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Pseudo-volumetric reconstruction of a variable-density turbulent jet and the fine scales


Pseudo-volumetric reconstruction of an air jet using a TR-SPIV dataset and Taylor’s hypothesis. Vortices are visualized using the Q-criterion with a threshold set at a value three times the mean. x1 – jet axial direction. (x2,x3) – in-plane directions at a jet cross-section.

Fluid turbulence is inherently a three-dimensional (3D) phenomenon that comprises spatially-coherent structures. To study turbulence is to understand the mutual interactions among these coherent structures and also on how they are affected by large-scale forcings and boundary conditions imposed on the flow.

In this project, I am interested in the dynamics and kinematics of the fine scales in a variable-density turbulent jet; the jet flow is non-Boussinesq (with an initial Atwood number of 0.6) in which the density field is not passive and modifies the flow. To obtain a 3D dataset of the jet, I use a combination of time-resolved stereoscopic particle image velocimetry (TR-SPIV) and quantitative laser-induced fluorescence (LIF) at a jet cross-section. Using Taylor’s hypothesis, a pseudo-volumetric representation of the jet volume is reconstructed from the time-resolved density and velocity data. An example of this reconstruction is shown in the figure above for the control case of a Boussinesq air jet. The fine scales are tubular vortical structures that are coherent in space.

With the 3D dataset, the following questions concerning the role of large density gradients in driving the turbulence are asked: (1) What flow topologies are dominant? Are they different from constant-density turbulent flows? (2) How is the vortex-stretching mechanism responsible for a forward energy cascade affected?  (3) What improvements are needed in existing turbulence closure models in order to account for such variable-density effects?



Liquid turbulence in bubbly turbulent flows

Liquids laden with positively-buoyant bubbles are commonly found in nature (e.g.  natural gas seeps and multiphase plumes due to subsea oil spills) and in industrial processes (mixing tanks and pneumatic breakwaters). In many cases, the bubbles have diameters of a few millimeters and therefore possess turbulent wakes behind them as they rise in water. The dynamic interaction between the bubble wakes and between the wakes and any preexisting liquid turbulence create a complex turbulent field that is not fully understood and is at odd with the classic, forward-energy-cascade picture of turbulence. It is important to clarify this fundamental issue as many turbulence models are based on the classic picture.

To tackle the problem, I started a collaboration with numerical modelers – Bruno Fraga, Michael Dodd and Ronald Chan – in the 2018 Biannual Summer Research Program hosted by the Center of Turbulence Research at Stanford University. During the program, our team has developed two direct numerical simulation (DNS) codes to study homogeneous bubbly flows in a vertical channel using immersed boundary (IMB) method  and volume-of-fluid (VOF) method. We seek to answer the following three fundamental questions: (1) do bubbly flows have an inertial subrange? (2) what is the origin of the peculiar -3-spectral slope in the velocity spectra reported in physical experiments? and (3) what is the map of interscale energy transfer in bubbly flows?

This is an on-going project with the final goal to develop the next generation turbulence models for the prediction of bubbly flows using under-resolved Reynolds-averaged Navier Stokes (RANS) and large eddy simulation (LES) approaches.



Energy cascade in variable-density jets


Interscale energy transfer in a constant- (air) and variable-density (SF6) turbulent jet.

“Big whirls have little whirls that feed on their velocity, and little whirls have lesser whirls and so on to viscosity.” – Lewis F. Richardson (1922).

The poem by Richardson encapsulates one of the most celebrated idea in the phenomenological modeling of constant-density turbulence – the existence of an inertial subrange where energy cascades down from one turbulent eddy to another in a scale-local manner with a constant energy flux.

The situation is observed to change in a variable-density, non-Boussinesq turbulent SF6 jet where the small turbulent eddies were stretched by the mean flow gradients to become larger and carried with them the energy back to the mean flow (large eddies).  Also, the nonlinear interscale energy cascade (a result connected to the vortex-stretching mechanism)  was strengthened by the variable-density effect.

These conclusions were drawn by generalizing the von Karman-Howarth-Monin (KHM) equation to include variable-density effects, and subsequently applying the equation to an experimental dataset.

Lai, C.C.K., Charonko, J.J. and Prestridge, K. (2018). A Karman-Howarth-Monin equation for variable-density turbulenceJournal of Fluid Mechanics, 843:382-418.


Dilution of brine discharges from seawater desalination in coastal water bodies


Driven by water security, freshwater production by seawater desalination technologies has become popular in coastal cities around the globe. As a by-product of the desalination process,  a concentrated brine solution must be disposed of into nearby coastal water bodies. The discharge often takes the form of negatively-buoyant, high-speed turbulent jets released from a diffuser manifold located on the seafloor. The amount of mixing between these jets and the ambient seawater determines whether regulatory standards on salt concentration and temperature will be met at the end of mixing zone.

A comprehensive Froude-scaling (Fr-) experimental campaign was carried out in a shallow water basin for a range of jet discharge angles, discharge volume fluxes and ambient crossflow conditions.  The focus were three-fold: (1) to determine the optimal range of discharge angles for a given volume flux; (2) to measure dilution in dense jets with 3D-trajectories (a typical configuration in coastal discharges) and (3) to develop a predictive numerical model that can handle the near-far field transition of the discharge.

Choi, K.W., Lai, C.C.K. and Lee, J.H.W. (2015). Mixing in the intermediate field of dense jets in cross currents, Journal of Hydraulic Engineering, ASCE, 142(1).

Lai, C.C.K. and Lee, J.H.W. (2014). Initial mixing of inclined dense jets in perpendicular crossflowEnvironmental Fluid Mechanics, 14(1):25-49.

Lai, C.C.K. and Lee, J.H.W. (2012). Mixing of inclined dense jets in stationary ambient, Journal of Hydro-environment Research, 6(1):9-28.

Liquid turbulence in dilute bubble plumes


(Left) a schematic sketch of a dilute bubble plume and (right) the liquid turbulent kinetic energy budget equation for dilute bubble plumes.

When air bubbles are added into water, they induce motions in the surrounding water via the transfer of their potential energy to the liquid.  In many scenarios, the induced motions create a large vertical movement of water masses and thus mixing in the water column; some examples are subsea oil well blowouts, lake reaeration  projects and natural gas seeps in deep ocean. To control and predict such mixing, it is important to understand and quantify the energy conversion process. By measuring the liquid velocities of a dilute bubble plume formed inside a unstratified, stagnant water tank, the following were found: (1) the turbulent kinetic energy (t.k.e.) production P_B by the bubbles is much larger than that by liquid mean shear; (2) an increasing fraction of the available work done by bubbles is deposited into liquid turbulence as one moves away from the plume centerline and (3) the induced liquid velocity fluctuations in this heterogeneous bubbly flow have very similar characteristics to those of homogeneous bubbly swarms rising with and without a background liquid turbulence, and therefore the fluctuations can possibly be modeled by a universal form.

Lai, C.C.K. and Socolofsky, S.A. (2018). The turbulent kinetic energy budget in a bubble plume (accepted), Journal of Fluid Mechanics. 

Fraga, B., Stoesser, T., Lai, C.C.K. and Socolofsky, S.A. (2016). A LES-based Eulerian-Lagrangian approach to predict the dynamics of bubble plumesOcean Modeling, 97:27-36.

Physics of jet turbulence and its RANS modeling

The turbulent jet discharged into a quiescent environment is a canonical turbulent flow that has abundant engineering applications. For industrial process design, the Reynolds-averaged Navier-Stokes (RANS) approach is often used because of its low computation costs and quick turnover time when compared to large-eddy simulations (LES). The faithfulness to jet physics of the turbulence closure model employed in a RANS simulation thus determines the quality of the simulation. Using the data from a time-resolved, stereoscopic particle image velocimetry (SPIV) experiment, the budgets of the turbulent kinetic energy and the turbulent dissipation rate were computed for a jet, and the model coefficients appearing in the standard k-epsilon turbulence closure model were evaluated.  An optimized set of coefficients is proposed for use in jet simulation. Further, the more sophisticated realisable k-epsilon model was found to be incompatible with the experimentally-observed constant eddy viscosity in the jet core; the model will have to use a spatially-varying turbulent Schmidt/Prandtl number to compensate for its predicted non-constant eddy viscosity.

Lai, C.C.K. and Socolofsky, S.A. (2018). Budgets of turbulent kinetic energy, Reynolds stresses and dissipation in a turbulent round jet discharged into a stagnant ambient, Environmental Fluid Mechanics,