# Estimating Energy Efficient Design Parameters for Trash Racks at Low Head Hydropower Stations

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## Abstract

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## 1. Introduction

`a`design equation to improve the estimation of head loss on both rack options. Furthermore, it was also noted that several trash racks problems such as vortex formations, vibrations, and instantaneous change in intake discharge are dynamic, therefore, understanding the dynamic properties of trash rack fitting, in general, is critical [38,39]. Sadrnejad [40] proposed an effective added-mass method for assessing the intensity of vibration in submerged structures. Tsikata et al. [41] investigated turbulent flow in the vicinity of the trash racks models. The bar thickness, depth, and center-to-center spacing were kept constant in all experiments. At three different stream velocities, the flow properties were examined by aligning the direction of approaching flow with the bars. The tests were recorded with the stream velocity constant for four distinct bar inclinations relative to the direction of approaching flow. A high-resolution particle image velocimetry (PIV) approach was employed for each test condition. According to this study, head loss and bar inclination have a nonlinear relationship.

## 2. Materials and Methods

## 3. Modelling with CFD Code FLOW-3D

_{F}= volume fraction of fluid in each cell; Ax, Ay, and Az = fractional areas open to flow in the subscript directions; ρ = density; P′ is defined as the pressure; g

_{i}= gravitational force in the subscript direction; f

_{i}represents the Reynolds stresses, and A

_{j}= cell face areas. Equations (1) and (2) are partial differential equations. They are discretized both in time and space. Due to the complex nature of turbulence, it is often simplified and approximated using an average approach (e.g., Reynolds-averaged Navier–Stokes).

## 4. Model Setup

## 5. Sensitivity Analysis

#### 5.1. Sensitivity Analysis for Grid Size

#### 5.2. Sensitivity Analysis for Boundary Conditions

_{min}, downstream of trash racks as X

_{max}, and right and left side of the flow as the Y

_{min}& Y

_{max}, respectfully. To properly select and apply input and output boundary conditions of flow in X

_{max}and X

_{min}based on experimental studies, a stable flow with a certain height of the fluid through the trash racks should be introduced to the model. Hence, using boundary conditions existing in FLOW-3D, the fluid height for X

_{min}is applied with the boundary conditions of fluid height. It is fully in accordance with the model through which the results’ validation and calibration are performed. Moreover, Z

_{min}is the floor and Z

_{max}is the upper boundary of the flow domain. Chanel and Doering [52] indicated that boundary conditions should match the physical conditions of the problem. Considering this fact, among the different sets of tested boundary conditions, one of the sets (Figure 4) validated the model: X

_{min}as ‘Specified Averaged Depth Velocity’, X

_{max}as ‘Outflow’, Y

_{min}& Y

_{max}as ‘Symmetry’ to reflect the identical flows on another side of right and left boundaries, Z

_{min}as ‘Wall’, and Z

_{max}as the ‘Specified Pressure’ boundary.

#### 5.3. Sensitivity Analysis to Turbulence Model

## 6. Model Validation

#### 6.1. Scenario Modeling

#### 6.2. Development of Equation for Head Loss through Trash Racks

## 7. Results and Discussion

#### 7.1. Model Validation

#### 7.2. Flow Characteristic through Rack Bars

#### 7.2.1. Impact of Bar Spacing (Category-1 of Scenario Modeling)

_{c}>) varied between 0.23 and 0.26.

#### 7.2.2. Impact of the Inclination Angle of Bars (Category-2 of Scenario Modeling)

_{c}) varied between 0.20 and 0.27. The change in inclination of trash racks, however, does not alter the blockage ratio for any of the simulated arrangements. It implies that inclination angle is itself an influencing factor to induce the loss in head of approaching flow.

#### 7.2.3. Impact of Blockage Ratio (Category-3 of Scenario Modeling)

_{c}>), in this case, varied between 0.23 and 0.26.

#### 7.3. Derivation of an Empirical Equation

#### 7.4. Comparison of the Proposed Equation with Existing Head Loss Equations

## 8. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

u, v, and w | velocities in the x-, y-, and z-directions; |

V | volume fraction of fluid in each cell; |

Ax, Ay, and Az | fractional areas open to flow in the subscript directions; |

ρ | density; |

P′ | pressure; |

g_{i} | gravitational force in the subscript direction; |

f_{i} | Reynolds stresses; |

A_{j} | cell face areas; |

Stl | stereo lithographic; |

s | clear spacing between bars; |

α | inclination angle of the trash racks with channel bed; |

p | blockage ratio; |

$\Delta \mathit{h}$ | head loss; |

${\mathit{h}}_{\mathit{r}}$ | head loss by Kirschmer; |

${\mathit{k}}_{\mathit{F}}$ | Kirschmer shape factor; |

$\mathit{K}$ | Escande head loss coefficient; |

$\mathit{k}$ | Fellenius head loss coefficient; |

$\mathbf{\varnothing}$ | Shape factor |

$\mathit{s}$ | Bar thickness for Orsborn equation |

${\mathit{A}}_{\mathit{N}}$ | net area through rack bars; |

$\mathit{A}\mathit{g}$ | gross are through rack bars; |

$\Delta {\mathit{h}}_{\mathit{c}}$ | head loss coefficient; |

v | velocity of approaching flow; |

g | gravitational acceleration; |

U/S | upstream; |

$\mathit{t}$ | thickness of vertical rack; |

${\mathit{R}}^{\mathbf{2}}$ | determination coefficient; |

$\mathbf{a}\mathbf{d}\mathbf{j}.{\mathit{R}}^{2}$ | adjusted determination coefficient; |

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**Figure 2.**(

**a**): Geometry of intake trash racks imported in CFD Code. (

**b**): Intake geometry after applying mesh.

**Figure 5.**Definition sketch of clear spacing (

**s**) and inclination angle (α). (

**a**) Front view of rack bars; (

**b**) Side view of rack bar.

Set No. | X | Y | Z | |||
---|---|---|---|---|---|---|

X_{min.} | X_{max.} | Y_{min.} | Y_{max.} | Z_{min.} | Z_{max.} | |

Set 1 | Specified Pressure | Outflow | Symmetry | Symmetry | Wall | Specified Pressure |

Set 2 | Specified Pressure | Specified Pressure | Symmetry | Symmetry | Wall | Specified Pressure |

Set 3 | Volume Flow Rate | Outflow | Symmetry | Symmetry | Symmetry | Specified Pressure |

Set 4 | Specified Velocity | Outflow | Symmetry | Symmetry | Wall | Specified Pressure |

Parameter | Existing Trash Rack | Category 1 | Category 2 | Category 3 | ||||
---|---|---|---|---|---|---|---|---|

(a) | (b) | (c) | (a) | (b) | (c) | (a) | ||

Clear spacing ‘s’ (mm) | 100 | 50 | 75 | 125 | 100 | 100 | 100 | 100 |

Inclination angle ‘α’ | 75° | 75° | 75° | 75° | 60° | 70° | 80° | 75° |

Blockage ratio ‘p’ | 0.09 | 0.17 | 0.12 | 0.07 | 0.09 | 0.09 | 0.09 | 0.13 |

Equation Developed by | Formulation for Head Loss |
---|---|

Kirschmer | $\Delta {h}_{r}={k}_{F}\times {\left(\frac{t}{b}\right)}^{\frac{4}{3}}\times \mathrm{sin}\alpha \times \frac{{v}^{2}}{2g}$ |

USBR | $\Delta h=\left(1.45-0.45\frac{{A}_{N}}{{A}_{g}}-{\left(\frac{{A}_{N}}{{A}_{g}}\right)}^{2}\right)\times \frac{{v}^{2}}{2g}$ |

Orsborn | $\Delta h=\varnothing \times {\left(\frac{s}{b}\right)}^{\frac{4}{3}}\times \mathrm{sin}\alpha \times \frac{{v}^{2}}{2g}$ |

Fellenius | $\Delta {h}_{r}=k\times \frac{t}{t+b}\times \frac{{v}^{2}}{2g}$ |

Escande | $\Delta {h}_{r}=\left(\frac{1}{K}-1\right){}^{2}\times \frac{{v}^{2}}{2g}$ |

CFD Results | Site Data | % Difference in Flow Depth | % Difference in Hydraulic Head | ||
---|---|---|---|---|---|

U/S Hydraulic Head (m) | Flow Depth (m) | U/S Hydraulic Head (m) | Flow Depth (m) | ||

232.78 | 8.6 | 233.59 | 9.4 | 8.6 | 0.35 |

Approach Velocity (m/s) | Upstream of Trash Rack | Downstream of Trash Rack | Head Loss (m) | ||||
---|---|---|---|---|---|---|---|

Observation Points (m) | Total Hydraulic Head (m) | Observation Points (m) | Total Hydraulic Head (m) | ||||

x | y | x | y | ||||

0.5 | 27.32 | 11.85 | 233.313 | 29.62 | 11.85 | 233.310 | 0.0030 |

0.6 | 27.32 | 11.85 | 233.318 | 29.62 | 11.85 | 233.314 | 0.0043 |

0.7 | 27.32 | 11.85 | 233.323 | 29.62 | 11.85 | 233.317 | 0.0060 |

0.8 | 27.32 | 11.85 | 233.330 | 29.62 | 11.85 | 233.323 | 0.0074 |

0.9 | 27.32 | 11.85 | 233.338 | 29.62 | 11.85 | 233.328 | 0.0010 |

1 | 27.32 | 11.85 | 233.346 | 29.62 | 11.85 | 233.334 | 0.0120 |

Term | Coefficient | p-Value |
---|---|---|

Constant | 0.21419 | 0.000 |

$\mathit{t}\mathit{a}\mathit{n}$ (90 − α) | −0.0441 | 0.035 |

$\frac{\mathit{t}}{\mathit{s}}$ × $\mathit{t}\mathit{a}{\mathit{n}}^{\mathbf{2}}$ (α) | −0.02104 | 0.002 |

p × $\mathit{t}\mathit{a}{\mathit{n}}^{\mathbf{2}}$ (α) | 0.04622 | 0.000 |

Equation for Trash Racks Losses | MRE (%) |
---|---|

Kirschmer | 46.8 |

USBR | 36.5 |

Orsborn | 40.8 |

Fellenius | 19.1 |

Escande | 71.3 |

Present Study | 3.6 |

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**MDPI and ACS Style**

Latif, M.A.; Sarwar, M.K.; Farooq, R.; Shaukat, N.; Ali, S.; Hashmi, A.; Tariq, M.A.U.R. Estimating Energy Efficient Design Parameters for Trash Racks at Low Head Hydropower Stations. *Water* **2022**, *14*, 2609.
https://doi.org/10.3390/w14172609

**AMA Style**

Latif MA, Sarwar MK, Farooq R, Shaukat N, Ali S, Hashmi A, Tariq MAUR. Estimating Energy Efficient Design Parameters for Trash Racks at Low Head Hydropower Stations. *Water*. 2022; 14(17):2609.
https://doi.org/10.3390/w14172609

**Chicago/Turabian Style**

Latif, Muhammad Ahsan, Muhammad Kaleem Sarwar, Rashid Farooq, Nadeem Shaukat, Shoaib Ali, Abrar Hashmi, and Muhammad Atiq Ur Rehman Tariq. 2022. "Estimating Energy Efficient Design Parameters for Trash Racks at Low Head Hydropower Stations" *Water* 14, no. 17: 2609.
https://doi.org/10.3390/w14172609