A Hybrid Dynamic Model for the Thermal Compressor Heat Pump and Validation with Experimental Data ^†

Thermally driven heat pumps primarily use thermal energy to drive a compression cycle. The thermal energy can be waste heat, natural-gas combustion, or solar, helping increase efficiency and reduce greenhouse-gas emissions. We study a thermal compressor heat pump (TCHP) in which Stirling-type thermal compressors (TCs) are heat-driven rather than electrically driven, delivering a nominal heat capacity of 8 kW with CO${}_2$ as the refrigerant. Unlike most existing dynamic models of CO${}_2$ cycles, which focus on electrically driven or single-stage systems, this work targets a heat-driven multi-stage configuration and includes transient validation. Like any vapor compression cycle (VCC), a TCHP requires a dynamic model for control and optimization; its predictive reliability must be validated on experimental data. We therefore describe the test bench and performance expressions, collect steady-state and transient datasets, and derive a hybrid dynamic model: finite-volume (FV) differential equations for slow components and quasi-static submodels (linear regressions and correlations) for fast elements. The contribution of this work is the development and experimental validation of a hybrid FV model for a multi-stage heat-driven CO${}_2$ TCHP. Validation against both steady-state and transient datasets shows good agreement. On 15 steady-state operating points, the model reproduces pressures within ∼1 bar mean absolute error (MAE) and system-level performance (total recovered heat, $CO{P}_{\mathrm{th}}$) within ∼6% mean absolute percentage error (MAPE), with $R^2\gtrsim 0.8$; component heat-rate predictions are within ∼20% MAPE. Under transient step tests on expansion valve openings and burner fan speed, the thermal COP and total recovered heat track within $4\%$ MAPE (up to $R^2=0.96$), pressures within $1.5$ bar MAE, and the evaporator heat rate within 14–$22\%$ MAPE.