Passive Scalar Research Articles

Detection of Passive Scalar Interface Directly from PIV Particle Images in Inhomogeneous Turbulent Flows

This article proposes a technique to estimate the cross-sectional scalar interface (outer boundary) in an inhomogeneous turbulent flow from a conditioned particle image velocimetry (PIV) experiment, which is suitable for medium to high Reynolds numbers. The scalar interface is estimated directly by using conditioned PIV particle images which have distinguishably high particle seeding density in the area of interest, whereas conventionally in water based experiments, scalar interface is often determined from planar laser induced fluorescence (PLIF) or equivalent dye images. By comparing quantities in the vicinity of this scalar interface, it also shows that in terms of separate turbulent and non-turbulent regions, this technique could also replace the function of PLIF images in water experiments, with slightly lower spatial resolution. At the same time, if velocity information is also required simultaneously then the cost of a separate camera-laser system can be saved. The effect of particle field inhomogeneity on the PIV accuracy can be well reduced to an insignificant level by an image local normalisation treatment. This article shows that the interfacial layer could be detected fairly accurately by enhancing the particle images by wavelet based thresholding methods. The degree of detection accuracy is quantified by synthetic particle image analyses, where a scalar interface can be artificially pre-defined. The proposed technique is tested in two water based experiments but is expected to be particularly useful in gas-phase based experiments or some combustion applications, where liquid-phase dye cannot be applied.

Fuel and chemistry effects in high Karlovitz premixed turbulent flames

Direct numerical simulations of turbulent premixed flames at high Karlovitz numbers are performed using detailed chemistry. Different fuels, chemical mechanisms, and equivalence ratios are considered and their effects on turbulent flame speed, geometry of the reaction zone, and fuel burning rate are analyzed. Differential diffusion effects are systematically isolated by performing simulations with both non-unity and unity Lewis numbers. Heavy fuels with above unity Lewis numbers are considered. In the unity Lewis number limit, the n-heptane, iso-octane, toluene, and methane flames at a given reaction zone Karlovitz number present similar normalized turbulent flame speeds and fuel burning rates close to their respective laminar values. When differential diffusion effects are included, the turbulent flame speeds are lower than their unity Lewis number counterparts due to a reduction in the fuel burning rate. The turbulent reaction zone surface areas increase with the turbulence intensity but are not strongly affected by fuel, equivalence ratio, chemical mechanism, or differential diffusion. The geometry of the reaction zone is studied through the probability density functions of strain rate and curvature which are very similar when normalized by Kolmogorov scales at the reaction zone. The dependence of the chemical source terms on the scalar dissipation rate in the unity Lewis number case is shown and the distributions of scalar dissipation rate on the reaction surface are similar to those of passive scalars in homogeneous isotropic turbulence. The reduced burning rates in the presence of differential diffusion are discussed. The present results indicate that mean turbulent flame properties such as burning velocity and fuel consumption can be predicted with the knowledge of only a few global laminar flame properties. Once normalized by the corresponding laminar flame quantities, fuel and chemistry effects in high Karlovitz number premixed turbulent flames are mostly limited to differential diffusion.

Phase Segregation of Passive Advective Particles in an Active Medium.

Localized contractile configurations or asters spontaneously appear and disappear as emergent structures in the collective stochastic dynamics of active polar actomyosin filaments. Passive particles which (un)bind to the active filaments get advected into the asters, forming transient clusters. We study the phase segregation of such passive advective scalars in a medium of dynamic asters, as a function of the aster density and the ratio of the rates of aster remodeling to particle diffusion. The dynamics of coarsening shows a violation of Porod behavior; the growing domains have diffuse interfaces and low interfacial tension. The phase-segregated steady state shows strong macroscopic fluctuations characterized by multiscaling and intermittency, signifying rapid reorganization of macroscopic structures. We expect these unique nonequilibrium features to manifest in the actin-dependent molecular clustering at the cell surface.

Theoretical study of anisotropic MHD turbulence with low magnetic Reynolds number

Flows of electrically conducting fluids under the action of external magnetic field present an example of strongly anisotropic turbulence. Such flows are not only important for different engineering applications, but also provide an interesting framework for studies of quasi-two-dimensional turbulence with strongly modified transport properties in easily controllable laboratory experiments. We present theoretical results that advance our understanding of magnetohydrodynamic (MHD) flows with low magnetic Reynolds number by treating this phenomenon within the quasi-normal scale elimination (QNSE) theory. Previous applications of the theory to turbulent flows with stable stratification and solid body rotation have demonstrated that QNSE is a powerful tool for studies of anisotropic turbulent flows. We derive expressions for scale-dependent eddy viscosities and eddy diffusivities in the directions parallel and normal to the external magnetic field and investigate progressive anisotropization of turbulent transport of momentum and passive scalar. The theory yields analytical expressions for anisotropic one-dimensional spectra of MHD turbulence. In particular, the theory sheds light upon the modification of the Kolmogorov k−5/3 spectrum by anisotropic Ohmic (Joule) dissipation.

An evaluation of gas transfer velocity parameterizations during natural convection using DNS

AbstractDirect numerical simulations (DNS) of free surface flows driven by natural convection are used to evaluate different methods of estimating air‐water gas exchange at no‐wind conditions. These methods estimate the transfer velocity as a function of either the horizontal flow divergence at the surface, the turbulent kinetic energy dissipation beneath the surface, the heat flux through the surface, or the wind speed above the surface. The gas transfer is modeled via a passive scalar. The Schmidt number dependence is studied for Schmidt numbers of 7, 150 and 600. The methods using divergence, dissipation and heat flux estimate the transfer velocity well for a range of varying surface heat flux values, and domain depths. The two evaluated empirical methods using wind (in the limit of no wind) give reasonable estimates of the transfer velocity, depending however on the surface heat flux and surfactant saturation. The transfer velocity is shown to be well represented by the expression, , where is a constant, is the buoyancy flux, is the kinematic viscosity, is the Schmidt number, and the exponent depends on the water surface characteristics. The results suggest that and and for slip and no‐slip boundary conditions at the surface, respectively. It is further shown that slip and no‐slip boundary conditions predict the heat transfer velocity corresponding to the limits of clean and highly surfactant contaminated surfaces, respectively.

Passive scalars in turbulent channel flow at high Reynolds number

We study passive scalars in turbulent plane channels at computationally high Reynolds number, thus allowing us to observe previously unnoticed effects. The mean scalar profiles are found to obey a generalized logarithmic law which includes a linear correction term in the whole lower half-channel, and they follow a universal parabolic defect profile in the core region. This is consistent with recent findings regarding the mean velocity profiles in channel flow. The scalar variances also exhibit a near universal parabolic distribution in the core flow and hints of a sizeable log layer, unlike the velocity variances. The energy spectra highlight the formation of large scalar-bearing eddies with size proportional to the channel height which are caused by a local production excess over dissipation, and which are clearly visible in the flow visualizations. Close correspondence of the momentum and scalar eddies is observed, with the main difference being that the latter tend to form sharper gradients, which translates into higher scalar dissipation. Another notable Reynolds number effect is the decreased correlation of the passive scalar field with the vertical velocity field, which is traced to the reduced effectiveness of ejection events.

Effect of Oscillation Structures on Inertial-Range Intermittence and Topology in Turbulent Field

AbstractUsing the incompressible isotropic turbulent fields obtained from direct numerical simulation and large-eddy simulation, we studied the statistics of oscillation structures based on local zero-crossings and their relation with inertial-range intermittency for transverse velocity and passive scalar. Our results show that for both the velocity and passive scalar, the local oscillation structures are statistically scale-invariant at high Reynolds number, and the inertial-range intermittency of the overall flow region is determined by the most intermittent structures characterized by one local zero-crossing. Local flow patterns conditioned on the oscillation structures are characterized by the joint probability density function of the invariants of the filtered velocity gradient tensor at inertial range. We demonstrate that the most intermittent regions for longitudinal velocity tend to lay at the saddle area, while those for the transverse velocity tend to locate at the vortex-dominated area. The connection between the ramp-cliff structures in passive scalar field and the corresponding saddle regions in the velocity field is also verified by the approach of oscillation structure classification.

On spectral energy transfer in convective turbulence

The specific features of cascade processes in fully developed turbulence that exists against the background of a density (temperature) gradient are investigated. The gradient is either parallel (turbulence in a stably stratified medium) or anti-parallel (convective turbulence) to the gravitational force. We mainly address the question of realizability of the Obukhov-Boldgiano regime (OB), which implies a balance between buoyancy forces and nonlinear interactions in an extended part of the inertial range. There are no foolproof evidences that prove the existence of OB, although the fragments of spectra with slopes, similar to “-11/5” and “-7/5”, have been observed in some numerical simulations of convective turbulence. This paper presents a critical comparison of these results with the results obtained using a shell model, which allows us to perform simulations in a wide range of governing parameters. The shell model is introduced by generalizing a class of helical shell models to the case of buoyancy driven turbulence. It is shown that, in fully developed turbulence that is characterized by a range of scales with a constant spectral energy flux, the buoyancy forces cannot compete with nonlinear interactions and, therefore, have no impact on the inertial range dynamics. In convective turbulence, exactly these forces provide turbulence with energy, but only at the largest scales. Under conditions of stable stratification, the buoyancy forces reduce the energy of turbulent pulsations. In both cases the OB regime does not appear in the inertial range, where the Kolmogorov’s “-5/3” law is established, and the temperature behaves like a passive scalar. Our simulations indicate that the previous interpretations of the observed deviations from the “-5/3” spectrum as the OB regime are wrong because they appear in the case of an insufficient separation between the buoyancy and dissipation scales.

A structure-based model for the transport of passive scalars in homogeneous turbulent flows

A structure-based model has been constructed, for the first time, for the study of passive scalar transport in turbulent flows. The scalar variance and the large-scale scalar gradient variance are proposed as the two turbulence scales needed for closure of the scalar equations in the framework of the Interacting Particle Representation Model (IPRM). The scalar dissipation rate is modeled in terms of the scalar variance and the large-scale enstrophy of the velocity field. Model parameters are defined by matching the decay rates in freely isotropic turbulence. The model is validated for a large number of cases of deformation in both fixed and rotating frames, showing encouraging results. The model shows good agreement with DNS results for the case of pure shear flow in the presence of either transverse or streamwise mean scalar gradient, while it correctly predicts the presence of direct cascade for the passive scalar variance in two dimensional isotropic turbulence.

CFD Modelling of a Two Stroke Engine to Predict and Reduce Short Circuit Losses

<div class="section abstract"><div class="htmlview paragraph">One of the major reason for lower efficiency and higher unburned hydrocarbon and carbon monoxide emission for two stroke engine is short circuit losses during the scavenging process. An attempt has been made in this study to understand and improve this phenomenon. A three dimensional transient CFD model is developed for a loop scavenged, Schnullar type, 70 cc two stroke engine. Three major processes, namely, blow down (expansion); scavenging and compression have been modelled. The model is validated with PIV measurement done in motoring mode. Model is also validated with experimental data for trapping efficiency with Watson method and for in-cylinder pressure during expansion, blow down and intake events. A good correlation is observed between experimental and simulation results. CFD model is used to quantify various parameters, such as, delivery ratio, trapping efficiency, scavenging efficiency, and amount of fresh mass short circuit at different load and speed points. Around 20 to 25% short circuit losses are observed at all the load cases analyzed. The mechanism for this short circuit loss is understood with the help of a passive scalars based visualization method. Two major root causes identified are, port design and exhaust pressure wave dynamics. Three different designs of ports are analyzed. With the best design, the short circuit loss is reduced by 12%. Same design has been tested on a chassis dynamo-meter, that resulted into a reduction of 10% in HC (hydro-carbon) emission in a mass emission test on a drive cycle and 10% to 25% improvement in WOT (wide open throttle) wheel force in mid and higher speed operating points.</div></div>

Squaring the Circle: Geometric Skewness and Symmetry Breaking for Passive Scalar Transport in Ducts and Pipes.

We study the role geometry plays in the emergence of asymmetries in diffusing passive scalars advected by pressure-driven flows in ducts and pipes of different aspect ratios. We uncover nonintuitive, multi-time-scale behavior gauged by a new statistic, which we term "geometric skewness" S^{G}, which measures instantaneously forming asymmetries at short times due to flow geometry. This signature distinguishes elliptical pipes of any aspect ratio, for which S^{G}=0, from rectangular ducts whose S^{G} is generically nonzero, and, interestingly, shows that a special duct of aspect ratio ≈0.53335 behaves like a circular pipe as its geometric skewness vanishes. Using a combination of exact solutions, novel short-time asymptotics, and Monte Carlo simulations, we establish the relevant time scales for plateaus and extrema in the evolution of the skewness and kurtosis for our class of geometries. For ducts limiting to channel geometries, we present new exact, single-series formulas for the first four moments on slices used to benchmark Monte Carlo simulations.

Passive scalar mixing in Mc

We investigate passive scalar mixing in spatially developing supersonic shear layer flows formed by two planar streams by means of large eddy simulation. After validation of the numerical procedures employing a high-order hybrid WENO/compact scheme by comparing the results of simulation with the results obtained from a well characterized experimental case, the effects of the convective Mach number, Mc, flow velocity ratio, r = U1/U2, and fluid density ratio, s = ρ1/ρ2, between Stream 1 and Stream 2 on passive scalar mixing are considered by examining the variation of mixing layer thickness and the mixing efficiency represented by the transport of the passive scalar. Mc is specified from 0.2 to 0.8. The evolution of large-scale coherent structures is well reproduced, with vortices undergoing rolling up, pairing, merging, and breaking up. The mixing layer thickness and mixing efficiency both decrease as Mc increases. As s increases, the mixing layer thickness increases, and the mixing efficiency of an entrained fluid decreases. As r increases, the mixing layer thickness decreases while the mixing efficiency increases. While the present results are not applicable to the examination of micro-mixing properties, which require assessment by experimental methods or high computing cost direct numerical simulation, they are useful for evaluating the effects of different flow parameters on macro-performance, which is equally important for scramjet combustor design and evaluation in engineering.

Global chaotization of fluid particle trajectories in a sheared two-layer two-vortex flow.

In a two-layer quasi-geostrophic approximation, we study the irregular dynamics of fluid particles arising due to two interacting point vortices embedded in a deformation flow consisting of shear and rotational components. The two vortices are arranged within the bottom layer, but an emphasis is on the upper-layer fluid particle motion. Vortices moving in one layer induce stirring of passive scalars in the other layer. This is of interest since point vortices induce singular velocity fields in the layer they belong to; however, in the other layer, they induce regular velocity fields that generally result in a change in passive particle stirring. If the vortices are located at stagnation points, there are three different types of the fluid flow. We examine how properties of each flow configuration are modified if the vortices are displaced from the stagnation points and thus circulate in the immediate vicinity of these points. To that end, an analysis of the steady-state configurations is presented with an emphasis on the frequencies of fluid particle oscillations about the elliptic stagnation points. Asymptotic relations for the vortex and fluid particle zero-oscillation frequencies are derived in the vicinity of the corresponding elliptic points. By comparing the frequencies of fluid particles with the ones of the vortices, relations between the parameters that lead to enhanced stirring of fluid particles are established. It is also demonstrated that, if the central critical point is elliptic, then the fluid particle trajectories in its immediate vicinity are mostly stable making it harder for the vortex perturbation to induce stirring. Change in the type of the central point to a hyperbolic one enhances drastically the size of the chaotic dynamics region. Conditions on the type of the central critical point also ensue from the derived asymptotic relations.

Power and nonpower laws of passive scalar moments convected by isotropic turbulence.

The scaling behavior of the moments of two passive scalars that are excited by two different methods and simultaneously convected by the same isotropic steady turbulence at R_{λ}=805 and Sc=0.72 is studied by using direct numerical simulation with N=4096^{3} grid points. The passive scalar θ is excited by a random source that is Gaussian and white in time, and the passive scalar q is excited by the mean uniform scalar gradient. In the inertial convective range, the nth-order moments of the scalar increment δθ(r) do not obey a simple power law, but have the local scaling exponents ξ_{n}^{θ}+β_{n}log(r/r_{*}) with β_{n}>0. In contrast, the local scaling exponents of q have well-developed plateaus and saturate with increasing order. The power law of passive scalar moments is not trivial. The universality of passive scalars is found not in the moments, but in the normalized moments.

The Spatio-temporal Statistical Structure and Ergodic Behaviour of Scalar Turbulence Within a Rod Canopy

Connections between the spatial and temporal statistics of turbulent flow, and their possible convergence to ensemble statistics as assumed by the ergodic hypothesis, are explored for passive scalars within a rod canopy. While complete ergodicity is not expected to apply over all the spatial domain within such heterogeneous flows, the fact that canopy turbulence exhibits self-similar characteristics at a given depth within the canopy encourages a discussion on necessary conditions for an ‘operational’ ergodicity framework. Flows between roughness elements such as within canopies exhibit features that distinguish them from their well-studied classical boundary-layer counterparts. These differences are commonly attributed to short-circuiting of the energy cascade and the prevalence of intermittent von Karman vortex streets in the deeper layers of the canopy. Using laser-induced fluorescence measurements at two different depths within a rod canopy situated in a large flume, the spatio-temporal statistical properties and concomitant necessary conditions for ergodicity of passive scalar turbulence statistics are evaluated. First, the integral time and length scales are analyzed and their corresponding maximum values are used to guide the construction of an ensemble of independent realizations from repeated spatio-temporal concentration measurements. As a statistical analysis for an operational ergodicity check, a Kolmogorov–Smirnov test on the distributions of temporal and spatial concentration series against the ensemble was conducted. The outcome of this test reveals that ergodicity is reasonably valid over the entire domain except close to the rod elements where wake-induced inhomogeneities and damped turbulence prevail. The spatial concentration statistics within a grid-cell (square domain formed by four corner rods) appear to be less ergodic than their temporal counterparts, which is not surprising given the periodicity and persistence of von Karman vortices in the flow field. Also, a local advection velocity of dominant eddies is inferred using lagged cross-correlations of scalar concentration time series at different spatial locations. The computed probability density function of this advection velocity agrees well with the laser Doppler anemometry measurements for the same rod canopy.

Hyperbolicity in the Ocean

Some manifestations of hyperbolicity in the ocean, the important concept in dynamical systems theory, are discussed. It is shown how to identify hyperbolic points, hyperbolic trajectories and their stable and unstable manifolds solving advection equations for passive scalars in a satellite-derived AVISO velocity field and computing finite-time Lyapunov exponents by the singular-value decomposition method. To validate our simulation we use available tracks of oceanic drifters following near surface currents in some areas in the Northwestern Pacific Ocean. The tracks illustrate how drifters “feel” the presence of hyperbolic points, hyperbolic trajectories and stable and unstable manifolds and change abruptly their trajectories when approaching a hyperbolicity region.

Direct numerical simulation of near-wall turbulent flow and ionic mass transport in electrochemical reactors using a hybrid finite element/spectral method

An experimental study and direct numerical simulation of near-wall turbulent flow and ionic mass transport was performed in a cylindrical electrochemical reactor for Reynolds numbers up to 18,000 (friction Reynolds number of 1245). The experimental part involved the determination of velocity gradients close to the wall of a rotating cylinder. These velocity gradients are determined by electrochemical mass transport measurements to a rotating cylinder electrode and to micro-electrodes embedded in a rotating cylinder. Simulation of the fluid flow with passive scalar is accomplished using a hybrid finite element method (FEM) in meridian planes coupled to a Fourier expansion in the azimuthal direction. It was shown that the method reproduces the turbulent flow statistics with high accuracy. Due to its high parallel efficiency and the possibility of stretched meshes in finite element planes near the wall, this hybrid method is suitable to study laboratory electrochemical systems. Coupling with mass and energy transport equations allows prediction of the concentration and temperature fields. This feature makes the model suitable for large-scale design and optimization of different electrochemical processes where accurate prediction of near-wall turbulence and ionic mass transport is required.

Study of the interference of plumes released from two near-ground point sources in an open channel

The dispersion and mixing of passive scalars released from two near-ground point sources into an open-channel flow are studied using direct numerical simulation. A comparative study based on eight test cases has been conducted to investigate the effects of Reynolds number and source separation distance on the dispersion and interference of the two plumes. In order to determine the nonlinear relationship between the variance of concentration fluctuations of the total plume and those produced by each of the two plumes, the covariance of the two concentration fields is studied in both physical and spectral spaces. The results show that at the source height, the streamwise evolution of the cross correlation between the fluctuating components of the two concentration fields can be classified into four stages, which feature zero, destructive and constructive interferences and a complete mixing state. The characteristics of these four stages of plume mixing are further confirmed through an analysis of the pre-multiplied co-spectra and coherency spectra. From the coherency spectrum, it is observed that there exists a range of ‘leading scales’, which are several times larger than the Kolmogorov scale but are smaller than or comparable to the scale of the most energetic eddies of turbulence. At the leading scales, the mixing between the two interfering plumes is the fastest and the coherency spectrum associated with these scales can quickly approach its asymptotic value of unity.

Passive scalars, moving boundaries, and Newton's law of cooling

We study the evolution of passive scalars in both rigid and moving slab-like domains, in both horizontally periodic and infinite contexts. The scalar is required to satisfy Robin-type boundary conditions corresponding to Newton's law of cooling, which lead to nontrivial equilibrium configurations. We study the equilibration rate of the passive scalar in terms of the parameters in the boundary condition and the equilibration rates of the background velocity field and moving domain.

Footprint Evaluation for Flux and Concentration Measurements for an Urban-Like Canopy with Coupled Lagrangian Stochastic and Large-Eddy Simulation Models

A footprint algorithm, based on a Lagrangian stochastic (LS) model embedded into a parallelized large-eddy simulation (LES) model, is used for the evaluation of flux and concentration footprints of passive scalars in flow in and above an urban-like canopy layer of a neutrally stratified $$440 \hbox { m}$$ deep boundary layer. The urban-like canopy layer is realized by an aligned array of cuboids whose height H is $$40\hbox { m}$$ . The canopy flow involves strong small-scale inhomogeneities although it is homogeneous at the large scale. The source height is $$1\hbox { m}$$ (0.025H) above the ground in the street canyons, roughly mimicking traffic emissions. Footprints are evaluated for four heights from 0.25H to 2.5H, and for up to eight different horizontal sensor positions per measurement height, comprising sensor positions inside as well as outside of the street canyon that extend perpendicular to the mean wind direction. The LES-LS footprints are compared with footprints estimated by a conventional model (Kormann and Meixner, in Boundary-Layer Meteorol 99:207–224, 2001). It becomes evident that the local heterogeneity of the flow has a considerable impact on flux and concentration footprints. As expected, footprints for measurements within and right above the canopy layer show complex and completely different footprint shapes compared to the ellipsoidal shape obtained from conventional footprint models that assume horizontal homogeneity of the turbulent flow as well as the sources of passive scalars. Our results show the importance of street-canyon flow and turbulence for the vertical mixing of scalar concentration.