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A T-junction is a fundamental fluid element prevalent in pipe networks of water supplies and power plants. In the present study, a double T-junction was investigated for flow instability and fluid vibration. Both axi-aligned and skewed double T-junctions are examined from viewpoint of flow instability. With single-phase flow in an open-ended double T-junction, fluid vibration is induced in both side branches because of a high shear rate with a point of inflection. The frequency of vibration in the downstream branch is higher than that in the upstream branch. Except for the upstream branch in the skewed double T-junction, the frequency is higher than that in a single T-junction. The fluid vibrations are closely associated with the fluid interference created by the presence of the two side branches.

An incident involving the rupture of a tube in a steam generator incident occurred unexpectedly in 1991 at the Mihama Nuclear Electric Power Plant, Unit 2, in Japan. A small 22-mm-diameter tube with wall thickness of 1.3 mm was fractured by a vibration arising from fluid elastic interaction related to Karman vortex generation. Radioactive primary coolant from the reactor flowed out into ocean [

With respect to external flows, Brown & Roshko [

An arterial branch from the abdominal aorta to the renal artery is basically similar to a single T-junction. Over the past three decades, Karino et al. [

For a double T-junction, there are several studies concerning flow induced pressure pulsations in a gas transport system [

The present experimental study deals with an open-ended double T-junction. We aimed to clarify the mechanism underlying the fluid-induced vibration in these double T-junctions for single-phase flow. Flow visualization was carried out by two dimensional particle image velocimetry (2D-PIV) and the velocity measurement obtained by two dimensional laser Doppler anemometry (2D-LDA).

The shearing separation layer is produced at the median plane in the side branches between the low-velocity flow along the near wall and the main flow associated with the high-velocity along the distant wall. The flow vibration was investigated along the shearing separation layer where the shear rate is larger than that at tube wall sufficiently downstream of the side branch; the velocity profile has an obvious point of inflection. Furthermore, the point of inflection in high-shear-rate flow between two vortices immediately downstream of the inlet in the side branch was also examined. Consequently, in two side branches, the frequency in the downstream side branch is higher than that in the upstream side branch. Except for the upstream side branch of the skewed T-junction, the Strouhal numbers for these branches are higher than that of a single T-junction.

For the axi-aligned and skewed T-junctions in _{T} = 12.2 mm and R_{S} = 7 mm as a representative of the radii of the trunk and side branches [_{T} and Q_{S}, respectively. The same flow ratio of Q_{S}/Q_{T} = 0.25 is maintained for both side branches. A spacing of Ls = 30 mm between the two side branches is set for the experiment. This is the minimum distance for which the fluid interference is extremely expected between the side branches because the outer diameter of the side branch is 20 mm. Both the upstream and downstream corners of both side branches are square-edged. For the axi-aligned double T-junction in

The velocity components and the flow visualization of cross-sections for the velocity field are also given in

Cross-sections in the side branch where flow visualizations of velocity vector fields were performed are marked as sections S_{3}, S_{5} and S_{7}. The line of shearing separation layer in the side branch is decided by operators based on PIV results. Details of the measurement procedure for LDA are described in the previous study [

The working fluid is 53% aqueous glycerin with a refractive index of 1.41 (identical to that of silicone resin), a density of ρ = 1.13 g/cm^{3}, and a kinematic viscosity of ν = 7.00 × 10^{−6} m^{2}/s at 293 K (20˚C). The working fluid flows into the T-junction model through the 2000-mm-long inlet from the constant head tank. The working fluid then flows through an ultrasonic flow meter (TS410, Transonic System Co. Ltd., Ithaca, NY).

The measurements were primarily carried out with Re_{T} = 2R_{T}U_{T}/ν = 800 at a laminar steady flow in the trunk for both axi-aligned and skewed T-junctions. U_{T} denotes the mean velocity in the upstream trunk [

For the axi-aligned T-junction, the velocity vector field over the median plane that included all tube axes is shown in _{3} in Branch 2 maintaining large momentum. This flow behavior might be related to the high-shear-rate and the high frequency vibration associated with Branch 2, as described below.

Secondary vortices are seen in _{3} in Branches 1 and 2.

The position of vibration marked by dot in _{1} and p_{2} in both side branches in _{2} in Branch 2 is 40% higher than that of f = 8.2 Hz at p_{1}in Branch 1. This difference is strongly associated with the movement of core fluid upstream in the trunk flowing into Branch 2. Furthermore, the auto-correlation in Branch 2 is much clearer than that in Branch 1.

In the secondary velocity profiles at the vortex boundary formed in cross-section S_{3} of both side branches in ^{−1}, which is the value obtained along the tube wall sufficiently downstream of the side branch, the shear rate of 140.6 s^{−1} in Branch 2 is 1.5 times larger. In contrast, the shear rate of 58.0 s^{−1} in Branch 1 is one half of the reference shear rate. The shear rate in Branch 2 is clearly higher than that in Branch 1.

The tangential velocity profile for Branches 1 and 2 in ^{−1} and 143.9 s^{−1}, respectively, with Branch 2 being 1.5 times larger than the reference shear rate. This indicates that a high-shear- rate flow with a point of inflection vibrates at higher frequency.

For both double T-junctions, the relationship between Reynolds and Strouhal numbers is plotted in _{S} = 2R_{S}U_{S}/ν and St_{S} = 2fR_{S}/U_{S}, respectively, where U_{S} is the mean velocity in the side branch. Finally, the Strouhal numbers of 0.66 and 0.93 at the Reynolds number of 370 in Branches 1 and 2 are approximately 10% and 55%, respectively, both larger than that of 0.60 at corresponding Reynolds in a single T-junc- tion in the previous study [

In skewed side branches, the velocity vector field across the median planes for side branches and trunk are shown in

The tangential velocity profile along the shearing separation layer in Figures 10(a)-(c) for cross-sections S_{3}, S_{5} and S_{7} in Branch 2 has distinctly the point of inflection P, and the shear rates are 188.5 s^{−1}, 195.0 s^{−1} and

131.7 s^{−1}, respectively. These shear rates are higher than the reference shear rate of 97.9 s^{−1}. For Branch 1, the shear rate at each section is approximately comparable or slightly smaller than the reference shear rate, and the points of inflection are not clearly defined, as described below.

The temporal variation of the axial velocity component in both side branches was obtained in _{5} and S_{7}. Um in Branch 2 in

the fluid vibration appears. The power spectra corresponding to these temporal variations are plotted in

Whether the fluctuation is noise or vibration, it is identifiable by an auto-correlation analysis, which we have reformed on the above results in

The tangential velocity profile along the shearing separation layer in Figures 10(a)-(c) for cross-sections S_{3}, S_{5} and S_{7} in Branch 2 has distinctly the point of inflection P, and the shear rates are 188.5 s^{−1}, 195.0 s^{−1} and 131.7 s^{−1}, respectively. These shear rates are higher than the reference shear rate of 97.9 s^{−1}. For Branch 1, the shear rate at each section is approximately comparable or slightly smaller than the reference shear rate, and the points of inflection are not clearly defined, as described above.

The temporal variation of the axial velocity component in both side branches was obtained in _{5} and S_{7}. Um in Branch 2 in

First, we have expected that the frequency in Branch 1 of the double T-junction would be higher than that in Branch 2, because the flow rate through the trunk in Branch 1 is higher than that in Branch 2. Contrary to

expectation, the frequency of 11.6 Hz in Branch 2 is higher than that of 8.2 Hz in Branch 1 for the axi-aligned double T-junction. Even the frequency in Branch 2 for a skewed double T-junction is a little higher than that of 7.5 Hz corresponding to in the single T-junction [

In the axi-aligned double T-junction, the shear rate of 140.6 s^{−1} at the vortex boundary in section S_{3}of Branch 2 as shown in ^{−1} in Branch 1 is one half of the reference shear rate. Obviously, the shear rate in Branch 2 is much higher than that in Branch 1. The shear rate of 143.9 s^{−1} along the shearing separation layer in Branch 2 in ^{−1}. In

This behavior suggests that there is a great possibility that a high frequency vibration can be induced in pipeline network and fluid power plant. This vibration is a consequence of interference in fluid mechanism between two side branches. The spacing of the branches was Ls = 30 mm. When this spacing is reduced to an ideal minimum length, e.g. Ls = 14 mm, the frequency in Branch 2 might be quite higher because of fluid interference.

Generally, fluid dynamics involves non-linear phenomena for which predictions remain hard to extract from the past results, and unexpected flow behavior is the norm. Furthermore, the flow rate in fluid power plants and pipeline networks is quite large. In the present study, the order of Reynolds number is less than 10^{3}. However, in a fluid power plant, the Reynolds number is much larger, e.g. 10^{5} or 10^{6}. We cannot confirm the phenomenon at higher Reynolds number with the current double T-junctions. In the current LDA system used, the data sampling rate is 1 μs and the data rate is comparable to 3 kHz. If the Reynolds number is 10^{6}, much higher data sampling rate and higher data rates will be required: at least 10 ns and 300 kHz, respectively.

In the present study, the aim was to experimentally clarify the mechanism underlying the fluid-induced vibration in double T-junction using flow visualization and velocity measurement. Single phase flows with local high- shear-rates were established in both an axi-aligned and a skewed double T-junctions. The Strouhal numbers of 0.66 in Branch 1 and 0.93 in Branch 2 for axi-aligned branches were 10% and 55%, respectively, both larger than that the Strouhal numbers of 0.60 at corresponding condition in a single side branch. For skewed branches, Branch 2 had a Strouhal numbers of 0.88, which is only 45% larger than that in a single side branch but still comparable with that of Branch 2 for axi-aligned side branches. These results are closely associated with the inflection point for high-shear-rate arising as consequence of the fluid interference between the two side branches.

Part of this study was supported by a Grant-in-Aid for Scientific Research (B) (15H03914). With respect to the present study, the authors declare no conflicts of interest.

Ryuhei Yamaguchi,Gaku Tanaka,Hao Liu,Toshiyuki Hayase, (2016) Fluid Vibration Induced in T-Junction with Double Side Branches. World Journal of Mechanics,06,169-179. doi: 10.4236/wjm.2016.64014