Visualization of Flow Past a Bluff Body

In this configuration, we will consider a uniform steady flow of water with velocity (dubbed free-stream velocity) approaching a circular cylinder (Figure 1). Depending on flow conditions as characterized by the Reynolds number, this flow might become unstable and give rise to vortex-shedding. Vortex shedding is typical in flow past bluff bodies which, as opposed to streamlined bodies, exhibit boundary layer separation over a substantial portion of their surface. This boundary layer separation leads to the formation of vortices behind the body that could eventually detach periodically into the wake. When periodical detachment takes place, the vortices generate alternating areas of low pressure behind the body that could become resonant loads if the shedding frequency coincides with the natural frequency of the body. This vortex shedding process is called the "Von Kármàn vortex street" (Figure 2). This repeating pattern of swirling vortices is caused by unsteady flow separation around the bluff body and occurs at certain ranges of Reynolds number. Avoiding this scenario is of significant importance in designing engineering structures such as smoke stacks and bridge pillars since it could result in catastrophic failure.

Figure 1. Flow past a circular cylinder. Schematic of basic configuration. A homogeneous stream with velocity approaches a straight cylinder of diameter whose axis of symmetry is perpendicular to the approaching velocity.

The Reynolds number is a dimensionless parameter defined as the ratio of inertial forces to viscous forces:

(1)

Where is the kinematic viscosity of the fluid, a characteristic velocity ( in the present case), and the cylinder diameter. The Reynolds number is arguably the most important parameter in the characterization of fluid flow and will be used throughout the present experiment as the metric for the emergence of the Von Kármàn vortex street. In particular, when the Reynolds number is around 5, the flow exhibits two stable counter-rotating vortices behind the cylinder. As the Reynolds number increases, these two vortices elongate in the direction of the flow. When the Reynolds number reaches a value of approximately 37, the wake becomes unstable and begins to oscillate sinusoidally as a result of an imbalance between pressure and momentum. A further increase in Reynolds number up to 47 causes the two counter-rotating vortices to detach from the cylinder in an alternating sequence that follows the sinusoidal wake oscillation [4,5,6].

The frequency with which vortices are shed off the cylinder is not constant; it varies with the value of the Reynolds number. Shedding frequency is characterized by the Strouhal number, which is the other dimensionless parameter of relevance in this particular fluid flow configuration:

  (2)

Here, is the vortex shedding frequency and the length and velocity scales are the same as for the Reynolds number. Vortex shedding frequency can then be characterized by the Strouhal number as a linear function of the inverse square root of the Reynolds number [7]:

  (3)

This function is not always monotonic, it exhibits further transitions as a result of secondary instabilities owed to the non-linearity of fluid flow. As a result, the coefficients and would change according to the Reynolds number range. Table 1 shows the values of these coefficients for the flow regimes that have been well characterized in the literature [7].

During the present experiments, we will use flow lines to study external flow around a circular cylinder. These flow lines are defined as follows:

• Pathline: path that a fluid particle follows as it moves with the flow.

•  Streakline: continuous locus of all the fluid particles whose motion originated at the same spatial location.

• Timeline: set of fluid particles that were tagged at the same instant of time while forming a continuous locus.

•  Streamline: continuous line that is everywhere tangent to the velocity field at an instant in time.

The first three lines are relatively easy to generate experimentally, while streamlines are merely a mathematical concept that in general have to be produced by post-processing an instantaneous capture of the velocity field. While this is always true, the analysis simplifies significantly in steady flows because pathlines, streaklines, and streamlines coincide with each other. Conversely, these lines do not generally coincide with each other in unsteady flows. The implementation of this technique is generally simple and requires only low-cost equipment, as opposed to more sophisticated and expensive techniques such as Particle Image Velocimetry [1], Particle Tracking Velocimetry [8,9], and Molecular Tagging Velocimetry [10].

Figure 2. Representative results. (A) continuous sheet of hydrogen bubbles that shows streaklines as a result of upstream disturbances. The shadow cast by the rod is used to determine the conversion from machine to real units. A vortex shedding cycle is also illustrated to help determine shedding frequency appropriately. (B) timelines generated with hydrogen bubbles. Since timeline frequency is well-defined, they can be used to measure flow velocity accurately; counting the timelines enclosed in the red lines will be used for this estimation. Please click here to view a larger version of this figure.

Table 1. Values of the coefficients and for different Reynolds number intervals (from [8]).

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.

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.