In this paper, the possibility of the flow rate measurement for a circular pipe flow by using a wo-ven screen with the property of straightening un-uniform flows is discussed. The resistance coefficient and the flow rate coefficient are estimated from the pressure difference caused by the woven screen under the experiment ranges of the wire Reynolds number, Red = 2.2 × 102-1.8 × 103, and of the open area ratio, β = 0.28-0.65. As a result, the resistance coefficient decreases and the flow rate coefficient increases as the wire Reynolds number Red or the open area ratio β increases. In addition, both coefficients are not affected by the difference between uniform and turbulent pipe flows approaching the woven screen. Therefore, the possibility of a flow-meter having the property to straighten the un-uniform flow is expected.
It is a significant assignment to measure the flow rate exactly in engineering fields using pipe line flows. A flow- meter generally requires a long runway approaching it and/or a straightening device, such as perforated plates, honeycombs or woven screens upstream of it. As for a woven screen, often used to straighten un-uniform flows such as a prejudice flow and a turbulent flow in many engineering fields [1] [2] , there have been a lot of studies on resistance thus far [3] - [10] . In recent years, the requirements of downsizing the apparatus have appeared.
Therefore, an idea of measuring the flow rate by using a woven screen is proposed in this paper, because it is expected that it could play both the role of straightening the flow as well as measuring the flow rate. The possibility as a flow-meter having the ability to straighten an un-uniform flow from the measurements of the flow rate coefficient and resistance coefficient of a woven screen for two different pipe flow fields is discussed.
2. Experimental Approach
Figure 1 shows a summary of this experiment and nomenclature. The experimental apparatus is composed of the entrance nozzle and a straight circular pipe with an inner diameter of D = 42 mm. On the inner wall of the pipe, there are many pressure measurement holes (diameter 0.5 mm) along the flow direction. The woven screen is set at the position L = 210 mm or 1080 mm downstream from the tip of the entrance nozzle. The woven screen is made of stainless steel wires of 1.0 mm diameter and has four open area ratios. The wire Reynolds number, Red, is defined in Equation (1) based on the wire diameter, the velocity averaged in the pipe’s cross section and the kinematic viscosity of the air was varied from 2.2 × 102 to 1.8 × 103.
Table 1 shows the geometric parameters of woven screen models used in this study. M is number of the meshes, and β is the open area ratio defined as. Figure 2 shows the velocity distribution in the pipe’s cross section measured at the positions of L = 1080 mm and 210 mm under the Reynolds number based on the circular pipe diameter, ReD = 8.3 × 103 − 8.7 × 104, before the woven screens is set. The velocity in the pipe is obtained from the pressure difference between total pressure measured by a small handmade total pressure tube and static pressure taken from a pressure hole in the position nearest to the tip of the total pressure tube.
It is understood that the velocity distributions obtained at the pipe’s cross section in the case of L = 1080 mm are almost consistent with the 1/6-power law as shown in Figure 2(a). Because the inner flow in the case of L = 1080 mm can be regarded as a developed turbulent pipe flow, thereafter it is called “the turbulent pipe flow”. On the other hand, the velocity distributions in the case of L = 210 mm are almost uniform, except in the vicinity of the pipe wall as shown in Figure 2(b). Because the constant velocity region occupies about 70% in the pipe’s cross section, thereafter the inner flow is called “the uniform pipe flow”. For all pressure measurements, a Gottingen type manometer (minimum scale 0.05 mm) is used.
3. Experimental Results and Discussions3.1. Wall Pressure Distribution
Figure 3 shows a typical example of the x direction distribution of a wall pressure coefficient Cp upstream and downstream of the woven screen. The wall pressure coefficient is defined as
Wall pressure distribution in circular pipe (β = 0.65, Turbulent pipe flow, Re<sub>d</sub> = 990)
where P is the wall pressure, P∞ is the atmospheric pressure and ρair is the density of the air. It is noted that the wall pressure varies linearly over the wide range of, and that a difference in the wall pressure coefficient, , occurs between the regions upstream and downstream of the woven screen.
3.2. Resistance Coefficient
Figure 4(a) shows the relationship between the resistance coefficient K and the wire Reynolds number Red. The resistance coefficient K is defined as
The resistance coefficient K decreases as the wire Reynolds number Red and the open area ratio β increase. Although the resistance coefficients K for each β is obtained under two different pipe flow approaching the woven screen, the turbulent flow and the uniform flow, they agree very well. Then, it is noted that the resistance coefficient is not affected by the difference of flow approaching the woven screen. This may be because two approaching-flows become similar to each other by the damming effect which occurs in front of the woven screen. Therefore, it is expected that the woven screen has a property which could straighten the turbulent pipe flow as well as the uniform pipe flow. The black-lines in Figure 4(a) exhibit the approximation of the obtained resistance coefficient K and are given by the following Equation (4), depending on the wire Reynolds number Red and the open area ratio β. They approximate the resistance coefficient K very well.
3.3. Flow Rate Coefficient
Figure 4(b) shows the variation of the flow rate coefficient α for the wire Reynolds number Red and the open area ratio β. The flow rate coefficient α is derived from general formulas, , where Ao is the open area of the woven screen. The flow rate coefficient α increases as the wire Reynolds number Red and the open area ratio β increases. In addition, it was noticed that the flow rate coefficient α obtained in two different pipe flows, the turbulent pipe flow and the uniform pipe flow, are close to each other. On the other hand, the flow rate coefficient α can be calculated from the wall pressure difference based on the following Equation (5), where A is the pipe cross-sectional area.
The black-lines in Figure 4(b) are converted from the black-lines in Figure 4(a), and agree with the experimental results of the flow rate coefficient α.
3.4. Reconfirmation from Direct Pressure Drop
Generally, in the case of the flow rate measurement using the pressure difference, the pressure difference is decided as the wall pressure drop between the front and the back of a device’s position. Therefore, the measurement of the pressure drop in the case of the transient pipe flow was attempted in the vicinity of the woven screen as shown in Figure 5. Because the pressure drop coefficient measured between two positions nearest to the woven screen, x = −1.05 D and 0.10 D, is fairly larger than the obtained from the pressure difference of the two pressure distribution lines as shown in Figure 3, the property as flow-meter is expected to be good when taking the pressure drop in the downstream position nearer to the woven screen.
4. Conclusion
The resistance coefficient K and the flow rate coefficient α of the woven screen placed in the circular pipe were experimentally investigated. As a result, although the flow rate coefficient α varies depending on the wire Reynolds number Red and the open area ratio β increases, both coefficients is not affected by the difference between
Influence of Reynolds number and open area ratio. (a) Resistance coefficient; (b) Flow rate coefficient.
Wall pressure distribution in circular pipe (β = 0.65, Transient pipe flow, Re<sub>d</sub> = 880)
a uniform and a turbulent pipe flows approaching the woven screen. Therefore, the possibility of a flow-meter having the ability of straightening an un-uniform flow can be expected. Furthermore, considering the pressure measurement points, the numbers of woven screens and/or combination with perforated plates and honeycombs, its ability as a straightening flow-meter will rise.
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