Abstract
Experimental data is often the result of long and costly experimentations. Many times, measurements are used directly without (or with few) analysis and treatment. This paper, therefore, presents a detailed methodology to use steady-state measurements efficiently in the analysis of a thermodynamic cycle. The reconciliation method allows to correct each measurement as little as possible, taking its accuracy into account, to satisfy all constraints and to evaluate the most probable physical state. The reconciliation method should be used for multiple reasons. First, this method allows to close energy and mass balances exactly, which is needed for predictive models. Also, it allows determining some unknowns that are not measured or that cannot be measured precisely. Furthermore, it fully exploits the collected measurements with redundancy and it allows to know which sensor should be checked or replaced if necessary. An application of this method is presented in the case of a reversible HP/ORC unit. This unit is a modified heat pump which is able to work as an organic Rankine cycle by reversing its cycle. Combined with a passive house comprising a solar roof and a ground heat exchanger, it allows to get a positive energy building. In this study case, the oil mass fraction is not measured despite its strong influence on the results. The reconciliation method allows to evaluate it. The efficiency of this method is proven by comparing the error on the outputs of steady-state models of compressor and exchangers. An example is given with the prediction of the pinch-point of an evaporator. In this case, the normalized root mean square deviation (NRMSD) is decreased from 14.3 to 4.1 % when using the reconciliation method. This paper proves that the efficiency of the method and also that the method should be considered more often when dealing with experimentation.
Highlights
Numerical values are always affected by random errors plus gross errors
It fully exploits the collected measurements with redundancy and it allows to know which sensor should be checked or replaced if necessary. An application of this method is presented in the case of a reversible heat pump/organic Rankine cycle (HP/ORC) unit. This unit is a modified heat pump which is able to work as an organic Rankine cycle by reversing its cycle
This paper presents the application of a mathematical tool, called the reconciliation method (RM)
Summary
Numerical values are always affected by random errors plus gross errors (error that cannot be explained with statistical distribution). The measurements have to be validated: energy and mass balances have to be verified taking into account the propagation of errors due to measurement devices This step insures the quality of the data, but is necessary to apply correct physical constraints (2) in the reconciliation method. Mev;w:cp;w: Tev;w;su À Tcd;w;ex 1⁄4 m_ r hev;ex ÀÀhev;su þ m_ oil:cp;oil: Tev;ex À Tev;su ð8Þ mcd;w:cp;w:ðTcd;w;ex À Tcd;w;suÞ 1⁄4 mr hcd;su À hcd;ex þ moil:cp;oil:ðTcd;su À Tcd;exÞ ð9Þ Assuming these assumptions, 5 constraint equations allows exploiting the redundancy of the measurements. The number of unknowns is equal to 29: there are 21 measurements to reconcile, plus two additional variables (expander heat transfer coefficient and ambient temperature), plus the oil fraction and 5 Lagrange multipliers (2). The redundancy level is equal to the number of constraints in this case, 6
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