Chapter 3: System Configurations and Modeling This chapter involves formulating and defining system parameters and design conditions for the Organic Rankine cycle, the parabolic trough solar collector & the overall power generation from the cycle. The thermodynamic properties of the ORC, the thermodynamic and heat transfer analysis of the heating fluid in the PTSC are all discussed in this chapter. In addition, integration of the complete system is also provided.
3.1 Organic Rankine Cycle (ORC) Modeling
Power production for the system will be utilized from the Organic Rankine Cycle in this paper. The Organic Rankine cycle has organic fluids as its working fluid as compared to the conventional Rankine Cycle which uses water as its working fluid. Since the integration of this Organic Rankine Cycle will be with a PTSC, the Organic Rankine Cycle will use a heat exchanger to heat the organic fluid rather than the conventional method of using a boiler that heats the working fluid in a Rankine Cycle. The heat transfer fluid provides thermal energy to vaporize the organic fluid in the heat exchanger or the evaporator. The heat transfer fluid transfers the thermal energy it gains from the PTSC to the organic fluid in this process. The vaporized organic fluid is then expanded in the turbine where the pressure is dropped to produce electricity and provide superheated organic fluid at the condenser pressure. The organic fluid then enters the condenser where it is cooled and again pumped into the evaporator. Figure 5 shows the schematic diagram of the simple ORC.
6381753638550Figure 1: Schematic Diagram of Simple ORC
Figure SEQ Figure * ARABIC 1: Schematic Diagram of Simple ORC
High pressure organic fluid enters the evaporator in liquid form, where it is heated to vapor form to the required turbine inlet temperature. The heat transfer fluid enters the heat exchanger and leaves as a fluid and transferring thermal energy to the organic fluid. The following equations will be used for modeling equations of the heat exchanger or evaporator.
209804022860Figure 2: Evaporator Schematic00Figure SEQ Figure * ARABIC 2: Evaporator Schematic
The superheated vapor state of organic fluid will enter the turbine, giving work output and in turn expanding the fluid to the condenser pressure. Below is the schematic of the turbine and the modeling equations for the thermodynamic analysis of the tubine.
4787902144395Figure 3: Turbine/Expander Schematic00Figure SEQ Figure * ARABIC 3: Turbine/Expander Schematic478790000
Wturbine= morganic(h3-h4) (3.6)
The superheated organic fluid is then cooled and condensed in the condenser as heat is transferred to the cooling water passed through the condenser. Below is a schematic for the condenser and the modeling equations for the condenser.
1549400104775Figure 4: Condenser Schematic00Figure SEQ Figure * ARABIC 4: Condenser Schematic
2104390351790Figure 5: Pump Schematic00Figure SEQ Figure * ARABIC 5: Pump Schematic
h6= wpump+ h5(3.11)
wpump=v5 (P6-P5) (3.12)
3.1.5 EfficiencyThe efficiency of the Organic Rankine cycle can be computed from the turbine output and the energy input from the PTSC which can be formulated as the following:
?= Wturbine- WpumpQPTSC (3.13)
3.2 PTSC ModelingThe Parabolic trough solar collector contains solar collectors, receiver and an absorbing tube. The solar collector is manufactured to have a parabolic shape and its objective is to reflect solar rays towards the absorbing tube. The absorbing tube has absorbing characteristics as it is made from metal and coated with black paint on its surface to increase heat absorption. Also the tube is normally lined by a glass cover for reduction of heat losses via convection and radiation.
The model of the PTSC is done by analyzing the collector, receiver and glass cover separately, then combing the parameters to analyze the energetic and exergetic performances of the PTSC. Figure 6 shows the schematic diagram of a PTSC, and how the rays of sunlight are reflected by the collector onto the receiver.
15525752545715Figure 6: PTSC cross-section schematic 43
Figure SEQ Figure * ARABIC 6: PTSC cross-section schematic 43
https://www.researchgate.net/publication/271951654_A_design_method_and_numerical_study_for_a_new_type_parabolic_trough_solar_collector_with_uniform_solar_flux_distributionhttps://www.sciencedirect.com/science/article/pii/S0038092X17308988?_rdoc=1&_fmt=high&_origin=gateway&_docanchor=&md5=b8429449ccfc9c30159a5f9aeaa92ffb3.2.1 Heat Transfer Formulation for PTSC
The solar energy that is used by the PTSC is the solar energy after negating losses from optical design flaws such as tracking errors, condition and cleanliness of reflective mirrors and glazing. After this, the solar energy passes through the glass envelop (qgo,SAbs) and absorbed by the receiver pipe (qpo,SAbs). The HTF receives the energy after the energy absorbed by the receiver pipe is transferred via conduction from the outside of the pipe to the inside of the pipe (qpo-pi,cond) followed by convection from the inside of the pipe to the HTF (qpi-htf,conv ). Hence the following relationship can be established https://www.sciencedirect.com/science/article/pii/S0360544212004744?_rdoc=1&_fmt=high&_origin=gateway&_docanchor=&md5=b8429449ccfc9c30159a5f9aeaa92ffb.
qpi-htf,conv = qpo-pi,cond(3.17)
Not all the energy is transferred to the HTF and is reflected back to the environment. A small portion of the energy that passes into the glass cover is reflected back to the glass envelope via convection (qpo-gi,conv) and radiation (qpo-gi,rad). This energy is then conducted through the glass cover wall via conduction (qgi-go,cond) . This energy and the energy absorbed by the glass cover wall is lost to the environment through convection (qgo-a,conv ) & radiation (qgo-a,rad). Using these statements the following equations can be formulated:
qpo,SAbs = qpo-gi,conv + qpo-gi,rad + qpo-pi,cond(3.18)
qpo-gi,conv + qpo-gi,rad = qgi-go,cond(3.19)
qgi-go,cond + qgo,SAbs = qgo-a,conv + qgo-a,rad(3.20)
qLoss = qgo-a,conv + qgo-a,rad(3.21)
From Newtons law of cooling, the following formulation of convective heat transfer and the heat transfer coefficient (hf) can be applied between the inside of the receiver pipe and the HTF:
qpi-htf,conv = hf?Dpi (Tpi- Thtf)(3.22)
hf = NuDpi kfDpi(3.23)
Where NuDpi is the Nusselt number for inside diameter of the receiver pipe.
NuDpifpi8ReDpi-1000Prf 1+12.7fpi/8 (Prf2/3-1)PrfPrpi0.11For 0.5< Prf <2000 and 2300 < ReDpi <5x 106
fpi = 1.82log(ReDpi) – 1.64-2Prf = Prandtl number evaluated at the HTF temperature, Tf (-)
Prpi = Prandtl number evaluated at the receiver pipe inside
surface temperature, Tpi (-)
qpi-po,cond= 2?kpipe(Tpi-Tpo)ln DpoDpikpipe = receiver pipe thermal conductivity at the average receiver pipe temperature (Tpi + Tpo)/2 (W/m-°C)
kpipe=(0.013)Tpi-po+15.2If stainless steel 304L or 316L is chosen, the thermal conductivity is calculated
with this equation.
kpipe=(0.0153)Tpi-po+14.775If stainless steel 321H is chosen, the thermal conductivity is calculated
with this equation.
qpo-gi,conv=?Dpohpo-gi(Tpo-Tgi)convection heat transfer between the receiver pipe and glass envelope wall (qpo-gi,conv).
hpo-gi= kstdDpo2InDgiDpo+b?DpoDgi+1For: RaDgi< (Dgi/(Dgi-Dpo))4where kstd = thermal conductivity of the annulus gas at standard temperature and pressure (W/m-°C)
?=2.331 x 10-20(Tpo-gi+273)Pa?2The molecular diameters of air = ?
the convection heat transfer coefficients (hpo-gi)
qpo-gi,conv=2?keffInDgiDpo(Tgi-Tpo) For: 0.7?Prpo-gi?6000 and 102 ?FcylRapo-gi ?107Prpo-gi = Prandtl number for gas properties evaluated at Tpo-gi (-)
RaDpo = Rayleigh number evaluated at Dpo (-)
Average temperature (Tpo + Tgi)/218)
keffkag=0.386Prpo-gi0.861 + Prpo-gi14FcylRaDpo14kag = thermal conductivity of annulus gas at Tpo-gi (W/m-°C)
Fcyl=InDgiDpo4Lc3Dgi-3?5-Dpo-3?55Critical length: Lc=(Dgi-Dpo)220)
qpo-gi,rad=??Dpo(Tpo4-Tgi4)1?po+(1-?gi)Dpo?giDgiradiation heat transfer between the receiver pipe and glass envelope (qpo-gi,rad)
qgo-a,conv=hgo-a?Dgo(Tgo-Ta)hgo-a = convection heat transfer coefficient for air at (Tgo – Ta)/2 (W/m2-°C)
hgo-a=kairDgoNuDgokair = thermal conductivity of air at (Tgo – Ta)/2 (W/m-°C)
NuDgo = average Nusselt number based on the glass envelope outside diameter Dgo (-)
NuDgo=0.60+0387RDgo-a161+(0.559/Prgo-a)9168272105<RaDgo<1012RaDgo = Rayleigh number for air based on the glass envelope outside diameter, Dgo (-)
Type equation here.24)
RaDgo=g?(Tgo-Ta)Dgo3vgo-a2Prgo-avgo-a = kinematic viscosity for air at Tgo-a (m2/s)
Prgo-a = Prandtl number for air at Tgo-a (-)
Prgo-a=vgo-a?go-a?go-a = thermal diffusivity for air at Tgo-a (m2/s)
NuDgo=CReDgomPranPraPrgo14 0.7<Pra<500and 1< ReDgo <10628)
k?=cos(?)+0.000884?-0.00005369?2solar incidence angle (?)
Coating Emittance, ?po= 0.000327(T+273.15)-0.06597131)
qgo,SolAbs=qsol?env?envSolar Irradiance term (qsol)32)
?env=eshetregeedmedaeun?clK?esh =Receiver shadowing (bellows, shielding, supports), 0.974(-)
etr = Tracking error, 0.994 (-)
ege = Geometry error (mirror alignment), 0.98 (-)
?cl = Clean mirror reflectance, 0.935 (-)
edm = Dirt on mirrors (reflectivity/?cl) reflectivity is an input parameter, usual value: 0.88e0.93
eda = Dirt on receiver, (1 þ edm)/2 (-)
eun = Unaccounted, 0.96 (-)
FR=mcpArUL1-Exp-ULF’Armcp F’ is the collector efficiency Factor
F’=1UL1UL+DpohfDpi+Dpo2kfInDpoDpiUL Represents the collector heat loss coefficient which is the summation of the coefficients for conduction through the glass cover, convection form the outside of the receiver pipe to the annulus space and ambient air, and radiation from the outside of the receiver pipe to the sky.
3.2.1 PTSC energy modelThe PTSC is able to extract energy from the direct beam irradiation (Gbeam), therefore the solar energy that is extracted by the collector can be defined by the equations below 44:Qsolar = Aa . Gbeam (3.14)
Where Aa is the aperture area of the collector.
We can calculate the thermal output from the PTSC by analyzing the change in temperature using the following equation
Quseful = mcp(Thtf out-Thtf in) (3.15)
Assume all process are run at equilibrium and a steady state processes. The instantaneous thermal efficiency PTSC can be calculated by the equation below:
?th,collector= QusefulQsolar (3.16)
The analysis for the PTSC is done under steady state conditions as mentioned in the assumptions; the rate of useful energy produced by the PTSC is the difference between the amount of heat absorbed by the heating fluid and the direct or indirect losses from the surface to the surroundings. The useful energy collected by the PTSC is given by:
where the aperture area Aa is defined as:
The concentration ratio of the PTSC is defined as the ratio of the aperture area to the receiver area, it is as follows:
The PTSC can utilize only a portion of the total sun radiation. This portion is called the beam radiation and it is absorbed by the receiver, therefore it depends on the receiver efficiency. The beam radiation is given by:
The heat removal factor is the ratio of the actual heat delivered to the heat delivered if the collector plate was at a uniform temperature equal to the temperature of the entering fluid. The heat removal factor is as follows:
A new model for the overall heat transfer coefficient and the overall heat loss coefficient is presented in this thesis. The overall heat transfer coefficient depends on the overall heat loss coefficient, convective heat transfer coefficient inside the absorber tube of the PTSC, and the conduction heat transfer coefficient of the heating fluid through the absorber tube of the PTSC. On the other hand, the heat loss coefficient was modeled based on the following assumptions and heat transfer mechanisms:
Conduction heat transfer through the receiver.
Conduction heat transfer through the glass cover.
Convective hear transfer between the glass cover and the ambient.
Radiation heat transfer between the receiver and the glass cover.
Radiation heat transfer between the glass cover and the ambient.
According to the previous assumptions and by adding the thermal resistances of each heat transfer mechanisms, the overall heat loss coefficient and heat transfer coefficient are as follows:
The collector efficiency factor F’ is the ratio of the actual useful energy gain to the useful energy gain produced if the collector absorbing surface is at the local fluid temperature. The efficiency factor is defined as:
In order to carry out the analysis, the glass cover temperature is assumed and the parameters are calculated. To check the accuracy of the assumption, the cover temperature can be calculated and checked as follows:
The efficiency of the PTSC can be calculated from the following equation:
Table 6 shows the design input parameters for the analysis of the energy model of the PTSC.
3.3.5 PTSC exergy model.The exergetic analysis done on the PTSC is fairly simple; the exergetic efficiency is the ratio of the output exergy to the input exergy. In case of the PTSC, the exergy output is the exergy stored by the fluid that passes through the receiver tube, while the exergy input is the exergy of the solar radiation absorbed by the PTSC.
Table SEQ Table * ARABIC 6: PTSC energy model design parametersParameter Symbol Unit Value
Outlet temperature To?391
Receiver temperature Tr?334
Glass cover temperature Tc?105
Ambient Temperature Tamb?25
Sun Temperature TsK5770
Beam radiation IBW/m2560
Wind Velocity vwindm/s5
The exergy efficiency is as follows:
Where the exergy output and exergy input are given as follows:
The exergy destruction is the difference between the input and the output exergy, and it can be calculated using the following equation:
The entropy generation can be simply calculated using the following equation:
3.5 Integrated Solar-Regenerative Rankine Cycle model (ISRRC)The Integrated Solar-Regenerative Rankine Cycle (ISRRC) consists of the solar power input which is the PTSC and a regenerative Rankine Cycle. The regenerative Rankine cycle mainly consists of a boiler, steam turbine, condenser, pump, open feed water heater and a feed pump. In case of the solar integration, the boiler is substituted by a solar field and a heat exchanger to carry the heat from the heating fluid to the water as shown in Figure 8. Figure 9 shows the T-S diagram of the ISRRC. The heating fluid is heated in the solar field until the required design temperature where it is then pumped into the heat exchanger to heat the water. The water exits the heat exchanger as steam and it is directed to a steam turbine where a fraction of it is used for power production, and a fraction is extracted and directed towards the open feed water heater which works as a heat exchanger. The portion of the steam that was not extracted expands completely and it is led to the condenser where the pressure drops and the steam changes phase to saturated liquid as it exits the condenser. The saturated liquid is then pumped to the feed water heater pressure where it mixes directly with steam extracted from the turbine. The feed water heater is called an open feed water heater because of the direct mixing that takes place. In the ideal case, the mixture leaves the feed water heater as saturated liquid with no pressure loss. The saturated liquid is directed to the feed pump where it is pumped to match the heating fluid pressure in order for the heat exchange to take place. The water leaves the heat exchanger as steam and the cycle is repeated.
Figure SEQ Figure * ARABIC 10: ISRRC Schematic Diagram
Figure SEQ Figure * ARABIC 11: T-S diagram for the ISRRCWhen comparing between the ISRC and ISRRC, the thermal efficiency of the ISRRC cycle is higher than that of the ISRC. The increase in the temperature of the turbine inlet reduces the work of the turbine for a set power output, therefore increasing the efficiency of the cycle. The pressure of the feed water heater and the amount of steam extracted affects the performance of the cycle greatly. The optimization of the feed water pressure is shown in the results section. The thermodynamic analysis of the ISRRC is shown below. Table 9 shows the design input parameters for both the ISRC and ISRRC cycles.
Table SEQ Table * ARABIC 9: ISRC and ISRRC Input Design ParametersPower Cycles
Parameter Symbol Unit Value
Cycle – – ISRC ISRRC
Type – – Conventional
Rankine Cycle Regenerative
Net Power OutputWnetMWe150 150
Steam turbine efficiency ?st%85 85
Pumps efficiency ?p%78 78
Steam Turbine Pressure Pstbar100 100
Feed water Pressure Pfbar- 9
Condenser Pressure Pcbar0.1 0.1
3.5.1 Open feed water heater.The mass balance and energy balance on the open feed water heater yields the following equations:
The fraction of steam extracted from the turbine y is given as:
The previous equation means that for every kg of steam that enters the steam turbine a mass fraction y is going to be extracted and directed to the open feed water heater.
3.5.2 Steam turbine.The specific work output of the turbine can be calculated using the following equation:
3.5.3 Condenser.The specific heat rejected by the condenser is described by the following equation:
3.5.4 Pumps.The specific work of the pumps is calculated given by the following equation:
where wcp,RRC is the specific ideal work of the condenser pump given by:
where v6 is the specific volume of the saturated water, P5 and P6 are the pressures of the feed water heater and the condenser respectively.
The feed pump ideal work wfp,RRC is calculated from the following equation:
where v6 is the specific volume of the saturated water, P5 and P3 are the pressures of the feed water heater and the steam turbine respectively.
3.5.5 Heat exchanger.The design of the heat exchanger is the same as section 3.4.4; the mass flow rate of the steam can be also calculated from Equation (3.126). However the net specific work of the ISRRC can be calculated from the following equation:
3.6 Thermal Energy StorageThe thermal energy storage allows for flexible working hours and can increase the production of the plant, however integrating the TES will lead to a decrease in the efficiency because of the thermal losses. In this analysis a two tank molten salt storage is used as a TES, with a full load storage capacity of 7.5 hours or 10 hours depending on the mode of the operation discussed in the following section. Another heat exchanger is added after the PTSC and it can be modeled using the equations from section 3.4.4. The heat exchanger is supplied in order to exchange the heat between the heating fluid and the molten salt in the tanks. The energy balance on that heat exchanger is provided as follows:
where Thot, Tcold are the design temperatures of the two tanks presented in Tables 10 and 11. Along with the input design parameters and the storage volume calculated on SAM (Solar Advisory Model) based on the previous data provided in Table 6 and Table 9, the storage salt used is Hitec Salt and it operates between the temperatures of 142 and 538?. The volume of tank is considered to be the volume needed to fill one tank completely while the other one is empty. Nonetheless, a minimum amount of salt is required to be present in both tanks at any given time. The efficiency of the ISRC/TES can be calculated using the following equation:
3.6.1 Modes of operation.In the analysis, three modes of operation are examined. In the 1stmode, no thermal energy storage is used. The operation time is limited to the PTSC working hours, and the energy produced is directly utilized for power production.
The 2ndmode of operation allows for 7.5 hour storage period, meaning that the fluid is stored during the charging cycle, and after the PTSC is shut, the fluid is discharged starting the discharging cycle. Table 10 shows the input design parameters for the 2nd mode of operation.
The 3rd mode of operation allows for a longer storage period of 10 hour. The fluid stored in the two tank molten salt storage systems will be discharged for a longer period of time compared to the 2nd mode of operation. However, because of that higher storage time period, the volume of the storage tank increases as seen from Table 11, where the input design parameters for the 3rd mode of operation are presented. The increase in the volume will naturally lead to an increase in the cost of the storage system.
Table SEQ Table * ARABIC 10: TES design parameters for the 2nd mode of operationParameter Symbol Unit Value
Storage Media Type – – Sensible
Storage Media – – Hitec Salt
Cold Tank Temperature Tcold?250
Hot Tank Temperature Thot?365
TES Density ?saltkg/m31829.31
TES Specific heat CpsaltkJ/kgK1.56
Storage Volume VTESm343726.2
Tank Height htankm20
Tank Diameter Dtankm53
TES Thermal Capacity QtankMWh2981
TES Capacity tstoragehour7.5
Table SEQ Table * ARABIC 11: TES design parameters for the 3rd mode of operationSymbol Unit Value
Storage Media Type – – Sensible
Storage Media – – Hitec Salt
Cold Tank Temperature Tcold?250
Hot Tank Temperature Thot?365
TES Density ?saltkg/m31829.31
TES Specific heat CpsaltkJ/kgK1.56
Storage Volume VTESm358301.6
Tank Height htankm20
Tank Diameter Dtankm61
TES Thermal Capacity QtankMWh3975
TES Capacity tstoragehour10
3.6.2 ISRC/TES and ISRRC/TES systems.The Integrated Solar Rankine Cycle/TES system and the Integrated Solar Regenerative Rankine Cycle/TES system can be divided into three main subsystems: The solar field, power block, and storage system. The solar field is basically the PTSC field, while the power block is the conventional Rankine cycle for the ISRC and the Regenerative Rankin Cycle for the ISRRC. The TES System consists of two tanks filled with Hitec salt. The properties of the Hitec salt shown in Tables 10 and 11 differ depending on the modes of operation. The ISRC and ISRRC will operate on either a full load operation, or a partial load operation depending on the beam radiation.
In the charging cycle and for the full load operation during the hours where the demand by the power cycle is met by operating the PSTC alone. The heating fluid from the PTSC field by passes the TES system and is directed toward the power cycle heat exchanger to heat up the water as seen in Figure 10 (a) for the ISRC/TES system and Figure 12 (a) for the ISRRC/TES system. While operating on partial load, when the mass flow rate from the PTSC field exceeds the designed flow rate for solar energy production, i.e. during high solar radiation periods; the excess flow rate from the solar field will pass through the storage tank heat exchanger to charge the two tank Hitec salt storage system as seen in Figure 10 (b) and Figure 12 (b). The salt from the cold tank is heated and then directed to the hot tank where it is stored for later use. The system is controlled by the three way open valves placed between the PTSC solar field and the TES system. During the charging cycle the valves are open to let the heating fluid enter the heat exchanger and charge the system.
In the discharging cycle and for full load operation during the night hours where the PTSC is not in operation. The salt flows from the hot tank into the heat exchanger where it heats the water to steam, then the Hitec salt is directed back to the cold storage tank to be stored as seen in Figure 11 (a) for the ISRC/TES system and Figure 13 (a) for the ISRRC/TES system. While operating on partial load, during the low beam radiation hours mostly before sunset, both the TES system and the PTSC are in operation. The water from the power cycle is first heated up by the Hitec salt flowing from the hot storage tank, and then it is heated by the heating fluid from the PTSC field as seen in Figure 11 (b) and Figure 13 (b). The three way valves are used to regulate the flow between the PTSC field and TES system.
The same thermal storage salt is used in both integrated cycles, the molten salt used is Hitec and it possess great performance parameters; however there are still concerns about the freezing temperature of the salt in the tanks. Most molten salts freeze at high temperatures around100?; in the Hitec case the freezing temperature is 142? , which might occur if the temperature in the cold tank drops during long periods of charging. Therefore, it is suggested to add a set of auxiliary heaters to maintain the design point temperature and heat the salt in case of temperature drop.
Figure SEQ Figure * ARABIC 12: ISRC/TES Charging Cycle Schematic Diagram for (a) Full load, and (b) Partial load
Figure SEQ Figure * ARABIC 13: ISRC/TES Discharging Cycle Schematic Diagram for (a) Full load, and (b) Partial load
Figure SEQ Figure * ARABIC 14: ISRRC/TES Charging Cycle Schematic Diagram for (a) Full load, and (b) Partial load
Figure SEQ Figure * ARABIC 15: ISRRC/TES Discharging Cycle Schematic Diagram for (a) Full load, and (b) Partial load