Visualization of Flow Past a Bluff Body

Overview

Source: Ricardo Mejia-Alvarez, Hussam Hikmat Jabbar and Mahmoud N. Abdullatif, Department of Mechanical Engineering, Michigan State University, East Lansing, MI

Owing to the non-linear nature of its governing laws, fluid motion induces complicated flow patterns. Understanding the nature of these patterns has been the subject of intense scrutiny for centuries. Although personal computers and supercomputers are extensively used to deduce fluid flow patterns, their capabilities are still insufficient to determine the exact flow behavior for complex geometries or highly inertial flows (e.g. when momentum dominates over viscous resistance). With this in mind, a multitude of experimental techniques to make flow patterns evident have been developed that can reach flow regimes and geometries inaccessible to theoretical and computational tools.

This demonstration will investigate fluid flow around a bluff body. A bluff body is an object that, due to its shape, causes separated flow over most of its surface. This is in contrast to a streamlined body, like an airfoil, which is aligned in the stream and causes less flow separation. The purpose of this study is to use hydrogen bubbles as a method of visualizing flow patterns. The hydrogen bubbles are produced via electrolysis using a DC power source by submerging its electrodes in the water. Hydrogen bubbles are formed in the negative electrode, which needs to be a very fine wire to ensure that the bubbles remain small and track fluid motion more effectively. This method is suitable for steady and unsteady laminar flows, and is based on the basic flow lines that describe the nature of the flow around objects. [1-3]

This paper focuses on describing the implementation of the technique, including details about the equipment and its installation. Then, the technique is used to demonstrate the use of two of the basics flow lines to characterize the flow around a circular cylinder. These flow lines are used to estimate some important flow parameters like flow velocity and the Reynolds number, and to determine flow patterns.

Procedure

1. To produce a continuous sheet of bubbles:

Set the equipment according to the electrical diagram shown in Figure 3.
Fix the positive electrode in the water at the downstream end of the test section (see Figure 4 for reference).
Fix the negative electrode upstream and near the point of interest to release the bubbles into the stream before the flow reaches the object of study (see Figure 4 for refere

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Results

Figure 2 shows two representative results of hydrogen bubble visualization of a Von Kármàn vortex street. Figure 2(A) shows an example of a field of streaklines as evidenced by disturbances in the hydrogen bubble sheet. This image is used to extract the diameter of the rod in machine units. Figure 2(B) shows an example of a field of timelines. This image is used to estimate the approaching

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Application and Summary

In this study, the usage of hydrogen bubbles was demonstrated to extract qualitative and quantitative information from images of flow around a circular cylinder. The quantitative information extracted from these experiments included the free-stream velocity (), vortex-shedding frequency (), Reynolds number (Re), and the Strouhal number (St). In particular, the results for St vs Re exhibited very good agreement with pre

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References

Zöllner, F. Leonardo da Vinci 1452-1519: sketches and drawings, Taschen, 2004.
White, F. M. Fluid Mechanics, 7^th ed., McGraw-Hill, 2009.
Adrian, Ronald J., and Jerry Westerweel. Particle Image Velocimetry. Cambridge University Press, 2011.
Gerrard, J. H., The wakes of cylindrical bluff bodies at low Reynolds number, Phil. Trans. Roy. Soc. (London) Ser. A, Vol. 288, No. 1354, pp. 351-382 (1978)
Coutanceau, M. and Bouard, R., Experimental determination of the viscous flow in the wake of a circular cylinder in uniform translation. Part 1. Steady flow, J. Fluid Mech., Vol. 79, Part 2, pp. 231-256 (1977)
Kovásznay, L. S. G., Hot-wire investigation of the wake behind cylinders at low Reynolds numbers, Proc. Roy. Soc. (London) Ser. A, Vol. 198, pp. 174-190 (1949)
Fey, U., M. König, and H. Eckelmann. A new Strouhal-Reynolds-number relationship for the circular cylinder in the range . Physics of Fluids, 10(7):1547, 1998.
Maas, H.-G., A. Grün, and D. Papantoniou. Particle Tracking in three dimensional turbulent flows - Part I: Photogrammetric determination of particle coordinates. Experiments in Fluids Vol. 15, pp. 133-146, 1993.
Malik, N., T. Dracos, and D. Papantoniou Particle Tracking in three dimensional turbulent flows - Part II: Particle tracking. Experiments in Fluids Vol. 15, pp. 279-294, 1993.
Tropea, C., A.L. Yarin, and J.F. Foss. Springer Handbook of Experimental Fluid Mechanics. Vol. 1. Springer Science & Business Media, 2007.
Monaghan, J. J., and J. B. Kajtar. Leonardo da Vinci's turbulent tank in two dimensions. European Journal of Mechanics-B/Fluids. 44:1-9, 2014.
Becker, H.A. Dimensionless parameters: theory and methodology. Wiley, 1976.

Tags

Flow Visualization Bluff Body Flow Patterns Vortex Shedding Separation Circular Cylinder Boundary Layer Wake Vortices Low Pressure Von Karman Vortex Street Reynolds Number

1. To produce a continuous sheet of bubbles:

Set the equipment according to the electrical diagram shown in Figure 3.
Fix the positive electrode in the water at the downstream end of the test section (see Figure 4 for reference).
Fix the negative electrode upstream and near the point of interest to release the bubbles into the stream before the flow reaches the object of study (see Figure 4 for reference). The water completes the circuit between the two electrodes.
Turn on the flow facility
Set the dial of the frequency controller to position 2. This will establish a flow rate of about 9x10^-4 m³/s.
Turn on the DC power supply and increase the voltage up to about 25 V, the current will set itself around 190 mA.
Set the wave form in the signal generator to Square Wave (symbol: ). This generates a 0 V - 5 V square signal that activates the solid-state relay (closing the circuit) in its high position and opens it in the low position
For this particular case, the frequency of the square wave is not important. It just needs to be non-zero.
Maximize the DC offset (+5 V) in the signal generator. With this setting, the circuit is always closed and the system generates bubbles continuously.

Figure 3. Connections diagram.

Figure 4. Test section. Flow goes from left to right. The negative electrode generates a layer of hydrogen bubbles that are swept away with the flow. The positive electrode is set at the downstream end of the test section to avoid its disturbances. Please click here to view a larger version of this figure.

2. To produce timelines:

Turn on the flow facility
Set the dial of the frequency controller to position 2. This will establish a flow rate of about 9x10^-4 m³/s.
Turn on the DC power supply and increase the voltage up to about 25 V, the current will set itself around 190 mA.
Set the wave form in the signal generator to Square Wave (symbol: ). This generates a 0 V - 5 V square signal that activates the solid-state relay (closing the circuit) in its high position and deactivates it (opening the circuit) in the low position
Set the DC offset in the signal generator at +1 V.
Set the frequency of the square wave in the signal generator at 10 Hz.
Set the symmetry of the square wave slightly negative (-2) to increase the space between timelines while conserving the right frequency.

3. To use flow lines to study Von Kármàn vortex streets:

Measure the diameter of the rod,, using a caliper. Use S.I. units for this measurement (m).
Fix a cylindrical rod downstream of the negative electrode.
Cast the light of the high-intensity discharge lamp on the layer of hydrogen bubbles. Make sure the light is not directly behind of the line of view to prevent oversaturation of the imaging system
Align the visualization system with the rod; in a way that only the circular tip is visible in front of the camera.
Add a mark in the visualization window and downstream of the rod to use it as the reference to count vortex-shed cycles per unit time.

4. Data analysis for flow past a circular cylinder:

Determination of the conversion factor from machine units to real space units:
1. Measure the width of the shadow cast by the rod on the bubble sheet (see figure 2(A) for reference). Take this measurement right at the rod to avoid distortion with distance. This is the diameter of the rod in machine units, (points or pixels, depending on format)
2. Use the following equation to determine the conversion factor from machine units to real world units:
Determination of flow velocity:
1. Choose a group of undistorted timelines upstream of the bluff body.
2. Measure the distance between the first and last timeline in machine units, (points or pixels).
3. Count the number of timelines in the group, .
4. Take note of the frequency of the square wave signal as produced by the signal generator, .
5. Determine the approaching flow velocity from the following equation:
Determination of the Reynolds number:
1. Find the kinematic viscosity of the working fluid (e.g. water m²/s).
2. Calculate the Reynolds number using equation (1). For that, considering the diameter of the rod () measured in step 3.1, the approaching velocity () determined with equation (5), and the kinematic viscosity determined in step 4.3.1
Determination of the Strouhal number: the vortices in the wake of the rod are moving at a different velocity as the timelines in the free stream. Hence, the frequency of vortex shedding needs to be estimated independently.
1. Define a fixed reference downstream of the rod. This reference could be a fine string attached to the exterior of the tunnel or a digital line added to a video of the flow process.
2. Count the number of vortex shedding cycles, , crossing the reference during a defined period of time . A vortex shedding cycle is illustrated in Figure 2(A).
3. Calculate the shedding frequency from the following equation:
4. Use the results from equations (5) and (6) in equation (2) to calculate the Strouhal number.

Skip to...

0:07

Overview

0:55

Principles of Flow Separation

4:21

Producing Bubbles and Timelines in the Flow Facility

5:57

Setting up the Bluff Body

6:41

Studying and Analyzing the Von Karman Vortex Street

8:02

Representative Results

9:07

Applications

10:07

Summary

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