Available online at www.sciencedirect.com ScienceDirect Energy Procedia 00 (2017) 000 000 www.elsevier.com/locate/procedia IV International Seminar on ORC Power Systems, ORC2017 13-15 September 2017, Milano, Italy Impact of major leakages on characteristics of a rotary vane expander for ORC Vaclav Vodicka a, *, Vaclav Novotny a,b, Jakub Mascuch a, Michal Kolovratnik b a University Centre for Energy Efficient Buildings, Czech Technical University in Prague, Trinecka 1024, Bustehrad, 27343, Czech Republic b Faculty of Mechanical Engineering, Czech Technical University in Prague, Technicka 4, Prague 6, 166 07, Czech Republic Abstract Volumetric expanders are used for low to medium power output ORC applications. For low power output ORCs (< 10 kw), rotary vane expanders represent a suitable choice. Their isentropic efficiency is often reported as the most important or even the only metrics for comparison. Such approach however neglects the effect of leakages within the expander on the rest of the cycle, especially on the evaporator pressure. Filling factor of rotary vane expanders may be affected, among other leakages, by delayed closure of working chamber. This work describes a semi-empirical model with two different leakages lumped leakage area between inlet and outlet and leakage between working chambers due to delayed contact of vane and stator. Primary purpose of the model is to demonstrate the effect of the delayed chamber closure. Results of the model for several case scenarios are presented, showing an impact of these leakages on an overall cycle performance, isentropic efficiency and filling factor. It is demonstrated that isentropic efficiency of the rotary vane expander might not be always sufficient to compare vane expanders or their modifications even within a same ORC. 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the IV International Seminar on ORC Power Systems. Keywords: ORC; rotary; vane; expander; filling factor; leakages * Corresponding author. Tel.: +420-22435-6722 E-mail address: vaclav.vodicka@cvut.cz 1876-6102 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the IV International Seminar on ORC Power Systems.
2 V. Vodicka et al. / Energy Procedia 00 (2017) 000 000 1. Introduction Low power applications are one of the directions in current energy research [1]. Particularly there is also a demand for units with power output of less than 10 kw. For these applications in a field of heat to electricity conversion, thermodynamic cycles based typically on an ORC are considered as the most perspective and therefore most of the research is focused on them. A crucial component of the ORC is an expander, for given small power outputs typically realized by volumetric expansion machines [2]. Rotary vane expanders (RVE) could be a suitable option for simple and low cost ORCs because of their simple design and low manufacturing costs. On the other hand, they exhibit lower isentropic efficiency compared to other volumetric expanders due to leakages and higher friction losses [3]. Leakages have significant impact not only on isentropic efficiency of the expander but also on a whole cycle due to possible reduction of evaporator pressure. Volumetric performance of the expander is often expressed by a filling factor. Rotary vane expanders can suffer by vane chatter [4]. It means that the vanes are not in a permanent contact with the stator surface. This can affect a filling phase and cause leakages across the vanes between adjacent chambers. The effect can rapidly influence the filling factor and the volumetric ratio of the expander but the impact on isentropic efficiency and power output may be much smaller. In this work we present a simple semi-empirical model of RVE with two different leakages lumped leakage area between the inlet and the outlet and a leakage between working chambers due to delayed contact of a vane and the stator during the filling phase of the RVE. Primary purpose of the model is to demonstrate the effect of these two leakages and their strong impact on specific characteristics of the expander. Finally, several model results are presented including a case demonstrating the same ORC unit operating with two different expanders both with the same isentropic efficiency and having different power production. Nomenclature Subscripts c number of chambers (-) c chamber h specific enthalpy (J kg -1 ) ev evaporator p pressure (Pa) exp expander r ratio (-) in inlet v specific volume (m 3 kg -1 ) init initial A area (mm 2 ) is isentropic F force (N) leak leakages FF filling factor (-) out outlet / output Ṁ mass flow rate (kg s -1 ) rot rotational N speed (rpm) su supply P mechanical power (W) theor theoretical Q heat flux (W) v volumetric V volume (m 3 ) wf working fluid η efficiency (-) 2. Leakages within a rotary vane expander The problem of leaks within the rotary vane expander is very complex. Leakages are influenced by a variety of parameters such as pressure ratio, number, size and shape of the leakage paths, thermodynamic properties of a working fluid, proportion of lubricating oil in the working fluid, etc. The vane expander is a periodically working machine, so many of these parameters change during the working cycle. The flow through different leakage paths will therefore also change. In simple models of volumetric expanders, the leakage description is simplified. In the scroll expander model described by Lemort et al. [5], all the leaks are replaced by one main flow area through which the working substance flows continuously. Although this is a significant simplification, Lemort et al. has shown that
V. Vodicka et al./ Energy Procedia 00 (2017) 000 000 3 in terms of overall machine behavior the given description is sufficient (deviation of predicted and measured mass flow rate was several percent). Leakages within RVE can strongly affect not only expander characteristics but also cycle conditions. Equation (1) describes the evaporator energy balance. It is evident that in case of constant heat input and constant enthalpy of the working fluid entering the evaporator, the output enthalpy of the vapor from the evaporator is a function of the mass flow of the working fluid. M wf hout, ev hin, ev ) Qin, ev ( (1) Thus, if there is no control valve between the evaporator and the expander, and if the heat input, superheat of the vapor entering the expander and the condensing pressure are kept constant, the pressure of vapor entering the expander is dependent on the mass flow rate through the expander. Assuming steady-periodic conditions, total mass flow rate through the expander can be defined as a sum of a theoretically displaced mass flow rate and a mass flow rate through the leaks (Eq. (2)). M wf Mtheor. M leak (2) Theoretically displaced mass flow rate (given by Eq. (3)) depends on the rotational speed, initial volume of a working chamber, number of chambers and on a specific volume of the vapor inside a working chamber after the chamber is closed. M theor, exp V c, init v N c, init rot, exp 60 c (3) Mass flow rate through the leaks is usually modeled as a simple isentropic flow through a nozzle [5]. It depends mainly on a pressure difference across the nozzle and on a flow area. It follows from the above that the evaporation pressure can be highly influenced by the rotational speed of the expander and by the leakages. RVEs are characterized by built-in volumetric ratio r v (see Eq. (4)). If they are working in a cycle with offdesign conditions (the expander outlet/inlet specific volume ratio differs from the built-in volumetric ratio), over or under-expansion occurs which results in thermodynamic losses and lower isentropic efficiency. Theoretically, the RVE with a high leakage rate can affect its inlet pressure in that way that the inlet pressure is much lower and the expander outlet/inlet specific volume ratio approaches the built in-volumetric ratio. This results into lower underexpansion losses. The isentropic efficiency (defined in Eq. (5)) of such expander can be therefore in some cases almost constant even if the leakage rate increases. r v Vc, out (4) V c, init Pmech, exp is (5) M h h ) wf ( in, exp out, is Therefore a volumetric performance of the RVE is better represented by a filling factor, which is defined in Eq. (6). It is a ratio between an actual and a theoretically displaced mass flow rate.
4 V. Vodicka et al. / Energy Procedia 00 (2017) 000 000 FF M V wf c, init v N su 60. (6) c rot,exp Total mass flow rate through the expander decreases with an inlet pressure drop. Thus, for a constant rotational speed and inlet vapor superheat, the filling factor increases with the leakage area inside the expander and decreases with the inlet pressure drop. There are several leakage pathways in the RVE [6] which are shown in Fig. 1a. The most significant are: Clearance between the rotor and the stator in a sealing arc area Clearance between the stator and the rotor faces Around the tips of the vanes if there is a poor or even no contact between the vane tip and stator surface Around the vane sides Other negligible Fig. 1. (a) Main leakage pathways of rotary vane expanders (b) Simplified scheme of main forces acting on a vane, detail of an inlet region Yang et al. [7] reported that the sealing arc leakages are the most important even in their case of very small ratio of stator axial length to stator diameter. The second most important leakage was through a clearance between stator and rotor faces. However, the reported data may not be fully transferrable to RVEs with other geometry and working conditions. These two leakage pathways behave in a similar way as can be seen in Fig. 1a. Both leaks allow the working fluid to flow directly from the high to the low pressure area. Leakages around the vanes (and partially also leakages between the stator and rotor faces) allow the working fluid to flow from a chamber with high pressure to another chamber with low pressure. This affects the whole expansion process, so that the course of the pressure decrease within the working chamber may be different compared to the isentropic expansion. Yang et al. [8] and originally Badr et al. [6] also experimentally showed that a problem with the loss of contact between the vane and stator surface can occur in a RVE. The probable reason is that the force resulting from a pressure difference above and below the vane is higher than centrifugal force acting on the vane, see Fig. 1b. When the centrifugal force acting on the vane is higher than the force from a pressure difference, the vane touches the stator surface and closes the chamber. This results in the vane chatter. Moreover, the vane can close the chamber much later. This phenomenon can of course negatively affect RVE characteristics. Delayed closure of the chamber from the working fluid supply results in a longer filling phase and larger initial volume of the working chamber V c,init. Thus the resulting effective volumetric ratio of the RVE can be significantly lower, which affects the under-expansion losses. Moreover, the mass flow rate displaced by the expander is significantly higher as well as the filling factor.
V. Vodicka et al./ Energy Procedia 00 (2017) 000 000 5 If vanes lose contact with the stator surface during expansion, excessive leakages between adjacent chambers can occur, which again affects the pressure decrease within the chamber. As a result of the leakages that affect the expansion process, more work per revolution can be done. However, the total mass flow rate through the expander will be also higher. If the inlet pressure of the vapor flowing into the expander remained constant, it would certainly mean lower isentropic efficiency. In case that the inlet pressure is coupled with the total mass flow rate through the expander, the isentropic efficiency may remain almost constant. 3. Model description The aim of the model is to demonstrate the approximate behavior of the expander and its effect on the cycle if it is influenced not only by common leaks but also by loss of contact of the vanes with the stator during the filling phase. A coupled system of evaporator, expander and condenser was considered according to the Fig. 2. For the evaporator a constant heat input of 50 kw was considered to be transferred to a working fluid hexamethyldisiloxane (MM). The liquid MM enters the evaporator at constant temperature of 80 C. The condenser keeps constant outlet pressure, here for condensing temperature of 80 C it is 53.7 kpa. Vapor superheat at the expander inlet is kept also constant at 15 K above saturation, so the inlet pressure is dependent on the mass flow rate through the expander. These parameters were chosen according to an existing CHP unit based on an ORC at UCEEB CTU in Prague. The expander model, schematically depicted in Fig. 2 between the evaporator and the condenser, is represented by two inlet pressure drops represented by flow area A 1 (inlet manifold) and A 2 (chamber inlet) see Fig. 1b, by an ideal volumetric expander and by a bypass to account for the leakages represented by a flow area A leak. Fig. 2. Mathematical model of RVE with evaporator and condenser Following assumptions were taken. Main leakages (through the sealing arc and through the clearance between the stator and rotor faces) are for simplicity modeled together as an isentropic flow through a nozzle of the area A leak, which is sufficient given their nature and the purpose of this model. As was shown on the expander geometry in Fig. 1b, both leakages bypass the expander before chamber inlet pressure drop. Leakages around the rotor faces occur also after the flow passes chamber inlet (represented by A 2, see Fig. 1b) but the impact of the pressure drop at the chamber inlet to the mass flow rate through this leakage path is very low, as long as this pressure drop is small. Delayed closure of the chambers is also considered, which means higher initial chamber volume V c,init and thus lower effective volumetric ratio r v as the outlet volume of the chamber is always the same. Leakages during the expansion process (after a vane closes the working chamber) and other minor leakages are not considered. It is clear that the rotational speed of the expander has a great impact on the isotropic efficiency and the filling factor. However, the aim is to show only the effect of leaks, therefore the rotational speed is considered to be constant in the model. The expander carries out an isentropic expansion to a pressure which is determined by the inlet pressure, inlet temperature and volumetric ratio of the expander. After that occurs an adiabatic expansion at constant chamber
6 V. Vodicka et al. / Energy Procedia 00 (2017) 000 000 volume. Depending on a value of the pressure in the chamber after the isentropic expansion, under or over-expansion loss takes effect. Friction of vanes was not considered because it should be approximately constant when the rotational speed is constant. Additionally, it has practically no effect on the leakages or the volumetric ratio. All the input parameters for the expander model were chosen according to an existing RVE of own design that is used within the ORC at UCEEB CTU in Prague. Table 1. Input parameters for the expander model Parameter Value Nominal initial chamber volume (cm 3 ) V c, init 15.7 Final chamber volume (cm 3 ) V c, out 37.7 Nominal volumetric ratio (-) r v 2.4 Number of vanes / working chambers (-) c 8 Rotational speed (min -1 ) N rot 3000 Inlet manifold flow area (mm 2 ) A 1 785 Chamber inlet flow area (mm 2 ) A 2 375 In the model the mass flow rate through the inlet pressure drops is modelled as an isentropic flow through a constricted area. Total mass flow rate through the expander is given by Eq. (2) and (3). The expander power output is determined from isentropic expansion and contribution of under- or over-expansion. Similar model was described by Lemort et al. [5]. Modelling was performed for several cases where the leakage flow area A leak and expander effective volumetric ratio r v (which influences initial chamber volume V c,init ) were the input parameters for the model. As written above, these parameters simulated the leaks within the expander and the delayed contact of the vanes and the stator at the end of chamber filling. The presented model deliberately does not include a model of friction of vanes and other mechanical losses, a model of outlet pressure drop and of other losses that may occur within a real rotary vane expander. These losses would unnecessarily complicate the problem of volumetric losses and make it difficult to understand the presented results. 4. Model results and discussion Using the above mentioned assumptions and the mathematical model, the following results were obtained. Figure 3a shows the impact of the leakage area on the expander inlet pressure, isentropic efficiency, filling factor and power output, while volumetric ratio is kept constant at r v = 2.4. It means that the working chambers are closed properly. It can be seen that with an increasing leakage area A leak, the inlet pressure, the isentropic efficiency and the expander power output are decreasing. Of course, the filling factor is increasing. Another situation occurs if the leakage area is fixed at A leak = 35 mm 2 and the value of the volumetric ratio r v starts to decrease (see Fig.3b). It means that in addition to common leaks, the expander exhibits a problem with a loss of contact between the vanes and the stator and the working chambers are closed later. With decreasing volumetric ratio r v, the inlet pressure is decreasing and the filling factor is increasing again. The decrease in the expander power output is not too large at first and the curve of isentropic efficiency is surprisingly flat. This is because the under-expansion losses are decreasing, although the total mass flow rate through the expander and the filling factor are greater with lower r v. Note that if the leakage area A leak was lower, the curve of isentropic efficiency would begin to show a slightly declining trend. Numerical results for several cases are summarized in Tab. 2. The first case corresponds to a properly working expander with no loss of contact between the vanes and the stator and with no leakages. The filling factor is lower than one because of the inlet pressure drop. Isentropic efficiency is affected by under-expansion losses because the built-in volumetric ratio of the expander is too low (the expander inlet pressure is too high respectively). In cases 2 and 3, the filling factor of the expander is the same although the higher mass flow rate and the lower expander inlet
Isentropic efficiency Inlet pressure [MPa] Expander performance [kw] Filling factor Isentropic efficiency Inlet pressure[mpa] Expander performance [kw] Filling factor V. Vodicka et al./ Energy Procedia 00 (2017) 000 000 7 pressure are caused by different problems. In case 2, the expander is affected only by the delayed chamber closure, whereas in case 3, the expander is affected only by the larger leakage area A leak. 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 Fig. 3. (a) Results of major parameters for expander with different leakage path area while other parameters are constant, r v = 2.4 (b) Results of major parameters for expander with different volumetric ratio while other parameters are constant, A leak = 35 mm2 It can be seen that the power output and the isentropic efficiency of the expander are quite different. It can be concluded that delayed closure of the working chambers can largely affect the filling factor and the inlet pressure but the effect on the expander power output is not as significant as in the case of large leaks. In case 4, the isentropic efficiency of the expander is the same as in case 3. However, due to the large leaks and the loss of contact between the vanes and the stator, the expander inlet pressure is greatly affected, which results in lower under-expansion losses. The overall performance of the expander is the lowest in the 4th case. Table 2. Comparison of model results for several interesting cases Case A leak [mm 2 ] effective r v 4,0 3,0 2,0 1,0 0,0 0,0 0 5 10 15 20 25 30 35 40 45 Actual expander volumetric ratio Isentropic efficiency Filling factor Inlet pressure Expander power output p in,exp [kpa] Ṁ [kg/s] η is FF P out [kw] 1 0 2.40 435.4 0.139 0.727 0.992 4.37 2 0 1.62 318.3 0,149 0.658 1.453 3.53 3 35 2.40 318.3 0,149 0.551 1.453 2.96 4 35 1.82 271.1 0,155 0.551 1.763 2.76 0,6 0,5 0,4 0,3 0,2 0,1 3,0 2,5 2,0 1,5 1,0 0,5 0,0 0,0 1 1,2 1,4 1,6 1,8 2 2,2 2,4 Actual expander volumetric ratio Isentropic efficiency Filling factor Inlet pressure Expander power output Verifying the presented results using experimental data outweighs the scope of this article. For the basic idea, however, two measured experimental states from the experimental ORC unit with RVE will be briefly presented (see Tab. 3). In the first case (1 experimental ), the problem with loss of contact between the vanes and the stator was expected. In the second case (2 experimental ), another type of vanes with higher weight was used. The weight of the vanes has a direct effect on the centrifugal force acting on the vanes, and it was expected that at the same rotational speed the working chambers were closed properly. The above-described model was furthermore complemented by some losses, such as mechanical losses of vanes and bearings, or pressure loss at the expander outlet. These losses primarily affect the predicted expander performance. The model was able to identify parameters of the volumetric ratio r v according to an assumption, that in the first case there is loss of contact of the vanes and stator. Due to the nature of the experiment, predicted leakage area A leak was expected to be the same in both cases. The resulting deviation is probably due to the fact that the model parameters identification is not fully correct or another minor loss is missing in the model. However, the effect of the deviation on the model result is relatively small. Filling factor is lower in the second case due to proper chamber closure; isentropic efficiency is lower due to increased friction of the vanes. If we did not take into account the loss of contact between the vanes and the stator in the first case, the leakage area A leak would increase to 56 mm 2 (to match the mass flow rate from the model and from
8 V. Vodicka et al. / Energy Procedia 00 (2017) 000 000 measurement) but the predicted expander output would be nearly 0,2 kw lower, which does not correspond to the measurement. Case Table 3. Quick overview of experimental data and parameters evaluated by the comprehensive model p in,exp [kpa] p out,exp [kpa] Ṁ [kg/s] N rot [rpm] P out [kw] η is FF A leak [mm 2 ] 1 experimental 309 64 0.141 3026 2.31 0.516 1.4 40 2.0 2 experimental 339 64 0.139 3024 2.21 0.47 1.26 44 2.4 r v A more detailed model of a RVE and more detailed comparison of model results with experimentally measured data are the subjects of future work. 5. Conclusion We propose a modified semi-empirical model of a rotary vane expander used for ORC with two different leakages lumped leakage area between inlet and outlet and leakage caused by a loss of contact between vanes and a stator during a filling phase. These leakages significantly affect the isentropic efficiency and the filling factor. In addition, if the expander is directly coupled to the evaporator with a constant heat input, they further affect the evaporator pressure and the inlet pressure to the expander respectively. The inlet pressure can be affected in a way, that the isentropic efficiency may be constant or exhibit only a small decrease with the increasing problem of the loss of contact between the vanes and the stator. Therefore, the isentropic efficiency may not be sufficient to compare rotary vane expanders, especially if the problem with delayed closure of chambers within a RVE cannot be excluded. Results from the model suggest, that a delayed closure of the working chambers can largely affect the filling factor and the inlet pressure but the effect on the expander power output or isentropic efficiency is not as significant as in the case of large leaks. Finally, two measured experimental states of RVE are briefly presented for the basic idea. The problem with both types of leaks within the measured RVE was expected. The model supplemented by some other losses (especially friction losses and outlet pressure loss) was able to predict a problem with delayed chamber closure according to the expectations. Acknowledgements This work has been supported by the Ministry of Education, Youth and Sports within National Sustainability Programme I (NPU I), project No. LO1605 - University Centre for Energy Efficient Buildings Sustainability Phase and by the Grant Agency of the Czech Technical University in Prague, grant No. SGS OHK2-036/16. References [1] Pehnt, M, et al. Micro cogeneration: towards decentralized energy systems. Springer Science & Business Media, 2006. [2] Qiu G, Hao L, Saffa R. Expanders for micro-chp systems with organic Rankine cycle. Applied Thermal Engineering 2011; 31.16: 3301-3307. [3] Imran M, Usman M, Park BS, Lee DH. Volumetric expanders for low grade heat and waste heat recovery applications. Renewable and Sustainable Energy Reviews 2016; 57: 1090-1109. [4] Badr O, Probert SD, O'Callaghan P. Performances of Multi-vane Expanders. Applied Energy 1985; 20: 207-234. [5] Lemort V, et al. Testing and modeling a scroll expander integrated into an Organic Rankine Cycle. Applied Thermal Engineering 2009; 29.14: 3094-3102. [6] Badr O, Probert SD, O'Callaghan P. Multi-Vane Expanders: Internal-Leakage Losses. Applied Energy 1985; 20: 1-46. [7] Yang B, Sun S, Peng X, et al. Modeling and Experimental Investigation on the Internal Leakage in a CO2 Rotary Vane Expander. International Compressor Engineering Conference 2008. Paper 1852. [8] Yang B, Peng X, He Z, et al. Experimental investigation on the internal working process of a CO2 rotary vane expander. Applied Thermal Engineering 2009; 29: 2289-2296.