This study is focused on the simulation and optimization of packed-bed solar thermal energy storage by using sand as a storage material and hot-water is used as a heat transfer fluid and storage as well. The analysis has been done by using the COMSOL multi-physics software and used to compute an optimization charging time of the storage. Parameters that control this optimization are storage height, storage diameter, heat transfer fluid flow rate, and sand bed particle size. The result of COMSOL multi-physics optimized thermal storage has been validated with Taguchi method. Accordingly, the optimized parameters of storage are: storage height of 1.4 m, storage diameter of 0.4 m, flow rate of 0.02 kg/s, and sand particle size 12 mm. Among these parameters, the storage diameter result is the highest influenced optimized parameter of the thermal storage from the ANOVA analysis. For nominal packed bed thermal storage, the charging time needed to attain about 520 K temperature is more than 3500 s, while it needs only about 2000 s for the optimized storage which is very significant difference. Average charging energy efficiency of the optimized is greater than the nominal and previous concrete-based storage by 13.7%, and 13.1%, respectively in the charging time of 2700 s.

Occasionally, more and more solar energy is being used for various purposes because of its affordability and dependability from both an environmental and financial standpoint. However, because it is sporadic, storage optimization is required to increase its consistency. When liquids or solids are heated or cooled, thermal energy can be stored. In the latent phase, thermal energy is stored during the phase transition, typically in proximity to an isothermal process, but in the sensible phase, thermal energy is stored in the material by increasing its temperature. The heat transfer fluid goes through an interior structure, such as a concrete matrix, or a solid storage material made up of spheres, irregularly shaped pebbles, or gravel, in packed-bed thermal reservoirs. The packing is enclosed in a steel containment vessel that has the potential to be pressured, together with one or more layers of insulation (Sarbu et al. [

Sensible thermal energy is the simplest and most common form of the build-up of thermal energy. Thermal stores that use specific heat of the substance accumulate energy by an increase in the temperature of the medium (a solid or liquid). This system operates on heat capacity and change in the temperature of the material during accumulating and discharging energy from the storage. The amount of thermal energy accumulated in a homogeneous material depends on its specific heat, temperature changes, and the volume change of material.

The amount of sensible thermal energy accumulated in a homogeneous material depends on its specific heat, temperature changes, and the volume change of material according. Development of effective and economical methods of storage of thermal energy obtained from Renewable Energy Sources is today a key issue for the development of renewable energy. Out of the locally available and cheap, that can store thermal energy are different types of sands (Diago et al. [

Rizeiqia et al. [

Concerning the numerical models developed for packed beds, a comparative investigation was published by Hanmant Rao et al. [

Trevisan et al. [

Phase change materials (PCMs) which are high potential for latent thermal energy storage (LTES) are broadly studied by many authors for different applications such as for building sector, drying, industrial purpose as well as home utility scale for hot water and food preparation (Manish et al. [

The aspect ratio is the diameter to height ratio

It has been reviewed in the aforementioned articles that almost all studies focused on sand as sensible thermal energy storage for low and high temperatures and literature review of different latent heat phase change materials (Barbi et al. [

The hot water is then enforced to flow through the stainless-steel tube (hot pipe) in a thermosyphon way and transfers the heat energy to the sand and fluid inside the storage tank. In the discharging phase of the stored heat is transferred through the stainless-steel tube from the storage material to injera baking pan. However, if the system is required to bake the pan cake directly from the receiver, the valves must be adjusted to guide the hot water to the baking pan. Then, the hot water after heating the pan will return to the thermal storage tank when off-sun baking and to the receiver when directly baking. The diagram below is briefly described how the system works.

The main objective of this study laid in the simulation and optimization of thermal energy storage. Based on the energy requirement of the injera baking pan for a session sizing, and simulation of the storage has been implemented. Hence, this procedure embraced a detailed description and numerical computations using the COMSOL multi-physics software which is the finite element-based program to optimize the thermal storage.

The circulation has simulated for different flow rates aiming of optimization. After optimization and at the time of installation loop aspect ratio

The 3-dimensional view of the packed bed thermal energy storage system is provided in

A simple storage process is the combined effect of three main sub-processes explicitly charging, storing and discharging. The capacity of the energy stored in the storage media is proportional to the temperature increase and the specific heat capacity or in this case packed bed sand in the storage container and is governed by:

The sand thermal energy storage system design investigated in this paper typically consists of a cylindrical sand packed bed. A larger product of density and heat capacity

For the fluid thermal storage alone, the stored hot fluid (at a higher temperature of

The thermal power delivery can be expressed as:

If the time of thermal power delivery is

Considering the space allotment, length and the heat transfer within the storage easily, the storage diameter

By considering the minimum surface area

Using the Engineering Equation Solver (EES) the optimal aspect ratio become 1. But due to the heat transfer rate and space and height allotment of the storage, for this study 0.4 aspect ratio is selected in designing the other parameters.

In conclusion, as the size of the storage material increases, the surface area per volume of the same mass will increase. Accordingly, the heat transfer coefficient of the storage in the charging phase will be improved because of increasing the contact of the hot and cold heat transfer fluid respectively with the solid media.

The particles’ diameter has a very significant influence on the heat transfer between particles and fluid and within the solid. Small solid size increases the total fluid/solid heat exchange surface and enhances stratification as it is observed by Lew et al. [

The mass flow rate for the system can be derived from the total energy required and the time taken to bake injera. Hence, the energy flow rate of the system between the baking reservoir and the thermal storage is:

Initially, the storage is filled with fluid and sand at an ambient temperature of 25°C. But, after a charging and discharging cycle reaching the stable state, the lower temperature has been adjusted to 100°C based on the outlet the temperature of the baking pan in few kinds of literature conducted researches and numerical models reviewed above. The inlet temperature of the heat transfer fluid is adjusted to 250°C. The specific heat capacity of hot water from the thermodynamic property of hot water or steam using Engineering Equation Solver (EES) and that of sand is 0.85 kJ/kg K. The density of sand is 1600 kg/m^{3}.

The average time taken to bake as reviewed is 2 up to 3 h. An average time of 2.5 h is taken to design for this work.

Therefore, the mass flow rate of the system can be obtained from the following relation:

For this study, the energy requirement for Injera baking as has been calculated is 37.841 MJ. This energy is estimated as higher energy consumption due to safety in case of high sunshine hour days.

The whole energy stored in the material after fully charged is expressed in the formula below. Here, the temperature of the solid and fluid will be the same as in Jaluria [

The ideal storage material or the thermocline storage using the fluid that is hot water alone is considered first to design the volume capacity of the storage material. In cases where a solid medium is mainly used for the thermal storage, with a fluid flowing through in direct contact with particle bed to carry heat in and out, the storage tank volume,

According to the given values and

Mass of the storage:

The total volume of the storage is equal to 0.173 m^{3}. The volume ratio of the storage is 4:1 sand to hot water, respectively. Hence, the sand volume is 0.1384 m^{3} and hot water 0.0346 m^{3}.

Before, modeling of the heat transfer within the packed bed mathematically, some considerations must be specified. Hence the following conditions are considered: The assumptions generally made for mathematical analysis of heat transfer in sand bed storage systems are the following: (i) there is no heat transfer between the vessel and the environment which is thermally insulated, i.e., heat loss to the environment is neglected, (ii) sand particles are arranged uniformly, and (iii) the flow is axial that is top to down only.

Initially _{C} in this case. But at any other time, i.e.,

Based on the above designed parameters and their properties from literatures, the following properties and control variable are considering during the design and simulation of the thermal storage. Properties of sand and water is given in

Storage properties | Thermal conductivity (W/m K) | Specific heat (kJ/kg K) | Density (kg/m^{3}) |
---|---|---|---|

Sand | 2.4 | 850 | 1600 |

Water | – | 4128 | 1000 |

Control parameters | Unit | Quantity |
---|---|---|

Storage height | m | 1.125 |

Storage diameter | m | 0.45 |

Sand particle size | m | 12 |

Flow rate | kg/s | 0.0167 |

Inlet velocity (u) | m/s | 4.4543e^{−4} |

Sand initial temperature |
°C | 100 |

Water initial temperature |
°C | 100 |

Inlet temperature (T_{in}) |
°C | 250 |

Thermal storage system pressure | Bar | 45 |

The thermocline storage efficiency is defined as an overall process efficiency that is a combination of the charging, storing, and discharging efficiencies. Based on the first law of Thermodynamics, efficiency is the fraction of heat recovered by the charging, storing, and discharging processes. The following equation is formulated by Chan et al. [

For this study charging energy efficiency only has been evaluated. This is the efficiency based on the storage material capability to gain thermal energy from HTF at a given period of time. The Charging energy efficiency had been reported by Mawire et al. [

In this section, storage height, storage diameter, mass flow rate, and sand particle size, of the solar thermal energy storage will be simulated and optimized concerning the charging time. These parameters are derived from the nominal parameters values of the solar thermal energy storage system designed and simulated in previous work. To find the optimal combined parameter out of the four parameters aforementioned, different values are given for each factor. These values are the levels of the parameters. In this study, there are totally four parameters or factors and three levels. The three levels are a guess value, a minimum and maximum value. The total trail of these factors and levels in combination is eighty-one which is difficult to simulate in COMSOL Multiphysics with the same time due to time and computer capacity available. Therefore, it is necessary to optimize these parameters in two phases. Phase one combination of the parameters which are twenty-seven trial blends of storage height, storage diameter, and flow rate. Phase two optimization embraces three levels of sand particle size factor with the total trials of three. The good result of the trials is based on the larger the better principle for temperature distribution and surface enthalpy of the storage within the charging time, correspondingly.

Phase one optimization has twenty-seven blended trials as can be observed in

Trials | H (m) | Flow rate (kg/s) | D (m) |
---|---|---|---|

1 | 0.85 | 0.01 | 0.4 |

2 | 0.85 | 0.01 | 0.46 |

3 | 0.85 | 0.01 | 0.52 |

4 | 0.85 | 0.015 | 0.4 |

5 | 0.85 | 0.015 | 0.46 |

6 | 0.85 | 0.015 | 0.52 |

7 | 0.85 | 0.02 | 0.4 |

8 | 0.85 | 0.02 | 0.46 |

9 | 0.85 | 0.02 | 0.52 |

10 | 1.8 | 0.01 | 0.4 |

11 | 1.8 | 0.01 | 0.46 |

12 | 1.8 | 0.01 | 0.52 |

13 | 1.8 | 0.015 | 0.4 |

14 | 1.8 | 0.015 | 0.46 |

15 | 1.8 | 0.015 | 0.52 |

16 | 1.8 | 0.02 | 0.4 |

17 | 1.8 | 0.02 | 0.46 |

18 | 1.8 | 0.02 | 0.52 |

19 | 1.4 | 0.01 | 0.4 |

20 | 1.4 | 0.01 | 0.46 |

21 | 1.4 | 0.01 | 0.52 |

22 | 1.4 | 0.015 | 0.4 |

23 | 1.4 | 0.015 | 0.46 |

24 | 1.4 | 0.015 | 0.52 |

25 | 1.4 | 0.02 | 0.4 |

26 | 1.4 | 0.02 | 0.46 |

27 | 1.4 | 0.02 | 0.52 |

Optimization of parameters is done to have great control over quality, productivity and cost aspects of the process. Taguchi method is used to validate the optimization simulated in COMSOL Multiphysics for this study. This method is a statistical analysis technique and was innovated and contributed by Genichi Taguchi to robust design and quality planning activities through the integrated use of loss functions and orthogonal arrays in industrial level. The Taguchi method contains system design, parameter design, and tolerance design procedures to achieve a robust process and result in the best product quality (Karna et al. [_{9} orthogonal array is used to represent the twenty-seven trials that were simulated in COLMSOL and these trials are reduced to only nine blended parameters. Hence, the L_{9}, i.e., nine trials form of Taguchi method with three factors of storage height, storage diameter, and mass flow rate, and three levels of for is shown in

Trials | H (m) | Flow rate (kg/s) | D (m) |
---|---|---|---|

1 | 0.85 | 0.01 | 0.4 |

2 | 0.85 | 0.015 | 0.46 |

3 | 0.85 | 0.02 | 0.52 |

4 | 1.8 | 0.01 | 0.46 |

5 | 1.8 | 0.015 | 0.52 |

6 | 1.8 | 0.02 | 0.4 |

7 | 1.4 | 0.01 | 0.52 |

8 | 1.4 | 0.015 | 0.4 |

9 | 1.4 | 0.02 | 0.46 |

It can be noticed from

Having completed, phase one optimization with storage height, storage diameter and flow rate, phase two optimization with sand particle size parameterizing is followed. In this phase, three levels of the sand particle sizes are studied holding the first phase optimized parameters (storage height = 1.4 m, storage diameter = 0.4 m, and flow rate = 0.02 kg/s) constant. The sizes are 9, 11, and 14 mm and inserted into COMSOL.

The 2D simulated nominal designed storage in

The temperature conditions for the cut point 2D graph presented in at the top, middle and bottom of the storage as a function of charging time is plotted in the following

The simulation results of twenty-seven trails are tabulated and graphically compared to select the best blend of parameters.

Temperature Distribution of a sand particle at the bottom specified point (x = 0.2 m, y = 0.02 m) indicated in the following figures of

In this split, the charging time of all trials is much more than the split graph of

From

Trials | H (m) | Flow rate (kg/s) | D (m) | t (s) | Temperature (K) | Enthalpy (kJ/kg) |
---|---|---|---|---|---|---|

1 | 0.85 | 0.01 | 0.40 | 3600 | 482.12 | 780.09 |

2 | 0.85 | 0.01 | 0.46 | 3600 | 448.83 | 642.68 |

3 | 0.85 | 0.01 | 0.52 | 3600 | 438.03 | 598.09 |

4 | 0.85 | 0.015 | 0.40 | 3600 | 515.42 | 917.56 |

5 | 0.85 | 0.015 | 0.46 | 3600 | 472.91 | 742.09 |

6 | 0.85 | 0.015 | 0.52 | 3600 | 453.63 | 662.49 |

7 | 0.85 | 0.02 | 0.40 | 3600 | 522.40 | 946.35 |

8 | 0.85 | 0.02 | 0.46 | 3600 | 494.95 | 833.07 |

9 | 0.85 | 0.02 | 0.52 | 3600 | 465.78 | 712.63 |

10 | 1.8 | 0.01 | 0.40 | 3600 | 495.95 | 837.20 |

11 | 1.8 | 0.01 | 0.46 | 3600 | 466.72 | 716.52 |

12 | 1.8 | 0.01 | 0.52 | 3600 | 445.68 | 629.67 |

13 | 1.8 | 0.015 | 0.40 | 3600 | 519.98 | 936.37 |

14 | 1.8 | 0.015 | 0.46 | 3600 | 493.50 | 827.07 |

15 | 1.8 | 0.015 | 0.52 | 3600 | 462.84 | 700.50 |

16 | 1.8 | 0.02 | 0.40 | 3600 | 522.61 | 947.23 |

17 | 1.8 | 0.02 | 0.46 | 3600 | 513.61 | 910.40 |

18 | 1.8 | 0.02 | 0.52 | 3600 | 473.72 | 745.53 |

19 | 1.4 | 0.01 | 0.40 | 3600 | 515.96 | 919.76 |

20 | 1.4 | 0.01 | 0.46 | 3600 | 477.07 | 759.25 |

21 | 1.4 | 0.01 | 0.52 | 3600 | 446.26 | 632.07 |

22 | 1.4 | 0.015 | 0.40 | 3600 | 522.95 | 948.65 |

23 | 1.4 | 0.015 | 0.46 | 3600 | 505.41 | 876.23 |

24 | 1.4 | 0.015 | 0.52 | 3600 | 458.34 | 681.93 |

25 | 1.4 | 0.02 | 0.40 | 3600 | 523.13 | 949.40 |

26 | 1.4 | 0.02 | 0.46 | 3600 | 521.32 | 941.90 |

27 | 1.4 | 0.02 | 0.52 | 3600 | 469.62 | 728.50 |

From the

For the optimized parameters, the charging time for sand and hot water at the same height of the thermal storage point is different as indicated in the above discussion. The reason is that the heat transfer fluid and the hot water storage are homogenous that makes the heat transfer faster than to the sand.

Based on the response variable of the average temperature profile of the thermal storage, the Taguchi method in the Minitab software has analyzed and validated the result of COMSOL optimized blended parameters. The result of the optimization of parameters using Taguchi is provided in

Trials | H (m) | Flow rate (kg/s) | D (m) | Temperature (Kelvin) | SNRA4 | MEAN4 |
---|---|---|---|---|---|---|

1 | 0.85 | 0.01 | 0.4 | 482.12 | 53.66 | 482.12 |

2 | 0.85 | 0.015 | 0.46 | 472.91 | 53.49 | 472.91 |

3 | 0.85 | 0.02 | 0.52 | 465.78 | 53.36 | 465.78 |

4 | 1.8 | 0.01 | 0.46 | 466.72 | 53.38 | 466.72 |

5 | 1.8 | 0.015 | 0.52 | 462.84 | 53.30 | 462.84 |

6 | 1.8 | 0.02 | 0.4 | 522.61 | 54.36 | 522.61 |

7 | 1.4 | 0.01 | 0.52 | 446.26 | 52.99 | 446.26 |

8 | 1.4 | 0.015 | 0.4 | 522.95 | 54.36 | 522.95 |

9 | 1.4 | 0.02 | 0.46 | 521.32 | 54.34 | 521.32 |

The largest Signal-to-Noise ratio from SNRA4 is 54.36934453 in the blended parameters of H = 1.4 m, flow rate 0.015 kg/s and D = 0.4 m which is trial 22 in

From this Signal-to-Noise ratio in the figure, it can be simply identified that where the optimal point for the three parameters. Since the starting point for the optimization is the larger the better for the cross-section average temperature profile of the system, the optimal points are storage height (H) at 1.4 m, the flow rate at 0.02 kg/s and storage diameter (D) at 0.4 m. Hence, the finest combination of the parameters of the storage is (H = 1.4 m, flow rate = 0.02 kg/s, and D = 0.4) which is perfectly equal to the blended parameter optimized using COMSOL multi-physics in

To know the contribution of these parameters in the optimization process of the thermal storage, ANOVA analysis result is necessary. This analysis result is put in

Criterion | Test statistic | F | Num | Denom | |
---|---|---|---|---|---|

Wilks | 0.10993 | 8.096 | 2 | 2 | 0.110 |

Lawley-hotelling | 8.09629 | 8.096 | 2 | 2 | 0.110 |

Pillai’s | 0.89007 | 8.096 | 2 | 2 | 0.110 |

Roy’s | 8.09629 |

Criterion | Test statistic | F | Num | Denom | |
---|---|---|---|---|---|

Wilks | 0.04369 | 21.89 | 2 | 2 | 0.044 |

Lawley-hotelling | 21.8899 | 21.89 | 2 | 2 | 0.044 |

Pillai’s | 0.95631 | 21.89 | 2 | 2 | 0.044 |

Roy’s | 21.88997 |

Criterion | Test statistic | F | Num | Denom | |
---|---|---|---|---|---|

Wilks | 0.02502 | 38.963 | 2 | 2 | 0.025 |

Lawley-hotelling | 28.962 | 28.963 | 2 | 2 | 0.025 |

Pillai’s | 0.97498 | 38.963 | 2 | 2 | 0.025 |

Roy’s | 38.96260 |

General Linear Model: Temperature

From the ANOVA analysis of the parameter’s contribution displayed here above, the

The optimized temperature distribution in the storage cross-section average temperature is analyzed for the three sand particle size parameters. For the cut point 2D analysis, a specified point for sand bed and hot water temperature is also evaluated as in the case of phase one optimization.

Parameterizing of the sand particles size of the thermal storage has not shown any significant change in the sand and hot water temperature as indicated in the respective graph on

In the packed bed sensible thermal energy storage (STES), pressure drop is key concern since higher pressure drop leads into lower energy storage efficiency. As can be observed fro the graph of

From the surface temperature simulated below, the temperature profile is varying with time. Surface temperature comparison between nominal and optimized solar thermal energy storage system (STES) are shown in

In this section, the temperature profile of the point in the bottom (outlet), the middle and the top (inlet) of the packed bed storage for sand and hot water storage materials are analyzed and compared depending the charging time. The detailed discussion on the comparisons of optimal and nominal thermal energy storage is argued from the following graph.

The

The bottom hot water temperature of the optimized storage and the middle sand particle temperature of the nominal storage has gotten a temperature of 520 K approximately at the same charging time of about 1900 s. This is an admiring significant difference between the optimized and nominal parameters in charging time of the storage. Because the time taken to charge the optimal storage is approximately the same with the charging time to charge half of the nominal storage. The hot water and sand particle at the middle of the optimized storage attained a temperature of 520 K at approximately 900 and 1000 s respectively while for the nominal storage, it needs about 1900 and 2000 s, respectively.

From the temperature and enthalpy graph plotted in

Even, there is no article report for the same storage material designed and optimized, Prasad et al. have reported the charging energy efficiency of concrete, cast iron and cast steel in the title of Design and optimization of lab-scale sensible heat storage. For this study, the concrete charging energy efficiency has been chosen to compare and the results are shown in

The charging energy efficiency of the optimized sand thermal storage approached to 100% charged approximately in 2000 s whereas for the nominal sand thermal storage is about 87% charged for the same time. The charging energy efficiency of the previous work on concrete is higher than the optimized and nominal sand thermal storage of this study up to about 600 and 1600 s, respectively. Above the charging time of 600 and 1600 s charging energy efficiency, the optimized and nominal sand based thermal storage respectively are greater than concrete charging energy efficiency. For instance, the charging energy efficiency of sand optimized thermal storage in 2000 s is approximately 100% whereas for the thermal storage of sand nominal and concrete from literature is about 87% and 80%. During the charging time of 0 to 2700 s, the average charging energy efficiency of the optimized sand thermal storage is greater than the nominal sand thermal storage and previous work concrete sensible thermal storage by 13.7% and 13.1%, respectively.

Mass of the storage:

The total volume of the storage is equal to 0.173 m^{3}. The volume ratio of the storage is 4:1 sand to hot water, respectively. Hence, the sand volume is 0.1384 m^{3} and hot water 0.0346 m^{3}.

The enthalpy

In phase one optimizing that includes storage height, storage diameter, and flow rate, the optimum blended parameters obtained are storage height 1.4 m, storage diameter 0.4 m and flow rate0.02 kg/s considering the charging time for temperature and enthalpy distribution. These results have been validated by Taguchi method. From the ANOVA analysis in Minitab software, out of these parameters, storage diameter with 2.5%

The result of the average cross-section temperature and average total enthalpy of the optimized storage have been changed to 523.15 K, and 0.53 MJ/kg in the charging time of 4000 s.

In contrast to the nominal storage that attained nearly 0.49 MJ/kg of enthalpy with the provided charging time of 4000 s, the optimized storage recorded this amount of enthalpy with the charging time of 1400 s which is a very significantly different result.

Similarly, while the cross-section average temperature of optimized thermal storage charged and reached about with the charging time of 2000 s, the nominal one attained this temperature 1500 s later to the optimized, i.e., 3500 s.

During the charging time of 0 to 2700 s, the average charging energy efficiency of the optimized sand thermal storage is greater than the nominal sand thermal storage and previous work on concrete by 13.7% and 13.1% respectively.

Sensible Thermal Energy Storage

Phase Change Material

Global Positioning System

Heat Transfer Fluid

Specific heat of the sand

Specific heat capacity of fluid

Initial Sand Temperature

Initial fluid temperature

Diameter of the storage

Height of the storage

Density

Signal-to-Noise ratio

Volume

Flow rate

Time change

Porosity

Surface area

Mass flow rate

Hot temperature

Cold temperature

Specific volume

The author, Matiewos Mekonen Abera, acknowledges the Jimma University and Aksum University for providing the necessary support. Partial support from JiT Center of Excellence is gratefully acknowledged.

The authors received no specific funding for this study.

The authors confirm contribution to the paper as follows: Matiewos Mekonen Abera: study conception and design; Venkata Remayya Ancha: data collection; Balewgize Amare: analysis and interpretation of results; L. Syam Sundar: data analysis and comparison of the data; Kotturu V. V. Chandra Mouli: initial drat writing. All authors reviewed the results and approved the final version of the manuscript.

This statement should make clear how readers can access the data used in the study and explain why any unavailable data cannot be released.

The authors declare that they have no conflicts of interest to report regarding the present study.