Energy optimization in ice hockey halls I. The system COP as a   multivariable function, brine and design choices
  This work is the first in a series of articles addressing the energy optimization in ice hockey halls. Here we adopt an analytical method, called functional optimization, to find which design and operating conditions maximize the Coefficient Of Performance of the entire cooling system (brine pumps and cooling tower), which we call ${\rm COP}_{sys}$. This is addressed as a function of several variables, like electric consumption and brine physical properties. By maximizing such function, the best configuration and brine choices for the system can thus be determined accurately and rigorously. We investigate the importance of pipe diameter, depth and brine type (ethylene glycol and ammonia) for average-sized ice rinks. An optimal brine density is found, and we compute the weight of the electric consumption of the brine pumps on ${\rm COP}_{sys}$. Our formulas are validated with heat flow measurement data obtained at an ice hockey hall in Finland. They are also confronted with technical and cost-related constraints, and implemented by simulations with the program COMSOL Multiphysics. The multivariable approach here discussed is general, and can be applied to the rigorous preliminary study of diverse situations in building physics and in many other areas of interest. 
Andrea Ferrantelli, Paul Mel\'ois, Miska R\"aikk\"onen and Martti   Viljanen
physics.gen-ph