Bulletin of the American Physical Society
2005 58th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 20–22, 2005; Chicago, IL
Session ES: Turbulent Scalar Mixing I |
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Chair: Lance Collins, Cornell University Room: Hilton Chicago Stevens 4 |
Sunday, November 20, 2005 4:10PM - 4:23PM |
ES.00001: Spectral mixing model for an inhomogeneous scalar field Yang Liu, Lance Collins The transport equation for the composition probability density function (PDF) requires a closure approximation for the molecular mixing term. Single-point closures generally assume an Oboukov--Corrsin scalar cascade that is controlled by the integral times scale of the turbulence. In this talk, we present an alternative closure for the composition PDF derived from the eddy damped quasi normal Markovian (EDQNM) spectral theory. The PDF is described using Monte Carlo particles; however, the particles carry a spectral distribution of each scalar field. A Langevin type equation then describes scalar exchanges within the particle (cascade) and across particles (mixing). The model correctly predicts the relaxation of an initial double delta function into a near Gaussian at long times (e.g., see Eswaran and Pope; Phys. Fluids 31:506, 1987). The explicit representation of molecular mixing in the spectral closure allows the model to describe molecular effects such as differential diffusion. We recently generalized the model for the case of a spatially inhomogeneous scalar field. Results for one-dimensional diffusion of a scalar field will be shown. [Preview Abstract] |
Sunday, November 20, 2005 4:23PM - 4:36PM |
ES.00002: EDQNM spectral theory for turbulent reacting flows Yanjun Xia, Yang Liu, T. Vaithianathan, Lance Collins The eddy damped quasi normal Markovian (EDQNM) spectral theory has been shown to accurately predict energy and scalar spectra under a variety of conditions (e.g., isotropic energy and scalar, anisotropic energy and scalar, homogeneous turbulent shear flow). In this paper, we present an extension of the theory to the case of two initially unmixed scalars undergoing an isothermal bimolecular reaction. Assuming a uniform reaction rate constant, the chemical source term introduces a second-order nonlinearity that can be closed by the EDQNM procedure. If we further assume realizability constraints are satisfied (Ulitsky and Collins; J. Fluid Mech. 412:303, 2000), the model yields spectral distributions for reactants and product fields. Moreover, as molecular diffusion is exact in this representation, the effect of variations in the scalar diffusivities (i.e., differential diffusion) on the mean chemical source term can be calculated. The results show remarkable sensitivity of product-reactant correlations to the molecular diffusivity ratios. We also investigate how these effects scale with the turbulence Reynolds number. [Preview Abstract] |
Sunday, November 20, 2005 4:36PM - 4:49PM |
ES.00003: Analysis of higher-order conditional moment closures for combustion with extinction and reignition Sean Smith, Rodney Fox, Venkat Raman In order to further understand and improve higher-order conditional moment closures (CMC) for combustion with extinction and reignition, \textit{a priori} and \textit{a posteriori} analyses of reacting isotropic turbulence have been completed. The analyses use data from the direct numerical simulations (DNS) of Sripakagorn et al. (Comb. Flame 136, 351, 2004), and include the transport of a passive scalar and a reaction-progress variable for a reversible reaction at three Damkohler numbers. The DNS data are used to investigate the validity and accuracy of the multi-environment conditional probability density function (MECPDF) model (Fox and Raman, Phys. Fluids 16, 4551, 2004) as compared to that of a second-order CMC model (Klimenko and Bilger, Prog. Energy Comb. Sci. 25. 595, 1999). The study also investigated constraints for any CMC model that accounts for third or higher conditional moments. The results indicate that the mixture-fraction and the mixed conditional dissipation rates can be closed accurately with an extension to the model proposed by Kilmenko and Bilger, even at lower Damkohler numbers and for higher-order conditional moments. [Preview Abstract] |
Sunday, November 20, 2005 4:49PM - 5:02PM |
ES.00004: Simulation and modeling of passive scalar mixing in turbulent jets Pradeep Babu, Krishnan Mahesh Direct numerical simulation of passive scalar transport in a spatially evolving turbulent jet is performed at Reynolds number of $2400$ and Schmidt number of unity. Good comparison withexperimental data is obtained. The simulation results are used to study role of diffusion in scalar transport. Diffusion--dominated regions are very thin near the jet center, but are fairly thick and `brush--like', near the jet edge. Longer residence times near the jet edge are proposed as a reason for this behavior. A simple kinematic model is proposed, that predicts the experimentally observed variation of scalar fluctuations with Reynolds number, Schmidt number and radial location. The model assumes that scalar fluctuations at a fixed location in the jet result from the oscillation of scalar fronts, whose thickness depends on Reynolds and Schmidt numbers, and whose oscillation amplitude depends on the level of turbulent fluctuations. The value of $c_{\rm rms}/\overline c$ is predicted to decrease, and asymptote to a constant value as the ratio of the oscillation amplitude of the scalar fronts to their thickness increases. This prediction is consistent with the experimental data discussed by Dimotakis (2000, {\it J. Fluid Mech.}, {\bf 409:}~69--98) in the context of mixing transition. The model results also suggest that Reynolds number and Schmidt number dependencies are likely to be stronger, away from the jet centerline, where the scalar fronts are thicker and the levels of turbulence smaller. [Preview Abstract] |
Sunday, November 20, 2005 5:02PM - 5:15PM |
ES.00005: Conditional Mixing Statistics in a Self-Similar Scalar Mixing Layer Stephen de Bruyn Kops, Mikael Mortensen Conditional scalar mixing statistics from a three-dimensional direct numerical simulation (DNS) of a scalar mixing layer are presented in the context of modeling non-premixed turbulent combustion. The simulation is closely matched to a particular laboratory experiment but with slight adjustments so that the simulated flow is very nearly self-similar. All statistics commonly used in mixing models are presented, along with comparisons to models and laboratory data where available. A model for the conditional scalar dissipation rate (CSD), recently introduced by Mortensen, is tested against the data set, as is a Lagrangian stochastic trajectory technique recently published by Sawford. It is concluded that (i) the DNS data set provides an excellent, high resolution description of the scalar mixing layer that can be used for developing and verifying models for scalar mixing; (ii) the self-consistent CSD model of Mortensen is necessary for consistent implementations of the conditional moment closure, but, for the current flow it gives only small adjustments to the more commonly adopted model of Girimaji; and (iii) Sawford's Lagrangian technique very closely predicts the DNS results. [Preview Abstract] |
Sunday, November 20, 2005 5:15PM - 5:28PM |
ES.00006: Momentum and Scalar transport in a turbulent jet in crossflow : a DNS study Suman Muppidi, Krishnan Mahesh We discuss the velocity field and passive scalar mixing characteristics of a turbulent round jet in crossflow. Direct numerical simulation is performed at conditions matching that of experiment (Su \& Mungal 2004). The velocity ratio is 5.7, the Reynolds number is 5000, the crossflow is laminar and the jet originates from a turbulent pipe flow. The results of the simulation will be compared to data of velocity and scalar fields available from Su \& Mungal's experiment. A separate simulation of fully developed turbulent flow in a pipe is performed (Re = 5000) and the time--dependent velocity field from this simulation is used as the inflow boundary condition for the jet. The results of the pipe flow simulation show a good agreement with existing results (Eggels et al. 1994). [Preview Abstract] |
Sunday, November 20, 2005 5:28PM - 5:41PM |
ES.00007: Simultaneous PIV and PLIF measurement of passive scalar mixing in a confined planar jet Hua Feng, Michael Olsen, James Hill, Rodney Fox Simultaneous velocity and concentration fields in a confined liquid-phase planar jet with a Reynolds number based on hydraulic diameter of 50,000 were obtained using combined particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF). Data at six downstream locations were analyzed for flow statistics such as mean velocity, Reynolds stresses, turbulent kinetic energy, concentration mean and variance, turbulent fluxes, turbulent viscosity and diffusivity, and turbulent Schmidt number. Spatial correlation fields of turbulent fluxes and concentration were then determined. The $R_{u'\phi'}$ correlation was elliptical in shape with a major axis tilted downward with respect to the streamwise axis, whereas the $R_{v'\phi'}$ correlation was a horizontally oriented ellipse. The $R_{\phi'\phi'}$ correlation field was found to be an ellipse with the major axis inclined at about 45-degrees with respect to the streamwise direction. Linear stochastic estimation was used to determine conditional flow structures. Large-scale structures were observed in the conditional velocity fields that are elliptical in shape with a streamwise major axis. The size of the structure initially increased linearly with respect to downstream distance, but then grew more slowly as the flow evolved towards channel flow. [Preview Abstract] |
Sunday, November 20, 2005 5:41PM - 5:54PM |
ES.00008: Study of turbulent mixing in a confined planar wake Ying Liu, Hua Feng, Rodney Fox, Michael Olsen, James Hill Liquid-phase turbulent transport and mixing for a Reynolds number of 37,500 in a confined planar wake were investigated using particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF). The velocity and concentration field data were analyzed for flow statistics such as mean velocity, Reynolds stress, spreading rate, turbulent kinetic energy, turbulence dissipation rate, mixture-fraction mean, mixture-fraction variance and one-point concentration PDF. CFD models, including a two-layer $k-\varepsilon$ turbulence model, gradient-diffusion models that close the scalar fluxes, and a scalar dissipation rate model that are used in a RANS/PDF scheme, were validated against PIV/PLIF data collected at six downstream locations. Low-Reynolds-number effects on turbulent mixing were taken into consideration through the mechanical-to-scalar time-scale ratio. The experimental and computational results were found to be in good agreement. [Preview Abstract] |
Sunday, November 20, 2005 5:54PM - 6:07PM |
ES.00009: Mixing of two scalars in turbulent channel flow Etienne Costa-Patry, Laurent Mydlarski When two (identical) scalars disperse from two distinct sources in the same turbulent flow, the scalar fluctuations are mixed and result in a combined variance. In general, this value is not the sum of the variances from the individual sources -- the combined variance depends on the covariance between the two scalar fluctuations. Given that many common engineering problems involve the transport of more than one scalar, the mixing of two or more scalars in turbulent flows is therefore of interest. The mixing of multiple scalars emitted from concentrated sources in homogeneous, isotropic turbulence has been thoroughly studied \footnote{Warhaft, Z., 1984, {\it J. Fluid Mech.}, {\bf 144}, pp.363-387}. However, since most engineering flows are inhomogeneous, it is also of interest to study the mixing of two scalars in fully-developed, high-aspect-ratio, turbulent channel flow -- the simplest realization of an inhomogeneous, turbulent flow. In the present work, scalars (temperature in air) are emitted from concentrated sources by heating fine wires that traverse the channel. Using cold-wire thermometry to measure the two fluctuating scalar fields, various statistics pertaining to their correlation will be presented. The similarities and differences with homogeneous, isotropic turbulence will be emphasized. [Preview Abstract] |
Sunday, November 20, 2005 6:07PM - 6:20PM |
ES.00010: Relative dispersion of passive scalar plume in a turbulent boundary layer Qian Liao, Edwin Cowen Recent studies on relative dispersion have been exclusively focused on statistics of particle pair separation. Less attention was paid to its application in dispersing contaminant plumes or puffs. Since introduced by Richardson (1926), distance-neighbor function has been used to characterize the detail structure of concentration field in a dispersing cloud. Its evolution was described by a diffusion equation (Batchelor, 1952), where the diffusivity is proportional to the four-third power of the separation length. The present experimental study provided an evidence for this hypothesis. A passive fluorescent tracer is continuously released from a flush-bed mounted source into the turbulent boundary layer of a laboratory open channel flow. A two-dimensional Particle Image Velocimetry - Laser Induced Florescence (PIV-LIF) technique is applied to measure the instantaneous horizontal velocity-concentration field. Assuming one-dimensionality, the distance-neighbor function is calculated as the lateral auto-correlation of concentration distribution. Thus the relative diffusivity can be directly calculated from the streamwise evolution of the distance-neighbor function. The relative diffusivity is found to be dependent on the instantaneous separation, and can be described by a 4/3 power law in the inertial sub-range. The Richardson-Obukhov constant is also determined from experimental results. An extended model for relative diffusivity is provided based on the structure of turbulent velocity field and it agrees with measurements excellently. [Preview Abstract] |
Sunday, November 20, 2005 6:20PM - 6:33PM |
ES.00011: Scale relations, coherence, and Reynolds number effects in turbulent mixing with differential diffusion C.J. Brownell, L.K. Su Measurements confirm a non-negligible effect of differential molecular diffusion in turbulent mixing at moderate Reynolds numbers. This is significant to reacting flow systems, where local laminarization arises from heat release. Through planar measurements of scalar and velocity fields in turbulent, non-reacting jets, we explore the effects of differential diffusion over a range of length scales, the correlation of differential diffusion at varying scales to the large-scale mixing organization of the jet, and the effect of the local Reynolds number, including those that span the turbulent transition. For example, we have found that the maximum variance of differential diffusion occurs away from the jet centerline, confirming previous numerical studies. Also, under certain conditions, slower-diffusing scalars are preferentially advected to the perimeter of the jet which may arise from buoyancy effects. [Preview Abstract] |
Sunday, November 20, 2005 6:33PM - 6:46PM |
ES.00012: The effect of background turbulence on differential diffusion in a turbulent jet Thomas Lavertu, Adam Wahab, Laurent Mydlarski, Susan Gaskin Whenever multiple scalars of unequal molecular diffusivities are mixed in a turbulent flow, differential diffusion may occur\footnote{Saylor, J.R. and Sreenivasan, K.R., 1998. {\it Phys. Fluids}, {\bf 10}, p. 1135.}. The present work studies differential diffusion of two scalars in a round, turbulent (water) jet of Reynolds numbers up to $Re_D (\equiv U_j D/\nu) \approx 10,600$. The jet issues into an approximately isotropic, turbulent background flow generated by a random synthetic jet array\footnote{Variano, E.A., Bodenschatz, E., and Cowen, E.A., 2004. {\it Exp. Fluids}, {\bf 37}, p. 613.}. By means of laser-induced fluorescence, punctual concentration measurements are made radially across the jet's cross-section, yielding instantaneous concentrations of each scalar ($c_1$ and $c_2$). Statistics of the instantaneous, normalized concentration difference ($z \equiv c_2 / \langle c_2 \rangle - c_1 / \langle c_1 \rangle$) are employed to quantify the effects of differential diffusion. The effect of the background turbulence on the differential diffusion will be discussed. In particular, these results will be compared with previous work done in a quiescent background. [Preview Abstract] |
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