# Induced Circulation by Plunging and Submerged Jets in Circular Water Storage Tanks Using CFD

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## Abstract

**:**

## 1. Introduction

## 2. Background Jet Theory

#### 2.1. Plunging Jet

#### 2.2. Submerged Jet

## 3. Models Description

## 4. Computational Fluid Dynamics Model

#### 4.1. Introduction

#### 4.2. Mesh

#### 4.3. Multiphase Flow

## 5. Results and Discussion

#### 5.1. Plunging Jet

#### 5.2. Submerged Jet

#### 5.3. Velocity Fields Comparison

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

3D | Three-Dimensional |

CFD | Computational Fluid Dynamics |

SST | Shear Stress Transport |

## References

- Panguluri, S.; Grayman, W.M.; Clark, R.M. Water Distribution System Analysis: Field Studies, Modeling and Management: A Reference Guide for Utilities; Report; U. S. Environmental Protection Agency: Washington, DC, USA, 2005.
- Monteiro, L.S.P.P.; Viegas, R.M.C.; Covas, D.I.C.; Menaia, J.A.G.F. Assessment of Current Models Ability to Describe Chlorine Decay and Appraisal of Water Spectroscopic Data as Model Inputs. J. Environ. Eng.
**2017**, 143, 04016071. [Google Scholar] [CrossRef] - Mostafa, N.G.; Matta, M.E.; Halim, H.A. Simulation of Chlorine Decay in Water Distribution Networks Using EPANET—Case Study. Civ. Environ. Res.
**2013**, 3, 100–116. [Google Scholar] - Grayman, W.M.; Clark, R.M. Using Computer Models to Determine the Effect of Storage on Water Quality. Am. Water Work. Assoc.
**1993**, 85, 67–77. [Google Scholar] [CrossRef] - Kennedy, M.S.; Moegling, S.; Sarikelle, S.; Surava, K. Assessing the Effects of Storage Tank Design on Water Quality. Am. Water Work. Assoc.
**1993**, 85, 78–88. [Google Scholar] [CrossRef] - Fisher, I.; Sathasivan, A.; Chuo, P.; Kastl, G. Effects of stratification on chloramine decay in distribution system service reservoirs. Water Res.
**2009**, 43, 1403–1413. [Google Scholar] [CrossRef] - Bumrungthaichaichan, E.; Wattananusorn, S. CFD modeling of pump-around jet mixing tanks: A reliable model for overall mixing time prediction. J. Chin. Inst. Eng.
**2019**, 42, 428–437. [Google Scholar] [CrossRef] - Clark, R.M.; Abdesaken, F.; Boulos, P.F.; Mau, R.E. Mixing in Distribution System Storage Tanks: Its Effect on Water Quality. J. Environ. Eng.-ASCE
**1996**, 122, 814–821. [Google Scholar] [CrossRef] - Rossman, L.A.; Grayman, W.M. Scale-Model Studies of Mixing in Drinking Water Storage Tanks. J. Environ. Eng.-ASCE
**1999**, 125, 755–761. [Google Scholar] [CrossRef] - Olson, C.T.; DeBoer, D.E. The Effects of Tank Operation and Design Characteristics on Water Quality in Distribution System Storage Tanks; Report; Regional Water System Research Consortium: Brookings, SD, USA, 2011. [Google Scholar]
- Duan, H.F.; Li, F.; Tao, T. Multi-objective Optimal Design of Detention Tanks in the Urban Stormwater Drainage System: Uncertainty and Sensitivity Analysis. Water Resour. Manag.
**2016**, 30, 2213–2226. [Google Scholar] [CrossRef] - Prasad, T.D.; Walters, G.A.; Savic, D.A. Booster Disinfection of Water Supply Networks: Multiobjective Approach. J. Water Resour. Plan. Manag.
**2004**, 130, 367–376. [Google Scholar] [CrossRef] - Angeloudis, A.; Stoesser, T.; Falconer, R.A. Predicting the disinfection efficiency range in chlorine contact tanks through a CFD-based approach. Water Res.
**2014**, 60, 118–129. [Google Scholar] [CrossRef] [PubMed] - Musz-Pomorska, A.; Widomski, M.K. Modelling Studies of Water Chlorination Efficiency in Municipal Water Supply Network. Ecol. Chem. Eng. A
**2020**, 27, 1–13. [Google Scholar] [CrossRef] - Grayman, W.M.; Rossman, L.A.; Deininger, R.A.; Smith, C.D.; Arnold, C.N.; Smith, J.F. Mixing and Aging of Water in Distribution System Storage Failities. AWWA
**2004**, 96, 70–80. [Google Scholar] [CrossRef] - Patwardhan, A.W. CFD modeling of jet mixed tanks. Chem. Eng. Sci.
**2002**, 57, 1307–1318. [Google Scholar] [CrossRef] - Jaunâtre, J. Numerical Simulation of Threedimensional Flows in Water Storage Tanks—Application to Norra Ugglarps Reservoirs in South Sweden. Ph.D. Thesis, Lund University, Lund, Sweden, 2013. [Google Scholar]
- Angeloudis, A.; Stoesser, T.; Kim, D.; Falconer, R.A. CFD Study of Flow and Transport Characteristics in Baffled Disinfection Tanks. In Proceedings of the 35th IAHR World Congress, Chengdu, China, 8–13 September 2013. [Google Scholar]
- Stamatopoulos, K.; Alberini, F.; Batchelor, H.; Simmons, M.J.H. Use of PLIF to assess the mixing performance of small volume USP 2 apparatus in shear thinning media. Chem. Eng. Sci.
**2016**, 145, 1–9. [Google Scholar] [CrossRef] [Green Version] - Tian, X.; Roberts, P.J. Mixing in Water Storage Tanks. I: No Buoyancy Effects. J. Environ. Eng.-ASCE
**2008**, 134, 974–985. [Google Scholar] [CrossRef] - Aparicio-Mauricio, G.; Rodriguez, F.A.; Pijpers, J.J.H.; Cruz-Diaz, M.R.; Rivero, E.P. CFD modeling of residence time distribution and experimental validation in a redox flow battery using free and porous flow. J. Energy Storage
**2020**, 29, 101337. [Google Scholar] [CrossRef] - Martins, N.M.C.; Covas, D.I.C.; Meniconi, S.; Capponi, C.; Brunone, B. Characterisation of low-Reynolds number flow through an orifice: CFD results vs. laboratory data. J. Hydroinform.
**2021**, 23, 709–723. [Google Scholar] [CrossRef] - Martins, N.M.C.; Delgado, J.N.; Ramos, H.M.; Covas, D.I.C. Maximum transient pressures in a rapidly filling pipeline with entrapped air using a CFD model. J. Hydraul. Res.
**2017**, 55, 506–519. [Google Scholar] [CrossRef] - Martins, N.M.C.; Soares, A.K.; Ramos, H.M.; Covas, D.I.C. CFD modeling of transient flow in pressurized pipes. Comput. Fluids
**2016**, 126, 129–140. [Google Scholar] [CrossRef] - Okita, N.; Oyama, Y. Mixing Characteristics in Jet Mixing. Jpn. Chem. Eng.
**1963**, 27, 252–260. [Google Scholar] [CrossRef] [Green Version] - Khan, L.A.; Wicklein, E.A.; Teixeira, E.C. Validation of a Three-Dimensional Computational Fluid Dynamics Model of a Contact Tank. J. Hydraul. Eng.-ASCE
**2006**, 132, 741–746. [Google Scholar] [CrossRef] - Marek, M.; Stoesser, T.; Roberts, P.J.W.; Weitbrecht, V.; Jirka, G.H. CFD Modeling of Turbulent Jet Mixing in a Water Storage Tank. In Proceedings of the Congress-International Association for Hydraulic Research, Venice, Italy, 1–6 July 2007. [Google Scholar]
- Zhang, J.P.; Huck, P.M.; Stubley, G.D.; Anderson, W.B. Application of a multiphase CFD modelling approach to improve ozone residual monitoring and tracer testing strategies for full-scale drinking water ozone disinfection processes. J. Water Supply Res. Technol.
**2008**, 57, 79–92. [Google Scholar] [CrossRef] [Green Version] - Xavier, M.L.M.; Janzen, J.G. Effects of inlet momentum and orientation on the hydraulic performance of water storage tanks. Appl. Water Sci.
**2016**, 7, 2545–2557. [Google Scholar] [CrossRef] [Green Version] - Tian, X.; Roberts, P.J. Mixing in Water Storage Tanks. II: With Buoyancy Effects. J. Environ. Eng.-ASCE
**2008**, 134, 986–995. [Google Scholar] [CrossRef] - Montoya Pachongo, C.; Laín Beatove, S.; Torres Lozada, P.; Cruz-Vélez, C.H.; Escobar Rivera, J.C. Effects of water inlet configuration in a service reservoir applying CFD modelling. Ing. E Investig.
**2016**, 36, 31–40. [Google Scholar] [CrossRef] - Bonetto, F.; Lahey, R.T. An experimental study on air carryunder due to a plunging liquid jet. Int. J. Multiph. Flow
**1993**, 19, 281–294. [Google Scholar] [CrossRef] - Lezzi, A.M.; Prosperetti, A. The stability of an air film in a liquid flow. J. Fluid Mech.
**1991**, 226, 319–347. [Google Scholar] [CrossRef] - Burgess, J.; Molloy, N.; McCarthy, M. A note on the plunging liquid jet reactor. Chem. Eng. Sci.
**1972**, 27, 442–445. [Google Scholar] [CrossRef] - Bonetto, F.; Lahey, R.T.; Drew, D.A. An Experimental Study of Plunging Liquid Jet Induced Air Carryunder and Dispersion; Center for Multyiphase, Rensselaer Polythecnic Institute: Troy, NY, USA, 1993. [Google Scholar]
- Labousse, M.; Bush, J.W.M. The hydraulic bump: The surface signature of a plunging jet. Phys. Fluids
**2013**, 25, 094104. [Google Scholar] [CrossRef] - Sophocleous, M. Understanding and explaining surface tension and capillarity: An introduction to fundamental physics for water professionals. Hydrogeol. J.
**2010**, 18, 811–821. [Google Scholar] [CrossRef] - Lemanov, V.V.; Terekhov, V.I.; Sharov, K.A.; Shumeiko, A.A. An experimental study of submerged jets at low reynolds numbers. Tech. Phys. Lett.
**2013**, 39, 421–423. [Google Scholar] [CrossRef] - Landa, P.S.; McClintock, P.V.E. Development of turbulence in subsonic submerged jets. Phys. Rep.
**2004**, 397, 1–62. [Google Scholar] [CrossRef] - Monteiro, L.; Pinheiro, A.; Carneiro, J.; Covas, D.I.C. Characterization of drinking water storage tanks in Portugal. Ing. Del Agua
**2021**, 25, 49–58. (In Portuguese) [Google Scholar] [CrossRef] - Pinheiro, A.; Monteiro, L.; Carneiro, J.; do Céu Almeida, M.; Covas, D. Water Mixing and Renewal in Circular Cross-Section Storage Tanks as Influenced by Configuration and Operational Conditions. J. Hydraul. Eng.
**2021**, 147, 04021050. [Google Scholar] [CrossRef] - Wüthrich, B. Simulation and Validation of Compressible Flow in Nozzle Geometries and Validation of OpenFOAM for This Application. Master’s Thesis, Swiss Federal Institute of Technology Zurich, Zürich, Switzerland, 2007. [Google Scholar] [CrossRef]
- Holzmann, T. Mathematics Numerics Derivations And OpenFOAM (v7) The Basics for Numerical Simulations; Holzmann CFD: Loeben, Germany, 2019. [Google Scholar] [CrossRef]
- Zalesak, S.T. Fully Multidimensional Flux-Corrected Transport Algorithms for Fluids. J. Comput. Phys.
**1979**, 31, 335–362. [Google Scholar] [CrossRef] - Denton, J.D.; Dawes, W.N. Computational fluid dynamics for turbomachinery design. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci.
**1998**, 213, 107–124. [Google Scholar] [CrossRef] - Menter, F.R.; Kuntz, M.; Langtry, R. Ten years of industrial experience with the SST turbulence model. Turbul. Heat Mass Transf.
**2003**, 4, 625–632. [Google Scholar] - El Halal, Y.; Marques, C.; Rocha, L.; Isoldi, L.; Lemos, R.; Fragassa, C.; dos Santos, E. Numerical Study of Turbulent Air and Water Flows in a Nozzle Based on the Coanda Effect. J. Mar. Sci. Eng.
**2019**, 7, 21. [Google Scholar] [CrossRef] [Green Version] - Giles, B.D. Fluidics, the Coanda Effect, and some orographic winds. Arch. Meteorol. Geophys. Bioklimatol. Ser. A
**1977**, 25, 273–279. [Google Scholar] [CrossRef] - Hegde, M. Fluid Mechanics and the Plateau-Rayleigh Instability; Report; University of California: Burkley, CA, USA, 2013. [Google Scholar]
- Tran, T.; de Maleprade, H.; Sun, C.; Lohse, D. Air entrainment during impact of droplets on liquid surfaces. J. Fluid Mech.
**2013**, 726, R3. [Google Scholar] [CrossRef] [Green Version] - Cervantes-Alvarez, A.M.; Escobar-Ortega, Y.Y.; Sauret, A.; Pacheco-Vazquez, F. Air entrainment and granular bubbles generated by a jet of grains entering water. J. Colloid Interface Sci.
**2020**, 574, 285–292. [Google Scholar] [CrossRef] [PubMed] - Qu, X.L.; Khezzar, L.; Danciu, D.; Labois, M.; Lakehal, D. Characterization of plunging liquid jets: A combined experimental and numerical investigation. Int. J. Multiph. Flow
**2011**, 37, 722–731. [Google Scholar] [CrossRef] - Martin, C.I.; Matioc, B.V. Existence of Wilton Ripples for Water Waves with Constant Vorticity and Capillary Effects. SIAM J. Appl. Math.
**2013**, 73, 1582–1595. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**The plunging liquid jet when it: (

**a**) maintains the cylindrical shape; (

**b**) breaks into droplets.

**Figure 3.**Inlet–outlet configuration–schematics: (

**a**) top view; (

**b**) plunging jet (P); and (

**c**) submerged jet (S).

**Figure 4.**Mesh refinements: (

**a**) top view; (

**b**) nozzle above the water level; (

**c**) nozzle below the water level; and (

**d**) outlet region.

**Figure 6.**Wave propagation at different time steps from the beginning of the flow: (

**a**) ${t}_{1}=$0.50 s; (

**b**) ${t}_{2}=$0.60 s; and (

**c**) ${t}_{3}=$0.70 s.

**Figure 8.**Plunging jet: velocity vectors and contours at 200 s in the horizontal plane at (

**a**) $z=$ 0.25H; (

**b**) $z=$ 0.5H; (

**c**) $z=$ 0.75H; and in the vertical plane at (

**d**) $y=$ 0.5${D}_{T}$.

**Figure 10.**Plunging jet: velocity vectors and contours at 200 s in the horizontal plane at (

**a**) $z=$ 0.25H; (

**b**) $z=$ 0.5H; (

**c**) $z=$ 0.75H; and in the vertical plane at (

**d**) $y=$ 0.5${D}_{T}$.

**Figure 11.**Flow pattern establishment and velocity fields at $z=0.5H$ of the (

**a**) plunging jet and (

**b**) of the submerged jet.

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**MDPI and ACS Style**

Martins, N.M.C.; Covas, D.I.C.
Induced Circulation by Plunging and Submerged Jets in Circular Water Storage Tanks Using CFD. *Water* **2022**, *14*, 1277.
https://doi.org/10.3390/w14081277

**AMA Style**

Martins NMC, Covas DIC.
Induced Circulation by Plunging and Submerged Jets in Circular Water Storage Tanks Using CFD. *Water*. 2022; 14(8):1277.
https://doi.org/10.3390/w14081277

**Chicago/Turabian Style**

Martins, Nuno M. C., and Dídia I. C. Covas.
2022. "Induced Circulation by Plunging and Submerged Jets in Circular Water Storage Tanks Using CFD" *Water* 14, no. 8: 1277.
https://doi.org/10.3390/w14081277