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6 L. Guillaume et al. / Applied Energy xxx (2016) xxx–xxx Finally it is proposed to compare both fluids for the same low and high pressure levels to investigate the impact of the fluid on the turbine performance in terms of power output, isentropic effi- ciency, mass flow rate, rotational speed and lubrication mass flow rate. Twenty-four experimental points were performed for this comparison, twelve with each fluid. 3. Theory/calculation Firstly the energy balance over the system components is inves- tigated, to cross-check the precision and the quality of the mea- surements. This step, although often overlooked, is of primary importance because of the numerous measurement issues that can arise in experimental campaigns. Then the three mass flow rates required to investigate the turbine performance are detailed and the reduced (or corrected) mass flow rate, which will be useful in the comparisons of the tur- bine performance proposed in this study for the two fluids, is defined. Finally, the efficiencies of the rotating machines and of the ORC system are defined in order to compare, for both fluids, the perfor- mance achieved according to the different test conditions. 3.1. Thermal energy balance Possible unbalances can indicate measurement errors or uncon- sidered parasitic phenomena such as ambient losses. The energy balance over the components is calculated as follow: Q_amb þErþW_ sh 1⁄4m_sf cpsf ðTsf;I Tsf;IIÞm_ ðhwf;II hwf;IÞ ð1Þ where hI ; T I and hII ; T II are the inlet (I) and the outlet (II) enthalpy and temperature values of both the working fluid (wf) and the sec- ondary fluid (sf). Specific enthalpies are computed using the open- source CoolProp library [26]. m_ sf and cp;sf are the mass flow and the specific heat capacity of the secondary fluid while m_ is the working fluid mass flow rate. Q_ amb corresponds to the heat ambient losses of the component, Er is the measurement error and W_ sh is the shaft power supplied or consumed by the component. 3.2. Mass flow rates The flow sent by the pump is split in three parallel flows: the main flow which is expanded in the turbine (m_ tur ), the flow required for the lubrication of the bearings (m_ lub ) and the flow required for the cooling of the generator (m_ gen). These mass flow rates are measured using Coriolis flow meters and the total mass flow rate can therefore be computed as follow: m_ 1⁄4m_tur þm_lub þm_gen ð2Þ This total mass flow rate is considered in the definitions of the effi- ciency of both the pump and the turbine. These components are studied here as systems or black boxes for which all the losses are taken into account. It means, for the pump system: the frequency drive, electrical motor and pump losses. And it means, for the expansion machine system: the turbine, bearings and generator losses. 3.3. Reduced mass flow rate The reduced mass flow rate of the turbine is defined as follow: _ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi M_co1⁄4Mtur Twf;ex;tur 3.4. Pump efficiency The pump performance was evaluated in a dedicated study. For the needs of the current comparison, a semi-empirical model of the pump, taking into account the leakage and the mechanical losses is used. So the power consumption of the pump, according to the pressure difference between the inlet and outlet and to the mass flow rate, can be calculated using the following isentropic and vol- umetric efficiency definitions: es;pp 1⁄4 ev;pp 1⁄4 W_ m_ðh h Þ wf ;s;pp 1⁄4 W_ el;pp wf ;ex;s;pp W_ el;pp wf ;su;pp ð4Þ ð5Þ m_ qwf;su Nrot;pp Vs;pp 3.5. Efficiency of the turbine-generator set In a first approach, a global efficiency of the turbine-generator set is used to characterize the performance of the component. It is defined through Eq. (6). Then, in order to investigate the poten- tial of improvement of the set, the efficiency of each of the three main components constituting the set (i.e., the turbine, the bear- ings system and the generator), as depicted in Fig. 14, is defined. eoverall 1⁄4 W_ el;tur 1⁄4 W_ el;tur ð6Þ W_ wf ;s;tur m_ tur ðhwf ;su;tur hwf ;ex;s;tur Þ The geometry of the turbine being unknown, it is proposed to use the static-to-static definition (7) of the isentropic efficiency of the turbine instead of the total-to-static definition that should be used for a single stage turbine. W_ etur;is 1⁄4 sh ð7Þ The enthalpy increase of the working fluid from the inlet to the outlet of the bearings system can be evaluated based on the mea- surements. This enthalpy increase is the result of internal losses in the bearings due to frictions and to the injection of liquid but is also the consequence of a heat transfer by convection between the fluid expanded in the turbine and the fluid lubricating the bear- ings. Considering these phenomena indivisible in the scope of this paper, the bearing efficiency is defined as follow: _ elub 1⁄4 Wsh m_ lub ðhwf;ex;lub hwf;su;lubÞ ð8Þ W_ sh In the same way, the enthalpy increase of the working fluid from the inlet to the outlet of the generator can be evaluated and the efficiency of the generator can be calculated. egen 1⁄4 W_ el;tur ð9Þ W_ sh m_ lub ðhwf;ex;lub hwf;su;lubÞ Finally, these three efficiencies can be linked to the global effi- ciency (6) through Eq. (10). eoverall 1⁄4 etur;is elub egen ð10Þ 3.6. Cycle efficiency The cycle efficiency is calculated based on the first law of thermodynamics. m_ tur ðhwf;su;tur hwf;ex;s;turÞ ð3Þ gcycle 1⁄4 W_ W_ el;tur el;pp ð11Þ Pwf ;ex;tur Q_ e v Please cite this article in press as: Guillaume L et al. Performance of a radial-inflow turbine integrated in an ORC system and designed for a WHR on truck application: An experimental comparison between R245fa and R1233zd. Appl Energy (2016), http://dx.doi.org/10.1016/j.apenergy.2016.03.012PDF Image | WHR on truck ORC radial inflow turbine integrated
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