Experimental characterization of a lab-scale cement based thermal energy storage system

Applied Energy 256 (2019) 113937

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Experimental characterization of a lab-scale cement based thermal energy storage system

T

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Johannes Nordbeck , Sebastian Bauer, Christof Beyer Institute of Geosciences, University of Kiel, Kiel, Germany

H I GH L IG H T S

present a new modular cement based solid-liquid thermal energy storage concept. • We prototype storage unit is characterized through dedicated experiments. • AA lab-scale balance model is developed to describe its energy storage characteristics. • Theheatmethodology can be scaled and applied to multi-unit storage systems. •

A R T I C LE I N FO

A B S T R A C T

Keywords: Sensible heat storage Modular system Helical heat exchanger Lab scale experiment Storage characterization Heat balance modeling

In this study, a new modular cement based solid-liquid heat storage concept is presented. Advantages of this storage concept are its scalability, facilitated by a flexible modular construction, and its potential double purpose as heat storage and foundation structure. The storage system may be integrated in new as well as existing buildings, or be installed in the subsurface. A lab scale 1 m3 prototype storage unit was constructed, consisting of a helical heat exchanger embedded in a cement-based thermal filling material. Dedicated heat charging and discharging as well as heat loss experiments were performed at storage temperatures of 60 °C and 80 °C within a well-controlled laboratory environment in order to characterize the heat transfer processes and storage characteristics as well as the performance of the heat storage prototype. The maximum thermal capacity at 80 °C supply temperature is found to be 52 kWh/m3, with maximum charging/discharging rates of up to 8 kW and heat losses of 4.4 kWh/24 h at full capacity. Based on the found characteristics, a heat balance model is developed and parameterized. Simulated and experimental temperatures and heating rates are in very good agreement, which shows that the dominant heat transfer processes and material characteristics are well understood and quantified.

1. Introduction In Germany space heating and hot water supply have a share of 32% (829 TWh) of the final energy consumption. This share differs strongly depending on the area of application: In the commerce, trade and service sectors space heating and hot water take up 53% or 211 TWh while in private households the share is as much as 84% or 568 TWh of total energy consumption [1]. Between 50 and 60% of that energy is produced from fossil fuels such as gas, oil and coal [2]. The energy transition initiative of the German government aims to reduce the dependence on fossil fuels for energy production and promotes an increase in the use of renewable energies to reach a share of 30% of primary energy consumption forecasted by 2030 (820 TWh) [3]. Especially in the private households and trade sectors, the use of renewable sources of heat would reduce fossil fuel consumption considerably. However, the ⁎

temporal disparities between demand and supply from renewable heat sources like e.g. solar thermal energy, or alternative heat sources like e.g. industrial waste heat require thermal energy storage systems, to store excess heat from fluctuating sources, or to displace and match peak energy loads [4]. There are generally three types of heat storage technologies [5]: Sensible heat storage is the most frequently used storage concept in many domestic and commercial applications, as investment costs are comparatively low and a high level of technical readiness has been reached [6]. Sensible heat is stored by changing the temperature of a storage medium, such as water, oil, rock [7] or concrete [8]. In latent heat storage, heat can be stored and released by so called phase change materials [9], e.g. water in ice storage systems [10], while in thermochemical heat storage reaction enthalpies of chemical or adsorption processes (e.g. on silica gels or zeolites [11]) are used for storage. For

Corresponding author. E-mail address: [email protected] (J. Nordbeck).

https://doi.org/10.1016/j.apenergy.2019.113937 Received 5 June 2019; Received in revised form 7 August 2019; Accepted 21 September 2019 0306-2619/ © 2019 Elsevier Ltd. All rights reserved.

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and be tailored to match the specific spatial constrictions of the urban environment as well as the storage capacity and rates required. Due to the high mechanical stability of the cement material, the systems can also serve as building foundation. In contrast to ATES or BTES systems there are no strict requirements regarding the geological subsurface. Thus, the new storage system can be employed in most subsurface settings. A prototype module was constructed and the storage performance characterized in terms of storage capacity, achievable heat charging and discharging rates as well as the heat loss using a set of dedicated storage experiments. Using the identified characteristics of the storage system, a heat balance model is derived to represent the experimental results and quantify storage characteristics. The specifically designed and highly controlled experiments of the prototype module provide spatially and temporally highly resolved data sets, which may additionally serve as a reference for the verification of simulation models of helical heat exchangers in cement based heat storage systems.

application of seasonal heat storage for building or district heating, storage systems with sufficient capacities are required [12]. For this purpose, sensible heat storage via technologies like aquifer or borehole thermal energy storage (ATES, BTES), which both use the geological subsurface as the storage medium, and hot water thermal energy storage (HWTES) are usually employed [13]. Small scale or daily domestic applications commonly employ HWTES systems with volumes of several 100 L and storage capacities of 10–300 kWh, but also large-scale water tank systems that provide storage volumes of > 1000 m3 [14] up to seasonal storage in excavated pits of > 50,000 m3 volume are in use [15], providing storage capacities of > 2000 MWh. In these systems, thermal stratification of the water has to be accounted for [16]. Likewise, ATES or BTES systems can be used for seasonal heat storage, providing capacities of 15–40 kWh/ m3 at storage volumes between 10,000 and 500,000 m3 depending on operating temperatures, achievable pumping rates, size of the aquifer or number and depth of boreholes, respectively [17]. ATES systems are typically operated at storage temperatures below 40 °C [18], which is not high enough to directly supply temperatures required for hot water or space heating and thus requires the use of heat pumps. A few examples of ATES systems with storage temperatures > 40 °C, however, have been installed in Germany, such as for the German parliament in Berlin [19] or for residential buildings in Rostock [20]. BTES systems usually operate at storage temperatures > 60 °C (e.g. Braedstrup in Denmark [21] or Emmaboda in Sweden [22]) and thus, depending on underground properties, may provide higher energy storage densities than typical “low temperature” ATES systems. The application of both ATES and BTES requires specific geological prerequisites, such as layers with suitable hydraulic and thermal properties as well as low natural groundwater flow rates [23], which may restrict these technologies as heat storage options at specific sites. Sensible heat storage in non-geological solids includes materials such as concrete or ceramics, which are common in high temperature industrial applications (> 400 °C; e.g. [24]). Energy piles, however, are used for heating and cooling of buildings [25] and for seasonal heat storage [26]. The piles are installed into boreholes with depths of up to 40 m [27] and consist of steel reinforced concrete with helix type or multi-U pipe heat exchangers, using the concrete as well as the surrounding soil as heat storage medium. Concrete has a high mechanical load capacity, is easy to handle and can endure cyclic thermal loading [28]. Energy piles thus also act as structural reinforcement or foundation for buildings [29]. Typical thermal loads in such systems are in a temperature range of 15 K [30]. Because heat demand is mainly agglomerated in densily populated urban regions, where surface space for installation of storage systems is accordingly rare, subsurface heat storage options are required [31,32]. To enable direct use of the stored heat for heating or providing hot water, as well as to allow a higher storage efficiency, these systems should have high operating temperatures of more than 40 °C. Due to the large range of storage capacities and storage temperatures needed, a scalable and versatile heat storage system would be advantageous, which can be implemented in urban subsurface environments and widely independent of geological boundary conditions. This work therefore investigates a laboratory scale prototype module of a scalable, cement based heat storage system for storage temperatures of up to 90 °C, where heat exchange is achieved using an embedded helix type heat exchanger. The solid porous cement matrix is saturated with water, which significantly increase the energy density and thus the storage capacity of the system in comparison to dry cement or concrete materials [33]. All components of the storage system consist of comparatively inexpensive, commercially available and easy to process standard materials, which facilitates the employment of the system as a feasible and economically efficient alternative to conventional thermal energy storage systems in domestic applications. Arrays of these storage modules can be installed into the subsurface next to or below a building, but also in cellars or designated storage spaces, e.g.,

2. Experimental setup The new cement based modular thermal storage concept was tested on a lab-scale prototype storage unit in a controlled environment, i.e. under only slightly varying lab temperature and extensive monitoring. Four experimental runs are presented here in total, which were performed to produce detailed datasets describing the charging, discharging and heat loss characteristics of the laboratory storage unit. The storage unit was constructed by installing a tubular helical heat exchanger in a porous, water saturated thermal filling material contained by a polypropylene (PP) barrel (Fig. 1). The cylindrical barrel has an inner diameter of 110 cm, a height of 116 cm and a corresponding volume of 1.1 m3. The lid of the barrel consists of an inner disk of 56 cm diameter and an outer hollow ring with outer diameter of 111.4 cm and diameter of the cut out of 50 cm. The disk can be tightened onto the ring with 18 steel bolts. The inlet and outlet pipes of the heat exchanger protrude from two holes inside the inner disk. Three additional holes were drilled into the lid for sensor cables (see below). For the heat exchanger geometry a helical shape was chosen, as this shape allows for large pipe lengths and thus high interfacial areas, supporting high charging/discharging rates [34,35]. The helical heat exchanger (Fig. 1a,b) consists of an aluminum-polyethylene composite pipe (Wavin PE-Xc) and is used to circulate water as a heat carrier fluid through the storage unit. The pipe has inner and outer diameters of 2 and 2.5 cm, respectively. The wall thickness thus is 2.5 mm. It has a height of 91 cm (lowermost to topmost coil) in order to leave enough space to the barrel lid above and the bottom below the helical heat exchanger HHX. The height of the lowest coil above the bottom of the barrel is 7 cm. The longer the total pipe length, the higher the heat transfer rates that can be achieved, which suggests a large diameter and a low pitch (i.e. vertical distance) between individual coils. On the other hand, thermal volumes of the heat storage matrix should be approximately balanced between the inner region, enclosed by the heat exchanger, and the outer region, i.e. between the heat exchanger and the barrel walls, in order to sustain high heat transfer rates. With respect to the thermomechanical behaviour, the HHX near-field was identified as a critical region by Miao et al. [36], who analyzed the influence of pitch height on critical tensile stress during heat charging for the storage system studied in this paper. They found that a tube pitch of 7 cm is a viable choice, as a smaller pitch would significantly alter the mechanical response. Based on these considerations, a pitch of 7 cm and a diameter of 82 cm were chosen for the HHX as a compromise between high pipe length and a balanced distribution of the storage matrix. The total coiled pipe length inside the storage unit thus is 33.5 m and is held in helical shape by a slim frame on the inside of the helix. Wooden spacers are clamped onto the bottom and top of the frame, which keep the heat exchanger centered inside the barrel. The thermal filling material (TFM) consists of Füllbinder L 2

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Fig. 1. (a) Sketch of the experimental setup with heat charging (red) and discharging (blue) configurations, temperature sensors 1–20 inside the TFM, sensors 21–23 outside and two sensors inside inlet and outlet tubes (Tf), (b) heat exchanger with frame and wooden spacers for helix, temperature sensors and inner lid on top, and (c) experimental setup as seen in the lab with insulated inlet and outlet pipes and sensor cables protruding from the lid and combined Eco-skin and Armaflex insulation on the outside of the storage unit.

of 10.7 ⋅ 10−6 K−1 [33] which is important in order to maintain a good thermal contact between heat exchanger and heat storage material. In the construction of the heat storage unit, the water cement mixture was prepared in a weight ratio of 0.8 using a high-speed colloidal mixer and filled into the barrel with the kind help of Bau-ABC Rostrup. To prevent displacement or uplift of the heat exchanger during the filling procedure, it was filled with water and kept in place inside the barrel by the spacers. After a setting period of 30 days the TFM fills the barrel up to a height of 105 cm (1 m3). Substracting the volume required by the heat exchanger and its frame (approximately 30 L), the thermal storage volume, consisting of the TFM, amounts to 0.97 m3

(Schwenk Zement KG), which is a commercially available cement-based filling and sealing material with high weight contents of calcite (> 60%), quartz (ca. 10%) and hydraulic binder (30%) [37]. The TFM has a high porosity of 0.54 and a very low hydraulic permeability on the order of 1 ⋅ 10−14 m2 [33]. This is typical for cement based materials and low enough to prevent thermal convection. The material was selected after screening a range of typically used cement based filling materials. The specific TFM was chosen for its comparatively high thermal conductivity and heat capacity of 0.96 W/m/K and 3.4 MJ/m3/ K under fully water saturated conditions, as well as its low volume change after 24 h of curing of −1.57% and it’s low thermal expansion

3

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[39]. A total of 20 K-type thermocouples were installed inside the storage unit in four radial transects before the filling with the TFM in order to record temperatures at the center, between center and heat exchanger, directly next to the heat exchanger (inwards and outwards) and near the inner wall of the barrel, covering the vertical extent of the storage unit. The sensors were fixed on cords, which were spanned between the wooden spacers. The measurement locations are shown in Fig. 1. This setup was designed to characterize both the fast heat exchange processes near the heat exchanger as well as the long term temperature development in the storage unit. Two thermocouples along with two additional Pt-100 sensors for double-checking the measurements were installed inside the inlet and outlet pipes to measure the supply and return flow temperatures. Three thermocouples measure the room temperature at different locations and increasing distance to the storage unit. All temperature sensors are connected to a data acquisition device. The estimated temperature measurement error is ± 0.45 °C for the thermocouples [40]. Temperatures and flow rates were recorded in minute intervalls during all experiments.

with an estimated error of ± 1%, which equals ± 1 cm of height of the TFM inside the barrel. 30 L of water are added on top of the TFM, to keep it from drying out and ensure a full saturation of the pore space. The total thermal volume (VTFM) is thereby 1 m3, the remaining 0.1 m3 above the TFM is filled by air and water vapor. The thermal properties (i.e. thermal conductivity and volumetric heat) of the fully water saturated TFM, as prepared for the construction of the storage unit, were measured on three small samples of 5 cm diameter and 10 cm length at an average laboratory temperature of 20 °C and atmospheric pressure with a Decagon KD2 Pro thermal properties analyzer (Decagon Devices). They were determined to be 0.96 W/m/K and 3.42 MJ/m3/K, respectively, and thus correspond very well with the properties given in Miao et al. [33]. The KD2 Pro analyzer is accurate within ± 10% inside a range of 0.2–4 W/m/K for conductivity and ± 10% for volumetric specific heat at conductivities above 0.1 W/m/K [38]. Although containing a fairly large amount of thermal mass for a labscale experiment, the TFM is still subject to temperature changes in the laboratory environment. These changes interfere with temperature or heat balance measurements inside the TFM. To minimize this effect, the heat storage unit was insulated at the bottom by placing it on a 10 cm Styrodur plate (BASF), which is in turn placed on a heavy duty PE pallet. The top and lateral surfaces of the storage unit were insulated by 2 cm of Armaflex (an elastomer material, Armacell International S.A.) and 10 cm of Eco-Skin (Austria Email AG), which is a polyester fibre mat covered by a 1 mm coating of PE on the outside. Table 1 summarizes the geometrical dimensions of all parts of the storage unit and Table 2 lists the respective material properties according to material data sheets and own measurements in case of the TFM. Heat source and pump for the heat carrier fluid are combined in a heat bath system (CC-215B, Peter Huber Kältemaschinenbau GmbH), which consists of a heater, a 15 L hot water reservoir and a suction pump with a combined power of 2 kW. It provides a constant supply temperature and a flow rate between 100 and 200 L/h. Rubber hoses with inner and outer diameters of 9 and 16 mm connect the inlet and outlet pipes of the heat exchanger with the heat bath system to complete the thermal charging cycle. The distance between hot water source and heat storage inlet is 4 m, along which the system loses heat to the surrounding laboratory. To minimize this heat loss, all hoses and pipes that are part of the charging cycle, were insulated with Armaflex elastomer tubes with a wall thickness of 2 cm. For extracting heat energy previously stored in the storage unit, two ball valves are turned to direct cold water from a nearby water tap into the inlet and the return flow from the outlet into a nearby sink. A magnetic inductive flowmeter (model SM6004, ifm electronic GmbH) measures and records the water flow rate with an accuracy of ± 2%

3. Experimental heat charging and discharging tests Two thermal charging and discharging tests were performed on the storage unit to prove the technical feasibility of the new heat storage concept. The first experiment (E1) was performed at 60 °C supply temperature of the heating bath during the charging phase. To investigate impacts of increased storage temperatures, a second experiment (E2) was performed at 80 °C supply temperature. Fig. 2 gives an overview of the experimental boundary conditions (i.e. the fluid inlet and laboratory temperatures Tf,in and Tl, and the flow rate of the working fluid qw) and monitoring results (i.e. the charging/discharging rate Qc/d, fluid return temperature Tf,out and thermal filling material (TFM) temperatures at sensor locations) for both experiments. The operational cycles of experiments E1 and E2 are specifically designed to determine the maximum charging/discharging rates and maximum thermal capacity of the storage unit, in order to characterize the optimal performance achievable. The experiments started with a 24 h period of de-aeration by circulating water through the system at laboratory temperature Tl in order to purge the air from the heat exchanger. After 24 h the heater was activated. Constant inlet temperatures Tf,in of 59.3 and 78.9 °C were reached after 6 and 16 h of heating-up, respectively, and kept constant for 6 days of heat charging the storage unit in order to reach stationary storage temperatures Ts. The charging phase in each experiment was immediately followed by the heat discharging phase with cold tap water over a period of 4 days (E1) and 3 days (E2), respectively. During the discharging phase, Tf,in fluctuates between 15.5 and 19.2 °C due to the variability in the water supply temperature of the university water system. Fig. 2a shows Tf,in and the return temperature Tf,out over the course of both experiments. During the charging phase Tf,in > Ts, thus heat transfer occurs towards the storage unit. The fluid temperature spread between inlet and outlet Tf,in – Tf,out remains constant at 11 °C during the first 6 (E1) and 16 h (E2) of heating up. When the charging proceeds and Ts approaches Tf,in, the temperature spread decreases and is almost constant after 6 days of charging, which means the storage unit is fully charged. The discharging phase starts with Tf,in ≪ Ts, thus heat transfer occurs towards the working fluid. Tf,out is subsequently higher than Tf,in and at the beginning, the temperature spread is large but decreases strongly until the storage unit is fully discharged (i.e. when Tf,out = Tf,in). The rate of heat charging/discharging (or power) Qc/d [W] can be quantified from the fluid temperature spread between inlet and outlet Tf,in – Tf,out (Eq. (1)) with cwρw [J/m3/K] the volumetric heat capacity of the working fluid (i.e. water) and its flow rate qw [m3/s].

Table 1 Dimensions and geometrical specifications of the experimental heat storage unit. Geometrical parameter

Description

Size [cm]

Barrel diameter

Inner/outer diameter of PP-barrel

Barrel height Barrel wall thickness Barrel lid thickness Barrel lid diameter (inner lid) Barrel bottom Heat exchanger height Heat exchanger radius Heat exchanger pitch Heat exchanger pipe Insulation mantle faces and top Insulation bottom

Height from inside bottom to lid Wall thickness Inner disk/outer ring thickness Inner lid diameter

110/ 111.4 116 0.7 3/0.7 56

Bottom thickness Height of helix Radius of helix Distance between two coils Inner/outer diameter of Al-PE-pipe Insulation (Armaflex + Ecoskin) thickness at top and mantle faces of the barrel Insulation thickness at bottom face of the barrel

1 91 41 7 2/2.5 12 10

Qc / d = c w ρw qw (Tf , in − Tf , out ) 4

(1)

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Table 2 Material properties for the experimental heat storage unit. Storage part

Density [kg/m3]

Thermal conductivity [W/m/K]

Volumetric heat [MJ/m3/K]

Porosity

PP barrel Insulation (10 cm Eco-Skin) Insulation (2 cm Armaflex) Insulation bottom (Styrodur) Heat exchanger Al-PE pipe Thermal filling material (Füllbinder L)

950 50 50 50 1515 2276

0.4 0.038 0.033 0.034 0.4 0.96a

1.824 – – – 1.590 3.423

– – – – – 0.543

a

Measured at 20 °C laboratory temperature.

Fig. 2. (a) Inlet & outlet temperatures, (b) flow rate, (c) charging & discharging rates, (d) laboratory temperatures, (e)–(h) temperature curves inside the thermal filling material (temperatures measured at sensors 2, 4, 7, 9, 12, 14, 17 and 19 are only shown in the supplementary information to this manuscript in order to increase the clarity of diagrams). 5

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qw averages at 122 and 124 L/h during the heat charging phases of E1 and E2 (Fig. 2b), respectively. The time span required for a complete displacement of the fluid volume in the heat exchanger between inlet and outlet thus is 5 min. When switching to tap water during the discharging phases, qw changes to average values of 95 and 135 L/h in E1 and E2, which results in displacement times of 6.5 and 4.6 min. Like Tf,in, also qw fluctuates, depending on the water use of the university water system. The maximum heat charging rate Qc/d is 1.6 kW for both experiments (Fig. 2c), as it is capped at the maximum power of the heater. Qc/d declines as Ts approaches the target supply temperature (which takes 6 and 16 h in E1 and E2, respectively). After 6 days of heat charging a steady state is reached and the working fluid temperature spread between inlet and outlet Tf,in – Tf,out and accordingly Qc/d remain almost constant over time. During this stage of the experiments, heat input into the storage unit equals heat losses from the storage to the laboratory environment, which occur, whenever Ts > Tl. As the storage unit has reached its target temperature (i.e. is fully charged) in each experiment, maximum heat loss rates Qloss [W] can be determined during the stationary phases and amount to 115 W in E1 and 182 W in E2 (Fig. 2c), which is 2.8 kWh/24 h and 4.4 kWh/24 h, respectively. According to EU regulation 811/2013 (CDR EU, 2013) [41] this translates to an energy efficiency class of D, which is comparable to the heat loss of a 1000 L hot water storage tank with standard insulation (8 cm expanded polystyrene and 2 cm polyester fibre mat; [42]). Heat losses from the storage unit across the insulation are influenced by Tl, which also fluctuates between 17 and 22 °C (Fig. 2d). During E2 it is on average 2 °C higher than during E1. Once the discharging process is started, peak discharging rates are obtained as 5 kW and 8 kW over a short period of a few minutes. These rates decline to < 2 kW after 2 and 5 h, respectively, and approach 0 as Ts approaches Tf,in. Heat losses also occur during the discharging phase, but decrease significantly, when the storage is cooled down as the differences between Ts and Tl become small. The temperature curves inside the TFM show the propagation of the heat transfer front during charging/discharging processes (Fig. 2e–h). The heating or cooling front propagates outwards from the heat exchanger towards the insulation (E1/E3 – sensors 5, 10, 15, 20), and inwards towards the center of the unit (E1/E3 – sensors 1, 6, 11, 16). Heat transfer is clearly dominated by conduction, as there is no obvious vertical temperature layering, which might have been caused by convection processes in the porous matrix or cracks of the TFM. The temperature curves measured by the sensor grid allow an estimation of a representative volume averaged storage temperature Ts [K] over time by assuming a radial symmetry of the temperature field and spatial integration of the measurements over the storage unit. A representative annular volume Vi is associated to each of the 20 sensors in the measurement grid inside the TFM (making up the total TFM volume of 1 m3, if added up) and a weighted sum of the temperature measurements Ti is calculated as Ts, with weights according to volume fractions Vi. This procedure essentially corresponds to a nearestneighbor interpolation on a quasi regular grid of measurements. Taking into account the initial temperature of the storage Ts0, the stored amount of heat Hs [J] can be determined by Eq. (2),

Hs (t ) = cρVTFM (Ts (t ) − Ts0)

c/d c/d s s

Fig. 3. Cumulative total heat charge and discharge Hc/d and actually stored amounts of heat Hs for experiments E1 and E2.

recovered from the storage unit. At the end of the experiments, 36.6 and 52.0 kWh were recovered in E1 and E2, respectively, which amounts to fractions of 68 and 67% of the heat invested in charging the storage. Heat losses thus amount to 18.2 and 26.2 kWh after 6 days of charging and 17.1 and 25.7 kWh in total at the end the experiments. During both experiments, more heat was recovered than was actually stored, as during the discharge phase the storage unit was cooled slightly below the initial temperature Ts0 due to the tap water temperature provided by the water supply system. As the heat charging/discharging process is purely conductive, the corresponding rates Qc/d are dependent on local temperature gradients between heat exchanger and the TFM, the effective heat conductivity across the charging/discharging front and the interfacial area of this front with the still uncharged (or not yet discharged) TFM volume. Fig. 4a shows the experimentally determined Qc/d against Ts (red/blue arrows indicate the temporal succession of measurements during charging/discharging phases of both experiments). The horizontal progression of Qc/d during the early charging phases (i.e. until average Ts of 32 and 49 °C are reached in E1 and E2) shows the capping of Qc/d at the maximum heater power of 1.6 kW. Once the heat bath has reached constant supply temperatures, the Qc/d decline with increasing Ts, as the thermal gradients across the charging front flatten out. The discharging rates show a reversed behaviour: high initially at high Ts and declining with decreasing Ts. Fig. 4b shows the same Qc/d against the temperature difference between heat exchanger fluid and storage ΔTfs = Tf – Ts, which drives the heat transfer process, and where Tf =(Tf,in + Tf,out)/2 is assumed as the average fluid temperature between inlet and outlet of the storage unit. Both, charging and discharging rates, are very similar up to a ΔTfs of approximately 20 K. The different Qc/d between the two discharging curves at higher ΔTfs, however, result from the 20 K temperature difference in Ts at the start of the respective discharging phases: At ΔTfs = 25 K heat has been discharged in E2 for already 10 h, while in E1 the discharging process was just started. Despite the same driving temperature difference, Qc/d in E2 thus are temporarily smaller than in E1. As mentioned above Qc/d depends on the heat conductivity of the TFM λTFM [W/m/K] as well as the shape of the charging/discharging front and the steepness of the temperature gradient. Qc/d therefore is strongly dependent on the internal heat distribution and the charging/ discharging status of the storage unit, due to the propagation of the heating/cooling zone throughout the storage unit. At the start of a heat charging phase, e.g., the “interfacial area” between heated and unheated TFM volumes is large as the radial fronts propagating from individual coils of the helical heat exchanger do not interfere with each other, and thermal gradients are steep as the heat exchanger near-field is still cold. Accordingly, Qc/d is initially high. While the charging proceeds and Ts increases, heated zones around individual heat exchanger coils start to overlap which reduces temperature gradients and

(2) 3

and is shown in Fig. 3 for both experiments. In Eq. (2), cρ [J/m /K] is the volumetric heat capacity of the TFM and VTFM [m3] its volume. After three days of heat charging > 90% of the maximum storage heat capacity (according to the respective supply temperature) is reached in both experiments. Maximum Hs for E1 and E2 at the end of the charging phase are 35.5 and 51.5 kWh. Fig. 3 also shows the cumulative total heat charge and discharge Hc/d, which results from temporal integration of Qc/d according to Eq. (1). Hc/d is larger than Hs, as it also includes the heat lost across the insulation during the charging phases and reaches 53.7 and 77.7 kWh after six days of thermal charging, respectively. During the discharging phases, however, Hc/d represents only the heat 6

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Fig. 4. Charging/discharging rate Qc/d against (a) storage temperature Ts and (b) driving temperature difference between heat exchanger fluid and storage ΔTfs; ratio Qc/d/ΔTfs against (c) Ts and d) ΔTfs. The arrows indicate the temporal succession of measurements taken during charging and discharging phases. The grey boxes in (d) highlight the deviation of charging from discharging data points.

process. When most of the heat is discharged and Ts approaches Tf (i.e. for Ts < 25 °C) the fluctuations in Qc/d/ΔTfs around an average value of 40 W/K mostly reflect the variability in the tap water temperature, as even small variations in ΔTfs result in strong changes in the ratio Qc/d/ ΔTfs. As for the charging process, the storage behaviour can be best characterized in between the early phase of the discharging process (i.e. after 3.5 (E1) and 4 h (E2)) and before the convergence of Ts and Tf, where data points show an approximately linear behaviour. During these phases of E1 and E2 the observed Qc/d/ΔTfs for discharging are between 40 and 68 W/K. Fig. 4d displays the same Qc/d/ΔTfs data against the driving temperature difference ΔTfs and highlights the deviation of charging from discharging data points during the initial 6 h (E1) and 16 h (E2) of heating at maximum heater power (bend in curves at higher ΔTfs, grey box (I)) and the initial 3.5 h of peak discharging rates (grey boxes (II)). Deviations between charging and discharging data points are also highlighted when the change in heat content is only small, i.e. when the unit is at nearly full capacity (after 2–3 days of heat injection) or when the stored heat has been nearly fully discharged (ΔTfs < 5 K in both cases, grey box (III)). As explained above, under these conditions the achievable Qc/d is notably affected by external boundary conditions (maximum heater power, laboratory and tap water temperatures) and data obtained during these phases thus should be interpreted with caution as they do not reflect the storage behaviour during the intrinsic usage of a storage, i.e. for highly dynamic changes in heat content for charging/discharging. In between, i.e. in the range 10 K < ΔTfs < 20 K, however, all charging/discharging Qc/d/ΔTfs data points are within a relatively narrow range of 40–68 W/K. As explained above, near full charge of the storage unit (i.e. after 2–3 days of charging) the heat transfer behaviour is dominated by heat losses across the insulation, which is driven by the temperature difference between laboratory environment and the storage unit ΔTls = Tl–Ts. As the insulation efficiency of the storage unit is not well characterized from the experimental data of E1 and E2, additional passive cooling experiments E3 and E4 were performed, to analyze the heat loss behaviour over time. After 6 days of heat charging at supply

thus Qc/d. The same logic applies also for the discharging process. In case of a strong dependency of λTFM on temperature (as discussed in Hailemariam and Wuttke [43] and Schedel at al. [44]) Qc/d would be further reduced with proceeding charge (i.e. with increasing Ts), but less strongly decreased with proceeding discharge (i.e. with decreasing Ts). A strong temperature dependency is thus not supported by the experiments. Fig. 4c shows charging/discharging rates divided by the driving temperature difference, Qc/d/ΔTfs [W/K] plotted against the storage temperature Ts. The ratio Qc/d/ΔTfs can be interpreted as the thermal conductance of the heat exchanger – TFM heat transfer and, according to Fourier’s law, should therefore be equal to the product of heat conductivity λTFM and an interfacial area divided by the distance of heat transfer. For the charging process, the Qc/d/ΔTfs curves of both experiments show a very similar behaviour of decreasing values with increasing Ts (i.e. with proceeding charge), starting at 100 and 125 W/K in E1 and E2, until Ts approaches temperatures approximately 5 K below the targeted storage temperatures of the respective experiments, i.e. 56 W/ K at Ts = 55 °C after 69 h in E1 and 67 W/K at Ts = 75 °C after 112 h in E2. Beyond these temperatures, Qc/d/ΔTfs increases again to reach maximum values of 85 and 74 W/K as ΔTfs approches constant minima of about 1.33 and 2.45 K in E1 and E2, respectively. This reflects that the heat transfer is driven mainly by heat loss from the storage unit across the insulation. The experimental phases best suited to characterize the storage behaviour during the charging of the storage unit are thus in the quasi linear region of Fig. 4c between the initial heatingup of the heat bath (i.e. after 6 and 16 h in E1 and E2) and the convergence of Ts and Tf (i.e. when ΔTfs < 5 K after 52.5 and 78 h in E1 and E2). Here, the experimentally observed Qc/d/ΔTfs of both experiments are between 52 and 67 W/K. For the discharging process, the data curves should be analyzed in the contrary direction, as the storage discharge starts at high Ts. Here, Qc/d/ΔTfs decreases in both experiments with decreasing Ts (i.e. proceeding discharge) starting at 136 and 117 W/K. As this constitutes a cooling process, the behaviour is in principle similar to the charging 7

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Fig. 5. (a) Temporal decline of stored heat Hs and (b) ratio of heat loss rate and driving temperature difference between laboratory and storage Qloss/ΔTls against storage temperature Ts.

temperatures of 60 (E3) and 80 °C (E4), nearly constant Ts were established. The heat bath and pump system then was deactivated and the storage unit was left to cool down passively, i.e. without further circulation of a working fluid. Fig. 5a shows the temporal decline of the stored heat Hs due to the passive cooling, while Fig. 5b (in analogy to Fig. 4c) shows the ratio of heat loss rates to the driving temperature difference Qloss/ΔTls against Ts. Regarding the heat transfer between storage unit and laboratory environment, this ratio can also be interpreted as the corresponding storage insulation thermal conductance. In contrast to Qc/d/ΔTfs during active charging/discharging, Qloss/ΔTls shows little dependency on the storage temperature or the cooling progress during the passive cooling experiments. In E3, an average value of Qloss/ΔTls = 2.02 W/K with a standard deviation of ± 0.05 W/ K is found, in E4 the corresponding values are 2.14 ± 0.02 W/K. The parameter ranges and their variability observed in the two experiments thus agree very well. In summary, two dominant processes could be identified from the experiments: charging and discharging heat transfer from the heat exchanger to the TFM and heat loss from the TFM across the insulation. Both processes are solely driven by heat conduction and thus are linear with respect to all material or geometric parameters of the system and the driving temperature gradients.

Qc / d = λTFM

dfs

(Tf , in − Ts )

(4)

As discussed above (cf. Fig. 4), division of Qc/d by the fluid-storage temperature difference can be interpreted as the thermal conductance of the heat exchanger – storage interface Cfs [W/K] (i.e. the reciprocal of the thermal resistance Rfs [K/W], Eq. (5)), where Tf is the average fluid temperature between inlet and outlet of the storage unit (see above).

Afs Qc / d 1 = λTFM = Cfs = (Tf − Ts ) dfs Rfs

(5)

The Qc/d/ΔTfs data shown in Fig. 4 suggest, that during a transient storage process Cfs varies with temperature and charging/discharging history of the storage unit within a range of 40–68 W/K. For the spatially aggregated model approach used here, however, this parameter is treated as a constant. Heat transfer across the storage insulation will usually occur as a loss of stored heat, as the temperature of a (partially) charged storage unit in most applications (and in the performed experiments) will probably be above the ambient temperature. As this heat flux is also conductive the transfer or loss rate Qloss [W] is calculated by Eq. (6), where λins [W/m/K] is the heat conductivity of the insulation material, Als [m2] is the surface area of the insulated storage unit exposed to the laboratory environment, dls [m] is the thickness of the insulation, and (Tl–Ts) is the laboratory – storage temperature difference. In analogy to Eq. (5), the thermal conductance of the lab-storage interface Cls [W/K] can be derived by division of Qloss by the driving temperature difference (see Eq. (7)).

4. Heat balance model In order to simulate the experimental data and quantitatively characterize the storage behaviour, a heat balance model for the storage module was derived and applied, based on the experimental analysis presented above. As the thermal resistance (i.e. the inverse of thermal conductance) of the thermal filling material (TFM) is significantly lower than the resistance of the storage insulation (cf. Figs. 4c,d and 5b), a spatially aggregated lumped capacitance approach is suited to describe the heat balance of the system. With this approach, the storage material is described as a thermal box of spatially uniform temperature during the transient heat transfer processes [45]. For the heat balance of the storage unit the charging/discharging heat flux between heat exchanger and TFM and the heat loss from the TFM across the insulation towards the laboratory environment are accounted for. The heat balance thus is given by Eq. (3), with all quantities as defined above.

dHs = Qc / d + Qloss dt

Afs

Qloss = λins

Als (Tl − Ts ) dls

Qloss A 1 = λins ls = Cls = (Ts − Tl ) dls Rls

(6)

(7)

The Qloss/ΔTls data presented in Fig. 5b shows only little variation of this quantity with Ts, hence it is justified to also treat Cls as a constant parameter in the heat balance model. With Eqs. (2), (4) and (6), Eq. (3) can be solved for the rate of change of the mean storage temperature Ts (Eq. (8)). The return temperature of the heat carrier fluid Tf,out can be estimated from the energy balance of the storage process (i.e. using Eq. (1)) as shown in Eq. (9).

(3)

[Cfs (Tf , in − Ts ) + Cls (Tl − Ts )] dTs = dt cρVTFM

As the heat transfer within the storage unit is linear and clearly conductive, Qc/d, as expressed in Eq. (1), should be equivalent to a Fourier’s law type expression accounting for the TFM heat conductivity, λTFM [W/m/K], the interfacial area of the heating/cooling front propagating from the heat exchanger, Afs [m2], the effective heat transfer length (i.e. the distance of the heating or cooling front from the heat exchanger), dfs [m], and the driving temperature difference, which is approximated by (Tf,in–Ts) (Eq. (4)).

Tf , out = Tf , in −

(8)

Cfs (Tf , in − Ts ) c w ρw qw

(9)

All model parameters except the thermal conductivity of the insulation λins and the geometrical parameter Afs/dfs of the fluid-storage heat transfer interface can be directly determined by measurements of 8

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the appropriateness of the calibrated thermal conductances Cfs and Cls. For E4, the model prediction deviates slightly from the measured Ts data by up to 2.68 °C towards the end of the cooling experiment (Fig. 6), with a RMSD of 2.24 °C and a NSE of 0.94. In order to match both cooling experiments comparably well, a slightly increased thermal conductance Cls in between the experimentally estimated mean values of E3 and E4 (see above) would be necessary. Nevertheless, for E2, a very good agreement is achieved using the parameters as calibrated on the basis of E1 and E3, with differences in observed and simulated data and model performance metrics (Fig. 7d–f; Table 3) comparable to those obtained for the calibration data. 5. Discussion Fig. 6. Measured and modelled storage temperatures Ts in passive cooling experiments E3 and E4.

The set of charging/discharging and passive cooling experiments in combination with the heat balance modeling allowed a quantification of the key characteristics of the heat storage system, i.e. the storage capacity, charging, discharging and heat loss rates, as well as the fraction of recovered heat. The storage capacities of the storage unit prototype with helical heat exchanger (HHX) and a storage matrix volume of 1 m3 after fully charging the storage unit amount to 35.5 (60 °C) and 51.5 kWh (80 °C) (relating to the initial storage temperatures at the start of the experiments), or 0.95 kWh/m3/K temperature increase. The prototype thus is comparable to a standard hot water storage tank (HWST) for small-scale residential use of approximately 800 L volume in terms of storage capacity. In our experimental setup, the heat charging rate is limited to the maximum power of the employed heater (i.e. 1.6 kW), while during extraction peak rates of up to 5 and 8 kW were achieved for experiments at maximum storage temperatures of 60 (E1) and 80 °C (E2). Thus, also heat charging rates higher than 1.6 kW will generally be possible with a stronger heat source, e.g. accordingly dimensionized solar thermal panels, which could be used in applications for domestic or commercial building heat supply. Due to the conductive heat transfer inside the low-permeability thermal filling material (TFM) charging/ discharging rates of a storage unit in operation also depend on the internal temperature gradients, and thus decreased to less than 1.5 kW after 6.5 (E1) and 16.5 h (E2) of charging, and 4.5 (E1) and 9.5 h (E2) of discharging, respectively (note, that the longer supply time of heat transfer rates > 1.5 kW during charging compared to discharging is due to the limited heater power, which results in a slower temperature change within the storage unit during charging). Charging rates per unit length of the HHX pipe thus are 45–50 W/m for the initial 6.5 h (E1) and 16.5 h (E2), while discharging rates are higher at 45–100 W/m (E1; for the initial 6 h) and 45–140 W/m (E2; for the initial 9.5 h). For daily storage cycles in building heat supply applications, also the return temperature and a continous hot water supply are important characteristics. For a single 1 m3 storage unit at 60 °C, return temperatures of > 30 °C, which is a typical minimum required by floor heating systems, can be sustained for more than 4 h while discharging. Increasing the storage temperature to 80 °C extends this period to > 5 h. The achievable heat transfer rates and supply times of minimum return temperatures could be increased by an application specific optimization of the HHX design. This could be achieved by varying the pipe materials, the diameter to storage volume ratio, the coil pitch or by adding thermal conductivity enhancing additives to the storage matrix (e.g. graphite, [48]). Due to the conductive nature of the heat transfer process, heat transfer rates and temperature supply times, however, will probably remain below the performance of HWSTs of comparable capacity. This limitation will be alleviated in larger storage systems, which can be customized by scaling of storage unit size or the number of coupled storage units in a modular system in order to meet specific performance requirements such as the supply of minimum charging/ discharging rates over defined durations and return temperature ranges.

the material properties or geometric dimensions of the storage units components (section 2, Tables 1 and 2). Values of λins and Afs/dfs define the thermal conductances in the system, Cls and Cfs, and were determined by fitting Eq. (8) to the experimental data as explained below, with initial estimates derived from the experimental data shown in Figs. 4 and 5. In a first step λins is determined by fitting the model temperature curves of Ts(t) to the experimental data of experiment E3 (Fig. 6). The model boundary condition here is the lab temperature Tl. The measured average temperature of the fully charged storage unit is used as the initial model temperature Ts0. During passive cooling Qc/d = 0, which means Cfs = 0, i.e. only the lab-storage interface term (Eq. (7)) controls the heat transfer in the system. Temporal integration of Eq. (8) provides the solution for Ts(t). A nonlinear least-squares approach was used to fit λins to the experimental data of E3 [46], resulting in a fitted value of λins = 0.044 W/m/K, which is slightly higher than the thermal conductivity of the Eco-Skin insulation layer, as the cleading of the barrel is not perfect and λins also includes the PE barrel wall of 0.7 cm thickness with a higher thermal conductivity (cf. Table 2). With Als = 5.53 m2 and dls = 12.7 cm as determined by the geometric dimensions of the storage unit (Table 1) the fitted λins results in a model thermal conductance Cls = 1.90 W/K, which is slightly lower than the experimentally estimated mean values of 2.02 (E3) and 2.14 (E4). Fig. 6 shows the measured and simulated storage temperatures of E3, which match very well with a maximum deviation of 0.19 °C and a root mean square deviation (RMSD) of 0.1 °C. The corresponding Nash-Sutcliff model efficiency (NSE; [47]) is 1.0, indicating a nearly perfect agreement. In a second step λins is fixed in order to fit Eq. (8) (including both terms Cfs and Cls) to the experimental data of E1 by adapting the geometrical component Afs/dfs of the second unknown parameter Cfs. Here, λTFM is assumed fixed at 0.96 W/m/K as measured for the TFM (section 2, Table 2). Boundary conditions are inlet and lab temperatures Tf,in and Tl, and the measured initial storage temperature is used as Ts0. Qc/d (Eq. (4)) and Tf,out (Eq. (9)) were calculated with the simulated Ts(t) data. The normalized residuals of the simulated storage and outlet temperatures and the charging/discharging rates were included in the objective function of the least squares procedure, which resulted in a constant fitted effective ratio Afs/dfs = 45.1 m, and Cfs thus equals 43 W/K. This value matches the bottom end of the experimental data of 40–68 W/K in the range of 10 K < ΔTfs < 20 K (Fig. 4). Fig. 7a–c shows the fitting results in comparison to the experimental data: Storage and outlet temperatures of E1 match very well, while the peak charging/discharging rates are underestimated at the beginning of the charging/discharging phases by 0.75 and 1.03 kW, respectively. For the rest of the experiment, however, a very good match is still obtained with NSEs between 0.94 and 1.0 for the different quantities (Table 3). Finally, the model is applied to simulate experiments E2 and E4, which cover a wider temperature range than E1 and E3, without further adjustment of the model parameters in order to validate the model and 9

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Fig. 7. Measured and modelled data for storage temperature Ts (a, d), outlet temperature Tf,out (b, e), and charging/discharging rates Qc/d, (c, f) in experiments E1 and E2.

increase the storage and heating systems efficiencies. Because in this study we focus on the characterization of the storage medium, a standard heat bath with a maximum power consumption of the pump of 64 W was employed. The experiments presented in this paper, however, were not particularly aimed at obtaining optimal storage or system efficiencies, with a heater power limit of 1.6 kW, not-adjustable inlet temperatures during heat extraction with tap water as the working fluid, and experimental schedules (i.e. completely charging/discharging, extended steady state situations where Qc/d = Qloss over periods of several days) which do not represent storage cycles with high temporal dynamics as typically expected e.g. in domestic applications for hot water supply and space heating. For such operational cycles, generally higher efficiencies can be expected. Heat transfer rates and storage efficiencies would be also increased in larger systems consisting of multiple units, e.g. in a subsurface or geothermal composite storage system (cf. Fig. 1), as individual units would be partially shielded from heat loss by neighboring units and/or the surrounding ground. Overall, the comparison of results for the 60 (E1) and 80 °C (E2) experiments shows that increasing the temperature and thereby the energy density of the storage system allows for higher storage capacities, higher charging/discharging rates and longer supply times of specific return temperature levels, but also increased heat losses. For use in practical applications, domestic or commercial, it is therefore advisable to reinforce and optimize the insulation of the storage system and thus the storage efficiency, which certainly can be achieved for professionally manufactured systems compared to the self-made laboratory prototype.

Table 3 Nash-Sutcliffe model efficiency coefficient (NSE), root mean square deviation (RMSD) and normalized RMSD of the models for storage and outlet temperatures Ts and Tf,out, and charging/discharging rates Qc/d, in experiments E1–E4.

NSE RMSD NRMSD

E3 Ts

E1 Ts

E1 Tf,out

E1 Qin

E4 Ts

E2 Ts

E2 Tf,out

E2 Qin

1.00 0.10 0.005

0.99 1.48 0.039

1.00 0.84 0.020

0.94 0.10 0.037

0.94 2.24 °C 0.066

0.99 2.42 0.045

1.00 1.08 0.018

0.91 0.17 0.037

The system efficiency, which can be defined as the ratio of total energy input to the effectively usable energy, is an important characteristic for any energy storage system. For thermal energy storage, this corresponds to the total heat charged (including heat losses) in relation to the total heat discharged. At the end of the experiments, fractions of 68 and 67% of the heat invested in charging the storage unit were recovered in E1 and E2, respectively. Maximum loss rates at full charge amount to 115 W (i.e. 2.8 kWh/24 h) and 182 W (i.e. 4.4 kWh/ 24 h), which corresponds to specific heat loss rates per unit surface of 19 W/m2 and 31 W/m2, respectively. These characteristics are well comparable to standard HWST of comparable capacity, which generally show operational efficiencies between 50 and 85% [49]. In addition to potential heat loss, the electricity consumption of the circulator pump for the heating circuit is an important aspect of the systems total energy efficiency and should be adressed in the dimensioning of a storage system for a particular application. High efficiency pumps may achieve an energy consumption of less then 10 W [50] and can therefore 10

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Hailemariam and Wuttke [43] and Schedel et al. [44], would further limit the appropriateness of a constant Cfs in the model. The observed extent of agreement between model and experimental data, however, suggests at most only a minor interrelation. Despite the overall very good reproduction of measurements, the heat balance model is not fully prognostic, as it includes two calibration parameters, Cfs (as discussed above) and the thermal conductance of the storage insulation Cls. Both parameters can be estimated from the experimental data presented in this paper and the model thus could be used to simulate and analyze charging/discharging cycles differing from those investigated here. Detailed and reliable prognoses of storage behaviour for other configurations (e.g. for sensitivity analysis and storage unit optimization with respect to different unit shape or size, heat exchanger geometry, individual components materials etc.) or for the layout of coupled large scale multi-unit heat storage systems for specific applications requires more complex and independently parameterized CFD simulations on spatially discretized numerical grids and considering the spatial zonation and temperature dependency of parameters. Nevertheless, the presented data sets provide the basis for such further analyses of the presented storage concept and can be used for the development and verification of numerical models of the modular solid-liquid heat storage system employing helical heat exchangers. Moreover it can serve as reference data for the testing of heat transfer models for related geothermal installations such as helical ground source heat pumps, energy baskets or energy pile foundations. The data set therefore is freely available in the Supporting Information to this article or directly from the authors upon request.

The experiments were specifically designed to identify the governing heat transport processes, the achievable charging/discharging rates and storage capacities and the heat loss behaviour of the prototype storage unit for the new heat storage concept. By examining the process characteristics in detail, it is found that the heat charging/ discharging and heat loss processes can be roughly approximated using effective heat transfer coefficients between HHX and TFM, as well as TFM and laboratory environment, respectively. Considering the complex geometric setup of the HHX structure and the barrel, the geometrically complex transient advancing of the temperature fronts in the TFM, the mutual influence of heat from individual HHX coils and the boundary conditions, this is a rather surprising finding. The comparison of temperatures and heat flux rates observed in the experiment and simulated by the aggregated heat transfer model thus results in a very good agreement with NSEs generally higher than 0.92. This shows, that despite the conceptual simplification of the storage unit as a spatially aggregated box of uniform temperature and fitted characteristic parameters the model can approximately predict the overall behaviour of the storage very well and under different boundary conditions such as an increased storage temperature. Although the dominant heat transfer processes Qc/d and Qloss hence were correctly identified, adequately represented and quantified over the major run-time of the experiments, the discussed processes are actually more complex. The model underestimates peak charging and discharging rates, when the temperature spread between TFM and HHX fluid is largest, i.e. at the beginning of a charging/discharging cycle (Fig. 7c, f). This limitation is caused by two circumstances. First, due to the spatial arrangement and resolution of the sensor grid, the spatially integrated Ts is possibly slightly underestimated by the measurements at the start of the discharging process at t = 168 h, when the temperature gradient near the heat exchanger is very steep, as in the spatial integration of measured temperatures, the signals transferred by the eight sensors placed in direct contact with the HHX (3, 4, 8, 9, 13, 14, 18 and 19, cf. Fig. 1a) artificially disperse the cooling zone around the HHX (the same logic applies also for the charging process at t = 24 h, although the effect is reduced due to the heater power limit). This results in an underestimation of the driving temperature difference ΔTfs = Tf – Ts at early times of a discharging (or charging) phase. Second, the Qc/d/ΔTfs data shown in Fig. 4 suggests, that during a transient storage process the thermal conductance of the charging/discharging process Cfs (or rather the ratio of interfacial area to heat transfer length Afs/dfs of the propagating heating/cooling front, cf. section 3) varies within a range of 40 to 68 W/K over the charging/ discharging history of the storage unit, and especially at the start of a charging/discharging phase Qc/d may peak at even higher values for short durations. In the heat transfer model this quantity, and thus the effective HHX-TFM heat transfer coefficient, is treated as a constant parameter at a calibrated value of 43 W/K, although it obviously depends on the charging history of the storage unit. As the spatial temperature distribution, especially close to the HHX pipe, would have to be evaluated continuously over the charging/discharging duration in order to accurately quantify the transient nature of Cfs, this behaviour cannot be easily captured by any aggregated model approach. Accordingly, this simplification contributes to the underestimation of peak Qc/d. Once peak Qc/d have decreased, the constant value, however, proves well suited to quantify the charging/discharging behaviour, as the agreement of simulated and measured data is very good over the major time spans of the experiments. In fact, a high fraction of Qc/d/ΔTfs data points in Fig. 4 especially for the discharging process are rather below than above 50 W/K, which is not immediately visually obvious due to the high density of data points in the diagrams. For the charging process, in contrast, most of the data points remain above 50 W/K, as near full capacity the heat loss term Qloss and thus boundary effects gain dominance over Qc/d, and the Qc/d/ΔTfs data points start to increase. In an unbounded system, the ratio Qc/d/ΔTfs is likely to continuously decrease with proceeding charge. A significant temperature dependency of the TFM thermal conductivity λTFM, as discussed between

6. Conclusions The necessary conversion of heat supply systems in densely populated urban regions for an integration of significant shares of renewable energy sources requires flexible, scalable and space-saving heat storage systems with high energy densities, high thermal efficiency and adequate charging/discharging rates. This study presents an experimental and simulation based evaluation of a lab-scale prototype of a new modular cement based solid-liquid heat storage system, which may contribute to this objective. The experimental and modeling data discussed here allows for the following summarizing conclusions:

• The new modular cement based solid-liquid heat storage unit was • •

•

11

successfully tested and characterized by a series of dedicated charging/discharging and passive cooling experiments under controlled laboratory conditions. Heat exchange and cooling rate coefficients could be quantitatively determined. Modelling of the different experiments using a spatially aggregated heat balance model approach facilitated the revision of system and process understanding as well as the quantitative characterization of the storage behaviour. The heat balance model can be used to simulate the storage behaviour of the investigated lab-scale prototype, e.g. for different storage cycles or boundary conditions. The model, however, is not fully prognostic, e.g. for material or geometrical sensitivity analysis and optimization, or the implementation of the new storage concept in specific practical applications, which requires specific adaptations, system upscaling and operational optimizations of the modular system. The heat storage system is comparable to a standard hot water thermal storage tank of similar capacity in terms of volume or space requirements, storage efficiency and heat loss behaviour, while the heat transfer rates achieved with the laboratory prototype are lower than for typical hot water systems due to the purely conductive heat transfer. Optimization of heat exchanger material and geometry as well as storage matrix heat conductivities, however, may allow for an increase in achievable heat transfer rates of the solid-liquid heat storage system.

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• Moreover, the solid-liquid heat storage system has the big advantage

•

•

of a high structural strength, which allows its integration in or below a buildings foundation in the subsurface, and thus enables a spacesaving integration in densely developed urban environments, where room for voluminous above ground or basement installations usually is scarce. Accordingly, the spatial dimensions and configuration of a single- or multi-module system can be adapted and optimized to specific spatial and performance constraints of a particular application. For this purpose, process based and independently parameterized simulations on spatially discretized and sufficiently resolved numerical grids are required. The experimental data of this work, due to its highly resolved quality, provides a suitable basis for the development and verification of such numerical models. A similar approach, as published by Beier et al. [51], has proven very fruitful and the data provided has been used for model verification purposes in many papers. The general methodology of storage behaviour characterization by experimental process and parameter identification and simulation based quantitative analysis and prognosis can be transferred and applied to larger systems of coupled multiple storage units as well as other sensible heat storage systems, if appropriate operating and monitoring data is available.

[8]

[9]

[10] [11]

[12]

[13]

[14]

[15]

[16] [17]

Supplementary material [18]

The experimental data sets and additional diagrams are available in an Excel spreadsheet as supplementary material to this article from the journal homepage or from the authors upon request.

[19]

Acknowledgements

[20]

We gratefully acknowledge the support of this work by Mr. Henok Hailemariam (Geomechanics and Geotechnics department, Kiel University), Mr. Paul Liedtke and Ms. Katharina Bilitz for helping with the experimental work, Mr. David Urban-Werner (Bau-ABC Rostrup) and Mr. Bernd Wilke (Schwenk Zement KG).

[21]

[22]

[23] [24]

Funding We gratefully acknowledge funding provided by the Federal Ministry for Economic Affairs and Energy, Germany (BMWi, Grant 0325547B) and the support of the Project Management Jülich, Germany (PTJ).

[25]

[26]

Appendix A. Supplementary material

[27]

Supplementary data to this article can be found online at https:// doi.org/10.1016/j.apenergy.2019.113937.

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