Session AM: Turbulent Mixing I

Simultaneous planar measurements of multiple mole fractions in a gas phase turbulent jet with differential diffusion

Previous work has demonstrated the usefulness of planar Rayleigh scattering to the study of gas-phase differential diffusion. These Rayleigh scattering measurements typically yield the differential diffusion parameter z, a measure of the normalized difference between two scalars. However, this method cannot provide information about all individual mole fractions in a three-species flow. In this work, we present results from a planar imaging experiment that combines Rayleigh scattering and PLIF to yield the instantaneous mole fractions of all relevant species in a differentially diffusing turbulent flow. In a premixed jet of acetone and helium with an air coflow, PLIF measures the absolute acetone mole fraction while Rayleigh scattering measures the differential diffusion parameter. From these measurements, the mole fractions of helium and air can then be calculated. With this data, we explore the relationship between differential diffusion and the mole fractions of individual species. We are also interested in the influence of differential diffusion on the large-scale organization of the jet, and the effects of Reynolds number on the observed mixing structures.   

Turbulent CO$_2$ Transport at an Unsheared Free Surface by Coupled Quantitative Imaging Techniques

We present laboratory measurements of simultaneous velocity and concentration fields for the transfer of CO$_2$ across a free surface. The interface is subject to turbulence generated far beneath the surface by an array of randomly firing synthetic jets. This results in turbulence with a high Reynolds number, low mean flow and extensive horizontal homogeneity. Particle image velocimetry and a pH-sensitive laser induced fluorescence allow the measurement of both velocity and scalar fields at a resolution of $\sim 10$ times the Kolmogorov and Batchelor microscales, respectively. From these data, we calculate the spatiotemporal scalar flux in a plane tangent to and intersecting the free surface. We discuss these measurements, from both a coherent structure and statistical viewpoint, to elucidate the fundamental physics of turbulent scalar transport at a free surface in the absence of mean shear. Quadrant analysis shows a large asymmetry in the transport process, and mass flux spectra show the relative importance of a wide range of lengthscales.   

Mixing characteristics in the near-field of a swirling jet

Swirl is known to increase the spreading of turbulent jets. The purpose of the present work is to investigate the effect of rotation on the mixing characteristics of a passive scalar in the near-field of a turbulent swirling jet. Contrary to previous experiments, which leave traces of the swirl generating method especially in the near-field, the swirl was imparted by discharging a slightly heated air flow from an axially rotating and thermally insulated pipe (6 m long, diameter 60 mm). This gives well-defined axi-symmetric streamwise and azimuthal velocity distributions as well as a well-defined temperature profile. By means of a specially designed combined X-wire and cold-wire probe it was possible to simultaneously acquire the instantaneous axial and azimuthal velocity components as well as the temperature and hence their joint statistics. The comparison of the experiments performed at a Reynolds number of 24000 and a swirl number (ratio between the angular velocity of the pipe wall and the bulk velocity in the pipe) of 0.5 with those for the non-swirling jet clearly shows that the addition of swirl to the jet increases the spreading and radial heat transport. It is also shown that the streamwise velocity and temperature fluctuations are highly correlated.   

Experimental study of turbulence in a counter-rotating swirling flow

Numerous experimental studies of turbulence have been carried out in a variant of the Von K\'{a}rm\'{a}n swirling flow: flow between two counter-rotating discs or impellers in a closed vessel. Turbulence of very high Reynolds number can be achieved, with a flow in the central region that has zero mean velocity in time. However, there is limited coverage in the literature of isotropy, interaction between modes of flow, and low-frequency fluctuations in this flow. This work presents the results of an experimental study of such a flow, using bladed impellers and several configurations, with an $\mbox{R}_{\lambda}$ of approximately 500. High-speed Particle Imaging Velocimetry was used to measure the velocity of microspheres mixed in the flow. The bulk motion of the flow was studied, revealing pumping and bulk rotation in the fluid, and the velocity correlation function of the velocity fluctuations was calculated, showing anisotropic turbulence with an integral length scale significantly smaller than the vessel radius, and largely independent of Reynolds number. The frequency content of velocity fluctuations was studied.   

Eulerian and Lagrangian velocity statistics in compressible turbulence on a free surface

The statistics of velocity differences are analyzed for compressible turbulence on a free surface in both Eulerian and Lagrangian frames. Despite non-applicability of Kolmogorov 1941 theory (K41), prior measurements (J. Cressman et. al., New J. Phys., 6, 2004), have shown Kolmogorov scaling for Eulerian structure functions ($S_n(r) = \langle (\delta v_{||}(r))^n \rangle \sim r^{n/3}$). Here we measure the Eulerian third-order ($S_3(r)$) and Lagrangian second-order ($D_2(\tau)$) structure functions. The Eulerian third-moment is suprisingly consistent with K41 ($S_3(r) = -\frac{4}{5}\overline \varepsilon r)$). K41 predicts the lagrangian second-moment should scale linearly with time ($D_2(\tau) = C_0 \overline\varepsilon \tau$) in the inertial time-scales, however this scaling is not observed. Instead, the Lagrangian second-moment scales as $D_2(\tau) \sim \tau^{1/2}$. Absence of a suitable theory makes it difficult to explain the experimental observations.   

Anisotropy of the scalar field downstream of a concentrated source in turbulent channel flow

The scalar field downstream of a concentrated line source in fully-developed, high-aspect-ratio turbulent channel flow is studied\footnote{R.A. Lavertu and L. Mydlarski, 2005. {\it J. Fluid Mech.}, {\bf 528}, p. 135.}. Such a flow was selected to isolate the role of the inhomogeneity, which is confined to only one direction (i.e., the wall-normal direction). The scalar under consideration is temperature and is measured by means of cold-wire thermometry. Small-scale statistics of the scalar field, with an emphasis on the scalar dissipation rate ($\langle\varepsilon_\theta\rangle$), are studied. The anisotropy of the different components of $\langle\varepsilon_\theta\rangle$ will be presented, as well as their downstream return to isotropy. A comparison with the experiments of Rosset et al.\footnote{L. Rosset, P. Parantho$\ddot{e}$n, J.-C. Lecordier, and M. Gonzalez, 2001. {\it Phys. Fluids}, {\bf 13}, p. 3729.} indicates that the anisotropy $\langle\varepsilon_{\theta_y}\rangle / \langle\varepsilon_{\theta_x}\rangle$ downstream of a centreline source in channel flow is smaller that observed in turbulent plane jets.   

Conditional statistics for passive-scalar mixing in confined turbulent shear flows

The conditional moment closure is one of the fundamental closure models used for turbulent flows. Although there is a large body of literature on turbulent shear flows, conditional statistics of experimental data are scarce, despite their necessity for understanding turbulent flows and validating numerical models. In the present work, a combined particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) system was employed to investigate turbulent mixing in a confined liquid-phase plane-wake flow and in a confined liquid-phase rectangular-jet flow. The Reynolds number based on bulk velocity and hydraulic diameter was 37,500 for the wake flow and 50,000 for the jet flow. The Schmidt number for the passive scalar was approximately 1,250. Velocity components conditioned on the scalar for both the wake and jet flows were evaluated. It was noticed that the $\beta $-PDF predicted the experimental data very well for all observed locations. Since the joint velocity-scalar PDF was not jointly Gaussian in these flows, the conditional mean velocity was found to agree with a linear model only when the mixture fraction is close to the local mean mixture fraction. The gradient PDF model was also tested against the experimental data. The model predicted the cross-stream conditional velocity very well, but gave poor predictions for the streamwise conditional velocity. Finally, the scalar fluctuations conditioned on velocity are analyzed using existing models.   

Turbulent Mixing of Unstably Stratified Fluids in a Vertical Tube

Quantitative time dependent measurements of irreversible mixing caused by the development of the Raleigh-Taylor instability (RTI) on an initially unstable two-layer stratification of miscible fluids are taken from a series of laboratory experiments. The experiments are carried out in high-aspect ratio tanks of both square and circular cross-section, and are observed until the flow becomes quiescent. The effects of vertical wall roughness, Atwood number and rotation on the evolution of the time-dependent flow is investigated using a light attenuation technique in conjunction with the available potential energy framework. We obtain detailed time-dependent measures of the irreversible mixing, and its efficiency during flow evolution. We find that the flow passes through four distinct phases which have distinct mixing characteristics. During the turbulent phase of the flow the turbulent mixing is highly efficient, with almost precisely half the potential energy lost from the flow leading to irreversible mixing, with the other half being lost to dissipation.   

Mixing and dispersion in stably stratified sheared turbulence

Direct numerical simulations are performed to study turbulent dispersion in stably stratified homogeneous shear flow. Lagrangian statistics are obtained for subcritical, critical, and supercritical flow conditions. In particular, we examine the density perturbation following fluid particles which has two components: that due to vertical advection in the stratified fluid (isopycnal displacement) and that due to the change in particle density by molecular diffusion (diapycnal mixing). For subcritical and critical flows, the isopycnal displacement increases while diapycnal mixing counterbalances this at a rate which limits the density perturbation carried. In subcritical flow, the buoyancy flux is described by the dispersion coefficient. For supercritical flows, stratification strongly suppresses the isopycnal displacement. The particle density relaxes to the background mean value through diapycnal mixing as the particle settles into its new equilibrium height. In these flows, the correlation between vertical velocity and mixing is no longer negligible. Implications on dispersion modeling for stratified turbulence is considered.   

Effects of buoyancy on flow evolution in momentum-driven turbulent jets

Local buoyancy effects are potentially significant in systems such as reacting flows with heat release, or atmospheric flows with natural convection, and can pose challenges for modeling efforts that do not explicitly represent small flow scales. The present experiments aim to isolate the effects of local buoyancy variations on turbulent jet mixing in flow regimes where the global flow scaling is momentum driven. Jet Reynolds numbers range up to 2500. Prior results from scalar field measurements indicate that the mixing is noticeably affected on the jet boundary relative to non-buoyant flows. Here, scalar and velocity field measurements allow us to investigate the mechanism by which these small-scale buoyancy fluctuations affect, for example, turbulent intensities in the scalar and velocity fields, or the relationship between turbulent velocity fluctuations and mean scalar field profiles. Also interesting is the effect of buoyancy on instability modes in the jet evolution. The measurements have sufficient spatial resolution and dynamic range to provide information on the manifestation of buoyancy effects at different flow scales, with direct implications for simulations of flows with buoyancy.   

Stretching Statistics in the Transition to Nonperiodic Flow

We experimentally study the mixing properties of fluid flow exhibiting chaotic advection. The system we use is a two dimensional fluid layer above a spatially random magnet array electromagnetically driven by a time periodic current. As the amplitude of the forcing is increased, the flow shows a transition from periodic to nonperiodic behavior. Using particle tracking velocimetry, we obtain time resolved velocity fields with high spatial resolution. These fields are used to reconstruct the Lagrangian trajectories, i.e. flow map, over time intervals less than the forcing period. Using the flow map, stretching fields (Voth et. al. PRL 88 254501) and spatially local Lyaponov exponents are determined. Statisitcal properties of the stretching are used to characterize the mixing properties of the system. The mixing properties as a function of Reynold's number are used to highlight the transition from periodic to turbulent flow.   

Flow NMR in complex systems

The combination of NMR imaging for spatial resolution with pulsed-field gradient (PFG) NMR for the measurement of displacements is an ideal tool for the investigation of flow in complex systems. The non-invasive nature of the NMR experiment permits the investigation of flow in arbitrary geometry. For each pixel the velocity is determined by direction and magnitude. Other NMR parameters like relaxation times and chemical shift are applied to generate contrast, when in the experiment only one component of a complex system is excited. Thus both the spatial distribution and the velocity map for each component are measured separately. Applications show flow in a Couette cell, a modified Couette generating high local shear and flow in a pipe varying the cross section. Due to the differences in viscosity the global external shear field results in different flow pattern, resulting in a bent interface at the onset of shear induced mixing. A 3D surface representation shows the spatial distribution of the components.