14:00
Transport and Mixing 1
14:00
15 mins
#9
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TURBULENT MIXING IN A CHANNEL FLOW
Dimitrios Papavassiliou, Quoc Nguyen
Abstract: In this study, a combination of Direct Numerical Simulation (DNS) and Lagrangian Scalar Tracking (LST) [1-5] is employed to investigate mixing of scalars released at different locations of a turbulent channel flow. Since the smallest scales of turbulence are much larger than a single molecule, molecular diffusion is needed to bring molecules together. Specifically when particles are released from the wall in anisotropic turbulence, the effects of molecular diffusion and turbulent convection might even lead to temporary separation between passive scalars with different molecular diffusivities, rather than mixing [1,2]. Herein, we use the DNS/LST approach to investigate the mixing of puffs (instantaneous sources) and plumes (continuous sources of scalars). The goal is to investigate the effects of molecular diffusion on mixing in each case, and to explore the effect of the location of the point of release on mixing efficiency.
The velocity field in a fully developed Poiseuille channel flow is obtained using a DNS for a Newtonian and incompressible fluid. The DNS methodology has been published and validated with experimental results [6, 7]. The computational box has dimensions of 16πh x 2h x 2πh in the streamwise, x, wall-normal, y, and spanwise, z, directions, respectively, with a half channel height (h) of 300, making the friction Reynolds number equal to 300. Scalar markers representing mass particles are then released into the flow field. A scalar tracking algorithm [8] was applied to track the trajectories of these markers in space and time in a Lagrangian framework. Data were generated for Schmidt number (Sc) covering four orders of magnitude (Sc = 0.7, 6, 200 and 2400), with the markers released into the channel at different distances from the bottom channel wall, (y = 0, 15, 75, and 300. Both puffs [5] and plumes are examined. A mixing efficiency metric is defined [2], and the mixing is characterized for each case. The differences between puffs and plumes are highlighted and the effects of molecular diffusivity for scalars released in the viscous wall region are examined. It is found that the mixing zone shape and the mixing intensity depend on the Sc of the markers when the location of release of one of the plumes is within the viscous wall sublayer. Designing mixers or reactors, where the location of mixing is important to know, should take into account such findings.
Acknowledgements: The support of the National Science Foundation (grant number CBET-18-0260), the University of Oklahoma Supercomputing Center for Education and Research, and XSEDE (CTS-090025) are acknowledged
References
[1] Q.T. Nguyen, and D.V. Papavassiliou, A statistical model to predict streamwise turbulent dispersion from the wall at small times, Physics of Fluids, 28: Article 125103, 2016.
[2] Q.T. Nguyen, and D.V. Papavassiliou, Flow induced separation in wall turbulence, Physical Review E, 91: Article 033019, 2015.
[3] Q.T. Nguyen, and D.V. Papavassiliou, Scalar mixing in anisotropic turbulent flow, AIChE Journal, 64: 2803-2815, 2018.
[4] Q.T. Nguyen, and D.V. Papavassiliou, Quality Measures of Mixing in Turbulent Flow and Effects of Molecular Diffusivity, Fluid, 3: Article 53, 2018.
[5] P.M. Le, and D.V. Papavassiliou, Turbulent dispersion from elevated line sources in channel and Couette flow, AIChE Journal, 51(9): 2402-2414, 2008
[6] A. Gunther, D.V. Papavassiliou, M.D. Warholic, and T.J. Hanratty, Turbulent flow in a channel at a low Reynolds number, ” Experiments in Fluids, Vol. 25, pp. 503-511, 1998
[7] Q.T. Nguyen, and D.V. Papavassiliou, Turbulent plane Poiseuille-Couette flow as a model for fluid slip over superhydrophobic surfaceces, Physical Review E, 88: Article 063015, 2013.
[8] K. Kontomaris, K., and T.J. Hanratty, Algorithm for Tracking fluid particles in a spectral simulation of turbulent channel flow, Journal of Computational Physics, 103: 231-242, 1992.
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14:15
15 mins
#70
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Two-point small-scale flow properties measured by means of Lagrangian rigid fiber tracking
Mattia Cavaiola, Stefano Olivieri, Andrea Mazzino
Abstract: The dynamics of a rigid fiber in a spatially-periodic steady flow is studied exploiting direct numerical simulations complemented by a state-of-the-art immersed boundary method (IBM) \cite{bib:IBM2007}. The rigid fiber is two-way coupled to spatially-periodic solutions of the incompressible Navier-Stokes equations (the so-called ABC and BC flows \cite{dombre_frisch_greene_hénon_mehr_soward_1986,bib:ABC1994}) with the aim of investigating whether relevant properties of the fluid flow (e.g. its gradients) can be measured in terms of a few fiber properties: position and velocity of the fiber end points. Our work is motivated by the results recently obtained by Rosti et al. \cite{bib:Rosti2018} which showed that a flexible fiber can be used as a proxy of two-point statistics of turbulence. The results that we will present here extend such an idea to rigid fibers. These latter are easier to fabric than elastic fibers and are good candidates to motivate new experimental, non-invasive, techniques to access small-scale, multi-point, properties of fluid flows. The idea is to replace single particles, used in PIV techniques to
measure fluid properties, by single fibers (or assembly of them) to access multi-point fluid properties.
To achieve this goal, we perform fully-resolved simulations considering a laminar, cellular flow (e.g. the BC flow) representative of the smallest scales of turbulent flows, imposing a volume forcing such that the computed solution corresponds to the analytical one.
The fiber is one-dimensional in space, inextensible, freely moving in the fluid (Fig.~\ref{fig1}a) and can be characterized by linear density ${\rho}_{1}$ and bending rigidity ${\gamma}$.
In order to have an essentially rigid behavior, we choose an adequate value of $\gamma$, while we consider different values of $\rho_1$ to investigate the role of inertia in the capability of the fiber on measuring accurately the two-point properties of the flow.
By projecting the velocity difference between the fiber ends along the direction normal to the fiber, the comparison with that calculated from the analytical solution shows good agreement (Fig.~\ref{fig1}b).
This preliminary result confirms the idea that such Lagrangian description can be used to monitor the main features of the fluid motion, with future developments considering assembly of fibers in a way to describe the full structure of the velocity gradient, as well as more complex kinds of flow (e.g., three-dimensional and unsteady).
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14:30
15 mins
#306
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Non-Gaussianity in turbulent relative dispersion
Benjamin Devenish, David Thomson
Abstract: See attached file.
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14:45
15 mins
#104
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A STRUCTURAL SUBGRID-SCALE MODEL FOR LARGE-EDDY SIMULATION OF RELATIVE DISPERSION OF PARTICLES IN ISOTROPIC TURBULENT FLOWS
Guodong Jin
Abstract: A kinematic simulation with an approximate deconvolution (KSAD) hybrid model is proposed to predict the Lagrangian relative dispersion of fluid particles in a large eddy simulation (LES) of isotropic turbulent flows. In the model, a physical connection between the resolved and subgrid scales is established through the energy flux rate at the filter width scale. Due to the lack of subgrid-scale (SGS) turbulent structures and SGS model errors, the LES cannot accurately predict the two- and multi-point Lagrangian statistics of the fluid particles. To improve the predictive capability of the LES, we use an approximate deconvolution model (ADM) to improve the resolved scales near the filter width and a kinematic simulation (KS) to recover the missing velocity fluctuations beneath the subgrid scales. To validate the proposed hybrid model, we compare the Lagrangian statistics of two- and four-particle dispersion with the corresponding results from the direct numerical simulation (DNS) and the conventional LES. It is found that a significant improvement in the prediction of the Lagrangian statistics of fluid particles is achieved through the KSAD hybrid model. Furthermore, a parametric study regarding the wavenumbers and orientation wavevectors is conducted to reduce the computational cost. Good results can be obtained using a small number of wavenumber modes and orientation wavevectors. Thus, we can improve the prediction of the Lagrangian dispersion of fluid particles in the LES by applying the KSAD hybrid model at an acceptable computational cost.
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15:00
15 mins
#534
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ANISOTROPIC PASSIVE SCALAR FLUCTUATIONS WITH UNIFORM MEAN GRADIENT IN STATISTICALLY HOMOGENEOUS ISOTROPIC TURBULENCE
Tatsuya Yasuda, Toshiyuki Gotoh, Takeshi Watanabe, Izumi Saito
Abstract: We study anisotropic fluctuations of passive scalar convected by forced periodic turbulence. The turbulent velocity field is generated by the white Gaussian isotropic force which has zero mean and the spectrum support at low wavenumbers. We consider two kinds of turbulent passive scalar turbulent flows; one is sustained with a Gaussian random source and
the other is with a uniform mean scalar gradient. Here, the respective scalar fluctuations are shown by θ and q. Given that the turbulent velocity fields of our direct numerical simulations (DNSs) are statistically isotropic, θ becomes statistically isotropic either but q becomes axisymmetric along the direction of uniform mean scalar gradient [1]. We evaluate the degree of anisotropy in scalar fluctuations by expanding two second-order scalar structure functions S 2 θ and S 2 q in Legendre polynomials [1], where S 2 θ (r, t) ≡ h(θ(x + r, t) − θ(x, t)) 2 i and S 2 q (r, t) ≡ h(q(x + r, t) − q(x, t)) 2 i, r and h·i being a separation vector and the space average. The expansion coefficients S 2 θ,l (r, t) and S 2 q,l (r, t) are computed as S 2 θ,l (r, t)
2l + 1 = 4π Z 1 S 2 θ (r, t)P l (μ)dΩ, S 2 q,l (r, t)−1, 2l + 1, =
4π
Z
1
S 2 q (r, t)P l (μ)dΩ ,
(1)
−1
where Ω is a solid angle and P l (μ) is the lth-order Legendre polynomial. We have encountered a technical difficulty when
computing the surface integral over a sphere with the radius r in Eq. 1, which has brought us to consider the usage of more
accurate numerical computation method. For computing it more accurately, we employ an efficient and accurate algorithm
for the SO(3) decomposition, which was recently presented by Iyer et al [2]. In Fig. 1, we plot the time average (denoted
by h·i t ) of 0th-isotropic sectors (hS 2 θ,0 i t and hS 2 q,0 i t ), 2nd-anisotropic sectors (hS 2 θ,2 i t and hS 2 q,2 i t ), and 4th-anisotropic
sectors (hS 2 θ,4 i t and hS 2 q,4 i t ), which are computed by using the method above. It is noticed that hS 2 θ,2 i t is smaller than
hS 2 θ,0 i t and hS 2 q,2 i t by a factor of about 10 3 and 10, respectively. hS 2 θ,0 i t is found to be larger than anticipated, but we
speculate that it will become smaller as more samples over time are taken since S 2 θ,2 (r, t) can be positive or negative.
In our talk, we will present results with a variety of numerical conditions in order to demonstrate anisotropic features of passive scalar fluctuations, not only by turbulence statistics but also by flow visualizations. We emphasise that passive scalar fields appear very differently with or without a uniform mean scalar gradient although they are advected by the
same reasonably isotropic turbulent flow, which is forced at moderate wavenumbers.
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15:15
15 mins
#582
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Turbulent mixing in variable-density helium-air jet
Yacine BRAHAMI, Michael GAUDING, Dominik DENKER, Emilien VAREA, Luminita DANAILA
Abstract: Variable density He-Air jet is investigated with a particular
attention payed to the near-field (initial times). The aim is to: i)
predict how fast mixing occurs after He injection in ambiant air, and
ii) to theoretically underline similarity scales pertaining to
different statistics. The methodology is qualified as follows.
1) Theory. Starting from the first principles in
variable-density flows, we derive scale-by-scale energy transport
equations that account for density fluctuations and highlight mixed
density-kinetic energy statistics.
2) Direct Numerical Simulations (DNS). The analysis is
performed by means of direct numerical simulation (DNS) data of a
turbulent temporally evolving planar jet. Statistics are evaluated at different
locations and different times. The DNS was computed with the high-fidelity
in-house code CIAO to accurately resolve all relevant scales. More
precisely, CIAO's low Mach solver was used with a 4th order spatial
discretization scheme and semi-implicit Crank-Nicholson time
integration.
3) Experiments. Helium is seven times lighter than the
air, thus the scalar is qualified as 'active' and measurements should
consider the non-linear coupling of the two fields. Therefore, simultaneous
measurements of both velocity and scalar are required. To do so, we used a
coupled 2-dimensional 3-components Stereo Particle Image Velocimetry
(2D3C PIV) and Planar Laser Induced Fluorescence (PLIF) to determine all
velocity components and He concentration over the same field of
view. The scalar allows for the local density to be evaluated.
4) Phenomenological description and modelling.
Generalized similarity scales are deduced following the approach of
Gauding et al. 2017. A good collapse of the normalized structure functions in the
dissipative range is achieved by deriving generalized, order-dependent
scales, that take the internal and external
fluctuations of density, viscosity, and velocity into account. To
further predict how fast mixing occurs, and because transport
equations involve both second and third-order statistics, we develop a
characteristic-time model and validate it against numerical and experimental data. This finally allows us to predict effectiveness of the mixing for different initial conditions.
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15:30
15 mins
#181
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Lagrangian perspective on turbulent passive scalar mixing
Joerg Schumacher, Paul Goetzfried, Mohammad S. Emran, Emmanuel Villermaux
Abstract: The mixing of a freely decaying passive scalar in a three-dimensional, statistically stationary turbulent Navier-Stokes flow is studied by means of direct numerical simulations for Schmidt numbers up to 64 \cite{Goetzfried2019}. The scalar is represented in two different ways: in the Lagrangian frame of reference as a cloud of up to 4.8 billion individually advected massless tracer particles subject to a stochastic Wiener process along the tracer tracks that describes scalar diffusion or in the standard Eulerian frame of reference as an advection-diffusion equation of the continuum concentration field. In both cases, the scalar is initially seeded in a small cubic subvolume. The mean mixing time $\langle t_s\rangle$ is determined by the mean compressive strain rate $\langle\lambda_3\rangle<0$ which is obtained from the probability density functions of the local finite-time Lyapunov exponents in the Lagrangian frame, $\lambda_i(t)$ with $i=1,2$ and 3. The direct comparison of Lagrangian and Eulerian passive scalars gives a good agreement of the scalar variance for shorter times and for the probability density functions of the scalar taken with respect to the whole simulation domain. It is also shown how the multi-layer aggregations of scalar filaments and sheets in the Lagrangian frame are increasingly influenced by the noise due to discreteness with progressing dilution of the initially high tracer particle concentration. This limits the Lagrangian approach in its present form and for the obtainable Schmidt numbers to studies of shorter time periods. A simple one-dimensional advection-diffusion model of a solitary strip \cite{Villermaux2019} is applied to derive the probability density function of the scalar concentration, $P(\Theta,t)$, from the one of the compressive local finite-time Lyapunov exponent, $p(\lambda_3,t)$. Model prediction with and without self-convolution and numerical data of the scalar distributions agree qualitatively, however with quantitative differences particularly for small scalar concentrations.
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