Session LB: Turbulent Mixing II

Modeling the turbulent scalar fluxes in heated compressible flows

We use results from Direct Numerical Simulations of compressible flow in a heated channel (M{\_}cl = 0.34, 1.5) to advance an explicit, algebraic model for the turbulent scalar fluxes. The scalar fluxes of interest are the heat fluxes which enter into the equation for total energy and the mass fluxes which enter into the equations for turbulence kinetic energy and density variance. Both fluxes are usually modeled via gradient-transport hypothesis which does not account for the dependencies implied in the exact equations. Moreover, in fully-developed flows, the streamwise fluxes, which are greater than the fluxes in the direction of normal to the flow, are predicted as zero in models based on this hypothesis -- an outcome which is at variance with all results from experiments and simulations. The starting point is model is derived from the representation of the turbulent heat fluxes as a function of the Reynolds stresses, the mean strain rate and the mean vorticity. The time scales for the fluctuations in the scalar fields are often assumed to be proportional to the mechanical time scale. We test this assumption using the DNS results. The focus is on the near-wall region which determines the rate of heat transfer to the wall, and proposals for incorporation of a direct dependence of the heat fluxes on the gradients of mean density are examined.   

Performance of Turbulence Models in the Prediction of Heat Transfer from a Hemispherical Surface Due to Turbulent Jet Impingement

Impinging jet configurations are encountered in numerous industrial and engineering applications. Among these include cooling of a hot surface, turbine blade cooling, and airplane wing leading edge de-icing. In the design and operation of these applications, the knowledge of the heat transfer coefficient distribution along the cooling surface is important. We evaluated the performance of several turbulence models in the prediction of convective heat transfer due to round jet impingement onto convex spherical surfaces against available experimental data. The jet exit Reynolds number, the jet diameter, and the jet exit to the spherical surface distance were varied according to the experimental values. Based on calculated errors, the superiority of one model over the others cannot be established conclusively. However, the realizable k-epsilon model generally predicted the Nusselt number distribution more accurately than the other models for most cases.   

Mole fraction measurements in three species gas-phase turbulent flows

Planar imaging techniques are applied to measure the mole fractions of all major species in a nonreacting, acetone-helium jet issuing into air. Planar laser-induced fluorescence is used to measure the mole fraction of acetone, and planar Rayleigh scattering is used to measure the difference between the acetone and helium concentrations. Due to their differing molecular transport properties, and in particular disparate values of molecular diffusivity, the acetone and helium evolve differently and display different downstream concentration fields. Mole fraction profiles show a large-scale similarity between the concentrations of the two jet gases. The acetone field, due to the significantly lower diffusivity of acetone with air, has more small scale structure than the helium field. Scalar spectra for each jet species are presented, as well as the spectrum of the scalar difference, which represents the differential diffusion. Preliminary results suggest an anti-correlation to the scalars, particularly on the outside of the jet. For mixing simulations, this implies that there may be limitations to simulations that assume diffusivity can be represented with a single variable.   

Reynolds number dependence of thermal diffusion from a line source in decaying grid turbulence

Existing experiments on line source dispersion in isotropic turbulence are for low Reynolds numbers (Taylor scale Reynolds numbers of less than 100) and there has been no attempt to systematically vary the Reynolds number. Here we present new results of passive temperature fluctuations produced by a fine heated wire in decaying grid turbulence. The Taylor Reynolds number is varied from approximately 50 to 500 by means of active and passive grids. We study the dependence of the mean and r.m.s. temperature profiles on the Reynolds number. The effects of source size are also investigated. The results are compared with the recent modeling work of Viswanathan and Pope (Physics of Fluids, to be published) who find significant Reynolds number dependence but small effects when varying the source size. The peak centerline ratio of the r.m.s. to the mean of the scalar is also examined and compared with predictions. This work is funded by the US National Science Foundation.   

Experimental validation of a new closure scheme for turbulent diffusion using simultaneous PIV and PLIF

In this work the focus is on the moments of the probability density function (PDF) of scalar concentration, which normally can be inverted to approximate the PDF. To solve the moment equations of the PDF one requires a closure approximation for both the convective and dissipative terms. Sullivan (2004) proposed closures that provide a good qualitative representation of measured moment distributions across a plume from a line source in grid turbulence for the lowest four central moments. Simultaneous measurements of velocity and scalar concentration, using particle image velocimetry (PIV) and planer laser-induced fluorescence (PLIF) respectively, on a plume in a grid turbulence water tunnel experiment are used to quantitatively explore the closure scheme. The closures are validated by analyzing the velocity and concentration fields and considering an axisymmetric plume in cylindrical coordinates system.   

Optimization of pulsed jets in crossflow

Recent experiments (M'Closkey et al. 2002, Shapiro et al. 2006, Johari 2006, Eroglu \& Briedenthal 2001) on pulsed jets in crossflow show that jet penetration and spread can be optimized at specific pulse conditions. We performed DNS to study the evolution and mixing behavior of jets in crossflow with fully modulated square wave excitation. We attempt to explain the wide range of optimal pulsing conditions found in different experiments. Pulsing generates vortex rings. Sau and Mahesh (J. Fluid Mech., 2008) show that vortex rings in crossflow exhibit three distinct flow regimes depending on stroke ratio and velocity ratio. We use the behavior of a single vortex ring in crossflow to explain the evolution of pulsed jets in crossflow. Simulations suggest that the optimal conditions can be predicted from the transition between different regimes of vortex rings. It is observed that the duty cycle modifies the optimal conditions depending on the interaction in the near field. Simulation results and comparison with experiments will be discussed.   

Quantitative Measurement of Scalar Dissipation Rates in Turbulent Jets Using Planar Laser Imaging

Quantitative planar measurements in turbulent jet flows of scalar quantities, such as jet fluid mass fractions, $Y$, are relatively common, but planar measurements of the scalar dissipation rate, $\chi\propto\nabla Y\cdot\nabla Y$, are not. A complete understanding of the scalar dissipation rate field is important to applications such as turbulent non-premixed combustion. The particular challenge facing the measurement of $\chi$ is spatial resolution. Here, using planar Rayleigh scattering to measure $Y$ in helium-air and nonreacting acetylene-air jets, we measure $\chi$ from the near field up to $\approx 40$ jet diameters, $d$, from the jet exit using a series of five imaging windows. With this approach, the individual windows can be sized to ensure adequate pixel resolution to measure the local $\chi$, while the full set of data allows the measurement of the $\chi$ scaling over the entire axial range. Results indicate that the $\chi$ decay rates are slower than predicted from classical scaling arguments, and also slower than measured decay rates of kinetic energy dissipation. The data also permit assessment of the effects of spatial filtering on the measured $\chi$, which is relevant to efforts to model $\chi$ in combustion simulations.   

A dynamic subgrid-scale eddy diffusivity model with a global model coefficient for passive scalar transport in complex geometry

In the present study, a dynamic subgrid-scale eddy diffusivity model is proposed for large eddy simulation of passive scalar transport in complex geometry. The eddy viscosity model proposed by Vreman [Phys. Fluids, 16, 3670 (2004)], which guarantees theoretically zero SGS dissipation for various laminar shear flows, is utilized as the base eddy diffusivity model. The model coefficient is determined by the dynamic procedure based on the method proposed by Park {\it et al}. [Phys. Fluids, 18, 125109 (2006)] such that the model coefficient is globally constant in space but varies only in time. The large eddy simulations of passive scalar transport in turbulent channel flow and turbulent boundary layer are conducted and the proposed model shows nearly the same performance as the dynamic Smagorinsky model does. Since the proposed model does not require any {\it ad hoc} clipping and averaging over the homogeneous direction, it can be readily applied to transport of passive scalar in complex flows. Some other examples such as heat transfer in a ribbed channel will be shown in the final presentation.   

Large eddy simulations of turbulent coaxial jet flows with pulsation

Large eddy simulations of turbulent confined coaxial jet flows were performed at Re=9,000 based on the bulk velocity and outer radius of annular jet. Pulsations were superimposed on the inflow jets. The mean velocity ratio of annular jet to central jet is 1.667. The pulsation amplitudes of annular and central jets are 5{\%} and 20{\%}, respectively. Main control parameters were the pulsation frequency and the phase difference between annular and central jets. Effects of inflow pulsation on flow dynamics and mixing were investigated. We found that there exist two optimal pulsation frequencies: one is observed at St=0.327 for the minimum reattachment length on the chamber wall and the other is at St=0.180 for the maximum mixing in the shear layer. At the optimal pulsation frequency with the minimum reattachment length, effects of the phase difference between annular and central jets were scrutinized by examining the phase- or time-averaged turbulent statistics. The most effective phase difference for the reduction of reattachment length is obtained at 30$^{\circ}$, and for the maximum mixing enhancement is obtained at 270$^{\circ}$. For the phase difference 210$^{\circ}$, the reattachment length and mixing efficiency are almost the same as those of no-pulsation. Dynamics and interactions of vortical structures in the shear layers developed between two jet flows and between annular jet and chamber flow were studied. The mechanism of mixing enhancement was also discussed.