# Experimental Observation of Inertial Particles through Idealized Hydroturbine Distributor Geometry

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Design

#### 2.2. Experimental Variables

#### 2.2.1. Collision Geometry

- (a)
- CylinderThe cylinder was constructed from extruded PVC with a smooth surface finish. The center of the cylinder was used as the origin of the coordinate system used in these tests, with the x-axis in the direction of the flow, the y-axis in the transverse flow direction, and the z-axis in the vertical direction. The external diameter of the cylinder geometry was $D=42.2$ mm.
- (b)
- Stay Vane and Wicket Gate ArrayThe centroid of the central wicket gate was defined as the origin of the coordinate system used in these tests with the same coordinate system as the cylinder tests.Each hydroturbine unit at Ice Harbor Dam has a total of 20 wicket gates in the distributor which introduces rotational inertia to the flow in the scroll case, as shown in Figure 1. The incident flow direction, relative to the chord of the stay vanes, is a function of the azimuth and radial distance from the turbine axis. The distribution of incident flow directions was calculated for 3 radial locations from the leading edge of the stay vane; 100 mm, 200 mm and 300 mm. The results indicated a prevalent incident flow direction of approximately 20° relative to the stay vane chord angle. The stay vanes of the experimental tests were therefore orientated at an angle of 20° to the longitudinal axis of the flume.The cross-sectional dimensions of the stay vane and wicket gate geometry were determined using Froude scaling by a factor of 1/12 and were manufactured using CNC machining from 6061 T6 Aluminum with a black anodized finish. The resulting chord length (c) and thickness (t) of the experimental-scale wicket gate were $c=118.5$ mm and $t=24.5$ mm, respectively, as shown in Figure 3c. The harmonic mean length scale of the wicket gate (L) was calculated as $L={\left(0.5({t}^{-1}+{c}^{-1})\right)}^{-1}=40.6$ mm [24]. The cross-section of each stay vane and wicket gate was constant along the length span.The harmonic mean length scale of the stay vane is approximately equal to the diameter of the cylinder geometry. The Reynolds numbers for the cylinder and vane experiments are therefore equivalent to within 4% when calculated using this length scale, such that $Re=UD/\nu \approx UL/\nu $.

#### 2.2.2. Bead Shape

- (a)
- Rod: The rod-shaped bead geometry is based on the scaled geometry of the ‘Sensor Fish’ device [25] which is designed to represent a 100 mm long juvenile fish. The dimensions of the rod were determined using the same 1/12 Froude scaling applied to the blade geometries. This resulted in a bead with a diameter of 2.0 mm and a length of 8.0 mm.
- (b)
- Sphere: A sphere with equal volume as the rod represents a further simplification of the bead geometry by removing the geometric significance of the bead rotation upon collision. This corresponded to a diameter of 3.6 mm.

#### 2.2.3. Wicket Gate Angle

#### 2.2.4. Release Offset

#### 2.2.5. Bulk Flow Speed

#### 2.3. Velocity Characterization

#### 2.4. High-Speed Video Recording

#### 2.5. Experimental Procedure

## 3. Results

#### 3.1. Velocity Measurements

#### 3.2. Particle Collision Results

#### 3.2.1. Cylinder

- Bead Shape:Tests [1–4] vs. [5–8]No significant difference between the collision rates of sphere- and rod-shaped particles were observed. Furthermore, there is no significant difference between the rate of observation of any of the bead passage codes used to describe the bead passage as a result of the bead shape. That is, the error bars of each bead passage code for the spherical bead tests overlap with the error bars for the rod-shaped bead tests with the corresponding experimental conditions.
- Release Offset:Tests [1–2] vs. [3–4] and [5–6] vs. [7–8]A significant decrease in collision rates (Code 4) was observed when release location was offset to $y=D/2$. There is a corresponding increase in particle passage with no deviation (Code 1). This is expected as the mean of the lateral distribution is offset from the center of the cylinder by $\Delta =D$, moving many bead trajectories outside the region of influence of the cylinder.
- Flow Speed:Test 1 vs. 2, 3 vs. 4, 5 vs. 6, 7 vs. 8An increase in flow speed showed consistent trends in observed collision rates. However, the changes in collision rate in response to flow speed were not significant within the confidence intervals of this experiment.These emergent trends are best understood by recalling the increase in particle distribution as a function of increasing Reynolds Number (Figure 9). For the bead injections at $y=0$, this increased bead spread causes a slight reduction in collision rate as the flow speed is increased. This is a result of a larger proportion of the beads arriving at the collision geometry at a greater distance from the cylinder axis. This effect is observed for both the spherical beads (Tests 1–2) and rod-shaped beads (Tests 5–6).For the bead injections at $y=D/2$, the opposite trend was observed, with collision rates increasing as a function of flow speed. In this case, the increase in particle distribution allowed a greater number of beads to disperse over the lateral offset distance to collide with the cylinder geometry. Again, this effect is observed for both the spherical beads (Tests 3–4) and rod-shaped beads (Tests 7–8).

#### 3.2.2. Vane Array

- Wicket Gate Angle:Tests [9–16] vs. [17–24]Increasing the wicket gate angle from the upper 1% angle to the lower 1% setting caused an increase in collision rates, with varying degrees of statistical significance. The experiments with an injection location of $y=0$ are of particular interest in observing this effect (Tests 9–10, 13–14, 17–18, 21–22) as these had notably greater collision rates, for the same reasons as discussed above for the cylinder collision target object. The collision rates of these experiments are plotted in Figure 14.In all cases tested, the collision rates at the upper 1% angle exceeded those at the lower 1% angle. This observation can be interpreted by considering the difference in incident particle distribution between the two cases. The lower 1% wicket gate angle is less aligned with the stay vane than the upper 1% angle, and therefore generates a greater curvature of the streamlines through the vane array than the more streamlined upper 1% configuration. This causes the mean lateral location of the incident bead distribution to be offset by $-18\u2a85y\u2a85-13$ mm. This shift in the lateral distribution is shown graphically in Figure 9 by the white vertical line being offset in the $-y$ direction for the lower 1% configurations (Tests 17, 18, 21, and 22). The resulting collision rates for both the stay vane and wicket gate are reduced as the bulk of the beads pass to the $-y$ side of the central stay vane and wicket gate.This trend is observed for all cases compared in Figure 14, but is most exaggerated for the rod-shaped beads where a mean reduction in strike rate of up to 10% was observed as result of the wicket gate angle adjustment. This corresponds to the pairs of experiments with the greatest difference in mean lateral distribution y-ordinates; namely, Test 21 relative to Test 13 and Test 22 relative to Test 14 (see Figure 9).
- Bead Shape:Tests [9–12] vs. [13–16], [17–20] vs. [21–24]No difference in collision rates as a function of bead shape is observed outside of the error ranges calculated. However, for beads released at $y=0$ as shown in Figure 14, the mean collision rates for the spherical beads are approximately 7% less than the collision rates for the rod-shaped beads when the wicket gate angle is set at the upper 1% position (Tests 9–10 vs. 13–14).
- Release Offset:Tests [9–10] vs. [11–12], [13–14] vs. [15–16], [17–18] vs. [19–20], [21–22] vs. [23–24]As with the cylinder tests, a significant decrease in collision rates was observed when release location was offset to $y=G/2$. There is a corresponding increase in particle passage with no deviation (Code 1). Again, this is expected as the mean of the lateral bead distribution is offset from the central stay vane to the middle of the gap between stay vane pairs.
- Flow Speed:Tests 9 vs. 10, 11 vs. 12, 13 vs. 14, 15 vs. 16, 17 vs. 18, 19 vs. 20, 21 vs. 22, 23 vs. 24As with the cylinder tests, the flow speed effects showed consistent trends in collision rates, though these were not significant within the error margins of the present experiment. However, the observed trends of flow speed on mean collision rates is best understood by recalling the increased dispersion of the beads at the higher flow speeds. In general, for the beads released at $y=0$, the increased dispersion causes a reduction in collisions as the spread of the beads away from the central vane reduces the likelihood of collision (Tests 9 vs. 10, 13 vs. 14, 21 vs. 22). The single exception to this observation is the case of the spherical beads at the lower 1% vane angle (Test 17 vs Test 18). For those released at $y=G/2$, the increased dispersion accounts for the slight trend of increased collision rate as more beads traverse the lateral offset to the collision object (Tests 11 vs. 12, 15 vs. 16, 19 vs. 20, 23 vs. 24).

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. ADV Velocity Processing

#### Appendix A.1. Correlation and SNR Filtering

#### Appendix A.2. Phase-Space Filtering

#### Appendix A.3. Doppler Noise Removal

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**Figure 1.**Computational model of Ice Harbor Dam [23] showing representative horizontal flow velocity in the intake and distributor. The horizontal direction is defined as being perpendicular to runner axis.

**Figure 2.**Schematic of test section of recirculating water flume showing bead injector tube and vane array installation.

**Figure 3.**Collision geometry: (

**a**) cylinder and (

**b**) stay vane and wicket gate array. The details of the stay vane and wicket gate configuration is shown in (

**c**).

**Figure 5.**Dual high-speed cameras show spherical bead passage through vane array at upper 1% configuration (Test 5).

**Figure 6.**Experimental photographs of bead injection and passage. (

**a**) Injection tube showing the release of rod-shaped beads into flume; (

**b**) Bead passage through vane array, viewed from the downstream end of the flume (in -x direction).

**Figure 7.**Transverse velocity profiles of mean flow velocity for the (

**a**) cylinder and (

**b**) vane array collision geometries at $Re=2.1\times {10}^{4}$. The velocity profiles were measured at mid-depth ($z=0$) across four stream-wise locations in the flume; one upstream of the collision geometry ($x=-10D$), and three downstream ($x=10D,15D,20D$).

**Figure 8.**Histograms showing vertical distributions of beads at $x=-2D$ for selected tests. The distribution mean is shown with a light grey line for each test. The extent of the y-axis of these plots is equal to the length of the collision objects.

**Figure 9.**Histograms showing lateral distributions of beads at $x=-2D$ for tests with lateral release location of $y=0$. The distribution mean is shown with a vertical grey line for each test.

**Figure 10.**Summary of bead passage codes for cylinder tests, showing 95% confidence interval of observed rates.

**Figure 12.**Summary of bead passage codes for vane array tests, showing 95% confidence interval of observed rates.

Test # | Target Shape | Wicket Gate Angle | Bead Shape | Release Offset (Δ) | $\mathit{Re}$ ($\times {10}^{4}$) |
---|---|---|---|---|---|

1 | Cylinder | N/A | Sphere | 0 | $1.0$ |

2 | Cylinder | N/A | Sphere | 0 | $2.1$ |

3 | Cylinder | N/A | Sphere | $D$ | $1.0$ |

4 | Cylinder | N/A | Sphere | $D$ | $2.1$ |

5 | Cylinder | N/A | Rod | 0 | $1.0$ |

6 | Cylinder | N/A | Rod | 0 | $2.1$ |

7 | Cylinder | N/A | Rod | $D$ | $1.0$ |

8 | Cylinder | N/A | Rod | $D$ | $2.1$ |

9 | Vane Array | Upper 1% | Sphere | 0 | $1.0$ |

10 | Vane Array | Upper 1% | Sphere | 0 | $2.1$ |

11 | Vane Array | Upper 1% | Sphere | $G/2$ | $1.0$ |

12 | Vane Array | Upper 1% | Sphere | $G/2$ | $2.1$ |

13 | Vane Array | Upper 1% | Rod | 0 | $1.0$ |

14 | Vane Array | Upper 1% | Rod | 0 | $2.1$ |

15 | Vane Array | Upper 1% | Rod | $G/2$ | $1.0$ |

16 | Vane Array | Upper 1% | Rod | $G/2$ | $2.1$ |

17 | Vane Array | Lower 1% | Sphere | 0 | $1.0$ |

18 | Vane Array | Lower 1% | Sphere | 0 | $2.1$ |

19 | Vane Array | Lower 1% | Sphere | $G/2$ | $1.0$ |

20 | Vane Array | Lower 1% | Sphere | $G/2$ | $2.1$ |

21 | Vane Array | Lower 1% | Rod | 0 | $1.0$ |

22 | Vane Array | Lower 1% | Rod | 0 | $2.1$ |

23 | Vane Array | Lower 1% | Rod | $G/2$ | $1.0$ |

24 | Vane Array | Lower 1% | Rod | $G/2$ | $2.1$ |

Code | Description |
---|---|

1 | Minimal deviation in trajectory |

2 | Moderate deviation in trajectory |

3 | Significant deviation in trajectory |

4 | Collision |

$\mathit{Re}=1.0\times {10}^{4}$ | $\mathit{Re}=2.1\times {10}^{4}$ | |
---|---|---|

U (m/s) | 0.26 | 0.53 |

V (m/s) | 0.00 | 0.00 |

W (m/s) | 0.00 | 0.00 |

${\sigma}_{u,c}$ (mm/s) | 1.4 | 1.5 |

${\sigma}_{v,c}$ (mm/s) | 1.7 | 2.7 |

${\sigma}_{w,c}$ (mm/s) | 1.4 | 2.3 |

k $\left({\mathrm{mm}}^{2}{\mathrm{s}}^{-2}\right)$ | 3.4 | 7.3 |

${u}_{t}$ (mm/s) | 1.5 | 2.2 |

$TI$ (%) | 0.58 | 0.42 |

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**MDPI and ACS Style**

Harding, S.F.; Richmond, M.C.; Mueller, R.P. Experimental Observation of Inertial Particles through Idealized Hydroturbine Distributor Geometry. *Water* **2019**, *11*, 471.
https://doi.org/10.3390/w11030471

**AMA Style**

Harding SF, Richmond MC, Mueller RP. Experimental Observation of Inertial Particles through Idealized Hydroturbine Distributor Geometry. *Water*. 2019; 11(3):471.
https://doi.org/10.3390/w11030471

**Chicago/Turabian Style**

Harding, Samuel F., Marshall C. Richmond, and Robert P. Mueller. 2019. "Experimental Observation of Inertial Particles through Idealized Hydroturbine Distributor Geometry" *Water* 11, no. 3: 471.
https://doi.org/10.3390/w11030471