A comparative study on the modeling of a latent heat energy storage system and evaluating its thermal performance in a greenhouse
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Abstract
Thermal Energy Storage (TES) systems can be compared with batteries. As batteries can be charged when electricity is available for using during the power failure, TES systems can do the same for the thermal energy, i.e., they can absorb the available heat in one cycle, called charge cycle, and release it in a consecutive cycle, called discharge cycle. Among different kinds of TES systems, Phase Change Materials (PCM) have drawn considerable attention, since by changing from one phase to another, they can exchange a significant amount of energy in a small temperature difference. In this quest, a one dimensional mathematical model is solved using two different techniques and the results are compared together; one method is based on the enthalpy and the other is based on the effective heat capacity as well. Secondly, through eight experiments designed by using factorial approach, effects of inlet air velocity and temperature on the outlet stream has been investigated. The results proved that having a determined temperature difference between the inlet air and the PCM in both hot and cold cycles can enhance the efficiency. Finally, the feasible applications of a LHTES system for reducing the temperature swing in a greenhouse is studied numerically and the results are compared with experimental values. As a result, by using this passive coolant system diurnal internal temperature can be reduced for 10 °C.
Nomenclature
- a
Width of flat slabs [m]
- A
Area of cross section of duct = ab [m^{2}]
- A_{i}
Area of each face of the greenhouse [m^{2}]
- A_{G}
Total area of the greenhouse faces [m^{2}]
- b
Air gap between parallel slabs [m]
- c_{p}
Heat capacity of PCM [J/kg°C]
- c_{pg}
Heat capacity of air [J/kg°C]
- D_{e}
Equivalent Diameter (m)
- Δx
Spatial length [m]
- Δt
Time step [sec]
- E
Efficiency
- h
Heat transfer coefficient between air and flat slabs [W/m^{2}°C]
- i
Spatial step counter
- j
Time step counter
- k_{p}
Thermal conduction of PCM [W/m^{2}°C]
- L
Length of the Bed [m]
- m_{ACH}
Mass flow rate of air change [kg/s]
- m_{LHTES}
Mass flow rate of air which passes through LHTES [kg/s]
- m_{p}
Mass of PCM [kg]
- Nu
Nusselt
- P
Perimeter [m]
- Pe
Peclete number
- Pr
Prantl number
- Q
Transferred heat [J]
- Re
Reynolds Number
- S_{i}
Solar radiation [w/m^{2}]
- t
Time [sec]
- T
Temperature of the inside air of the LHTES [°C]
- T_{E}
Environmental temperature [°C]
- T_{G}
Temperature of the inside air of the greenhouse [°C]
- T_{i}
Initial temperature [°C]
- T_{p}
PCM temperature [°C]
- U
Dimensionless parameter of regenerator
- U_{G}
Natural heat transfer coefficient between the greenhouse and outlet environment [W/m^{2}°C]
- U_{p}
Overall heat transfer coefficient [W/m^{2}°C]
- V
Total volume of the greenhouse [m^{3}]
- x
Length variable [m]
- τ
Process termination [s]
- τ_{G}
Transmittance of the greenhouse cover to the direct solar radiation
- _{ρ}
Density of air [kg/m^{3}]
- β
Thermal Expansion [K^{−1}]
- α
Thermal diffusivity [m^{2}/s]
- ν
Air velocity [m/s]
- δ
Thickness of slabs [m]
- _{Λ}
Dimensionless parameter of regenerator
- _{Π}
Dimensionless parameter of regenerator
- γ_{G}
Constant of the proportion of solar radiation entering the greenhouse
1 Introduction
The ever-increasing trend of global warming and greenhouse gas emissions, combined with pollution and limited energy resources are the main reasons behind the attempts devoted to improve the use of various energy sources. The other solution which must be taken into account is to improve the energy efficiency. With regard to this solution, latent heat thermal energy storage (LHTES) systems are interesting candidates for reduction of mismatch between energy supply and demand.
Since energy is produced and transferred in the form of heat in many countries, thermal energy storage (TES) deserves to be studied in detail. One of the oldest usages of TES goes back to the time when ice was provided from frozen lakes and rivers in the winter. The collected ice was then kept in well insulated warehouses in order to satisfy the needs for food conservation and air conditioning through the year. The air conditioning of Hungarian Parliament Building in Budapest is still done by ice harvested from Lake Balaton in the winter [1].
Storing of thermal energy takes place by using a change in the internal energy like: sensible heat, latent heat or thermochemical [2]. Among these methods, LHTES systems have drawn considerable attention due to their high storage capacity and also their near isothermal operation [1, 2]. PCMs can absorb or release a high amount of energy in a small temperature difference via phase change from solid to liquid or vice versa, respectively.
So many studies have been performed for the modeling of LHTES systems and so many methods have been illustrated. One of the major techniques is related to the moving boundary problems. Unknown interface of phase change and its nonlinear movements have made the moving boundary problems so complex [3, 4]. Furthermore, this formulation can produce acceptable results mostly for PCMs with single temperature of phase change. However, most of the materials are not pure and their phase change occurs in a temperature range instead of a single point. Another approach, as suggested by Regin [5], is called “Enthalpy Formulation”. This formulation does not require knowing where phase change takes place. The other method (which can also be categorized as a subset of enthalpy formulation) is “Effective Heat Capacity”. In this method, the correlation between the heat capacity and temperature in the phase change transition range can be obtained by using differential scanning calorimetry (DSC) analysis. Therefore the formulation can be derived without considering the phase change [6].
30-40% of energy consumption is related to the buildings [7] and the significant portion of this amount is used in hot summer days by cooling systems having compressor. Consequently many studies have focused on the usage of LHTES systems in cooling applications which is called free cooling. In order to condition the indoors air by changing the material phase, PCM can be embedded in a heat exchanger. During the night, PCM solidifies and the energy can be released (discharge cycle) and subsequently during the hot day, via a move through the heat exchanger, air is cooled and PCM melts (charge cycle) [8, 9].
The results of the simulations using the empirical model presented by Lazaro et al. [10] showed that the capability of the same PCM to maintain temperature levels below a certain temperature depends upon the heating power. Therefore, for any application where an almost constant temperature is required, the power demand must be taken into account. To maintain a specific temperature level when the cooling demand is high, the PCM phase change temperature should be lower. On the other hand, for very low cooling demands, the phase change temperature should be close to the objective temperature level.
Greenhouses are enveloped places in which temperature of the air must be kept in a certain limitation due to agricultural requirements. Providing this temperature limitation for crop thermal comfort is a major challenge, since the coverings need to allow light into the structure, they conversely cannot insulate very well and consequently unwanted heat loss/gain occurs. Lazaar et al. [11] conducted an experimental study to evaluate the performance of a LES unit inside a tunnel greenhouse. A shell and tube heat exchanger containing 10 kg of CaCl_{2}.6H_{2}O as PCM was used in this work. They proved that by using the built LHTES system, the air temperature inside the greenhouse can be reduced by a difference of 5 °C to 8 °C in comparison to a greenhouse without the storage system.
Bouadila et al. [12] made an experimental study to evaluate the nighttime recovered heat of the solar air heater with latent heat storage collector (SAHLSC) in an east-west oriented greenhouse. It was shown that by using this passive heating system, 31% of the total heating requirements can be provided. Furthermore, they concluded that the payback period of the proposed system is approximately 5 years, if the passive heater be used only three months a year.
In the present research work, a one-dimensional model for a LHTES system containing flat slabs of PCM is solved through two different methods; in one method Effective Heat Capacity is used to reckon the latent heat during phase transition, while in the later one which is called Enthalpy approach, phase change temperature is assumed to be constant. Afterwards a detailed study is performed on a small scale LHTES system by using numerical and experimental data. Finally, temperature changes of a greenhouse located in Tunisia, with and without using LHTES system, are calculated theoretically and the results are compared with experimental values.
2 Mathematical model
2.1 LHTES system
For this part two approaches are used. In both approaches, assumptions and equations are quite the same. The only division lies in the calculation of the latent heat. The first method uses effective heat capacity (C_{p} = C_{p}(T)), while the later one separates the phase change process into three sections; one in the solid phase, second during the phase change and third, the liquid phase.
2.1.1 First approach-effective heat capacity
- 1-
Axial conduction in the air is neglected in the direction of the flow. This assumption is verified by the fact that the Peclet number is greater than 100 as recommended by [13] (Pe > 225).
- 2-
Temperature variations of the air normal to the flow are not considered.
- 3-
No super cooling happens in the PCM.
- 4-
Thermophysical properties of the PCM are constant and are the same for both phases, except the heat capacity in case of “Effective Heat Capacity”, which is a function of temperature. This is due to the fact that temperature variations in the system are limited.
- 5-
Thermophysical properties of air are constant. This assumption is valid because temperature variations in the process are limited.
- 6-
Heat transfer coefficient is the same for all the slabs.
- 7-
Heat loss to the surrounding is negligible.
- 8-
Air residence time in the bed is small in comparison with the period duration.
- 9-
Heat transfer by radiation is neglected.
- 10-
Heat capacity and thermal resistance of PCM containers are not considered.
- 11-
Due to the low thickness of slabs containing PCM (3 mm), natural convection in the melted parts of the PCM is neglected.
In Eq. (3), a dimensionless parameter can be introduced:
Λ represents the ratio of “regenerator length” to the "mass flow rate of the passing air". The transferred heat in each control volume is:
Substituting Eq. (3) into Eq. (5) gives:
Since all the heat transferred to the air is provided by the PCM, energy balance for each control volume of the PCM can be written as:
This dimensionless parameter is defined as the ratio of “mean bed temperature change” to the “mean air temperature change”. The dimensionless parameters in Eqs. (4) and (10) are the same as reduced length and utilization factor of sensible heat storage (SHS), respectively [14]. By using this similarity, another dimensionless parameter can be introduced, known as reduced period, which is a criterion of the bed heat capacity:
Finally by substituting Eqs. (4), (10) and (11) into Eq. (9), Eq. (12) can be developed as:
Generally, the introduced heat transfer correlations for the flow of air between the parallel plates are divided into two categories: constant and equal temperatures and constant and equal wall heat fluxes. However, since the problems associated with the phase change materials take place in a constant temperature or a limited temperature swing, the case of constant and equal temperatures is used [15].
2.1.2 Second approach-enthalpy method
2.2 Air temperature inside the greenhouse
- 1-
Temperature gradient inside the greenhouse is ignored.
- 2-
Internal air is completely dry and does not have any moisture.
- 3-
Greenhouse is empty.
- 4-
Solar radiation is the same for all the faces of the greenhouse.
3 Experimental setup
Specifications of the flat slabs
Dimensions of flat slabs [mm] | Mass of the injected PCM in each container [gr] | Numbers of each container |
---|---|---|
3 × 38 × 210 | 26 | 2 |
3 × 53 × 210 | 38 | 2 |
3 × 75 × 210 | 53 | 1 |
4 Results
4.1 Validation of the LHTES models
As illustrated in foregoing plots, the accuracy of the two solutions is almost equal for the same equations. These models are quite similar before and after the phase change. The major difference between two models lies during the phase transition; while using “Effective Heat Capacity” model, by changing the value of “heat capacity” proportional to the temperature of the PCM in each time interval, the outlet temperature changes slowly. On the other hand in “Enthalpy Method” the outlet air temperature is almost kept constant in accordance to constant temperature of the phase transition.
Since in this study the used PCM (PEG1000), melts/solidifies during a wide temperature difference, “Effective Heat Capacity” is used in the following calculations.
4.2 Parametric study of the LHTES models
In order to evaluate the performance of the built LHTES system, the following correlation was used for efficiency:
As shown in Fig. 13, process duration has a significant effect on the efficiency. So for evaluating the effect of Λ on the efficiency, considering a constant criterion for the process duration seems to be necessary. Thus for all of the calculations, process termination, i.e., the time in which inlet and outlet temperatures become the same, was considered for the process duration. As shown in Fig. 14, by increasing Λ, efficiency can be improved. It means that in the same length reducing the inlet air velocity is the solution to improve the performance of the LHTES system.
4.3 Experimental results
Cold cycle related data and results
Experiment | 1 | a | b | ab |
---|---|---|---|---|
Inlet air temperature [_{°C}] | 15 | 20 | 15 | 20 |
Air velocity between slabs [m/s] | 0.2 | 0.2 | 0.26 | 0.26 |
Process termination [min] | 117 | 130 | 92 | 103 |
Q_{max} [J] = m_{g}c_{pg}(T_{initial} − T_{inlet}(t))τ | 265,973 | 249,123 | 262,192 | 250,229 |
\( {Q}_{real}\ \left[\mathrm{J}\right]={m}_g{c}_{pg}{\int}_0^{\tau}\left({T}_{out}(t)-{T}_{inlet}(t)\right) d\theta \) | 97,187 | 85,728 | 95,363 | 80,249 |
Efficiency [%] | 36.5 | 34.4 | 36.37 | 32.07 |
Hot cycle related data and results
Experiment | 1 | a | b | ab |
---|---|---|---|---|
Inlet air temperature [_{°C}] | 50 | 55 | 50 | 55 |
Air velocity between slabs [m/s] | 0.2 | 0.2 | 0.26 | 0.26 |
Process termination [min] | 205 | 152 | 180 | 135 |
Q_{max} [J] = m_{g}c_{pg}(T_{initial} − T_{inlet}(t))τ | 410,010 | 374,700 | 473,088 | 415,991 |
\( {Q}_{real}\ \left[\mathrm{J}\right]={m}_g{c}_{pg}{\int}_0^{\tau}\left({T}_{out}(t)-{T}_{inlet}(t)\right) d\theta \) | 191,687 | 187,290 | 198,437 | 193,702 |
Efficiency[%] | 46.7 | 49.98 | 41.94 | 46.56 |
- 1-
In the cold cycle, increasing the passing air velocity and reducing its temperature, are two possible ways to shorten the process duration.
- 2-
Increasing passing air velocity reduces the efficiency. It is probably related to the shortened residence time of the air in the bed.
- 3-
In the cold cycle, increasing inlet air temperature reduces the efficiency.
- 1-
In the hot cycle, increasing passing air velocity and increasing its temperature are two possible ways for shortening the process duration.
- 2-
Increasing passing air velocity reduces the efficiency. It is probably related to the shortened residence time of the air in the bed.
- 3-
In the hot cycle, increasing the inlet air temperature increases the efficiency.
As can be seen there is a consistency between numerical and experimental results and analyses.
4.4 The feasibility study on the possible applications of LHTES
4.4.1 Simulation of the greenhouse
Other parameters for the greenhouse and the LHTES system
Description | Value |
---|---|
Greenhouse volume[m^{3}] | 3 (height) × 1.5(width) × 2(length) |
Cover | Single polyethylene |
τ_{G} = 0.6 [15] | |
γ_{G} = 0.4 [11] | |
U_{G} = 8 | |
Air | ρ_{air} = 1.12 [kg/m^{3}] |
c_{pg} = 1005 [J/kg. ^{°}C] | |
Air change per hour(ACH) | 1 |
Number of slabs | 16 |
Dimensions of slabs [m] | 0.42 × 0.205 × 0.003 |
Velocity of air between slabs [m/s] | 1.335 |
PCM | ρ = 1093 [kg/m^{3}] |
ΔT_{m} = 33 − 40 [^{°}C] | |
Total mass = 10 kg |
4.4.2 Effect of mass flow rate on air temperature inside the greenhouse
5 Conclusion
With the importance of thermal energy, there is a major need to expand the optimizing utilities. In the present research work, by using experimental and numerical studies, a small scale built heat exchanger packed with flat slabs of PCM has been evaluated comprehensively. A one dimensional model considering the axial conduction in the PCM has been solved through two different approaches; both solutions have been validated by experimental values gained from the built prototype. Through comparing both mechanisms, it can be concluded that effective heat capacity solution is preferred when the phase transition takes place in a wide temperature range and also an accurate correlation exists between temperature and heat capacity. However, in the lack of the precise correlation, the proposed Enthalpy method can generates promising outputs.
Experimental investigations on the effects of inlet temperature and velocity of the passing air have proved that process termination and efficiency can be affected significantly, i.e., higher temperature difference can shorten the process termination and enhance the efficiency, while higher velocities can reduce the process duration and efficiency.
Existence of the “greenhouse effect” in greenhouses leads to a peak in diurnal temperature. To evaluate the applicability of LHTES systems as a solution for this problem, a scale up study has been performed numerically and it has been proved that by using PCMs, the excess unwanted heat during the hot days can be absorbed and the internal air can be cooled for 10 °C during the hottest hours. Importance of using a multi-speed fan is an important note that must be brought to attention; i.e., during hot days lower speed improves the cooling performance of LHTES while during short nights higher speed guaranties complete solidification. For further investigations, more realistic experimental studies may be proper for those who are interested.
Notes
Acknowledgements
The authors would like to thank “Iranian Fuel Conservation Organization” and research department of Tarbiat Modares University for their financial supports.
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