- 00:07Overview
- 00:55Principles of Flow Separation
- 04:21Producing Bubbles and Timelines in the Flow Facility
- 05:57Setting up the Bluff Body
- 06:41Studying and Analyzing the Von Karman Vortex Street
- 08:02Representative Results
- 09:07Applications
- 10:07Summary
Visualização do Fluxo ao Redor de um Corpo Parado
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Overview
Fonte: Ricardo Mejia-Alvarez, Hussam Hikmat Jabbar e Mahmoud N. Abdullatif, Departamento de Engenharia Mecânica, Michigan State University, East Lansing, MI
Devido à natureza não linear de suas leis de governo, o movimento fluido induz padrões de fluxo complicados. Entender a natureza desses padrões tem sido objeto de intenso escrutínio há séculos. Embora computadores pessoais e supercomputadores sejam amplamente usados para deduzir padrões de fluxo de fluidos, suas capacidades ainda são insuficientes para determinar o comportamento exato de fluxo para geometrias complexas ou fluxos altamente inerciais (por exemplo, quando o momento domina sobre a resistência viscosa). Com isso em mente, uma infinidade de técnicas experimentais para tornar evidentes padrões de fluxo que podem atingir regimes de fluxo e geometrias inacessíveis às ferramentas teóricas e computacionais.
Esta demonstração investigará o fluxo de fluidos em torno de um corpo blefe. Um corpo blefe é um objeto que, devido à sua forma, causa fluxo separado sobre a maior parte de sua superfície. Isso contrasta com um corpo simplificado, como um aerofólio, que está alinhado no córrego e causa menos separação de fluxo. O objetivo deste estudo é usar bolhas de hidrogênio como método de visualização de padrões de fluxo. As bolhas de hidrogênio são produzidas através da eletrólise usando uma fonte de energia DC submergindo seus eletrodos na água. Bolhas de hidrogênio são formadas no eletrodo negativo, que precisa ser um fio muito fino para garantir que as bolhas permaneçam pequenas e rastreiem o movimento do fluido de forma mais eficaz. Este método é adequado para fluxos laminar constantes e instáveis, e é baseado nas linhas de fluxo básicas que descrevem a natureza do fluxo em torno dos objetos. [1-3]
Este artigo se concentra em descrever a implementação da técnica, incluindo detalhes sobre o equipamento e sua instalação. Em seguida, a técnica é usada para demonstrar o uso de duas das linhas básicas de fluxo para caracterizar o fluxo em torno de um cilindro circular. Estas linhas de fluxo são usadas para estimar alguns parâmetros importantes de fluxo, como a velocidade de fluxo e o número de Reynolds, e para determinar padrões de fluxo.
Principles
Procedure
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 fluid velocity. The parameters extracted from this particular experiment are summarized in table 2.
Table 2. Representative results for flow past a circular cylinder.
| Parameter | Value |
| D_o | 0.003 m |
| D_i | 14.528 pts |
| f_s | 2.169 Hz |
| f_tl | 10 Hz |
| L | 130.167 "pts" |
| M | 4842.67 "pts" ∕"m" |
| N_s | 60 |
| N_tl | 7 |
| T | 27.66 s |
| U_∞ | 0.0384 m/s |
| ν | 1.004×[10]^(-6) m2/s |
| Re | 115 |
| St | 0.169 |
Since the Reynolds number is 115 for the present example, the validity of this result can be tested using equation (3) for 
(7)
From which we obtain:
(8)
After comparing this estimation with our experimental result (see table 2 for reference), we can conclude that our experiment offered a satisfactory result. Figure 5 shows a set of experimental results compared with the predictions of equation (7).
Figure 5. Experimental results. Comparison of current experimental results against predictions of the relation between the Reynolds number and the Strouhal number for flow past a circular cylinder.
Applications 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 previous studies [3].
Due to the slow velocity used in the current experiments, perturbations in the bubble sheet produce a streaky bubble layer. These streaks are basically streaklines. As the hydrogen bubble sheet travels downstream, these streaklines thicken and become more irregular. This is the result of turbulence intensity in the free-stream. The effect is attenuated as the velocity of the tunnel is increased since the bubbles leave the test section before presenting a significant dispersion. Streaklines can also be produced at pre-selected locations by coating the wire while leaving small parts of it exposed to water.
The current flow behavior is directly applicable to flow past engineering structures such as the pillars of bridges and offshore oil-rigs, wind turbine towers, or power line poles to name a few. And in fact, this behavior is exhibited by bluff bodies with geometries other than cylindrical such as sky scrapers. Given that vortices generate fluid-structure interactions that make structures oscillate, knowing the vortex shedding frequencies at which a given structure will be exposed is critical for its design. In that regard, the engineer has to make sure that the natural frequency of the structure is not such that it will resonate with the vortex shedding frequency, because this effect will inevitably lead to catastrophic failure of the structure. Using appropriate scaling laws [10] and hydrogen bubbles in a water tunnel, an engineer can simulate the interaction of flow with a structure prior to its construction to make sure that its design is safe or to find out if it needs any modifications.
Besides bluff bodies, hydrogen bubble visualization is a very powerful tool to study flow around streamlined bodies such as airfoils or ship hulls. By making use of flow lines generated with this technique, one can determine parameters such as the angle of attack at which stall takes place, or even estimate lift characteristics based on flow velocity. More importantly, the pattern of distortion of fluid lines will help the engineer to optimize its design.
Visualization with hydrogen bubbles is not restricted to external flows like the above mentioned. This method can also be used to observe the flow through open channels or fully confined flow systems. In the latter case, the walls will need to be transparent to ensure optical access. For example, if one is interested in designing a flow diffuser for sub-sonic flow, hydrogen bubbles can be used to determine geometric and flow conditions for which the diffuser will exhibit flow separation and instability. Based on those observations, the design could be experimentally optimized to ensure its proper functionality.
References
- Zöllner, F. Leonardo da Vinci 1452-1519: sketches and drawings, Taschen, 2004.
- White, F. M. Fluid Mechanics, 7th 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.
Transcript
Due to the nonlinear nature of its governing laws, fluid motion induces complicated flow patterns. These flow patterns are influenced by many factors, one of which is flow past an obstacle such as a bluff body. A bluff body is an object that, due to its shape, causes separated flow over most of its surface. Depending on the flow conditions, this flow may become unstable, giving rise to oscillating flow patterns in the wake called vortex shedding. This video will introduce the basics of flow separation and vortex shedding caused by a bluff body and demonstrate a technique used to visualize the resulting flow patterns.
First, let’s consider the uniform steady flow of water with velocity U infinity called the free stream velocity approaching a circular cylinder. Boundary layer separation on the object’s surface leads to the formation of vortices around the body that eventually detach into the wake. When periodic detachment takes place, the vortices generate alternating areas of low pressure behind the body. This process is called the Von Karman vortex street. This repeating pattern occurs at certain ranges of Reynolds number, a dimensionless parameter defined as the ratio of inertial forces to viscous forces. Here, nu is the kinematic viscosity of the fluid, V is the characteristic velocity or U infinity in this case, and D is the cylinder diameter. For example, in the setup in the following demonstration, when the Reynolds number is around five, the flow exhibits two stable counter-rotating vortices behind the cylinder. As the Reynolds number increases, these vortices elongate in the direction of the flow. When the Reynolds number reaches approximately 37, the wake becomes unstable and oscillates sinusoidally as a result of an imbalance between pressure and momentum. The frequency in which vortices are shed off the cylinder is not constant, rather it varies with the value of the Reynolds number. This shedding frequency is characterized by the Strouhal number, which is another dimensionless parameter. The Strouhal number is defined as shown where f is the vortex shedding frequency. Experimental analysis of flow patterns uses four types of flow lines. A path line is the path that a given fluid particle follows as it moves with the flow. A streak line is the continuous locus of all fluid particles whose motion originated from the same location. A streamline is an imaginary line that is instantaneously and locally tangent to the velocity field. Note that path lines, streak lines, and streamlines coincide with each other under steady flow conditions. In the current flow, this corresponds to regions of the flow upstream from the bluff body or far enough from the influence of its wake. On the other hand, path lines, streak lines, and streamlines differ from each other under unsteady flow conditions. In the current flow, this corresponds basically to the wake of the bluff body. Finally, timelines are the continuous locus of fluid particles that were released to the flow at the same instant in time. In the following experiment, we will use a continuous sheet of tiny hydrogen bubbles to analyze flow patterns using timelines and streak lines. Now, let’s take a look at how to set up the flow experiment.
First, assemble the equipment according to the electrical diagram shown. Fix the positive electrode in the water at the downstream end of the test section. Next, fix the negative electrode upstream. This should be near the point where the bubbles are released into the stream before the flow reaches the object of study. Turn on the flow facility. Then set the dial of the frequency controller to position two in order to establish a mean velocity of about 0.04 meters per second. This velocity corresponds to a flow rate of about 50 to the minus fifth cubed meters per second. Now turn on the DC power supply and increase the voltage to about 25 volts with the current around 190 milliamps. On a signal generator, set the output to a square wave with a zero-volt to five-volt square signal that closes the circuit in its high position and opens it in the low position. Maximize the DC offset to five volts so that the circuit is always closed and the system generates bubbles continuously. To produce timelines, change the DC offset in the signal generator to one volt. Then set the frequency of the square wave to 10 Hertz. Timelines will be produced in the flow. Then set the symmetry of the square wave to minus two in order to increase the space between timelines.
First measure the diameter of the rod using a caliper in SI units. Fix the cylindrical rod downstream of the negative electrode. Cast high-intensity light on the layer of hydrogen bubbles, making sure that the light is not directly behind the line of view to prevent over saturation of the imaging system. Align the visualization system with the rod so 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 point to count vortex shed cycles.
First measure the width of the shadow cast by the rod on the bubble sheet. Take the measurement right at the rod to avoid distortion with distance. Use the rod diameter to determine the conversion factor from machine units to real-world units. Next, choose a group of nearly undistorted timelines away from the bluff body and the influence of its wake. Measure the distance L between the first and last timeline in machine units. Count the number of timelines in the group and note the frequency of the square wave. Determine the approaching flow velocity from the following equation. Now using the kinematic viscosity of water, calculate the Reynolds number. Next, determine the Strouhal number by observing the vortices in the wake of the rod. Note that the vortices move at a different velocity as compared to the timelines in the free stream. Using the fixed string as reference, count the number of vortex shedding cycles, NS, crossing the reference point during a defined period of time. Calculate the shedding frequency. Then use the results to calculate the Strouhal number.
Now that we have gone over the procedure and analysis, let’s take a look at the results. The validity of the result can be determined using a relationship between the Reynolds number and the Strouhal number. The coefficients St* and m depend on the Reynolds number range and can be found in the literature. The Reynolds number in this example is 115. Thus, the values of St* and m can be used to calculate the Strouhal number. The calculated value for the Strouhal number is 0.172, which correlates well to the measured value of 0.169. When this experiment was conducted with varying operational parameters, the calculations of the Reynolds and Strouhal numbers correlated well to the mathematical relationship between the two numbers. This shows how well the bubble method can be used to understand flow patterns around a bluff body.
Understanding flow patterns is essential to the design and operation of many types of engineering applications. Pillars of bridges and offshore oil rigs are designed to withstand the turbulence caused by current flow past the structure. Knowing the vortex shedding frequencies at which a given structure will be exposed is critical for its design. In that regard, engineers have to make sure that the natural frequency of the structure is not such that it will resonate with the vortex shedding frequency because this will inevitably lead to catastrophic failure of the structure. It is also essential to study fluid flow around a streamline object such as an air foil or ship hull. By making use of flow lines, engineers can determine parameters such as the angle at which an airplane stalls or even estimate lift characteristics based on flow velocity.
You’ve just watched Jove’s video on visualizing flow lines around a bluff body. You should now understand the basics of fluid flow patterns and the Von Karman vortex street, how to set up an experiment to visualize these flow patterns, and how to study the flow behavior. Thanks for watching.