# Experimental and Numerical Study of Multiple Jets Impinging a Step Surface

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{x}/D = 1.74 and S

_{y}/D = 0.87. These results highlight the effect of this variable on the formation of the impingement boundary layer generated in the vicinity of the target surface. Nayak and Singh [8] analyzed the effect of geometrical aspects on the performance of impinging jets (2700 < Re < 6900) for different crossflow configurations, jet-to-plate spacing, and mass flow rate, and they found that the heat transfer increased for large H and high mass flow rates. Buzzard et al. [9] evaluated the combination of small rectangular shape roughness with a larger rectangular pin (900 < Re < 11,000) and concluded that the heat transfer was enhanced by small rectangle roughness since the local vorticity and the mixing between ambient air and the jet flow was increased by these structures. Alenezi et al. [10] and Tepe et al. [11] highlighted the importance of rib height since ribs that were too high could induce a lower heat transfer rate when compared with flat plates. In this case, the flow must travel a longer distance between the wall and the upper edge of the rib before re-attachment. In that sense, it seems that a rib height that matches with the boundary layer thickness and is located between the stagnation region and the wall jet region enhances the local heat transfer mainly due to the increased turbulence due to the flow recirculation before and after the rib [10]. Yuan-Hsiang and Yao-Hsien [12] experimentally investigated the heat transfer distribution from multiple jets impinging on target plates with different roughness, for 2500 < Re < 7700. The authors found that the change in surface geometry broke the flow development and enhanced the flow mixing. Their study showed that surfaces with partial roughness increased the heat transfer by 50% for the case of longitudinal grooves. Nadda et al. [13] compared different surface geometries and verified that multiple arc protrusion rib geometry generated the best heat transfer performance in impingement jets. A recent research study conducted by Ren et al. [14] (1000 < Re < 15,000) mentioned that a surface with square pin fins could increase the heat transfer by 20% to 300% compared with a flat plate, mainly due to the thermal transport and near-wall mixing. The increased wetted area and the increased turbulence intensity caused by the breaking of the viscous sublayer were additional factors that enhance the heat transfer. Nagesha et al. [15], for 10,000 < Re < 27,500, demonstrated that the heat transfer enhancement in rough target surfaces was due to the area increase and to turbulence enhancement. However, this enhancement depended on the target shape. For example, while multi-protrusions increased the turbulence generation, this increase was not observed in V-grooves due essentially to the air trapped inside the cavities. These studies allow the conclusion that non-flat plates increase the complexity of the flow field and that in some cases the heat transfer is enhanced, while in others both heat transfer and surface coverage can be reduced.

## 2. Experimental Method

#### 2.1. Experimental Apparatus

#### 2.2. PIV Measurements

#### 2.3. Heat Transfer Measurements

^{®}HFS-4 thin film heat flux sensor, which was mounted at the center of the target plate (Figure 4). The heat flux sensor was based on a thermopile formed around an electrically insulating layer. A large number of thermocouple pairs were connected in series measuring the temperature difference across the thermal barrier which was proportional to the heat flow through the sensor [31]. This sensor followed Fourier’s law of thermal conduction to determine the heat flux, as expressed in Equation (1). The average heat flux, $\overline{q}$, was determined across a known thickness, Δx, of material whose thermal conductivity, k, was provided by the manufacturer [32].

^{®}material, Δx = 0.18 mm, whose thermal conductivity was considered equal to k = 0.045 W/m·K, according to the manufacturer information. Moreover, the information provided indicated that the heat flux sensor output for a temperature close to 120 °C, which represents the operating temperature achieved by the target plate, was equal to 1.8 µV/W/m

^{2}. The heat flux and temperature measurements were recorded by a NI 9213 data acquisition system. An algorithm was written using the LabVIEW-based software to process the data and values of temperature and heat flux in function on time were obtained and analyzed.

#### 2.4. Experimental Method

#### 2.5. Data Reduction and Uncertainty Estimation

#### 2.5.1. PIV Measurements

_{p}. Therefore, the PIV uncertainty can be quantified as Equation (4):

_{p}= 1.96 [38], according to Equation (7). This equation was used for ${u}_{\mathit{Ux}}$ and ${u}_{\mathrm{Uy}}$ considering a standard deviation ${\mathsf{\sigma}}_{\mathit{Ux}}$ and ${\mathsf{\sigma}}_{\mathit{Vy}}$, respectively.

#### 2.5.2. Heat Transfer Measurements

_{j}< 35 °C); therefore, it could be calculated for each air jet’s temperatures through Equation (10). This equation was obtained from a linear regression of the tabled thermal conductivity values data in function of air temperature (T

_{j}).

_{p}is the expansion factor obtained by means of a t-Student distribution for 95% and using the degrees of freedom (DOF) (i.e., DOF = N − 1), in which N represents the samples number.

## 3. Numerical Method

#### 3.1. Governing Equations

**u**is the velocity vector, p is the fluid pressure field, and T the temperature. ρ, µ, and κ are constant physical properties of the fluid and represent the density, kinematic viscosity, and thermal diffusivity, respectively. These variables were defined for air at ambient temperature, 25 °C, according to [33].

#### 3.2. Physical Domain and Boundary Conditions

#### 3.3. Turbulence Modelling

_{ω}is the cross-diffusion term [48].

#### 3.4. Discretization

#### 3.5. Grid Independency

^{+}factor, had to be lower than 2 [48]. As can be observed in Table 2, only the medium and fine grids complied with this requirement.

^{+}< 2)—and considering that the number of elements applied in previous studies, which modeled roughened surfaces with the SST k-ω [10,44,46], was close to the one applied in this study—the mesh used for the flat plate case was also implemented for the non-flat plate.

#### 3.6. Numerical Algorithm

^{®}solved the Navier–Stokes and energy equations using the finite volume method and the discrete values of any variable were stored at the cell centers. Since the governing equations were non-linear and coupled to one another, the solution process involved iterations wherein the entire set of governing equations was solved repeatedly until the solution converged. To solve these equations, a pressure-based coupled algorithm was implemented. Since in coupled algorithm the momentum and continuity equations are solved in a closely coupled manner, the rate of solution convergence significantly improved compared with other algorithms, such as pressure-based segregated [41].

## 4. Results and Discussion

#### 4.1. Multiple Jet Impingement Flow Dynamics

#### 4.2. Velocity Profile over the Target Plate

_{max}), as well as the distance from the central jet axis (x/D).

#### 4.3. Velocity Profile over the Central Jet Axis

#### 4.4. Average Heat Transfer over a Flat and Non-Flat Plate

## 5. Numerical Model Validation

_{f}is the free area determined by the ratio between the total nozzle exit area and the total target area. The coefficients A, B, m, and n are defined in [60], while a is described in [61].

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Symbol | Quantity | SI Unit |

A_{f} | Non-dimensional area | - |

D | Diameter | (m) |

D_{ω} | Cross-diffusion term | - |

D_{k} | Generation of k | (kg/m·s^{3}) |

G_{ω} | Generation of ω | (kg/m^{3}·s^{2}) |

h | Heat transfer coefficient | (W/m^{2}K) |

H | Nozzle-to-plate distance | (m) |

k | Turbulent kinetic energy; Thermal conductivity | (m^{2}/s^{2}); (W/mK) |

k_{p} | Expansion factor | - |

N | Samples number | - |

$\overline{\mathrm{Nu}}$ | Average Nusselt number | - |

p | Pressure | (Pa) |

$\overline{q}$ | Average heat flux | (W/m^{2}) |

Re | Reynolds number | - |

S | Jet-to-jet spacing | (m) |

S_{k}, S_{ω} | Source term | (W/m^{3}) |

t | Time | (s) |

T | Temperature | (°C) |

u | Uncertainty/velocity | (dependent variable)/(m/s) |

$\overline{U}$ | Average velocity | (m/s) |

${y}^{+}$ | Dimensionless distance of the first node to the wall | - |

x, y, z | Cartesian coordinates | - |

u, v, w | Velocity according to the Cartesian coordinates | (m/s) |

Greek Symbol | ||

${\mathsf{\Gamma}}_{k},{\mathsf{\Gamma}}_{\mathsf{\omega}}$ | Effective diffusivity of k, ω | (kg/m·s) |

ΔS | Magnification factor | |

Δx | Thickness | (m) |

Δx_{p} | Particle’s displacement | (m) |

ε | Random error | (dependent variable) |

κ | Thermal diffusivity | (m^{2}/s) |

μ | Dynamic viscosity | (Pa/s) |

ρ | Density | (kg/m^{3}) |

σ | Standard deviation | - |

ω | Specific dissipation rate | (1/s) |

Subscript | ||

∞ | Ambient air | |

c_{f} | Crossflow | |

j | Jet | |

max | Maximum | |

w | Wall |

## References

- Intelligence, M. Printed Circuit Board Market-Growth, Trends, Forecasts (2020–2025); Mordor Intelligence: Hyderabad, India, 2020. [Google Scholar]
- Lau, C.-S.; Abdullah, M.; Ani, F.C. Three-dimensional thermal investigations at board level in a reflow oven using thermal-coupling method. Solder. Surf. Mt. Technol.
**2012**, 24, 167–182. [Google Scholar] [CrossRef] - Whalley, D.C. A simplified model of the reflow soldering process. J. Mater. Process. Technol.
**2004**, 150, 134–144. [Google Scholar] [CrossRef] - Balázs, I.; Harsányi, G. Heating characteristics of convection reflow ovens. Appl. Therm. Eng.
**2009**, 29, 2166–2171. [Google Scholar] - Tsai, T.-N. Thermal parameters optimization of a reflow soldering profile in printed circuit board assembly: A comparative study. Appl. Soft Comput.
**2012**, 12, 2601–2613. [Google Scholar] [CrossRef] - Caliskan, S.; Baskaya, S. Experimental investigation of impinging jet array heat transfer from a surface with V-shaped and convergent-divergent ribs. Int. J. Therm. Sci.
**2012**, 59, 234–246. [Google Scholar] [CrossRef] - Chauhan, R.; Thakur, N. Heat transfer and friction factor correlations for impinging jet solar air heater. Exp. Therm. Fluid Sci.
**2013**, 44, 760–767. [Google Scholar] [CrossRef] - Nayak, R.; Singh, S. Effect of geometrical aspects on the performance of jet plate solar air heater. Sol. Energy
**2016**, 137, 434–440. [Google Scholar] [CrossRef] - Buzzard, W.C.; Ren, Z.; Ligrani, P.M.; Nakamata, C.; Ueguchi, S. Influences of target surface small-scale rectangle roughness on impingement jet array heat transfer. Int. J. Heat Mass Transf.
**2017**, 110, 805–816. [Google Scholar] [CrossRef] - Alenezi, A.H.; Almutairi, A.; Alhajeri, H.M.; Addali, A.; Gamil, A.A.A. Flow Structure and Heat Transfer of Jet Impingement on a Rib-Roughened Flat Plate. Energies
**2018**, 11, 1550. [Google Scholar] [CrossRef] [Green Version] - Tepe, A.Ü.; Uysal, Ü.; Yetişken, Y.; Arslan, K. Jet impingement cooling on a rib-roughened surface using extended jet holes. Appl. Therm. Eng.
**2020**, 178, 115601. [Google Scholar] [CrossRef] - Lo, Y.-H.; Liu, Y.-H. Heat transfer of impinging jet arrays onto half-smooth, half-rough target surfaces. Appl. Therm. Eng.
**2018**, 128, 79–91. [Google Scholar] [CrossRef] - Nadda, R.; Kumar, R.; Kumar, A.; Maithani, R. Optimization of single arc protrusion ribs parameters in solar air heater with impinging air jets based upon PSI approach. Therm. Sci. Eng. Prog.
**2018**, 7, 146–154. [Google Scholar] [CrossRef] - Ren, Z.; Yang, X.; Lu, X.; Li, X.; Ren, J. Experimental Investigation of Micro Cooling Units on Impingement Jet Array Flow Pressure Loss and Heat Transfer Characteristics. Energies
**2021**, 14, 4757. [Google Scholar] [CrossRef] - Nagesha, K.; Srinivasan, K.; Sundararajan, T. Enhancement of jet impingement heat transfer using surface roughness elements at different heat inputs. Exp. Therm. Fluid Sci.
**2020**, 112, 109995. [Google Scholar] [CrossRef] - De Oliveira, M.A.; De Moraes, P.G.; De Andrade, C.L.; Bimbato, A.M.; Pereira, L.A.A. Control and Suppression of Vortex Shedding from a Slightly Rough Circular Cylinder by a Discrete Vortex Method. Energies
**2020**, 13, 4481. [Google Scholar] [CrossRef] - Slama, M.; Bex, C.C.; Pinon, G.; Togneri, M.; Evans, I. Lagrangian Vortex Computations of a Four Tidal Turbine Array: An Example Based on the Nepthyd Layout in the Alderney Race. Energies
**2021**, 14, 3826. [Google Scholar] [CrossRef] - Spring, S.; Xing, Y.; Weigand, B. An Experimental and Numerical Study of Heat Transfer From Arrays of Impinging Jets with Surface Ribs. J. Heat Transf.
**2012**, 134, 082201. [Google Scholar] [CrossRef] - Casanova, J.O.; Granados-Ortiz, F. Numerical simulation of the heat transfer from a heated plate with surface variations to an impinging jet. Int. J. Heat Mass Transf.
**2014**, 76, 128–143. [Google Scholar] [CrossRef] - Brakmann, R.; Chen, L.; Weigand, B.; Crawford, M. Experimental and Numerical Heat Transfer Investigation of an Impinging Jet Array on a Target Plate Roughened by Cubic Micro Pin Fins1. J. Turbomach.
**2016**, 138, 111010. [Google Scholar] [CrossRef] - Shukla, A.K.; Dewan, A. Convective Heat Transfer Enhancement using Slot Jet Impingement on a Convective Heat Transfer Enhancement using Slot Jet Impingement on a Detached Rib Surface. J. Appl. Fluid Mech.
**2017**, 10, 1615–1627. [Google Scholar] - Jing, Q.; Zhang, D.; Xie, Y. Numerical investigations of impingement cooling performance on flat and non-flat targets with dimple/protrusion and triangular rib. Int. J. Heat Mass Transf.
**2018**, 126, 169–190. [Google Scholar] [CrossRef] - McInturff, P.; Suzuki, M.; Ligrani, P.; Nakamata, C.; Lee, D.H. Effects of hole shape on impingement jet array heat transfer with small-scale, target surface triangle roughness. Int. J. Heat Mass Transf.
**2018**, 127, 585–597. [Google Scholar] [CrossRef] - Chen, L.; Brakmann, R.G.; Weigand, B.; Poser, R.; Yang, Q. Detailed investigation of staggered jet impingement array cooling performance with cubic micro pin fin roughened target plate. Appl. Therm. Eng.
**2020**, 171, 115095. [Google Scholar] [CrossRef] - Menter, F.R. Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J.
**1994**, 32, 1598–1605. [Google Scholar] [CrossRef] [Green Version] - Melling, A. Tracer particles and seeding for particle image velocimetry. Meas. Sci. Technol.
**1997**, 8, 1406–1416. [Google Scholar] [CrossRef] - Keane, R.D.; Adrian, R.J. Theory of cross-correlation analysis of PIV images. Appl. Sci. Res.
**1992**, 49, 191–215. [Google Scholar] [CrossRef] - Westerweel, J. Fundamentals of digital particle image velocimetry. Meas. Sci. Technol.
**1997**, 8, 1379–1392. [Google Scholar] [CrossRef] [Green Version] - Zhang, C.; Vasilevskis, S.; Kozlowski, B. Particle Image Velocimetry-User Guide; Department of Civil Engineering, Aalborg University: Aalborg, Denmark, 2018. [Google Scholar]
- Cao, X.; Liu, J.; Jiang, N.; Chen, Q. Particle image velocimetry measurement of indoor airflow field: A review of the technologies and applications. Energy Build.
**2014**, 69, 367–380. [Google Scholar] [CrossRef] [Green Version] - Childs, P.R.N.; Greenwood, J.R.; Long, C.A. Heat flux measurement techniques. Proc. Inst. Mech. Eng. Part C
**1999**, 213, 655–677. [Google Scholar] [CrossRef] - Assaad, M.C.; Kimble, B.; Huang, Y.-M.; Burgan, R.; Fralick, G.C.; Wrbanek, J.D.; Gonzalez, J.M. Thin-Film Heat Flux Sensor for Measuring the Film Coefficient of Rubber Components of a Rolling Tire. Tire Sci. Technol.
**2008**, 36, 275–289. [Google Scholar] [CrossRef] - Cengel, Y.A.; Ghajar, A.J. Heat and Mass Transfer: Fundamentals and Applications, 5th ed.; McGraw-Hill Education: New York, NY, USA, 2011. [Google Scholar]
- Sabharwall, P.; Conder, T.; Skifton, R.; Stoots, C.; Kim, E.S. PIV Uncertainty Methodologies for CFD Code Validation at the MIR Facility; Idaho National Laboratory: Idaho Falls, ID, USA, 2013. [Google Scholar]
- Sciacchitano, A. Uncertainty quantification in particle image velocimetry. Meas. Sci. Technol.
**2019**, 30, 092001. [Google Scholar] [CrossRef] [Green Version] - Barbosa, F.; Costa, C.; Teixeira, S.; Teixeira, J.C. Measurement Errors and Uncertainty Quantification of a 2D-PIV Experimental Setup for Jet Flow Characterization. ASCE-ASME J. Risk Uncertain. Eng. Syst. Part B Mech. Eng.
**2020**, 6, 1–59. [Google Scholar] - Dantec Dynamics. Dynamic Studio, User’s Guide; Dantec Dynamics: Skovlunde, Denmark, 2016. [Google Scholar]
- ASME. Test. Uncertainty. Instruments and Appartus; The American Society of Mechanical Engineers: New York, NY, USA, 1998. [Google Scholar]
- Sciacchitano, A.; Wieneke, B. PIV uncertainty propagation. Meas. Sci. Technol.
**2016**, 27, 84006. [Google Scholar] [CrossRef] [Green Version] - JCGM. Evaluation of Measurement Data—Guide to the Expression of Uncertainty in Measurement; Joint Committee for Guides in Metrology: Sèvres, France, 2008. [Google Scholar]
- ANSYS. Ansys Fluent Theory Guide; ANSYS: Canonsburg, PA, USA, 2013. [Google Scholar]
- Zhu, K.; Yu, P.; Yuan, N.; Ding, J. Transient heat transfer characteristics of array-jet impingement on high-temperature flat plate at low jet-to-plate distances. Int. J. Heat Mass Transf.
**2018**, 127, 413–425. [Google Scholar] [CrossRef] - Barbosa, F.V.; Silva, J.P.V.; Teixeira, S.F.C.; Soares, D.F.; Santos, D.N.F.; Delgado, I.A.C.; Teixeira, J.C.F. Cfd Prediction of Multiple Jet Impingement in a Reflow Soldering Process. In Transactions on Engineering Technologies. WCE 2018; Ao, S.I., Gelman, L., Kim, H.K., Eds.; Springer: Singapore, 2019. [Google Scholar]
- Debnath, S.; Khan, H.U.; Ahmed, Z.U. Turbulent swirling impinging jet arrays: A numerical study on fluid flow and heat transfer. Therm. Sci. Eng. Prog.
**2020**, 19, 100580. [Google Scholar] [CrossRef] - Tepe, A.Ü.; Yetişken, Y.; Uysal, Ü.; Arslan, K. Experimental and numerical investigation of jet impingement cooling using extended jet holes. Int. J. Heat Mass Transf.
**2020**, 158, 119945. [Google Scholar] [CrossRef] - Shah, S. Numerical analysis of heat transfer between multiple jets and flat moving surface. Int. J. Heat Mass Transf.
**2021**, 171, 121088. [Google Scholar] [CrossRef] - Menter, F.R.; Ferreira, J.C.; Esch, T. The SST Turbulence Model with Improved Wall Treatment for Heat Transfer Predictions in Gas Turbines. In Proceedings of the International Gas Turbine Congress, Tokyo, Japan, 2–7 November 2003; pp. 1–7. [Google Scholar]
- Wen, Z.-X.; He, Y.-L.; Cao, X.-W.; Yan, C. Numerical study of impinging jets heat transfer with different nozzle geometries and arrangements for a ground fast cooling simulation device. Int. J. Heat Mass Transf.
**2016**, 95, 321–335. [Google Scholar] [CrossRef] - Rhie, C.M.; Chow, W.L. Numerical Study of the Turbulent Flow past an Airfoil with Trailing Edge Separation. AIAA J.
**1983**, 21, 1525–1532. [Google Scholar] [CrossRef] - Ferziger, J.H.; Peric, M. Computational Methods for Fluid Dynamics, 3rd ed.; Springer: New York, NY, USA, 1996. [Google Scholar]
- Lee, J.; Lee, S. Stagnation Region Heat Transfer of a Turbulent Axisymmetric Jet Impingement. Exp. Heat Transf.
**2010**, 12, 137–156. [Google Scholar] [CrossRef] - Viskanta, R. Nusselt-Reynolds Prize Paper-Heat Transfer to Impinging Isothermal Gas and Flame Jets. Exp. Therm. Fluid Sci.
**1993**, 6, 111–134. [Google Scholar] [CrossRef] - Barbosa, F.; Teixeira, S.; Teixeira, J. Experimental and numerical analysis of the influence of the nozzle-to-plate distance in a jet impingement process. Int. J. Thermodyn.
**2020**, 23, 81–91. [Google Scholar] [CrossRef] - Weigand, B.; Spring, S. Multiple Jet Impingement-A Review. Heat Transf. Res.
**2011**, 42, 101–142. [Google Scholar] [CrossRef] - Zuckerman, N.; Lior, N. Jet Impingement Heat Transfer: Physics, Correlations, and Numerical Modeling. Adv. Heat Transf.
**2006**, 39, 565–631. [Google Scholar] - Kalifa, R.B.; Habli, S.; Saïd, N.M.; Bournot, H.; le Palec, G. Parametric analysis of a round jet impingement on a heated plate. Int. J. Heat Fluid Flow
**2016**, 57, 11–23. [Google Scholar] [CrossRef] - Angioletti, M.; Di Tommaso, R.; Nino, E.; Ruocco, G. Simultaneous visualization of flow field and evaluation of local heat transfer by transitional impinging jets. Int. J. Heat Mass Transf.
**2003**, 46, 1703–1713. [Google Scholar] [CrossRef] - Caliskan, S.; Baskaya, S.; Calisir, T. Experimental and numerical investigation of geometry effects on multiple impinging air jets. Int. J. Heat Mass Transf.
**2014**, 75, 685–703. [Google Scholar] [CrossRef] - Nozaki, A.; Igarashi, Y.; Hishida, K. Heat transfer mechanism of a swirling impinging jet in a stagnation region. Heat Transf.-Asian Res.
**2003**, 32, 663–673. [Google Scholar] [CrossRef] - Florschuetz, L.W.; Metzger, D.E.; Takeuchi, D.I.; Berry, R.A. Multiple Jet Impingement Heat Transfer Characteristic—Experimental Investigation of in-Line and Staggered Arrays with Crossflow. NASA Contract. Rep.
**1980**, 3217, 84. [Google Scholar] - Obot, N.T.; Trabold, T. Impingement Heat Transfer Within Arrays of Circular Jets: Part 1—Effects of Minimum, Intermediate, and Complete Crossflow for Small and Large Spacings. J. Heat Transf.
**1987**, 109, 872–879. [Google Scholar] [CrossRef] - Chitsazan, A.; Glasmacher, B. Numerical Investigation of Heat Transfer and Pressure Force from Multiple Jets Impinging on a Moving Flat Surface. Int. J. Heat Technol.
**2020**, 38, 601–610. [Google Scholar] [CrossRef] - Badra, J.; Masri, A.R.; Behnia, M. Enhanced Transient Heat Transfer from Arrays of Jets Impinging on a Moving Plate From Arrays of Jets Impinging on a Moving Plate. Heat Transf. Eng.
**2013**, 34, 361–371. [Google Scholar] [CrossRef]

**Figure 1.**Experimental apparatus: (

**a**) 3D model; (

**b**) main structure; (

**c**) impinging plate; (

**d**) control equipment. (Reprinted from Flávia V. Barbosa, Sérgio D. T. Sousa, Senhorinha F. C. F. Teixeira, José C. F. Teixeira, Application of Taguchi Method for the Analysis of a Multiple Air Jet Impingement System with and without Target Plate Motion, 176, September 2021, Copyright (2021), with permission from Elsevier).

**Figure 2.**Target plate configurations: (

**a**) flat plate; (

**b**) non-flat plate. The scheme represents the location of the heat flux and the numbers are the location of thermocouples over the surface for each configuration.

**Figure 8.**Velocity field measured experimentally of multi-jets impinging a flat and non-flat plate at Re = 5000, H/D = 2, and S/D = 3. (

**a**) Flat plate; (

**b**) non-flat with 1 D step; (

**c**) non-flat with 2 D step.

**Figure 10.**Velocity profile over the jet axis. (

**a**) Central jet (x/D = 0); (

**b**) right adjacent jet (x/D = 6).

**Figure 11.**Velocity field obtained numerically of multi-jets impinging a flat and non-flat plate at Re = 5000, H/D = 2, and S/D = 3. (

**a**) Flat plate; (

**b**) non-flat with 1 D step; (

**c**) non-flat with 2 D step.

**Table 1.**Systematic uncertainties. (Reprinted from Flávia V. Barbosa, Sérgio D. T. Sousa, Senhorinha F. C. F. Teixeira, José C. F. Teixeira, Application of Taguchi Method for the Analysis of a Multiple Air Jet Impingement System with and without Target Plate Motion, 176, September 2021, Copyright (2021), with permission from Elsevier).

Source | Method of Measurement | Uncertainty |
---|---|---|

Heat Flux | Heat flux sensor | ±0.577 (W/m^{2}) |

Nozzle diameter and heat flux sensor area | Caliper | ±0.011 (mm) |

Target and jets temperature | Thermocouples type K | ±0.115 (°C) |

Grid | N° of Elements | Max y^{+} |
---|---|---|

Coarse | 387,072 | 3.27 |

Medium | 756,000 | 1.69 |

Fine | 1,134,000 | 1.64 |

Plate Geometry | Average Nusselt Number |
---|---|

Flat | 29.90 ± 0.45 |

Non-flat—Step 1 D | 32.72 ± 0.49 |

Non-flat—Step 2 D | 37.39 ± 0.56 |

$\overline{\mathbf{Nu}}{.}_{}$ | |||
---|---|---|---|

Numerical Result | Experimental Data | Florshuetz et al. [61] | Obot and Trebold [62] |

28.65 | 29.90 ± 0.45 | 32.63 | 25.55 |

$\overline{\mathbf{Nu}}$ | ||
---|---|---|

Target Plate | Numerical Result | Experimental Data |

1 D step | 31.35 | 32.72 ± 0.49 |

2 D step | 31.69 | 37.39 ± 0.56 |

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## Share and Cite

**MDPI and ACS Style**

Barbosa, F.V.; Teixeira, S.F.C.F.; Teixeira, J.C.F.
Experimental and Numerical Study of Multiple Jets Impinging a Step Surface. *Energies* **2021**, *14*, 6659.
https://doi.org/10.3390/en14206659

**AMA Style**

Barbosa FV, Teixeira SFCF, Teixeira JCF.
Experimental and Numerical Study of Multiple Jets Impinging a Step Surface. *Energies*. 2021; 14(20):6659.
https://doi.org/10.3390/en14206659

**Chicago/Turabian Style**

Barbosa, Flavia V., Senhorinha F. C. F. Teixeira, and José C. F. Teixeira.
2021. "Experimental and Numerical Study of Multiple Jets Impinging a Step Surface" *Energies* 14, no. 20: 6659.
https://doi.org/10.3390/en14206659