10:30
Transport and mixing 2
Chair: Nicholas Ouellette
10:30
15 mins
|
Stratified external mixing at moderate Richardson number.
Jason Olsthoorn, Stuart B. Dalziel
Abstract:
\begin{summary}
Stratified turbulent mixing remains an unsolved problem. Turbulent mixing is complicated
by its intermittent nature, its highly vortical motion and the large range of scales of its
coherent structures. In order to help reduce the problem to a more tractable form, we
consider vortex rings as a reproducible, idealized form of a turbulent coherent structure of a defined length and
velocity scale.
We generate vortex rings in a stably stratified two-layer fluid of varying Richardson
number and observe the vortex ring induced mixing. While previous work has looked at the effect of individual vortex
rings on the stratified interface, we analyze the aggregate mixing induced over many vortex
ring generations. Over successive vortex rings collisions, the mixing rate converges
to a constant for a range of Richardson numbers.
\end{summary}
\section{Experiments}
The current experiments were performed within a 0.2m x 0.4m x 0.5m tank. This tank was filled with a two-layer salt-water stratification with a sharp density interface. A fresh-water layer was generated above a layer of salt water, the density of which was varied between experiments. A 3.9cm hollow cylinder is then inserted into the fluid and attached to a linearly-actuated cycle pump. The working of the pump generated vortex rings at the base of the cylinder which propagated downward, impacting the density interface vertically. Figure \ref{setup} is a picture of the experimental setup near the completion of a run.
Particle Image velocimetry (PIV) was used to quantify the velocity field of each vortex ring along a two-dimensional vertical slice of the water tank. Data was collected through the centre of the vortex rings. PIV provides us with the vortex ring diameter, the propagation speed of the vortex ring, and an estimate for the total kinetic energy contained in the vortex ring. The formation number of these vortex rings was such that only a single, clear vortex ring was observed.
Similarly, we use a conductivity probe to analyze the density profile of the flow over the course of many vortex ring interactions. A single vortex ring was generated every 75s in order to allow for the macroscopic motion associated with each ring to dissipate before a new ring was generated. Every ten such vortex ring generations, the conductivity probe measured a single density profile. The sensitivity to the intergenerational time was established by varying the temporal inter-vortex ring spacing to ensure that the residual motion within the tank was negligible. The conductivity probe moved at a rate of $\sim$0.5cm/s with a density measurement acquisition rate of 50Hz. For each experiment, 61 density traverses were taken over a total of 600 vortex ring generations.
\section{Results}
In order to estimate the energy injection into the system, we approximate the vortex rings as spherical vortices with all of their energy in translational motion (not a Hills vortex). That is, the kinetic energy (KE) is given as
\[ \hbox{KE} = \alpha \left[ \frac 12 \rho_0 U^2 \right] \left[ \frac{4}{3} \pi \left(\frac{a}{2}\right)^3 \right]. \]
This kinetic energy approximation provides an order of magnitude estimate of the kinetic energy of a single vortex ring injected into the stratification. Figure \ref{MixVsRi} plots the normalized mixing rate after an initial adjustment period versus the transition Richardson number (Ri$_T$). We see clearly that the scaled mixing rate is constant over a range of vortex ring parameters and Ri.
|
10:45
15 mins
|
Assessment of Models for Near Wall Behavior and Swirling Flows in Nuclear Reactor Sub-system Simulations
Thomas M. Smith, Mark A. Christon, Emilio Baglietto, Hong Luo
Abstract: Accurate simulation of turbulence remains one of the most challenging problems in nuclear reactor analysis and design. Due to limitations in computing resources, Reynolds averaged Navier Stokes models (RANS) continue to play an important role in reactor simulations. The Consortium for advanced simulations of light water reactors (CASL) is a Department of Energy technology hub that is investing in research and developmentof a state-of-the-art computational fluid dynamics capabilityto meet the challenges of turbulent simulation of nuclear reactors. In this presentation, we assess several RANS eddy viscosity models appropriate for single-phase incompressible turbulent flows. Specifically, we compare the single equation Splalart-Allmaras to several variations of the $k-\varepsilon$ model. The assessment takes into consideration elements of full system reactor cores such as complex geometries, heterogeneous meshes, swirling flow, near wall flow behavior, heat transfer and robustness issues. The goal of this strategically
oriented assessment is to provide an accurate and robust turbulent simulation capability for the CASL community. Metrics of performance will be constructed by comparing different models on a strategically chosen set of problems that represent reactor core sub-systems.
|
11:00
15 mins
|
Inertial particles do not always concentrate on a wall in turbulence
Gregory Falkovich
Abstract: Small aerosols drift down temperature or turbulence gradient since faster particles fly longer distances before equilibration. That fundamental phenomenon, called thermophoresis or turbophoresis, is widely encountered in nature and used in industry. It is universally believed that particles moving down the kinetic energy gradient must concentrate in minima (say, on walls in turbulence). Here we show that this is incorrect: escaping minima is possible for inertial particles whose time of equilibration is longer than the time to reach the minimum. The best way out is always through: particles escape by flying through minima or reflecting from walls. We solve the problem analytically and find the phase transition as a sign change of the mean velocity. That means separation: light particles concentrate in a minimum while heavy particles spread away from it (gravity can reverse the effect). We also solved analytically the problem for inelastic collisions and derive the phase diagram for the transition in the inertia-inelasticity plane. We also present direct numerical simulations which support the theory and in addition reveal the dependence of the transition of the flow correlation time, characterized by the Stokes number. That discovery changes understanding of that fundamental phenomenon and may find numerous applications.
|
11:15
15 mins
|
Turbulence-generated vortices in fluid layers
Gregory Falkovich
Abstract: Under the pumping at intermediate scales and small-scale dissipation, an inverse cascade in a finite box tends to produce a coherent box-size flow called condensate. If that condensate is stable, it grows, as is the case for incompressible 2d turbulence and optical or Langmuir turbulence
with repulsive (defocusing) nonlinearity. If the condensate is unstable, as is the case for optical and Langmuir turbulence with attractive (focusing) nonlinearity, it produces finite-time singularities (self-focusing or wave collapse) which stabilize turbulence at large scales. Here we discover a third possibility: inverse cascade in a compressible 2d turbulence (also turbulence in a thin fluid layer) produces box-size long-living vortices, which fluctuate and oscillate strongly and are accompanied by large-scale shock waves that dissipate the energy. Turbulence provides for a net energy flux into vortex but a zero net momentum flux. We analyze the spectra of kinetic energy and density in both intervals of direct and inverse cascade and show different physics that determines those cascades in compressible 2d turbulence.We present both basic analytic theory and extensive numerics.
|
11:30
15 mins
|
Role of the strain-rate tensor in turbulent scalar-transport modeling
Siddhartha Verma, Guillaume Blanquart
Abstract: We examine the geometric orientation of the subfilter-scale scalar-flux vector in homogeneous isotropic turbulence. Vector orientation is determined using the eigenframe of the resolved strain-rate tensor. The Schmidt number is kept sufficiently large so as to leave the velocity field, and hence, the strain-rate tensor, unaltered by filtering in the viscous-convective subrange. Strong preferential alignment is observed for the case of Gaussian and box filters, whereas the sharp-spectral filter leads to close to a random orientation. The orientation angle obtained with the Gaussian and box filters is largely independent of the filter-width and the Schmidt number. It is shown that the alignment direction observed numerically using these two filters is predicted very well by the tensor-diffusivity model. Further a-priori tests indicate poor alignment of the Smagorinsky and stretched vortex model predictions with the exact subfilter flux.
|
11:45
15 mins
|
DIRECT NUMERICAL SIMULATION OF DYNAMIC ROTATING JETS
Koichi Tsujimoto
Abstract: Jets are the most basic flow used in industrial field and are widely used for heating, cooling, mixing. Recently, the improvement
of mixing efficiency is required in order to downsize many industrial equipments and upgrade their performance. In the case of
jets, their characteristic, such as the diffusion, depends on the inlet condition. Therefore, by controlling jet to give appropriate inlet conditions, the mixing efficiency can be improved. Thus far previous studies have mainly investigated excitation control associated with the instability of jets. However, in our previous study, as a new method we proposed dynamic control to enhance mixing or diffusion of free jets and have found its characteristics[1]. In this study, we focus on the vector control in which an inflow is rotating around the streamwise direction. In order to investigate the performance of the proposed method, the DNS of axisymmetric jet under the vector control are conducted and its structures are visualized; the mixing efficiency based on a mixing measure are quantified.
|
|