Feasibility Study of Freeze Recovery Options in Parabolic Trough Collector Plants Working with Molten Salt as Heat Transfer Fluid

energies Article Feasibility Study of Freeze Recovery Options in Parabolic Trough Collector Plants Working with Molten Salt as Heat Transfer Fluid Cristina Prieto 1,2,* , Alfonso Rodríguez-Sánchez 1, F. Javier Ruiz-Cabañas 1and Luisa F. Cabeza 3 1C/Energía Solar n◦1, Abengoa Energia, 41014 Sevilla, Spain; [email protected] (A.R.-S.); [email protected] (F.J.R.-C.) 2Camino de los Descubrimientos s/n, Department of Energy Engineering, University of Seville, 41092 Seville, Spain 3 GREiA Research Group, INSPIRES Research Centre, Universitat de Lleida, Pere de Cabrera s/n, 25001 Lleida, Spain; [email protected] *Correspondence: [email protected]; Tel.: +34-609336340 Received: 14 May 2019; Accepted: 10 June 2019; Published: 18 June 2019   Abstract: Parabolic trough collector (PTC) technology is currently the most mature solar technology, which has led to the accumulation of relevant operational experience. The overall performance and efficiency of these plants depends on several components, and the heat transfer fluid (HTF) is one of the most important ones. Using molten salts as HTFs has the advantage of being able to work at higher temperatures, but it also has the disadvantage of the potential freezing of the HTF in pipes and components. This paper models and evaluates two methods of freeze recovery, which is needed for this HTF system design: Heat tracing in pipes and components, and impedance melting in the solar field. The model is used to compare the parasitic consumption in three molten salts mixtures, namely Solar Salt, HiTec, and HiTec XL, and the feasibility of this system in a freezing event. After the investigation of each of these subsystems, it was concluded that freeze recovery for a molten salt plant is possible. Keywords: parabolic trough collector; molten salt; freeze recovery; heat tracing; impedance melting 1. Introduction Today, current trends in energy supply are unsustainable from environmental, economic, and social points of view, and stricter low-carbon economy policies push this demand further. Therefore, the development of advanced energy technologies is very much needed [ 1 , 2 ]. Crucial players to achieve such sustainable development goals are renewable energies, and in this new scenario concentrated solar power (CSP) is one of the most interesting alternatives [3,4]. Parabolic trough, linear Fresnel, tower, and parabolic dish are the main different options in CSP technology, depending on how the focus of sunrays and the position of the receiver is implemented (Figure 1). Line focus systems track the sun with mirrors arranged in one axis (parabolic trough and linear Fresnel systems), while point focus systems use two axes (tower and dish systems). On the other hand, the receiver can be fixed (linear Fresnel and tower systems) or mobile (parabolic trough and dish systems). Energies 2019,12, 2340; doi:10.3390/en12122340 www.mdpi.com/journal/energies Energies 2019,12, 2340 2 of 20 Energies 2019, 12, x FOR PEER REVIEW 2 of 21 conventional steam turbine generator after a heat transfer exchange with a secondary HTF, water/steam. Figure 1. Main concentrated solar power (CSP) technologies [2]. The tower technology uses large sun-tracking mirrors, also called heliostats, to focus the sunlight on a receiver that is located at the top of the tower to produce electricity from the sun [5]. The HTF is usually molten salt or water/steam, and it is heated when it flows through the receiver. Again, it is used in a conventional steam turbine generator to produce electricity, either directly or by using a heat exchanger. The linear Fresnel technology [6], on the other hand, uses mirrors mounted on trackers on the ground that are flat or slightly curved. The mirrors reflect sunlight to a receiver tube located above them. Sometimes, a small parabolic mirror is placed on the receiver to increase the focus of the sunlight. The last technology is parabolic dish systems, in which the concentrator is a dish with a parabolic-shaped focus point, with the receiver located at the focal point [5]. The sun is tracked with a two-axis structure where the concentrators are mounted. The receiver is usually mounted next to the heat engine that uses the collected heat to produce electricity on site. Here, Stirling and Brayton cycle engines are used. The HTF, thermal energy storage (TES), and power cycle can be selected from different options in each technology. One of the most important components to achieve high overall performance and efficiency in CSP systems is the HTF [7]. The main requirements for a proper HTF were summarized by Benoit et al. [8], based on the review of existing and potential HFTs used in CSP receivers. To increase the efficiency of the cycle, the HTF should be able to work in a wide working temperature range and should present high thermal stability. If this is accomplished, the cost of the solar field, which is the main saving factor in a CSP plant, is reduced. Next, in order to increase the heat transfer between the HTF, the TES material, and the power block driving fluid, and in addition to withstand high pressure and temperature changes, the HTF should have good thermophysical properties. Finally, the HTF should be non-hazardous, have a low corrosive behaviour, and should be costeffective. More information about different types of HTF suitable for CSP plants and other high temperature applications (such as liquids, supercritical fluids, and gases) is presented in other studies [7,9,10], such information on their cost and thermal and physical properties. CSP technology with a PTC system is currently the most mature solar technology, leading to the accumulation of relevant operational experience [11]. The most widely used heat transfer fluid (HTF) in parabolic trough plants is a eutectic mixture of the organic compounds biphenyl oxide and diphenyl oxide [12–14]. The operation temperature of the solar thermal power plant is limited to up to 400 °C when using an organic HTF [14,15], since when operating above this temperature the HTF degrades [15]. Significantly higher efficiency of the solar thermal power system can be achieved if a more stable HTF is used, such as binary or ternary mixtures of nitrate salts within the needed operating temperature [15–17]. These eutectic mixtures would allow operating temperatures of 500 °C or higher [10,16]. The most widely considered candidates are Solar Salt, HiTec®, and HiTec XL® [12,18]. Solar Salt is a binary salt mixture of 60 wt.% NaNO3 and 40 wt.% KNO3. HiTec is a ternary mixture of alkaliFigure 1. Main concentrated solar power (CSP) technologies [2]. Parabolic trough collector (PTC) systems concentrate the sun in a parabolically curved trough-shaped reflector. The receiver is a tube located along the inner side of the collector [ 5 ]. The heat transfer fluid (HTF), usually synthetic oil, is heated by the energy concentrated in the receiver, where it flows through the tube along the trough collector and is then used to generate electricity in a conventional steam turbine generator after a heat transfer exchange with a secondary HTF, water/steam. The tower technology uses large sun-tracking mirrors, also called heliostats, to focus the sunlight on a receiver that is located at the top of the tower to produce electricity from the sun [ 5 ]. The HTF is usually molten salt or water/steam, and it is heated when it flows through the receiver. Again, it is used in a conventional steam turbine generator to produce electricity, either directly or by using a heat exchanger. The linear Fresnel technology [ 6 ], on the other hand, uses mirrors mounted on trackers on the ground that are flat or slightly curved. The mirrors reflect sunlight to a receiver tube located above them. Sometimes, a small parabolic mirror is placed on the receiver to increase the focus of the sunlight. The last technology is parabolic dish systems, in which the concentrator is a dish with a parabolic-shaped focus point, with the receiver located at the focal point [ 5 ]. The sun is tracked with a two-axis structure where the concentrators are mounted. The receiver is usually mounted next to the heat engine that uses the collected heat to produce electricity on site. Here, Stirling and Brayton cycle engines are used. The HTF, thermal energy storage (TES), and power cycle can be selected from different options in each technology. One of the most important components to achieve high overall performance and efficiency in CSP systems is the HTF [ 7 ]. The main requirements for a proper HTF were summarized by Benoit et al. [ 8 ], based on the review of existing and potential HFTs used in CSP receivers. To increase the efficiency of the cycle, the HTF should be able to work in a wide working temperature range and should present high thermal stability. If this is accomplished, the cost of the solar field, which is the main saving factor in a CSP plant, is reduced. Next, in order to increase the heat transfer between the HTF, the TES material, and the power block driving fluid, and in addition to withstand high pressure and temperature changes, the HTF should have good thermophysical properties. Finally, the HTF should be non-hazardous, have a low corrosive behaviour, and should be cost-effective. More information about different types of HTF suitable for CSP plants and other high temperature applications (such as liquids, supercritical fluids, and gases) is presented in other studies [ 7 , 9 , 10 ], such information on their cost and thermal and physical properties. CSP technology with a PTC system is currently the most mature solar technology, leading to the accumulation of relevant operational experience [ 11 ]. The most widely used heat transfer fluid (HTF) in parabolic trough plants is a eutectic mixture of the organic compounds biphenyl oxide and diphenyl oxide [ 12 – 14 ]. The operation temperature of the solar thermal power plant is limited to up to 400 ◦ C when using an organic HTF [ 14 , 15 ], since when operating above this temperature the HTF degrades [15]. Significantly higher efficiency of the solar thermal power system can be achieved if a more stable HTF is used, such as binary or ternary mixtures of nitrate salts within the needed operating Energies 2019,12, 2340 3 of 20 temperature [ 15 – 17 ]. These eutectic mixtures would allow operating temperatures of 500 ◦ C or higher [ 10 , 16 ]. The most widely considered candidates are Solar Salt, HiTec ® , and HiTec XL ® [ 12 , 18 ]. Solar Salt is a binary salt mixture of 60 wt.% NaNO 3 and 40 wt.% KNO 3 . HiTec is a ternary mixture of alkali-nitrates/nitrites, and finally, HiTec XL is a ternary mixture of sodium, potassium, and calcium nitrates. Their melting properties are given in Table 1. Table 1. Properties of the three heat transfer fluid (HTF) candidates [12,19,20]. Solar Salt Composition (by weight) 60% NaNO3, 40% KNO3 Freeze Temperature, ◦C 220–238 (non-eutectic range at this mixture) Density, kg/m32090 −0.636 ×T (◦C) Specific heat, J/kg C 1443 +0.172 ×T (◦C) Dynamic Viscosity, Pa·s (22.14 − 0.120 × T ( ◦ C) +2.281 × 10 −4× (T ( ◦ C)) 2− 1.474 × 10 −7× (T ( ◦ C)) 3 )/1000 Thermal conductivity, W/m◦C0.443 +1.9 ·10−4×T (◦C) Hitec® Composition (by weight) 40% NaNO2, 7% NaNO3, 53% KNO3 Freeze Temperature, ◦C 142 (eutectic point) Density, kg/m32080 −0.733 ×T (◦C) Specific heat, J/kg C 1.56 Dynamic Viscosity, Pa·s 0.00622 −0.0000102 ×T(◦C) Thermal conductivity, W/m◦C 0.588 −0.000647 ×T (◦C) Hitec XL® Composition (by weight) 7% NaNO2, 45% KNO3, 48% Ca(NO3)2 Freeze Temperature, ◦C 120 (eutectic point) Density, kg/m32240 −0.8266 ×T (◦C) Specific heat, J/kg C 1536 −0.2624 ×T (◦C) −0.0001139 ×(T (◦C))2 Dynamic Viscosity, Pa·s1,372,000 ×(T (◦C)) −3.364 Thermal conductivity, W/m◦C 0.519 The biggest drawback of these nitrate salt mixtures is that they freeze inside the tubing in the system, since their melting points vary from 120 ◦ C to 220 ◦ C. Therefore, freeze protection has to be considered in any PTC plant. On the other hand, HiTec XL and HiTec have a lower melting point, therefore the problem of freezing is easier to control. On the other hand, the thermal stability of these mixtures is lower than Solar Salt [10,12,19,20]. The benefit of using molten salts as heat transfer fluids results from the increase in the allowable maximum operating temperature [ 15 , 21 ]. However, molten salts with the desired thermal stability limit have freezing/melting points well above ambient temperature. As such, a freeze protection and recovery system (freeze P/R) is needed for three key functions: 1. Pre-heat plant for initial salt fill, or pre-heat loops for fill after maintenance. 2. Prevent freeze events for the duration of the plant life. 3. Recovery from freeze events for the duration of the plant life. Preheating of the plant is required to prevent the formation of salt plugs during the initial plant fill and to minimize thermal shock to piping and equipment. Preheating will be needed on a loop level to refill the loop with salt after maintenance has been performed on a loop. Once the plant is filled with salt, the system will then be used to prevent freeze events by maintaining a temperature above the freeze point of the salt, should such situations arise. If a plug or blockage does form anywhere in the plant, the system will apply heat to the affected zone to prevent a larger freezing event and/or melt the frozen zone. The freeze P/R system is not intended to provide heating under normal operation of the plant. The freeze protection/recovery system proposed in this paper includes two main sections: Heat tracing and impedance heating [ 22 , 23 ]. Heat tracing involves the application of heat trace cables to all plant surfaces that might be compromised in a freeze event. This includes all pipes, headers, joints, Energies 2019,12, 2340 4 of 20 and valves [ 24 ]. If the plant undergoes a freeze risk, the salt in these areas must be melted. Since no external energy hits these components during normal operation, heat tracing is the only practical option of introducing a heat input. Impedance melting is accomplished by applying a voltage over a necessary number of absorber tubes in the solar field. This voltage, given a resistivity of the tube, induces a current in the absorber tube that results in a heat generation term. A good understanding of the working philosophy of freeze protection systems is needed to minimize the parasitic consumption of solar plants, being one of the criteria to select the final HTF in the parabolic trough collector plants. Different modelling studies have been published for state-of-the-art of PTC plants [ 11 , 25 ]. However, state-of-the-art PTC plants have never been the subject of a specific feasibility study of heat tracing systems when using high melting point salts as a HTF. The work carried out in this document describes the freeze protection systems used in parabolic trough plants with three mixtures of molten salt, and the modelling for their implementation and optimization in the plant performance model. 2. Heat Tracing 2.1. Heat Trace System Description The scope of the heat trace study was to develop the capability of predicting heat tracing requirements for salt HTF plants. Heat tracing is accomplished by the application of resistive heating cables being applied to the surface to be heated. These cables produce large heat generation terms when a direct electrical current is applied to them. This heat generation term can be used for freeze recovery or system preheating. Figure 2shows several ways heat trace cables are mounted to different piping elements, such as pipes, valves, and joints. Energies 2019, 12, x FOR PEER REVIEW 4 of 21 Impedance melting is accomplished by applying a voltage over a necessary number of absorber tubes in the solar field. This voltage, given a resistivity of the tube, induces a current in the absorber tube that results in a heat generation term. A good understanding of the working philosophy of freeze protection systems is needed to minimize the parasitic consumption of solar plants, being one of the criteria to select the final HTF in the parabolic trough collector plants. Different modelling studies have been published for state-ofthe-art of PTC plants [11,25]. However, state-of-the-art PTC plants have never been the subject of a specific feasibility study of heat tracing systems when using high melting point salts as a HTF. The work carried out in this document describes the freeze protection systems used in parabolic trough plants with three mixtures of molten salt, and the modelling for their implementation and optimization in the plant performance model. 2. Heat Tracing 2.1. Heat Trace System Description The scope of the heat trace study was to develop the capability of predicting heat tracing requirements for salt HTF plants. Heat tracing is accomplished by the application of resistive heating cables being applied to the surface to be heated. These cables produce large heat generation terms when a direct electrical current is applied to them. This heat generation term can be used for freeze recovery or system preheating. Figure 2 shows several ways heat trace cables are mounted to different piping elements, such as pipes, valves, and joints. Figure 2. Several mounting configurations for heat trace cables based on the type of pipe element (valve, joint, or pipe). The only type of heat trace cable that can withstand the required exposure temperatures over 250 °C are those using mineral insulated (MI) cable. Mineral wool thermal insulation with an aluminium jacket will be used on all traced piping. Mineral wool insulation will be used on valve bodies and bonnets with removable blankets on the actuators. The system has one redundant cable per heat trace zone and this redundant cable will be on header and feeder piping, but not loop and drop-down piping. The systems were designed with the premise that feeder pipes and headers must never freeze. 2.2. Model Description The schematic shown below in Figure 3 shows a cross section of the pipe, the heat transfer mechanisms that result in heat losses from the heat transfer fluid, and the location of heat addition from the heating system. Figure 2. Several mounting configurations for heat trace cables based on the type of pipe element (valve, joint, or pipe). The only type of heat trace cable that can withstand the required exposure temperatures over 250 ◦ C are those using mineral insulated (MI) cable. Mineral wool thermal insulation with an aluminium jacket will be used on all traced piping. Mineral wool insulation will be used on valve bodies and bonnets with removable blankets on the actuators. The system has one redundant cable per heat trace zone and this redundant cable will be on header and feeder piping, but not loop and drop-down piping. The systems were designed with the premise that feeder pipes and headers must never freeze. Energies 2019,12, 2340 5 of 20 2.2. Model Description The schematic shown below in Figure 3shows a cross section of the pipe, the heat transfer mechanisms that result in heat losses from the heat transfer fluid, and the location of heat addition from the heating system. Energies 2019, 12, x FOR PEER REVIEW 5 of 21 Figure 3. Schematic and heat transfer mechanisms through insulated pipe. The heat tracing system will be placed directly onto the surface of the steel pipe. While the heating cables are in discrete locations, they will be approximated as being evenly distributed over the entire surface of the pipe. Insulation will then be placed around the pipe and heat tracing system. The insulation will, if necessary, consist of high temperature insulation at the inner surface, followed by lower temperature insulation. If the cost of insulation is high, a multilayer configuration can be used, using a first layer of greater performance and cost that is in contact with the cable, and a second layer of lower cost on the external side. The two layers of insulation will ensure that the insulation functions properly at high temperatures but also cuts down on the overall cost of the insulation. Finally, an aluminium cladding will effectively seal the pipe and provide insulation from precipitation and protect it from unforeseen abuse during operation. The heat transfer fluid will flow through the pipe, resulting in heat loss through the pipe walls and out to the ambient surroundings. The total length of heat trace cable necessary for headers, valves, joints, and pipes is calculated based on the preheat and melting conditions and pipe diameters. The heat from the HTF will be lost through convective heat transfer with the inner pipe surface. This heat will then be transferred by conduction through the pipe wall, insulations, and the aluminium cladding. Finally, the heat is lost to the ambient surroundings by radiation and convective heat transfer. In addition, the potential for internal heat addition is supplied by the heat tracing system. This heater will be able to supply heat to the pipe walls. The schematic in Figure 4 shows the thermal circuit. In practice, heat loss also occurs at the pipe supports, but this will be ignored for this optimization. It is also worth noting that the radiation losses are to the sky, while the external convection losses are to the surroundings. For this subroutine, it has been assumed that both the radiation and convection losses occur to the ambient surroundings, as indicated in Figure 3. The dashed line indicates that the outer insulation is an option that may be necessary. Figure 3. Schematic and heat transfer mechanisms through insulated pipe. The heat tracing system will be placed directly onto the surface of the steel pipe. While the heating cables are in discrete locations, they will be approximated as being evenly distributed over the entire surface of the pipe. Insulation will then be placed around the pipe and heat tracing system. The insulation will, if necessary, consist of high temperature insulation at the inner surface, followed by lower temperature insulation. If the cost of insulation is high, a multilayer configuration can be used, using a first layer of greater performance and cost that is in contact with the cable, and a second layer of lower cost on the external side. The two layers of insulation will ensure that the insulation functions properly at high temperatures but also cuts down on the overall cost of the insulation. Finally, an aluminium cladding will effectively seal the pipe and provide insulation from precipitation and protect it from unforeseen abuse during operation. The heat transfer fluid will flow through the pipe, resulting in heat loss through the pipe walls and out to the ambient surroundings. The total length of heat trace cable necessary for headers, valves, joints, and pipes is calculated based on the preheat and melting conditions and pipe diameters. The heat from the HTF will be lost through convective heat transfer with the inner pipe surface. This heat will then be transferred by conduction through the pipe wall, insulations, and the aluminium cladding. Finally, the heat is lost to the ambient surroundings by radiation and convective heat transfer. In addition, the potential for internal heat addition is supplied by the heat tracing system. This heater will be able to supply heat to the pipe walls. The schematic in Figure 4shows the thermal circuit. In practice, heat loss also occurs at the pipe supports, but this will be ignored for this optimization. It is also worth noting that the radiation losses are to the sky, while the external convection losses are to the surroundings. For this subroutine, it has been assumed that both the radiation and convection losses occur to the ambient surroundings, as indicated in Figure 3. The dashed line indicates that the outer insulation is an option that may be necessary. Energies 2019,12, 2340 6 of 20 Energies 2019, 12, x FOR PEER REVIEW 6 of 21 Tsalt = Temperature of the HTF (K) T1 = Temperature at the inner radius of the pipe (K) T2 = Temperature at the outer radius of the pipe (K) T3 = Temperature at the outer radius of the high temperature insulation (K) T4 = Temperature at the outer radius of the lower temperature insulation (K) T5 = Temperature at the outer radius of the aluminium cladding (K) Tamb = Temperature of the surrounding air (K) R’conv,1 = Thermal resistance of pipe against heat convection ((m·K)/W) R’pipe = Thermal resistance of pipe against heat conduction ((m·K)/W) R’ins,1 = Thermal resistance of inner insulation against heat conduction ((m·K)/W) R’ins,2 = Thermal resistance of outer insulation against heat conduction ((m·K)/W) R’Al = Thermal resistance of aluminium cladding against heat conduction ((m·K)/W) R’conv,2 = Thermal resistance of ambient environment against heat convection ((m·K)/W) R’rad = Thermal resistance of ambient environment against radiation ((m·K)/W) q’heater = Heat addition from heating system (W/m) Figure 4. Circuit schematic of pipe heat transfer. The equations for the thermal resistances are: 𝑅, 󰆒=  𝑅 󰆒= ( )  𝑅, 󰆒= ( ) , 𝑅, 󰆒= ( ) , 𝑅 󰆒= ( )   𝑅, 󰆒=  𝑅 󰆒=    (1) where: r1 = Inner radius of the pipe (m) r2 = Outer radius of the pipe (m) r3 = Outer radius of the high temperature insulation (m) r4 = Outer radius of the lower temperature insulation (m) r5 = Outer radius of the aluminium cladding (m) kpipe = Thermal conductivity of the pipe (W/(m·K)) kins,1 = Thermal conductivity of the high temperature insulation (W/(m·K)) kins,2 = Thermal conductivity of the lower temperature insulation (W/(m·K)) kAl = Thermal conductivity of the aluminium cladding (W/(m·K)) h1 = Convection heat transfer coefficient between the pipe and HTF (W/(m2·K)) h2 = Convection heat transfer coefficient between the cladding and the air (W/(m2·K)) hrad = Radiation heat transfer coefficient (W/(m2·K)) The thermal conductivities vary with temperature and thus will be evaluated at the midpoint temperature of the respective material. The equations for the convection and radiation heat transfer coefficients are: ℎ=  ℎ=  ℎ=𝜀𝜎(𝑇+𝑇 )(𝑇+𝑇) (2) where: ksalt = Thermal conductivity of the HTF (W/(m·K)) kair = Thermal conductivity of air (W/(m·K)) Nusalt = Nusselt number of the salt Nuair = Nusselt number of the air εAl = Emissivity of the aluminium cladding Figure 4. Circuit schematic of pipe heat transfer. The equations for the thermal resistances are: R0 conv,1 =1 2πh1r1R0 pipe =lnr2 r1 2πkpipe R0 ins,1 =lnr3 r2 2πkins,1 R0 ins,2 =lnr4 r3 2πkins,2 R0 Al =lnr5 r4 2πkAl R0 conv,2 =1 2πh2r5R0 rad =1 2πhradr5 (1) where: r1=Inner radius of the pipe (m) r2=Outer radius of the pipe (m) r3=Outer radius of the high temperature insulation (m) r4=Outer radius of the lower temperature insulation (m) r5=Outer radius of the aluminium cladding (m) kpipe =Thermal conductivity of the pipe (W/(m·K)) kins,1 =Thermal conductivity of the high temperature insulation (W/(m·K)) kins,2 =Thermal conductivity of the lower temperature insulation (W/(m·K)) kAl =Thermal conductivity of the aluminium cladding (W/(m·K)) h1=Convection heat transfer coefficient between the pipe and HTF (W/(m2·K)) h2=Convection heat transfer coefficient between the cladding and the air (W/(m2·K)) hrad =Radiation heat transfer coefficient (W/(m2·K)) The thermal conductivities vary with temperature and thus will be evaluated at the midpoint temperature of the respective material. The equations for the convection and radiation heat transfer coefficients are: Energies 2019,12, 2340 7 of 20 h1=ksaltNusalt 2r1 h2=kairNuair 2r5 hrad =εσT2 5+T2 amb(T5+Tamb)(2) where: ksalt =Thermal conductivity of the HTF (W/(m·K)) kair =Thermal conductivity of air (W/(m·K)) Nusalt =Nusselt number of the salt Nuair =Nusselt number of the air εAl =Emissivity of the aluminium cladding σ=Stefan–Boltzmann Constant =5.67·10−8W/m2·K4 The Nusselt number of the salt varies depending on whether the HTF is experiencing laminar or turbulent flow. The flow of a fluid through a pipe is said to be laminar if the Reynolds number is less than 2300. The Reynolds number for the salt must be calculated to determine the appropriate Nusselt number equation. The Nusselt number of the air is dependent upon whether the pipe is experiencing forced or natural convection. The equations for the Nusselt numbers of the salt and the ambient air are: Nusalt,lam =4.36 (3) Dittus-Boelter [26] Nusalt,turb =0.023Re 4 5 saltPrn salt for          0.6 ≤Prsalt ≤160 Resalt≥10,000 Lpipe/2r1≥10          Churchill and Bernstein [26] Nuair,forced =0.3 +0.62Re1/2 air Pr1/3 air 1+0.4 Prair 2/31/4"1+Reair 282, 0005/8#4/5 for Prair·Reair ≥0.2 Churchill and Chu [26] Nuair,forced =             0.6 +0.387Ra1/6 air 1+0.559 Prair 9/168/27              2 for Raair ≤1012 where: Resalt =Reynolds number of the HTF Reair =Reynolds number of the air Raair =Rayleigh number of the air Prsalt =Prandtl number of the HTF Prair =Prandtl number of the air Lpipe =Length of the pipe (m) n=0.4 for heating and 0.3 for cooling Another consideration in the insulation optimization subroutines is the heating system that will be located on the pipe surface. This heating system will be operated when the temperature of the heat transfer fluid approaches freezing temperatures. The time it takes for the salt to approach freezing temperatures, given a specific ambient air temperature and initial salt temperature, is calculated by a complex transient conduction equation. The optimization subroutine utilizes the lumped capacitance Energies 2019,12, 2340 8 of 20 model assumption, which allows for a more simplified approach. This model assumes that the internal temperature of an object is constant throughout, so the rate at which that object will cool will be faster than that of the transient model. This is true because under the lumped capacitance model the temperature of the object will linearly decrease with time (assuming the object is hotter than its surroundings), while the transient model follows a curve more closely approximated by exponential regression. If the pipe can be approximated using lumped capacitance, this may be too conservative, but it will indicate whether the salt within the pipe will freeze. Assuming lumped capacitance, the time for the salt to approach freezing temperatures can be calculated from the equation below: t=πρsaltCp,saltr2 1R0 thermalln Tinitial −Tamb Tfreeze,safe −Tamb !(4) where: t=Time to freeze (s) ρsalt =Density of the HTF (kg/m3) Tinitial =Initial temperature of the salt (K) Tfreeze,safe =30 K above the freeze temperature of the salt (K) R0thermal =Thermal resistance over temperature range ((m·K)/W) This calculation will also be conservative, since this equation assumes that the salt is stagnant within the pipe. In the molten salt plant this will never occur, as the salt will always be flowing. This equation will therefore yield a time that is much less than the time it would take for flowing salt to approach freezing temperatures, which is on the safe side for evaluating the freezing risk. Assumptions The properties of air vary according to temperature and pressure. For the purposes of this study, the average temperature will be determined from a data file containing hourly weather data during the year. The data file contains columns detailing the temperature, wind velocity, and direct normal insolation every hour during a year for a specific location. The atmospheric pressure will be assumed constant (at 1 atm). These values will then be used to determine the necessary air properties. The properties of the heat transfer fluid are measured with respect to temperature variance. The properties of the heat transfer fluid will be evaluated using the inlet temperature as the bulk temperature of the fluid. The properties of the ambient air will be evaluated at the film temperature between the air and the surface of the aluminium cladding. Several assumptions and simplifications will be made to perform this heat transfer analysis of the CSP pipes. These assumptions are listed below: 1. The system is in a steady state 2. Uniform HTF temperature (per length unit) 3. All materials have uniform properties throughout (radially) 4. One dimensional heat transfer in the pipe (radially) 5. Negligible contact resistances 6. Heating system only contributes a heat input (no insulating properties or contact resistance) 7. Radiation and convective heat losses occur at the same temperature 8. Insulation has been applied appropriately and contains no leaks or discontinuities 9. External humidity has a negligible effect (no evaporative cooling or heat transfer effects) 10. When wind is present, it is a cross-flow Heat tracing is used to preheat the pipes in the solar field, including the feed pipes and headers for both the cold and hot salt. It is important to understand the transient behaviour of their warm-up. Furthermore, it is important to understand the transient melting behaviour of the salt in the tubes. If Energies 2019,12, 2340 9 of 20 the salt would freeze in the feed pipes and headers, it would be necessary for the heat tracing to be sufficiently large to melt the salt in a reasonable amount of time (Figure 5). Energies 2019, 12, x FOR PEER REVIEW 9 of 21 Figure 5. Thermal networks used for modelling melting (left) and preheating (right). The model was created in Engineering Equation Solver (EES) using a thermal network between the three components. During preheating, the heat introduced by the heat tracing can either flow through the insulation and into the ambient environment, or it can be stored in the pipe and insulation. This creates a system of differential equations that must be solved. During melting, the salt consumes the generated heat. Although this creates another differential equation, the solution method is the same for both. A fourth order explicit Runga–Kutta (RK) numerical estimation is used to simultaneously solve the 2 or 3 differential equations. This is done using the four step RK estimation process. The result is the temperature of the pipe, insulation, and salt at each time step. The temperature of the salt is recorded until melting occurs. At this point the model records the amount of heat absorbed by the salt and records how much of the salt is melted. Using this method, the total time taken to heat the salt from cold to fully molten can be calculated. 3. Impedance Heating 3.1. Impedance System Description Electric heating of the heat collection elements will be provided by an impedance heating system. The system passes a high current, at a low voltage, through the stainless steel pipe in the heat collection element. The power in the electric current is converted to thermal energy as the product of its resistance (R) and the square of the current (I). The impedance heating system for the receiver tubes will consist of a standalone panel and transformer. Each system is designed to heat a total length of 141.66 m of receiver tube with a 2 mm wall thickness constructed of 316 Ti Stainless Steel. The resistance of the receiver tube is assumed to be 0.0015 V/m. This means that there will be one system per collector and eight systems per loop. There are two possible configurations of an impedance heating system: End-point and midpoint. Figures 6 and 7 show the differences between the two systems. It is preferred that the midpoint system be used because this system is non-intrusive and does not require any electrical isolation on the receiver tube that must be in contact with salt and high temperatures. The end-point system will only be considered if an isolating flange that can work under salt conditions is discovered. R cond R cond R cond R conv R rad q ht Insulation Pi p e Sal t R cond R cond R conv R rad q ht Insulation Pi p e Vacuum Air Figure 5. Thermal networks used for modelling melting (left) and preheating (right). The model was created in Engineering Equation Solver (EES) using a thermal network between the three components. During preheating, the heat introduced by the heat tracing can either flow through the insulation and into the ambient environment, or it can be stored in the pipe and insulation. This creates a system of differential equations that must be solved. During melting, the salt consumes the generated heat. Although this creates another differential equation, the solution method is the same for both. A fourth order explicit Runga–Kutta (RK) numerical estimation is used to simultaneously solve the 2 or 3 differential equations. This is done using the four step RK estimation process. The result is the temperature of the pipe, insulation, and salt at each time step. The temperature of the salt is recorded until melting occurs. At this point the model records the amount of heat absorbed by the salt and records how much of the salt is melted. Using this method, the total time taken to heat the salt from cold to fully molten can be calculated. 3. Impedance Heating 3.1. Impedance System Description Electric heating of the heat collection elements will be provided by an impedance heating system. The system passes a high current, at a low voltage, through the stainless steel pipe in the heat collection element. The power in the electric current is converted to thermal energy as the product of its resistance (R) and the square of the current (I). The impedance heating system for the receiver tubes will consist of a standalone panel and transformer. Each system is designed to heat a total length of 141.66 m of receiver tube with a 2 mm wall thickness constructed of 316 Ti Stainless Steel. The resistance of the receiver tube is assumed to be 0.0015 V/m. This means that there will be one system per collector and eight systems per loop. There are two possible configurations of an impedance heating system: End-point and mid-point. Figures 6and 7show the differences between the two systems. It is preferred that the mid-point system be used because this system is non-intrusive and does not require any electrical isolation on the receiver tube that must be in contact with salt and high temperatures. The end-point system will only be considered if an isolating flange that can work under salt conditions is discovered. Energies 2019,12, 2340 16 of 20 Energies 2019, 12, x FOR PEER REVIEW 16 of 21 Figure 13. Melting time as a function of the total solar collector assembly impedance voltage with the following system configurations: Solar radiation = 0 W/m 2 , wind speed = 5 m/s, glazing intact, air in annulus at 1 atm, ambient temperature = 15 °C. Figure 14 shows the melting time relative to the current system configurations for various stainless steel types. A 10–15% decrease in the melting time can be achieved by switching to 201 or 301 stainless steel. While this is an improvement, this change does not improve the overall situation significantly. The goal of the model development was to design the system necessary to supply adequate impedance heating to recover from a freeze event. To do this, an operational target was developed. The metrics used in the target are summarized in Table 6. One day was chosen as a melting time as a standard time from a commercial plant. Lost vacuum was chosen as the worst case because it is assumed that any collectors with broken envelopes would be repaired prior to melting. On the other hand, lost vacuums are not easy to diagnose and are often only replaced at infrequent intervals. Therefore, during a freeze event, some tubes with lost vacuums would need to be melted. Impedance heating provides a constant heat input along the entire length of the pipe. Furthermore, axial thermal conduction in the pipe and salt is minimal. This allows for each heat collection element (HCE) to be modelled as an island. That is, a HCE with no vacuum will melt at the same rate, no matter whether it is surrounded by tubes with vacuums intact, with no vacuum, or with no glazing. We assume that in every loop there will be at least one HCE with no vacuum, constraining our melting time to the melting time of an HCE with no vacuum. Figure 13. Melting time as a function of the total solar collector assembly impedance voltage with the following system configurations: Solar radiation =0 W/m 2 , wind speed =5 m/s, glazing intact, air in annulus at 1 atm, ambient temperature =15 ◦C. Figure 14 shows the melting time relative to the current system configurations for various stainless steel types. A 10–15% decrease in the melting time can be achieved by switching to 201 or 301 stainless steel. While this is an improvement, this change does not improve the overall situation significantly. Energies 2019, 12, x FOR PEER REVIEW 17 of 21 Figure 14. Relative melting times for different types of stainless steel based on resistivity. Table 6. Operation target metrics. Metric Target Melting time 1 day Worst case configuration Lost vacuum A system using each salt was analysed for two electrical configurations: One transformer per SCA and two transformers per SCA. For the one transformer setup a connection cable length of 80 m was used. For the two-transformer setup 40 m was used. Figure 15 shows a design layout for a system with one transformer per SCA. The cable lengths are shown with the arrow tipped lines going to and from the transformer. The necessary voltage to reach the target conditions was calculated assuming no solar radiation. These results are tabulated in Table 7. HiTec and Solar Salt systems will need to have two transformers per SCA. Finally, the total melting time of the system was investigated. It was not considered that the whole field is melted simultaneously, so as not to penalize the cost of the transformers that feed the impedance currents. Different cases of loop simultaneity were considered. The number of loops capable of melting simultaneously was the parameter to optimize. Based on the cost of the DC conductor necessary to feed each loop and the complexity of the utility of switching the plant from a 240 MW source to a 150 MW sink, the actual number was estimated to be around 10. This results in total plant melting times from 100 to 300 days. This represents a significant financial penalty for freezing. 5. Conclusions Parabolic trough collector (PTC) technology with thermal oil as the HTF is currently the most mature solar technology that is implemented at commercial scale. The use of molten salts as HTF has the advantage of being able to work at higher temperature to increase plant efficiency, and the disadvantage of the potential freezing of the HTF in pipes and components. Two methods of freeze recovery needed in this design have been developed to evaluate the technical feasibility of molten salt in PTC systems. A model of heat tracing in pipes and components, and a model of impedance melting in the solar field has been developed in this paper to compare the freezing protection system in three molten salts mixtures, namely Solar Salts, Hitec and Hitec XL. Figure 14. Relative melting times for different types of stainless steel based on resistivity. The goal of the model development was to design the system necessary to supply adequate impedance heating to recover from a freeze event. To do this, an operational target was developed. The metrics used in the target are summarized in Table 6. Table 6. Operation target metrics. Metric Target Melting time 1 day Worst case configuration Lost vacuum One day was chosen as a melting time as a standard time from a commercial plant. Lost vacuum was chosen as the worst case because it is assumed that any collectors with broken envelopes would be Energies 2019,12, 2340 17 of 20 repaired prior to melting. On the other hand, lost vacuums are not easy to diagnose and are often only replaced at infrequent intervals. Therefore, during a freeze event, some tubes with lost vacuums would need to be melted. Impedance heating provides a constant heat input along the entire length of the pipe. Furthermore, axial thermal conduction in the pipe and salt is minimal. This allows for each heat collection element (HCE) to be modelled as an island. That is, a HCE with no vacuum will melt at the same rate, no matter whether it is surrounded by tubes with vacuums intact, with no vacuum, or with no glazing. We assume that in every loop there will be at least one HCE with no vacuum, constraining our melting time to the melting time of an HCE with no vacuum. A system using each salt was analysed for two electrical configurations: One transformer per SCA and two transformers per SCA. For the one transformer setup a connection cable length of 80 m was used. For the two-transformer setup 40 m was used. Figure 15 shows a design layout for a system with one transformer per SCA. The cable lengths are shown with the arrow tipped lines going to and from the transformer. The necessary voltage to reach the target conditions was calculated assuming no solar radiation. These results are tabulated in Table 7. HiTec and Solar Salt systems will need to have two transformers per SCA. Energies 2019, 12, x FOR PEER REVIEW 18 of 21 Figure 15. A design schematic for a system with one transformer per solar collector assembly (SCA), given with one possible voltage and amperage. Table 7. Necessary electrical system characteristics to meet the target condition of a one-day melting time for a tube with a compromised vacuum. NA represents that no American wire gauge (AWG) rating is sufficient. Parameter HiTec XL HiTec Solar Salt 1 transformer per SCA Voltage (V) 69.37 77.26 104 Current (A) 260.2 289.8 390.1 Connector Area (mm 2 ) 64,937 280,108 infinity Connector Gauge (AWG) 2 n.a. n.a. 2 transformers per SCA Voltage (V) 34.69 38.63 52 Current (A) 260.2 289.8 390.1 Connector Area (mm 2 ) 7616 9289 18,479 Cable Gauge (AWG) 11 11 7 In the heat tracing model, all piping included in the heat trace system was heated using a mineral insulted (MI) cable. This is the only type of heat trace cable that can withstand exposure temperatures over 250 °C. Mineral wool thermal insulation with an aluminium jacket was used on all traced piping. Mineral wool insulation was used on valve bodies and bonnets with removable blankets on the actuators. The heat tracing model has been created to size the heat tracing system for any pipe. In addition, the model has been applied to the overall pipe sizing and costing model to make future system cost estimations more accurate. Figure 15. A design schematic for a system with one transformer per solar collector assembly (SCA), given with one possible voltage and amperage. Energies 2019,12, 2340 18 of 20 Table 7. Necessary electrical system characteristics to meet the target condition of a one-day melting time for a tube with a compromised vacuum. NA represents that no American wire gauge (AWG) rating is sufficient. Parameter HiTec XL HiTec Solar Salt 1 transformer per SCA Voltage (V) 69.37 77.26 104 Current (A) 260.2 289.8 390.1 Connector Area (mm2)64,937 280,108 infinity Connector Gauge (AWG) 2 n.a. n.a. 2 transformers per SCA Voltage (V) 34.69 38.63 52 Current (A) 260.2 289.8 390.1 Connector Area (mm2)7616 9289 18,479 Cable Gauge (AWG) 11 11 7 Finally, the total melting time of the system was investigated. It was not considered that the whole field is melted simultaneously, so as not to penalize the cost of the transformers that feed the impedance currents. Different cases of loop simultaneity were considered. The number of loops capable of melting simultaneously was the parameter to optimize. Based on the cost of the DC conductor necessary to feed each loop and the complexity of the utility of switching the plant from a 240 MW source to a 150 MW sink, the actual number was estimated to be around 10. This results in total plant melting times from 100 to 300 days. This represents a significant financial penalty for freezing. 5. Conclusions Parabolic trough collector (PTC) technology with thermal oil as the HTF is currently the most mature solar technology that is implemented at commercial scale. The use of molten salts as HTF has the advantage of being able to work at higher temperature to increase plant efficiency, and the disadvantage of the potential freezing of the HTF in pipes and components. Two methods of freeze recovery needed in this design have been developed to evaluate the technical feasibility of molten salt in PTC systems. A model of heat tracing in pipes and components, and a model of impedance melting in the solar field has been developed in this paper to compare the freezing protection system in three molten salts mixtures, namely Solar Salts, Hitec and Hitec XL. In the heat tracing model, all piping included in the heat trace system was heated using a mineral insulted (MI) cable. This is the only type of heat trace cable that can withstand exposure temperatures over 250 ◦ C. Mineral wool thermal insulation with an aluminium jacket was used on all traced piping. Mineral wool insulation was used on valve bodies and bonnets with removable blankets on the actuators. The heat tracing model has been created to size the heat tracing system for any pipe. In addition, the model has been applied to the overall pipe sizing and costing model to make future system cost estimations more accurate. The model has evaluated the recovery after a freezing event, obtaining that the melting times are acceptable for all pipe diameters proposed in the study. The result of the model also shows how HiTec salt requires less heat trace power in its operation. When evaluating the three fluids, it is concluded that the recovery from freezing in a molten salt plant is possible. The threat of system wide HTF freeze events does not invalidate the concept of molten salt HTFs. In the impedance model, the receiver tubes were heated with impedance heating, which consisted of a standalone panel and transformer for each collector. Each impedance heating system was a mid-point system to avoid the need for electrical isolation between the receiver tubes and adjacent piping. Energies 2019,12, 2340 19 of 20 The impedance heating model has analysed the performance under off-design conditions (tubes with lost vacuum and high wind losses), showing the increase in the melting time for tubes with a compromised vacuum. This requires working with two SCA transformers for HiTec and Solar Salt. Additionally, more than 100 days will be needed to completely melt a fully frozen solar field. Even when the melting times involved are not ideal, the reliability of an impedance-based recovery system is high and, as such, freeze events do not stand in the way of future work on molten salt HTF systems. The models developed show that both systems are technically feasible, since the plant may recover from a freezing event in all studied cases, although the recovery times considerably penalize the performance of the plant. Therefore, an economical detailed study including capital expenditure and operational expenditure (CAPEX and OPEX) is necessary to see which system is the best for a commercial plant. Author Contributions: Conceptualization: C.P., L.F.C., A.R.-S., F.J.R.-C. Formal analysis: C.P., L.F.C. Methodology: C.P., L.F.C., A.R.-S., F.J.R.-C. Funding acquisition: C.P.; A.R.-S., F.J.R.-C. Methodology: C.P., L.F.C. Writing—original draft: C.P. Writing—review and editing: L.F.C. Funding: The work partially funded by the Spanish government under the granted project Composol (CDTI ITC-2011106) and under the granted project RTI2018-093849-B-C31. This work is partially supported by ICREA under the ICREA Academia programme. 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