Bulletin of the American Physical Society
65th Annual Meeting of the APS Division of Fluid Dynamics
Volume 57, Number 17
Sunday–Tuesday, November 18–20, 2012; San Diego, California
Session M22: Turbulence Mixing IV |
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Chair: Diego Donzis, Texas A&M University Room: 30C |
Tuesday, November 20, 2012 8:00AM - 8:13AM |
M22.00001: Experimentally Informed Turbulent Diffusivity Modeling for an Angled Jet in Cross-Flow Julia Ling, Filippo Coletti, Sayuri Yapa, Gianluca Iaccarino, John Eaton A key source of error in many turbulent heat transfer simulations is the modeling of the turbulent heat flux. This heat flux is often approximated using the gradient diffusion hypothesis with a fixed turbulent Prandtl number based on empirical values from simple turbulent flows. However, in more complex configurations, this model is known to be inaccurate. A methodology has been developed which uses experimental data to determine optimal uniform anisotropic turbulent diffusivity values for an angled jet in cross-flow. This configuration has applications in film cooling for gas turbine blades. The measurements, obtained by magnetic resonance imaging techniques, provide 3D time-averaged velocity and concentration fields. The mean velocity field is fed into a Reynolds-Averaged Advection Diffusion solver, which uses a spatially-uniform anisotropic turbulent diffusivity model to solve for the mean coolant concentration distribution. This distribution can be compared to the experimentally-obtained concentration field by means of an error metric that quantifies the difference between the computational and experimental concentration fields. By minimizing this error, an optimal value of the anisotropic turbulent diffusivity is determined. [Preview Abstract] |
Tuesday, November 20, 2012 8:13AM - 8:26AM |
M22.00002: Large-eddy simulation of short-range dispersion from localized sources in an urban-like canopy David Philips, Riccardo Rossi, Gianluca Iaccarino Results from large-eddy simulation of passive scalar dispersion from point source releases in an urban-like canopy are presented. The canopy is comprised of a periodic array of variable height buildings with square cross-sectional areas. The buildings are immersed in a turbulent, pressure-driven flow with a roughness Reynolds number, $Re_\tau=433$. Pressure gradient direction is varied between $0^{\circ}$, $45^{\circ}$, and $90^{\circ}$ to examine the effects on dispersion when the prevailing wind encounters staggered, skewed, or aligned building arrangements, respectively. Additionally, source location is varied to assess the impact of local building geometry on plume development. Plume trajectories and growth rates for the various scenarios are examined. The vertical development of the plume is better characterized by the roughness parameterization of the canopy than the horizontal development which is more sensitive to local geometry. [Preview Abstract] |
Tuesday, November 20, 2012 8:26AM - 8:39AM |
M22.00003: Small-scale statistics of passive scalars released from concentrated sources in turbulent channel flow Laurent Mydlarski, Emmanuel Germaine, Luca Cortelezzi In 2010, we presented complementary experimental and numerical results pertaining to the large-scale statistics of a turbulent passive scalar released downstream of a line source in fully-developed turbulent channel flow. Our latest results relate to the evolution of the scalar dissipation rate ($\varepsilon_{\theta}\equiv \alpha \langle (\partial \theta / \partial x_i)^2 \rangle$) downstream of the line source, for two different wall-normal source locations. We present experimental and numerical PDFs of the 3 different temperature derivatives ($\partial \theta / \partial x_\gamma$), as well as the different components of $\varepsilon_{\theta}$ ($\varepsilon_{\theta_\gamma}$), and conditional expectations of $\varepsilon_{\theta_\gamma}$. We also examine the anisotropy of the components of $\varepsilon_{\theta_\gamma}$ and note that these can asymptote to an anisotropic final state. This is attributed to the presence of the mean velocity gradient in the channel, which induces an additional production term (in the wall-normal direction) in the $\varepsilon_{\theta}$ budget. However, it also appears that the degree of this final anisotropy decreases with increasing Reynolds number and proximity to the wall (the two being correlated). [Preview Abstract] |
Tuesday, November 20, 2012 8:39AM - 8:52AM |
M22.00004: Local structure of scalar flux in turbulent passive scalar mixing Aditya Konduri, Diego Donzis Understanding the properties of scalar flux is important in the study of turbulent mixing. Classical theories suggest that it mainly depends on the large scale structures in the flow. Recent studies suggest that the mean scalar flux reaches an asymptotic value at high Peclet numbers, independent of molecular transport properties of the fluid. A large DNS database of isotropic turbulence with passive scalars forced with a mean scalar gradient with resolution up to $4096^3$, is used to explore the structure of scalar flux based on the local topology of the flow. It is found that regions of small velocity gradients, where dissipation and enstrophy are small, constitute the main contribution to scalar flux. On the other hand, regions of very small scalar gradient (and scalar dissipation) become less important to the scalar flux at high Reynolds numbers. The scaling of the scalar flux spectra is also investigated. The $k^{-7/3}$ scaling proposed by Lumley (1964) is observed at high Reynolds numbers, but collapse is not complete. A spectral bump similar to that in the velocity spectrum is observed close to dissipative scales. A number of features, including the height of the bump, appear to reach an asymptotic value at high Schmidt number. [Preview Abstract] |
Tuesday, November 20, 2012 8:52AM - 9:05AM |
M22.00005: Universality of spectrum of passive scalar variance at very high Schmidt number in isotropic steady turbulence Toshiyuki Gotoh Spectrum of passive scalar variance at very high Schmidt number up to 1000 in isotropic steady turbulence has been studied by using very high resolution DNS. Gaussian random force and scalar source which are isotropic and white in time are applied at low wavenumber band. Since the Schmidt number is very large, the system was integrated for 72 large eddy turn over time for the system to forgot the initial state. It is found that the scalar spectrum attains the asymptotic $k^{-1}$ spectrum in the viscous-convective range and the constant $C_B$ is found to be 5.7 which is larger than 4.9 obtained by DNS under the uniform mean scalar gradient. Reasons for the difference are inferred as the Reynolds number effect, anisotropy, difference in the scalar injection, duration of time average, and the universality of the constant is discussed. The constant $C_B$ is also compared with the prediction by the Lagrangian statistical theory for the passive scalar. The scalar spectrum in the far diffusive range is found to be exponential, which is consistent with the Kraichnan's spectrum. However, the Kraichnan spectrum was derived under the assumption that the velocity field is white in time, therefore theoretical explanation of the agreement needs to be explored. [Preview Abstract] |
Tuesday, November 20, 2012 9:05AM - 9:18AM |
M22.00006: Statistical and Geometrical Properties of the Scalar Gradient in Homogeneous Isotropic Turbulence Michael Gauding, Jens Henrik Goebbert, Fabian Hennig, Norbert Peters The mixing of a passive scalar in statistically homogeneous isotropic turbulence is investigated. Here, the scalar gradient plays an important role, since production of small scales and smoothing down by molecular diffusion depend on it. The single-point probability density function (pdf) of the scalar gradient is characterized by long stretched exponential tails. We derive an equation for the probability density function of the scalar gradient from first principles. This equation is not closed due to the highly nonlocal and non-linear character of the equations of motion. We employ a statistical framework to simplify the unclosed terms which also provides insight into the mechanisms of scalar gradient production, diffusion, and dissipation. We further introduce a simple closure for the tails of the scalar gradient pdf. This closure can be motivated by special alignment properties of the scalar gradient with its dissipation tensor. The theory is validated by means of direct numerical simulations with various Schmidt and Reynolds numbers. [Preview Abstract] |
Tuesday, November 20, 2012 9:18AM - 9:31AM |
M22.00007: ILES of Passive Scalar Mixing in Forced Isotropic Turbulence Adam Wachtor, Fernando Grinstein, Rick DeVore, Ray Ristorcelli, Len Margolin Predictability of scalar mixing by an under-resolved turbulent velocity field is investigated using ILES. Turbulent mixing of a passive scalar by forced, compressible, isotropic turbulence with a prescribed mean scalar gradient is studied. The simulation strategy uses a multi-dimensional FCT algorithm, with low wavenumber momentum forcing imposed separately for the solenoidal and dilatational velocity components. Effects of grid resolution on the flow and scalar mixing are investigated at turbulent Mach numbers 0.13 and 0.27. ILES captures the mixing transition as function of effective Reynolds number determined by grid resolution, including asymptotic behaviors and characteristic turbulent metrics. [Preview Abstract] |
Tuesday, November 20, 2012 9:31AM - 9:44AM |
M22.00008: Passive scalar mixing in variable-density, buoyant turbulent flows Phares L. Carroll, Guillaume Blanquart The interplay between turbulence and buoyancy is not fully characterized despite its presence in a wide range of environmental phenomena and engineering problems. Although classical Kolmogorov theory states that the dissipative scales are purely isotropic, there is evidence that this no longer holds in the presence of buoyancy. In this a-priori analysis, we consider two incompressible, miscible fluids with different densities that are subject to external body forces (gravity). The simulation results are used to probe the effect of variable-density and buoyancy on turbulence generation, small-scale isotropy, kinetic energy evolution, and turbulent mixing. The presence of isotropic behavior at the Taylor micro- and dissipative scales is examined via the Favre Reynolds stress anisotropy tensor. Analysis is conducted on the alignment of vorticity with the direction of principle strains to verify observed directional preferences. The role of buoyancy in the generation of turbulence is isolated by examination of appropriate energy spectra. Finally, the efficacy of mixing at varying Atwood and Schmidt numbers is analyzed using the probability density function (PDF) of mixture-averaged specific volume, the PDF of the scalar dissipation rate, and the scalar energy spectra. [Preview Abstract] |
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