- Email: [email protected]
Mixing enhancement in thermal energy storage molten salt tanks
Energy Conversion and Management 168 (2018) 320–328
Contents lists available at ScienceDirect
Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
Mixing enhancement in thermal energy storage molten salt tanks ⁎
T
Alfredo Iranzo , Christian Suárez, José Guerra Thermal Engineering Group, Energy Engineering Department, School of Engineering, Universidad de Sevilla, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain
A R T I C LE I N FO
A B S T R A C T
Keywords: Mixing CFD Numerical model Thermal energy storage Molten salts Concentrated solar power plant
An appropriate degree of mixing in molten salt tanks for Thermal Energy Storage (TES) in Concentrated Solar Power Plants (CSPPs) is required in order to ensure the safe operation of the tank. Otherwise, cooling due to thermal heat losses is prone to result in a high thermal stratification of the salts and eventually local solidification. In this work, the mixing performance of different configurations of ejectors is investigated by means of Computational Fluid Dynamics (CFD). A set of different ejector configurations has been resolved, modifying the number of ejectors, flow direction, and ejector angle. The best configurations are identified, where the highest fluid circulation capacity is achieved by 10 ejectors directing the jet flow in the tangential direction with an inclination angle of 0° with respect to the tank bottom surface. This is increasing the fluid circulation capacity of the tank by more than 100% with respect to the usual configuration implemented in such tanks (ejectors directed to the tank central vertical axis, at 30° angle). In addition, such configuration ensures an enhanced flow circulation in the bottom part of the tank (with an increase of more than 6 times in the flow velocity in the lower section of the tank), reducing the risk of local salt solidification due to heat loss through the bottom surface. However, the shortest mixing times (95% and 99%) are achieved by the configuration with 10 ejectors pumping flow towards the central tank axis with an inclination angle of 0°.
1. Introduction One of the promising technologies for renewable electricity generation is Concentrated Solar Power Plants (CSPPs). As an additional benefit, solar thermal power plants have the ability to store thermal energy, which enables the decoupling of the electric power generation from the intermittency of the available solar irradiation. Currently, commercial thermal storage systems are mostly based on a two-tank sensible heat thermal storage with molten salts. A simplified sketch of a facility integrating such a Thermal Energy Storage (TES) system is presented in Fig. 1. The heated heat transfer fluid (HTF) from the solar field is sent towards the steam generation circuit, and/or to the TES system in order to increase its degree of charge. As mentioned previously, the TES system consists of two molten salt tanks, able to exchange salts via a heat exchanger heated by the HTF from the solar field. During charging operation, molten salts stored in the cold salt tank are heated by a side stream of the HTF not used for steam generation. The heated salts are stored in the hot salt tank until they are later needed when solar energy is not available. In order to heat the HTF, the TES system is used in the opposite or discharge mode, where the salts are transferred from the hot tank to the cold tank through the heat exchanger, heating the HTF which is then sent towards the steam generation circuit. It is worth to mention that some novel
⁎
Corresponding author. E-mail address: [email protected] (A. Iranzo).
https://doi.org/10.1016/j.enconman.2018.04.113 Received 27 February 2018; Received in revised form 27 April 2018; Accepted 29 April 2018 0196-8904/ © 2018 Elsevier Ltd. All rights reserved.
systems are being proposed using molten salts directly as HTF [1–3]. Molten Salts Tanks are typically cylindrically shaped tanks with over 20 m diameter [4]. An appropriate degree of mixing within the molten salt tanks is required in order to ensure a safe operation, which is obviously more important in the cold salt tank. Otherwise, despite the thermal insulation being used, cooling due to thermal heat losses are prone to result in thermal stratification of the salts and eventually partial solidification [5–8]. This is particularly important for long stops of the plant (such as during maintenance operations) where up to twomonth duration can be expected. For such cases, tanks typically include electrical heaters installed in the bottom, in order to provide heat during long stops compensating the heat losses. Again, it is particularly important to ensure that the heat released by the electrical heaters is uniformly distributed within the tank, avoiding dead zones that could become local cold spots for salts solidification. Mixing could be achieved just by natural convection, but more often a set of ejectors are included in the tank, in order to induce a flow circulation and mixing within the tank volume. How to define the ejector configuration that enhance the mixing performance is the objective of this research work. The approach followed for achieving this objective is the development of a model based on Computational Fluid Dynamics (CFD), as experimental measurements in such large tanks during operation is highly prohibitive in terms of costs and technical difficulties. CFD is commonly
Energy Conversion and Management 168 (2018) 320–328
A. Iranzo et al.
Fig. 2. Tank geometry and main components (inner injection ring, outer recirculation ring, extraction pipe). Symmetry plane depicted in red.
the tank via the recirculation ring. Given the tank symmetry with respect to the middle plane (in red in Fig. 2), the simulation of only one half of the tank is required. 3. Modelling methodology The model has been developed in the commercial software ANSYSCFX [15]. The salts used in the tank correspond to a mixture of 60% NaNO3 and 40% KNO3, where the physical properties of the mixture were obtained from Sandia technical report on CSP design [16] (see Table 1): According to the data in [16], the following correlations for the physical properties can be derived, which were used for the CFD modelling:
Fig. 1. Simplified Block diagram of for Thermal Energy Storage System for CSPP.
used for the design and research of fluid flow and heat transfer processes associated to CSP [9–12]. Regarding the particular investigations on molten salt tanks, Schulte-Fischedick et al. [13] carried out a 2D and 3D CFD analysis of the cool down behaviour of a molten salt thermal storage system (880 MWh storage tanks). Heat losses, velocities, and temperature distributions were analysed, revealing that the highest heat flux was found at the lower edges of the tanks, leading to local solidification after a relatively short period of time (3.25 days for the empty cool tank). Rivas et al. [14] also integrated the steam generator in a CFD model of a pilot-scale thermocline tank. The bulk and circulation of the molten salts inside the tank and steam generator with steam coils were studied in a transient 2D-axisymmetric simulation. Such works present very useful results relevant for TES tanks, but it is worth to mention that no previous works are found specifically studying the mixing characteristics of molten salts tanks for TES, despite the importance of such systems for the future deployment of solar thermal power plants. Therefore, the objective of this research work is aiming at the analysis and enhancement of mixing in thermal energy storage molten salt tanks.
Density(kg/m3) = 2090−0.636·Temperature
(1)
Heat capacity(J/kg °C) = 1443 + 0.172·Temperature
(2)
Thermal conductivity(W/m °C) = 0.443 + 1.9E−4·Temperature
(3)
Viscosity(mPa s) = 22.714−0.120·Temperature + 2.281E−4·Temperature2 −1.474E−7·Temperature3
(4)
Where the unit of Temperature in Equations (1) to (4) is °C.The model will consider the tank at a high capacity (10.8 m height, which means 11.000 m3 of salts) as this will be the case where mixing is more challenging for a given design. Salts temperature at typical design point of the cold salt tank (285 °C) is considered, with a recirculation flow of 650 m3/h. 3.1. Correlations for mixing time estimation Some preliminary estimations of the mixing times can be carried out based on the tank and ejector basic data and general correlations. As an example, as a first approximation it can be estimated that a free jet may entrain 15 to 20 times its pumped flow rate [17]. Assuming that mixing time (95%) is requiring five flow turnovers, this results in:
2. Description of the tank The tank under analysis is presented in Fig. 2, corresponding to a Cold Salt Tank. The tank diameter used in this study is 36 m, a relatively large tank representative of current technologies, where mixing is becoming relevant to ensure a safe operation. Considering a salt filling height of around 11 m, the tank could store 11.000 m3 of salts, enough for roughly 2.5 full load operation of a 100 MW CSPP. The tank is featuring two different salts injection piping rings (Fig. 2). The inner ring is perforated with roughly 100 holes and corresponds to the injection of salts from the charging heat exchanger (Fig. 1). This will be referred to as distribution ring. The outer ring corresponds to the injection of recirculation salts, i.e. salts that are extracted from the tank and injected again via a set of ejectors equally distributed along the ring, in order to achieve the mixing of the salts. This will be referred to as recirculation ring. Salts are pumped out of the tank via a vertical pipe (closest to the external wall in Fig. 2) to re-enter
θM ,approx =
5V 20Q
(5)
Table 1 Physical properties of 60% NaNO3 and 40% KNO3 molten salts at cold salt tank [16].
321
Temperature (°C)
Density (kg/m3)
Heat capacity (J/ kg °C)
Viscosity (mPa s)
Thermal conductivity (W/ m °C)
260 288 316
1924.64 1906.97 1889.31
1488 1492 1497
4.343 3.558 2.929
0.492 0.498 0.503
Energy Conversion and Management 168 (2018) 320–328
A. Iranzo et al.
where V is the tank volume and Q is the jet volume flow rate. This approximation results in approximately 4–6 h. According to Gray’s correlation for the mixing time [17], supposed to be conservative, the jet mixing time can be estimated as:
θM =
30Vdj Q (HT )0.5
(6)
where V is the tank volume, H is the tank height, T is the tank diameter, Q is the jet volume flow rate, and dj is the jet diameter. According to this correlation the mixing time is 7.8 h. The correlation from Grenville [17,18] is an empirical expression:
vj θM dj
1.5
T H = 5.69 ⎜⎛ ⎟⎞ ⎜⎛ ⎟⎞ ⎝ dj ⎠ ⎝ dj ⎠
0.5
(7)
where vj is the jet flow velocity. This correlation yields a mixing time of 1.75 h. Fosset [17,19] derived another correlation:
θM =
8T 2 (Qvj )0.5
Fig. 3. Ejector sketch and working principle.
(8)
Which is providing a mixing time of 8.8 h. The analysis above clearly shows that despite the fact that such correlations provide a reasonable estimate of the mixing time range, they are considering overall quantities only and are missing the effects that particular designs may have on the mixing characteristics. As an example, each of the correlations (6) to (8) considering a given tank with ejectors, would provide the same results regardless of the ejectors orientation, which however will be having an effect on the local and bulk mixing characteristics. As a result of this lack of accuracy, a detailed investigation of the mixing performance for molten salts tanks equipped with ejectors in different configurations have been carried out in this work, with particular focus on the cold salt tank.
defined at the ejector discharge location, with 260 m3/h per ejector (primary + secondary flow), and the corresponding jet velocity and direction, where a 8″ ejector discharge diameter is considered. Then, the corresponding negative mass source (mass sink) is defined at a location backwards from the ejector discharge, in order to consider the secondary flow entrained by the ejector, with a mass sink of 190 m3/h per ejector. As explained before, the jet entrainment developed after the ejector discharge in the bulk fluid is calculated by the CFD solution. The primary ejector flow of 650 m3/h for all ejectors are extracted from the tank via the extraction pipe, where the volume flow is suctioned in order to guarantee the mass conservation within the tank. Following this approach with the CFD model, the following configurations have been analysed:
3.2. Methodology and configurations analysed - Number of ejectors: 6 or 10 ejectors equally spaced in the tangential direction along the recirculation ring (3 or 6 ejectors in the half tank). - Direction of the ejectors (jet): towards the tank central vertical axis, or tangential to the recirculation ring. In case of tangential direction, the symmetry planes boundary conditions are substituted by periodic boundaries with respect to the tank vertical axis, in order to allow the fluid to circulate tangentially around the tank. - Angle of the ejectors (jet) with respect to the tank bottom surface: 15°, 30°, 45°, 60°, 75°.
In order to investigate the mixing characteristics of the different ejector configurations, a parametric analysis of different ejector configurations was carried out with a CFD model. The model is considering one half of the tank due to its geometry, as depicted in Fig. 2. The main simplification of the model is the use of a set of point sources for the ejectors, instead of the detailed geometry of the ejectors. That means that the jet flow induced by each ejector is modelled by means of a local mass source located at the ejector position. This allows for a faster screening of different ejectors locations and configurations, as the same mesh can be used for all cases without the need for re-meshing each ejector configuration. The local point sources are defined in the model for each ejector location, defined by its coordinates, the total fluid mass source (kg/s), the fluid temperature, and the fluid velocity components (thus defining the jet direction as well). The best configurations can therefore be identified using this approach based on CFD modelling. A sketch on the ejector working principle is depicted in Fig. 3. The ejector itself is pumping a primary flow (65 m3/h for a 10 ejectors system and the operating conditions considered in the tank). This primary flow induces a secondary recirculation flow by means of the Venturi effect generated by the ejector design. A total ejector flow (primary + secondary) is therefore discharged into the tank’s bulk fluid. According to common manufacturers, the secondary flow is roughly 3 times the primary flow, and this will be considered by the simulations (thus 65 m3/h + 195 m3/h = 260 m3/h for each ejector). A fluid entrainment pattern is later developed as is well known for all non-confined jet flows. This bulk entrainment is calculated by the CFD model and must therefore not be considered as a boundary condition or mass source. The mass source for each ejector is defined as a double mass source in order to correctly capture the fluid flow. A positive mass source is
In all cases, the total flow rate recirculated is maintained constant, so that the mixing efficiency can be compared between the cases on the basis of the same pumping power. The base case is defined according to a typical configuration found in TES tanks: 10 ejectors (1 ejector every 36 degrees of the tank), ejectors directed towards the tank central vertical axis, and with an angle of 30° with respect to the tank bottom surface.
3.3. Geometry, meshing and numerical model A mesh of one half of the tank according to Fig. 2 has been generated with ANSYS ICEM CFD [15], based on tetrahedral elements. A set of prism layers have been set at the tank walls (bottom, side walls, tubing walls) as shown in Fig. 4. The mesh used in the analysis is containing 15.7 million elements and 2.7 million nodes, with a minimum face angle of 6.5° and a maximum aspect ratio less than 10. A mesh independence analysis was carried out in order to ensure the quality of the results minimizing the discretization errors. Five different meshes were generated, each having 322
Energy Conversion and Management 168 (2018) 320–328
A. Iranzo et al.
Fig. 6. Flow velocity at the ejector mid-plane (base case). Fig. 4. Meshing detail around the inner distribution ring pipe. Bottom surface, symmetry plane surface and piping are displayed.
10.8 m. The average flow velocity is computed in the interior of each of the volumes, and results will be compared for the different configurations. In addition, the percentage of the fluid above certain values of velocities (5, 10, 15 mm/s) for each sub-volume will be analysed as well for each configuration. Mixing performance of each configuration has been also addressed by means of the calculation of mixing times. This is presented in Section 4.4. 4.1. Analysis of base case and configurations varying the ejectors angle The first configuration to be analysed is the base case (10 ejectors, directed towards the tank central vertical axis, and with an angle of 30° with respect to the tank bottom surface). The flow field induced by the ejector in a vertical plane along the jet mid-plane is presented in Fig. 6 (tank wall is located on the left, tank axis on the right, recirculation and distribution rings displayed as blank circles). The jet-type flow is clearly identified, as well as both mass source and mass sink defined to model the ejector. The jet influence reaches up to roughly nine metres long into the bulk fluid. The effect of the angle of the ejectors has been investigated with the model, by modifying the jet velocity components in the local source points definition. Angles of 15°, 30° (base case), 45°, 60°, 75° have been analysed. Fig. 7 shows the flow velocity field for different angles: 15°, 30° (base case), 45°. It is worth to observe the interaction of the jet flow with the inner distribution ring for 15° angle, which would likely cause mechanical issues in the ring fixing clamps. The results of the analysis carried out for the average flow velocity in the tank sub-volumes for the different configurations is presented in Fig. 8. It is observed that the average velocity follows the same trend for all sub-volumes considered for all ejector angles, except for the smallest sub-volume (0.1 m height from the tank bottom). In this case, the best ejector angle providing the higher average velocity is 15°. This is obviously caused by the enhanced flow circulation in the bottom part of the tank for such low ejector inclination. The increase in the average velocity is however not significant, and a drawback of such configuration is the high mechanical stress exerted by the jet flows over the inner piping ring. As a result, from the results presented in Fig. 6 it can be concluded that the configuration with ejector angle of 30° is providing the best results in terms of the average flow velocity (and therefore fluid circulation) within the tank. This is indeed the typical configuration used in TES tanks. As an additional study, the percentage of each sub-volume with velocities above certain values (5, 10, 15 mm/s) are provided in Fig. 9. It is again observed that for the lowest volume of the tank (0.1 m height) the ejector angle of 15° would be the optimal configuration. However, when larger tank volumes are considered, it is clear from the results presented in Fig. 9 that the ejector angle of 30° is the optimal configuration.
Fig. 5. Results of the mesh independence study. M1 to M5 indicates the meshes used, where M4 is the mesh used for the simulations.
four times more nodes and elements than the previous one. The coarsest mesh contained 290.000 elements, whereas the finest mesh contained 53.1 million elements. The volume average grid spacing Δx was ranging from 0.27 m in the coarsest mesh to 0.047 m in the finest mesh. After convergence of simulations (RMS residuals < 1.0E-04 and global equation imbalances < 0.1%) the results were compared for all five meshes. The average velocity was used as the main variable for the mesh dependency study, where the values of the volume average in the full tank, and in sub-volumes defined by a height at 0.2 m and 0.4 m were calculated. The results are presented in Fig. 5, where it is observed that the mesh containing 15.7 million elements and 2.7 million nodes (M4 in Fig. 5) is the one offering mesh-independent results. The subsequent refined mesh does not provide any significant difference in the results. This mesh is therefore selected for all further simulations presented in this work. At the top liquid surface located at 10.8 m height a free-slip wall has been defined in order to model the gas-liquid free surface. The SST turbulence model [15] has been used due to its well-proven accurate results in flows encountered in industry [20]. The High-Resolution scheme [15] in ANSYS-CFX has been used as discretization scheme.
4. Model results In this section the results of the different configurations analysed are presented. In order to quantify the fluid circulation capacity of each configuration, the average flow velocity in different sub-volumes of the tank has been calculated. As one of the main concerns (when analysing local cold spots potentially leading to solidification) is the salts closed to the tank bottom, special care is focused on the average flow velocity in sub-volumes close to the bottom surface. The sub-volumes considered are defined by the height of salts considered from the tank bottom: 0.1 m, 0.2 m, 0.3 m, 0.4 m, and finally the full tank volume at 323
Energy Conversion and Management 168 (2018) 320–328
A. Iranzo et al.
Fig. 7. Flow velocity at the ejector mid-plane for ejector angle 15°, 30° (base case), 45°.
4.2. Analysis of configurations varying the number of ejectors The configuration with 6 ejectors has been simulated and compared against the base case. Ejectors pointing towards the central vertical axis and with 30° angle as in the base case are considered. As the objective is to maintain the pumping power of the system, the total volume flow rate is maintained the same for both configurations. This means that the impulsion flow rate is higher in the configuration with 6 ejectors (433 m3/h instead of 260 m3/h per ejector, with an entrained mass sink of 316 m3/h instead of 190 m3/h per ejector). The jet velocity defined for the local mass source is thus 3.57 m/s in the configuration with 6 ejectors, versus 2.14 m/s in the base case configuration with 10 ejectors. The results of the comparison are shown in Fig. 10, where it is observed that the configuration with 10 ejectors is generating a better fluid circulation than the configuration with 6 ejectors. 4.3. Analysis of configurations varying the ejectors direction The configuration with a tangential direction of the ejectors (not pointing towards the tank central axis, but towards the tangential direction of the recirculation ring) has been resolved with the CFD model. As in the base case, 10 ejectors with 30° angle is maintained. The symmetry planes of the tank at both sides of the central vertical axis are defined in the tangential configuration as periodic boundaries, allowing
Fig. 8. Average velocity within the tank sub-volumes considered for ejector angles 15°, 30°, 45°, 60°, 75°. 324
Energy Conversion and Management 168 (2018) 320–328
A. Iranzo et al.
Fig. 9. Percentage of sub-volumes with velocity above 5, 10, 15 mm/s for ejector angles 15°, 30°, 45°, 60°, 75°. Fig. 10. Percentage of sub-volumes with velocity above 5, 10, 15 mm/s for configurations with 6 and 10 ejectors.
fluid to traverse them with a periodic condition (so that the flow field is mapped from one side onto the other side). Symmetry planes are not suitable for such configurations as per definition the normal flow at symmetry planes is zero (and therefore the tangential flow induced by the ejectors could not develop as in the real tank). The velocity field at the horizontal plane of the tank at the ejectors level is depicted in Fig. 11, where the tangential flow circulating in the clock-wise direction is clearly identified. Figs. 12 and 13 present the results of the flow velocity analysis comparison, where it is clearly observed that the tangential flow configuration is achieving a better fluid circulation capacity in the tank. It must be noted that such tangential configuration is not typically found in TES tanks for CSPPs, and therefore the results obtained in this work may be of benefit for future designs. However, such potential designs would need to consider the mechanical forces exerted over the ring clamps by the reaction force caused by the jet, in the tangential direction as well. Such force is not compensated along the ring pipe as it is the case with ejectors pointing towards the central axis, and should be therefore considered in the mechanical design of the system. It must be noted that when ejectors are oriented in the tangential direction, no more jet interaction with the inner piping ring can be present. Therefore, for this particular configuration, a new case with no inclination of the ejectors is proposed (angle = 0°). The results are presented in Figs. 14 and 15. Where it is observed that the configuration with 0° angle is performing even better than the one with ejectors angle at 30°, with an increase in the fluid circulation velocity for all tank heights considered.
Fig. 11. Flow field (horizontal plane at the ejectors height) developed for the tangential configuration.
Thus, from the results presented above based on the CFD model developed, it is concluded that the configuration that provides the best fluid circulation capacity in the cold salt tank is 10 ejectors oriented in the tangential direction at 0° inclination angle with respect to the tank bottom surface. In a final design, the mechanical design would however need to consider the tangential forces over the recirculation ring and clamps. A quantitative comparison of the fluid circulation capacity of the best configuration identified with respect to the base case is showing that in terms of average velocity, the molten salts bulk in the tangential 0° case is having almost three times the velocity of the base 325
Energy Conversion and Management 168 (2018) 320–328
A. Iranzo et al.
Fig. 14. Average velocity of sub-volumes for configurations with tangential flow at 0° and 30°.
Fig. 12. Average velocity of sub-volumes for configurations with axial and tangential flow.
Fig. 15. Percentage of sub-volumes with velocity above 5, 10, 15 mm/s for configurations with tangential flow at 0° and 30°.
Fig. 13. Percentage of sub-volumes with velocity above 5, 10, 15 mm/s for configurations with axial and tangential flow.
identified. configuration. When it comes to analysing the lower section of the tank, differences are even higher, featuring more than 10 times the velocity flow for the first 10 cm height, and more than 6 times the velocity flow for the first 20 cm height. This general enhancement is caused by the positive effect of jets pumping in the same direction, with respect to the base case with opposing jets. The even more increased enhancement in the particular region of the lower tank volume is caused by the jets having a pumping angle parallel to the tank bottom surface. When comparing the percentage of the tank bulk fluid presenting a velocity over 1 cm/s, almost 100% of the tank is well mixed for the tangential 0° case, whereas only 50% of the tank is well mixed in the base case configuration. It is therefore ensured that no fluid dead-zones will be appearing within the tank bulk fluid with the best ejector configuration
4.4. Mixing time calculations The configuration identified in the previous analysis presents the highest fluid circulation capacity with no dead-zones within the tank bulk fluid. It is however required to investigate the real mixing time of the molten salts in the tank. It is well known in the mixing industry that a pure rotational flow may present low mixing performance despite the flow velocity, if the bulk fluid rotates with a solid rigid pattern without intermediate baffles or internals breaking the flow pathlines and promoting turbulence and mixing [17]. As the proposed configuration is inducing a rotational flow pattern, a more detailed analysis has been performed by investigating the mixing times for all configurations. 326
Energy Conversion and Management 168 (2018) 320–328
A. Iranzo et al.
maximum tracer concentration within the tank is monitored. According to (9), the mixing time (95%) is reached once the tracer concentration in the tank is within 0.1577 and 0.1743 (mass fraction). Fig. 16 presents the time evolution of the tracer concentration at all monitor points as well as the maximum and minimum values. The results are presented for the base case (top), the case with tangential direction at 0° (middle) and the case with angle 0° pointing towards the axis (bottom). The results show that the mixing time θM,95 (all tracer concentrations within the required range) is 0.46 h, 0.92 h, and 0.33 h, respectively. It is therefore interesting to point out that the case with highest fluid circulation identified previously (namely ejectors in tangential direction at 0° angle) is actually not appropriate when the mixing time is analysed. The cause of this is that the configuration with ejectors in tangential direction at 0° angle is achieving a high flow circulation as all ejectors positively interact with each other in terms of fluid acceleration. However, the fluid within the tank considered is mostly rotating in a solid-rigid motion pattern, as very few internals are breaking the fluid rotating motion pathlines. This results in longer mixing times. The full comparison of the mixing time (95% mixing denoted as θM,95 and 99% mixing denoted as θM,99) calculated for all configurations is presented in Fig. 17. Both configurations with ejectors pumping fluid in the tangential direction present significantly higher mixing times than the configurations pointing towards the central vertical axis. Among them, the configuration with 10 ejectors with an angle of 0° presents the least mixing times (0.33 h for θM,95 and 0.41 h for θM,99). Such results indicate that for the selection of an optimal configuration many effects and parameters must be considered. The case with the highest flow circulation capacity (three times the capacity of the base configuration) is presenting one of the longest fluid mixing times (three times longer than in the base configuration). It is a design criterion to define which are the values required for each particular application in order to ensure a safe operation of the tank without a risk of salt solidification even in long stops required by plant maintenance operation. As a result of this conclusion aiming at defining a future work, further simulations are required in order to quantify the transient temperature decay profile in the coldest location of the tank due to heat loss for the configurations analysed. This will provide useful information regarding the optimal ejector configuration in terms of maintaining the adequate fluid temperature long enough to ensure a safe tank operation.
5. Conclusions
Fig. 16. Time evolution of the tracer concentration Ct in the tank volume. Maximum, minimum and C∞ values are marked in red. The concentration range for θM,95 is marked with black dotted lines. Top: 10 ejectors 30° towards axis (base case). Middle: 10 ejectors 0° tangential direction. Bottom: 10 ejectors 0° towards axis.
In this work, the mixing performance in cold salt tanks using molten salts for CSPPs has been investigated by means of CFD modelling. A set of different ejector configurations has been resolved, modifying the number of ejectors, flow direction, and ejector angle. The best configurations are identified, where the highest fluid circulation capacity is achieved by 10 ejectors directing the jet flow in the tangential direction with an inclination angle of 0° with respect to the tank bottom surface. This is increasing the fluid circulation capacity of the tank by more than 100% with respect to the usual configuration implemented in such tanks (ejectors directed to the tank central vertical axis, at 30° angle). In addition, such configuration ensures an enhanced flow circulation in the bottom part of the tank (with an increase of more than 6 times in the flow velocity in the lower section of the tank), reducing the risk of local salt solidification due to heat loss through the bottom surface. However, the shortest mixing times (95% and 99%) are achieved by the configuration with 10 ejectors pumping flow towards the central tank axis with an inclination angle of 0°. It is therefore required to further analyse how the configurations identified perform, in terms of ensuring appropriate temperature levels in the tank during a transient process involving heat losses.
The mixing time (95% and 99%) has been calculated with the CFD model, as proposed in previous studies [21,22]. For this, a transient simulation is defined where a set of local monitor points are spread within the domain. A tracer is released at t = 0 s in the transient simulation, and the tracer concentration evolution at the monitor points is monitored with time. The mixing time θM can be defined as the degree of uniformity (U) of the tracer concentration at each location:
θM = U = 1−
(C∞−Ct ) C∞
(9)
Where C∞ is the tracer final concentration at t = ∞ and Ct is the tracer concentration at any time. For the CFD simulations, 100 kg/s of tracer during 300 s (5 min) are injected into the tank at each ejector, thus the final tracer concentration would be 0.16604 (mass fraction). A set of twelve monitor points have been defined forming a matrix in the tank radius and height, and for the sake of reliability, also the minimum and 327
Energy Conversion and Management 168 (2018) 320–328
A. Iranzo et al.
Fig. 17. Mixing times (95% and 99%) for all ejector configurations.
References
2015;98:20–9. [11] Daabo AM, Al Jubori A, Mahmoud S, Al-Dadah RK. Parametric study of efficient small-scale axial and radial turbines for solar powered Brayton cycle application. Energy Convers Manage 2016;128:343–60. [12] Nižetić S, Penga Ž, Arıcı M. Contribution to the research of an alternative energy concept for carbon free electricity production: Concept of solar power plant with short diffuser. Energy Convers Manage 2017;148:533–53. [13] Schulte-Fischedick J, Tamme R, Herrmann U. CFD analysis of the cool down behaviour of molten salt thermal storage systems. In: ASME 2008 2nd international conference on energy sustainability collocated with the heat transfer, fluids engineering, and 3rd energy nanotechnology conferences. American Society of Mechanical Engineers; 2008. p. 515–24. [14] Rivas E, Rojas E, Bayón R, Gaggioli W, Rinaldi L, Fabrizi F. CFD model of a molten salt tank with integrated steam generator. Energy Procedia 2013;49:956–64. [15] ANSYS-FLUENT. ANSYS, Inc., Southpointe 2600 ANSYS Drive Canonsburg, PA 15317. [16] Solar Power Tower Design Basis Document. Prepared by Alexis B. Zavoico, Nexant, San Francisco, CA 94104. Sandia National Laboratories, Albuquerque, New Mexico 87185 and Livermore, California 94550. SAND2001-2100 Unlimited Release Printed July 2001. [17] Leng, D. E., Katti, S. S., Atiemo-Obeng, V. Industrial Mixing Technology. In: Albright’s Chemical Engineering Handbook, edited by Lyle f. Albright. Ed. CRC, 2009. [18] Grenville RK, Tilton JN. A new theory improves the correlation of blend time data from turbulent jet mixed vessels. Chem Eng Res Des 1996;74:390–6. [19] Fossett H, Prosser LE. The application of free jets to the mixing of fluids in bulk. Proc I Mech Eng 1949;160:224–32. [20] Menter FR. Review of the shear-stress transport turbulence model experience from an industrial perspective. Int J Comput Fluid Dynam 2009;23:305–16. [21] Patwardhan AW. CFD modeling of jet mixed tanks. Chem Eng Sci 2002;57:1307–18. [22] Jayanti S. Hydrodynamics of jet mixing in vessels. Chem Eng Sci 2001;56:193–210.
[1] Trabelsi SE, Qoaider L, Guizani A. Investigation of using molten salt as heat transfer fluid for dry cooled solar parabolic trough power plants under desert conditions. Energy Convers Manage 2018;156:253–63. [2] Wang K, He Y-L. Thermodynamic analysis and optimization of a molten salt solar power tower integrated with a recompression supercritical CO2 Brayton cycle based on integrated modelling. Energy Convers Manage 2017;135:336–50. [3] González-Gómez PA, Gómez-Hernández J, Briongos JV, Santana D. Thermo-economic optimization of molten salt steam generators. Energy Convers Manage 2017;146:228–43. [4] Relloso S, Delgado E. Experience with molten salt thermal storage in a commercial parabolic trough plant; Andasol 1 commissioning and operation. In: Proceedings of 15th international SolarPACES symposium; September 2009, p. 14–18. [5] Suárez C, Iranzo A, Pino FJ, Guerra J. Transient analysis of the cooling process of molten salt thermal storage tanks due to standby heat loss. Appl Energy 2015;142:56–65. [6] Rodríguez I, Pérez-Segarra CD, Lehmkuhl O, Oliva A. Modular object-oriented methodology for the resolution of molten salt storage tanks for CSP plants. Appl Energy 2013;109:402–14. [7] Fernández-Torrijos M, Sobrino C, Almendros-Ibáñez JA. Simplified model of a dualmedia molten-salt thermocline tank with a multiple layer wall. Sol Energy 2017;151:146–61. [8] Zaversky F, García-Barberena J, Sánchez M, Astrain D. Transient molten salt twotank thermal storage modeling for CSP performance simulations. Sol Energy 2013;93:294–311. [9] Patel SK, Prasad D, Ahmed MR. Computational studies on the effect of geometric parameters on the performance of a solar chimney power plant. Energy Convers Manage 2014;77:424–31. [10] Sultana T, Morrison GL, Taylor RA, Rosengarten G. Numerical and experimental study of a solar micro concentrating collector. Energy Convers Manage
328
Contents lists available at ScienceDirect
Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
Mixing enhancement in thermal energy storage molten salt tanks ⁎
T
Alfredo Iranzo , Christian Suárez, José Guerra Thermal Engineering Group, Energy Engineering Department, School of Engineering, Universidad de Sevilla, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain
A R T I C LE I N FO
A B S T R A C T
Keywords: Mixing CFD Numerical model Thermal energy storage Molten salts Concentrated solar power plant
An appropriate degree of mixing in molten salt tanks for Thermal Energy Storage (TES) in Concentrated Solar Power Plants (CSPPs) is required in order to ensure the safe operation of the tank. Otherwise, cooling due to thermal heat losses is prone to result in a high thermal stratification of the salts and eventually local solidification. In this work, the mixing performance of different configurations of ejectors is investigated by means of Computational Fluid Dynamics (CFD). A set of different ejector configurations has been resolved, modifying the number of ejectors, flow direction, and ejector angle. The best configurations are identified, where the highest fluid circulation capacity is achieved by 10 ejectors directing the jet flow in the tangential direction with an inclination angle of 0° with respect to the tank bottom surface. This is increasing the fluid circulation capacity of the tank by more than 100% with respect to the usual configuration implemented in such tanks (ejectors directed to the tank central vertical axis, at 30° angle). In addition, such configuration ensures an enhanced flow circulation in the bottom part of the tank (with an increase of more than 6 times in the flow velocity in the lower section of the tank), reducing the risk of local salt solidification due to heat loss through the bottom surface. However, the shortest mixing times (95% and 99%) are achieved by the configuration with 10 ejectors pumping flow towards the central tank axis with an inclination angle of 0°.
1. Introduction One of the promising technologies for renewable electricity generation is Concentrated Solar Power Plants (CSPPs). As an additional benefit, solar thermal power plants have the ability to store thermal energy, which enables the decoupling of the electric power generation from the intermittency of the available solar irradiation. Currently, commercial thermal storage systems are mostly based on a two-tank sensible heat thermal storage with molten salts. A simplified sketch of a facility integrating such a Thermal Energy Storage (TES) system is presented in Fig. 1. The heated heat transfer fluid (HTF) from the solar field is sent towards the steam generation circuit, and/or to the TES system in order to increase its degree of charge. As mentioned previously, the TES system consists of two molten salt tanks, able to exchange salts via a heat exchanger heated by the HTF from the solar field. During charging operation, molten salts stored in the cold salt tank are heated by a side stream of the HTF not used for steam generation. The heated salts are stored in the hot salt tank until they are later needed when solar energy is not available. In order to heat the HTF, the TES system is used in the opposite or discharge mode, where the salts are transferred from the hot tank to the cold tank through the heat exchanger, heating the HTF which is then sent towards the steam generation circuit. It is worth to mention that some novel
⁎
Corresponding author. E-mail address: [email protected] (A. Iranzo).
https://doi.org/10.1016/j.enconman.2018.04.113 Received 27 February 2018; Received in revised form 27 April 2018; Accepted 29 April 2018 0196-8904/ © 2018 Elsevier Ltd. All rights reserved.
systems are being proposed using molten salts directly as HTF [1–3]. Molten Salts Tanks are typically cylindrically shaped tanks with over 20 m diameter [4]. An appropriate degree of mixing within the molten salt tanks is required in order to ensure a safe operation, which is obviously more important in the cold salt tank. Otherwise, despite the thermal insulation being used, cooling due to thermal heat losses are prone to result in thermal stratification of the salts and eventually partial solidification [5–8]. This is particularly important for long stops of the plant (such as during maintenance operations) where up to twomonth duration can be expected. For such cases, tanks typically include electrical heaters installed in the bottom, in order to provide heat during long stops compensating the heat losses. Again, it is particularly important to ensure that the heat released by the electrical heaters is uniformly distributed within the tank, avoiding dead zones that could become local cold spots for salts solidification. Mixing could be achieved just by natural convection, but more often a set of ejectors are included in the tank, in order to induce a flow circulation and mixing within the tank volume. How to define the ejector configuration that enhance the mixing performance is the objective of this research work. The approach followed for achieving this objective is the development of a model based on Computational Fluid Dynamics (CFD), as experimental measurements in such large tanks during operation is highly prohibitive in terms of costs and technical difficulties. CFD is commonly
Energy Conversion and Management 168 (2018) 320–328
A. Iranzo et al.
Fig. 2. Tank geometry and main components (inner injection ring, outer recirculation ring, extraction pipe). Symmetry plane depicted in red.
the tank via the recirculation ring. Given the tank symmetry with respect to the middle plane (in red in Fig. 2), the simulation of only one half of the tank is required. 3. Modelling methodology The model has been developed in the commercial software ANSYSCFX [15]. The salts used in the tank correspond to a mixture of 60% NaNO3 and 40% KNO3, where the physical properties of the mixture were obtained from Sandia technical report on CSP design [16] (see Table 1): According to the data in [16], the following correlations for the physical properties can be derived, which were used for the CFD modelling:
Fig. 1. Simplified Block diagram of for Thermal Energy Storage System for CSPP.
used for the design and research of fluid flow and heat transfer processes associated to CSP [9–12]. Regarding the particular investigations on molten salt tanks, Schulte-Fischedick et al. [13] carried out a 2D and 3D CFD analysis of the cool down behaviour of a molten salt thermal storage system (880 MWh storage tanks). Heat losses, velocities, and temperature distributions were analysed, revealing that the highest heat flux was found at the lower edges of the tanks, leading to local solidification after a relatively short period of time (3.25 days for the empty cool tank). Rivas et al. [14] also integrated the steam generator in a CFD model of a pilot-scale thermocline tank. The bulk and circulation of the molten salts inside the tank and steam generator with steam coils were studied in a transient 2D-axisymmetric simulation. Such works present very useful results relevant for TES tanks, but it is worth to mention that no previous works are found specifically studying the mixing characteristics of molten salts tanks for TES, despite the importance of such systems for the future deployment of solar thermal power plants. Therefore, the objective of this research work is aiming at the analysis and enhancement of mixing in thermal energy storage molten salt tanks.
Density(kg/m3) = 2090−0.636·Temperature
(1)
Heat capacity(J/kg °C) = 1443 + 0.172·Temperature
(2)
Thermal conductivity(W/m °C) = 0.443 + 1.9E−4·Temperature
(3)
Viscosity(mPa s) = 22.714−0.120·Temperature + 2.281E−4·Temperature2 −1.474E−7·Temperature3
(4)
Where the unit of Temperature in Equations (1) to (4) is °C.The model will consider the tank at a high capacity (10.8 m height, which means 11.000 m3 of salts) as this will be the case where mixing is more challenging for a given design. Salts temperature at typical design point of the cold salt tank (285 °C) is considered, with a recirculation flow of 650 m3/h. 3.1. Correlations for mixing time estimation Some preliminary estimations of the mixing times can be carried out based on the tank and ejector basic data and general correlations. As an example, as a first approximation it can be estimated that a free jet may entrain 15 to 20 times its pumped flow rate [17]. Assuming that mixing time (95%) is requiring five flow turnovers, this results in:
2. Description of the tank The tank under analysis is presented in Fig. 2, corresponding to a Cold Salt Tank. The tank diameter used in this study is 36 m, a relatively large tank representative of current technologies, where mixing is becoming relevant to ensure a safe operation. Considering a salt filling height of around 11 m, the tank could store 11.000 m3 of salts, enough for roughly 2.5 full load operation of a 100 MW CSPP. The tank is featuring two different salts injection piping rings (Fig. 2). The inner ring is perforated with roughly 100 holes and corresponds to the injection of salts from the charging heat exchanger (Fig. 1). This will be referred to as distribution ring. The outer ring corresponds to the injection of recirculation salts, i.e. salts that are extracted from the tank and injected again via a set of ejectors equally distributed along the ring, in order to achieve the mixing of the salts. This will be referred to as recirculation ring. Salts are pumped out of the tank via a vertical pipe (closest to the external wall in Fig. 2) to re-enter
θM ,approx =
5V 20Q
(5)
Table 1 Physical properties of 60% NaNO3 and 40% KNO3 molten salts at cold salt tank [16].
321
Temperature (°C)
Density (kg/m3)
Heat capacity (J/ kg °C)
Viscosity (mPa s)
Thermal conductivity (W/ m °C)
260 288 316
1924.64 1906.97 1889.31
1488 1492 1497
4.343 3.558 2.929
0.492 0.498 0.503
Energy Conversion and Management 168 (2018) 320–328
A. Iranzo et al.
where V is the tank volume and Q is the jet volume flow rate. This approximation results in approximately 4–6 h. According to Gray’s correlation for the mixing time [17], supposed to be conservative, the jet mixing time can be estimated as:
θM =
30Vdj Q (HT )0.5
(6)
where V is the tank volume, H is the tank height, T is the tank diameter, Q is the jet volume flow rate, and dj is the jet diameter. According to this correlation the mixing time is 7.8 h. The correlation from Grenville [17,18] is an empirical expression:
vj θM dj
1.5
T H = 5.69 ⎜⎛ ⎟⎞ ⎜⎛ ⎟⎞ ⎝ dj ⎠ ⎝ dj ⎠
0.5
(7)
where vj is the jet flow velocity. This correlation yields a mixing time of 1.75 h. Fosset [17,19] derived another correlation:
θM =
8T 2 (Qvj )0.5
Fig. 3. Ejector sketch and working principle.
(8)
Which is providing a mixing time of 8.8 h. The analysis above clearly shows that despite the fact that such correlations provide a reasonable estimate of the mixing time range, they are considering overall quantities only and are missing the effects that particular designs may have on the mixing characteristics. As an example, each of the correlations (6) to (8) considering a given tank with ejectors, would provide the same results regardless of the ejectors orientation, which however will be having an effect on the local and bulk mixing characteristics. As a result of this lack of accuracy, a detailed investigation of the mixing performance for molten salts tanks equipped with ejectors in different configurations have been carried out in this work, with particular focus on the cold salt tank.
defined at the ejector discharge location, with 260 m3/h per ejector (primary + secondary flow), and the corresponding jet velocity and direction, where a 8″ ejector discharge diameter is considered. Then, the corresponding negative mass source (mass sink) is defined at a location backwards from the ejector discharge, in order to consider the secondary flow entrained by the ejector, with a mass sink of 190 m3/h per ejector. As explained before, the jet entrainment developed after the ejector discharge in the bulk fluid is calculated by the CFD solution. The primary ejector flow of 650 m3/h for all ejectors are extracted from the tank via the extraction pipe, where the volume flow is suctioned in order to guarantee the mass conservation within the tank. Following this approach with the CFD model, the following configurations have been analysed:
3.2. Methodology and configurations analysed - Number of ejectors: 6 or 10 ejectors equally spaced in the tangential direction along the recirculation ring (3 or 6 ejectors in the half tank). - Direction of the ejectors (jet): towards the tank central vertical axis, or tangential to the recirculation ring. In case of tangential direction, the symmetry planes boundary conditions are substituted by periodic boundaries with respect to the tank vertical axis, in order to allow the fluid to circulate tangentially around the tank. - Angle of the ejectors (jet) with respect to the tank bottom surface: 15°, 30°, 45°, 60°, 75°.
In order to investigate the mixing characteristics of the different ejector configurations, a parametric analysis of different ejector configurations was carried out with a CFD model. The model is considering one half of the tank due to its geometry, as depicted in Fig. 2. The main simplification of the model is the use of a set of point sources for the ejectors, instead of the detailed geometry of the ejectors. That means that the jet flow induced by each ejector is modelled by means of a local mass source located at the ejector position. This allows for a faster screening of different ejectors locations and configurations, as the same mesh can be used for all cases without the need for re-meshing each ejector configuration. The local point sources are defined in the model for each ejector location, defined by its coordinates, the total fluid mass source (kg/s), the fluid temperature, and the fluid velocity components (thus defining the jet direction as well). The best configurations can therefore be identified using this approach based on CFD modelling. A sketch on the ejector working principle is depicted in Fig. 3. The ejector itself is pumping a primary flow (65 m3/h for a 10 ejectors system and the operating conditions considered in the tank). This primary flow induces a secondary recirculation flow by means of the Venturi effect generated by the ejector design. A total ejector flow (primary + secondary) is therefore discharged into the tank’s bulk fluid. According to common manufacturers, the secondary flow is roughly 3 times the primary flow, and this will be considered by the simulations (thus 65 m3/h + 195 m3/h = 260 m3/h for each ejector). A fluid entrainment pattern is later developed as is well known for all non-confined jet flows. This bulk entrainment is calculated by the CFD model and must therefore not be considered as a boundary condition or mass source. The mass source for each ejector is defined as a double mass source in order to correctly capture the fluid flow. A positive mass source is
In all cases, the total flow rate recirculated is maintained constant, so that the mixing efficiency can be compared between the cases on the basis of the same pumping power. The base case is defined according to a typical configuration found in TES tanks: 10 ejectors (1 ejector every 36 degrees of the tank), ejectors directed towards the tank central vertical axis, and with an angle of 30° with respect to the tank bottom surface.
3.3. Geometry, meshing and numerical model A mesh of one half of the tank according to Fig. 2 has been generated with ANSYS ICEM CFD [15], based on tetrahedral elements. A set of prism layers have been set at the tank walls (bottom, side walls, tubing walls) as shown in Fig. 4. The mesh used in the analysis is containing 15.7 million elements and 2.7 million nodes, with a minimum face angle of 6.5° and a maximum aspect ratio less than 10. A mesh independence analysis was carried out in order to ensure the quality of the results minimizing the discretization errors. Five different meshes were generated, each having 322
Energy Conversion and Management 168 (2018) 320–328
A. Iranzo et al.
Fig. 6. Flow velocity at the ejector mid-plane (base case). Fig. 4. Meshing detail around the inner distribution ring pipe. Bottom surface, symmetry plane surface and piping are displayed.
10.8 m. The average flow velocity is computed in the interior of each of the volumes, and results will be compared for the different configurations. In addition, the percentage of the fluid above certain values of velocities (5, 10, 15 mm/s) for each sub-volume will be analysed as well for each configuration. Mixing performance of each configuration has been also addressed by means of the calculation of mixing times. This is presented in Section 4.4. 4.1. Analysis of base case and configurations varying the ejectors angle The first configuration to be analysed is the base case (10 ejectors, directed towards the tank central vertical axis, and with an angle of 30° with respect to the tank bottom surface). The flow field induced by the ejector in a vertical plane along the jet mid-plane is presented in Fig. 6 (tank wall is located on the left, tank axis on the right, recirculation and distribution rings displayed as blank circles). The jet-type flow is clearly identified, as well as both mass source and mass sink defined to model the ejector. The jet influence reaches up to roughly nine metres long into the bulk fluid. The effect of the angle of the ejectors has been investigated with the model, by modifying the jet velocity components in the local source points definition. Angles of 15°, 30° (base case), 45°, 60°, 75° have been analysed. Fig. 7 shows the flow velocity field for different angles: 15°, 30° (base case), 45°. It is worth to observe the interaction of the jet flow with the inner distribution ring for 15° angle, which would likely cause mechanical issues in the ring fixing clamps. The results of the analysis carried out for the average flow velocity in the tank sub-volumes for the different configurations is presented in Fig. 8. It is observed that the average velocity follows the same trend for all sub-volumes considered for all ejector angles, except for the smallest sub-volume (0.1 m height from the tank bottom). In this case, the best ejector angle providing the higher average velocity is 15°. This is obviously caused by the enhanced flow circulation in the bottom part of the tank for such low ejector inclination. The increase in the average velocity is however not significant, and a drawback of such configuration is the high mechanical stress exerted by the jet flows over the inner piping ring. As a result, from the results presented in Fig. 6 it can be concluded that the configuration with ejector angle of 30° is providing the best results in terms of the average flow velocity (and therefore fluid circulation) within the tank. This is indeed the typical configuration used in TES tanks. As an additional study, the percentage of each sub-volume with velocities above certain values (5, 10, 15 mm/s) are provided in Fig. 9. It is again observed that for the lowest volume of the tank (0.1 m height) the ejector angle of 15° would be the optimal configuration. However, when larger tank volumes are considered, it is clear from the results presented in Fig. 9 that the ejector angle of 30° is the optimal configuration.
Fig. 5. Results of the mesh independence study. M1 to M5 indicates the meshes used, where M4 is the mesh used for the simulations.
four times more nodes and elements than the previous one. The coarsest mesh contained 290.000 elements, whereas the finest mesh contained 53.1 million elements. The volume average grid spacing Δx was ranging from 0.27 m in the coarsest mesh to 0.047 m in the finest mesh. After convergence of simulations (RMS residuals < 1.0E-04 and global equation imbalances < 0.1%) the results were compared for all five meshes. The average velocity was used as the main variable for the mesh dependency study, where the values of the volume average in the full tank, and in sub-volumes defined by a height at 0.2 m and 0.4 m were calculated. The results are presented in Fig. 5, where it is observed that the mesh containing 15.7 million elements and 2.7 million nodes (M4 in Fig. 5) is the one offering mesh-independent results. The subsequent refined mesh does not provide any significant difference in the results. This mesh is therefore selected for all further simulations presented in this work. At the top liquid surface located at 10.8 m height a free-slip wall has been defined in order to model the gas-liquid free surface. The SST turbulence model [15] has been used due to its well-proven accurate results in flows encountered in industry [20]. The High-Resolution scheme [15] in ANSYS-CFX has been used as discretization scheme.
4. Model results In this section the results of the different configurations analysed are presented. In order to quantify the fluid circulation capacity of each configuration, the average flow velocity in different sub-volumes of the tank has been calculated. As one of the main concerns (when analysing local cold spots potentially leading to solidification) is the salts closed to the tank bottom, special care is focused on the average flow velocity in sub-volumes close to the bottom surface. The sub-volumes considered are defined by the height of salts considered from the tank bottom: 0.1 m, 0.2 m, 0.3 m, 0.4 m, and finally the full tank volume at 323
Energy Conversion and Management 168 (2018) 320–328
A. Iranzo et al.
Fig. 7. Flow velocity at the ejector mid-plane for ejector angle 15°, 30° (base case), 45°.
4.2. Analysis of configurations varying the number of ejectors The configuration with 6 ejectors has been simulated and compared against the base case. Ejectors pointing towards the central vertical axis and with 30° angle as in the base case are considered. As the objective is to maintain the pumping power of the system, the total volume flow rate is maintained the same for both configurations. This means that the impulsion flow rate is higher in the configuration with 6 ejectors (433 m3/h instead of 260 m3/h per ejector, with an entrained mass sink of 316 m3/h instead of 190 m3/h per ejector). The jet velocity defined for the local mass source is thus 3.57 m/s in the configuration with 6 ejectors, versus 2.14 m/s in the base case configuration with 10 ejectors. The results of the comparison are shown in Fig. 10, where it is observed that the configuration with 10 ejectors is generating a better fluid circulation than the configuration with 6 ejectors. 4.3. Analysis of configurations varying the ejectors direction The configuration with a tangential direction of the ejectors (not pointing towards the tank central axis, but towards the tangential direction of the recirculation ring) has been resolved with the CFD model. As in the base case, 10 ejectors with 30° angle is maintained. The symmetry planes of the tank at both sides of the central vertical axis are defined in the tangential configuration as periodic boundaries, allowing
Fig. 8. Average velocity within the tank sub-volumes considered for ejector angles 15°, 30°, 45°, 60°, 75°. 324
Energy Conversion and Management 168 (2018) 320–328
A. Iranzo et al.
Fig. 9. Percentage of sub-volumes with velocity above 5, 10, 15 mm/s for ejector angles 15°, 30°, 45°, 60°, 75°. Fig. 10. Percentage of sub-volumes with velocity above 5, 10, 15 mm/s for configurations with 6 and 10 ejectors.
fluid to traverse them with a periodic condition (so that the flow field is mapped from one side onto the other side). Symmetry planes are not suitable for such configurations as per definition the normal flow at symmetry planes is zero (and therefore the tangential flow induced by the ejectors could not develop as in the real tank). The velocity field at the horizontal plane of the tank at the ejectors level is depicted in Fig. 11, where the tangential flow circulating in the clock-wise direction is clearly identified. Figs. 12 and 13 present the results of the flow velocity analysis comparison, where it is clearly observed that the tangential flow configuration is achieving a better fluid circulation capacity in the tank. It must be noted that such tangential configuration is not typically found in TES tanks for CSPPs, and therefore the results obtained in this work may be of benefit for future designs. However, such potential designs would need to consider the mechanical forces exerted over the ring clamps by the reaction force caused by the jet, in the tangential direction as well. Such force is not compensated along the ring pipe as it is the case with ejectors pointing towards the central axis, and should be therefore considered in the mechanical design of the system. It must be noted that when ejectors are oriented in the tangential direction, no more jet interaction with the inner piping ring can be present. Therefore, for this particular configuration, a new case with no inclination of the ejectors is proposed (angle = 0°). The results are presented in Figs. 14 and 15. Where it is observed that the configuration with 0° angle is performing even better than the one with ejectors angle at 30°, with an increase in the fluid circulation velocity for all tank heights considered.
Fig. 11. Flow field (horizontal plane at the ejectors height) developed for the tangential configuration.
Thus, from the results presented above based on the CFD model developed, it is concluded that the configuration that provides the best fluid circulation capacity in the cold salt tank is 10 ejectors oriented in the tangential direction at 0° inclination angle with respect to the tank bottom surface. In a final design, the mechanical design would however need to consider the tangential forces over the recirculation ring and clamps. A quantitative comparison of the fluid circulation capacity of the best configuration identified with respect to the base case is showing that in terms of average velocity, the molten salts bulk in the tangential 0° case is having almost three times the velocity of the base 325
Energy Conversion and Management 168 (2018) 320–328
A. Iranzo et al.
Fig. 14. Average velocity of sub-volumes for configurations with tangential flow at 0° and 30°.
Fig. 12. Average velocity of sub-volumes for configurations with axial and tangential flow.
Fig. 15. Percentage of sub-volumes with velocity above 5, 10, 15 mm/s for configurations with tangential flow at 0° and 30°.
Fig. 13. Percentage of sub-volumes with velocity above 5, 10, 15 mm/s for configurations with axial and tangential flow.
identified. configuration. When it comes to analysing the lower section of the tank, differences are even higher, featuring more than 10 times the velocity flow for the first 10 cm height, and more than 6 times the velocity flow for the first 20 cm height. This general enhancement is caused by the positive effect of jets pumping in the same direction, with respect to the base case with opposing jets. The even more increased enhancement in the particular region of the lower tank volume is caused by the jets having a pumping angle parallel to the tank bottom surface. When comparing the percentage of the tank bulk fluid presenting a velocity over 1 cm/s, almost 100% of the tank is well mixed for the tangential 0° case, whereas only 50% of the tank is well mixed in the base case configuration. It is therefore ensured that no fluid dead-zones will be appearing within the tank bulk fluid with the best ejector configuration
4.4. Mixing time calculations The configuration identified in the previous analysis presents the highest fluid circulation capacity with no dead-zones within the tank bulk fluid. It is however required to investigate the real mixing time of the molten salts in the tank. It is well known in the mixing industry that a pure rotational flow may present low mixing performance despite the flow velocity, if the bulk fluid rotates with a solid rigid pattern without intermediate baffles or internals breaking the flow pathlines and promoting turbulence and mixing [17]. As the proposed configuration is inducing a rotational flow pattern, a more detailed analysis has been performed by investigating the mixing times for all configurations. 326
Energy Conversion and Management 168 (2018) 320–328
A. Iranzo et al.
maximum tracer concentration within the tank is monitored. According to (9), the mixing time (95%) is reached once the tracer concentration in the tank is within 0.1577 and 0.1743 (mass fraction). Fig. 16 presents the time evolution of the tracer concentration at all monitor points as well as the maximum and minimum values. The results are presented for the base case (top), the case with tangential direction at 0° (middle) and the case with angle 0° pointing towards the axis (bottom). The results show that the mixing time θM,95 (all tracer concentrations within the required range) is 0.46 h, 0.92 h, and 0.33 h, respectively. It is therefore interesting to point out that the case with highest fluid circulation identified previously (namely ejectors in tangential direction at 0° angle) is actually not appropriate when the mixing time is analysed. The cause of this is that the configuration with ejectors in tangential direction at 0° angle is achieving a high flow circulation as all ejectors positively interact with each other in terms of fluid acceleration. However, the fluid within the tank considered is mostly rotating in a solid-rigid motion pattern, as very few internals are breaking the fluid rotating motion pathlines. This results in longer mixing times. The full comparison of the mixing time (95% mixing denoted as θM,95 and 99% mixing denoted as θM,99) calculated for all configurations is presented in Fig. 17. Both configurations with ejectors pumping fluid in the tangential direction present significantly higher mixing times than the configurations pointing towards the central vertical axis. Among them, the configuration with 10 ejectors with an angle of 0° presents the least mixing times (0.33 h for θM,95 and 0.41 h for θM,99). Such results indicate that for the selection of an optimal configuration many effects and parameters must be considered. The case with the highest flow circulation capacity (three times the capacity of the base configuration) is presenting one of the longest fluid mixing times (three times longer than in the base configuration). It is a design criterion to define which are the values required for each particular application in order to ensure a safe operation of the tank without a risk of salt solidification even in long stops required by plant maintenance operation. As a result of this conclusion aiming at defining a future work, further simulations are required in order to quantify the transient temperature decay profile in the coldest location of the tank due to heat loss for the configurations analysed. This will provide useful information regarding the optimal ejector configuration in terms of maintaining the adequate fluid temperature long enough to ensure a safe tank operation.
5. Conclusions
Fig. 16. Time evolution of the tracer concentration Ct in the tank volume. Maximum, minimum and C∞ values are marked in red. The concentration range for θM,95 is marked with black dotted lines. Top: 10 ejectors 30° towards axis (base case). Middle: 10 ejectors 0° tangential direction. Bottom: 10 ejectors 0° towards axis.
In this work, the mixing performance in cold salt tanks using molten salts for CSPPs has been investigated by means of CFD modelling. A set of different ejector configurations has been resolved, modifying the number of ejectors, flow direction, and ejector angle. The best configurations are identified, where the highest fluid circulation capacity is achieved by 10 ejectors directing the jet flow in the tangential direction with an inclination angle of 0° with respect to the tank bottom surface. This is increasing the fluid circulation capacity of the tank by more than 100% with respect to the usual configuration implemented in such tanks (ejectors directed to the tank central vertical axis, at 30° angle). In addition, such configuration ensures an enhanced flow circulation in the bottom part of the tank (with an increase of more than 6 times in the flow velocity in the lower section of the tank), reducing the risk of local salt solidification due to heat loss through the bottom surface. However, the shortest mixing times (95% and 99%) are achieved by the configuration with 10 ejectors pumping flow towards the central tank axis with an inclination angle of 0°. It is therefore required to further analyse how the configurations identified perform, in terms of ensuring appropriate temperature levels in the tank during a transient process involving heat losses.
The mixing time (95% and 99%) has been calculated with the CFD model, as proposed in previous studies [21,22]. For this, a transient simulation is defined where a set of local monitor points are spread within the domain. A tracer is released at t = 0 s in the transient simulation, and the tracer concentration evolution at the monitor points is monitored with time. The mixing time θM can be defined as the degree of uniformity (U) of the tracer concentration at each location:
θM = U = 1−
(C∞−Ct ) C∞
(9)
Where C∞ is the tracer final concentration at t = ∞ and Ct is the tracer concentration at any time. For the CFD simulations, 100 kg/s of tracer during 300 s (5 min) are injected into the tank at each ejector, thus the final tracer concentration would be 0.16604 (mass fraction). A set of twelve monitor points have been defined forming a matrix in the tank radius and height, and for the sake of reliability, also the minimum and 327
Energy Conversion and Management 168 (2018) 320–328
A. Iranzo et al.
Fig. 17. Mixing times (95% and 99%) for all ejector configurations.
References
2015;98:20–9. [11] Daabo AM, Al Jubori A, Mahmoud S, Al-Dadah RK. Parametric study of efficient small-scale axial and radial turbines for solar powered Brayton cycle application. Energy Convers Manage 2016;128:343–60. [12] Nižetić S, Penga Ž, Arıcı M. Contribution to the research of an alternative energy concept for carbon free electricity production: Concept of solar power plant with short diffuser. Energy Convers Manage 2017;148:533–53. [13] Schulte-Fischedick J, Tamme R, Herrmann U. CFD analysis of the cool down behaviour of molten salt thermal storage systems. In: ASME 2008 2nd international conference on energy sustainability collocated with the heat transfer, fluids engineering, and 3rd energy nanotechnology conferences. American Society of Mechanical Engineers; 2008. p. 515–24. [14] Rivas E, Rojas E, Bayón R, Gaggioli W, Rinaldi L, Fabrizi F. CFD model of a molten salt tank with integrated steam generator. Energy Procedia 2013;49:956–64. [15] ANSYS-FLUENT. ANSYS, Inc., Southpointe 2600 ANSYS Drive Canonsburg, PA 15317. [16] Solar Power Tower Design Basis Document. Prepared by Alexis B. Zavoico, Nexant, San Francisco, CA 94104. Sandia National Laboratories, Albuquerque, New Mexico 87185 and Livermore, California 94550. SAND2001-2100 Unlimited Release Printed July 2001. [17] Leng, D. E., Katti, S. S., Atiemo-Obeng, V. Industrial Mixing Technology. In: Albright’s Chemical Engineering Handbook, edited by Lyle f. Albright. Ed. CRC, 2009. [18] Grenville RK, Tilton JN. A new theory improves the correlation of blend time data from turbulent jet mixed vessels. Chem Eng Res Des 1996;74:390–6. [19] Fossett H, Prosser LE. The application of free jets to the mixing of fluids in bulk. Proc I Mech Eng 1949;160:224–32. [20] Menter FR. Review of the shear-stress transport turbulence model experience from an industrial perspective. Int J Comput Fluid Dynam 2009;23:305–16. [21] Patwardhan AW. CFD modeling of jet mixed tanks. Chem Eng Sci 2002;57:1307–18. [22] Jayanti S. Hydrodynamics of jet mixing in vessels. Chem Eng Sci 2001;56:193–210.
[1] Trabelsi SE, Qoaider L, Guizani A. Investigation of using molten salt as heat transfer fluid for dry cooled solar parabolic trough power plants under desert conditions. Energy Convers Manage 2018;156:253–63. [2] Wang K, He Y-L. Thermodynamic analysis and optimization of a molten salt solar power tower integrated with a recompression supercritical CO2 Brayton cycle based on integrated modelling. Energy Convers Manage 2017;135:336–50. [3] González-Gómez PA, Gómez-Hernández J, Briongos JV, Santana D. Thermo-economic optimization of molten salt steam generators. Energy Convers Manage 2017;146:228–43. [4] Relloso S, Delgado E. Experience with molten salt thermal storage in a commercial parabolic trough plant; Andasol 1 commissioning and operation. In: Proceedings of 15th international SolarPACES symposium; September 2009, p. 14–18. [5] Suárez C, Iranzo A, Pino FJ, Guerra J. Transient analysis of the cooling process of molten salt thermal storage tanks due to standby heat loss. Appl Energy 2015;142:56–65. [6] Rodríguez I, Pérez-Segarra CD, Lehmkuhl O, Oliva A. Modular object-oriented methodology for the resolution of molten salt storage tanks for CSP plants. Appl Energy 2013;109:402–14. [7] Fernández-Torrijos M, Sobrino C, Almendros-Ibáñez JA. Simplified model of a dualmedia molten-salt thermocline tank with a multiple layer wall. Sol Energy 2017;151:146–61. [8] Zaversky F, García-Barberena J, Sánchez M, Astrain D. Transient molten salt twotank thermal storage modeling for CSP performance simulations. Sol Energy 2013;93:294–311. [9] Patel SK, Prasad D, Ahmed MR. Computational studies on the effect of geometric parameters on the performance of a solar chimney power plant. Energy Convers Manage 2014;77:424–31. [10] Sultana T, Morrison GL, Taylor RA, Rosengarten G. Numerical and experimental study of a solar micro concentrating collector. Energy Convers Manage
328