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Turbulent structures of buoyant jet in cross-flow studied through large-eddy simulation

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Abstract

In the present paper we study buoyant (plume) and non-buoyant (jet) fluid injection in a neutrally stratified uniform cross-flow. Both cases are of practical importance in environmental fluid mechanics. The study is carried out numerically, using highly resolved large-eddy simulation in conjunction with the Lagrangian dynamic sub-grid scale model for both momentum and scalar transport equations. The velocity ratio is \(\kappa =8\). In the plume case, the Froude number is \(F=10\), such to allow the use of the Boussinesq approximation. The simulations are successfully validated against experimental data and well established semi-empirical relations. The study shows the existence of three different regions as regards the plume evolution, each of them characterised by different peculiarities: in momentum-buoyancy region the plume exhibits an almost steady cylindrical shape with relative small turbulence structures; in deflection region the plume is deviated horizontally and a high shear rate is detected; in entrainment region the vortex pair develops, along with the sausage-like turbulent structure. The comparison between the plume and the jet case shows that the latter has a higher eccentricity while its trajectory height is sensibly lower. Also, the sausage-like structures are not present. Finally, an empirical formula for the jet trajectory is given, although its full validation will require additional studies.

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Abbreviations

\({\textsc {s}}_{ik}\) :

Fluctuation strain rate tensor

\(B_{j0}\) :

Initial buoyancy flux

\(c_s\) :

Smagorinsky constant for momentum

D :

Diameter of cylindrical nozzle

\(E_{\psi \psi }\) :

Time power spectra of \(\psi \)

g :

Gravity acceleration magnitude

\(k_n\) :

Mass coefficient

p :

Dynamic pressure

Q :

Second invariant of velocity gradient tensor

\(Q_{j0}\) :

Initial volume flux

\(s_j\) :

Plume active scalar (salinity)

\(S_{ik}\) :

Strain rate tensor

u :

Velocity magnitude

\(z^*\) :

Height where entrainment starts

\(z_B\) :

Height of buoyancy influence

\(z_M\) :

Height of momentum influence

\(\alpha _s\) :

Molecular salinity diffusivity

\(\beta \) :

Calibration parameter

\(\beta _s\) :

Volumetric contraction coefficient of salinity

\(\varDelta \) :

Filter/grid width

\(\delta _{ik}\) :

Kronecker delta

\(\epsilon \) :

Dissipation rate of TKE

\(\eta \) :

Kolmogorov length scale

\(\nu \) :

Molecular kinematic viscosity

\(\rho \) :

Space-time variable density

\(\tau _{ik}\) :

SGS stress tensor

\(\kappa \) :

Velocity ratio

\(\textit{F}\) :

Froude number

\(\textit{Re}\) :

Reynolds number

\(\textit{Sc}\) :

Schmidt number

\(\langle \psi \rangle \) :

Time averaged quantity

\(\overline{\psi }\) :

Grid space filter

\(\psi \) :

Generic variable

\(\psi '\) :

Variation from mean value

\(\psi _{0}\) :

Reference value

\(\psi _{{\textsc {sgs}}}\) :

Sub-grid scale quantity

\(\psi _{cf}\) :

Uniform cross-flow value

\(\psi _{j0}\) :

Initial plume value

\(\psi _{j}\) :

Plume related quantity

\(\widehat{\psi } \) :

Test space filter

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Acknowledgements

This work was supported by Regione Friuli-Venezia Giulia - DITENAVE - Progetto “CFD open source per opera morta - COSMO” n. CUP J94C14000090006.

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Authors and Affiliations

  1. IEFLUIDS S.r.l., Piazzale Europa 1, 34127, Trieste, Italy

    Carlo Cintolesi & Andrea Petronio

  2. Department of Engineering and Architecture, University of Trieste, via A. Valerio 10, 34127, Trieste, Italy

    Vincenzo Armenio

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  1. Carlo Cintolesi
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Correspondence to Carlo Cintolesi.

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Cintolesi, C., Petronio, A. & Armenio, V. Turbulent structures of buoyant jet in cross-flow studied through large-eddy simulation. Environ Fluid Mech 19, 401–433 (2019). https://doi.org/10.1007/s10652-018-9629-1

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