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Effects of turbulent Schmidt number on CFD simulation of \(45^\circ \) inclined negatively buoyant jets

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Abstract

Employing inclined negatively buoyant jets is one of the most advantageous means to discharge brine or waste in coastal environments. However, numerical prediction of mixing parameters for this kind of flow is still a challenge. In this investigation, CFD simulations of \(45^\circ \) inclined dense jets were conducted using realizable k–\(\epsilon \) model with buoyancy corrections and different values of turbulent Schmidt number (\(Sc_t\)) within two approaches in a finite volume model (Open FOAM). In the first approach, seven scenarios with different values of \(Sc_t\) were simulated. In the second one, a Regional Turbulent Schmidt Number (RTSN) configuration was introduced based on different behaviors of the flow in jet-like, plume-like, and inner/outer regions. Regarding the first approach, results showed that changing the turbulent Schmidt number has significant consequences for mixing and geometrical parameters. Reducing \(Sc_t\) from 1.0 to 0.4 led to more than \(\sim 60\%\) and \(\sim 40\%\) improvements in dilution ratio at return point and centerline peak, respectively. Using RTSN approach successfully improved the mixing parameters along with keeping nearly unchanged the accuracy of geometrical parameters. That was the case, specifically at return point in comparison with using any other constant \(Sc_t\) for the whole domain (first approach). This local (regional) change in turbulent Schmidt number compensates for flaws of Boussinesq approximation in the linear two-equation turbulence modeling of inclined negatively buoyant jets. Comparing to the previous LES results, the RTSN approach combined with the realizable k–\(\epsilon \) model stands as an economically superior solution employing much lower grid numbers.

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Notes

  1. The open source CFD toolbox https://www.openfoam.com.

  2. Launder, Reece, and Rodi.

Abbreviations

\(b_c\) :

Charachteristic radial distance

C :

Concentration/salinity

\(C_0\) :

Initial concentration at nozzle

\(C_m\) :

Maximum local concentration

\(C_{1\epsilon }\),\(C_{2\epsilon }\),\(C_{3\epsilon }\) :

Constant

D :

Diameter

\(D_t\) :

Turbulent diffusion rate

\(Fr_d, Fr\) :

Densimetric Froude number

G :

Production due to buoyancy

g :

Acceleration due to gravity

\(H_0\) :

Nozzle tap height

k :

Turbulent kinetic energy

\(l_m\) :

Momentum length scale

M :

Initial momentum flux

P :

Pressure/production due to shear

\(Pr_t\) :

Turbulent Prandtl number

Q :

Initial volume flux

\(R_e\) :

Reynolds number

\(R_f\) :

Flux Richardson number

S :

Salinity/concentration/dilution ratio

\(Sc_t\) :

Turbulent Schmidt number

\(S_m\) :

Dilution ratio at centerline peak

\(S_r\) :

Dilution ratio at return point

\(S_\varPhi \) :

Source term

s :

Streamwise distance

T :

Temperature

\(U_0\) :

Initial velocity at nozzle

\(\overline{u'_i u'_j}\) :

Reynolds stress tensor

\(\overline{u'_i\phi '}\) :

Turbulent scalar flux

\(X_m\) :

Horizontal distance of centerline peak from nozzle level

\(X_r\) :

Horizontal distance of return point from nozzle level

\(Y_m\) :

Vertical distance of centerline peak from nozzle level

\(Y_t\) :

Vertical distance of terminal rise height location from nozzle level

\(\beta \) :

Thermal/saline expansion/contraction coefficient

\(\varGamma _{total}\) :

Total diffusion rate

\(\varDelta \rho \) :

Density difference

\(\delta _{ij}\) :

Kronecker delta

\(\zeta _{ij}\) :

Stress tensor

\(\epsilon \) :

Dissipation rate of turbulent kinetic energy

\(\theta _0\) :

Nozzle angle to horizontal

\(\nu \) :

Kinematic viscosity

\(\nu _t\) :

Eddy viscosity

\(\rho _a\) :

Ambient density

\(\rho _r\) :

Reference fluid density

\(\rho _0\) :

Initial density/jet density at nozzle

\(\sigma _t\) :

Schmidt/Prandtle number

\(\varPhi \) :

Scalar

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Authors and Affiliations

  1. Faculty of Civil Engineering, K.N. Toosi University of Technology, P. O. Box 15876-4416, Tehran, Iran

    Sina Tahmooresi & Davoud Ahmadyar

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  1. Sina Tahmooresi
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  2. Davoud Ahmadyar
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Correspondence to Sina Tahmooresi.

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Tahmooresi, S., Ahmadyar, D. Effects of turbulent Schmidt number on CFD simulation of \(45^\circ \) inclined negatively buoyant jets. Environ Fluid Mech 21, 39–62 (2021). https://doi.org/10.1007/s10652-020-09762-6

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  • DOI: https://doi.org/10.1007/s10652-020-09762-6

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