Applied Thermal Engineering

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1 Applied Thermal Engineering (2012) 70e76 Contents lists available at SciVerse ScienceDirect Applied Thermal Engineering journal homepage: Influence of supercritical ORC parameters on plate heat exchanger design Sotirios Karellas a, *, Andreas Schuster b, Aris-Dimitrios Leontaritis a a Laboratory of Steam Boilers and Thermal Plants, School of Mechanical Engineering, National Technical University of Athens, 9 Heroon Polytechniou, Zografou, Athens, Greece b Institute of Energy Systems, Technische Universität München, Munich, Germany article info abstract Article history: Received 13 May 2011 Accepted 6 September 2011 Available online 16 September 2011 Keywords: Organic Rankine Cycle (ORC) Supercritical Heat transfer coefficients Plate heat exchangers The applications of Organic Rankine Cycle (ORC) appear to be growing in the field of waste heat utilization. This thermodynamic cycle can be successfully used in the field of biomass combustion, geothermal systems or solar desalination systems, providing efficient systems. In the last years, a very intense investigation on the utilization of low temperature waste heat for supplying ORC systems has brought new research potential in the area of thermodynamic optimisation of this cycle. More specifically, the use of supercritical fluid parameters in the ORC processes seems to become more and more attractive leading to lower exergy destruction systems together with higher heat utilization systems. However, the investigation of the heat exchanger design and the heat exchange coefficients is of high importance for these applications as the effective heat transfer reflects on the overall process energetic and exergetic efficiency. It is important to study the relatively unknown heat transfer mechanisms around the critical point to improve both the heat exchanger surface and the design algorithms. The aim of this paper is to investigate the influence of the ORC parameters on the heat exchanger design. More specifically, the basic parameters of the design of the heat exchangers will be defined in the cases of supercritical fluid parameters and the convective coefficients as well as resulting heat transfer surface will be calculated for various fluid parameters. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction The difference between the Organic Rankine cycle (ORC) and the classical ClausiuseRankine cycle is the use of organic working fluid instead of wateresteam. Compared to water-based cycles, ORCs have a lot of advantages in applications in which a low temperature heat source is used (e.g. geothermal energy, solar desalination and waste heat recovery) [1], such as higher thermal efficiency and lower working fluid mass flow [2e6]. One of the main challenges of an ORC process is the choice of the appropriate working fluid and of the particular cycle design with which maximum thermal efficiency as well as effective heat source utilization can be achieved [7]. Apart from the subcritical Organic Rankine cycle, many investigations can be found in literature about applications of this cycle in supercritical parameters, e.g. [8]. These parameters result to lower exergy destruction providing important advantages which lead to more effective heat utilization, especially in the cases of low temperature level waste heat. However, in the current literature no * Corresponding author. Tel.: þ ; fax: þ address: sotokar@mail.ntua.gr (S. Karellas). work can be found, determining the heat transfer mechanisms under supercritical organic fluid state, directly related to ORC applications. Conclusively, the dimensioning of the heat exchangers using the existing models for subcritical parameters can lead to inaccurate results and false conclusions. Therefore, the main challenge and aim of this paper is the dimensioning of the heat exchanger, which prerequisites the appropriate determination of the design parameters and thus the investigation of the heat transfer mechanisms under supercritical conditions. 2. Thermodynamic approach of supercritical ORC Fig. 1 shows the process of a sub (points 1e5) - and supercritical (points 1, 2 0,3 0,4 0, 5) ORC in a T-s-Diagram for a constant superheated vapour temperature. Even for constant temperature of the superheated vapour, the heat input occurs at a higher average temperature level in the case of supercritical vapour parameters, compared to subcritical. In reality, such high superheating of the subcritical vapour as shown in the diagram could not be realized due to the tremendous heat exchange area needed due to the low heat-exchange coefficient of the gaseous phase [9] /$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi: /j.applthermaleng

2 S. Karellas et al. / Applied Thermal Engineering (2012) 70e76 71 Nomenclature A surface (m 2 ) b distance between plates (mm) cp specific heat capacity (kj/kgk) d hydraulic diameter (m) _H enthalpy flow (kw) h specific enthalpy (kj/kg) _m mass flow (kg/s) n exponent Nu Nusselt number P power (kw) p pressure (MPa) PHE plate heat exchanger _Q heat flow (kw) Re Reynolds number R f fouling factor (m 2 K/W) s specific entropy (kj/kgk) T, t temperature ( C) U mean overall heat transfer coefficient (W/m 2 K) Subscripts/superscripts b bulk fluid w wall cr critical HEx heat exchanger HS heat source max maximum mech mechanical ORC Organic Rankine Cycle th thermal tot total pc pseudo-critical sh superheated Greek symbols a heat transfer coefficient (W/m 2 K) d plate thickness (mm) ε heat exchanger efficiency h efficiency l thermal conductivity (W/mK) The thermal efficiency of the cycle is defined as follows: h th ¼ P mech _Q Organic fluid (1) P mech is the net mechanical power produced with the ORC process (which will be assumed as equal to the net electrical power). This power output of the subcritical process is analogue to the enthalpy fall in the turbine minus the enthalpy rise in the pump: P mech ¼ _m ORC ½ðh 3 h 4 Þ ðh 2 h 1 ÞŠ (2) The heat input to the ORC process is done usually with the help of thermal oil and is equal to: _Q Organic fluid ¼ _m ORC ðh 3 h 2 Þ (3) where h 1, h 2, h 3 and h 4 are the specific enthalpies according to Fig. 1. In the case of supercritical process, the enthalpy fall (h 3 0 -h 4 0 )is much higher than in the subcritical one, when on the other hand, the feed pump s additional specific work to reach supercritical pressure, which corresponds to the enthalpy rise (h 2 0 -h 2 ), is very low. Therefore, according to equation (1), the efficiency of the process is higher in the case of supercritical ORC parameters and this fact opens new frontiers in the investigation of ORC applications. The efficiency of the heat exchange system which transfers the heat from the heat source to the organic fluid is defined by the following equation: h HEx ¼ _Q Organic fluid _Q HS (4) Finally, the efficiency of the whole system is defined as follows: h System ¼ P mech _Q HS ¼ h HEx h th (5) As the system efficiency is directly linked with the efficiency of the heat exchange system, it is obvious that the aim is to maximise the transferred heat. The exploitation of the heat source in a supercritical ORC as well as the function and the efficiency of the plate heat exchanger can be seen in the diagrams shown in Figs. 2 and 3. Fig. 2 shows the enthalpy flow of the heat source to the ORC Fig. 1. Sub and supercritical ORC. Example of R245fa. Fig. 2. T- _ H diagram of R245fa. Live vapour parameters: 60 bar, 220 C.

3 72 S. Karellas et al. / Applied Thermal Engineering (2012) 70e76 Fig. 3. T- _ Q diagram of R134a. Live vapour parameters: 30 bar, 140 C (subcritical), 50 bar, 140 C (supercritical). Fig. 5. Mean overall heat transfer coefficient for various partitions and working fluid R134a at 140 C. medium. Fig. 3 presents the characteristic T- _ Q diagrams of a heat exchanger under subcritical and supercritical parameters. On both diagrams, it is possible to have an overview of the whole procedure from the inlet to the outlet point of the heat exchanger of the two flows, the heat source and the organic flow. The closer the two curves are, the lower the exergy destruction of the heat transfer procedure is. Another important characteristic is the pinch point, which is defined as the point of the procedure where the temperature difference between the two flows is minimum. As can be seen in Fig. 3, in the supercritical cycle, there is no evaporation range, the state changes from liquid to vapour when the pseudo-critical temperature is reached. On the other hand, in the subcritical cycle the evaporation takes place under constant temperature which is represented by the horizontal part of the fluid curve. As a result, the two curves are much closer in the case of supercritical conditions and therefore the exergy destruction during the heat exchange is much lower compared to subcritical conditions. However, when the two curves are close, the logarithmic temperature difference (LMTD) between the heat source and the organic fluid in each point is smaller and therefore a lower heat exchanger thermal efficiency is expected. So in order to achieve the same heat flux and live vapour temperature, and thus the same heat exchanger efficiency as it happens in both cases of Fig. 3, a much larger heat transfer area is required in the case of supercritical conditions. Conclusively, it is very important to investigate the heat transfer around the critical point which is quite unknown. There is a high challenge in understanding of plate heat exchangers in order to use them in supercritical ORCs. In order to analyse the heat transfer mechanisms in these heat exchangers, the relevant heat transfer coefficients will be investigated. 3. Calculation of the mean overall heat transfer coefficient The most challenging issue in the design of a heat exchanger for supercritical fluid parameters is the calculation of the mean overall heat transfer coefficient U as well as the necessary area of the heat exchanger. The aim of this paper is to investigate the influence of the main ORC parameters, such as vapour pressure and superheating temperature, on the heat exchanger design. In Fig. 4, the heat transfer between the hot medium and the organic medium is presented. Due to the variable inclination of the curve of the organic medium, a global logarithmic temperature difference between the input and the output of the organic fluid is not an acceptable assumption. As already discussed, the thermal properties of the fluid in supercritical state are strongly dependent on temperature, especially in the pseudo-critical temperature range, the definition of which will be discussed later in this paper. The U value of the heat exchanger also depends on those properties and therefore cannot be considered constant through the heat transfer procedure. For those reasons a numerical approach to the problem is required. The heat exchanger is divided into n elementary areas assuming equal enthalpy difference. The necessity for partitioning the heat exchanger can be perceived more easily with the help of Figs. 5e8. For the calculation of the calculation error, the results of a 1000 points partition of the heat exchanger are used as a reference value. Figs. 5 and 7 show the calculated mean overall heat transfer coefficient U for various numbers of elementary areas, into which the heat exchanger is divided, for working fluid R134a and R227ea respectively. It should be remarked that for pressure values close to the critical (40.6 bar for R134a and bar for R227ea) the procedure converges sufficiently, when the heat exchanger is partitioned at least into 32 sections. For a partition of 32 points the calculation error is 3.25% for R134a at 41 bar and 2.35% for R227ea at 30 bar. The errors without partitioning the heat exchanger are 52.60% and 50.67% respectively. Consequently, the partitioning of the heat exchanger is obligatory, in order to achieve sufficiently accurate results, as it has already been discussed theoretically. As the pressure rises, the calculation error gets reduced and the procedure converges even with less sections. For example, when Fig. 4. T- _ Q diagram of the heat exchanger. Fig. 6. Calculation error of the mean overall heat transfer coefficient U for various partitions and working fluid R134a at 140 C.

4 S. Karellas et al. / Applied Thermal Engineering (2012) 70e76 73 _Q i;iþ1 ¼ _m ORC ðh i ðt i ; p sc Þ h iþ1 ðt iþ1 ; p sc ÞÞ (7) In this approach, the heat transfer is considered without pressure losses and therefore the supercritical pressure p sc is also considered to be constant. As the transferred heat from the heat source to the organic fluid is known, the temperature of the heat source medium (HS) can also be defined as follows: Fig. 7. Mean overall heat transfer coefficient for various partitions and working fluid R227ea at 140 C. using an 8-section partition, the calculation error is 1.73% for R134a at 65 bar and 2.34% for R227ea at 55 bar. That is a result of the smoother variation of the thermo-physical properties of the fluid under greater pressure, around the pseudo-critical temperature, as it will be discussed later on this article. On the contrary, when the live vapour pressure is close to the critical pressure of the fluid, the rapid and significant variation of the thermo-physical properties demand the partitioning of the heat exchanger into more sections, so that this variation can be taken into account and better calculation accuracy is achieved. A characteristic example of the dependence of the calculation error on pressure is the fact that even without partitioning the heat exchanger (2 points - inlet and outlet temperature), the calculation error falls from 52.60% at 41 bar to 48.24% at 46 bar, 40.3% at 55 bar and 25.22% at 65 bar, for R134a. Figs. 6 and 8 show the calculation error of the mean overall heat transfer coefficient U for various partitions and working fluid R134a and R227ea respectively. The error curves on both diagrams converge to zero faster (for less sections) as the pressure rises. However, in any case the error is unacceptably big when the heat exchanger is not partitioned, which once more proves the necessity of a numerical approach For the calculations presented on the current article, the heat exchanger is divided into 500 sections, which achieves a calculation error in the order of 0.01%. Equation (6) can be used for each section, where the logarithmic temperature difference is provided from the input and output of each elementary area of the heat exchanger (DT i and DT iþ1 respectively). _Q ¼ UADT log ¼ UA DT i DT iþ1 (6) DTi ln DT iþ1 In the heat transfer process, the heat flow between two points i and i þ 1 is considered (Fig. 4): - The heat that is transferred from the heat source to the ORC medium is: _Q ORC ¼ _ Q HS (8) Therefore the heat provided from the heat source from point 1 to point i (Fig. 4) is equal to: _Q ORC;1 i ¼ Q _ HS;1 i ¼ _m HS c p ðt HS1 t HSi Þ0 _Q HS;1 i t HS;i ¼ t HS;1 (9) _m HS c p The heat flow of the heat source is supposed to be linear. Dependence of the specific heat capacity on temperature is not considered. Using equations (7)e(9), the corresponding temperatures of points i and i þ 1 can be calculated. With all the points of the procedure defined, all the necessary fluid properties for the calculation of the U value are known. In each elementary area of the heat exchanger the factor UA is: ðuaþ i;iþ1 ¼ _Q i;iþ1 DT log _Q i;iþ1 ¼ DT i DT iþ1 DTi ln DT iþ1 (10) The special feature of fluids at supercritical pressure is that their thermodynamic properties vary rapidly with temperature and pressure. Fig. 9 shows the specific heat capacity and Prandtl number variation as a function of temperature, for R227ea and R245fa at critical and supercritical pressure. The specific heat capacity as well as the Prandtl number of both fluids change significantly near the critical temperature at critical pressure. For supercritical pressure there is a temperature where the Cp and the Prandtl number rise to a peak and then fall steeply. This temperature is the so-called pseudo-critical temperature. Thermo-physical properties undergo significant changes near the pseudo-critical point in a similar way to the critical point but with relatively smaller variation. In Fig. 9, the variation of the Prandtl number before and after the critical temperature should be commented. In subcritical temperatures it has a value around 4, so the medium can be described as Fig. 8. Calculation error of the mean overall heat transfer coefficient U for various partitions and working fluid R227ea at 140 C. Fig. 9. Variation of the cp and Pr with temperature.

5 74 S. Karellas et al. / Applied Thermal Engineering (2012) 70e76 liquid. With the rise of temperature it almost instantly drops to 1 and the medium can be described as gas. Conclusively the phase change takes place almost instantly in the critical or pseudo-critical point, according to the applied pressure. Fig. 10 shows the variation of thermal conductivity and dynamic viscosity of the fluid as a function of temperature. Both properties have an important influence on the heat transfer between the plate and the fluid. There is an easily noticeable variation around the critical point. For those reasons, the classical heat transfer correlations, as the Dittus Boelter correlation (see equation 16) for the calculation of the Nusselt number cannot be used. Therefore, the Nusselt number is calculated using the Jackson correlations for supercritical fluid parameters [10] [11], which include a correction factor which neutralises the effect of the variation of the thermo-physical properties around the pseudo-critical point: 0:3 n Nu b ¼ 0:0183Re 0:82 b Pr 0:5 rw cp (11) rb where b refers to bulk fluid temperature and w to wall temperature In this last equation, the average specific heat capacity of the medium is considered: c p ¼ h w h b T w T b (12) And if T pc is the pseudo-critical temperature, then the exponent of equation (11) is defined as follows [12]: c pb n ¼ 0:4 for T b < T w < T pc and 1:2 T pc < T b < T w Tw n ¼ 0:4 þ 0:2 1 for T T b < T pc < T w pc Tw Tb n ¼ 0:4 þ 0: T pc T pc for T pc < T b < 1:2T pc (13) Fig. 11 shows the results of the calculations of Nusselt number, using the correlations proposed by Jackson (11) and Dittus Boelter (16). The calculations have been made for the organic fluid R245fa, superheated at 220 C under a pressure of 40 bar (the pseudocritical temperate at 40 bar is 159 C). It is clearly visible on the diagram, that in the temperature range around the pseudo-critical point, the Dittus Boelter correlation gives greater values of Nu, due to the misleading values of Cp and Prandtl number. On the other Fig. 11. Nusselt number, according to Jackson and Dittus Boelter, as a function of temperature of the organic fluid. hand, the Jackson correlation, using a correction factor (Fig. 12), provides more stable and accurate results. The convective heat transfer coefficient is: Nu ¼ ad Nul 0a ¼ l d The mean overall heat transfer coefficient U is defined as: (14) 1 U ¼ 1 a þ 1 þ d a hot l þ R f (15) a hot is calculated using the Dittus Boelter correlation [13]: Nu ¼ 0:023Pr n Re 0:8 (16) where n ¼ 0.4 for heating processes and 0.3 for cooling processes. As the factor UA and the mean overall heat transfer coefficient U are known for each step, the necessary elementary area A i can also be calculated. The total heat exchanger area A tot is: i A tot ¼ X¼ m A i (17) i ¼ 1 The minimum temperature difference between the heat source medium and the supercritical fluid is defined as the Pinch Point temperature difference DT pinch, which is kept constant at 10 K for all calculations. The DT pinch is controlled by the organic fluid and hot source medium mass flows. As for the geometry and the fluid velocity in the heat exchanger, a rectangular cross-section is used and the respective hydraulic diameter is calculated. The geometrical characteristics are presented in Table 1. In all numerical calculations presented in this work, fluid properties according to the Refprop Database by NIST were used [14]. Fig. 10. Variation of dynamic viscosity and thermal conductivity with temperature. Fig. 12. Correction factor of the Jackson correlation as a function of temperature of the organic fluid.

6 S. Karellas et al. / Applied Thermal Engineering (2012) 70e76 75 Table 1 Geometrical characteristics of the heat exchanger. Width b (distance between plates) d (plate thickness) 100 mm 2 mm 0.45 mm Table 2 Fluids considered. Fluid p crit [MPa] T crit ( C) R134a R227ea R245fa Fig. 14. Dependence of the needed heat exchanger area on the pressure for three organic fluids and superheating temperatures. 4. Results and discussion Setting the pinch point temperature difference at 10 K, the mean overall heat transfer coefficient U of the heat exchanger was calculated for various fluids, live vapour temperatures and pressures. Table 2 presents the three fluids that were considered and their critical points. Fig. 13 shows the influence of pressure and temperature on the U value. There is an almost linear relation in which the rise of pressure leads to lower mean overall thermal coefficients. An interesting observation is the influence of live vapour temperature on the shape of those lines. For lower temperatures, the absolute gradient of the U-p lines rises and therefore the impact of pressure upon the U value is even stronger. Under constant pressure, the live vapour temperature affects significantly the mean overall heat transfer coefficient. For example, when the working fluid is R134a at 65 bar, U drops from 2500 W/m 2 Kat160 C to 2200 W/m 2 Kat 180 C. During superheating, the heat transfer coefficient between the heat transfer fluid and the vapour of the working fluid is very low and thus affects the mean overall heat transfer coefficient. The greater the superheating is, the lower the mean overall heat transfer coefficient is. Regarding the necessary heat exchanger area as a function of pressure (Fig. 14), it should be noted that there are two factors which contribute to those results. Obviously, the first one is the drop of the U value. The second has to do with the T-H or T-Q diagram (Figs. 1e3). In order to keep the pinch point fixed at 10 K when the pressure rises, higher heat exchanger efficiency needs to be achieved. Therefore the surface of the heat exchanger needs to be larger as well. Fig. 15 shows the heat exchanger efficiency as a function of pressure. It should be noted that it is not possible to use the NTU method for the calculation of the heat exchanger efficiency, as in some parts of the heat transfer procedure, neither the temperature nor the specific heat capacity are constant. Normally, in a subcritical heat exchanger one of the two values is constant. In the sensible heat transfer procedures, cp is considered constant, where in latent heat transfer procedures (vaporisation) the temperature remains constant. Therefore, the following definition was used for the efficiency of the heat exchanger: ε ¼ Fig. 15. Heat exchanger efficiency. _ Q _Q max (18) _Q is the heat transferred to the organic fluid and Q _ max is the maximum transferable heat, defined as _Q max ¼ C _ min Thot;in T cold;in (19) _C min ¼ min _mc p Hot Source ; _mc p (20) ORC The heat exchanger efficiency was calculated for a fixed heat exchanger area of 3.5 m 2. Generally, rising pressure leads to higher efficiency rates. A significant observation is that there is a pressure range in all fluids (from critical pressure up to 10e15 bar above the supercritical pressure), where rising pressure leads to a slightly dropping heat exchanger efficiency. Finally, the impact of the heat exchanger area on the heat exchanger efficiency is qualitatively the same as in a sub-critical heat exchanger. 5. Conclusions Fig. 13. Mean overall heat transfer coefficient vs. pressure for three fluids and superheating temperatures. The application of ORC for waste heat utilization, especially in the case of supercritical parameters, seems to be very attractive and should become more and more applicable in many cases. In this paper, the heat transfer mechanisms of a plate heat exchanger, working in a supercritical ORC are investigated. Within the analysis

7 76 S. Karellas et al. / Applied Thermal Engineering (2012) 70e76 presented, the heat transfer coefficients applied to these heat exchangers have been thoroughly investigated. Overall, this paper suggests an accurate method for supercritical heat exchangers calculations and dimensioning and provides a very useful tool for future research on this field. It can be said that the application of supercritical fluid parameters in ORCs seems to raise the efficiency without disproportioned rise of installation costs. However, it is very important to further investigate the heat transfer mechanisms in partial loads and transient procedures. Moreover, all the results should be verified by experiments and tests in actual ORC installations. A technoeconomic investigation of real-scale supercritical ORC applications is also vital for the actual exploitation of this promising technology. Only after those fields are thoroughly investigated, final and reliable conclusions can be drawn. References [1] A. Schuster, S. Karellas, E. Kakaras, H. Spliethoff, Energetic and economic investigation of Organic Rankine Cycle, Applied Thermal Engineering 29 (2009) 1809e1817. [2] G. Angelino, P.C.D. Paliano, Multicomponent working fluid for organic rankine cycles (ORCs), Energy 23 (6) (1998) 449e463. [3] B.T. Liu, K.H. Chien, C.C. Wang, Effect of working fluid on organic rankine cycle for waste heat recovery, Energy 29 (2004) 1207e1217. [4] T.C. Hung, T.Y. Shai, S.K. Wang, A review of organic rankine cycles (ORCs) for the recovery of low-grade waste heat, Energy 22 (7) (1997) 661e667. [5] T.C. Hung, Waste heat recovery of organic rankine cycle using dry fluids, Energy Conversion and Management 42 (2001) 539e553. [6] T. Yamamoto, T. Furuhata, N. Arai, K. Mori, Design and testing of the organic rankine cycle, Energy 26 (2001) 239e251. [7] D. Wei, X. Lu, Z. Lu, J. Gu, Performance analysis and optimization of Organic Rankine Cycle (ORC) for waste heat recovery, Energy Conversion and Management 48 (2007) 1113e1119. [8] A. Schuster, S. Karellas, R. Aumann, Efficiency optimization potential in supercritical Organic Rankine Cycles, Energy 35 (2010) 1033e1039. [9] S. Karellas, A. Schuster, Supercritical fluid parameters in Organic Rankine Cycle applications, International Journal of Thermodynamics vol. 11 (No.3) (2008) 101e108. [10] J.D. Jackson, W.B. Hall, Forced convection heat transfer. in: S. Kakac, D.B. Spalding (Eds.), Turbulent Forced Convection in Channels and Bundles, vol. 2, 1979, p [11] J.D. Jackson, W.B. Hall, Influences of buoyancy on heat transfer to fluids flowing in vertical tubes under turbulent conditions. in: S. Kakac, D.B. Spalding (Eds.), Turbulent Forced Convection in Channels and Bundles, vol. 2, 1979, p [12] K.-H. Kang, H. Chang S-, Experimental study on the heat transfer characteristics during the pressure transients under supercritical pressures, International Journal of Heat and Mass Transfer vol. 52 (Issues 21e22) (2009) 4946e4955. [13] M. Sharabi, W. Ambrosini, S. He, J.D. Jackson, Prediction of turbulent convective heat transfer to a fluid at supercritical pressure in square and triangular channels, Annals of Nuclear Energy 35 (2008) 993e1005. [14] E. Lemmon, M. McLinden, M. Huber, NIST Reference Fluid Thermodynamic and Transport Properties e REFPROP. U.S. Department of Commerce, National Institute for Standards and Technology, Gaitherssburg, Maryland, USA, 2002.