(734d) Model-Based Analysis of a Thermofluidic Engine for Low-Grade Heat Recovery: Accounting for Irreversible Thermal Losses

The Non-Inertive-Feedback Thermofluidic Engine (NIFTE) is a two-phase thermofluidic oscillator that can convert low-grade heat into useful mechanical work. It consists of one hot and one cold heat exchangers alongside several compartments as illustrated on Fig. 1. The working fluid undergoes cyclic condensation and vaporization phases by contacting with the heat exchangers, which induce sustained fluid oscillations. Most previous mathematical models proposed to analyse the dynamic behaviour of NIFTE have considered linear descriptions [1-4]. These linear models provide useful insights about the operation of NIFTE, e.g. in terms of the minimum temperature difference required, the oscillation frequency and exergetic efficiencies; but despite their ability to give accurate quantitative predictions, they fail to explain the sustained robust periodic oscillations that have been observed experimentally on a NIFTE prototype. This is the so-called limit-cycle behaviour, which is essentially a nonlinear phenomenon. Markides et al. [5] first proposed a nonlinear inertive NTP model for NIFTE, and this model has been validated experimentally. Later, Wang et al. [6] conducted an optimization-based analysis using this model and they predicted the co-existence of multiple cyclic steady states for certain NIFTE configurations.

However, none of the previous (linear or nonlinear) models account for the thermal losses in the device, which can result in significant overestimation of the efficiencies reported in experiments. Solanki et al. [7,8] refined several linear models models by incorporating a dissipative thermal loss parameter to account for (i) the loss of exergy arising from irreversible heat transfer, and (ii) alternating parasitic condensation and re-evaporation within the engine. This refinement enables much closer predictions of the exergetic efficiencies of NIFTE, while having a limited effect on the predicted oscillation frequencies.

The main development in this work is a description of thermal losses in the nonlinear inertive NTP model of NIFTE to improve its predictive capability – namely, the inertive model with thermal loss (NTP-TL). We build on the electric-circuit analogy previously developed for the NTP model, by adding extra resistor and capacitor elements to describe the overall irreversible thermal losses. It is found that the NTP-TL model provides much smaller exergetic efficiencies in agreement with experimental observations, and also improves the oscillation frequency predictions compared with its linear counterparts. Finally, we apply an optimization-based approach based on NTP-TL to detect and characterize the cyclic steady states corresponding to various engine configurations, and we also conduct a (global) sensitivity analysis to determine those (combinations of) parameters having the greatest effect in terms of the exergetic efficiency. Overall, the NTP-TL model enables a more realistic understanding of the performance of the NIFTE prototype, and provides useful insights on how to design better prototypes.

References:
[1] Smith, T.C.B: Thermally driven oscillations in dynamic applications. PhD thesis. Cambridge: University of Cambridge, UK. 2006

[2] Markides, C.N. and Smith, T.C.B.: A dynamic model for the efficiency optimization of an oscillatory low grade heat engine. Energy, 36, 6967-6980, 2011

[3] Solanki, R., Galindo, A., and Markides, C.N.: Dynamic modelling of a two-phase thermofluidic oscillator for efficient low grade heat utilization: Effect of fluid inertia. Applied Energy, 89(1), 156-163, 2012

[4] Solanki, R., Galindo, A., and Markides, C.N.: The role of heat exchangeon the behaviour of an oscillatory two-phase low-grade heat engine. Applied Thermal Engineering, 53, 177-187, 2013.

[5] Markides, C.N., Osuosslale, A., Solanki, R., and Stan, G.B.V.: Nonlinear heat transfer processes in a two-phase thermofluidic oscillator. Applied Energy, 104, 958-977, 2013

[6] Wang, Y., Markides, C.N., and Chachuat, B.: Optimization-based Investigations of a Thermofluidic Engine for Low-grade Heat Recovery. Manuscript accepted by ADCHEM 2018

[7] Solanki, R., Mathie, R., Galindo, A., and Markides, C.N.: Modelling of a two-phase thermofluidic oscillator for low-grade heat utilisation: Accounting for irreversible thermal losses. Applied Energy, 106, 337-354, 2013

[8] Markides, C.N., Solanki, R., Galido, A.: Working fluid selection for a two-phase thermofluidic oscillator: Effect of thermodynamic properties. Applied Energy, 124, 167-185, 2014