Application and comparison of semi-empirical models for performance prediction of a kW-size reciprocating piston expander

Abstract

This work presents the modeling and performance prediction of a prototypal reciprocating piston expander in the kW range of power. Two semi-empirical models have been selected from the literature and opportunely adapted to the case of study, then calibrated and validated over a full set of available experimental data. The first modelling approach is based on polynomial correlations of the expander efficiencies and it has been extended to account for the heat losses to ambient. The second one consists of a lumped parameters approach, that uses a few key geometrical data of the expander and some physical equations to describe the expansion process. The aim of this study is to detect the best approach, between those selected, for the simulation of reciprocating expander adopted in micro-scale ORC systems; this can provide a helpful tool for predicting the performance of machines in off-design conditions, not requiring detailed information on its internal geometry. The calibration and validation procedures of the selected models have been performed thanks to an extensive experimental campaign on a test bench facility installed at the laboratory of the University of Bologna. Models comparison highlights that the lowest mean relative error value is obtained on the prediction of exhaust temperature, equal to 1 % and 2 % respectively for the polynomial and lumped model. Maximum relative errors are obtained in the prediction of rotational speed for the polynomial fitting model (equal to 10 %), and in the electric power output for the lumped approach (equal to 8 %). The global error function, calculated over the validation data set, is close to 5 % for both the applied modelling approaches. Within the calibration range, the semi-empirical models show similar performance results of the output variables (i.e. electric power output, isentropic electric efficiency, rotational speed and filling factor). Conversely, when compared outside of the calibration range, prediction maps can substantially differ: the polynomial fitting functions model proves to be less accurate in the unexplored range of working conditions, overestimating the expander rotational speed while underestimating the value of the filling factor at high pressure ratios, and overestimating the isentropic electric efficiency values at low pressure ratios.

Pressure Pulsation and Cavitation Phenomena in a Micro-ORC System

“…Commonly, the presence of simplified prototypes and/or different working conditions could determine several differences between the actual machine performance and the measured ones. To help the experimental analysis, a lumped-parameter model is often used for extending the analysis to other operating conditions or other fluids [7,8], increasing the design capabilities and limiting the cost and time.…”

Evaluate the validity of the empirical correlations of clearance and friction coefficients to improve a scroll expander semi-empirical model

“…The maximum deviation was found to be 5%, which means that this model has a very good accuracy [6]. Moreover, this semiempirical model can be adapted to screw expanders [9], [10], reciprocating piston expanders [11] and a roots expander [12] by using the same formulations.…”

Performance modelling and greenhouse impact assessment of a micro-ORC energy system working with HFCs, low GWP fluids and mixtures

“…The volumetric expander is simulated by means of the grey-box model, validated for the reference reciprocating expander in a previous work of the Authors [10]. The model follows a lumped parameters approach as illustrated by the scheme shown in Fig.…”

“…Equations of the model describe the internal expansion, the re-compression phenomena and additional characteristic power losses, such as under/overexpansion losses, pressure losses, internal leakages, heat dissipation, frictions and electro-mechanical conversion losses. The reader is invited to refer to [10] for a detailed description of the expander model. In this analysis the built-in volume ratio value is chosen equal to its optimum, which allows to obtain the maximum expander power output, as demonstrated in [4].…”