(英文原文)Influence of supercritical ORC parameters on plate heat exchanger design

In fluence of supercritical ORC parameters on plate heat exchanger designSotirios Karellas a ,*,Andreas Schuster b ,Aris-Dimitrios Leontaritis aa Laboratory of Steam Boilers and Thermal Plants,School of Mechanical Engineering,National Technical University of Athens,9Heroon Polytechniou,15780Zografou,Athens,Greece bInstitute of Energy Systems,Technische Universität München,Munich,Germanya r t i c l e i n f oArticle history:Received 13May 2011Accepted 6September 2011Available online 16September 2011Keywords:Organic Rankine Cycle (ORC)SupercriticalHeat transfer coef ficients Plate heat exchangersa b s t r a c tThe applications of Organic Rankine Cycle (ORC)appear to be growing in the field of waste heat utili-zation.This thermodynamic cycle can be successfully used in the field of biomass combustion,geothermal systems or solar desalination systems,providing ef ficient 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 speci fi-cally,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 coef ficients is of high importance for these applications as the effective heat transfer re flects on the overall process energetic and exergetic ef ficiency.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 in fluence of the ORC parameters on the heat exchanger design.More speci fically,the basic parameters of the design of the heat exchangers will be de fined in the cases of supercritical fluid parameters and the convective coef ficients as well as resulting heat transfer surface will be calculated for various fluid parameters.Ó2011Elsevier Ltd.All rights reserved.1.IntroductionThe difference between the Organic Rankine cycle (ORC)and the classical Clausius e Rankine cycle is the use of organic working fluid instead of water e pared 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 ef ficiency and lower working fluid mass flow [2e 6].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 ef ficiency as well as effective heat source utilization can be achieved [7].Apart from the subcritical Organic Rankine cycle,many inves-tigations 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 nowork 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 ORCFig.1shows the process of a sub (points 1e 5)-and supercritical (points 1,20,30,40,5)ORC in a T-s-Diagram for a constant super-heated 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 coef ficient of the gaseous phase [9].*Corresponding author.Tel.:þ302107722810;fax:þ302107723663.E-mail address:sotokar@mail.ntua.gr (S.Karellas).Contents lists available at SciVerse ScienceDirectApplied Thermal Engineeringjournal ho mep age:www.elsevi/locate/apthermeng1359-4311/$e see front matter Ó2011Elsevier Ltd.All rights reserved.doi:10.1016/j.applthermaleng.2011.09.013Applied Thermal Engineering 33-34(2012)70e 76The thermal efficiency of the cycle is defined as follows:h th¼P mech_QOrganic 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 mech¼_m ORC½ðh3Àh4ÞÀðh2Àh1Þ (2) The heat input to the ORC process is done usually with the help of thermal oil and is equal to:_QOrganic fluid¼_m ORCðh3Àh2Þ(3) where h1,h2,h3and h4are the specific enthalpies according to Fig.1.In the case of supercritical process,the enthalpy fall(h30-h40)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(h20-h2),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 organicfluid is defined by the following equation:h HEx¼_QOrganic fluid_QHS(4)Finally,the efficiency of the whole system is defined as follows:h System¼P mech_QHS¼h 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 and3.Fig.2shows the enthalpyflow of the heat source to theORCFig.1.Sub and supercritical ORC.Example ofR245fa.Fig.2.T-_H diagram of R245fa.Live vapour parameters:60bar,220 C.S.Karellas et al./Applied Thermal Engineering33-34(2012)70e7671medium.Fig.3presents the characteristic T-_Qdiagrams 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 de fined as the point of the procedure where the temper-ature 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 tempera-ture difference (LMTD)between the heat source and the organic fluid in each point is smaller and therefore a lower heat exchanger thermal ef ficiency is expected.So in order to achieve the same heat flux and live vapour temperature,and thus the same heat exchanger ef ficiency 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 coef ficients will be investigated.3.Calculation of the mean overall heat transfer coef ficient The most challenging issue in the design of a heat exchanger for supercritical fluid parameters is the calculation of the mean overallheat transfer coef ficient U as well as the necessary area of the heat exchanger.The aim of this paper is to investigate the in fluence of the main ORC parameters,such as vapour pressure and super-heating 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,espe-cially in the pseudo-critical temperature range,the de finition 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.5e 8.For the calculation of the calculation error,the results of a 1000points partition of the heat exchanger are used as a refer-ence value.Figs.5and 7show the calculated mean overall heat transfer coef ficient 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 (40.6bar for R134a and 29.25bar for R227ea)the procedure converges suf ficiently,when the heat exchanger is partitioned at least into 32sections.For a partition of 32points the calculation error is 3.25%for R134a at 41bar and 2.35%for R227ea at 30bar.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 suf ficiently 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,whenFig.3.T-_Qdiagram of R134a.Live vapour parameters:30bar,140 C (subcritical),50bar,140 C(supercritical).Fig.4.T-_Qdiagram of the heatexchanger.Fig.5.Mean overall heat transfer coef ficient for various partitions and working fluidR134a at 140C.Fig.6.Calculation error of the mean overall heat transfer coef ficient U for variouspartitions and working fluid R134a at 140 C.S.Karellas et al./Applied Thermal Engineering 33-34(2012)70e 7672using an 8-section partition,the calculation error is 1.73%for R134aat 65bar and 2.34%for R227ea at 55bar.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 signi ficant 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 calcu-lation 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 (2points -inlet and outlet temperature),the calculation error falls from 52.60%at 41bar to 48.24%at 46bar,40.3%at 55bar and 25.22%at 65bar,for R134a.Figs.6and 8show the calculation error of the mean overall heat transfer coef ficient 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 approachFor the calculations presented on the current article,the heat exchanger is divided into 500sections,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 (D T i and D T i þ1respectively)._Q ¼UA D T log ¼UA D T i ÀD T i þ1lnD T iD i þ1(6)In the heat transfer process,the heat flow between two points i and i þ1is considered (Fig.4):_Q i;i þ1¼_mORC ðh i ðt i ;p sc ÞÀh i þ1ðt i þ1;p sc ÞÞ(7)In this approach,the heat transfer is considered without pres-sure 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 de fined as follows:-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 1to point i (Fig.4)is equal to:_Q ORC ;1Ài ¼_Q HS ;1Ài ¼_m HS c p ðt HS1Àt HSi Þ0t HS ;i ¼t HS ;1À_Q HS ;1Ài_mHS c p (9)The heat flow of the heat source is supposed to be linear.Dependence of the speci fic heat capacity on temperature is not considered.Using equations (7)e (9),the corresponding temperatures of points i and i þ1can be calculated.With all the points of the procedure de fined,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:ðUA Þi ;i þ1¼_Q i ;i þ1D T log¼_Q i ;i þ1D i ÀD T i þ1lnD T i D T i þ1(10)The special feature of fluids at supercritical pressure is that their thermodynamic properties vary rapidly with temperature and pressure.Fig.9shows the speci fic heat capacity and Prandtl number variation as a function of temperature,for R227ea and R245fa at critical and supercritical pressure.The speci fic heat capacity as well as the Prandtl number of both fluids change signi ficantly 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 signi ficant 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 temper-atures it has a value around 4,so the medium can be describedasFig.7.Mean overall heat transfer coef ficient for various partitions and working fluid R227ea at 140C.Fig.8.Calculation error of the mean overall heat transfer coef ficient U for various partitions and working fluid R227ea at 140C.Fig.9.Variation of the cp and Pr with temperature.S.Karellas et al./Applied Thermal Engineering 33-34(2012)70e 7673liquid.With the rise of temperature it almost instantly drops to 1and 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.10shows the variation of thermal conductivity and dynamic viscosity of the fluid as a function of temperature.Both properties have an important in fluence 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:Nu b ¼0:0183Re 0:82bPr 0:5r wr b0:3c p p bn(11)where b refers to bulk fluid temperature and w to wall temperatureIn this last equation,the average speci fic heat capacity of the medium is considered:c p ¼h w Àh bT w ÀT b(12)And if T pc is the pseudo-critical temperature,then the exponentof equation (11)is de fined as follows [12]:n ¼0:4for T b <T w <T pc and 1:2T pc <T b <T wn ¼0:4þ0:2 T wT pc À1 for T b <T pc <T wn ¼0:4þ0:2 T w T pc À1 1À5 T bT pc À1for T pc <T b <1:2T pc(13)Fig.11shows 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 40bar (the pseudo-critical temperate at 40bar 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 C p and Prandtl number.On the otherhand,the Jackson correlation,using a correction factor (Fig.12),provides more stable and accurate results.The convective heat transfer coef ficient is:Nu ¼a d l 0a ¼Nu l (14)The mean overall heat transfer coef ficient U is de fined as:1¼1a þ1a hot þd l þR f (15)a hot is calculated using the Dittus Boelter correlation [13]:Nu ¼0:023Pr n Re 0:8(16)where n ¼0.4for heating processes and 0.3for cooling processes.As the factor UA and the mean overall heat transfer coef ficient U are known for each step,the necessary elementary area A i can also be calculated.The total heat exchanger area A tot is:A tot ¼X i ¼m i ¼1A i(17)The minimum temperature difference between the heat source medium and the supercritical fluid is de fined as the Pinch Point temperature difference D T pinch ,which is kept constant at 10K for all calculations.The D T 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 pre-sented in Table 1.In all numerical calculations presented in this work,fluid prop-erties according to the Refprop Database by NIST were used [14].Fig.11.Nusselt number,according to Jackson and Dittus Boelter,as a function of temperature of the organic fluid.Fig.12.Correction factor of the Jackson correlation as a function of temperature of the organic fluid.Fig.10.Variation of dynamic viscosity and thermal conductivity with temperature.S.Karellas et al./Applied Thermal Engineering 33-34(2012)70e 76744.Results and discussionSetting the pinch point temperature difference at 10K,the mean overall heat transfer coef ficient U of the heat exchanger was calculated for various fluids,live vapour temperatures and pres-sures.Table 2presents the three fluids that were considered and their critical points.Fig.13shows the in fluence of pressure and temperature on the U value.There is an almost linear relation in which the rise of pres-sure leads to lower mean overall thermal coef ficients.An inter-esting observation is the in fluence 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 signi ficantly the mean overall heat transfer coef ficient.For example,when the working fluid is R134a at 65bar,U drops from 2500W/m 2K at 160 C to 2200W/m 2K at 180 C.During superheating,the heat transfer coef ficient between the heat transfer fluid and the vapour of the working fluid is very low and thus affects the mean overall heat transfer coef ficient.The greater the superheating is,the lower the mean overall heat transfer coef ficient 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.1e 3).In order to keep the pinch point fixed at 10K when the pressure rises,higher heat exchanger ef ficiency needs to be achieved.Therefore the surface of the heat exchanger needs to be larger as well.Fig.15shows the heat exchanger ef ficiency 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 ef ficiency,as in some parts of the heat transfer procedure,neither the temperaturenor the speci fic 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 de finition was used for the ef fi-ciency of the heat exchanger:ε¼_Q _Q max(18)_Q is the heat transferred to the organic fluid and _Q max is themaximum transferable heat,de fined as_Q max ¼_C min ÀT hot ;in ÀT cold ;in Á(19)_C min ¼minÈÀ_mcp ÁHot Source ;À_mc p ÁORCÉ(20)The heat exchanger ef ficiency was calculated for a fixed heatexchanger area of 3.5m 2.Generally,rising pressure leads to higher ef ficiency rates.A signi ficant observation is that there is a pressure range in all fluids (from critical pressure up to 10e 15bar above the supercritical pressure),where rising pressure leads to a slightly dropping heat exchanger ef ficiency.Finally,the impact of the heat exchanger area on the heat exchanger ef ficiency is qualitatively the same as in a sub-critical heat exchanger.5.ConclusionsThe 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 analysisTable 1Geometrical characteristics of the heat exchanger.Width100mm b (distance between plates)2mm d (plate thickness)0.45mmTable 2Fluids considered.Fluid p crit [MPa]T crit ( C)R134a 4.06101.06R227ea 2.92101.75R245fa3.65154.01Fig.13.Mean overall heat transfer coef ficient vs.pressure for three fluids and super-heatingtemperatures.Fig.14.Dependence of the needed heat exchanger area on the pressure for three organic fluids and superheatingtemperatures.Fig.15.Heat exchanger ef ficiency.S.Karellas et al./Applied Thermal Engineering 33-34(2012)70e 7675presented,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 thisfield.It can be said that the application of supercriticalfluid param-eters 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 techno-economic investigation of real-scale supercritical ORC applications is also vital for the actual exploitation of this promising technology. 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