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Abstract
In this article, the ASHRAE method for borehole heat exchanger field design is deeply discussed in order to trace its theory and physical meaning. The aim of the article is corroborate previous studies in order to demonstrate that the current version of the method is not suitable for a reliable sizing of the borehole field since the criteria for calculating the temperature penalty term fail to large extent from a correct estimation. Based on the above findings (demonstrated by a comprehensive comparison with reference results pertaining a vast number of borefield configurations), a new version of the temperature penalty calculation procedure is presented that is able to maintain the ASHRAE formalism and simplicity while enhancing the accuracy of the design results.
Nomenclature
| B | = | borehole separating distance [m] or [ft] |
| c | = | ground specific heat [J/(kg K)] or [Btu/(lb F)] |
| E1 | = | exponential integral in ILS model [–] |
| Forb | = | Fourier number based on BHE radius, Forb = αgrτ/rb2 [–] |
| FoH | = | Fourier number based on BHE depth, FoH = αgrτ/H2 [–] |
| g | = | multi-BHE temperature response factor [–] |
| G | = | ICS temperature response factor [–] |
| H | = | depth of Borehole heat exchangers [m] or [ft] |
| k | = | thermal conductivity [W/(m K)] or [Btu/(h ft F)] |
| L | = | overall length of borehole heat exchangers [m] or [ft] |
| = | heat transfer rate [W] or [BTU/h] | |
| = | heat transfer rate per unit length [W/m] or [BTU/(h ft)] | |
| r, R | = | radius, radial coordinate [m] or [ft] |
| rb | = | borehole radius [m] or [ft] |
| Rbhe | = | borehole thermal resistance [mK/W] or [(h ft F)/Btu] |
| T | = | temperature [°C] or [F] |
| Tgr,∞ | = | undisturbed ground temperature [°C] or [F] |
| Tp | = | temperature penalty [°C] or [F] |
| Tp1 | = | auxiliary excess temperature in ASHRAE method [°C] or [F] |
| = | Greek letters | |
| α | = | thermal diffusivity, α = k/(ρc) [m2/s] or [ft2 /s] |
| ρ | = | density [kg/m3] or [lb/ft3] |
| θ8 | = | excess temperature, EquationEquation 11 |
| τ | = | time [s] |
| = | Subscripts | |
| ave | = | average along all BHE in a BHE field |
| 8 | = | present article method |
| A | = | ASHRAE original method |
| gr | = | ground related |
| h | = | 6-hour period |
| m | = | 1-month period |
| N | = | 10 years + 1 month + 6 hours |
| ref | = | at the reference depth, Href = 100 m |
| nom, bldg | = | rated power of the heat pump, building side |
| tot | = | overall number of BHE |
| y | = | 10-year period |
Acknowledgments
Davide Rolando, PhD, is greatly acknowledged for his valuable contribution in developing the calculation method here described and in optimizing its constants. For this reason, the present method has to be referred as the Fossa and Rolando method.