# Experimental Investigation on Mean Flow Development of a Three-Dimensional Wall Jet Confined by a Vertical Baffle

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## Abstract

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## 1. Introduction

_{m}denotes the local maximum mean velocity; y

_{m}is the wall-normal location where U

_{m}occurs; y

_{m/2}is the distance from the bottom wall to the point in the outer layer where the velocity is half of U

_{m}(called half-height); z

_{m/2}is the lateral location where the velocity has a half value of U

_{m}(called half-width). It should be noted that the lateral confinement is neglected.

## 2. Experimental Setup

## 3. PIV System and Data Analysis

_{m}, and thus varies with the streamwise distance due to the baffle confinement. It is anticipated that the offset x-z plane measurements at different x-axial locations can describe the vertical variations for mean velocities such as x- and z-axial velocity, U and W, respectively. Regarding x-y plane measurements, Law and Herlian [11] conducted the offset tests and found that the self-similar velocity profiles still occurred at various sections. Therefore, the offset x-y plane measurements from the jet centerline were not performed in the present study.

## 4. Results and Discussion

_{0}B/υ, where U

_{0}is jet exit velocity, B is square root of jet exit area, and υ is kinetic viscosity of water) The jet exit velocities of 0.5 m/s, 0.6 m/s and 0.7 m/s, which correspond to the three Reynolds numbers, were determined from the PIV measurements. The corresponding flow rates (Q) of 0.089 l/s, 0.109 l/s and 0.131 l/s were measured by the electromagnetic flowmeter. A water depth of 100 mm was set for the test section. All measurements in the lateral (x-z) and symmetry (x-y) planes are presented at least for the range of 10 ≤ x/B ≤ 24. It should be noted that the measurement locations have not been extended to both the wall and water surface considering the effect of reflection of the laser light on the accuracy of PIV data. The corresponding distances from the measurement edge to the wall and water surface are 1 mm and 5 mm, respectively.

#### 4.1. Spreading Rates

_{m/2}and half-width z

_{m/2}with downstream distance. More specifically, y

_{m/2}and z

_{m/2}are the wall-normal and lateral locations where 0.5U

_{m}occurs, respectively. In this figure, they were normalized by the square root of jet exit area (B) which is an appropriate scaling parameter as suggested by Padmanabham and Gowda [10] and Agelin-Chaab and Tachie [13]. The results for unconfined case obtained by Law and Herlian [11] are also included for comparison. The half-height increases approximately linearly in the region 16 < x/B < 23, but after x/B = 23 the value of y

_{m/2}grows dramatically (Figure 4a). This behavior may be closely related to a clockwise vortex formed in the region y/y

_{m/2}< 0.25 as mentioned in Section 4.2. Therefore, the position of U

_{m}tends to be deflected away from the bottom wall. The half-width starts to spread after x/B = 6 and varies nearly linearly with downstream distance in the region 6 < x/B < 23 (Figure 4b). However, the z

_{m/2}in the region 16 < x/B < 23 develops more rapidly compared to the early region 6 < x/B < 16. Beyond x/B = 23, although the confinement of the baffle can enhance the development of the jet flow field, the spreading of z

_{m/2}tends to significantly decrease, which is contrary to the variation of y

_{m/2}in the corresponding region. This is because the value of U close to the baffle gets considerably dropped due to most of the impinged jet fluid moving in both the lateral directions. In general, the variations of y

_{m/2}and z

_{m/2}are independent of Reynolds number within the present range.

_{m/2}/dx), a linear fit is applied to the data in the region 16 < x/B < 23 in Figure 4a. The variation of y

_{m/2}can be well described by the equation:

_{m/2}(Figure 4b) in the regions 6 < x/B < 16 and 16 < x/B < 23 can be well fitted, respectively. These two equations are written as:

_{m/2}/dx is 0.04. The dz

_{m/2}/dx value of 0.09 in the region 6 < x/B < 16 is comparable to the circular free jet. Further downstream (16 < x/B < 23), the lateral spreading becomes to diverge more rapidly and its slope (dz

_{m/2}/dx) is 0.19. For comparison, some of previous investigations for 3D circular wall jets are illustrated in Table 1. It is interesting to see that, in the region 16 < x/B < 23, the spreading rates of y

_{m/2}and z

_{m/2}for the confined wall jet in the present study, respectively, fall well within the ranges of 0.036 [31]–0.045 [10] and 0.17 [32]–0.33 [31] corresponding to the values in RD region for undisturbed jet reported in the literature. It should be pointed out that reaching RD region for the unconfined wall jet requires streamwise distance at least x/B = 20, as summarized in Table 1. These results imply that the baffle starts to alter the jet flow development after x/B = 16 and the fully developed region for the confined case appears to occur at least 4B earlier than the unconfined case.

#### 4.2. Mean Velocity Profiles

_{m}.

_{m/2}. The profiles of U collapse reasonably well in the region 10 < x/B < 23, while the quality of collapse at x/B = 10 is relatively poor because the exit flow could not fully develop in the vertical direction, as shown in Figure 5a. Additionally, in the region y/y

_{m/2}< 1.5, the present data are comparable to the unconfined 2D and 3D wall jet results from Verhoff [34] and Agelin-Chaab and Tachie [13], respectively. Some slight fluctuations of the profiles are observed as the jet evolves downstream to x/B = 24 near the baffle. This behavior is attributed to the confinement of the baffle. Further downstream, the confinement becomes more noticeable and negative values of U are observed in the region y/y

_{m/2}< 0.25. This occurs because most of the impinged jet fluid moves in both the lateral directions and resulting low momentum in the vertical direction could not overcome the adverse pressure gradient. As a result, a clockwise vortex is formed in the corner. It also can be seen from Figure 5a, near the baffle (x/B ≥ 24), there are some significant deviations which occur just approximately from y/y

_{m/2}= 1.5 to 3 due to the resulting reverse flow in the vicinity of the water surface. The deviations could be supported by profiles of wall-normal mean velocity (V) in the symmetry plane shown in Figure 5b. After the normal impingement, flow separation occurs close to the baffle and the flow is divided into corner jets [21,22] in both the lateral directions and upward wall jet along the baffle surface due to the Coanda effect, followed by most positive values of V beyond x/B = 23 shown in Figure 5b. As expected, the reverse flow is formed after impingement of the upward jet onto the water surface. For the region 21 ≤ x/B ≤ 24, some negative values of V are observed in the region y/y

_{m/2}> 3.4 due to the reverse flow. In the range of x/B ≤ 23, the magnitudes of V are negative over most of the water depth (y/y

_{m/2}< 3), indicating that the ambient fluid is being drawn towards the bottom wall, owing to the presence of a secondary mean vortex presented by Launder and Rodi [1]. In addition, compared to the measurements made by Law and Herlian [11] and Agelin-Chaab and Tachie [13], similar variations of V with water depth are observed but the values are slightly lower as illustrated in Figure 5b. However, their measurements reported were selected at least after x/B = 28 where the jet flow has been fully developed. It should be noted that considerable scattered points are shown in this figure due to the low accuracy of PIV in the wall-normal direction as described by Law and Herlian [11].

_{p}is analytical or previous x-axial mean velocities. The results of MARE for U profiles in x-y plane at different locations are summarized in Table 2. In the region (y/y

_{m/2}< 1.5) unconfined by the water surface, the maximum error is substantially within the range of MARE < 5% before x/B = 24, while the maximum error increases to 18.7% after x/B = 24. The relatively large error between the confined and unconfined cases indicates that the baffle confinement has noticeable impact upon the mean velocity distribution.

_{m/2}). Being similar to the U velocity distribution in the symmetry plane, measurements (10 < x/B < 23) in the lateral plane show reasonable collapse in the region z/z

_{m/2}< 1.2. However, when the flow evolves downstream (x/B > 16), there are some slight differences between the experimental data and previous observations (Figure 6a). This is critically because the profiles of current jet start to be affected by the confinement of the vertical baffle after x/B = 16. Far downstream (x/B ≥ 24), the confinement increases with increasing longitudinal distance and the velocity profiles across the entire sections seem to be unstable. For example, some significant fluctuations can be observed especially after x/B = 26 due to the presence of the baffle. For comparison, the results obtained by Law and Herlian [11] generally agree better with the present data. Similarly, Table 3 gives the MARE values for U profiles in x-z plane at different locations. Except for the region very close to the baffle (x/B ≥ 26), the maximum error between the present data and analytical and previous results (z/z

_{m/2}< 1.2) does not exceed the range of MARE < 5%. Figure 6b shows the W distribution at typical x/B locations. The lateral mean velocity (W) increases from zero at the symmetry plane to a peak value which occurs approximately at z/z

_{m/2}= 1.2 within the region x/B ≤ 24. Beyond x/B = 24, the location of the peak value is gradually delayed (i.e., z/z

_{m/2}= 1.6 for x/B = 25). From this figure, the W profiles in the region x/B ≤ 21 are relatively lower than those of Law and Herlian [11]. However, as the jet leaves the nozzle, the corresponding W values continuously increase. For example, the present observation at x/B = 22 is comparable to those of Law and Herlian [11]. When the jet develops downstream (x/B = 24), larger values of W can be observed compared to the results reported by Law and Herlian [11]. Further downstream (x/B > 24), the W profiles increase dramatically and are significantly higher as compared to previous results. This indicates that most of the fluid is deflected away from the centerline of the jet in the lateral plane due to the confinement of the vertical baffle.

#### 4.3. Decay of Local Maximum Velocity

_{m}virtually remains constant in the PC region (x/B < 3.75), while it starts to decrease gradually after x/B = 6. The U

_{m}decay in both the regions 6 < x/B < 16 and 16 < x/B < 23, respectively, can be expressed in power-law forms:

_{m}can be clearly seen from Figure 8 and the corresponding decay exponent is 1.11, a value that is compared very well with those of unconfined cases in the RD region summarized in Table 1. These results are consistent with the previous observations mentioned above. However, it is anticipated that a sharp reduction of U

_{m}can be observed by the strong confinement of the baffle as the jet develops further downstream (x/B > 24).

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Notation

B | square root of jet exit area |

N | number of instantaneous image pairs |

M | total number of data on one velocity profile in given region |

n | exponent describing the decay of U_{m} |

Q | flow rate through the jet pipe |

Re | jet exit Reynolds number based on jet exit velocity and square root of jet exit area |

U | x-axial mean velocity |

V | y-axial mean velocity |

W | z-axial mean velocity |

U_{0} | jet exit velocity |

U_{m} | local maximum mean velocity |

U_{p} | analytical or previous x-axial mean velocity |

x | longitudinal direction in the coordinate system |

y | wall-normal direction in the coordinate system |

y_{m} | wall-normal location where U_{m} occurs |

y_{m/2} | wall-normal location where 0.5U_{m} occurs |

z | lateral direction in the coordinate system |

z_{m/2} | lateral location where 0.5U_{m} occurs |

υ | kinetic viscosity of water |

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**Figure 3.**Convergence test for the experimental data for three different Reynolds numbers (Re) of 8333, 10,000, and 11,666: (

**a**) x-axial mean velocity (U) varies with the number of instantaneous image pairs (N), (

**b**) y-axial mean velocity (V) varies with the number of instantaneous image pairs (N), and (

**c**) z-axial mean velocity (W) varies with the number of instantaneous image pairs (N).

**Figure 4.**Mean flow developments of the 3D confined wall jet with Re = 8333, 10,000 and 11,666: (

**a**) velocity half-height y

_{m/2}, and (

**b**) velocity half-width z

_{m/2.}

**Figure 5.**Mean velocity profiles measured in x-y plane for Re = 11,666: (

**a**) U profiles, and (

**b**) V profiles.

**Figure 6.**Mean velocity profiles measured in x-z plane for Re = 11,666: (

**a**) U profiles, and (

**b**) W profiles.

**Figure 7.**Variations of U profiles at typical locations with Re = 8333, 10,000 and 11,666: (

**a**) x-y plane, and (

**b**) x-z plane.

Authors | Measuring Technique | Re | RD Region | dz_{m/2}/dx | dy_{m/2}/dx | n |
---|---|---|---|---|---|---|

Padmanabham and Gowda [10] | HWA | 95,400 | >20B | 0.216 | 0.045 | 1.15 |

Law and Herlina [11] | PIV | 5500, 12,200, 13,700 | >23B | 0.21 | 0.042 | 1.07 |

Agelin-Chaab and Tachie [12,13] | PIV | 5000, 10,000, 20,000 | >60B | 0.255 | 0.054 | 1.15 |

Després and Hall [16] | PIV | 108,000 | >45B | 0.25 | 0.047 | - |

Present data | PIV | 8333, 10,000, 11,666 | 16B–23B | 0.19 | 0.040 | 1.11 |

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**MDPI and ACS Style**

Chen, M.; Huang, H.; Zhang, X.; Lv, S.; Li, R.
Experimental Investigation on Mean Flow Development of a Three-Dimensional Wall Jet Confined by a Vertical Baffle. *Water* **2019**, *11*, 237.
https://doi.org/10.3390/w11020237

**AMA Style**

Chen M, Huang H, Zhang X, Lv S, Li R.
Experimental Investigation on Mean Flow Development of a Three-Dimensional Wall Jet Confined by a Vertical Baffle. *Water*. 2019; 11(2):237.
https://doi.org/10.3390/w11020237

**Chicago/Turabian Style**

Chen, Ming, Haijin Huang, Xingxing Zhang, Senpeng Lv, and Rengmin Li.
2019. "Experimental Investigation on Mean Flow Development of a Three-Dimensional Wall Jet Confined by a Vertical Baffle" *Water* 11, no. 2: 237.
https://doi.org/10.3390/w11020237