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Advances in Mechanical Engineering
Volume 2013 (2013), Article ID 658591, 8 pages
Study on the Fluidic Component of the Complete Fluidic Sprinkler
1Research Center of Fluid Machinery Engineering and Technology, Jiangsu University, Zhenjiang, Jiangsu 212013, China
2Grundfos R&D China, Suzhou, Jiangsu 215021, China
Received 3 September 2012; Revised 22 February 2013; Accepted 3 March 2013
Academic Editor: Shuyu Sun
Copyright © 2013 Hong Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The PXH fluidic sprinkler controlled by the outlet clearance is a new type sprinkler which is driven and controlled by the Coanda effect. This paper analyzes the offset jet with control stream in the simplified model. Based on the special design of the fluidic component of the fluidic sprinkler, a control stream coefficient was proposed and the air entrance hole distance was considered as one of the key factors that, influence the offset flow field. Based on the numerical simulations and the experiments, the influences made by different air entrance hole distances, offset ratios, and working pressures on the water-air two-phase flow field of the simplified fluidic component have been studied. The offset distance, the pressure distribution on the offset wall, the yaw angle of the main jet flow and their variations with the pressure, and the structural parameters were obtained. The air velocity variation in the air entrance hole was regarded as the judgment for a complete attachment. Visualization experiments and pressure distribution experiments were carried out and the experimental results show a good agreement with simulation results.
Coanda effect is frequently used in numerous industries, such as aviation, building construction, energy, and power, and so forth. With the diversified application, the study of the Coanda effect has also been expanded [1–6]. Most of the researches about the Coanda effect were derived from the research achievements made by Bourque and Newman . Pin  summarized the classic research methods, built the mathematical model of the dualistic incompressible offset jet with injecting control stream or pumping control stream, and proposed some equations about the stream centre line and the correlative parameters of the offset jet with control stream. Wang  simplified these equations and calculated the impingement angle and the dimensionless offset distance of the offset jet under different control stream volumes. However, all of these researches only investigated the one-phase flow, and ignored the influence of the different locations of the control stream on the offset field.
Previous research work about the fluidic component of the fluidic sprinklers mainly focused on the external characteristics of the sprinkler, for example, the spraying performance by the orthogonal tests, and so on. The design methods of the fluidic sprinklers were based on these experiments. Yuan et al.  simulated the flow in a fluidic sprinkler controlled by outlet for the first time, but the research ignored the influence of the structural parameters or the reattachment length. Li et al.  also had done some research on the inner flow of the fluidic component, on which this research is built.
To study the flow of the fluidic component, this paper proposed the control stream location (also named air entrance hole distance in this paper) coefficient based on the existing computational formula. Both the experimental and numerical simulation methods are used to study the influence of the air entrance hole distance on the offset flow field in the simplified component of the fluidic sprinkler.
2. Theoretic Analyses
All the mathematical models of the offset jet flow are built on certain hypotheses. Figure 1 shows the model of offset jet with control stream .
As shows in Figure 1, under the influence by the control stream and the pressure difference between the two sides of the fluidic component, the main jet flow sprays forward with the direction changing and finally impacts the sidewall at point . Then, the main jet flow attaches to the wall and flows downstream. Based on the previous research, the approximate value of the yaw angle of the main jet flow, , can be expressed as follows: where is the momentum of the main jet flow at the outlet of the jet nozzle, and is the momentum obtained when the control stream from the control nozzle arrives at the outlet of the jet nozzle. can be expressed as follows: where ρ is the density of the main jet flow, is the velocity of the outlet flow, and is the width of the nozzle. If the pressure at the control stream nozzle is , the discharge of the control stream nozzle is , the nozzle width is , the wall pressure in the low-pressure area is , and the density of the control stream is , according to the momentum theory, can be expressed as follows:
The main jet flow in the component is water flow and the control flow is air flow, which makes the flow in the component even more complex. From the research on the fluidic component of the fluidic sprinkler, we can find out that if the outlet velocity of the main jet flow is big enough, the entrainment of the main jet flow will affect the velocity of the air in the air entrance hole. The closer to the outlet of the main jet flow, the more intensive is the air entrainment, which will make the air velocity bigger in the air entrance hole. Meanwhile, the pressure difference between the two sides of the main jet flow is changing while the main jet flow develops from a straight spray jet to an offset jet. So, we should consider the influence caused by the location of the control stream nozzle, when investigating the flow inside the fluidic sprinkler. In this case, the air entrance hole in the wall of the fluidic component works as the control stream nozzle. This paper introduces a control stream coefficient, , which is influenced by the air entrance hole distance , the offset ratio , and the jet dispersion coefficient σ, as shown in Figure 2. Then, the yaw angle of the main jet flow β can be expressed as
The attachment angle of the offset jet flow is the angle at the intersection between the main jet flow centre line and the offset wall. According to the geometrical relationship and the analytic method, we can get the attachment angle of the offset jet, as follows:
As shown in (5), is correlative with the geometrical parameters. It can be regarded as influenced by the offset ratio /, the yaw angle of main jet flow , and the wall inclination angle .
The side wall of the fluidic component of the fluidic sprinkler is perpendicular to the nozzle outlet, so the wall inclination angle α is zero, as shown in Figure 2. The attachment angle of the offset jet flow θ is only correlative with β and /. As analyzed above, the air entrance hole distance h influences the yaw angle of the main jet flow , and the attachment angle of the offset jet . Based on the theoretical analyses, this paper has combined numerical simulations and experiments to study the offset field influenced by the difference distances of the air entrance hole.
3. Numerical Simulations of the Flow Field
3.1. Structural Models
To study the relationship between the air entrance hole distance and the yaw angle of the main jet flow, the attachment angle of the offset jet and the wall-attachment point distance and the simplified three-dimensional models with different sizes are made to process unsteady numerical calculation. The simplified model and the 3D model are shown in Figure 3. The channel of the simplified fluidic component is made longer to make the offset jet fully developed. The sidewall with air entrance hole is marked as side A, and the opposite sidewall is marked as side B.
3.2. Boundary Conditions
The authors choose the fundamental equations of 3D incompressible flow as the solving equations. The turbulence model is standard turbulence model. The fluid media are water and air and choose mixture model as two-phase flow model.
3.3. Simulation Results
3.3.1. Velocity Distribution
The region where the attachment point locates can be observed from the enlarged counters of the vertical velocity, as shown in Figure 5(a). The back flow in horizontal direction near the sidewall B is caused by the entrainment of the main jet flow, as shown in Figure 5(b). The entrainment effect brings air into the main jet flow from the air entrance hole. The horizontal velocity changes intensively near the air entrance hole, while the velocity changes a little in the downstream of the centerline of the main jet flow. That is the basic difference between the previous offset model and this model. The previous offset jet model usually ignored the horizontal velocity, taking the vertical velocity as the velocity of the jet. Actually, the air velocity in the air entrance hole and the pressure difference of the two sides of the main jet flow lead the flow to get attached to the wall, which means that the horizontal velocity component should be considered as one of the influencing factors.
3.3.2. Pressure Distribution
The enlarged view of the pressure distribution of the stable offset jet flow is shown in Figure 6. We can see that the pressure of the offset jet flow field varies highly.
A low-pressure vortex is formed in the region near the sidewall B. The static pressure is lower at the center and higher on the edge. The maximum pressure appears on the sidewall at the downstream of the vortex, with the pressure decreasing along the internal direction. The high-pressure vortex region has been formed between the air entrance hole and the nozzle on the sidewall B. It is the pressure difference between the high-pressure vortex region and the atmosphere that enables the function of the air complement. Likewise, the main jet flow is impelled to attach the low-pressure side by the differential pressure between the two sides.
3.3.3. Judgment of the Fully Attachment Time
From the numerical simulation, we can find that when the offset jet flow is developing, the volume between the sidewall A and the boundary of the main jet flow is enlarged, and the pressure difference between the volume and the atmosphere increases as well. The air velocity in the air entrance hole is also changing. The velocity of the air and the pressure difference between the volume and the atmosphere tends to constant after the main jet attached to the wall. As is shown in Figure 7, the velocity of the air gradually attains to a constant for the time 0.2 s. Based on the analysis above, this paper notes that the fully attachment time is the period from the beginning of the attachment to the end when the velocity of the air complement approaches to a constant.
3.3.4. Effect of the Structural Parameters on the Offset Field
The numerical simulation results of the offset field affected by air entrance holes distance are shown in Figure 8.
(1) Influence on the Fully Attachment Time. As shown in Figure 8(a), under the same working pressure, the fully attachment time changes with the air entrance hole distances. The fully attachment time decreases when the air entrance hole distance increases, but it is not influenced by the offset ratios.
(2) Influence on the Distance of Attachment Point. The relation between the location of the attachment point and the air entrance hole is more dependent on the offset ratio. In Figure 8(b), the attachment point distance is the shortest when h is 3 mm and offset ratio / is 0.2. Also, the shortest attachment point distance appears when D/b is 0.4, is 5 mm, / is 0.7, and is 10 mm. Because the volume of the fluidic element of the sprinkler is small, in order to get the offset jet in the limited flow channel, we should know the rules of the locations of the attachment point and the impact point firstly. So the optimum position of the air complement of the fluidic element should be changed according to the offset ratios.
(3) Influence on the Pressure Distribution. Because the dynamic pressure is produced by the jet velocity, the impact on the wall during the attachment will change the dynamic pressure, so the point with the largest dynamic pressure on the offset side wall can be taken as the impact point. In Figures 8(c) and 8(d), it is shown that the distances from the impact point to the nozzle decrease at the beginning and then increase with the air entrance hole distances increasing, and the tendency is the same as different ratios' change. But on the offset side, the maximum dynamic pressure varies with the distances of the air entrance hole, and the tendency varies with the different ratios.
3.3.5. Influence of Working Pressure on the Fluidic Element
Table 1 shows the parameters of the offset field under different inlet pressures when D/b is 0.2, and h is 5 mm. According to the data in the table, the air velocity in the complement holes, , increases with the working pressure; the fully attachment time, , decreases with it, which indicates that the air volume is in direct proportion to the entrainment of the flow. The location of the attachment point has no relationship with the working pressure. Both the yaw angle of jet and the impact angle of the offset jet increase with the pressure, but change little when the pressure is higher than 0.5 MPa. The maximum pressure on the wall and the minimum negative pressure in the flow field are increased with the working pressure.
4. Experimental Study
In order to confirm the results of the numerical simulation, a test rig is built to study the relationship between the offset field of the fluidic component and the offset ratio and the air entrance hole distance and the working pressure. The yaw angle and the impact angle of the offset jet flow are obtained from the flow field photographs of the fluidic element which has been taken in the visualization experiment. Meanwhile, the pressures on the wall under stable-attachment state are measured to investigate the influence of working pressure and structural parameters on the pressure distribution on the sidewall.
4.1. Test Procedure
The prototype is shown in Figure 9(a). The main observation part of the prototype is made up of organic glass. Two air entrance holes with the distance of 5 mm and 10 mm are set on Side A. The air entrance holes are plugged with special plug when they are not in use. Figure 9(b) shows the flow fields of straight jet and offset jet, respectively.
The phenomenon of stable attachment flow with different air entrance hole distances and different working pressures is recorded with a digital camera. The photographs are processed to make the boundary of the jet sharpened, and the streamline patterns are drawn upon. The yaw angle and the impact angle of the offset jet flow in the offset are measured from the photos to make comparison with the development of the jets.
The fluidic component prototype in the pressure test is the same as the one in the photographic test. The distribution of the pressure test points is shown in Figure 10. The air entrance holes on Side A are marked as pressure points 1a and 1b, which are 5 mm and 10 mm away from the outlet nozzle. Five pressure points are labeled as 2, 3, 4, 5, and 6 at Side A, which are 5 mm, 12 mm, 20 mm, 30 mm, and 50 mm away from the outlet of nozzle, as shown in Figure 10. The pressure gauge is typed YB-150A, with the accuracy 0.4 M, the span 0–0.1 MPa and −0.1–0 MPa, and the minimal scale 0.5 kPa. The main jet flow is impelled to be attached to Side B by opening and closing air entrance holes 1a and 1b manually (the pressure at 1a is measured when it is used as air entrance hole, so is 1b). The pressure distribution on the wall is detected by the pressure points. The results of the test are shown in Table 2.
From Table 2, it is clear that the yaw angle varies greatly with different air entrance hole distances. For the two prototypes with different offset ratios in this test, the stable yaw angle and the impact angle reach the highest values when h is 5 mm.
From the comparison shown in Figure 11, the tendency of the test results is consistent with the numerical simulation, and the values from the test are lower than that from the simulation. It is caused by the difference between the idealized conditions in the numerical simulation and the actual operation conditions. Also, the inevitable errors in the manufacture of the prototype will lead to the air leakage at the pressure test points, which makes the vacuum in the low-pressure region decrease and also the yaw angle and the impact angle.
The pressures on Side B with different offset ratios and different positions of the air entrance hole are presented in Figure 12. On Side B, the pressure increases at first and then decreases from Point 2 to Point 6, and the tendencies are identical with the results obtained from the simulation. A transition from a positive pressure to a negative pressure occurs on side B, which indicates that the attachment point is supposed to be located in this area. For these two prototypes in the test, when the hole 1a is open, the conversion place is located between pressure Point 2 and Point 3 (12 mm to 20 mm); when the hole 1b is open, the conversion place is located between pressure Point 3 and Point 4 (20 mm to 30 mm). These factors confirm the results from the numerical simulation of the location of the attachment point. At the same air entrance hole, the pressure conversion place on Side B has not changed with the pressure.
The main influencing factors on the offset flow field are analyzed theoretically at first, and then the flow in the fluidic component is investigated with numerical simulations and experimental tests. The conclusions are as follows.(1)The fully attachment time decreases with the increasing of the air entrance hole distance and the working pressure.(2)The location of the attachment point is influenced by the air entrance hole distance and the offset ratio. It has nothing to do with the working pressure. Therefore, the air entrance hole distances should be different as the offset ratio changes. (3)The location with maximum dynamic pressure goes forward at first and then backward when the air entrance hole distance is enlarged, and the tendency is not influenced by the offset ratio. The yaw angle and the attachment angle of the offset jet flow increase with the pressure increasing and vary little when the pressure is more than 0.5 MPa.(4)To optimize the structure of the fluidic component, we can change the air entrance hole distance to get the best offset ratio and to reduce the maximum dynamic pressure point distance and the attachment distance, in order to cut down the length of the fluidic component with the offset jet flow fully developed.
|:||Control stream nozzle width|
|:||Reattachment length on the lateral wall|
|:||The distance from the wall to the lower nozzle edge|
|:||Air velocity in the air entrance hole|
|:||Fully attachment time|
|:||Plumb distance between the intersection point on the lateral wall and the extended dividing streamline|
|:||Vertical distance to the jet centerline|
|:||Distance to nozzle exit along the centerline|
|:||Distance between jet virtual origin and the nozzle exit|
|:||Distance between nozzle outlet and the centerline of the air entrance hole|
|:||Radius of curvature|
|:||Control stream pressure|
|:||Control stream flux|
|:||Density of water|
|:||Jet yaw angle caused by control flow|
|:||Angle between jet centerline and sidewall on attachment point.|
Part of this research was supported by the National High-tech R&D Program of China (863 Program, no. 2011AA100506), National Agricultural Science and Technology Achievements Application Foundation of China (no. 2011GB2C100015), and part by Agricultural Foundation of Jiangsu (no. BE2010393).
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