# Transient-Flow Induced Compressed Air Energy Storage (TI-CAES) System towards New Energy Concept

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## Abstract

**:**

## 1. Introduction

## 2. System Description

## 3. Parametric Analysis

^{3}, 56 × 10

^{3}, 75 × 10

^{3}, 93 × 10

^{3}, 115 × 10

^{3}, 132 × 10

^{3}, and 155 × 10

^{3}.

## 4. Recovery Flow Behaviour

## 5. Dimensional Analysis

Velocity scale: | $\frac{{V}_{m}}{{(g{L}_{m})}^{1/2}}=\frac{{V}_{p}}{{(g{L}_{p})}^{1/2}}\Rightarrow \frac{{V}_{m}}{{V}_{p}}=\frac{{(g{L}_{m})}^{1/2}}{{(g{L}_{p})}^{1/2}}\Rightarrow {\lambda}_{V}={\lambda}_{L}^{1/2},$ | (6) |

Time scale: | $L=V.t\Rightarrow {\lambda}_{L}={\lambda}_{V}.{\lambda}_{t}\Rightarrow {\lambda}_{t}=\frac{{\lambda}_{L}}{{\lambda}_{V}}\Rightarrow {\lambda}_{t}={\lambda}_{L}^{1/2},$ | (7) |

Acceleration scale: | $a=\frac{dV}{dt}\Rightarrow {\lambda}_{a}=\frac{{\lambda}_{V}}{{\lambda}_{t}}\Rightarrow {\lambda}_{a}=1,$ | (8) |

Flow rate scale: | $Q=V.A\Rightarrow {\lambda}_{Q}={\lambda}_{V}.{\lambda}_{L}^{2}\Rightarrow {\lambda}_{Q}={\lambda}_{L}^{5/2},$ | (9) |

Mass scale: | $m=\rho .\forall \Rightarrow {\lambda}_{m}={\lambda}_{\rho}.{\lambda}_{L}^{3}\Rightarrow {\lambda}_{m}={\lambda}_{L}^{3}\hspace{0.17em},$ | (10) |

Force scale: | $F=m.a\Rightarrow {\lambda}_{F}={\lambda}_{m}.{\lambda}_{a}^{}\Rightarrow {\lambda}_{F}={\lambda}_{L}^{3},$ | (11) |

Pressure scale: | $p=\frac{F}{S}\Rightarrow {\lambda}_{p}=\frac{{\lambda}_{F}}{{\lambda}_{L}^{2}}\Rightarrow {\lambda}_{p}={\lambda}_{L}^{},$ | (12) |

Energy scale: | $E=F.L\Rightarrow {\lambda}_{E}={\lambda}_{F}.{\lambda}_{L}^{}\Rightarrow {\lambda}_{E}={\lambda}_{L}^{4},$ | (13) |

Power scale: | $P=\frac{E}{t}\Rightarrow {\lambda}_{P}=\frac{{\lambda}_{E}}{{\lambda}_{t}^{}}\Rightarrow {\lambda}_{P}={\lambda}_{L}^{7/2},$ | (14) |

## 6. Discussion

## 7. Conclusions

- The system showed a very controlled behaviour under the pressure surge occurrence, where the pressure surge can be stored in the form of compressed air in a vessel. The maximum pressure in the main pipeline is slightly higher than the maximum pressure of the air that provides a reliable calculation and prediction of the system.
- The attained hydraulic power consists of considerable values, while the amount of input work to induce pressure surge into the system is negligible. This fact promises a high-efficiency system in which most of the parts usually exist in advance in a water system. Hence, the initial investment will not be large to set-up a TI-CAES system in an existing water system.
- The analysis proved that the perturbation created in the main pipeline flow will be short-lasting and insignificant as changes in velocity profiles proved. The results show that the initial velocity of the main flow can be recovered in a very short time. Also, it was found that the velocity recovery and perturbation elimination is better for higher Reynolds numbers, making the TI-CAES system a better solution for water system with high Reynolds numbers.
- It was shown that higher VFRs will provide considerably higher power values. In addition, higher VFRs will not provide extreme pressure peaks, which is an important advantage increasing the safety measures of the system. So, bigger air volumes provide a safe and economic energy recovery attitude due to very controlled pressure spikes while offering significant work done by air expansion.
- The results show the TI-CAES concept offers a flexible, geography independent and efficient system that can provide high hydraulic power due to suppling a very high extra pressure head in the form of pressurized air.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Symbols | |

$a$ | acceleration [m/s^{2}] |

$c$ | wave speed [m/s] |

$D$ | pipe diameter [m] |

$E$ | energy [N.m] |

$F$ | force [N] |

$g$ | gravitational acceleration [m/s^{2}] |

$L$ | length [m] |

$m$ | mass [kg] |

$n$ | polytropic exponent [–] |

$p$ | pressure [bar] or [kPa] |

$P$ | hydraulic power [W] or [kW] |

$\forall $ | volume [m^{3}] |

$W$ | work [N.m] |

$t$ | time [s] |

$Q$ | flow rate [L/s] or [m^{3}/s] |

$V$ | flow velocity [m/s] |

Indices | |

$\mathrm{air}$ | air inside CAV |

$\mathrm{dim}$ | dimensionless value |

$0$ | initial (at time zero) |

$\mathrm{hyd}$ | hydraulic |

$\mathrm{int}$ | integrated value |

$\mathrm{L}$ | length |

$\mathrm{m}$ | model |

$\mathrm{max}$ | maximum value |

$\mathrm{out}$ | outlet |

$\mathrm{p}$ | prototype |

$\mathrm{tr}$ | related to transient condition |

Greek letters | |

$\gamma $ | specific weight [N/m^{3}] |

$\lambda $ | scale factor |

$\rho $ | fluid density [kg/m^{3}] |

Abbreviations | |

AA-CAES | Advanced Adiabatic Compressed Air Energy Storage |

BV | Ball Valve |

CAES | Compressed Air Energy Storage |

CAV | Compressed Air Vessel |

CV | Check Valve |

DA | Data Acquisition system |

HT | Hydro-pneumatic Tank |

PAT | Pump as Turbine |

PH-CAES | Pumped Hydro Compressed Air Energy Storage |

PSH | Pumped-Storage Hydropower |

PT | Pressure Transducer |

Re | Reynolds number |

TI-CAES | Transient-flow Induced Compressed Air Energy Storage |

UDV | Ultrasonic Doppler Velocimetry |

UPSH | Underwater Pumped-storage Hydropower |

VFR | Volume Fraction Ratio |

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**Figure 1.**(

**a**) Hydropower capacity growth, (

**b**) hydropower rank in the global electricity generation [1]

**Figure 2.**Experimental apparatus as part of the transient flow-induced compressed air energy storage (TI-CAES) system and energy conceptual ideas: (

**a**) electricity dispatch; (

**b**) pumping system.

**Figure 3.**Experimental pressure variation in charge/discharge stages of the CAV, for Re = 155,000: (

**a**) volume fraction ratio (VFR) = 8.33%; (

**b**) VFR = 66.67%.

**Figure 5.**The work done by the air expansion is the area below the pressure–volume graph in different VFRs.

**Figure 6.**The concept of average and real-time air pressure: (

**a**) average pressure for different VFR and Re numbers; (

**b**) ${p}_{air}$ for VFR = 3.33% and Re = 155,000; (

**c**) ${p}_{air}$ for VFR = 25.00% and Re = 155,000; (

**d**) ${p}_{air}$ for VFR = 66.67% and Re = 155,000.

**Figure 7.**The hydraulic power and ${p}_{air}$ changing during transient for Re = 155,000 and: (

**a**) VFR = 3.33%; (

**b**) VFR = 16.67%; (

**c**) VFR = 33.33%; (

**d**) VFR = 66.67%.

**Figure 9.**Velocity profiles along time: (

**a**) Re = 58,000; (

**b**) Re = 93,000; (

**c**) Re = 132,000; (

**d**) Re = 155,000.

**Figure 10.**Difference between the transient mean velocity (V

_{1}) and the initial mean velocity (V

_{0}) over the maximum initial velocity (V

_{max})

_{0}for all the tested conditions and time steps after starting the transient event as: (

**a**) 0.8; (

**b**) 1.0; (

**c**) 1.2; (

**d**) 1.4; (

**e**) for more time.

Parameter | Measuring Range |
---|---|

Pipe pressure [bar] | 0.00 to 6.62 |

Air pressure [bar] | 0.00 to 5.08 |

VFR [%] | 3.33 to 66.67 |

Flow Velocity [m/s] | 1.36 to 5.13 |

Flow Rate [L/s] | 1.76 to 7.43 |

Re number [–] | 36,000 to 155,000 |

Parameters | Definition |
---|---|

${({t}_{tr})}_{m}$ | time of transient (waterhammer) event |

${({\forall}_{CAV})}_{m}\hspace{0.17em}$ | volume of CAV |

${({\forall}_{air})}_{m}\hspace{0.17em}\hspace{0.17em}$ | volume of air inside CAV |

${(D)}_{m}$ | exit pipe diameter |

${({p}_{air})}_{m}$ | air pressure inside CAV |

${({Q}_{out})}_{m}$ | outlet flow from CAV |

${({P}_{hyd})}_{m}$ | hydraulic power of CAV |

${(E)}_{m}$ | available energy in CAV |

Parameters | ${({\mathit{t}}_{\mathit{t}\mathit{r}})}_{\mathit{m}}$ | ${({\forall}_{\mathbf{CAV}})}_{\mathit{m}}$ | VFR | ${({\forall}_{\mathbf{air}})}_{\mathit{m}}$ | ${(\mathit{D})}_{\mathit{m}}$ | ${({\mathit{p}}_{\mathbf{int}})}_{\mathit{m}}$ | ${({\mathit{Q}}_{\mathit{o}\mathit{u}\mathit{t}})}_{\mathit{m}}$ | ${({\mathit{P}}_{\mathbf{hyd}})}_{\mathit{m}}$ | ${(\mathit{E})}_{\mathit{m}}$ |
---|---|---|---|---|---|---|---|---|---|

[s] | [m^{3}] | [%] | [m^{3}] | [m] | [kPa] | [m^{3}/s] | [kW] | [kWh] | |

Dimensions | T | L^{3} | - | L^{3} | L | M L^{−1} T^{−2} | L^{3} T^{−1} | M L^{2} T^{−3} | M L^{2} T^{−2} |

Model Values | 18 | 0.0047 | 3.33 | 0.00016 | 0.02 | 117.27 | 0.00010 | 0.01140 | 0.00006 |

5.00 | 0.00023 | 125.04 | 0.00013 | 0.01563 | 0.00008 | ||||

6.67 | 0.00031 | 130.75 | 0.00016 | 0.02034 | 0.00010 | ||||

8.33 | 0.00039 | 133.09 | 0.00017 | 0.02292 | 0.00011 | ||||

11.67 | 0.00054 | 139.49 | 0.00020 | 0.02828 | 0.00014 | ||||

16.67 | 0.00078 | 140.21 | 0.00022 | 0.03116 | 0.00016 | ||||

25.00 | 0.00116 | 142.98 | 0.00025 | 0.03574 | 0.00018 | ||||

33.33 | 0.00155 | 146.70 | 0.00027 | 0.03912 | 0.00020 | ||||

50.00 | 0.00233 | 145.15 | 0.00029 | 0.04153 | 0.00021 | ||||

66.67 | 0.00310 | 137.86 | 0.00029 | 0.03960 | 0.00020 |

Parameters | ${\mathit{\lambda}}_{\mathit{L}}$ | ${({\mathit{t}}_{\mathit{t}\mathit{r}})}_{\mathit{p}}$ | ${({\forall}_{\mathbf{CAV}})}_{\mathit{p}}$ | VFR | ${({\forall}_{\mathbf{air}})}_{\mathit{m}}$ | ${(\mathit{D})}_{\mathit{m}}$ | ${({\mathit{p}}_{\mathbf{air}})}_{\mathit{m}}$ | ${({\mathit{Q}}_{\mathit{o}\mathit{u}\mathit{t}})}_{\mathit{m}}$ | ${({\mathit{P}}_{\mathbf{hyd}})}_{\mathit{m}}$ | ${(\mathit{E})}_{\mathit{m}}$ |
---|---|---|---|---|---|---|---|---|---|---|

[s] | [m^{3}] | [%] | [m^{3}] | [m] | [kPa] | [m^{3}/s] | [kW] | [kWh] | ||

Prototype Values | 1/10 | 56.92 | 4.70 | 3.33 | 0.16 | 0.20 | 1172.65 | 0.03 | 36.05 | 0.57 |

5.00 | 0.23 | 1250.37 | 0.04 | 49.43 | 0.78 | |||||

6.67 | 0.31 | 1307.46 | 0.05 | 64.32 | 1.02 | |||||

8.33 | 0.39 | 1330.94 | 0.05 | 72.49 | 1.15 | |||||

11.67 | 0.54 | 1394.85 | 0.06 | 89.44 | 1.41 | |||||

16.67 | 0.78 | 1402.08 | 0.07 | 98.53 | 1.56 | |||||

25.00 | 1.16 | 1429.77 | 0.08 | 113.03 | 1.79 | |||||

33.33 | 1.55 | 1467.00 | 0.08 | 123.71 | 1.96 | |||||

50.00 | 2.33 | 1451.50 | 0.09 | 131.33 | 2.08 | |||||

66.67 | 3.10 | 1378.60 | 0.09 | 125.22 | 1.98 |

Parameters | ${\mathit{\lambda}}_{\mathit{L}}$ | ${({\mathit{t}}_{\mathit{t}\mathit{r}})}_{\mathit{p}}$ | ${({\forall}_{\mathbf{CAV}})}_{\mathit{p}}$ | VFR | ${({\forall}_{\mathbf{air}})}_{\mathit{m}}$ | ${(\mathit{D})}_{\mathit{m}}$ | ${({\mathit{p}}_{\mathbf{air}})}_{\mathit{m}}$ | ${({\mathit{Q}}_{\mathit{o}\mathit{u}\mathit{t}})}_{\mathit{m}}$ | ${({\mathit{P}}_{\mathbf{hyd}})}_{\mathit{m}}$ | ${(\mathit{E})}_{\mathit{m}}$ |
---|---|---|---|---|---|---|---|---|---|---|

[s] | [m^{3}] | [%] | [m^{3}] | [m] | [kPa] | [m^{3}/s] | [kW] | [kWh] | ||

Prototype Values | 1/20 | 80.50 | 37.60 | 3.33 | 1.24 | 0.40 | 2345.31 | 0.17 | 407.89 | 9.12 |

5.00 | 1.86 | 2500.74 | 0.22 | 559.18 | 12.50 | |||||

6.67 | 2.48 | 2614.92 | 0.28 | 727.64 | 16.27 | |||||

8.33 | 3.10 | 2661.88 | 0.31 | 820.07 | 18.34 | |||||

11.67 | 4.35 | 2789.71 | 0.36 | 1011.94 | 22.63 | |||||

16.67 | 6.21 | 2804.16 | 0.40 | 1114.72 | 24.93 | |||||

25.00 | 9.31 | 2859.54 | 0.45 | 1278.83 | 28.60 | |||||

33.33 | 12.42 | 2934.00 | 0.48 | 1399.60 | 31.30 | |||||

50.00 | 18.62 | 2903.01 | 0.51 | 1485.79 | 33.22 | |||||

66.67 | 24.83 | 2757.21 | 0.51 | 1416.65 | 31.68 |

Parameters | ${\mathit{\lambda}}_{\mathit{L}}$ | ${({\mathit{t}}_{\mathit{t}\mathit{r}})}_{\mathit{p}}$ | ${({\forall}_{\mathbf{CAV}})}_{\mathit{p}}$ | VFR | ${({\forall}_{\mathbf{air}})}_{\mathit{m}}$ | ${(\mathit{D})}_{\mathit{m}}$ | ${({\mathit{p}}_{\mathbf{air}})}_{\mathit{m}}$ | ${({\mathit{Q}}_{\mathit{o}\mathit{u}\mathit{t}})}_{\mathit{m}}$ | ${({\mathit{P}}_{\mathbf{hyd}})}_{\mathit{m}}$ | ${(\mathit{E})}_{\mathit{m}}$ |
---|---|---|---|---|---|---|---|---|---|---|

[s] | [m^{3}] | [%] | [m^{3}] | [m] | [kPa] | [m^{3}/s] | [kW] | [kWh] | ||

Prototype Values | 1/25 | 90.00 | 73.44 | 3.33 | 2.43 | 0.50 | 2931.63 | 0.30 | 890.69 | 22.27 |

5.00 | 3.64 | 3125.92 | 0.39 | 1221.06 | 30.53 | |||||

6.67 | 4.85 | 3268.64 | 0.49 | 1588.92 | 39.72 | |||||

8.33 | 6.06 | 3327.35 | 0.54 | 1790.76 | 44.77 | |||||

11.67 | 8.49 | 3487.14 | 0.63 | 2209.73 | 55.24 | |||||

16.67 | 12.13 | 3505.20 | 0.69 | 2434.16 | 60.85 | |||||

25.00 | 18.19 | 3574.43 | 0.78 | 2792.52 | 69.81 | |||||

33.33 | 24.25 | 3667.50 | 0.83 | 3056.25 | 76.41 | |||||

50.00 | 36.38 | 3628.76 | 0.89 | 3244.46 | 81.11 | |||||

66.67 | 48.50 | 3446.51 | 0.90 | 3093.48 | 77.34 |

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## Share and Cite

**MDPI and ACS Style**

Besharat, M.; Dadfar, A.; Viseu, M.T.; Brunone, B.; Ramos, H.M.
Transient-Flow Induced Compressed Air Energy Storage (TI-CAES) System towards New Energy Concept. *Water* **2020**, *12*, 601.
https://doi.org/10.3390/w12020601

**AMA Style**

Besharat M, Dadfar A, Viseu MT, Brunone B, Ramos HM.
Transient-Flow Induced Compressed Air Energy Storage (TI-CAES) System towards New Energy Concept. *Water*. 2020; 12(2):601.
https://doi.org/10.3390/w12020601

**Chicago/Turabian Style**

Besharat, Mohsen, Avin Dadfar, Maria Teresa Viseu, Bruno Brunone, and Helena M. Ramos.
2020. "Transient-Flow Induced Compressed Air Energy Storage (TI-CAES) System towards New Energy Concept" *Water* 12, no. 2: 601.
https://doi.org/10.3390/w12020601