Short-term thermal dynamics in single U-tube borehole heat exchangers: an unbalanced trade-off between coefficient of performance and delivered energy under variable flow rate operation

Abstract

Variable-speed circulation pumps are common in ground-source heat pump (GSHP) installations, but the short-term response of borehole heat exchangers (BHEs) to variable flow is poorly resolved: line-source methods omit the in-borehole thermal capacity, and thermal-resistance-capacity (TRC) correlations fail at low flow. In this work, a transient single U-tube BHE model, Crank–Nicolson integrated, recomputes the convective coefficient and the fluid and pipe resistances each time step from a composite Nusselt correlation valid from stagnation to turbulence. The borehole is coupled to a heat pump through an effectiveness-NTU evaporator, so flow rate sets the approach temperature and hence the coefficient of performance (COP). The model is verified by independence studies and validated against an analytical solution, a finite-element simulation, a g-function and field data. Performance metrics for five 24h flow profiles (constant, square, sinusoidal, triangular, stepwise) sharing a mean flow rate of 0.30 kg s −1 are compared over time periods ranging between 24 h to 180 days, with the inlet supplied by the evaporator return rather than prescribed. No single profile leads on every measure. The square profile attains the highest COP, 3.43 against 3.25 for constant flow, and the highest system performance factor (SPF), yet is the least effective at converting circulated fluid into heat, with the energy-weighted effectiveness proposed here at 0.244 against 0.369, and delivers 66.9 against 126.8 kWh, 47% less. The optimum is sinusoidal, 0.375, delivering 125.5 kWh, within about 1% of constant flow. Constant flow maximizes delivered energy and the thermal-to-pumping energy ratio, 5363 against 785. COP and SPF are evaluated only while the compressor runs, so they reward profiles that idle; ranking flow strategies on them alone is unsafe. The trade-off is between instantaneous COP, which favors low-flow operation, and delivered energy, which favors steady flow at the mean rate; it is uneven, a 5.4% COP gain costing 47% of delivered energy.