# A New Cross-Flow Type Turbine for Ultra-Low Head in Streams and Channels

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## Abstract

**:**

## 1. Introduction

## 2. PRS Turbine Design for Ultra-Low Hydraulic Heads

_{b}. The second step is the stator design, i.e., nozzle and diffuser.

^{3}/s), the same velocity ratio (V

_{r}= 1.8) and the same rotor outer diameter (D = 913 mm). The efficiencies are defined as follows [14]:

_{2}, which is constant along all the runner outlet circus; the velocity component on the direction normal to any radius of the runner normal to the axis is constant inside part I [16] and its module is equal to V

_{2}; the two lateral walls are planar and their distance is equal to W, the width of the runner. According to these hypotheses, the flux V

_{2}per unit rotor outlet area can be obtained from the mass conservation equation as follows:

_{max}of the diffuser cross-section in part I is equal (Figure 6):

_{0}is the initial velocity and l is the distance of the section from the beginning of part III. The distance of the last cross-section, l

_{max}, is about 4 times R, a good compromise between the need to prevent the generation of vortices and to contain the overall length of the diffuser.

_{out}(Figure 8) are obtained by setting as V

_{out}, the velocity of fluid particles at the exit of this last part of the diffuser, equal to 1 m/s, in order to get negligible final kinetic energy.

#### CFD Analysis of UL-PRS Turbine

^{®}CFX in the case of 3D domains and ANSYS

^{®}Fluent in 2D analyses. Following the experience of previous studies [12,13], the RNG k-epsilon model was selected as the turbulence model, combined with a scalable wall function [14]. For the study of rotating machines, both ANSYS

^{®}CFD solvers adopt a sliding mesh strategy, where the runner and its swept zone are discretized within a rotating reference system.

^{2}, ρ is the density of the water, ρ

_{0}is the operating density and equal to 1.225 kg/m

^{3}, the density of air at 15 °C.

^{−5}[13,14].

_{max}in the last row is selected according to [13] to guarantee structural safety and maintain high hydraulic efficiency.

^{3}/s), velocity ratio (V

_{r}= 1.8) and outer runner diameter (D = 913 mm) and differ only for the nozzle axis orientation and the shape of the diffuser. The comparison clearly shows some advantages for the efficiencies of the UL-PRS turbine, mainly with head jumps lower than 3 m.

## 3. Case Study: Acqua Dei Corsari WWTP

^{2}.

^{3}/s, corresponding to the wastewater produced by 320,000 equivalent inhabitants (EinH), and is expected to increase to 1.0 m

^{3}/s in two years, equal to the wastewater produced by about 400,000 EinH. A small head jump h

_{1}of about 3.5 m is present at the end of the disinfection channel (red area in Figure 11). The clarified water flow passes through two rectangular weirs and reaches the discharge channel. In the case of heavy rain events, part of the water at the entrance of the plant bypasses sewage treatment and reaches the same discharge channel. The water manager, AMAP S.p.A., is willing to recover the energy from this head jump by installing a hydraulic turbine to reduce the energy costs linked to the treatment processes.

#### UL-PRS Turbine Solution

^{3}/s and 3.75 m. The available hydraulic jump ΔH = 3.75 m is given by the difference between the Total Energy Level T.E.L.

_{1}of the inlet channel (with respect to the bed of the discharge channel) and the T.E.L.

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

_{ls}, estimated in the suction pipe and in the butterfly valve, respectively, marked with 3 and 4 in Figure 12. Following the design criteria discussed in [9,10,11,12,13], a diameter D and width W equal to 913 mm and 609 mm are selected, respectively, for a rotational velocity ω equal to 75 rpm. The UL-PRS turbine (marked with 6 in Figure 12) is installed in a specific underground room downstream of the plant channel. In the case of overflow, part of the water bypasses the turbine and reaches the discharge channel through the original rectangular weirs (green dashed arrows). In the case of maintenance work of the turbine, it is possible to cut off the turbine and restore the actual layout of the WWTP just by closing the butterfly valve and the gate valve, marked with numbers 4 and 7, respectively.

_{pipe}equal to DN700, is connected to the rectangular inlet section of the nozzle of the turbine through a special convergent. 3D numerical analysis has been carried out for validation by computing the efficiency and the flow rate of the turbine for a given head drop ΔH. The turbine shows an efficiency equal to 80.8%, with a mass flow rate close to the design data (Q = 806 m

^{3}s

^{−1}; ΔH = 3.75 m; ω = 75 rpm; α = 15°; λ

_{max}= 100°; D = 913 mm; W = 609 mm).

## 4. Cost/Benefit Analysis

- Civil work costs: costs for the required modification of the existing infrastructure (black solid, thick lines in Figure 12). These costs include the excavation and building of a specific underground room downstream of the plant channel for turbine housing.
- Hydropower system costs: these include the cost of the turbine, the gearbox, and the electrical generator of an asynchronous type (Figure 12). We estimated a cost of 13,000 EUR for both the gearbox and the electrical generator with a high number of polar couples. For the UL-PRS turbine realization, we estimated a cost of 2500 EUR/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 the investigated nominal electrical power (P
_{e}< 20 kW), the control system cost can be expected to be equal to 40,000 EUR [15]. - Operation and maintenance (O&M) costs: in the case of micro hydro plants, the literature suggests assuming a yearly cost in the range of 2.2% to 3% of the cost of investment C
_{i}[19].

_{MWh}for the sale of energy. This guaranteed minimum price p

_{MWh}is equal to 158.9 EUR /MWh for 2022 [20].

_{O&Mmin}or C

_{O&Mmax}(Table 4). A single index well representing the global economic benefit of the plant is the payback period n

_{y}[years], given by the ratio between the cost of investment C

_{i}[€] and the average cash flows C

_{f}[€/year] of each solution in both cases of C

_{O&Mmin}or C

_{O&Mmax}.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

ARERA | Italian Regulatory Authority for Energy, Networks and Environment |

BCs | Boundary conditions |

CFD | Computational Fluid Dynamics |

CFT | Cross-flow Turbine |

EinH | Equivalent Inhabitants |

H-PRS | High Power Recovery System |

PRS | Power Recovery System |

O&M | Operation and Maintenance |

T.E.L. | Total Energy Level |

UL-PRS | Ultra-low Power Recovery System |

WWTP | Wastewater Treatment Plant |

## Symbols

C_{i} | total cost (EUR) |

C_{f} | average cash flows (EUR/Year) |

C_{O&Mmin} | minimum operation and maintenance annual cost (EUR/Year) |

C_{O&Mmax} | maximum operation and maintenance annual cost (EUR/Year) |

D | outer runner diameter (m) |

D_{pipe} | diameter of the pipe (m) |

ΔH | specific energy drop per unit weight (m) |

g | standard acceleration due to gravity (m s^{–2}) |

k | constant in linear law of the velocity (s^{–1}) |

l | distance from the beginning of part III (m) |

l_{max} | length of part III of the diffuser (m) |

N_{b} | number of blades (–) |

n_{y} | payback period (years) |

P | produced mechanical power of the turbine (W) |

P_{e} | nominal electrical power (kW) |

p | pressure plus the geodetic term (Pa) |

p′ | value of pressure (Pa) |

p_{MWh} | guaranteed minimum prices for the sale of energy (EUR/MWh) |

Q | mass flow rate (m^{3} s^{–1}) |

R | outer runner radius (m) |

r(λ) | radial distance r of the profile of the external wall of the diffuser from the axis of the rotor (m) |

S_{max} | maximum height of the diffuser in part I (m) |

t | blade thickness (m) |

t_{max} | blade maximum thickness (m) |

V(l) | generic velocity of particles in part III (m s^{–1}) |

V_{0} | velocity at the beginning of part III (m s^{–1}) |

V_{2} | runner outlet velocity (m s^{–1}) |

V_{out} | velocity at the end of part III (m s^{–1}) |

W | runner width (m) |

W(l) | generic width of part III of the diffuser (m) |

W_{out} | maximum width of part III of the diffuser (m) |

y | geodetic elevation respect the axis of the runner (m) |

α | absolute velocity inlet angle (radians) |

β | relative velocity inlet angle (radians) |

γ | water specific weight (N m^{–3}) |

η | hydraulic efficiency of the turbine (–) |

$\overline{\mathsf{\eta}}$ | normalized hydraulic efficiency of the turbine (–) |

λ | runner inlet/outlet angle (radians) |

λ_{max} | maximum runner angle (radians) |

ρ | density of the water (kg m^{–3}) |

ρ_{0} | density of the air at 15 °C (kg m^{–3}) |

ω | runner rotational velocity (rad s^{–1}) |

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**Figure 1.**Typical installation of a traditional cross-flow turbine where T.E.L. both time is the total energy level in the upstream and downstream channels, and ΔH is the usable hydraulic jump, lower than the entire available one.

**Figure 4.**Section view of the UL-PRS turbine in a symmetry plan: T.E.L. is the total energy level and ΔH is the gross available hydraulic jump.

**Figure 12.**(

**a**) Section and (

**b**) planimetric view of a UL-PRS type turbine plant, where: 1. Inlet channel; 2. Discharge channel; 3. Suction pipe; 4. Butterfly valve; 5. Underground room; 6. T Hydropower System (blue lines); 7. Gate valve. In thick solid lines, the modifications are proposed for the new solution.

Parameters | UL-PRS 1 | UL-PRS 2 | |
---|---|---|---|

Type of Domain | 2D | 3D | 2D |

Stator Domain elements | 42,337 | 8,885,639 | 40,352 |

Rotor Domain elements | 151,895 | 12,723,105 | 101,627 |

Total elements | 194,232 | 21,608,744 | 141,979 |

Parameters | UL-PRS 1 | UL-PRS 2 |
---|---|---|

Flow rate Q [m^{3}/s] | 0.840 | |

D [mm] | 913 | 652 |

Head ΔH [m] | 0.25–15 | 0.2–10 |

ω(ΔH) [rpm] | 19.4–150 | 24.3–171.6 |

W(ΔH) [mm] | 2360–305 | 3695–523 |

α [°] | 15 | 15 |

β [°] | 28.2 | 28.2 |

λ_{max} [°] | 100 | 100 |

N_{b} [-] | 33 | 35 |

t_{max} [mm] | 22 | 15.7 |

η_{max} [%] | 87.5 | 87.1 |

**Table 3.**Two-dimensional efficiency comparison between UL-PRS1 and PRS turbines for different head jumps.

Head ΔH [m] | UL-PRS 1 | PRS |
---|---|---|

7.50 | 87.3% | 85.9% |

5.00 | 87.0% | 85.4% |

3.75 | 87.5% | 85.1% |

3.00 | 86.8% | 84.6% |

2.00 | 86.5% | 84.8% |

1.00 | 86.2% | 84.1% |

0.50 | 85.4% | 83.6% |

0.25 | 84.1% | 82.4% |

0.20 | 83.7% | 81.4% |

0.15 | 80.9% | 79.5% |

Parameters | UL-PRS | Kaplan * | CFT * |
---|---|---|---|

Head ΔH [m] | 3.75 | 3.75 | 2.8 |

Flow rate Q [m^{3}/s] | 0.806 | 0.837 | 0.820 |

Hydraulic Efficiency | 0.808 | 0.864 | 0.835 |

Gearbox/belts/generator efficiency | 0.887 | 0.887 | 0.887 |

Global efficiency | 0.717 | 0.766 | 0.741 |

Nominal Power (P_{e}) [kW] | 21.2 | 23.6 | 16.7 |

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

Hydropower System [€] | 66,000 | 165,000 | 50,000 |

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

Total cost (C_{i}) [€] | 126,000 | 225,000 | 110,000 |

Specific cost [€/kW] | 5943 | 9534 | 6587 |

O&M cost (C_{O&Mmin}–C_{O&Mmax}) [€/year] | 2772–3780 | 4950–6750 | 2420–3300 |

Total producible energy [MWh] | 178.080–167.904 | 198.240–186.912 | 140.280–132.264 |

Average cash flows (C_{f}) [€/year] | 25,525–22,900 | 26,550–22,950 | 19,870–17,717 |

Payback period (n_{y}) [year] | 4.9–5.5 | 8.5–9.8 | 5.5–6.2 |

UL-PRS | Kaplan * | CFT * | |
---|---|---|---|

Entire available hydraulic jump | ✔ | ✔ | ✘ |

Risk of cavitation | ✘ | ✘ | ✔ |

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

Payback period | ✔ | ✘ | ✘ |

Nominal Power > 20 kW | ✔ | ✔ | ✘ |

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

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## Share and Cite

**MDPI and ACS Style**

Picone, C.; Sinagra, M.; Gurnari, L.; Tucciarelli, T.; Filianoti, P.G.F. A New Cross-Flow Type Turbine for Ultra-Low Head in Streams and Channels. *Water* **2023**, *15*, 973.
https://doi.org/10.3390/w15050973

**AMA Style**

Picone C, Sinagra M, Gurnari L, Tucciarelli T, Filianoti PGF. A New Cross-Flow Type Turbine for Ultra-Low Head in Streams and Channels. *Water*. 2023; 15(5):973.
https://doi.org/10.3390/w15050973

**Chicago/Turabian Style**

Picone, Calogero, Marco Sinagra, Luana Gurnari, Tullio Tucciarelli, and Pasquale G. F. Filianoti. 2023. "A New Cross-Flow Type Turbine for Ultra-Low Head in Streams and Channels" *Water* 15, no. 5: 973.
https://doi.org/10.3390/w15050973