100% 20% 20% 15 0% 20% 20% 16 100% 20% 20% 17 100% 20% 50% 18 100% 20% 50% 19 100% 20% 50% 20 100% 20% 50% 21 100% 20% 20% 22 0% 20% 20% 23 100% 20% 20% 24 0% 20% 20%
The total power input due to lighting is 28 kW (95.53 MBtu/h) and the maximum number of spectators is fixed at 200. The heat generated by the spectators is taken equal to 100 W (341.2 Btu/h) (ASHRAE 2005) and is assumed to be uniformly distributed over the stands. The resurfacing heat load is calculated according to chapter 34 of the 2002 ASHRAE Handbook--Refrigeration (2002) and is assumed to be uniformly distributed over the ice surface and over a time interval of ten minutes, resulting in a heat flux of 236 W/[m.sup.2] (74.8 Btu/h x [ft.sup.2]).
O. Bellache, PhD
N. Galanis, PhD
M. Ouzzane, PhD
R. Sunye, PhD
O. Bellache and M. Ouzzane are research scientists, R. Sunye is a project manager, and D. Giguere is a technical expert at the CANMET Energy Technology Centre-Varennes, Quebec, Canada. N. Galanis is a professor at the Department of Mechanical Engineering, Universite de Sherbrooke, Sherbrooke, Quebec “Sherbrooke” redirects here. For other uses, see Sherbrooke (disambiguation).
Sherbrooke (2006 population: 147,427) is a city in south-eastern Quebec, Canada, the only major city in the Eastern Townships. , Canada.
Table 1. Values of [phi], [[GAMMA].sub.[phi]], and [S.sub.[phi]] in Equation 1 Equation [phi] [[GAMMA].sub.[phi]] Mass 1 0 X-momentum U [mu] + [[mu].sub.t] Y-momentum V [mu] + [[mu].sub.t] Energy T [mu]/Pr + [[mu].sub.t]/[Pr.sub.t] Absolute humidity C ([mu] + [[mu].sub.t])/[[sigma].sub.c] Turbulent kinetic k [[mu].sub.t]/[[sigma].sub.k] energy Dissipation rate [epsilon] [[mu].sub.t]/[[sigma].sub.[epsilon]] Equation [S.sub.[phi]] Mass 0 X-momentum -[partial derivative]P/[partial derivative]x Y-momentum -[partial derivative]P/[partial derivative]y - [rho]g[beta](T - [T.sub.0]) - [rho]g[beta]*(C - [C.sub.0]) Energy [S.sub.T] Absolute humidity [S.sub.c] Turbulent kinetic G - [rho][epsilon] + [G.sub.B] energy Dissipation rate [[epsilon]([c.sub.[epsilon]1]G - [c.sub.[epsilon]2][rho][epsilon])/k] + [c.sub.[epsilon]3][G.sub.B]([epsilon]/k) [[mu].sub.t] = [rho][c.sub.[mu]][c.sub.d][k.sup.2]/[epsilon]; [Pr.sub.t] = 1 [G.sub.B] = -g[beta]([[mu].sub.t]/[Pr.sub.t])([partial derivative]T/ [partial derivative][x.sub.i]); G = [[mu].sub.t]([partial derivative][U.sub.i]/ [partial derivative][x.sub.j] + [partial derivative][U.sub.j]/ [partial derivative][x.sub.i]) x ([partial derivative][U.sub.i]/ [partial derivative][x.sub.j]) [c.sub.[epsilon]1] = 1.44; [c.sub.[epsilon]2] = 1.92; [c.sub.[epsilon]3] = 1.44; [c.sub.[mu]] = 0.09; [c.sub.d] = 0.1643; [[sigma].sub.k] = 1; [[sigma].sub.[epsilon]] = 1.3; [[sigma].sub.c] = 1 Table 2. Effect of Grid Points and Iterations on Calculated Results Mass Balance Energy Balance [summation]([dot.m.sub.ou] - [summation]([E.sub.ou] - [dot.m.sub.in])/[dot.m.sub.in] [E.sub.in])/[E.sub.in] Grid 100 x 50 0 0.02 [10.sup.4] iterations Grid 200 x 100 0 0.01 [10.sup.4] iterations Grid 100 x 50 0 0.02 [20.sup.4] iterations Grid 200 x 100 0 0.01 [20.sup.4] iterations Radiation Load, Condensation Load, W/[m.sup.2] W/[m.sup.2] (Btu/h x [ft.sup.2]) (Btu/h x [ft.sup.2]) Grid 100 x 50 47.7 11.8 [10.sup.4] (15.12) (3.74) iterations Grid 200 x 100 47.8 11.8 [10.sup.4] (15.15) (3.74) iterations Grid 100 x 50 47.7 11.8 [20.sup.4] (15.12) (3.74) iterations Grid 200 x 100 47.8 11.8 [20.sup.4] (15.15) (3.74) iterations Convection Load, Ground Load, W/[m.sup.2] W/[m.sup.2] (Btu/h x [ft.sup.2]) (Btu/h x [f.sup.2]) Grid 100 x 50 19.2 2.7 [10.sup.4] (6.08) (0.86) iterations Grid 200 x 100 19.3 2.8 [10.sup.4] (6.12) (0.89) iterations Grid 100 x 50 19.3 2.7 [20.sup.4] (6.12) (0.86) iterations Grid 200 x 100 19.3 2.8 [20.sup.4] (6.12) (0.89) iterations Refrigeration Load, W/[m.sup.2] (Btu/h x [ft.sup.2]) Grid 100 x 50 81.4 [10.sup.4] (25.81) iterations Grid 200 x 100 81.7 [10.sup.4] (25.91) iterations Grid 100 x 50 81.5 [20.sup.4] (25.84) iterations Grid 200 x 100 81.7 [20.sup.4] (25.91) iterations Table 3. Ice Sheet Loads, Base Case (#1) Daily Refrigeration Load W/[m.sup.2] kWh/[m.sup.2] (Btu/[ft.sup.2]) (Btu/h x [ft.sup.2]) Convection 0.475 (150.574) 19.8 (6.278) Radiation 1.045 (331.262) 43.5 (13.793) Condensation 0.260 (82.419) 10.8 (3.424) Resurfacing 0.470 (149.989) 19.6 (6.215) Heat gain 2.250 (713.245) 93.8 (29.743) above the ice