# Experimental Investigation on the Influence of a Double-Walled Confined Width on the Velocity Field of a Submerged Waterjet

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Setup and Procedures

#### 2.1. Facilities and Setup

^{3}/h. In the experiment, the operating pressure of the centrifugal pump could be continuously regulated through the control table by changing the working frequency of the motor powering the pump. The flow rate of the pump could be directly read out from the pipeline flowmeter. Considering the limitation of the pump head, the strength of the plexiglass tank and the accuracy of the PIV, the operating pressure was 0.34 MPa in this experiment.

^{3}. Taking a small amount of water consumption and pipe or connections leakage in the course of the experiment into consideration, the volume of the water tank was sufficient to meet the qualification of the operation. In addition, another feeding pipe was used.

#### 2.2. Nozzles and Flow Conditions

#### 2.3. Analysis of the Experimental Uncertainty

_{total}may be written as

_{95}is the value of the t distribution at the 95% level of confidence, and σ is the standard deviation.

## 3. Results and Discussion

_{c}or V

_{c}.

#### 3.1. The Flow Field Characteristics of the Double-Walled Confined Waterjet

#### 3.2. The Axial Velocity of the Double-Walled Confined Waterjet

_{c}, which appears in the denominator, normalized by the jet exit velocity U

_{e}. The centerline velocity U

_{c}was obtained by curve fitting the mean axial velocity profiles measured on the horizontal plane using the following equation

_{c}is the mean centerline velocity, y is the vertical coordinate, y

_{c}is the vertical position of the centerline, and r

_{1/2}is the jet half-width measured at U = U

_{c}/2, y

_{c}and r

_{1/2}were calculated using the non-linear, least-squares Levengerg-Marquardt algorithm.

#### 3.3. The Mean Velocity of the Double-Walled Confined Waterjet

_{c}= 0.6, for example, the dimensionless boundary lengths are 5, 4, 3.5, 2 when H/D = 5, 10, 13, 15 respectively. The double-walled confined condition is able to make the jet flow spread to both sides.

_{c}is about 0.9 and when it is 15, the value is about 1.2. It is believed that this kind of phenomenon can be explained by the following reasons. On the one hand, the submerged waterjet flow is close to wall at the stream location. The wall is not completely smooth so as to hold back and disturb the flow field. With the confined width decreasing, the force of friction and disturbance become larger and energy dissipation increases. On the other hand, because of the existence of the double-wall, the development of the waterjet flow at the vertical direction is limited, which results in the flow spreading along the horizontal direction. The axial velocity component decreases and the radial velocity component increases.

_{c}= 0 indicating that the velocity is affected significantly by the confined condition. However, other mean velocities are not affected too much. It should be noted that the dimensionless velocity V/V

_{c}> 0 when the z/H < 0. As the positive speed is defined as the fluid flowing upwards and the negative speed as downwards, the fluid, of which z/H < 0, is flowing far away from the wall. Thus, the fluid forms a negative pressure region near the wall. According to the above rules, we have reasons to believe that negative pressure will lead to the trend of inward movement of the wall, rather than outward expansion. Simultaneously, we also conclude that the position at which the wall begins to affect the jet will advance as the width decreases.

#### 3.4. The Turbulent Intensity of the Double-Walled Confined Waterjet

_{c}extracted from the horizontal plane for the H/D = 5, 10, 13, 15 cases is shown in Figure 10. These profiles are plotted against the non-dimensional coordinate y/D in this figure. At x/D = 20, Figure 10 shows that the turbulence intensity for different H/D values is slightly affected by the vertical confinement. The turbulence intensity of the flow field at the centerline is the most intense. As the position gradually moves, the turbulence intensity decreases gradually.

_{ms}/U

_{c}is equal to 0.1, the dimensionless lengths are 0.8, 0.7, 0.6 and 0.4 when the dimensionless confined width H/D = 5, 10, 13 and 15 respectively. This shows that with the decrease of the confined width, the turbulent area gradually expands, so the confined width has the effect of lateral expansion on the turbulence characteristic.

## 4. Conclusions

- The vertical confinement has an obvious effect on the decay rate of the mean centerline velocity. When the confined width changes from 15 to 5, the speed is reduced by 20%. The slower decay rate can be explained by the conservation of mass which demands an increase in the jet velocity compared to the free jet because the cross-sectional area of the jet becomes constrained by the boundaries.
- The vertical confinement has a significant effect on the jet spread. With the decrease of the confined width, the jet has a tendency to spread horizontally. The confinement has a profound effect on the axial velocity profiles in the vertical plane. As the flow goes downstream, the jet spreads to the boundaries and the axial velocity above and below the jet centerline increases rapidly.
- The vertical confined region induces a space hysteresis effect which changes the location of the transition region moving downstream. With the enlarging of the confined width, the position moves back.
- The fluid could form a negative pressure region near the confined wall, and negative pressure will lead to the trend of inward movement of the wall, rather than outward expansion.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 3.**Illustration of plexiglass water tank and measuring region: (

**a**) Structure of plexiglass water tank; (

**b**) Vertical plane; (

**c**) Horizontal plane.

**Figure 5.**Cloud image of velocity: (

**a**) Cloud image of average velocity; (

**b**) Cloud image of fluctuation intensity.

Item | Power | Impulse Frequency | Scanning Speed | Wavelength | Width |
---|---|---|---|---|---|

Value | 120 mJ/Pulse | 30 HZ | 3.75/s | 532 nm | 1 mm |

Item | Resolution | Image Acquisition Frequency | Region of View |
---|---|---|---|

Value | 1600 × 1200 pixels | 32 fps | 600 × 600 mm |

The Actual Width | 20 mm | 40 mm | 52 mm | 60 mm |
---|---|---|---|---|

The dimensionless width | 5 | 10 | 13 | 15 |

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**MDPI and ACS Style**

Ding, X.; Kang, Y.; Li, D.; Yuan, B.; Wang, X. Experimental Investigation on the Influence of a Double-Walled Confined Width on the Velocity Field of a Submerged Waterjet. *Appl. Sci.* **2017**, *7*, 1281.
https://doi.org/10.3390/app7121281

**AMA Style**

Ding X, Kang Y, Li D, Yuan B, Wang X. Experimental Investigation on the Influence of a Double-Walled Confined Width on the Velocity Field of a Submerged Waterjet. *Applied Sciences*. 2017; 7(12):1281.
https://doi.org/10.3390/app7121281

**Chicago/Turabian Style**

Ding, Xiaolong, Yong Kang, Deng Li, Bo Yuan, and Xiaochuan Wang. 2017. "Experimental Investigation on the Influence of a Double-Walled Confined Width on the Velocity Field of a Submerged Waterjet" *Applied Sciences* 7, no. 12: 1281.
https://doi.org/10.3390/app7121281