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Energy Procedía 69 (2015) 779 - 789
International Conference on Concentrating Solar Power and Chemical Energy Systems,
SolarPACES 2014
The design and numerical study of a 2MWh molten salt
thermocline tank
ZS Chang a' b, X Li a*, C Xu c, C Chang a, ZF Wang a
a Key Laboratory of Solar Thermal Energy and Photovoltaic System, Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing
100190, China
b University of Chinese Academy of Sciences, Beijing 100049, China c North China Electric Power University, Beijing, 100190, China
Abstract
The two tank molten salt thermal storage system is widely used in the commercialized solar thermal power plant. However, the thermocline storage system with a low-cost filler material is a more economically feasible option. In this study, a transient two-dimensional and two-temperature model is developed to investigate the heat transfer and fluid dynamics in a molten salt thermocline thermal storage system. After model validation, the effects of inlet flow boundary condition and storage medium properties including fluid and solid materials on the thermal performance of thermocline storage system are investigated. The results show that thermoclne thickness increases slowest with solar salt as heat transfer fluid (HTF) and Cofalit® as solid material in the thermocline tank. Any non-uniformity in the inlet velocity flow would only enhance mixing and widen the thermocline appreciably, which contributes to the loss of thermodynamic availability of stored energy. The thermocline thickness increases with the non-uniformity of the inlet velocity boundary condition. So smaller non-uniformity of inlet flow is better in non-uniform flow though it may causes larger fluctuations in average outlet temperature. Smaller inlet mass flow rate is better for the thermocline storage tank, while it also causes smaller discharging power. With the chosen basic design parameters such as fluid and solid materials, the size of a 2MWh thermocline tank is determined by a simple one-dimensional design method. Tank with larger H/D ratio has higher discharge efficiency. It helps to figure out the thermal stratification mechanism of a storage tank and thereby to determine optimum design and operating conditions.
© 2015TheAuthors.Published by ElsevierLtd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.Org/licenses/by-nc-nd/4.0/).
Peer review by the scientific conference committee of SolarPACES 2014 under responsibility of PSE AG
* Corresponding author. Tel.: +86-010-62558289. E-mail address: drlixin@mail.iee.ac.cn
1876-6102 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Peer review by the scientific conference committee of SolarPACES 2014 under responsibility of PSE AG doi: 10.1016/j.egypro.2015.03.094
Keywords: molten salt; thermocline; design; fluid and solid materials; non-uniform inlet flow
1. Introduction
Power generation using concentrated solar power plants (CSP) is one of the several promising, emerging renewable energy technologies. The advantage of CSP systems relative to other utility scale renewable energy technologies is the ability to store energy as high temperature heat and continue producing power when solar energy is not available. A lot of research efforts have been recently focused on the integration of solar thermal energy storage (TES) as a viable means to enhance dispatchability, increase the value of concentrated solar energy and make the plant more reliable.
Nomenclature
D specific heat capacity, J/kgK diameter of the tank, m V Greek symbols velocity, m/s
d p er , F g H diameter of the solid filler, m unit vector in the r and x direction, respectively inertial coefficient acceleration due to gravity, m/s2 tank height, m e n V P subcripts porosity of packed-bed region efficiency viscosity, kg/m-s density, kg/m3
h 1 K k l m interstitial heat transfer coefficient, W/m3K permeability of porous material, m2 thermal conductivity, W/mK length, m mass flow rate, kg/s air crit c dc eff air critical value cold fluid discharging effective value
Nu P P Pr Re T t Nusselt number thermal power, W pressure, Pa Prandtl number heat, J Reynolds number temperature, K time, s h i in l out s st store hot fluid insulation layers or tank steel inlet length outlet solid material steel wall energy stored
There are a number of viable candidates for TES systems that might be developed and applied on a commercial scale for CSP plants. Presently, sensible molten salt TES systems including two-tank system and one-tank thermocline system are widely applied or under development worldwide [1], as molten salt used as the storage medium and direct heat transfer fluid can offer the best balance of capacity, cost, efficiency and usability at high temperatures [7]. The two-tank system has a high-temperature tank and a low-temperature tank for storing molten salt. It is the most mature utility-scale TES system for CSP plants, and has been applied or projected in many CSP plants. However, the two-tank molten salt TES system has very limited space for cost reduction. The one-tank thermocline system has only one storage tank and would use molten salt as the direct heat transfer fluid, storing energy gathered in the solar field, and transferring that energy when needed. With the hot and cold fluid in a single tank, the thermocline storage system relies on thermal buoyancy to maintain thermal stratification and discrete high-and low-temperature regions of the TES system. A low-cost filler material used to pack the single storage tank acts
as the primary thermal storage medium and reduces the overall required quantities of the relatively higher cost molten salt heat transfer fluid. As thus the one-tank thermocline system provides a more cost-effective option for TES systems with a potential cost reduction of 20%-37% compared to the two-tank system [1]. The one-tank thermocline system has been investigated and developed worldwide recently. A small pilot-scale packed-bed molten salt thermocline system has been successfully demonstrated in Sandia National Laboratories [10]. M. M. Valmiki et al. presents an experimental study of the energy charge and discharge processes in a small oil packed bed thermocline thermal storage tank [17]. Some research efforts have led to the development of nitrate salt mixtures with low melting temperatures and high thermal stabilities for CSP applications [3]. Siegel et al presented measured thermophysical property data for several commercial and non-commercial molten salt mixtures that can be used in the system level design of parabolic trough and central receiver power plants [2]. Solid materials for high temperature thermal energy storage system in CSP have been widely investigated. Kenneth Guy Allen [6] investigated the rock type, properties, suitability and availability in rock bed storage system. It showed that the most suitable rock is likely to be igneous or metamorphic rock, without voids or minerals that will decompose when heated to temperatures of 500-600°C. A low-cost material inherited from the industrial vitrification of Asbestos was analysed as a good candidate of storage materials [4]. Quartzite rocks and sands were suitable to be used as the low-cost solid fillers which provided the bulk of thermal capacitance of the thermal storage [19].Yang and Garimella [12,13] carried out a series of numerical investigations on the molten-salt packed-bed thermocline system using the developed two-temperature model. Li et al. [15] presented dimensionless heat transfer governing equations for fluid and solid fillers for the packed-bed thermocline TES and studied various scenarios of thermal energy charging and discharging processes. Xu et al. [7,8,9] presented a transient two-dimensional dispersion-concentric model to investigate the discharging behavior of the packed-bed thermocline tank. A parametric analysis was carried out and various influencing factors were analyzed. Mario Biencinto developed a simulation model for solar thermal power plants with a thermocline storage tank with logistic function in TRNSYS, and assessed different operation strategies [5]. Most of the above studies were focused on evaluating the tank performance with a particular type of HTF and solid material under adiabatic conditions and the assumption of inlet plug flow. To the author's knowledge, there have been no studies regarding the evaluation of the thermocline TES system performance and the comparison of using different HTFs and different non-uniform inlet flow boundary conditions in the thermocline TES systems, though it is important to evaluate different materials in designing plants and how the system will perform in actual hardware with non-uniform inlet flow. In this study, a transient two-dimensional and two-temperature model is developed to investigate the heat transfer and fluid dynamics in a molten salt thermocline thermal storage system. After model validation, the effects of inlet flow boundary condition and storage medium properties including fluid and solid material on the thermal performance of thermocline storage system are investigated. With the chosen basic design parameters such as particle diameter, fluid and solid materials, the size of a 2MWh thermocline tank is determined by a simple one-dimensional design method.
2. Mathematical model
2.1. Governing equations
The general layout of the thermocline storage system is illustrated in Fig. 1.
The following assumptions are employed to simplify the analysis:
(1) The fluid flow and heat transfer are symmetrical about the axis.
(2) The distributors are not included in the computational domain and plug flow or assumed Hagen-Poiseuille flow is imposed at the inlet of the filler region.
(3) The flow of molten salt is laminar and incompressible.
(4) The solid fillers are spherical particles with the same diameter and constant properties.
Continuity equation:
m+VP ;)=o
Fig.1. Schematic diagram of the molten salt thermocline TES and the computational domain.
Momentum equation:
+ V * (P —) = £ + V - (¿Vg ) + ep^g + e ( £ + F pva g (2)
dt e K iJK
die3 175
where K =---- , F = , -. In the axisymmetric coordinate system shown in Fig. 1, the problem is two-
150(1 -e)2 Vl50f3
^ d e d ^ d ^ ^ ^ dimensional, incompressible fluid : V = er — + — — + ex —, V = vrer + vxex .
r dr r 3d x dx
As the volume expansion/shrinkage, viscous effects and kinetic energy changes the conduction or convection terms are omitted, Energy equation for the molten salt:
\ -1 + V- (p V Cp T ) = V- (keff VT ) + hi (T - T ) (3)
Energy equation for the solid fillers:
d ((1 s)pMCpJM )
Energy equation for the insulation layers and tank steel wall:
= V-(ksVTs)-hi(Ts -T) (4)
2.2. Boundary conditions and initial conditions
Boundary conditions are summarized in Table 1. At the beginning of the discharging process, it is assumed that the tank is filled with molten salt and solid fillers which have the same hot temperature, and the tank wall is in thermally equilibrium with the interior hot storage material and the outside ambient air with a velocity of 2m/s.
Table 1. Boundary conditions.
Number
Boundary conditions
BC1: x=0, 0<r<D/2; BC2: x=H, 0<r<D/2; BC3: 0<x<H,r=0; BC4: 0<x<H, r=D/2;
v, l+= v„ > l+= 0 > Tf += Tf,,. ■
= 0, vl = 0, ^
= o, r = o, dTf/
dx + dTs
V,I = I = 0' kff '/dx
=k dV , k V
/dr ' s f /dr
BC5: x=0 or x=H, D/2< r<D/2+lta+U+ls; dT / = dT / = dToít/ = Q
/ dx /dx / dx
BC6: 0<x<H,r=D/2+lin+lout+ls;
dT_ dr
= h(Tout -T), Nu = hH/ = 0.664Refl°5 Pr05, ReD =
bottom inlet top outlet
symmetry axis of the cylindrical tank the inner surface of the insulation inner layer
two cross sections of the insulation layers and tank steel wall adjacency to the fluid inlet and outlet valrD outmost wall of the valr thermocline tank
where V . and V . are the velocity and viscosity of ambient air, respectively.
2.3. Numerical method
The computational domain is discretized into finite volumes. All the variables are stored at the centers of the mesh cells. A second-order upwind scheme is used for the convective fluxes, while a central-differencing scheme is used for discretizing the diffusion fluxes. Iterations at each time step are terminated when the dimensionless residuals for all equations drop below 10-4. The computations are performed using the commercial software FLUENT through the SIMPLEC algorithm. User-defined functions are developed to account for Eqs. (2-4). Grid and time-step dependence are checked by inspecting results from different grid densities and time intervals. Based on this, Ax=Ar=0.01m and At=0.5s are chosen as this setting results in a temperature along the line r=0 throughout the discharge process that is within 3% of that for the case with Ax=Ar=0.005m and At=0.1s.
3. Model validation
E- 320
2D model molten salt temperature 2D modelrock temperature experimental data 1D model molten salt temperature
§ 80 -
experimental data oil temperature rock temperature
Axial height of the thermocline tank (m)
0.2 0.3 0.4 0.5 0.6 0.7 Axilal height of the thermocline tank (m)
Fig. 2. (a). comparison between thermocline profiles from numerical results of both 2-D model and 1-D model [15] and experimental results from Ref. [10] in a discharging cycle of the molten salt tank at time intervals of 30 minutes; (b) comparison between the numerical and experimental charging temperature distribution along the oil tank height at time intervals of 16 minutes from Ref. [17]
It has been successfully validated with experimental data taken from the literatures.
4. Comparative analysis results and discussion
The results of thermocline tank design efforts are strongly tied to the parameters such as: thermophysical properties of the heat transfer fluid and thermal storage media, the design velocity in charging and discharging cycle. In this section we report the results of our ongoing efforts to characterize the effects of different commercial nitrate salt heat transfer fluids, different solid materials, different inlet velocity profiles. Other parameters and properties used in the model: H=5m, D=2m, lin= lout=0.1m, lst =0.02m, porosity s=0.22; kin=0.1W/m-K, kst,eff=35W/m-K.
4. 1. Different molten salts
There are several nitrate salt mixtures currently under consideration for use in CSP systems. In particular the binary system KNO3-NaNO3 ("Solar salt" system) is well known and has been widely used for TES systems, which is usually considered to be a mixture of 60 wt% NaNO3 and 40 wt% KNO3. Other ternary mixtures include KNO3-NaNO2-NaNO3 (trade names include Hitec, Durferrit ASD, HTS) and Ca(NO3)2-KNO3-NaNO3 (trade name Hitec XL), which have been considered to replace the Solar Salt because of its low freezing point. The physical properties of three molten salts are listed in Table 2.
Table 2. Physical properties of molten salts.
Name Solar slat [7-9] (60% NaNÜ3, 40 % KNO3) Hitec [12] (7% NaNÜ3, 53% KNO3, 40% NaNÜ2) Hitec XL [2] (42% Ca(NÜ3)2, 43% NaNÜ3, 15% KNO3)
Density (kg/m3) p = 2090 - 0.636 xT, (oC) p = 2084 - 0.732 xT, (oC) p = 2240 - 0.827 xTt (oC)
Specific heat capacity Cp, = 1443 - 0.172 xT,{oC) Cp, = 1561.7 Cp, = 1545.54456
(J/kg-K) -0.33563 x T, (oC)
Thermal conductivity k, = 0.443 +1.9xlO-4 xTIC) k¡= 0.421 -6.53x1o-4(7] -260) k, = 0.519
(W/m-K)
Viscosity (kg/ms) ß, = [22.714 - 0.12 x T, (oC) p, = exp[-4.343 - M = 1061374 XT, )
+2.281X10-4 xT(oC)2 2.0143 x (ln T - 5.011)]
-1.474x10-7 xT(°C)3]x10-3
Melting point (oC) 221 142 130-140
Stability limit (oC) 600 450-538 550
Quartzite rock Hitec XL Quartzite rock
- Solar slat
- Quartzite rock
quartzite rock Hitec XL quartzite rock Solar salt quartzite rock
Tank axial distance (m)
1000 2000 3000 4000 5000 6000 7000 8000 9000 Discharging time (s)
Fig.3. (a) Variations in temperature profiles of HTF and quartzite rock at 7200s along the centerline of tank axial distance for different molten salts; (b) center point temperature profiles with the discharging time for different molten salts
Fig.3 shows that solar salt has the sharpest temperature gradient with tank axial distance (Fig.3.a) and quickest cooling rate in the center point of the tank (Fig.3.b). Temperature differences between centerline and near-wall area, solid and fluid are both very small (0.05K).
Thermocline thickness is defined as the covering length of the thermocline region and can be expressed as: min{H(Tout),H(Tcrit h)} - H(Tcrit c) in discharging cyde and H(Tclit,h) - max{H(T^),H(Tclit,c)} in barging cyc^ where Tcrith = Th - 5 and TcrUc = Tc + 5 represent the critical low and hot temperatures for evaluating the thermocline thickness, respectively.
Hitec Hitec XL Solar salt
Cofalit Granite rock Taconite Quartzite rock
3600 5400 7200
Discharging time (s)
4000 6000 8000 10000 Discharging time (s)
Fig.4. (a) The thermocline thickness with the discharging time for different molten salts; (b) The thermocline thickness with the discharging time
for different solid materials.
Fig.4.a shows the change of thermocline thickness with discharging time is similar for different molten salts, while thermocline movement velocity is different. Solar salt tank has the smallest and slowest thermoclne thickness. So solar salt is best as HTF of thermocline TES system.
4.2. Different solid materials
Properly specifying and qualifying the filler material as a significant component of this system is a major element for both first-cost and long-term maintenance costs associated with TES systems. The effect of solid material on the system performance is investigated through testing four promising thermal storage materials. The physical properties of these solid materials are summarized in Table 3.
Table 3. Physical properties of solid materials.
Solid material Density (kg/m3) Average specific heat Thermal conductivity Price
capacity (J/kg-K) (W/m-K) ($/t)
Quartzite rock[7-9] 2500 830 5.69 $11.2/t
Rock(granite) [6] 2893 845 3.0 $47.0/t
Taconite[16] 3200 800 30 $200/t
Cofalit®[4] 3120 860 2.7 $11.1/t
Solar salt Cofalite Solar salt -- Granite rock Solar salt Taconite Solar salt Quartzite rock
Tank axial distance (m)
36GG 54GG 72GG
Discharging time (s)
Solar salt Quartzite rock Solar salt Cofalit Solar salt - Granite rock Solar salt Taconite
Fig.5. (a) Variations in temperature profiles of HTF and solid material at 7200s along the centerline of tank axial distance for different solid materials; (b) center point temperature profiles with the discharging time for different solid materials
Fig.5 shows that thermocline tank still has the largest stored energy after same discharging time (Fig.5.a) and the longest discharging time (Fig.5.b) with Cofalit® as solid material, while both of them are the smallest for quartzite rock. It is because the volumetric heat capacity is different for different solid materials. Larger volumetric heat capacity solid material stores larger total energy. It also shows that temperature difference between HTF and solid is smaller for larger thermal conductivity solid material.
Fig.4.b shows the thermocline thickness increases slower for larger volumetric heat capacity solid material before the peak, as it can be seen that the thermocline thicknesses are close but smaller for larger volumetric heat capacity solid material at the same discharging time, while the peak of thermocline thickness is larger because the larger discharging time. Generally speaking, the Cofalit® is best for thermocline heat storage solid material with 29.31% larger in the volumetric heat capacity and only 9.09% larger in the largest thermocline thickness compared with quartzite rock, but the quartzite rock is still chosen as solid material in the design as it is much more available.
4.3. Different velocity profiles
Usually, a uniform distribution of the flow through the whole cross section of the inlet and outlet (plug flow) is assumed in the simulations of thermocline tank system with two distributor regions included at the upper and lower ends of the filler region in the storage tank. However, the idealized flow with complete mixing in the radial direction is hard to achieve in actual applications because the edge effect and difficulties in sophisticated-designed distributor. The inlet flow boundary condition of non-uniform velocity profile, as would be found in actual applications were not explored. So the effect is evaluated with Hagen-Poiseuille flow instead of plug flow as the inlet flow boundary
condition, which forms one of the focus of the present study. Three different parabolic velocity profiles are
assumed: V = V (1---), V = 4.186x10-4,8.372xlO-4,1.256x 10-3 m/s for case V1, V2, V3; respectively. The non-
шах ^ max ^ ^ j j j i. j
uniformity and mass flow rate are both V3>V2>V1.
§ 7GG
V2 solar salt
V2 quartizite rock
-V1 solar salt
V1 quartizite rock
V3 solar salt
V3 quartizite rock
E- 65G
V2 solar salt V2 quartizite rock Vl solar salt
- Vlquartizite rock
- V3 solar salt
V3 quartizite rock
Tank axial distance (m)
4GGG 6GGG 8GGG 1GGGG Discharging time (s)
Fig.6. (a) Variations in temperature profiles of HTF and solid material at 7200s along the centerline of tank axial distance for different inlet velocity profiles; (b) center point temperature profiles with the discharging time for different inlet velocity profiles.
Fig.6 shows that the temperature gradient in axial distance at the same time and discharging time are both larger with smaller Vmax, while the thermocline movement velocity and cooling rate in the center of thermocline tank in discharging time is smaller.
Q.8 i Q.7-) Q.6-Q.5 -Q.4 -Q.3 -Q.2 -Q.l -
8QQQ 12QQQ 16QQQ Discharging time (s)
72QQ lQ8QQ l44QQ l8QQQ Discharging time (s)
Fig.7. (a) Variations in the average top outlet temperature with the discharging time for different inlet velocity profiles; (b) thermocline thickness
with the discharging time for different inlet velocity profiles.
Fig.7 shows that the thermocline thickness increases slower and the largest thermocline thickness is smaller with smaller Vmax, which means the thermocline thickness increases with the non-uniformity of inlet velocity boundary condition. For V1 case, the smaller Vmax causes larger fluctuations in average outlet temperature. It is because the inlet non-uniform flow is still not fully mixed in radial direction after flowing the porous media in the tank with small Vmax. It illustrates that the uniform inlet flow is better than any non-uniform flow for thermocline tank with the same mass flow rate. It can be concluded that smaller intlet mass flow rate is better for the thermocline storage tank, while it also causes smaller discharging power, and the well-designed distributor is very important. Any motion in the second or third directions would only enhance mixing and widen the thermocline appreciably. The mixing during charge and discharge cycles is one of the major contributors to the loss of thermodynamic availability of stored energy.
4.4 Design method and results
With the chosen basic design parameters: P=1MW, Tdc=2h, solar slat and quartzite rock as HTF and solid material, respectively. Solid filler ds=1.9cm, porosity £ =0.22, Working temperature range: 290oC-560oC. The
design inlet velocity is 4.186x10-4 m/s. The size of a 2MWh thermocline tank is determined by simple one-dimensional design models [15, 20], validated by single phase one dimensional model (CIEMAT1D1SF) [21]. Then the normalized tank dimensions included in the standards are taken into account, in which H/D ratio for tanks with D<5 m should be between 1.5 and 4 [21]. The results of design cases are summarized in Table 4.
Table 4. Design cases.
Design case D H Discharge efficiency H/D ratio
1 1.6 7.4593 0.8339 4.662
2 1.7 6.6489 0.8287 3.9111
3 1.8 5.9673 0.8236 3.3152
4 1.9 5.3885 0.8186 2.8360
5 2.0 4.8924 0.8137 2.4462
6 2.1 4.4640 0.8089 2.1257
7 2.2 4.0912 0.8042 1.8597
8 2.3 3.7649 0.7996 1.6369
9 2.4 3.4774 0.7950 1.4489
Where n
f^mCp(Tout -Tc)dt
Tout > T + 0.95(7; - Tc ).
It shows that the design tank sizes in case 2-8 are feasible. Tank with larger H/D ratio has higher discharge efficiency.
5. Conclusion
In this study, a transient two-dimensional and two-temperature model is developed to investigate the heat transfer and fluid dynamics in a molten salt thermocline thermal storage system. After model validation, the effects of inlet flow boundary condition and storage medium properties including fluid and solid material on the thermal performance of thermocline storage system are investigated. With the chosen basic design parameters such as particle diameter, fluid and solid materials, the size of a 2MWh thermocline tank is determined by a simple one-dimensional design method.
(1)Thermoclne thickness increases slowest with solar salt as HTF. So solar salt is best as HTF in the thermocline storage system.
(2) Cofalit® is best for thermocline heat storage solid material with 29.31% larger in the volumetric heat capacity and only 9.09% larger in the largest thermocline thickness compared with quartzite rock.
(3) Smaller mass flow rate is better for the thermocline storage tank even with non-uniform inlet flow boundary condition, while it also causes smaller discharging power. Any non-uniformity of inlet flow or motion in the second or third directions would only enhance mixing and widen the thermocline appreciably, which contributors to the loss of thermodynamic availability of stored energy. Smaller non-uniformity of inlet flow is better though it may causes larger fluctuations in average outlet temperature.
(4) Thermocline heat storage tank with larger H/D ratio has higher discharge efficiency.
Acknowledgement
This work is supported by the National Natural Science Foundation of China (51106149), the Beijing Municipal Science & Technology Commission (D121100001012001), and the China National Hi-Tech R&D (863 Plan) (2013AA050502).
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