CFD and Experimental Study of 45° Inclined Thermal-Saline Reversible Buoyant Jets in Stationary Ambient

  • Hossein ArdalanEmail author
  • Fereidon Vafaei
Original Article


Inclined submerged jets are mostly employed in the disposal of effluent produced by industrial sites such as desalination and power plants. The optimal design of discharge systems has been a topic of interest in many studies seeking to improve the mixing of effluent and reduce its negative environmental impacts. In addition to salinity, the effluent produced by thermal desalination units, which are usually built near power plants, has a high temperature compared to the marine environment and is mixed with hot power plant effluent, eventually forming thermal-saline effluent. The present study numerically modeled thermal-saline effluent using realizable k − ε turbulence model for a discharge angle of 45° in a uniform, stationary environment. The experimental results were used to calibrate the model results. Generally, the geometrical characteristics obtained from the numerical and physical models were in good consistency, which indicates the ability of the model in predicting the behavior of thermal-saline jets.


Wastewater Desalination Thermal-saline Inclined dense jets OpenFoam 



This research was conducted in the course of the Doctoral Thesis of the first author at the K. N. Toosi University of Technology. Numerical and experimental modeling of the research were carried out at the Water Research Institute. The writers are appreciative of the institute model equipment supports.


B ratio of density difference = \( \frac{\Delta \rho }{\rho_a}\left( Non- dimenssional\right) \)

bv the radius defined by C=0.37Cm (l)

Cm maximum tracer concentration in cross section (psu)

Ccp tracer concentration at centerline peak (psu)

Cr tracer concentration at return point (psu)

C0 tracer concentration at source point (psu)

D port diameter (l)

Frd jet densimetric Froude number =\( u/\sqrt{g^{\prime }D} \) (Nondimenssional)

g acceleration due to gravity (l/t2)

g modified acceleration due to gravity =g(ρ0 − ρa/ρa) (l/t2)

h height of nozzle outlet above bed (l)

kt heat transfer coefficient (l2/t)

kC salinity transfer coefficient (l2/t)

LM jet to plume length scale (l)

Lq discharge length scale (l)

M jet momentum flux (l4/t2)

P Prandtl number (Nondimenssional)

Pt turbulent Prandtl number (Nondimenssional)

Q jet volume flux (l3/t)

R jet Reynolds number =ud/ν (Nondimenssional)

Sch Schmidt number (Nondimenssional)

Scht turbulent Schmidt number (Nondimenssional)

Sm (1 − Ccp/C0)=centerline peak point dilution (Nondimenssional)

Sr (1 − Cr/C0)= return point dilution (Nondimenssional)

T water temperature (θ)

u velocity (l/t)

Xm horizontal distance from jet exit to location of centerline peak (l)

Xt horizontal distance from jet exit to location of terminal rise height (l)

Xr horizontal distance from jet exit to location of return point (l)

Ym final centerline peak height (l)

Yt terminal rise height (refers to upper jet boundary) (l)

Greek Symbols

ρa Ambient density (M/l3)

ρ0 Effluent density (M/l3)

∆ρ Density difference (ρ0 − ρa) (M/l3)

∆C Concentration difference (C0 − Ca) (psu)

φ dense inclined jet geometrical characteristics (l)

θ initial discharge angle (R)

νt turbulent kinematic viscosity (l2/t)

ν kinematic viscosity (l2/t)


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Water Research Institute “WRI”TehranIran
  2. 2.Civil and Environmental Engineering DepartmentK.N. Toosi University of TechnologyTehranIran

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