Assemblies of heat pumps served by a single underground heat exchanger M.R. Errera a , S. Lorente b , A. Bejan c,⇑ a Federal University of Paraná, Department of Environmental Engineering, Curitiba, Paraná 81531-980, Brazil b Université de Toulouse, UPS, INSA, LMDC (Laboratoire Matériaux et Durabilité des Constructions), 135, avenue de Rangueil, F-31 077 Toulouse Cedex 04, France c Duke University, Department of Mechanical Engineering and Materials Science, Durham, NC 27708-0300, USA article info Article history: Received 11 February 2014 Accepted 14 March 2014 Keywords: Constructal design Heat pumps Geothermal Ground coupled Sustainable communities Urban design abstract In this paper we document the relationship between complex flow architecture and global performance for assemblies of heat pumps coupled thermally with the ground through a single U-shaped loop with circulating fluid. The assemblies vary according to heat pump numbers, sizes and locations along the loop. They are classified in a systematic way, and their performance is documented in three classes of designs: assemblies of heat pumps of the same size, heat pumps distributed equidistantly, and large numbers of heat pumps distributed almost continuously on a long loop. The work is based on numerical simulations, and on an analysis that holds in the limit of heat pumps distributed continuously. The rela- tionship between flow architecture and global performance (heat transfer density) serves as guide for the energy design of high-density urban settlements in the future. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction There is an increasing interest in the future of urban design as a growing vasculature with high-density transport ranging from building energy design (heating, air conditioning) to power distri- bution, transportation, and communications. The future points toward thicker urban settlements, and this means even higher den- sities of transport. One important class of high-density designs are buildings con- nected thermally to the ground [1–25]. The connection is effected by heat pumps that deposit or extract heat through fluid loops bur- ied in the ground. As neighborhoods become denser, and as the inhabited space expands vertically (above and below ground), the land area with which the buildings are coupled becomes essen- tial. This is why in Ref. [26] we proposed the idea of coupling two heat pumps in a single underground heat exchanger. We showed how the heat exchanger interacts with the soil volume, and that heat pumps of different sizes may operate better when they share a single underground loop. We also reported the effect of the pres- sure losses and overall performance of the design. In this paper we consider the design of assemblies of multiple heat pumps that operate while connected to a straight single loop underground heat exchanger (Fig. 1). The degrees of freedom of the design are the sizes of the heat pumps and the positions of their connections along the loop. We first consider assemblies with equal-size heat pumps and with variable connecting locations along the loop. We then position the heat pumps equidistantly along the loop and vary their sizes. The number of heat pumps varies from 1 to 4. Finally, we consider assemblies in the limit of large numbers of heat pumps distributed almost continuously on a long loop. In accord with constructal design [27,28] we seek the trends in how the global performance of the design depends on the flow architecture of the assembly. 2. Model Consider a group of buildings that use heat pumps to extract heat from the ground by sharing the same underground heat exchanger (Fig. 1). The limiting case is a single heat pump operat- ing with its own heat exchanger (configuration 1A1 in Table 1). More complex assemblies consist of two or more heat pumps dis- tributed along longer heat exchangers. We model the buried heat exchanger as a hairpin-shaped pipe. Heat pumps are connected to the loop on one leg for intake, and on the opposite location on the other leg to retrieve the working fluid. Therefore, in the intake leg the mass flow rate increases along the direction from the first to the n th heat pump, as more fluid is added in each. The mass flow rate decreases after the stream passes the U-turn (Fig. 2). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2014.03.039 0017-9310/Ó 2014 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. Tel.: +1 919 660 5309; fax: +1 919 660 8963. E-mail address: dalford@duke.edu (A. Bejan). International Journal of Heat and Mass Transfer 75 (2014) 327–336 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt