Formation of Necklace-Type Vortex System Upstream of a Gate Valve in Pipe Flow

A gate valve is one of the main elements of a circular pipeline, but the flow characteristics around the gate valve are hardly known. In this study, clarification of the flow field in front of the gate valve model in a pipe flow via flow visualization and PIV analysis was attempted. As a result, four kinds of steady necklace-type vortex systems, 2-vortex, 4-vortex, 6-vortex and 8-vortex systems, were clearly observed in a Reynolds number between 290 and 2130. In addition, the main vortex was observed in the Reynolds number range between 2130 and 4870 with difficulty. On this account, both the center position and vorticity in the main vortex are presented against Reynolds number.


Introduction
A gate valve has a feature that the pressure loss when fully opened is small and the valve opening degree can be finely adjusted.The gate valve is one of the main elements of a circular pipeline.However, the flow pasts a gate valve and the resistance characteristics of a gate valve have not been investigated sufficiently.Koram and Sparrow (1978) and Sparrow et al. (1980) reported heat transfer and pressure drop characteristics induced by an unsymmetric blockage element installed into the circular pipe [1] [2].Oguri (1991) and Yamada and Katoh (1993) studied a flow-meter using a segmental blockage element, such as a gate valve [3] [4].Yamada et al. (2015) also investigated flow field and loss coefficient produced by a gate valve model installed in a circular pipe [5].They first showed that one necklace-type vortex is formed in front and moves over the gate valve The flow resistance in the protrusion of various shapes installed into the pipe has been well studied.However, the flow field around a protrusion which is unaxisymmetric with circular pipe axis, e.g. a gate valve, in a circular pipe is not well-known.Particularly, excluding the study by Yamada et al., the flow field in front of the protrusion has hardly been investigated [5].Therefore, our interest was focused on the flow field in front of the gate valve model in circular pipes.Particularly, in this paper the feature of the necklace-type vortex (vortex system, vortex position, and vorticity) was investigated by flow visualization and PIV analysis against a wide Reynolds number.

Experimental Apparatus and Procedure
The measuring circular pipe employed in this experiment lies in a water channel flow which is 400 mm in width and 400 mm in depth.Figure 1 shows the coordinate system and nomenclature in the circular pipe.The circular pipe is made of transparent acrylic with an internal diameter of 42 mm and a wall thickness of 4 mm.An inlet long ellipse nozzle is attached in the entrance of the pipe to smooth the inflow.The radius of curvature of the gate valve model is D/2 and the thickness is t/D = 0.1.The height ratio of the gate valve model height to the pipe diameter is h/D = 0.6.Therefore, the blockage ratio of the model front to the cross section is 0.5.The gate valve model was attached in the position of 1700 mm from the nozzle exit.In the experiment, fine nylon particles with an average particle size of 50 µm and a specific gravity of 1.03 were mixed in the water channel to visualize the flow.Then, the flow upstream of the gate valve model was irradiated by the laser light sheet, and was captured by using a high-speed camera.Conditions for shooting are shown in Table 1.The Reynolds number, Re (=U m •D/ν), was defined based on measuring the pipe diameter, D, and the averaged velocity, U m , which was determined by using a flow-meter installed in the downstream of the measuring pipe.The mean velocity of the flow  field was calculated by a PIV analysis based on the correlation method.Furthermore, the template size for pattern matching was decided as 31 pixels × 31 pixels.Figure 2 shows the distribution of the mean velocity measured across the pipe without the gate valve model in each Reynolds number.Incidentally, uncertainty of velocity measured by the PIV in this research was about 6.5%, which was obtained by comparing Poiseuille flow velocity and the obtained velocity.

Experimental Results and Discussions
It is well known that necklace vortices are formed in front of a three-dimensional obstacle mounted on a wall.Surprisingly, various vortex systems to be similar with the necklace vortex systems shown by Nakahara and Yamada [8] were also confirmed upstream of the gate valve model in this experiment.Therefore, we named the clockwise vortices as V 1 , V 2 , V 3 , V 4 upstream of the gate valve model, and called the counter clockwise vortices as V 0 , 1 V′ , 2 V′ , 3 V′ as shown in Fig- ure 3(d).Incidentally, by visualizing the dye behavior invading into one vortex tube, Yamada et al. showed that the vortex in the case of the gate valve model is almost equal with the main vortex in ordinary necklace vortices [5].Therefore, we decided to call the vortices observed in this experiment a necklace-type vortex system.

Formation of Vortex System
Figure 3 shows the path lines image upstream of gate valve model in each Reynolds number.These path lines images were made by mutually superposing consecutive particle-images of 800.As shown in Figure 3, the steady necklace vortices were formed in the range of Re ≤ 2130.In the case of Re = 290, the flow field was regarded as a 2-vortex system, because the number of the steady vortices having different signs was 2. Accordingly, the flow field was regarded as a 4-vortex system in Re = 490, as a 6-vortex system in Re = 970 and as an 8-vortex system in Re = 2130.In the range of Re ≥ 2460, the flow field became more unsteady with increasing Reynolds number.Although, the center position of the main vortex V 1 in Re = 2460 and 4870 could be observed as well as the steady vortex system described above.Therefore, both formation and collapse of vortices may exist in the case of those Reynolds numbers.In the case of Re = 9740, it was difficult to confirm the formation of a time-averaged vortex system.
Figure 4 shows the variation of the steady vortex system against the Reynolds    8-vortex system.The 2-vortex system existed between Re = 180 and 290, the 4-vortex system existed between Re = 390 and 780, the 6-vortex system existed between Re = 880 and 1850, and the 8-vortex system existed in Re = 2130.Since the flow field was unsteady in Re = 2460, the range of Reynolds number in which the steady 8-vortex system appears is extremely small.

Characteristics of Vortex System
Figure 5 shows the ratio of the center point distance of the main necklace-type vortex, V 1 , to the circular pipe diameter, D. The x-direction distance from the gate valve model to the V 1 center point is defined as X V1 , the height from the bottom wall of the circular pipe to the center point of the V 1 is defined as Y V1 .
The dashed line is the approximate line calculated by using the least squares method in the Reynolds number range drawn by the dashed line.X V1 /D increased in the range of Re ≤ 500, and gradually decreased, linearly, in the range of Re > 500.Y V1 /D gradually decreased, linearly, until Re = 4920.Therefore, the center point of V 1 may gradually approach the gate valve model, and the scale of V 1 may gradually become smaller as Re increases.Figure 6 shows the stagnation point height Ys which is the distance from the circular pipe bottom wall to the stagnation point.Ys/D increased until Re = 1000, and gradually decreased as Re increases.Figure 7 shows the ratio of V 1 center height Y V1 to the stagnation point height Ys.Y V1 /Ys also gradually decreased with increasing Reynolds number.However, Y V1 /Ys might be regarded as a value of about 0.30 in the Reynolds number range between approximately 500 and 5000.Figures 8(a)-(c) show the contours of relative vorticity obtained from time-averaged velocity data calculated by the PIV analysis.The negative value represents a clockwise rotation.In Re = 970, there was the vorticity contour corresponding with the 6-vortex system, though V 3 could not be confirmed clearly as shown in Figure 8(a).In Re = 4870, the presence of unsteady main vortex was clarified by the contour of time-averaged vorticity, as shown in Figure 8(b).In Re = 9740, the vortex formation could not be confirmed as well as the pass-lines image.However, there was a small negative vorticity observed in the turbulent region upstream of the gate valve model, as shown in Figure 8(c).Figure 9 shows the maximum relative vorticity in the V 1 center point.The relative vorticity increased in proportion to the Reynolds number.However, the relative vorticity in the main vortex center may be constant in the range of Re > 2000, because the maximum value of (−D/U m )Ω in Re = 4870 was about 70 as shown in

Conclusions
The existence of the necklace-type vortex systems produced upstream of the gate valve model (h/D = 0.6) in the circular pipe was observed by using the flow visualization and PIV analysis.As a result, the following considerations about the characteristic of necklace-type vortices were gained: 1) Vortex systems were observed from two vortices to eight vortices in the range of Re ≤ 2130.In the range of Re ≥ 2460, unsteady necklace vortices were formed.
How to cite this paper: Shingai, K., Sadahiro, T. and Yamada, H. (2018) Formation of Necklace-Type Vortex System Upstream of a Gate Valve in Pipe Flow.Open Journal of Fluid Dynamics, 8, 133-140.https://doi.org/10.4236/ojfd.2018.82010model by using dye-method visualization.Recently, Alimonti (2014) reported an experimental characterization about pressure drop and flow rate of gate valves in vertical gas-liquid flows [6].Lin et al. (2016) calculated influence of flashboard location on flow resistance properties and internal features of the gate valve model in rectangular pipes [7].
number.As mentioned above, the steady flow field varied from a 2-vortexto an DOI: 10.4236/ojfd.2018.82010136 Open Journal of Fluid Dynamics

Figure 2 .
Figure 2. Velocity distribution in each Reynolds number without the gate valve model, measured in the position of 1700 mm downstream of the nozzle exit.

Figure 9 .
Figure 9. Vorticity distribution in V 1 center point.

Table 1 .
Conditions for shooting.