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Energy Procedia 46 (2014) 124 - 133
8th International Renewable Energy Storage Conference and Exhibition, IRES 2013
High temperature rock-bed TES system suitable for industrial-scale CSP plant - CFD analysis under charge/discharge cyclic conditions
S.A. Zavattonia, M.C. Barbatoa*, A. Pedrettib, G. Zanganehc, A. Steinfeldc,d
a Department of Innovative Technologies, SUPSI, Manno 6928, Switzerland. b Airlight Energy Manufacturing SA, Biasca 6710, Switzerland. c Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland. d Solar Technology Laboratory, Paul Scherrer Institute, 5232 Villigen PSI, Switzerland.
Abstract
The present study aims at dimensioning and modeling, by means of accurate time-dependent 3D computational fluid dynamics simulations, the behavior of a high temperature rock-bed TES system. The latter is exploited to fulfill the round-the-clock energy requirements of a reference 80 MWe industrial-scale CSP plant, based upon the Airlight Energy technology, which uses air as heat transfer fluid. The TES system behavior was analyzed through 15 consecutive charge/discharge cycles to evaluate the thickness evolution of the thermocline zone, and hence the overall thermal efficiency of the system, under cyclic conditions. The numerical model was satisfactorily validated with experimental data, gathered from a 6.5 MWhth TES system prototype, located in Biasca, designed and built by the Swiss company Airlight Energy SA. The good agreement between CFD simulations results and experimental data allowed the authors to assess the relevance of radiative heat transfer, even at relatively low temperature (300 350 °C), on the thermodynamics behavior of the TES system. Moreover, a porosity variation, with the packed bed depth, was also observed numerically and experimentally mainly due to the own weight of the packings (25m3 of natural river pebbles with 3 cm average diameter).
The CFD simulations were performed with Fluent code from ANSYS. © 2014The Authors.Publishedby ElsevierLtd.
Selectionand peer-reviewunderresponsibilityof EUROSOLAR - The EuropeanAssociationfor Renewable Energy
Keywords: Thermal Energy Storage (TES), Advanced Adiabatic Compressed Air Energy Storage (AA-CAES), high temperature, packed bed, Effective Thermal Conductivity (ETC), porous media, Computational Fluid Dynamics (CFD), porosity distribution, radiative heat transfer.
* Corresponding author. Tel.: +41 058 666 6639. E-mail address: maurizio.barbato@supsi.ch
1876-6102 © 2014 The Authors. Published by Elsevier Ltd.
Selection and peer-review under responsibility of EUROSOLAR - The European Association for Renewable Energy doi:10.1016/j.egypro.2014.01.165
1. Introduction
The integration of high-temperature thermal energy storage (TES) systems into concentrating solar power (CSP) plants, besides being a valuable solution to economically compete against solar photovoltaics (PV), allows to make solar energy dispatchable increasing substantially its value to the grid. The added value that TES systems may provide to CSP has been recently investigated by NREL [1] with a commercial production cost model analyzing two different scenarios of renewable penetration.
Nowadays, the most common TES solutions are based on two-tank systems with synthetic oils or molten salts. These solutions however have some remarkable drawbacks, among the others the high cost and the operating temperature limitation, of 400°C and 550°C respectively, due to the material degradation.
Thanks to their simplicity, high efficiency and affordability, packed beds systems may be a valuable alternative to the most common TES solutions available finding also an effective applicability in combination with the promising advanced adiabatic compressed air energy storage (AA-CAES) technology [2-3].
A single-tank packed bed TES system exploits the buoyancy-driven effect of the heat transfer fluid (HTF) to establish and maintain throughout the time a temperature gradient, namely the thermocline zone, which separates the hot and the cold regions within the tank. For this reason, during the charging phase, the TES system needs to be fed with hot air from the top; while, during discharging, cold air has to be supplied from the bottom.
2. Void fraction distribution of a generic packed bed
One of the main properties that characterize a porous media at macroscopic level is the porosity or void fraction. The latter is defined as the ratio of the void volume with respect to the total volume of the medium itself. When dealing with packed bed for high temperature applications, knowing the porosity distribution is of paramount importance in order to accurately understand the fluid flow and heat transfer capability of the system.
In the case of thermal energy storage applications, the porous media is generally composed of natural gravel and the basic assumption is to consider the particles as homogeneous spheres characterized by an equivalent diameter.
In the hypothesis of randomly packed spherical particles, far enough from the containing walls, the reference porosity in the bulk region ranges, on average, between 0.36 ^ 0.43 [4]. However, independently on the particle diameter, two univocal limit values of porosity can be achieved based upon the particle arrangements: the loose (Simple Cubic) and the close (Face Centered Cubic) packings. The former corresponds to a porosity value of 0.476 with the smallest particles density; whereas, the latter corresponds to the highest particle density and to a porosity value of 0.26 [5].
Different is the situation if the zone near the containing walls is considered. In this so-called near-wall region, the arrangement of the particles is modified affecting the overall packing structure for a distance of 5 particle diameters, dp, from the wall. In this region, the porosity distribution undergoes a sharp variation, from a value close to the unity to a minimum of 0.2 at a distance of 0.5 dp, due to the presence of the containing walls [6]. This porosity variation in the radial direction of the packed bed is known as the wall-effect or channeling. It is clearly an undesirable effect since it causes a lower flow resistance near the wall and hence a non-homogeneous fluid velocity in the axial cross-section of the bed.
The second aspect which may entail to a porosity variation, for large scale packed beds mainly, is the so-called thickness, or top-bottom, effect which is basically a porosity variation dependent on the height of the packed bed due to: a) the deformation of the pebbles due to the own weight of the packed bed, b) a variety of pore structures and sizes due to dimensional in-homogeneities of the natural rocks, c) the presence of debris and/or broken particles in the lower part due to the initial thermal shocks, d) the particles shape, or sphericity, that leads to a slight porosity reduction in the case of close random packing [7].
Several investigations report about the former effect [8-10], but no specific studies were found for the latter because, usually, it is considered negligible for almost all the practical cases; moreover, the available information are insufficient to model the phenomenon [11]. Only Zou and Yu analyzed the porosity variation with respect to the particle diameter and the height of the packed bed [12]. They noticed that the effect of porosity variation in the axial
direction becomes relevant only when the characteristic ratio dp/H, namely the particle diameter over the packed bed height, is greater than 0.05. Despite the former consideration, the authors do not provide any mathematical correlation for modeling this effect.
The thickness effect was investigated, by means of 3D time-dependent CFD simulations, in a previous study [13]; the latter was aimed at reproducing the behavior of an experimental pebble bed TES system, described in the next chapter. The influence of the thickness effect, on the overall heat transfer, was assessed modeling three different axial porosity distribution laws: constant porosity, linear variation (LPV) between two extreme values (loose and close packing arrangement) and quadratic variation (QPV) between the same extreme values of porosity. Simulations results showed that the effect of porosity variation allowed the CFD model to better represent the real behavior of the experimental TES system. Among the others, the quadratic porosity variation, experimentally observed in a purpose-built facility test [14], led to achieve the best description of experimental data. Moreover, this advanced porosity models allowed reducing the pressure drop simulation error from 40%, obtained with the constant porosity model, down to 11%.
3. Heat transfer in packed beds
According to the theoretical and experimental studies of Yagi and Kunii, earlier, and Kunii and Smith, afterwards, [15, 16], the heat transfer mechanisms in packed beds of unconsolidated particles can be considered as the sum of two contributions: the heat transfer mechanisms independent on the fluid flow and those dependent on the lateral mixing of the fluid. In the case of packed bed with stagnant fluid, five different heat transfer mechanisms take place: (1) thermal conduction through solid, thermal conduction (2) through the contact surfaces of two packings and (3) through the fluid film near the contact surface of two packings, radiant heat transfer (4) between surfaces of two packings and (5) between neighboring voids. The latter two have to be intended in the case the fluid is a gas. The remaining heat transfer mechanisms, occurring when fluid flows through the packed bed, are: (6) heat transfer by convection solid-fluid-solid and (7) heat transfer by advective mixing.
The effective thermal conductivity (ETC) is commonly used to model heat transfer in porous media since it allows to group all the aforementioned mechanisms within a single value. Stagnant ETC, in the case of motionless fluid, has been studied analytically and experimentally by various authors; therefore, assuming the packed bed made by homogeneous spheres, a considerable number of mathematical models are available [10]. Besides grouping all the heat transfer mechanisms, ETC also depends on both the thermal characteristics of fluid and solid phases and the geometry of the packed bed itself (particles diameter, shape, optical properties and vessel geometry); therefore, based upon the required quality of its estimation, various approaches can be applied. The two simplest ETC formulations are obtained considering the heat transfer occurring either in parallel or in series between the fluid and the solid phases (dotted lines in Fig.1).
As long as no natural convection occurs, the ETC values of parallel and series configurations provide upper and lower bounds, respectively, on the actual stagnant ETC [5]. More accurate models, [5], account also for the deformation of the particles, due to their own weight, as well as for particle roughness. For high temperature TES systems, thermal radiation may play a relevant role on the overall heat transfer, therefore the radiative characteristics of the bed have to be taken into account by the ETC. Thanks to its accuracy in the description of experimental data [10], the model derived by Kunii & Smith [16] was implemented, by means of purpose-built user-defined functions (UDFs), into the CFD code to accurately describe the heat transfer of a real packed bed TES system [17].
Kun ii&Smit \ h's mot Jel -
Para lel heat \ transfe r
-__ S eries h eat tran isfer
300 400 500 600 700 800 900 1000 1100 1200 Temperature [K]
Fig. 1. Variation of different ETC models with temperature.
Figure 1 shows the comparison between the two simplest ETC formulations aforementioned with the more accurate Kunii & Smith's model in which the importance of radiative heat transfer contribution at high temperatures is remarkable.
It is important to note that the standard approach of CFD codes, when dealing with porous media, is to compute the ETC neglecting radiation heat transfer contribution, unless a specific radiation model is activated, and assuming parallel heat transfer between the solid and the fluid phase [18]:
kETC =(l-£■)• ks +S-kf (1)
Where s represents the void fraction of the medium, ks and kf are the solid and the fluid thermal conductivity respectively. Therefore, the implementation of a more accurate model leads to avoid the underestimation of the ETC at high temperatures.
4. Industrial-scale TES system dimensioning
A high-temperature rock-bed TES system was proposed to fulfill the round-the-clock energy requirement of the reference 80 MWe CSP plant, based upon the Airlight Energy technology, with a total useful mirror area of about 1.05 km2. Thanks to the highest monthly DNI, the month of June was selected as reference for dimensioning the TES system for 12 hrs at most of charging followed by 12 hrs of discharging.
Air is used as HTF for the entire CSP plant; the temperature of the HTF, coming from the solar field and fed through the storage, is 650°C; whereas, the HTF temperature coming from the heat exchangers (HEs) of the power block is 270°C.
The industrial-scale TES system is based on a packed bed of river pebbles with an equivalent diameter of 3^4 cm. The latter are contained into a truncated cone shaped concrete vessel buried into the ground.
Design calculations showed that a volume of about 30,000 m3 of rocks is required to store the incoming solar energy. The threshold dimensions of the containing vessel are given by the mechanical properties of the concrete which led to the maximum height of the packed bed of 9.5 m with the upper diameter of 25.7 m. Therefore, considering the amount of pebbles, a total of 7 different units are required to contain the whole volume of rocks. It is however important to note that the seven units may be fully charged during the month of June only; one of the advantages of having more than a single unit is the possibility of excluding one or more units as the monthly DNI decreases optimizing therefore the system performances.
Microtherm® and FoamGlas® layers are used to insulate the core of the TES system from the external environment.
The air mass flow rate through each TES unit is about 89.6 kg/sec for both the charging and discharging phases.
5. CFD model
With the aim of evaluating its thermo-fluid dynamics behavior under cyclic chare/discharge working conditions, the industrial-scale TES system was analyzed by means of 3D time-dependent CFD simulations. Continuity, Navier-Stokes, energy, turbulent kinetic energy and turbulent dissipation rate transport equations were numerically solved with the finite volume method (FVM) approach [19] by means of Fluent code from ANSYS.
Left-hand side of Fig. 2 shows the CAD model of one of the seven units. In order to obtain a homogeneous plug-flow through the pebbles, four inflow/outflow pipes are assembled at the top, and at the bottom respectively, of each unit. The TES system is symmetric leading hence to the possibility of considering only a quarter of the whole unit as computational domain. It was discretized with a grid of almost 1,150,000 hexahedral elements. Right-hand side of Fig. 2 shows the main boundary conditions applied to the model.
external top
wall external lateral
ll external bottom
Fig. 2. Schematic CAD model of the TES system (l.h.s.) and relative boundary conditions (r.h.s.).
The realizable k -s model [20], with standard wall functions [21], was selected to account for the turbulence effects; full-buoyancy effects on the turbulent kinetic energy, and on its dissipation rate, were also considered [22].Thermal energy losses by means of conduction through the ground and convection/radiation from the lid towards the external environment were accounted for. The environment temperature was assumed equal to 308.15 K and 293.15 K during the charging phase and discharging phase respectively. The layers of concrete and insulating materials were numerically modeled, by means of the shell-conduction approach [23], with a single material of equivalent thermo physical properties. At the beginning of the time-dependent CFD simulation, namely at time t = 0 sec, the TES system unit was considered in its dead state, i.e. thermal equilibrium with its environment.
The rock-bed was treated as a continuum since both the criterions given by the dimensionless bed size L/dp >> 10, i.e. the minimum bed dimension L over the particle diameter dp, and the size parameter £ = n-dj/X >> 5, i.e. the particle size relative to the important wavelengths 1 of the radiation, are verified [24]. Therefore, the packed bed was modeled exploiting the porous media approach [18]. With this strategy, the porous medium is characterized by means of four main parameters namely: the ETC, the void fraction, the permeability K and inertial resistance coefficient C2 (related to the pressure drop evaluation).
The ETC, based upon the Kunii & Smith's model [15, 16], was implemented into the CFD code by means of a purpose-built user defined function (UDF). Thermal radiation heat transfer was accounted for by the ETC itself and hence none radiation model was activated for the computation.
Thanks to the remarkable improvement in the description of the experimental results, obtained in the previous study [13], a quadratic void fraction distribution was implemented in order to replicate the thickness effect. Instead, the effect of channeling was considered negligible since the characteristic ratio Dvesse/dp is well above the suggested threshold value of 40 [25].
The permeability and the inertial resistance coefficient need to be specified when flows through porous media are modeled. The normal approach of CFD codes is to model the porous media by the addition, to the standard fluid flow equations, of a momentum source term which, for the simplest case of homogeneous porous media reads:
HTF inflow/outflow
symmetry planes
HTF outflow/inflow
S = - — -V, - C2 • - -pM-vt (2)
, K 1 2 2 ^ 1 1
where S, is the source term for the i-th momentum equation, is the magnitude of the velocity. This momentum sink contributes to the pressure gradient in the porous cell, creating a pressure drop that is proportional to the fluid velocity (or velocity squared) in the cell [23]. The source term is composed of two parts: a viscous loss term, also known as "Darcy term" (the first term on the r.h.s. of Equation 2) and an inertial loss term (the second term on the r.h.s. of Equation 2). As long as the flow velocity remains sufficiently small, i.e. when the local Reynolds number ReK is smaller than 100 [18], the flow regime may be considered as laminar and the second term on the r.h.s. of Equation 2 may be dropped resulting into a special form of the Darcy's law known as the Blake-Kozeny equation [18].
In the case of packed beds with homogeneous spherical particles, the permeability and inertial resistance coefficient can be computed comparing the momentum source term (Equation 2), with the semi-empirical Ergun's equation [26].
M 150 -(1 -s)2 1.75 -(1 -e) 2
V = d 2 3 + -P-V2 (3)
l d p ■ s d p ■ s
where v is the flow velocity, P the pressure, p and p the fluid dynamic viscosity and density respectively and e is the void fraction. Therefore, the two coefficients can be identified as follows:
72 „3
d p -s3 150 •(! -s)2
K = -p-7T (4)
C _ 3.5 -(1 -g)
C2 - (5)
Due to their dependency on the void fraction distribution, an additional UDF was designed and compiled into the CFD code in order to automatically compute the values of the two coefficients at each computational node based upon the axial position into the packed bed.
5.1. Numerical schemes
The time accurate simulations were performed on a Linux Cluster with AMD multicore processors. All model equations were solved with second order accurate numerical schemes [19]. Convergence was considered achieved when mass and turbulence residuals were below 10-4 and energy residual was below 10-7.
5.2. Physical properties of the materials involved
Air was treated as ideal gas with thermo-physical properties (specific heat, thermal conductivity and viscosity) assigned as piecewise linear interpolations of tabulated data available in the literature [27]. The numerical solution of governing equations was performed with the "pressure based" approach, which assumes that mass density depends on temperature and on a fixed pressure reference value [22].
As far as concerning the thermal properties of the solid materials (rocks and concretes), they were experimentally measured and extrapolated afterwards, to cover a wider temperature range, by using Thikhomirov's and Kelly's correlations for thermal conductivity and heat capacity respectively [14]. The extrapolated values were then assigned to the relative material as piecewise linear profile.
6. CFD model validation
The CFD model was satisfactorily validated with experimental data coming from a 6.5 MWh^ experimental TES system prototype designed and built, in Biasca (CH), by the Swiss company Airlight Energy Manufacturing SA. The 4 m high TES prototype is composed by an insulated concrete vessel filled with almost 25 m3 of homogeneous river rocks (quartzite, limestone, calcareous sandstone, gabbro and helvetic siliceous limestone) with an average equivalent diameter of 0.03 m. The prototype has the shape of a truncated cone (4 m and 2.5 m upper and lower diameters respectively) with a dodecagonal cross section and is buried in order to reduce the need of a strong containing structure exploiting the surrounding earth.
The test case used as reference for validating the CFD model, consists of a continuous charging phase lasting for 82.5 hours. At the beginning of the experimental test, the storage was in its dead state. Hot air entering the TES system was provided by a tubular 58 kW electric heater.
Figure 3 reports the experimental measurements (solid lines) along with the CFD simulation results (dashed lines). The accurate description of the CFD model validation procedure may be found in [13, 17].
Time [h]
Fig. 3. Comparison between CFD simulation results (dashed lines) and experimental data (solid lines) [17].
Despite some slight differences for thermocouples T5 and T4, the description accuracy achieved for all the other is remarkable. Moreover, even though simulations results and experimental data for T5 and T4 curves are not overlapped, the temperature gradients are well described.
7. Numerical analysis of the industrial-scale TES system under cyclic conditions
A time-dependent 3D CFD simulation was run to evaluate the effectiveness of the packed bed TES system unit of providing the round-the-clock energy requirement of the reference CSP power plant. A total of 15 consecutive charge/discharge cycles were simulated allowing to observe the evolution of the thermocline zone into the packed bed and therefore the variation of the overall system efficiency.
The cycle was characterized by 12 hours of charging, with 650°C of inlet airflow from the top, followed by the discharging phase, with 270°C of inlet airflow from the bottom. The discharging phase was considered completed once the air outlet temperature from the storage unit was equal to 600°C.
The CFD results obtained showed that after the first eight cycles, the discharging phase duration was of 12 hours.
The evolution of the thermocline zone was observed monitoring the temperature distribution into the packed bed over time. Figure 4 shows the temperature distribution into the packed bed, as a function of the non-dimensional packing height, at the end of the 1st, the 5th, the 10th and the 15th charging phase (l.h.s.) and discharging phase respectively (r.h.s.).
700 600 500 400 300 200 100 0
-/j-l-
-/—I—
1st charge
5th charge
10th charge
15th charge
Dimensionless rock-bed height [-]
1st discharge
- • — 5th discharge y //
— — — 10th discharge
s*- / // /
\ ^ -, /
0.2 0.4 0.6 0.8
Dimensionless rock-bed height [-]
Fig. 4. Temperature distribution into the packed bed at the end of the 1st, 5th, 10th, and 15th charging phase (l.h.s.) and
discharging phase (r.h.s.) respectively.
The temperature distribution into the packed bed undergoes strong variations during the first cycles with the establishment of two separate thermocline zones given by the temperatures of the incoming HTF during the charging and discharging phases. This detrimental effect gradually reduces with consecutive cycles vanishing towards the 15th cycle.
As observable from both the graphs reported in Fig. 4, the thickness of the thermocline zone increases with the cycles, from a very thin thermocline at the beginning to a much wider at the end of the cycles analyzed. This increment translates into a larger entropy generation into the packed bed and therefore to a reduction of the exergy content. However, it can also be observed that the rate of degradation reduces during the time leading to the achievement of a stable condition.
From a graphical standpoint, the temperature distribution into the TES unit at the end of the 1st, 5th, 10th, and 15th charging phase is reported in Fig. 5. A remarkable thickening of the thermocline zone can be clearly observed especially looking at the first two pictures reported (end of the 1st and the 5th charging phase).
Fig. 5. Contours of static temperature into the TES unit at the end of the 1st, 5th, 10th, and 15th charging phase.
Temperature values are in °C.
The performance of the TES system unit were evaluated according to three first-law efficiency figures namely [14]: a) the charging efficiency (Equation 6), defined as the ratio of the energy stored at the end of the charging phase to the net input energy (inflow and outflow) and the pumping energy; b) the discharging efficiency (Equation 7), defined as the ratio of the energy recovered at the end of the discharging phase to the energy stored, during the previous charging phase, and the pumping energy; c) the cycle efficiency (Equation 8), defined as the ratio of the energy recovered at the end of the discharging phase to the net input energy (inflow and outflow) and the pumping energy relative to the charging and discharging phases.
„ - _EnStored_
VCh arg ing - , (6)
Input T Pumping-Charg ing
„ _ _EnRecovered_
^Discharg ing - En , En (7)
Stored Pumping-Disch arg ing
„ _ _EnRecov ered_
'¡Cycle ~ .e , E i E (")
Input Pumping-Chavg ing Pumping-Dischaig ing
The pumping energy for the charging and discharging phases was evaluated based upon the HTF mass flow rate and density, the efficiency of the fan, along with that of the power block, and the pressure drop through the storage unit over time. The latter showed a slight but constant increase throughout the cycles due to the increase in the air viscosity as a consequence of the increased average packing temperature.
Figure 6 shows the evolution of the quality factors during the 15 cycles analyzed.
Cicle number [-]
Fig. 6. First-law efficiency figures.
At the end of the first charging phase, the highest value of charging efficiency was achieved. The latter slightly decreases for the consecutive cycles approaching asymptotically the value of 96%. Instead, the discharging efficiency shows a sharp increase during the first 3-4 cycles reaching the value of about 95% beyond the 8th discharging phase.
The cycle efficiency provides a more general overview on the capability of the TES unit of storing and providing thermal energy. After the first 5 consecutive charging/discharging phases, the cycle efficiency is higher than 90% stabilizing afterwards around the final value of 92%.
The pumping energy and the heat losses, towards the external environment, remain below 7% and 0.3% of the net input energy during the charging phase.
8. Conclusions
A rock-bed based TES system was proposed, as viable alternative to current methods, for providing the round-the-clock energy requirement of a reference 80 MWe CSP plant based upon the Airlight Energy technology. This TES solution was analyzed by means of accurate 3D time-dependent CFD simulations under fifteen consecutive charge/discharge cycles with the aim of monitoring its performance evolution over time. The CFD model was firstly validated with experimental results coming from a small-scale 6.5 MWhth TES prototype. The good agreement between CFD simulations results and experimental data led the authors to confirm the importance of a proper modeling of the porosity distribution as well as the effective thermal conductivity of the packings in order to obtain a realistic description of the thermo-fluid dynamics behavior of this TES system.
The validated model was then applied to the real-scale TES unit; the simulation results obtained allowed to evaluate not only the capability of this TES solution to effectively fulfill the round-the-clock energy requirement of the reference CSP plant but also the very promising performance of this system with theoretical efficiencies up to 96%, 95% and 92% for the charging phase, the discharging phase and the overall cycle respectively.
Acknowledgements
This work has been developed in the framework of the SolAir-2 Project (project N. SI/500091) financed by the Swiss Federal Office of Energy (SFOE - OFEN - BFE) under the contract N. SI/500091-01.
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