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Performance of ice slurry as cooling fluid for an indoor ice rink

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Abstract

A slightly modified version of a previously published model calculating transient heat transfer under the ice of an indoor ice rink is used to evaluate the performance of two cooling fluids, a brine with 20 % calcium chloride (base case) and a calcium chloride ice slurry. Simulations are conducted for a typical meteorological year for Montreal, Canada and take into account heat entering the ice from above as well as surfacing operations and electrical underground heating used to avoid freezing which can damage the concrete slab. The results show that, for the same flow rate (28.5 l/s) and inlet temperature (−9 °C) of the cooling fluid, the ice slurry generates better ice quality (ice surface temperature is more uniform spacewise and less variable with time) but requires more pumping power. Parametric results obtained by decreasing the flow rate or by increasing the inlet temperature of the ice slurry indicate that it is possible to choose either of these operating parameters so that the resulting ice quality is better and the pumping power is lower than for the base case.

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Abbreviations

C :

Hydraulic resistance coefficient

c p :

Specific heat, in kilojoules per kilogram Kelvin

D :

Diameter, in meters

f :

Friction factor

h :

Specific enthalpy, in kilojoules per kilogram

L :

Length, in meters

M :

Mass, in kilograms

N p :

Number of passes

N t :

Number of tubes

\( \overset{\cdot }{m} \) :

Mass flow rate, in kilograms per second

P :

Pumping power, in Watts

ΔP :

Pressure, in kilopascal

Q :

Heat transfer rate, in kilowatts

R :

Thermal resistance, in Kelvin per kilowatts

Re :

Reynolds number

T :

Temperature, in degree Celsius

t :

Time, in seconds

V :

Velocity, in meters per second

x :

Mass concentration, in kilograms per kilogram

ρ :

Density, in kilograms per cubic meter

ϕ :

Volumetric ice concentration, in cubic meters per cubic meter

C:

Concrete

cf:

Cooling fluid

gr:

Ground

H:

Electrical heater

in:

Inlet of a zone

ice:

Ice surface

ins:

Insulation

out:

Outlet of a zone

s:

Solid particle

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Acknowledgments

The authors acknowledge the financial support of the Natural Sciences & Engineering Research Council (NSERC) of Canada.

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Authors and Affiliations

  1. Génie Mécanique, Université de Sherbrooke, Sherbrooke, QC, Canada, J1K2R1

    Simone Renaud-Boivin & Nicolas Galanis

Authors
  1. Simone Renaud-Boivin
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  2. Nicolas Galanis
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Corresponding author

Correspondence to Nicolas Galanis.

Appendix

Appendix

The coefficients in Eq. 5 are given by the following expressions:

$$ A(1.1)=\frac{{\left(M{c}_p\right)}_1}{\varDelta t}+\frac{1}{R_{\mathrm{ice}}} $$
(8)
$$ A(2.2)=-\left(\frac{{\left(M{c}_p\right)}_2}{\Delta t}+{\scriptscriptstyle \frac{1}{2}}{U}_2{S}_2+\frac{1}{R_{\mathrm{ice}}}+\frac{1}{R_{C1}}\right) $$
(9)
$$ A(3.3)=-\left(\frac{{\left(M{c}_p\right)}_3}{\varDelta t}+{\scriptscriptstyle \frac{1}{2}}{U}_3{S}_3+\frac{1}{R_{C1}}+\frac{1}{R_{C2}}\right) $$
(10)
$$ A(4.4)=-\left(\frac{{\left(M{c}_p\right)}_4}{\varDelta t}+{\scriptscriptstyle \frac{1}{2}}{U}_4{S}_4+\frac{1}{R_{C2}}+\frac{1}{R_{\mathrm{ins}}}\right) $$
(11)
$$ A(5.5)=-\left(\frac{{\left(M{c}_p\right)}_5}{\varDelta t}+{\scriptscriptstyle \frac{1}{2}}{U}_5{S}_5+\frac{1}{R_{\mathrm{ins}}}+\frac{1}{R_{\mathrm{sand}}}\right) $$
(12)
$$ A(6.6)=-\left(\frac{{\left(M{c}_p\right)}_6}{\varDelta t}+{\scriptscriptstyle \frac{1}{2}}{U}_5{S}_5+\frac{1}{R_{\mathrm{sand}}}+\frac{1}{R_{\mathrm{soil}}}\right) $$
(13)

Equivalent thermal capacities within Eqs. 8 to 13 are given by

$$ {\left(M{c}_p\right)}_1={\scriptscriptstyle \frac{1}{2}}{M}_{\mathrm{ice}}{c}_{p,\mathrm{ice}} $$
(14)
$$ {\left(M{c}_p\right)}_2={\scriptscriptstyle \frac{1}{2}}{M}_{\mathrm{ice}}{c_p}_{,\mathrm{ice}}+{\scriptscriptstyle \frac{1}{2}}{M}_{C1}{c}_{p,C1} $$
(15)
$$ {\left(M{c}_p\right)}_3={\scriptscriptstyle \frac{1}{2}}{M}_{C1}{c_p}_{,C1}+{M}_{cf}{c_p}_{, cf}+{\scriptscriptstyle \frac{1}{2}}{M}_{C2}{c_p}_{,C2} $$
(16)
$$ {\left(M{c}_p\right)}_4={\scriptscriptstyle \frac{1}{2}}{M}_{C2}{c_p}_{,C2}+{\scriptscriptstyle \frac{1}{2}}{M}_{\mathrm{ins}}{c_p}_{,\mathrm{ins}} $$
(17)
$$ {\left(M{c}_p\right)}_5={\scriptscriptstyle \frac{1}{2}}{M}_{\mathrm{ins}}{c_p}_{,\mathrm{ins}}+{\scriptscriptstyle \frac{1}{2}}{M}_{\mathrm{sand}}{c_p}_{,\mathrm{sand}} $$
(18)
$$ {\left(M{c}_p\right)}_6={\scriptscriptstyle \frac{1}{2}}{M}_{\mathrm{sand}}{c_p}_{,\mathrm{sand}}+{\scriptscriptstyle \frac{1}{2}}{M}_{\mathrm{soil}}{c_p}_{,\mathrm{soil}} $$
(19)

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Renaud-Boivin, S., Galanis, N. Performance of ice slurry as cooling fluid for an indoor ice rink. Energy Efficiency 7, 677–695 (2014). https://doi.org/10.1007/s12053-013-9247-1

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