A two-phase single-reciprocating-piston heat conversion engine: Non-linear dynamic modelling

Abstract

A non-linear dynamic framework is presented for the modelling of a novel two-phase heat engine termed ‘Up-THERM’, which features a single solid moving-part (piston). When applied across the device, a constant temperature difference between an external (low- to medium-grade) heat source and an external heat sink is converted into sustained and persistent oscillations of pressure and volumetric fluid displacement. These oscillations are transformed in a load arrangement into a unidirectional flow from which power is extracted by a hydraulic motor. The Up-THERM engine is modelled using a system of first-order differential equations that describe the dominant thermal/fluid processes in each component of the device. For certain components where the deviations from a linear approximation are non-negligible (gas spring in the displacer cylinder, check valves and piston valve, and heat exchangers), a non-linear description is employed. A comparison between the linear and non-linear descriptions of the gas spring at the top of the displacer cylinder reveals that the non-linear description results in more realistic predictions of the oscillation frequency compared to experimental data from a similar device. Furthermore, the shape of the temperature profile over the heat-exchanger surfaces is modelled as following a hyperbolic tangent function, based on findings from an experimental investigation. Following the validation of these important device components, a parametric study is performed on the Up-THERM engine model with the aforementioned non-linear component descriptions, aimed at investigating the effects of important geometric parameters and of the heat-source temperature on key performance indicators, namely the oscillation frequency, power output and exergy efficiency of the engine. The results indicate that the geometric design of the displacer cylinder, including the height of the gas spring at the top of the cylinder, and the heat-source temperature have the most significant influence on the performance of the engine. A maximum exergy efficiency of 2.8% and a maximum power output of 175 W are observed at the proposed operating temperature of 450 °C for a nominal Up-THERM design (based on the physical dimensions of a device prototype and water as the working fluid; the role of the working fluid is explored in follow-up paper Ref. [1]) but with shorter displacer cylinder gas-spring lengths relative to a nominal design. The results and insight can assist the further development of this technology, in particular as a prime mover in combined heat and power applications

Comparison of a Novel Organic-Fluid Thermofluidic Heat Converter and an Organic Rankine Cycle Heat Engine

“…The parameter β is related to the height of the heat exchanger where the temperature profile saturates, which is assumed to be at the maximum length of the heat exchanger. This temperature profile has been validated experimentally in Kirmse et al [17] and thus is deemed suitable for the present paper. As can be seen in Equation (3), the temperature of the heat-exchanger wall is dependent on the position y of the vapour-liquid interface.…”

“…Iterations are stopped when convergence is achieved. A detailed description of the calculation for the heat-transfer coefficient can be found in Kirmse et al [17] and Oyewunmi et al [18].…”

“…The piston valve in the displacer cylinder and the two check valves exhibit inherently non-linear behavior. The temperature profile in the heat exchanger walls is assumed to follow a hyperbolic tangent function, which has been validated experimentally in Kirmse et al [17]. Hence, these three components are modeled non-linearly.…”

“…Since the NIFTE modeling methodology has been validated against experimental data generated by a device prototype, it is regarded as an appropriate starting point for the modeling of the Up-THERM engine. The Up-THERM engine model is described in detail in Kirmse et al [17]. Oyewunmi et al [18] investigated the influence of different (especially organic) working fluids on the engine performance.…”

“…P th dV th (15) In the above equationẆ hm is the power output and P th dV th the exergy input into the cycle. The thermal pressure P th is the equivalent of the heat-source temperature in the fluid domain and the thermal volume equivalent to the entropy that is generated during heat addition in one cycle, see Equations (4) and (5).…”