# Open Water Flume for Fluid Mechanics Lab

## Abstract

**:**

## 1. Introduction

## 2. Basic Design and Pump Selection

^{2}. The length of the observation chamber was designed to be 60 cm. This length is needed to provide enough observation room for vortex trail and wakes behind objects exposed to water flow. The final length of the test chamber is 75 cm. The selection of the maximum speed and chamber dimension was based on a commercial water flume used in experiments on vortex-induced oscillation of cylinders [41]. An upstream manifold in a shape of converging chamber of about 44 cm is added to provide room for the water to reduce its turbulence and complex characteristics prior to enter the observation chamber. The height of the observation chamber was designed to be ~1.2 m, a little less than the average height of human eyes of ~1.4 m. The top side of the observation chamber is expected to be open to allow direct physical access to the flow and, more importantly, easy placement of objects exposed to the flow. Tight covering of the top side to achieve high speed of water flow is possible, but the pressure increase must carefully be calculated. The flow tank was designed to be mobile, so that it can be easily moved when needs arise. The overall length and width of the flow tank therefore is constrained to size of the school’s freight elevator of approximately 2.16 by 2.44 m

^{2}. This size put limitation on the total length of the equipment to be about 2.5 m. The overall budget of this device is set to be less than USD 10,000, based on the maximum fund by the sponsor for this project: Vibration Institute. As the project is scheduled for a senior design project, the design and construction must be finished in two semesters.

^{3}and 0.001 Pa.s [43,44], respectively, while the gravitational constant $g=9.81$ m/s

^{2}. Not knowing the pump to be purchased yet, we estimated the pump efficiency $\eta $ from commercial pump examples presented in textbooks [43,44]. Based on these examples, for the required flow rate of 214 gpm, the efficiency was found to be about $\eta \approx 60\%$. Using these data, we can estimate the required pump power to be only ${W}_{p}=793\mathrm{W}$ or about 1.06 hp. Note that the power calculation here is based on high flow rate but very low head loss, due to the very short pipe and minimal height involved in the current design. Consequently, such a pump, with such combination of low pump power and high flow rate, may not be available in the market. Here, students need to realize that the market availability of the pump puts a constraint in the design.

^{3}/s based on the required flow speed of 60 cm/s. The major loss is defined as $h=f\frac{L}{D}\frac{{\overline{V}}^{2}}{2g}$ and the friction factor for each section is determined from the Moody chart based on the associated Reynolds number and given roughness factors of the pipes [42,43,44,45]. Due to the short pipes involved in this design, this calculation renders net head much less than 1 m, well below the estimated head mentioned before. As expected, the required head is dominated by the height of the water column that must be overcome.

## 3. Static and Dynamic Analysis of Supporting Frame

^{2}hollow square tubing with a thickness of 2.11 mm. The static analysis involves calculations of dead loads acting on the system, which includes the weight of the water and the tank. Table 5 lists all possible static load items and its estimated amount. The list was prepared by students as part of the full static and dynamic structural analysis of the supporting frame. Several possible designs were analyzed and results from one design is presented here.

## 4. Computational Fluid Dynamics

^{®}Core™ i7-6600U CPU @ 2.60 GHz. One model is run using a desktop HP Compaq Elite 8300 CMT computer equipped with Intel

^{®}Core TM i7-3770 CPU at 3.40 GHZ and 16.0 GB RAM.

^{2}. At the end of the chamber, the water is collected in a rectangular drainage tank of $60\times 30\times 40{\mathrm{cm}}^{3}$. The CFD model does not include a horizontal transparent plastic pipe that returns the water back from the drainage chamber into the centrifugal pump.

## 5. Fabrication and Manufacturing

^{3}observation chamber was made of 0.635 cm thick transparent plexiglass. The corners are secured using both glue and bolts. To prevent leaking, rubber gasket is applied throughout. Finally, several holes are drilled on the upper edge of the chamber wall (not shown in the figure) to allow experiment platform to be secured onto.

## 6. Experiment Results and Discussion

- Velocity Measurement of flow in the observation chamber;
- Tests on flow straightener designs;
- Flow visualization using dye;
- Measurements of drags.

#### 6.1. Velocity Measurement of Flow in the Observation Chamber

#### 6.2. Tests on Flow Straightener Designs

^{3}, furnished with 12-by-12 holes, each about 1.2 cm in diameter. Model 3 is a combination of parallel 0.5”-PVC (12.7 mm in diameter) pipes that are hold together using 3D-printed blocks with holes on their ends. Among the three models, Model 1 is the cheapest, but is very tedious to make, as each pipe has to be glued one by one. During the bonding process, the pipes can be placed in between two parallel walls. Model 2 is the most expensive, when the printing time is included in the calculation. While the SolidWorks (Dassault Systèmes SolidWorks, Inc., Waltham, MA, USA) CAD model for this model is easy to make, it took more than 12 h to print the model using a regular desktop 3D-printer. The thin walls separating the holes require the model to be printed with high density (high infills), and this prolongs the printing process. While involving 3D-printed blocks, Model 3 is inexpensive, as the holes on these blocks are well separated from one another, requiring less printing density compared to Model 2. Nevertheless, the arrangement of the pipes into these blocks is quite tedious. In terms of durability, it was quickly found that Model 1 disintegrated quite easily after several tests in the water. Model 2 also shows signs of plastic fibers detached from the bulk structure after several tests. Model 3 is the most durable, but its effectiveness is the lowest.

^{3}cork to travel for 50 cm is measured using a manual stopwatch. This measurement results in smaller velocity compared to ones measured using the propeller. These Lagrangian velocities are displayed in Figure 14 using dark cross legends. The lower estimation can be attributed to the drag produced by the weight of the cork, as well as accuracy of the manual data collection. Nevertheless, the manual measurement using cork provides a simple and quick validation of the Eulerian method employed in the automatic measurement using digital flow meter.

#### 6.3. Flow Visualization Using Dye

#### 6.4. Measurements of Drags

^{®}Force Sensor—GDX-FOR) that uses strain gauge to measure as small as $\pm 0.1\mathrm{N}$ up to $\pm 50\mathrm{N}$ of axial force, sufficient range for our fluid application. A sampling rate of 50 Hz, out of a possible maximum of 1000 Hz, is used in our application. This device can be either directly connected to a laptop using a USB cable, or wirelessly using a Bluetooth to a mobile device. The stream data can be displayed on a laptop and recorded using a software Graphical Analysis available for free from Vernier. The force sensor can also be connected to the data acquisition card by Vernier—LabQuest Mini. This allows simultaneous measurement of multiple sensors with other data such as water speed, temperature, and lift. The ~7 × 4 × 5 cm

^{3}sensor device is placed on $~15\times 15\times 1.5{\mathrm{cm}}^{3}$ (1.36 kg) aluminum sled supported by four smooth wheels (rollers) that rest on the walls of the observation chamber (Figure 16). The sled was machined to include a hollowed pin on its top to secure the force sensor. A hole was drilled at the center of the sled to allow samples to be secured using bolt and nut. The other end of the bar is free. The force registration is performed by aligning the sensor’s hook to the flow direction and securing it to a reference point fixed to the chamber’s wall. The four smooth wheels reduce the contribution friction caused by the sled’s weight and maximize the registration of the hydrodynamic drag by the sensor.

## 7. Budget

## 8. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Sketch of 1st design of the flow tank loop given by students and (

**b**) the basic flow diagram for the calculation of pump head needed to determine the pump power.

**Figure 2.**Left panel (

**a**) shows the drawing of the water tank and its major components; 1. observation chamber, 2. centrifugal pump, 3. variable frequency drive or pump controller, 4. return pipe to the pump, 5. inlet manifold into the observation chamber, 6. holding tank, 7. structural frame, 8. wheels, and 9. ball valve. On the right, panel (

**b**) shows the final product of the water tank supported by frames and wheels.

**Figure 3.**The deformed shape of the supporting frame due to the dead loads indicate maximum deflection of about 0.001 inch occurs on the cross beam that supports the observation chamber. The 3D static analysis in ANSYS is performed by members of capstone senior design team.

**Figure 4.**Panel (

**a**) shows the computational domains involved in the analysis and panel (

**b**) shows the non-uniform mesh generation implemented for the analysis.

**Figure 5.**Convergence studies—data with dark labels indicate relationship between number of mesh and computation time, while the white markers indicate the relationship between the number of mesh and accuracy. The Laminar model shows the lowest accuracy and computing time. The Turbulent models can take 10 times longer time than the laminar flow, but its accuracy is very high.

**Figure 6.**Three-dimensional streamlines obtained from an (

**a**) Laminar model and (

**b**) Turbulent model. The Turbulent model captures well the twin circulation zone occurring in the drainage tank and the collecting chamber. The Laminar model fails to capture the circulation zone despite of the use of large number of elements.

**Figure 7.**Axial velocity profiles obtained at the horizontal mid-section of the observation chamber taken at different distances Y from the entrance obtained using (

**a**) Global Mesh refinement and using “Normal” scheme (Model B4) and (

**b**) Partial Refinement method (Model F).

**Figure 8.**Streamlines in the observation chamber and the diffusion chamber as well as in the collecting chamber produced by (

**a**) Laminar model, (

**b**) Turbulent model with Global Mesh “normal” refinement, and (

**c**) Turbulent model with Partial Refinement method. The mean velocity of these models at the inlet is 3 m/s.

**Figure 9.**Panel (

**a**) shows the circulation zone captured using laminar modeling; (

**b**) Partial Refinement results in 5498 tetrahedron elements in the drainage tank, a minimum element quality of 0.6541, and an element volume ratio of 0.001275; (

**c**) Global “Coarser Mesh” mesh with Turbulent model with 14,681 mixed elements, a minimum element quality 0.1307, and an element volume ratio 0.0021; and (

**d**) Global Mesh refinement with “Normal” mesh with Turbulent model with 61,052 mixed elements in the drainage tank, a minimum element quality of 0.1251, and an element volume ratio of $9.8\times {10}^{-4}$.

**Figure 10.**Panel (

**a**) shows the cardboard model used in the making of the diffusion channel. Panel (

**b**) shows the observation chamber being assembled, and panel (

**c**) shows the final product of drainage chamber before being assembled into the main body.

**Figure 11.**The panel (

**b**) displays the velocity reading by Vernier flow meter versus time when the pump operates at 40 and 50 Hz. The propeller is placed either near the floor of the chamber (“Bottom”) or approximately in mid-height (“Middle”). Data suggests minimum difference by the two methods. The panel (

**a**) shows the propeller being lowered in the “Middle” position in the observation chamber.

**Figure 12.**Models of flow straightener used in the flow experimentation—(

**a**) Model 1 is made of cut PVC pipes that are glued together in parallel arrangement. (

**b**) Model 2 is a full 3D-printed apparatus designed in SolidWorks. (

**c**) Model 3 is an assembly of PVC pipes fitted into 3D-printed block with holes.

**Figure 13.**This figure shows mean velocities from the flowmeter for various flow straightener models taken for a period of 120 s when the pump speed is 10 Hz. The blue line is the velocity of water flow without flow straightener. The velocity after the installation of Model 2 shows stability compared to other models.

**Figure 14.**This figure shows the comparison of time-averaged velocity data versus pump’s frequency. The data are obtained using Models 1 and 2 of the flow straighteners. The data from measuring the water velocity using floating cork are presented using cross symbols. Data from Model 1 shows minimal deviation from the reference data. The cork data underestimates the reference data, but it gives good estimate for a quick verification of the flow meter.

**Figure 15.**The flow behavior at about 10 cm/s. was observed using color dye injected by a syringe. The left panel (

**a**) shows the dispersion of the dye when no flow straightener was used. Turbulence characteristic can be seen from the dyes. Panels (

**b**,

**c**) shows the flow characteristic when Model 2 is used as flow straightener. Straight streamline is easily observed in this case.

**Figure 16.**The figure on the left panel (

**a**) shows the force sensor supported by the aluminum platform (sled) with its wheels placed along the wall of the observation chamber. The panel (

**b**) on the right shows the complete setup of the drag sensor secured on the observation chamber with the flow meter placed upstream to allow simultaneous measurements of flow speed and drag forces. The water flows from left to right.

**Figure 17.**This graph shows typical force data collected during a test. For this data, the time-averaged velocity is 0.594$\pm 0.01$ m/s (not shown), while the time-averaged force is 0.386$\pm 0.072$ N. The sample is 16 mm cylinder bar using data sampling of 50 Hz.

**Figure 18.**The mean velocity vs. mean force shows monotonic increase in the drag force with the increase in applied velocity. Error bars show standard deviations that increase with the velocity. The errors from the flow meter are relatively smaller compared to that from the force sensor.

**Figure 19.**Average drag coefficients (${\overline{C}}_{D}$) for the circular cylinder and square bar for various flow speeds (Reynolds numbers). The error bars indicate the “maximum” and “minimum” ${C}_{D}$ values calculated using the extreme values of speeds and forces obtained during the sampling period of 120 s. The average ${C}_{D}$ values across the range of Reynolds number for the cylinder and square bar are 1.48 and 1.58, respectively. The data marked by dark circles are obtained using formulation proposed by Tang et al. [54], and the dash line represents the constant known ${C}_{D}$ typically presented in textbooks.

**Figure 20.**Linear correlation between the drag force and ${\overline{V}}^{2}$ (square of the velocity) can be used to obtain the drag coefficients. The high ${R}^{2}$ numbers suggest that the linear regression fits the data very well. The gradient for the square bar data (empty square markers) is slightly higher than that of the cylindrical bar (circle markers).

Materials | Length (m) | Diameter (m) | Roughness (mm) | $\overline{\mathit{V}}$ (m/s) | Re | f | $\mathit{h}\left(\mathbf{m}\right)$ |
---|---|---|---|---|---|---|---|

Plexiglass | 0.6 | $0.15\times 0.15$ | 0.0015 | 0.6 | 100,921 | 0.018 | 0.001 |

Stainless Steel | 4.0 | $~0.4\times 0.3$ | 0.002 | 0.11 | 49,339 | 0.021 | <<0.001 |

Plastics | 1.0 | $\pi \times {0.05}^{2}$ | Smooth | 1.7 | 95,315 | 0.017 | 0.05 |

Components | Amount | K |
---|---|---|

Ball valve | 1 | 0.05 |

Couplings | 7 | 0.08 |

Entrances | 6 | 0.5 |

Sudden Expansion | 1 | 0.5 |

**Table 3.**List of potential centrifugal pumps available in McMaster–Carr and its working fluid, maximum flow rate, power requirement, maximum head, and unit price.

Pump # | Product Name | Working Fluid | Max. Flow Rate (gpm) | Power (hp) | Maximum Head (m) | Price (USD, 2018) |
---|---|---|---|---|---|---|

A | High-efficiency Circulation Pumps | Water, coolants, oil | 190 | 5 | 19 | ~1800 |

B | High-Flow Harsh-Environment Circulation Pump | Water, coolants | 375 | 3 | 20 | ~1105 |

C | High-Flow Inline Circulation Pumps for Water | Water only | 240 | 3 | 14.6 | ~2100 |

**Table 4.**An example of decision matrix for pump selection process. Each student involved in the project may participate in the selection process by filling out this table.

Product | Working Fluid | Flow Rate | Power | Maximum Head | Price | Total Score |
---|---|---|---|---|---|---|

A | 1 | 1 | 3 | 2 | 2 | 9 |

B | 3 | 2 | 2 | 3 | 3 | 13 |

C | 2 | 3 | 1 | 1 | 1 | 8 |

Components | Weight (kg) | Description |
---|---|---|

Water | 362.87 | Total weight of water at full capacity |

Observation chamber | 11.16 | This section is made out of acrylic |

Pump | 43.54 | Self-priming centrifugal pump |

Piping | 4.72 | Total weight of steel channels |

Manifolds | 29 | Inlet and outlet chambers, made out of stainless steel |

Steel strucure | 4.99 | Constructed out of 2 × 2 square tubings |

Total dead load | 456.28 |

**Table 6.**The first six natural frequencies of the supporting frames are listed in this table, along with the maximum deformation associated with the harmonic analysis.

Modes | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|

Freq. (Hz) | 23.53 | 36.21 | 39.28 | 70.91 | 73.18 | 86.59 |

Max $\delta $(mm) | 2.108 | 2.489 | 2.108 | 2.007 | 5.512 | 2.108 |

**Table 7.**This table lists CFD models used in this project and their associated number of elements and computation times. Only models A1 and A2 are executed using Laminar fluid model. All other models are executed using Turbulent model—RANS K-$\epsilon $ . All models are run in the HP ProBook, except Model D.

Model # | Mesh Method | Fluid Model | Number of Elements | Computation Time (s) |
---|---|---|---|---|

A1 | Partial Refinement | Laminar | 91,162 | 3630 |

A2 | Partial Refinement | Laminar | 289,796 | 21,787 |

B1 | Global Extremely Coarse | Turbulent | 21,011 | 6760 |

B2 | Global Extra Coarse | Turbulent | 43,753 | 17,861 |

B3 | Global Coarser Mesh | Turbulent | 76,983 | 34,030 |

B4 | Global Normal Mesh | Turbulent | 414,735 | 286,538 |

B5 | Global Fine Mesh | Turbulent | 9,797,088 | Failed to converge |

C | Partial Refinement | Turbulent | 113,624 | 25,626 |

D | Partial Refinement | Turbulent | 160,774 | 20,680 |

E | Partial Refinement | Turbulent | 160,378 | 35,046 |

F | Partial Refinement | Turbulent | 355,730 | 145,860 |

**Table 8.**List of the ${C}_{D}$ values obtained in our experiments compared to that presented in textbooks. The 2D and 3D refer to the two-dimensional and three-dimensional assumptions of the immersed bodies. The ${\overline{C}}_{D}$ refers to the averaged coefficient of drag. The ${\widehat{C}}_{D}$ is obtained using the linear regression analysis of ${\overline{F}}_{D}vs.{\overline{V}}^{2}$.

Sample | Diameter/Side | ${\overline{\mathit{C}}}_{\mathit{D}}$ | ${\widehat{\mathit{C}}}_{\mathit{D}}$ | $\mathbf{Known}\text{}{\mathit{C}}_{\mathit{D}}\text{}\left(2\mathbf{D}\right)$ [44] | $\mathbf{Known}\text{}{\mathit{C}}_{\mathit{D}}\text{}\left(3\mathbf{D}\right)$ [44] |
---|---|---|---|---|---|

Cylinder | 15.94 mm | $1.48\pm 0.25$ | 1.39 | 1.2 | 0.74–0.82 |

Square bar | 15.93 mm | $1.58\pm 0.13$ | 1.61 | 2.1 or 2.2 |

**Table 9.**List of major components of the flume, amount and its 2018 price. Note that the labor cost is not included here.

Item | Total Price (USD) | Percent of Total Cost (%) |
---|---|---|

3″ Self-priming centrifugal pump | 1105 | 19.91 |

Programmable 3-phase AC motor speed control | 723 | 13.03 |

Acrylic Sheet 0.7″ thickness | 298 | 5.37 |

Stainless Steel (various thickness) | 805.9 | 14.52 |

Low-carbon steel square tubes and sheets | 694.5 | 12.51 |

Various hoses, pipes, and fittings | 654 | 11.78 |

Various bearings and mountings | 138.8 | 2.50 |

PVC pipes, fitters, and elbows | 159 | 2.86 |

Welding screen | 240 | 4.32 |

Argon gas supply for welding | 504 | 9.08 |

Various shipping of items | 228.5 | 4.12 |

Total | 5551 | 100 |

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**MDPI and ACS Style**

Wulandana, R. Open Water Flume for Fluid Mechanics Lab. *Fluids* **2021**, *6*, 242.
https://doi.org/10.3390/fluids6070242

**AMA Style**

Wulandana R. Open Water Flume for Fluid Mechanics Lab. *Fluids*. 2021; 6(7):242.
https://doi.org/10.3390/fluids6070242

**Chicago/Turabian Style**

Wulandana, Rachmadian. 2021. "Open Water Flume for Fluid Mechanics Lab" *Fluids* 6, no. 7: 242.
https://doi.org/10.3390/fluids6070242