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Overview of Outfall Discharge Modeling with a Focus on Turbulence Modeling Approaches

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Advances in Fluid Mechanics

Part of the book series: Forum for Interdisciplinary Mathematics ((FFIM))

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Abstract

A better understanding of flow discharge behavior can aid in the optimum design of outfall systems while adhering to regulatory demands. Improvements in computational resources and techniques over the last two decades have allowed numerical modelling to be introduced as a promising approach for outfall discharge modeling and the extraction of data for the entire field of outfall regions. Thus, the application of numerical methods to jet and plume-type flows requires further attention. Among the available numerical techniques, computational fluid dynamics (CFD) method can provide more detailed information on the flow fields of outfall discharge systems without considering some of the simplified assumptions of length-scale and jet integral approaches. This chapter aims to present an overview on the current state-of-the-art in outfall discharge modeling and a summary of the research efforts conducted in this field. Different aspects related to the turbulence modeling approaches in CFD technique are also discussed, demonstrating the applicability of both Reynolds-averaged Navier–Stokes (RANS) and large eddy simulation (LES) in outfall discharge modeling. Finally, the knowledge gaps and future research needs are highlighted, which provide a more realistic view on the capabilities of the available techniques for the outfall engineering design.

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Abbreviations

AI:

Artificial Intelligence

AIZ:

Allocated Impact Zone

CFD:

Computational Fluid Dynamics

DES:

Detached Eddy Simulation

DNS:

Direct Numerical Simulation

EPA:

Environmental Protection Agency

FDM:

Finite Difference Method

FVM:

Finite Volume Method

GGDH:

General Gradient Diffusion Hypothesis

LES:

Large Eddy Simulation

LMZ:

Legal Mixing Zone

LRR:

Launder-Reece-Rodi

MGGP:

Multigene Genetic Programming

NPDES:

National Pollutant Discharge Elimination System

ODE:

Ordinary Differential Equation

OpenFOAM:

OPEN Field Operation And Manipulation

PDE:

Partial Differential Equations

RANS:

Reynolds-Averaged Navier–Stokes

RNG:

Re-Normalization Group

RSM:

Reynolds Stress Model

SGDH:

Standard Gradient Diffusion Hypothesis

SGGP:

Single-Gene Genetic Programming

SGS:

Sub-Grid Scale

SPH:

Smoothed Particle Hydrodynamics

SST:

Shear Stress Transport

WFD:

Water Framework Directive

ZID:

Zone of Initial Dilution

a, b, and c:

Empirical parameters in Millero and Poisson equation

B 0 :

Discharge buoyancy flux

b 0 :

Discharge buoyancy flux per unit length

C :

Fluid concentration

C 0 :

Initial jet fluid concentration

C a :

Ambient fluid concentration

\({c}_{1}\) to \({c}_{11}\):

Constants in dimensional analysis

\({D}\) :

Diffusion coefficient

\({D}_{ij}\) :

Transport term by diffusion

d 0 :

Jet nozzle diameter

F 0 :

Jet-densimetric Froude number

\(g\) :

Acceleration due to gravity

\({g}^{^{\prime}}\) :

Modified acceleration due to gravity

\({g}_{0}^{^{\prime}}\) :

Initial modified acceleration due to gravity

H a :

Ambient flow depth

h 0 :

Port height

\(k\) :

Turbulent kinetic energy per mass

\({k}_{eff}\) :

Heat transfer coefficient

L :

Diffuser length

l M :

Jet-to-plume Length Scale

\({L}_{p}\) :

Port-spacing

l Q :

Discharge Length Scale

M 0 :

Discharge momentum flux

m 0 :

Discharge momentum flux per unit length

p :

Fluid pressure

\(p\mathrm{^{\prime}}\) :

Fluctuating component of pressure

\(\overline{p }\) :

Mean/filtered component of pressure

\({P}_{ij}\) :

Production rate of \({R}_{ij}\)

Pr :

Prandtl number

Pr t :

Turbulent Prandtl number

\({Q}_{0}\) :

Discharge volume flux

q 0 :

Discharge volume flux per unit length

\({R}_{ij}\) :

Reynolds stress

\(Re\) :

Reynolds numbers

\({Re}_{0}\) :

Jet Reynolds Number

S :

Salinity

S 0 :

Jet discharge dilution

S c :

Centerline peak dilution

S i :

Impact dilution

S n :

Ultimate dilution

S t :

Terminal peak dilution

T :

Temperature

\({T}_{0}\) :

Jet discharge temperature

\({T}_{a}\) :

Ambient fluid temperature

\(t\) :

Time

\({U}_{0}\) :

Jet discharge velocity

\({U}_{a}\) :

Ambient flow velocity

\(u\mathrm{^{\prime}}\) :

Fluctuating component of velocity

\(\overline{u }\) :

Mean/filtered component of velocity

\(u\), \(v\), and \(w\):

Mean velocity in the x, y, and z directions

x c :

Horizontal distance to jet terminal rise height

x i :

Horizontal distance to jet impact point

x n :

Horizontal distance to near-field location

y c :

Maximum centerline height

\({y}_{l}\) :

Thickness of the spreading layer

\({y}_{t}\) :

Maximum terminal rise height

\(\Delta\) :

Filter size

\(\Delta x\), \(\Delta y\), and \(\Delta z\):

Grid cell sizes in \(x\), \(y\), and \(z\) directions

\(\Delta\uprho\) :

Density difference between the jet flow and the ambient fluid

\({\delta }_{ij}\) :

Kronecker delta

\({\varepsilon }_{ij}\) :

Dissipation rate of \({R}_{ij}\)

\({\theta }_{0}\) :

Jet discharge angle relative to the horizontal

\(\mu\) :

Dynamic viscosity of the fluid

\({\mu }_{t}\) :

Eddy viscosity

\(\upnu\) :

kinematic viscosity

\({\upnu }_{eff}\) :

Effective kinematic viscosity

\({\upnu }_{t}\) :

Turbulent kinematic viscosity

\({\Pi }_{ij}\) :

Transport term by turbulent pressure-strain interactions

\({\rho }_{0}\) :

Jet discharge density

\({\rho }_{a}\) :

Ambient flow density

\({\rho }_{t}\) :

Density of water changing with the temperature in Millero and Poisson empirical equation

\({\tau }_{ij}\) :

Sub-grid scale stresses

\(\mathrm{\varnothing }\left(t\right)\) :

Instantaneous variable

\({\mathrm{\varnothing }}^{^{\prime}}\) :

Fluctuating component of an instantaneous variable

\(\overline{\mathrm{\varnothing } }\) :

Mean component of an instantaneous variable

\({\Omega }_{ij}\) :

Transport term by rotation

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Authors and Affiliations

  1. Department of Civil Engineering, University of Ottawa, 75 Laurier Ave E, Ottawa, ON, K1N 6N5, Canada

    Mostafa Taherian, Seyed Ahmad Reza Saeidi Hosseini & Abdolmajid Mohammadian

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  1. Mostafa Taherian
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  2. Seyed Ahmad Reza Saeidi Hosseini
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  3. Abdolmajid Mohammadian
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Correspondence to Mostafa Taherian .

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Editors and Affiliations

  1. School of Basic Sciences and Humanities, German Jordanian University, Amman, Jordan

    Dia Zeidan

  2. Department of Mechanical, Aerospace & Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY, USA

    Lucy T. Zhang

  3. ISAE-ENSMA, Institut Pprime, Chasseneuil-du-Poitou, France

    Eric Goncalves Da Silva

  4. MNZ, Leipzig University of Applied Sciences, Leipzig, Germany

    Jochen Merker

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Taherian, M., Saeidi Hosseini, S.A.R., Mohammadian, A. (2022). Overview of Outfall Discharge Modeling with a Focus on Turbulence Modeling Approaches. In: Zeidan, D., Zhang, L.T., Da Silva, E.G., Merker, J. (eds) Advances in Fluid Mechanics. Forum for Interdisciplinary Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-19-1438-6_4

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