# Investigation of Stratified Thermal Storage Tank Performance for Heating and Cooling Applications

^{*}

## Abstract

**:**

## 1. Introduction

- Controls are simpler than phase change storage systems.
- Water can also serve as a water reservoir for fire protection.
- Stored water can serve as a standby source for heating/cooling in the case of power outage.
- Less costly than other mediums.

- Natural convection from the tank to the surrounding environment.
- Mixing of hot and cold water due to the kinetic force of water entering from the top or bottom of the tank.
- Thermal diffusion and conduction within the water inside the tank and with storage tank wall, piping and other materials inside the tank.
- Aspect ratio of the storage tanks.

## 2. Analysis

- Density$:\text{}999.7\text{}\mathrm{kg}/{\mathrm{m}}^{3}$
- Dynamic viscosity$:\text{}1.307\times {10}^{-3\text{}}\mathrm{kg}/\mathrm{ms}$
- Thermal expansion coefficient$:\text{}0.0733\times {10}^{-3}\text{}/\mathrm{K}$

- Reduced inflow velocity.
- Increased temperature difference.
- Increased distance between ports (increasing the aspect ratio).

## 3. Simulation

- Continuity:$$\frac{\partial \rho}{\partial t}+\nabla \xb7\left(\rho \mathit{U}\right)=0$$
- Momentum:$$\frac{\partial \left(\rho \mathit{U}\right)}{\partial t}+\nabla \xb7\left(\rho \mathit{U}\otimes \mathit{U}\right)=-\nabla \rho +\nabla \xb7\tau +{S}_{M}$$

^{−4}for pressure and momentum and 10

^{−6}for the rest of the values.

## 4. Results and Discussions

#### 4.1. Analytical

#### 4.2. Simulation

#### 4.2.1. Model Validation

#### 4.2.2. Simulation Results

## 5. Discussion

## 6. Conclusions

- Higher inlet velocities result in increased mixing of water.
- TES tanks with higher aspect ratios result in reduced mixing and heat loss due to smaller relative contact area between water temperature layers.
- Higher temperature differences between inlet water and stored tank water reduce mixing because of greater density differences between layers.
- Thermoclines can form at higher inlet velocities when the aspect ratio and temperature difference are greater.

## Author Contributions

## Conflicts of Interest

## Nomenclature

d | tank diameter |

g | acceleration due to gravity |

h | vertical distance between ports (tank height) |

Re | Reynolds Number |

Ri | Richardson Number |

ΔT | temperature difference of inlet and tank water |

v | inlet velocity |

Z | mixing coefficient |

Greek Letters | |

β | thermal expansion coefficient |

ρ | fluid density |

μ | dynamic viscosity |

Abbreviations | |

AR | Aspect Ratio |

CFD | Computational Fluid Dynamics |

TES | Thermal Energy Storage |

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**Figure 1.**Typical temperature profile in a stratified thermal storage tank [12].

**Figure 3.**Graph showing the mixing effect for different tank water temperatures and inlet velocities (inlet water temperature is 10 °C).

**Figure 5.**Variation of the temperature profile in a chilled water storage tank: predicted and measured values [2].

**Figure 6.**Simulation results of different TES systems after 1600 s: (

**a**) TES-1; (

**b**) TES-2; (

**c**) TES-3; (

**d**) TES-4; (

**e**) TES-5.

**Figure 7.**Temperature profile and thermocline in different tank designs (water velocity of 1.5 cm/s, tans water temperature 50 °C, inlet water temperature 6 °C).

**Figure 8.**Temperature profiles in TES-1 at temperature differences of (

**a**) 84 °C, (

**b**) 44 °C and (

**c**) 14 °C.

**Figure 10.**Temperature profiles in TES-1 at different inlet velocities: (

**a**) 8 cm/s; (

**b**) 7 cm/s; (

**c**) 6 cm/s; (

**d**) 5 cm/s; (

**e**) 4 cm/s; (

**f**) 3 cm/s; (

**g**) 2 cm/s.

**Figure 11.**Temperature profiles in TES-1 at different inlet velocities: non-dimensional temperature difference versus tank height.

Tank Number | Diameter, d (m) | Height, h (m) | Area, a $({\mathit{m}}^{\mathbf{2}})$ | Volume, V $({\mathit{m}}^{\mathbf{3}})$ | Aspect Ratio, AR (h/d) |
---|---|---|---|---|---|

TES-1 | 0.180 | 0.680 | 0.025 | 0.0173 | 3.778 |

TES-2 | 0.200 | 0.550 | 0.031 | 0.0173 | 2.750 |

TES-3 | 0.210 | 0.500 | 0.035 | 0.0173 | 2.381 |

TES-4 | 0.255 | 0.340 | 0.051 | 0.0173 | 1.333 |

TES-5 | 0.280 | 0.280 | 0.062 | 0.0173 | 1.000 |

TES | Stored Water Temperature (°C) | Inlet Velocity (cm/s) | Flow Rate ($\mathbf{L}/\mathbf{h})$ | Reynolds Number Re | Richardson’s Number Ri | Mixing Coefficient Z |
---|---|---|---|---|---|---|

1 | 90 | 0.90 | 3.97 | 1239 | 482 | 31,757 |

50 | 0.85 | 3.75 | 1170 | 270 | 45,045 | |

20 | 0.70 | 3.09 | 964 | 100 | 77,186 | |

2 | 90 | 0.85 | 3.75 | 1300 | 437 | 35,022 |

50 | 0.80 | 3.53 | 1123 | 246 | 49,331 | |

20 | 0.65 | 2.87 | 994 | 94 | 82,270 | |

3 | 90 | 0.85 | 3.75 | 1365 | 398 | 38,572 |

50 | 0.80 | 3.53 | 1285 | 224 | 54,330 | |

20 | 0.65 | 2.87 | 1044 | 85 | 90,609 | |

4 | 90 | 0.80 | 3.53 | 1560 | 305 | 50,358 |

50 | 0.75 | 3.32 | 1463 | 174 | 70,276 | |

20 | 0.60 | 2.65 | 1170 | 68 | 113,767 | |

5 | 90 | 0.80 | 3.53 | 1713 | 251 | 61,063 |

50 | 0.70 | 3.09 | 1499 | 164 | 74,286 | |

20 | 0.60 | 2.42 | 1178 | 66 | 115,816 |

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**MDPI and ACS Style**

Karim, A.; Burnett, A.; Fawzia, S.
Investigation of Stratified Thermal Storage Tank Performance for Heating and Cooling Applications. *Energies* **2018**, *11*, 1049.
https://doi.org/10.3390/en11051049

**AMA Style**

Karim A, Burnett A, Fawzia S.
Investigation of Stratified Thermal Storage Tank Performance for Heating and Cooling Applications. *Energies*. 2018; 11(5):1049.
https://doi.org/10.3390/en11051049

**Chicago/Turabian Style**

Karim, Azharul, Ashley Burnett, and Sabrina Fawzia.
2018. "Investigation of Stratified Thermal Storage Tank Performance for Heating and Cooling Applications" *Energies* 11, no. 5: 1049.
https://doi.org/10.3390/en11051049