Impact of the heat transfer fluid in a flat plate phase change thermal storage unit for concentrated solar tower plants

Available online at www.sciencedirect.com

ScienceDirect Solar Energy 101 (2014) 220–231 www.elsevier.com/locate/solener

Impact of the heat transfer fluid in a flat plate phase change thermal storage unit for concentrated solar tower plants Ming Liu ⇑, Martin Belusko, N.H. Steven Tay, Frank Bruno Barbara Hardy Institute, University of South Australia, Mawson Lakes Boulevard, Mawson Lakes, SA 5095, Australia Received 28 June 2013; received in revised form 8 December 2013; accepted 26 December 2013 Available online 22 January 2014 Communicated by: Associate Editor Ranga Pitchumani

Abstract Thermal energy storage allows improved dispatch-ability of power from a concentrated solar power plant and increases its annual capacity factor. The selection of an appropriate heat transfer fluid (HTF) is important for designing a cost-effective thermal storage system and to improve the cycle efficiency of the power plant. The current state-of-the-art HTF for tower power plants is molten salts, which have the drawback of having low degradation temperature and high melting temperatures respectively. Alternative HTFs under investigation allow for a much larger range of operation, and can offer other cost and performance advantages. In this study, a comparison of six gaseous and liquid HTFs was carried out to determine their suitability for use in a high temperature thermal storage unit with flat slabs of phase change materials. The comparison is in terms of their thermo-physical properties, heat transfer characteristics between the flat plates and the total delivered electrical energy to the grid. Using a validated mathematical model of phase change material in thin slabs, the HTF outlet temperature, heat transfer rate and liquid fraction profiles were predicted when using different HTFs at a constant heat capacity rate for both charging and discharging processes. For the capacity rate considered, liquid sodium was identified as the best HTF, delivering the highest electrical energy to the grid, achieving 99.4% relative to the ideal case. Solar salt achieved a value of 93.6%, while the gaseous fluids of atmospheric air, air at 10 bar, s-CO2 at 100 bar and steam at 10 bar achieved between 87.9% and 91.3% of the ideal delivered electricity. Gaseous fluids have the advantage of being able to be used as the working fluid in the power block. This study shows that gaseous fluids are comparable to liquid HTFs in PCM storage facilities. Ó 2014 Elsevier Ltd. All rights reserved. Keywords: Heat transfer fluid; Phase change material; Thermal energy storage; Solar thermal; Solar tower

1. Introduction Concentrated solar power (CSP) with thermal storage is becoming the renewable energy of choice to replace conventional power stations. Current thinking suggests that solar power towers will be the cheapest CSP technology in 2020 (Sargent and Lundy LLC Consulting Group,

Abbreviations: Heat transfer fluid, HTF; Phase change materials, PCMs; Phase change thermal storage unit, PCTSU; Supercritical CO2, s-CO2. ⇑ Corresponding author. Tel.: +61 (08) 83025132; fax: +61 (08) 83023380. E-mail address: [email protected] (M. Liu). 0038-092X/$ - see front matter Ó 2014 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.solener.2013.12.030

2003). Thermal energy storage solves the time mismatch between solar energy supply and electricity demand. The state-of-the-art thermal energy storage in tower power plants are two-tank direct sensible storage using molten salt made of 60 wt.% NaNO3 and 40 wt.% KNO3 (Kuravi et al., 2013). Fig. 1 presents a schematic of a solar tower power plant with a two-tank molten salt storage (Carlqvist, 2009). In the charging process, cold molten salt is pumped from a cold storage tank (290 °C) through the central receiver, where it is heated up to 565 °C and then stored in a hot tank. When the stored energy is needed, the hot molten salt is pumped to a steam generating system that produces superheated steam at nominal conditions of 540 °C and

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221

Nomenclature cp g h H k kf dotm Nu Pg Pe PL Pr Q Qideal Qact qdischarge

specific heat (kJ/kg K) gap width between two slabs (m) heat transfer coefficient of the HTF (W/ m2 K) half of the slab thickness (m) thermal conductivity of the PCM (W/m K) thermal conductivity of the HTF (W/m K) mass flow rate of the HTF (kg/s) Nusselt number (–) power to the grid (MW) electrical power (MW) pumping loss (kW) Prandtl number (–) energy stored in the PCM of volume V (kJ) ideal delivered electrical energy to the grid (MW h) actual delivered electrical energy to the grid (MW h) discharging thermal energy from the PCTSU (MW)

125 bar for a two-stage Rankine-cycle turbine. Then the cold molten salt is returned from the steam generator at 290 °C and stored in the cold tank. To realize a discharge duration of 6 h for a 50 MW power plant, approximately 7300 ton (3900 m3) NaNO3/KNO3 molten salt is required. The properties of NaNO3/KNO3 molten salt were obtained from the Solar Adviser Model (NREL, 2009). Compared with the state-of-the-art sensible energy storage, phase change materials (PCMs) have the advantage of potentially storing more energy per unit volume, achieving a lower cost per unit of stored energy (Gil et al., 2010). Phase change thermal storage has been applied in numerous low temperature applications and is a very promising technology for high temperature thermal storage in concentrated solar power applications. When solar radiation is available, the heat energy obtained from the solar receiver by the HTF can be stored in the PCM by changing the phase of the PCM from solid to liquid, which is called the charging process. Later on, when there is higher electricity demand or tariffs or during cloudy periods, the stored heat can be recovered and used for steam generation. During the discharging process, the PCM freezes, transferring the stored energy to the HTF. Flat plate phase change thermal storage unit (PCTSU) is one of the popular configurations currently in use and it has been studied by many researchers (Morrison and Abdel-Khalik, 1978; Ismail et al., 1999a, Zalba et al., 2004; Saman et al., 2005; Dolado et al., 2011; Liu et al., 2012a). A significant drawback of PCMs is the low thermal conductivity, and considerable work has been undertaken to increase conductivity (Tamme, 2007; Pincemin et al.,

Re Ts,c, Ts,d Tm TL TH v V dotV DH DP l f gp gps gratio q

Reynolds number (–) source temperatures in charging and discharging (°C) phase change temperature (°C) low temperature (K) high temperature (K) HTF velocity (m/s) PCM volume in the storage unit (m3) volumetric flow rate of the HTF (m3/s) latent heat energy of the PCM (kJ/kg) pressure drop in the PCTSU (Pa) dynamic viscosity (Pa s) friction factor (–) pump efficiency (–) power station efficiency (–) efficiency ratio (–) density (kg/m3)

2008; Steinmann et al., 2009; Shabgard et al., 2010). The configuration of PCM encapsulation in thin flat slab achieves a higher ratio of heat transfer surface to PCM volume compared to other encapsulations such as spheres, reducing the thermal resistance between the HTF and the PCM across the thickness of the slab. Consequently, the heat transfer is dominated by the convection heat transfer defined by the HTF and selecting the optimum HTF is critical for the charging/discharging rate of the storage system. Molten salts have been used as both a HTF and a storage medium in Solar Tres power tower solar power plants (Liu et al., 2012b). The solar field outlet temperature is above 550 °C. Molten salts present excellent thermal properties at higher temperatures, such as high density, high heat capacity, low viscosity and high thermal conductivity. Moreover, they are thermally stable, non-flammable, nontoxic and can be operated under ambient pressure. There are a few commercially available molten salts. One is a binary eutectic nitrate salt consisting of 60% NaNO3 and 40% KNO3, namely solar salt. Another developed molten salt is Hitec, which is made of 53% KNO3, 40% NaNO2 and 7% NaNO3. The maximum operation temperatures of solar salt and Hitec are 585 °C and 535 °C, respectively. The disadvantage of molten salts as HTFs is their high melting point (221 °C for solar salt and 142 °C for Hitec). Therefore, costly freeze protection is required. Liquid metal such as liquid sodium has a lower melting point of 97.7 °C and a higher boiling point of 873 °C than molten salts, resulting in a larger system operation temperature. The major disadvantage of sodium is its reaction

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Fig. 1. Schematic diagram of a solar tower power plant with a two-tank molten salt storage (Carlqvist, 2009).

with water; therefore, the system must be operated absolutely isolated from the environment. Sodium has been used as HTF in the nuclear industry since the 1950s and it has also been used in a central receiver project run during the 1980s (Boerema et al., 2012). Boerema et al. (2012) developed a receiver model and compared Hitec and liquid sodium as HTFs. Their study showed that with sodium as the HTF, the heat transfer coefficient is an order of magnitude greater than that for Hitec. Molten salts and sodium require a heat exchanger to transfer the heat to the working fluid in the power cycle. Using superheated steam or compressed air as the HTF can be directly fed into the steam or gas turbine to generate electricity. If they are used as a working fluid transferring energy into the thermal storage system, it allows the steam or gas turbine to be powered directly without a heat exchanger, increasing system efficiency and reducing cost. Compared with the Rankine cycle, the Brayton cycle using air in the gas turbine offers higher cycle efficiencies and lower investment cost. The compressed air can be heated up to 800 °C by using pressurized volumetric air receivers before entering into the combustor. Romero et al. (2002) summarized the solar power tower systems that have been tested all over the world along with new plants that are likely to be built. The HTFs used in the receiver include liquid sodium, saturated or superheated steam, molten salts, atmospheric and compressed air. Supercritical CO2 (s-CO2) is another promising HTF for future solar thermal power plants, which can also be used directly as the working fluid (Glatzmaier and Turchi, 2009). s-CO2 is a fluid state of CO2 where it is held at or above 304.25 K and 73.9 bar. It has been investigated in sodium-cooled fast reactors in next generation nuclear power plants (Ichimiya et al., 2007). s-CO2, like steam and air, is quite cheap, nontoxic, non-flammable and has no upper operation temperature. s-CO2 and air has an

added advantage of single-phase operation. However, s-CO2 has practical limits, operating at high pressures, higher than that used for steam. The purpose of thermal storage is to store useful work (Bejan, 2006). In a PCM storage facility, indirect heat exchange occurs between the HTF and the PCM during charging and discharging, which does not occur in a direct molten storage facility. This heat exchange has associated irreversibilities. Furthermore, due to the increase in the number of these irreversible processes, exergy losses within thermal systems are increased (Belusko et al., 2012), and are expected to be greater than in a molten salt sensible storage system. Therefore, minimising these exergy losses is critical to realizing the benefits of PCM in high temperature thermal storage. Given the significance of the HTF in defining the heat transfer process in a flat slab PCM system, a comparison of different HTFs is needed. The basis of any comparison will be the impact of the total delivered power from a tower based CSP plant. This paper aims to evaluate the thermal performance of a flat slab PCTSU, which indirectly stores energy being transferred from six currently used and promising HTFs. The HTFs under investigation include atmospheric air, compressed air at 10 bar, s-CO2 at 100 bar, steam at 10 bar, solar salt and liquid sodium. To analyze the heat transfer in the flat slab PCTSU, an experimentally validated mathematical model was used. 2. PCM plate mathematical model The flat slab PCTSU under analysis consists of a number of flat PCM plates surrounded by an adiabatic rectangular wall. Liquid/gaseous HTF flows along the passages between the plates (Fig. 2). It is derived directly from the construction principle of plate heat exchangers with one side of the fluid replaced by the PCM. The difficulty of

M. Liu et al. / Solar Energy 101 (2014) 220–231

Fig. 2. Schematic diagram of the PCTSU showing the PCM containers and circulating fluid channels.

was analytically represented by Belusko et al. (2012). Conditions for which 2-D heat flow can occur were identified by Eq. (1). In this study, for gaseous HTFs, this criterion is not met in the charging process subject to high Nusselt numbers, indicating that only 1-D phase change. This criterion is met for gaseous HTFs in the discharging process and for liquid sodium and molten salts for both charging and discharging, indicating that 2-D phase change occurs, however may not prove significant. The testing conducted by Liu et al. (2011b) also met the 2-D criterion, yet the 1-D model corrected well with experimental results. These tests were conducted with a liquid and with laminar flow maximising the impact of 2-D flow. The tests exceeded the criterion in excess of the gaseous HTFs and the salts for both discharging and charging, indicating that 2-D effects were more significant in the testing by Liu et al. (2011b). Therefore 1-D phase change in the PCM can be assumed with these HTFs. Assuming a 1-D phase change with liquid sodium will underestimate the heat transfer. H P 2kg=Nuk f

Fig. 3. Schematic of the solid-liquid interface of PCM slabs during phase change (reproduced from (Halawa and Saman, 2011)).

solving the heat transfer problem during the phase change process is due to the nonlinear movement of the solidliquid interface, namely moving boundary problems (MBPs) or Stefan problem (Zalba et al., 2003). This method was applied to PCM slabs in which a 2-D phase change boundary was modelled. Fig. 3 provides a representation of the solid-liquid interface which moves along both the vertical and horizontal directions (Halawa and Saman, 2011). The horizontal boundary is due to the heat transfer caused by the temperature difference between the HTF and the PCM. The near vertical boundary is due to the variation of PCM temperature along the horizontal plane. The parametric studies conducted by Morrison and AbdelKhalik (1978) demonstrated that axial conduction in the PCM along the horizontal direction is negligible due to the low thermal conductivity for both water and air. It was demonstrated by Halawa (2005) that assuming a 1-D heat transfer in which only a moving vertical phase change boundary exists, resulted in a negligible difference in the accuracy of the model for slab thicknesses less than 20 mm. In his study, the ratio of slab length to slab thickness is greater than 50 and a moderate temperature PCM was used. The temperature stratification in the vertical direction is very small for thin PCM slabs because they are exposed to the same forced convection on both the upper and lower surfaces (Halawa and Saman, 2011). In this case, the PCM slab is modelled as a series of nodes with a homogenous temperature. Under these conditions, the thermal conductivity of the PCM is not a factor. Applying the phase change boundary profile of Halawa and Saman (2011), the phase change process in PCM slabs

223

ð1Þ

where H is half of the slab thickness, k is the thermal conductivity of the PCM, g is the gap width, Nu is the Nusselt number and kf is the thermal conductivity of the HTF. The model considered half a thickness of the PCM slab and the HTF channel (Fig. 4) as the moving boundary is assumed symmetrical. The model also ignores any natural convection in the PCM, which has been shown to be small due to the thin slab thicknesses (Dolado et al., 2011; Halawa and Saman, 2011). Furthermore, since the temperature of each slab on either side of the HTF is equal, the radiation between the slabs is neglected. The energy balance equation for the HTF was solved using the finite difference method and the PCM temperature and liquid fraction were determined by incorporating the phase change processor algorithm developed by Halawa and Saman (2011). The convection heat transfer coefficient is calculated locally at each node. For the case of laminar flow between parallel plates, in the entrance region, the local Nusselt number (Nu) in Eq. (2) for constant wall temperature is recommended by Shah and London (Kay and Perkins, 1985, pp. 7–63). For fully developed laminar flow, the Nusselt number is equal to 7.5401 (Kay and Perkins, 1985, pp. 7–56). For turbulent flow in the entrance region and fully developed conditions, Eq. (3)and the Dittus–Boelter equation (Eq. (4)) are utilized to calculate the Nu respectively (Holman, 2010, pp. 280–282). For liquid metal (Pr  1), Hartnett and Irvine (Kay and Perkins, 1985, pp. 7–77)

Fig. 4. The geometry of the HTF-wall-PCM heat transfer.

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suggested an approximate Nu calculation for constant wall temperature (Eq. (5)). ( Nu ¼

1=3

1:233ðxþ Þ

xþ 6 0:001

þ 0:4 3 þ 0:488 245xþ

7:541 þ 6:874ð10 x Þ

e

Nu ¼ 0:036Re0:8 Pr1=3 ðDe=LÞ

xþ > 0:001

ðRe < 4000Þ

0:055

ðRe > 4000; L=De < 400Þ 0:8

Nu ¼ 0:023Re Pr

n

ð2Þ

ð3Þ

ðRe > 10; 000; ð4Þ

0:6 < Pr < 100; L=De > 60Þ Nu ¼ 6:573 þ 0:015ðPr  ReÞ0:8

ðPr  1Þ

ð5Þ

+

where x = (x/De)/(RePr). De is the equivalent diameter of the HTF passage and Re and Pr are the Reynolds number and Prandtl number. L is the distance between the entrance and node. n = 0.4 in melting process and n = 0.3 in freezing process. The model was validated using air as the HTF and a liquid under refrigeration conditions. The validation with air is presented in (Halawa et al., 2010). In the experiment, a total of 253.5 kg PCM29 (CaCl26H2O) was encapsulated into 96 conical capsule sheets, which were contained in a PCTSU with the dimension of 1.3 m  0.9 m  0.6 m. The air flows along the void space between pairs of PCM sheets. Due to the geometry difference, while keeping the heat transfer surface constant, the equivalent number of slabs, the slab thickness and the air gap were determined, on a constant volume basis. Further validation was conducted by Liu et al. (2011b), applying a liquid HTF under refrigeration conditions. The PCTSU in the experiments consists of 19 flat slabs of PCM separated by a 6 mm gap and each slab has dimensions of 0.26 m  1.70 m  0.025 m. The heat transfer fluid used was a glycol based liquid. Reasonable agreement was achieved between the predicted and experimental results and further details can be obtained in Liu et al. (2011b). The model has also been used to optimize the design of flat plate PCM thermal storage systems (Amin et al., 2012). To quantify the difference between the measured and the simulated HTF outlet temperatures (in degrees Celsius), the relative maximum error and an average error were estimated. The maximum error was always less than 11.8% for all the cases. The average error was 2.2% for the validation results with liquid HTF and 3.4% for the air case. In addition, the charge/discharge time determined by the experiment and the model was compared and the error was 1.7% for the liquid HTF case and 5.6% for the air case,

which demonstrates that the model is capable of predicting the charge/discharge time with good accuracy. Parametric studies have been conducted on the flat plate PCTSUs by varying the geometric configurations, such as the PCM slab thickness, slab dimensions and gap width (Halawa and Saman, 2011; Liu et al., 2011a; Amin et al., 2012). The result indicated that the heat transfer between the HTF and the PCM can be improved by applying a thinner slab and a smaller gap width. The heat exchange effectiveness of the storage system can achieve up to 0.99 with a slab thickness of 0.01 m and a gap width of 0.005 m (Amin et al., 2012). Such parameters deliver near supersonic velocities and therefore in this analysis, a slab thickness of 0.02 m and a corresponding gap width of 0.015 m were selected which delivers near optimum thermal performance of the storage system as indicated in Figs. 6 and 10 in Amin et al. (2012). By taking into account the thickness of the container (0.002 m), the PCM takes up 54% of the volume of the tank, which is similar to the packed bed storage system (53%) (Be´de´carrats et al., 2009). Some scope for optimization exists, and therefore the analysis provides a lower limit for the relative impact of HTFs. For the analyzed PCM slabs, the ratio of the heat transfer surface to PCM volume is 100 and the values are 60 and 75 for a packed bed system with the sphere diameter of 0.1 m and 0.075 m, respectively. 3. PCTSU system characterization The verified mathematical model was used to predict the thermal performance of a PCTSU for a 50 MWel solar tower power plant with a storage capacity of 840 MW hth to realize a discharge duration of 6 h, based on the overall efficiency of the power block and steam generator of 36%. To replace sensible storage with PCMs, one-tank indirect storage system is needed. For PCM storage, a suitable phase change temperature is required to achieve a similar conversion efficiency of the power block during the discharging phase. As a result, a eutectic PCM (PCM580) with a phase change temperature of 580 °C was selected and its thermo-physical properties are in Table 1 (Kenisarin, 2010). The thermal conductivity of the solid PCM is not given in the reference and it is assumed to be 0.5 W/ (m K), which is the value of most salt based PCMs (Kuravi et al., 2013). To charge the PCTSU, the source temperature from the central receiver will need to be sufficiently high in order to

Table 1 Thermo-physical properties of the eutectic PCM (PCM580) (Kenisarin, 2010). Composition (wt.%)

Phase change temperature (Tm, °C)

Latent heat of fusion (DH, kJ/kg)

Li2CO3(22)–Na2CO3(16)– K2CO3(62)

580

288

Specific heat (Cp, kJ/(kg K))

Thermal conductivity (k, W/(m K))

Solid

Liquid

Solid

Liquid

1.80

2.09

0.5

1.95

Solid density at 25 °C (qs, kg/m3)

2340

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deliver the thermal power capacity to the storage facility. The current objective for molten salt is to achieve operating temperatures above 650 °C in the SunShot program. A supply temperature for charging of 630 °C is assumed for molten salt and all other HTFs. Full charge is defined by the outlet temperature reaching the inlet temperature of 630 °C. This increase in supply temperature will have a negligible impact on the thermal efficiency of the receiver (Lovegrove and Stein, 2012). During the discharging process, a temperature of 290 °C is the assumed source temperature into the storage tank, applied to all HTFs. The discharging process will cease when the storage outlet temperature is below 565 °C. Based on the latent heat and sensible heat of PCM580 between the source temperatures in charging and discharging, the amount of storage material required to build the storage system is determined to be 1420 m3 (Eq. (6)). This amount translates to 180 slabs with

225

Table 2 PCTSU specifications. Parameter

Value

Number of slabs Slab length (m) Slab width (m) Slab thickness (m) Volume of PCM (m3) Gap (m) Container thickness (m) Thermal conductivity of the container (W/(m K)) Source temperature (inlet temperature, °C)

180 40 10 0.02 1420 0.015 0.002 16.3 (stainless steel) 630 (charging) 290 (discharging) 1255 (charging) 483 (discharging)

Heat capacity rate (kW/K)

a dimension of 40 m  10 m  0.02 m and the approximate dimension of the storage unit is 40 m  10 m  7.2 m

Fig. 5. Thermodynamic properties of the analyzed heat transfer fluids at temperature range of 290–630 °C: (a) density (kg/m3); (b) specific heat capacity (kJ/kg K); (c) thermal conductivity (W/m K) and (d) dynamic viscosity  105 (Pa s).

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excluding the enclosure. Pressure losses and associated pumping power was also considered in the analysis. Q ¼ qV ½cp;s ðT m  T s;c Þ þ DH þ cp;l ðT s;d  T m Þ

ð6Þ

where Q is the energy stored in the PCM of volume V, q is the PCM density, cp,s and cp,l are the specific heats of the PCM in the solid and liquid phases respectively, DH is the latent heat of fusion, Tm is the melting temperature, Ts,c and Ts,d are the source temperatures in charging and discharging, respectively. To compare the impact of each HTF, the power delivered to the grid by a CSP plant with a nominal rated electrical capacity of 50 MW was determined, which took into account pumping power. The assumed average design thermal capacity for the storage system is 140 MW, based on a 36% conversion efficiency, applied to both the charging and discharging processes. The power delivered will be determined applying an appropriate charging and discharging cycle, where the heat capacity rate (product of specific heat and mass flow rate) of each HTF will remain constant. Maintaining a constant capacity rate across all HTFs will enable a direct comparison of the impact the HTF has on the power to grid of the CSP plant. The charging process is based on each HTF being subject to the same solar thermal power, defined by an inlet temperature of 630 °C for 6 h. A comparison of HTFs identified that liquid sodium achieved the highest heat transfer rate, and a suitable mass flow rate was identified which enabled full charge to occur in 6 h after a few preliminary simulations with varying mass flow rates. The capacity rate obtained was 1255 W/K and was subsequently applied to all other HTFs. Consequently, the charge level within the storage system of the other HTFs will be lower depending on the heat transfer characteristics of each HTF. Discharging will apply a nominal heat capacity rate defined by the rated thermal input power of the plant, and applying a supply and sink temperature of 580 °C and 290 °C, equating to a capacity rate of 483 kW/K. Applying this capacity rate to each HTF, the average discharge temperature over 565 °C can be determined over the discharge period. Although, the discharge time will vary for each HTF, the average temperature will reflect the average useful heat transfer to each HTF. Based on the descriptions, the PCTSU system characterizations are summarized in Table 2.

upper temperature limit for the discussed gaseous HTFs. Properties for solar salt were taken from the Solar Adviser Model (NREL, 2009) and are suitable for temperatures up to 585 °C. For the purposes of this study, the properties beyond this temperature were extrapolated from the data. Properties of sodium were taken from Boerema et al. (2012). All the HTFs under investigation are Newtonian fluids. Fig. 5a shows that solar salt has the highest density being almost double that of sodium. The density of compressed air at 10 bar is almost 1.5 times of that of steam at 10 bar and 10 times of that of atmospheric air. The density of s-CO2 is the highest in the studied gaseous HTFs, which is around 15 times higher than that of compressed air. As shown in Fig. 5b, steam has the highest specific heat, which is almost twice of that of the other gaseous HTFs. The specific heat of solar salt is relatively constant at 1.5 kJ/(kg K) across the compared temperature range. The volumetric heat capacity can be calculated as the product of density and specific heat. Fig. 6 presents the volumetric heat capacity of the analyzed HTFs, which is similar to the density graph for each HTF in Fig. 5a. Solar salt has the highest volumetric heat capacity among the analyzed HTFs. To transfer the same amount of energy for equivalent operating temperatures, the HTF with higher specific heat will require a lower mass flow rate and the HTF with higher volumetric heat capacity will require a lower volumetric flow rate. Fig. 5c and d indicates that gaseous HTFs, regardless of the pressure, have quite similar and fairly low thermal conductivity and dynamic viscosity. Liquid sodium is the most thermally conductive HTF under analysis, being from 100 to 150 times more conductive than solar salt for temperatures from 630 °C to 290 °C. Solar salt has the highest viscosity, which is 4–10 times higher than sodium in the temperature range of 630–290 °C.

4. Comparison of various heat transfer fluids 4.1. HTF properties Fig. 5 shows the density, specific heat capacity, thermal conductivity and dynamic viscosity of the investigated HTFs across their available temperature range between 290 °C and 630 °C. Properties of atmospheric air, compressed air, s-CO2 and steam were taken from “Physical and chemical data” in Perry’s Chemical Engineers’ Handbook (Green and Perry, 2007). Theoretically, there is no

Fig. 6. Volumetric specific heat of the analyzed heat transfer fluids at temperature range of 290–630 °C.

M. Liu et al. / Solar Energy 101 (2014) 220–231

4.2. Impact of HTF The verified numerical model was used to simulate the heat transfer performance of the PCTSU for all the HTFs in both charging and discharging processes with the parameters specified in Table 2. A large portion of HTF outlet temperature occurs at 580 °C and 630 °C in charging and discharging, respectively. The HTF mass flow rate, velocity and Reynolds number, Prandtl number, Nusselt number and heat transfer coefficient for the six HTFs at 580 °C and 630 °C were presented in Table 3. The HTF velocity is less than 101 m/s and the Mach number is less than 0.3, hence the HTF could be assumed incompressible. Under the simulated heat capacity rate, liquid sodium has a high convection heat transfer coefficient, which is 82–98 times higher than other HTFs in the charging process and approximately 160 and 91 times higher than gaseous HTF and solar salt in the discharging process, respectively. Fig. 7a–c shows the predicted HTF outlet temperature from the PCTSU, heat transfer rate and liquid fraction profiles with the evaluated HTFs in the charging process (PCM melting). The profiles present the three stages of PCM charging/melting and the shape of the profile is a typical characteristic of a PCTSU during heating: (1) Sensible heating storage region (0–2 h). This initial period has a high heat transfer rate because of the large temperature difference between the HTF (630 °C) and the PCM (290 °C). This is followed by a sharp rise in the HTF outlet temperature to the melting temperature. In this region, sensible heat exchange in the solid state is dominant. (2) Latent heating storage region (2–5.6 h). After most of the PCM reaches the melting temperature, latent heat exchange becomes dominant. During this period, the PCM changes its phase from solid to liquid without changing its temperature. Therefore, the HTF outlet

227

temperature and heat transfer rate are almost constant for all of the HTFs at a temperature of 580 °C and heat transfer rate of 56–63 MW, respectively. (3) Sensible heating storage region (5.6 h-end of melting). This period occurs after most of the PCM completes phase change and it is driven by the temperature difference between the HTF and the PCM. The HTF outlet temperature gradually increases to the source temperature at 630 °C and the heat transfer rate gradually drops to zero with a lower slope than that in region (1). At the end of the charging process, a total amount of 840 MW h of energy is stored in the PCM. With the same heat capacity rate for all of the HTFs, liquid sodium has the highest average heat transfer rate because of its extremely high convection heat transfer coefficient. Consequently, the storage unit with sodium as the HTF completes the full charge in the shortest time period, being 6 h. At the end of 6 h, 8.9%, 7.3%, 7.8%, 0.5% and 0.1% of PCM580 are still solid with solar salt, air, compressed air, s-CO2 and steam as the HTF, respectively. This demonstrates that all of the HTFs considered can achieve similar heat transfer rates. Fig. 8a–c shows the predicted HTF outlet temperature, heat transfer rate and liquid fraction profiles from the PCTSU for the various HTFs during the discharge process (PCM freezing). The negative values of the heat transfer rate means that the PCM storage system supplies the heat to the power block. Initially, the HTF temperature remains close to 630 °C for 1.4 h for air and compressed air, 2.5 h for s-CO2 and steam and 3.5 h for solar salt. Liquid sodium being fully charged and having the highest heat transfer coefficient maintains the highest average discharge temperature for the longest. With a combination of poorer heat transfer and less stored energy the outlet temperature starts to decrease and the discharging stops when the temperature drops below 565 °C, beyond which, it is not suitable for power generation. The PCM storage tank is fully

Table 3 HTF convection heat transfer coefficients.

Charging process (@580 °C)

Discharging process (@630 °C)

Air Air @10 bar s-CO2 @100 bar Steam @10 bar Solar salt Liquid sodium Air Air @10 bar s-CO2 @100 bar Steam @10 bar Solar salt Liquid sodium

HTF mass flow rate (dotm, kg/s)

HTF velocity in channel (v, m/s)

Re

Pr

Nu

h (W/ m2 K)

1131 1132 1031

101.00 10.17 0.62

33,507 32,126 30,754

0.69 0.72 0.73

82.76 81.29 78.94

166 163 164

567 814 1000

7.97 0.02 0.05

19,940 855 5228

0.90 2.95 4.41E3

60.73 7.54 6.76

157 139 13,633

431 432 393

40.83 4.12 0.25

12,315 11,809 11,269

0.69 0.72 0.72

38.55 37.75 36.36

81 79 80

215 311 386

3.22 0.01 0.02

7124 438 2137

0.90 2.18 4.31E3

26.89 7.54 6.66

75 142 12,924

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discharged and the released thermal energy is 840 MW h with liquid sodium as the discharging HTF. The released energy is 790 774, 761, 749 and 748 MW h for solar salt, s-CO2, steam, air and compressed air respectively, which account for 93.6%, 91.3%, 89.9%, 87.9% and 87.9% of the total energy stored in the charging process for each respective HTF. When considering that the PCTSU was not fully charged for all other HTFs, these values highlight the limitations of the useful energy that can be stored within PCM systems. 4.3. Conversion efficiency of power block To determine the power to the grid, the thermal energy discharged needs to be converted to electrical power. The discharge temperature directly affects the conversion efficiency of power generation. Eq. (7)presents a Carnot based power station efficiency which can account for this varying discharge temperature. This equation incorporates an efficiency ratio (gratio) of the actual conversion efficiency to the ideal Carnot efficiency (61.5%) (Chapter 8 in Eastop and McConkey, 1993), based on the steam temperature range in this analysis of 540 °C to 40 °C. TL is the temperature at the condenser exhaust and TH is the temperature at the turbine inlet. The actual cycle efficiency for a simple steam power block is 36.0% (Pye et al., 2010), producing an efficiency ratio of 0.585.

gps ¼ ð1  ðT L =T H ÞÞ  gratio

ð7Þ

To account for the pumping losses due to the storage facility, the pumping power (PL) to charge and discharge the PCM system was determined using Eqs. (8) and (9)with the entrance and exit losses ignored. For laminar flow between parallel plates, the friction factor f can be estimated by f  Re = 24, which is recommended by Lundgren et al. cited in (Kay and Perkins, 1985, pp. 7–47). For turbulent flow, Blasius-type formula (Kay and Perkins, 1985, pp. 7–5) suggested the friction factor can be calculated by f = (1.58  lnRe  3.28)2. Pump efficiency, gp, was fixed at 50% while the power station efficiency, gps, was determined by using Eq. (7). The pumping power (PL) was deducted from the generated power (Pe) to determine the delivered power (Pg) to the grid (Eq. (10)).     L ð8Þ DP ¼ f   ðm_ 2 = 2  q  A2c De P L ¼ ðP  V_ Þ=ðgp  gps Þ

ð9Þ

Pg ¼ Pe  PL

ð10Þ

P e ¼ qdischarge  gps

ð11Þ

To ultimately compare a PCM thermal storage facility to a direct storage system, the ideal power station efficiency was found using Eq. (7)based on 630 °C and assumed a

Fig. 7. The predicted (a) HTF outlet temperature from the PCTSU; (b) heat transfer rate and (c) liquid fraction of the PCTSU with various HTFs in PCM charging process.

M. Liu et al. / Solar Energy 101 (2014) 220–231

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Fig. 8. The predicted (a) HTF outlet temperature from the PCTSU and (b) heat transfer rate and (c) liquid fraction of the PCTSU with various HTFs in PCM discharging process.

25 °C temperature decrease in the power block steam supply temperature, equating to 37.9%. Therefore, based on the design thermal capacity of the plant, the ideal delivered electrical energy (Qideal) to the grid is 318.4 MW h. To compare the delivered power generated by incorporating a phase change thermal storage system, the total electrical power supplied by using various HTFs was determined based on the applicable discharge time for each HTF. The calculation results are shown in Table 4. The results reveal that with the phase change storage, the total delivered electrical energy to the grid is less than that by using direct sensible storage. Among the investigated HTFs,

liquid sodium has the least exergy loss, following by the solar salt. The impact of the PCM model under predicting the heat transfer with liquid sodium, by assuming 1-D phase change, ultimately was negligible given that the actual power delivered is near the ideal case. On average, the gaseous HTFs deliver 281.5 MW h of electricity to the grid, which is 89.3% of that of the ideal electricity delivered by sensible storage. This result highlights that gaseous fluids can deliver reasonable electricity compared to liquid fluids in the PCM systems. The elimination of the heat exchanger will reduce the difference between gaseous and liquid HTFs.

Table 4 Electrical energy supplied by the PCTSU using different HTFs.

Air Air @10 bar s-CO2 @100 bar Steam @10 bar Solar salt Liquid sodium

Ave. discharge temperature (°C)

Ave. discharge time (h)

qdiscarge, (MW)

Total energy released (MJ)

DP (Pa)

gps (%)

PL (kW)

Pe (MW)

Pg (MW)

Qact, (MW h)

Qact/Qideal (%)

609.44 609.64 614.35 614.89 618.57 618.59

5.3 5.5 6.8 6.8 6.5 5.3

141.23 135.96 113.80 111.96 121.69 158.49

762.6 761.4 785.3 772.5 803.14 839.9

2348.5 239.8 13.6 108.3 2.5 1.6

37.1 37.1 37.2 37.2 37.3 37.3

75.55 0.78 2.72E03 0.28 1.36E05 2.32E05

52.4 50.4 42.3 41.7 45.4 59.1

52.3 50.4 42.3 41.7 45.4 59.1

277.3 277.4 288.0 283.4 295.1 313.4

87.9 88.0 91.3 89.9 93.6 99.4

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5. Conclusion This paper presents a comparison of six available or potential HTFs for use in a high temperature flat slab PCTSU. The HTFs under evaluation include atmospheric air, compressed air at 10 bar, s-CO2 at 100 bar, steam at 10 bar, solar salt and liquid sodium. The comparison is based on the same heat capacity rate for each HTF, subject to the same input thermal energy, for an average design thermal storage capacity of 140 MW. The storage system with liquid sodium is fully charged in the shortest time period, which is 25% shorter than that of solar salt. All of the other HTFs were charged for the same length of time that it took liquid sodium to fully charge, and therefore did not completely charge, reflecting lost energy due to poorer heat transfer ability. Furthermore, as irreversibilities occur during heat exchange in the indirect PCM storage system, exergy is lost and the deliverable energy to the grid is decreased. The PCM storage system with each HTF, was compared to the ideal sensible storage system. In the discharge process, liquid sodium is capable of producing 99.4% of the electricity to the grid compared with the ideal sensible heat storage. However, liquid sodium is considerably more expensive than other HTFs. Solar salt can produce 93.6% of the electricity to the grid and all gaseous HTFs deliver a similar delivered power between 87.9– 91.3%, for a volume fraction of 54%. Gaseous fluids, if used as the working fluid for power generation, have the added advantage of not requiring a heat exchanger. Therefore although the HTF has a limited impact on the electricity delivered for PCM indirect storage systems, significant cost savings can be achieved with lower performing HTFs. Furthermore, the analysis represents a lower limit and optimization will narrow the difference between the HTFs. Overall, using a PCM indirect storage system can deliver electricity power to the grid comparable to a direct storage system using a range of HTFs. Further research is warranted to optimize output and cost savings, as well as consider in more detail power generation configurations. Acknowledgment This project has been supported by the Australian Government through the Australian Renewable Energy Agency, part of the Clean Energy Initiative. References Amin, N.A.M., Belusko, M., Bruno, F., Liu, M., 2012. Optimising PCM thermal storage systems for maximum energy storage effectiveness. Sol. Energy 86, 2263–2272. Be´de´carrats, J.P., Castaing-Lasvignottes, J., Strub, F., Dumas, J.P., 2009. Study of a phase change energy storage using spherical capsules. Part I: experimental results. Energy Conv. Manag. 50 (10), 2527–2536. Bejan, A., 2006, Advanced Engineering Thermodynamics, J. Wiley & Sons. Belusko, M., Halawa, E., Bruno, F., 2012. Characterising PCM thermal storage systems using the effectiveness-NTU approach. Int. J. Heat Mass Trans. 55 (13–14), 3359–3365.

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