Design Guideline for Hydropower Plants Using One or Multiple Archimedes Screws
Abstract
:1. Introduction
2. Methods and Materials
2.1. Design Parameters of Archimedes Screws
2.2. Archimedes Screws Configurations in Hydropower Plants
2.2.1. Archimedes Screws in Series Configuration
2.2.2. Archimedes Screws in Parallel Configuration
2.3. Case Studies
2.4. Evaluation Criteria
3. Results and Discussion
3.1. Volumetric Flow Rate and Diameter of Archimedes Screws
3.2. Power and Diameter of Archimedes Screws
3.3. Analytical Equation
3.4. Evaluation of the Developed Equations
4. A Quick Design Guideline for Archimedes Screw Power Plants
4.1. Determination of the ASG Configuration
- -
- For the known available average flow rate and head, Equation (7) could be used for rough estimations about the possible amount of power that could be generated.
- -
- If the estimated power is less than the requirements, site properties could be checked to evaluate the possibilities of the series configuration of ASGs. e.g., to take advantage of low flow rates but reasonable available heads, ASGs could be installed in series to deal with technical considerations of a very long ASG.
- -
- To take advantage of high flow rates, instead of a very large (in diameter) and heavy ASG, it is possible to install ASGs in parallel. This approach could help to reduce the challenges of technical limitations and offers several advantages.
- -
- For very low flow rates and heads, using industrial pico-ASGs available in the market may facilitate the process or even save some costs. For example, currently, pico-ASGs can generate up to 500 W with a flow rate as low as 0.1 m3/s and 0.7 m of the head (more information is available in [6]). Obviously, several units of such screws could be used in parallel or in series to take advantage of higher flow rates or available heads. For higher flow rates and heads, custom ASGs designs could be more efficient options. For example, Fletcher’s Horse World Archimedes Screw can generate up to 7.2 kW using a design flow rate, head and outer diameter of 0.536 m3/s, 1.7 m [71,72] and 1.39 m [73], respectively.
4.2. Estimation of Archimedes Screws Design Properties
- Determine the site properties: the river’s historical data or hydrograph for the volumetric flow rate (Q) and the site geometry to find the appropriate head (H) and the Archimedes screw inclination angle (. Studies show that many ASGs are installed at [10].
- Determine the maximum and minimum overall diameter of the screw (Dmax, Dmin) based on the site properties and the Archimedes screw hydro power plants design assessments proposed in Section 5-1 of [6].
- Use Equation (1) to determine the screw(s) length.
- Use the historical dataset of the river’s flow rate to determine the flow duration curve (FDC). The probability that a system will take on a particular value or collection of values could be described by a mathematical expression which is known as a distribution function. The cumulative distribution function (CDF) of a variable for a value is the probability that this variable will take values less than or equal to this value [74]. Therefore, for a time series with items, for item with items equal or bigger than it:
- 5.
- Use the volume of flow rate that is provided on the flow duration curve (e.g., Q95) and use Equation (14) to estimate the corresponding diameter of the screw for this flow rate (DO).
- 6.
- Check the estimated diameter:
- -
- If , go to step 7.
- -
- If use a higher volume of flow rate (e.g., Q90) and repeat step 6.
- -
- If , several approaches could be considered:
- ○
- Identical screws: divide the volume of flow rate by i = 2 and follow the process from step 6. If it ends to again, repeat it for i = i + 1 until the condition passes. Then use the analytical Archimedes screw design method that is offered in [33] to design the screw. In this approach, “i” Archimedes screw generators with the same geometry will be designed to handle this flow rate. The advantage of this approach is that similar screws are easier to build, operate and maintain.
- ○
- Design based on the maximum diameter: design the screw for and use the analytical Archimedes screw design method that is offered in [33] to design the Archimedes screw generator. Then use Equation (15) to estimate the volumetric flow that passes through this screw and design the next Archimedes screw by following the process from step 6 for the remaining volume of flow rate. This approach could lead to reducing the number of Archimedes screws.
- ○
- Trial and error: consider a higher probability that means a lower flow rate (e.g., Q97.5 instead of Q95) and do and follow the process from step 6 and perform a trial and error. This approach could lead to an increase in the design of Archimedes screw turbines with higher reliability in generating power.
- 7.
- To utilize the remaining available volumetric flow rate, more Archimedes screws could be designed (parallel ASG power plants). The next flow rate to design the screw could be selected from the FDC based on the desired step size (Δ). For example, for the previous design flow rate of choose the next flow rate which is the flow exceeding for of the period and continue the design starting from step 5.
- 8.
- The design process should be halted based on logical constraints. For example, for economic reasons designing screws for volumetric flow rates less than the certain probability (e.g., Qlimit) is not reasonable. Or, due to site limitations, there may be some restrictions such as the total area of the power plant (the minimum required area to install the Archimedes screw generators is equal to the sum of the diameter times to the length of each screw. If it goes beyond the installation site limitations, some of the screws designed for flow rates with lower probabilities could be cancelled. In such conditions, an optimized larger screw for the flow rates with the highest probabilities or using variable speed screws could be considered as alternative solutions to utilize more flow rate).
- 9.
- Use Equation (7) to estimate the possible amount of power that each ASG can generate. Then, estimate the ideal overall power that the Archimedes screw hydropower plant could generate.
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
Notation | ||
Effective cross-sectional area at the screw’s inlet | (m2) | |
The inner diameter of the Archimedes screw | (m) | |
The outer diameter of the Archimedes screw | (m) | |
The estimated value | ||
The average of the estimations | ||
Upper (inlet) water level of the screw | (m) | |
Lower (outlet) water level of the screw | (m) | |
The available head | (m) | |
Gap width (The gap between the trough and screw) | (m) | |
The total length of the screw | (m) | |
MAPE | The mean absolute percentage error | (%) |
n | The number of data points in the dataset | |
Number of helical planed surfaces | (-) | |
The observed value | ||
The average of the observed data | ||
The percentage (percent) error | (%) | |
Total flow rate passing through the screw | (m3/s) | |
r | Radius | (m) |
R | Pearson correlation | (%) |
Pitch of the screw (Distance along the screw axis for one complete helical plane turn) | (m) | |
The fill height of the inner diameter of the screw at the inlet | (m) | |
The fill height of the screw at the inlet | (m) | |
The free surface elevations at the upstream | (m) | |
The free surface elevations at the downstream | (m) | |
The inclination angle of the screw | (rad) | |
The specific weight of water | (N/m3) | |
The screw’s pitch to outer diameter ratio ( | (-) | |
The average efficiency of the ASGs based on manufacturer’s specifications in Table 2 () | ||
Step size | (%) | |
A constant accounting for screw geometry and fill level | (m2/3s−1) | |
θ | Angle of sector | (rad) |
The constant value in the power function form | ||
The screw’s inner to outer diameter ratio () | (-) | |
The dimensionless inlet depth of the screw | (-) | |
The value of power in the power function form of diameter equation | (-) | |
ω | The rotation speed of the screw | (rad/s) |
The maximum rotation speed of the screw (Muysken limit) | (rad/s) | |
Subscripts | ||
inner | ||
minimum | ||
Maximum | ||
O | Outer |
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Parameter | Description | Unit | Variable | Description | Unit |
---|---|---|---|---|---|
L | Length of the screw | (m) | ω | Rotation speed of screw * | (rad/s) |
DO | Outer diameter of the screw | (m) | hu | Upper (inlet) water level | (m) |
Di | Inner diameter of the screw | (m) | hL | Lower (outlet) water level | (m) |
S | Screw’s pitch or period [39] (The distance along the screw axis for one complete helical plane turn) | (m) | Q | Volumetric flow rate passing through the screw | (m3/s) |
N | Number of helical planed surfaces (also called blades, flights or starts [39]) | (1) | Ratio | Description | Unit |
δ | Inner to outer diameter ratio δ = Di/DO | (1) | |||
β | Inclination Angle of the Screw | (rad) | σ | Pitch to outer diameter ratio σ = S/DO | (1) |
Gw | The gap between the trough and screw. | (m) | Ξ | Dimensionless inlet depth Ξ = hu/DO cos β | (1) |
Name | No. of ASGs | DO (m) | H (m) | Q (m3/s) | P (kW) | Location (River) | Refs. | |
---|---|---|---|---|---|---|---|---|
Totnes | 2 | 3.7 | 3.45 | 6.5 | 160 | Dart, UK | [48] | |
Hannoversch-Münden | 2 | 2.8 | 2.6 | 2 | 35.455 | Werra, DE | [49] | |
Low Wood | 2 | 3 | 7.2 | 4 | 200 | Leven, UK | [47] | |
Radyr | 2 | 3.5 | 3.5 | 11 | 200 | Taff, UK | [50] | |
Künzelsau | 2 | 4.1 | 1.72 | 8.95 | 132 | Kocher, DE | [51] | |
Ahornweg | 2 | 2.3 | 1.45 | 2 | 21 | Mühlbach, DE | [51] | |
Linton Falls | 2 | 2.4 | 2.7 | 2.6 | 50 | Trent, UK | [47] | |
Niklasdorf/Birgl and Bergmeister | 2 | 3.9 | 3.6 | 106 | Mur, AT | [51] | ||
Hausen III Neumatt | 2 | 3.4 | 5.8 | 5.5 | 235 | Wiese, DE | [51] | |
Höllthal | 2 | 4.3 | 2.22 | 10.5 | 220 | Alz, DE | [52] | |
Gunthorpe Weir | 2 | 4.3 | 2.03 | 14.15 | 165 | Trent, UK | [53] | |
Solvay | 2 | 2.3 | 2 | 2.5 | 35 | Saja, ES | [54] | |
Linton Lock | Linton Plant | 2 | 3 | 3.2 | 4.5 | 110 | Ouse, UK | [6,55] |
Widdington Plant | 5 | 3 | 14.5 | 335 | ||||
Plana | 3 | 4.1 | 3.5 | 8.73 | 220 | Vltava, CZ | [51] | |
Crescenzago | 3 | 3.2 | 2.1 | 5 | 75 | Lambro, IT | [51] | |
Olen | 3 | 4.3 | 10 | 5 | 360 | Albert Canal, BE | [51,56] | |
Ham | 3 | 4.3 | 10 | 5 | 360 | Albert Canal, BE | [51,56] | |
Hasselt | 3 | 5 | 10 | 5 | 400 | Albert Canal, BE | [11,27] | |
Rosko | 6 | 1.7 | 4.5 | 60 | Noteć, PL | [51,57] | ||
Steinsau | 6 | 1.4 | 3 | 30 | Ill, FR | [51] | ||
Marengo | 6 | 3 | 1.6 | 3.7 | 51 | Goito, IT | [58,59] |
Equation No. | Equation | R (%) | MAPE (%) |
---|---|---|---|
(5) | 69.81 | 10.59 | |
(8) | 83.28 | 10.64 | |
(14) | 74.38 | 9.69 |
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YoosefDoost, A.; Lubitz, W.D. Design Guideline for Hydropower Plants Using One or Multiple Archimedes Screws. Processes 2021, 9, 2128. https://doi.org/10.3390/pr9122128
YoosefDoost A, Lubitz WD. Design Guideline for Hydropower Plants Using One or Multiple Archimedes Screws. Processes. 2021; 9(12):2128. https://doi.org/10.3390/pr9122128
Chicago/Turabian StyleYoosefDoost, Arash, and William David Lubitz. 2021. "Design Guideline for Hydropower Plants Using One or Multiple Archimedes Screws" Processes 9, no. 12: 2128. https://doi.org/10.3390/pr9122128
APA StyleYoosefDoost, A., & Lubitz, W. D. (2021). Design Guideline for Hydropower Plants Using One or Multiple Archimedes Screws. Processes, 9(12), 2128. https://doi.org/10.3390/pr9122128