# Low-Head Hydropower for Energy Recovery in Wastewater Systems

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## Abstract

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## 1. Introduction

^{−3}of treated wastewater. The share of energy into operating costs is also shown by [5], where energy is the higher part in the OPEX yearly value, accounting for around 35%, followed by substances, disposal, maintenance and staff. The report points out that most impacting elements in the energy consumption of a conventional WWTP are the aeration of mixed liquor (50–70%), primary and secondary settling with sludge pumping (12–16%) and sludge dewatering (10–30%) [6]. For WWTPs, [7,8,9,10] it was underlined that the electric energy accounts for up to 80% of its GHG emissions.

## 2. Turbine Design and Selection

#### 2.1. Cross-Flow Turbine

_{V}= 0.98 and ξ = 1 according to [13]. The velocity ratio V

_{r}is the optimal ratio between the inlet velocity V and the runner velocity at the inlet surface, and, in the case of the free outlet flow, is equal to 2 according to [13]; α is the velocity inlet angle with respect to the tangent direction, assumed equal to 15° [11]. Equations (1) and (2) can be solved in the V and D unknowns for a given value of the runner rotational velocity ω.

_{max}(Figure 1) equal to 100°.

^{−1}, ΔH in m, ω in rad s

^{−1}, α e λ

_{max}in rad and Q in m

^{3}s

^{−1}. The gravity acceleration g is equal to 9.80665 m s

^{−2}. C

_{V}, while ξ and V

_{r}are nondimensional coefficients.

#### 2.2. Hydrostatic Pressure Machine (HPM)

^{−1}] of the ideal machine, neglecting leakage and turbulent losses [16], is:

_{L}= 3.0 [18].

_{1}to v

_{2}when the water enters the HPM must be considered. According to [18], these losses are also proportional to the downstream kinetic energy, a nondimensional coefficient C

_{acc}function of the two normal water depths:

^{−1}] is given by:

_{leak}is not constant, but is a fraction of the maximum leakage ${Q}_{leak}^{0}$, occurring when the rotational velocity is zero. Assuming a proportionality between Δh and Q

_{leak}results in:

_{max}. Q

_{max}is the discharge [m

^{3}s

^{−1}] occurring when, for fixed h

_{1}and h

_{2}normal depths, Δh = H and the produced power is zero (from Equation (7)). This implies, from Equations (5) and (7):

_{max}[18]. Because the power is proportional to the discharge, incorporating these leakage losses multiplying the efficiency with a leakage correction factor f

_{L}[16] results in:

## 3. Case Study: Acqua dei Corsari Wastewater Treatment Plant

^{2}and is located at the southeast end of the city of Palermo (Figure 4), at an average altitude of 10 m above sea level.

^{3}/s, but with the planned increment, it should rise up to about 1.0 m

^{3}/s. The water flow clarified from the disinfection channel (number 6 in Figure 5) crosses two rectangular weirs and reaches the discharge channel after a small head jump h

_{1}of about 3.5 m. This discharge channel also conveys the water bypassed by the sewage treatment in the case of heavy rain events. The AMAP S.p.A. wants to reduce the energy costs linked to the purification process by recovering energy from this head jump with the installation of a hydraulic turbine.

#### 3.1. Kaplan Turbine Solution

^{3}/s and a head drop equal to 3.75 m. The actual jump ΔH

_{k}= 3.75 m available for production is given by the difference between the level H

_{1}of the inlet channel (with respect to the bed of the discharge channel) and the level H

_{2}of the discharge channel, minus about 0.2 m of head losses H

_{losses}estimated in the suction pipe and in the butterfly valve, respectively marked with 3 and 4 in Figure 6. The turbine (referenced with 6) is put in a specific underground room downstream of the plant channel that should be constructed on purpose (marked 5 in Figure 6).

^{3}/s and a head drop ΔH = 3.75 m. In the range of flow rates of the WWTP (0.8–1.0 m

^{3}/s), the efficiency reduction is lower than 1%.

#### 3.2. Cross-Flow Turbine Solution

_{c}from 3.75 to 2.8 m, due also to head losses H

_{losses}equal to 0.2 m in the suction pipe and in the butterfly valve, marked with 4 in Figure 8. Following the design criteria of the previous section, a diameter D and width W equal to 0.83 m and 0.7 m are selected, respectively, for a rotational velocity ω equal to 75 rpm.

_{c}. The turbine shows an efficiency equal to 83.5%, with a computed discharge close to design data (Q = 0.820 m

^{3}s

^{−1}; ΔH

_{c}= 2.8 m; ω = 75 rpm; α = 15°; λ

_{max}= 100°; D = 0.84 m; W = 0.7 m). In Figure 9, Figure 10 and Figure 11, the computed volume fraction, pressure and velocity fields are shown.

#### 3.3. HPM Turbine Solution

_{2}equal to the level of the inlet channel bed plus a water depth h

_{2}= 0.75 m (Figure 12). According to the previous section, the diameter of the hub D

_{Hub}is equal to ΔH

_{H}= 2.75 m, the height of the blades is equal to h

_{2}and the outer diameter D is equal to 4.25 m. For this diameter and mass flow rate, the efficiency is given by Equation (15), which attains a maximum value η

_{hydro}= 56% for an upstream velocity v

_{1}equal to 0.3 m/s, corresponding to a width of the wheel W equal to 0.76 m and an angular velocity equal to 7 [rpm]. The HPM turbine is located in one of the two original rectangular weirs of a width W

_{c}equal to 1 m, in order to respect the ratio 1:1.3 between the wheel width and width of the rectangular weir suggested in [16,18]. In case of overflow, the exceeding discharges crosses the other original rectangular weir to directly reach the discharge channel (red dashed arrows in Figure 12).

_{1}and h

_{2}normal depths. The turbine shows an efficiency equal to 54.5%, with a computed discharge close to the design data (Q = 0.860 m

^{3}/s). In Figure 13 the distributions of the water volume fraction for four different simulation times t, and in Figure 14, the distributions of the pressure for four different simulation times t are shown.

## 4. Cost/Benefit Analysis

- Civil work costs: these include the cost for the required modification of the existing infrastructures: the upstream channel section for the HPM and the cost for excavation and building of a specific underground room downstream the plant channel for Kaplan and cross-flow-type turbines.
- Hydropower System costs: these include the cost of the turbine, the gearbox, electrical generator of the asynchronous type and belts if necessary. The Kaplan turbine is a commercial solution, and for the estimation of the cost, we request a quotation. For the CFT and HPM turbines, we estimated a cost of EUR 13,000 for both the gearbox and the electrical generator with a high number of the polar couples. For the CTF and HMP turbines realization, we estimated a cost, respectively, of EUR 2215/kW and EUR 2000/kW.
- Control system and installation costs: these include the cost of the control system for the regulation and management of the turbine, and the cost of installation. In the range of nominal electrical power investigated, the control system cost can be expected to be the same as that of the quotation for the Kaplan turbine for all solutions.

_{MWh}for the sale of energy from renewable power generation.

_{MWh}for the 2022 is equal to EUR 158.9/MWh [21].

_{i}[€] and the average cash flows C

_{f}[€/year] for each solution, the payback period n

_{y}[years] can be calculated for a preliminary estimation of amount of time it takes to recover the cost of investments.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Cross-flow turbine: (

**a**) Section view on symmetry plan of the turbine; (

**b**) Side view. D and W are diameter and width of the runner, V the runner velocity at the inlet surface, ω the runner rotational velocity, α is the velocity inlet angle with respect to the tangent direction and λ

_{max}the central angle of the inlet surface.

**Figure 2.**(

**a**) Blade profile; (

**b**) Tangent condition of external end [14]. D and D

_{i}are the outer and inner diameter of the runner, β

_{1}is the relative velocity inlet angle with respect to the tangent direction in P, r

_{b}and θ are the radius and the central angle of internal surface of the blade, respectively, t is the thickness along the radial direction, orthogonal to the internal surface and δ is the angle between the radial directions at the given point and the intersection of the internal blade surface with the runner inlet. t

_{0}is the thickness corresponding at δ

_{min}, r

_{f}the radius of the fillet of the tip of the blade, the tip of the blade is tangent in point P

_{1}to the cubic spline profile of the external surface, and in P

_{2}to the circular profile of the internal surface, and t

_{min}is the thickness located at the extremity (δ = θ).

**Figure 3.**Functional scheme of the HPM, where: T.E.L. is total energy level [m]; h

_{1}is the water depth of the upstream channel [m]; h

_{2}is the water depth of the downstream channel [m]; H is the head difference [m]; v

_{1}is the water upstream velocity [m s

^{−1}]; v

_{2}is the water downstream velocity [m s

^{−1}]; F

_{1}is the force acting on the blade per unit width [N m

^{−1}]; F

_{2}is the reaction force on the blade per unit width [N m

^{−1}] [17].

**Figure 5.**Acqua dei Corsari” WWTP plant, where: 1. Grilling processes; 2. Sands and oils removal; 3. Primary sedimentation; 4. Activated sludge process; 5. Final sedimentation; 6. Disinfection; 7. Prethickening; 8. Anaerobic sludge digestion; 9. Chemical conditioning; 10. Sludge mechanical dewatering; 11. Low-head hydropower.

**Figure 6.**(

**a**) Section and (

**b**) planimetric view of the Kaplan type turbine plant where: 1. Inlet channel; 2. Discharge channel; 3. Suction pipe; 4. Butterfly valve; 5. Underground room; 6. Kaplan turbine. The actual jump is ΔH

_{K}= 3.75 m; h

_{1}= 3.5 m is the level of the inlet channel; H

_{1}= 4.3 m is the level of the inlet channel (with respect to the bed of the discharge channel); H

_{2}= 0.35 m is the level of the dis-charge channel; H

_{losses}is head losses estimated about 0.2 m in the suction pipe and in the butterfly valve, respectively marked with 3 and 4.

**Figure 8.**(

**a**) Section and (

**b**) planimetric view of cross-flow-type turbine plant, where: 1. Inlet channel; 2. Discharge channel; 3. Suction pipe; 4. Butterfly valve; 5. Underground room; 6. Cross-flow turbine. The actual jump is ΔH

_{c}= 2.8 m; h

_{1}= 3.5 m is the level of the inlet channel; H

_{1}= 4.3 m is the level of the inlet channel (with respect to the bed of the discharge channel); H

_{losses}is head losses estimated about 0.2 m in the suction pipe and in the butterfly valve, respectively marked with 3 and 4; D = 0.84 m is the outer diameter of the runner.

**Figure 12.**(

**a**) Section and (

**b**) planimetric view of HPM plant: The actual jump is ΔH

_{H}= 2.75 m; h

_{1}= 3.5 m and h

_{2}= 0.75 are the level of the inlet channel in the sections before and after the wheel; H

_{1}= 4.3 m is the level of the inlet channel (with respect to the bed of the discharge channel); H

_{2}is the level of the discharge channel; D = 4.25 m is the outer diameter of the runner; W = 0.76 m is the width of the runner; W

_{c}= 1.0 m is the width of the channel. The angle between the rotor axis and the intersection between the blade plane and its orthogonal one, including the axis, is 51°.

**Figure 13.**Water volume fraction contours for HPM: (

**a**) t = 18 s; (

**b**) t = 21 s; (

**c**) t = 23 s; (

**d**) t = 25 s.

Parameters | Kaplan | Cross-Flow | HPM |
---|---|---|---|

Design Head ΔH [m] | 3.75 | 2.8 | 2.75 |

Design Flow rate Q [m^{3}/s] | 0.837 | 0.820 | 0.860 |

Hydraulic Efficiency | 0.864 | 0.835 | 0.545 |

Gearbox/belts/generator efficiency | 0.887 | 0.887 | 0.870 * |

Global efficiency | 0.766 | 0.741 | 0.474 |

Nominal Power (P_{Electrical}) [kW] | 23.6 | 16.7 | 11.0 |

Civil works [€] | 20,000 | 20,000 | 5000 |

Hydropower System [€] | 165,000 | 50,000 | 35,000 |

Control system and installation [€] | 40,000 | 40,000 | 40,000 |

Total (C_{i}) [€] | 225,000 | 110,000 | 80,000 |

Specific cost [€/kW installed] | 9534 | 6587 | 7273 |

Total producible energy [MWh] | 186.912 | 132.264 | 87.120 |

Average cash flows (C_{f}) [€/year] | 29,700 | 21,017 | 13,843 |

Payback period (n_{y}) [year] | 7.6 | 5.2 | 5.8 |

Kaplan | Cross-Flow | HPM | |
---|---|---|---|

Net available head jump | ✔ | ✘ | ✘ |

Risk of cavitation | ✘ | ✔ | ✔ |

Rotational velocity | ✔ | ✔ | ✘ |

Hydraulic Efficiency > 80% | ✔ | ✔ | ✘ |

Payback period | ✘ | ✔ | ✔ |

Nominal power | ✔ | ✘ | ✘ |

Building a specific underground room | ✘ | ✘ | ✔ |

Constructive simplicity of the turbine | ✘ | ✔ | ✔ |

Possibility to exclude turbine and restore the actual WWTP layout | ✔ | ✔ | ✘ |

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**MDPI and ACS Style**

Sinagra, M.; Picone, C.; Picone, P.; Aricò, C.; Tucciarelli, T.; Ramos, H.M.
Low-Head Hydropower for Energy Recovery in Wastewater Systems. *Water* **2022**, *14*, 1649.
https://doi.org/10.3390/w14101649

**AMA Style**

Sinagra M, Picone C, Picone P, Aricò C, Tucciarelli T, Ramos HM.
Low-Head Hydropower for Energy Recovery in Wastewater Systems. *Water*. 2022; 14(10):1649.
https://doi.org/10.3390/w14101649

**Chicago/Turabian Style**

Sinagra, Marco, Calogero Picone, Paolo Picone, Costanza Aricò, Tullio Tucciarelli, and Helena M. Ramos.
2022. "Low-Head Hydropower for Energy Recovery in Wastewater Systems" *Water* 14, no. 10: 1649.
https://doi.org/10.3390/w14101649