Fraction Fluctuations Research Articles

Quantifying the long-range structure of foams and other cellular patterns with hyperuniformity disorder length spectroscopy.

We investigate the local and long-range structure of several space-filling cellular patterns: bubbles in a quasi-two-dimensional foam, and Voronoi constructions made around points that are uncorrelated (Poisson patterns), low discrepancy (Halton patterns), and displaced from a lattice by Gaussian noise (Einstein patterns). We study local structure with distributions of quantities including cell areas and side numbers. The former is the widest for the bubbles making foams the most locally disordered, while the latter show no major differences between the cellular patterns. To study long-range structure, we begin by representing the cellular systems as patterns of points, both unweighted and weighted by cell area. For this, foams are represented by their bubble centroids and the Voronoi constructions are represented by the centroids as well as the points from which they are created. Long-range structure is then quantified in two ways: by the spectral density, and by a real-space analog where the variance of density fluctuations for a set of measuring windows of diameter D is made more intuitive by conversion to the distance h(D) from the window boundary where these fluctuations effectively occur. The unweighted bubble centroids have h(D) that collapses for the different ages of the foam with random Poissonian fluctuations at long distances. The area-weighted bubble centroids and area-weighted Voronoi points all have constant h(D)=h_{e} for large D; the bubble centroids have the smallest value h_{e}=0.084sqrt[〈a〉], meaning they are the most uniform. Area-weighted Voronoi centroids exhibit collapse of h(D) to the same constant h_{e}=0.084sqrt[〈a〉] as for the bubble centroids. A similar analysis is performed on the edges of the cells and the spectra of h(D) for the foam edges show h(D)∼D^{1-ε} where ε=0.30±0.15.

Computational fluid dynamics modelling of multiphase flows in double elbow geometries

This study investigates the effects of elbow on the transition and development of multiphase flow using computational fluid dynamics modelling techniques. The Eulerian - Multifluid VOF model coupled with an Interfacial Area Transport Equation has been employed to simulate air-water two-phase flow in a pipe with two standard 90 degree elbows mounted in series. Turbulence effects were accounted for by the RNG k-ε model. The effects of separation distance on two-phase flow development have been studied for initial slug and churn flow regimes. Computational fluid dynamics simulation results of phase distribution and time series of void fraction fluctuations were obtained and they showed good agreement with available experimental data. The results show that for initial slug flow regime, there is no flow regime transformation upstream and downstream of the two elbows. While at initial churn flow regime, flow regime transformation occurs at different sections of the flow domain before and after the two elbows. It was noticed that irrespective of the flow regime, the amplitudes and frequencies of void fraction fluctuation become smaller as the fluid flows along the pipe. Changes in the separation distance between the two elbows have larger effects on the flow at churn flow regime.

Analysis of dipole noise level characteristics of NACA0015 hydrofoil under different working conditions

In this paper, the flow field around NACA0015 hydrofoil is calculated under the condition of two-phase cavitating flow to provide a theoretical guidance for reducing the cavitation noise. A modified turbulence model coupled with the Zwart cavitation model is used to calculate the flow field. According to the computed sound source data, the dipole sound pressure distribution diagrams for the extremely short time and the complete time around the hydrofoil under different working conditions are obtained. The sound pressure distribution and the sound pressure amplitude are analyzed in detail. In addition, the field points around the hydrofoil are selected to generate the corresponding frequency response function curves, which are analyzed from the aspects of the trend, the variation and the extreme value. The results show that the dipole characteristics are gradually diminished and finally disappear with the increase of the frequency. At the frequency of the vapor volume fraction fluctuation, the noise level at the field point will have an extreme value.

Turbulent Bubble-Laden Channel Flow of Power-Law Fluids: A Direct Numerical Simulation Study

The influence of non-Newtonian fluid behavior on the flow statistics of turbulent bubble-laden downflow in a vertical channel is investigated. A Direct Numerical Simulation (DNS) study is conducted for power-law fluids with power-law indexes of 0.7 (shear-thinning), 1 (Newtonian) and 1.3 (shear-thickening) in the liquid phase at a gas volume fraction of 6%. The flow is driven downward by a constant volumetric flow rate corresponding to a friction Reynolds number of Reτ≈127.3. The Eötvös number is varied between Eo=0.3125 and Eo=3.75 in order to investigate the influence of quasi-spherical as well as wobbling bubbles and thus the interplay of the bubble deformability with the power-law behavior of the liquid bulk. The resulting first- and second-order fluid statistics, i.e., the gas fraction, mean velocity and velocity fluctuation profiles across the channel, show clear trends in reply to varying power-law indexes. In addition, it was observed that the bubble oscillations increase with decreasing power-law index. In the channel core, the bubbles significantly increase the dissipation rate, which, in contrast to its behavior at the wall, shows similar orders of magnitude for all power-law indexes.

Strongly reduced lattice thermal conductivity in Sn-doped rare-earth (M) filled skutterudites M x Co4Sb12-y Sn y , promoted by Sb-Sn disordering and phase segregation.

CoSb3 thermoelectric skutterudite has been filled with rare-earth metals (M = La, Ce, Yb) and partially doped with Sn in specimens of MxCo4Sb12−ySny stoichiometry. This has been achieved under high-pressure conditions at 3.5 GPa in a piston-cylinder hydrostatic press. A structural investigation using synchrotron X-ray diffraction data reveals a phase segregation in twin skutterudite phases with filling fraction fluctuation and different unit-cell sizes. As a result of three effects acting as phonon scatterers, namely the rattling effect of M at the wide 8a cages of the cubic Im3̄ structure, the phase segregation, and the intrinsic disorder introduced by Sn substitution at the Sb sublattice, the total thermal conductivity (κ) dramatically falls to reach minimum values under 2 W m−1 K−1, well below those typically exhibited by other thermoelectric materials based upon single-filled skutterudites. The power factor is substantially enhanced to 1.11 mW m−1 K−2 in Yb0.5Co4Sb11.6Sn0.4 with respect to the unfilled composition, as a result of the charge transfer promoted by the filler.

Large Eddy Simulation of low Reynolds number turbulent hydrogen jets - Modelling considerations and comparison with detailed experiments

The main objective of this work is to apply Large Eddy Simulation (LES) on hydrogen subsonic round jets in order to evaluate modelling strategies and to provide guidelines for similar applications. The ADREA-HF code and the experiments conducted by Sandia National Laboratories are used for that purpose. These experiments are very suitable for LES studies because turbulent fluctuations have been measured which is something rare in hydrogen experiments. Hydrogen is released vertically from a small orifice of 1.91 mm diameter into stagnant environment. Three experimental cases are simulated with different Reynolds number at the release area, namely 885, 1360 and 2384. Hydrogen mass fraction and velocity mean values and fluctuations are compared against the experimental data. Several grid resolutions are used to assess the effect on the results, using mainly the Smagorinsky subgrid scale model. In the lowest Reynolds number case, an Implicit LES code, used independently from a different scientific group, is also tested. In this case, the performance of the RNG-LES subgrid scale model of the ADREA-HF code is also examined. Additionally, the effect of Smagorinsky constant and of the Van Driest correction is evaluated. The amount of the resolved turbulence and of the velocity spectra are presented. Finally, the effect of the release modelling is discussed. The analysis shows that even a coarse discretization of the release area can give acceptable results for hydrogen safety engineering applications. However, dense grids are required for the more accurate prediction of the turbulent characteristics. The two LES codes gave similar results and the overall agreement with the experiment was satisfactory.

Dynamics of entropy wave generation in a simplified model of gas turbine combustor: A theoretical investigation

Entropy noise remains as a largely unexplored mechanism of combustion generated noise. Currently, little is known about the production sources of entropy waves in flames. To address this issue, the present work puts forward a theoretical investigation of the generation of entropy waves in a one-dimensional, ducted flow. A linear theory is developed for the dynamic responses of different sources of unsteady entropy generation including thermal, hydrodynamic, pressure, and chemical irreversibility. For the first time in the literature, dynamics of chemical sources of unsteady entropy generation are investigated extensively. It is found that the mixture fraction fluctuations are responsible for the production of almost all unsteady chemical entropy and the effect of chemical potential is negligibly small. For the Strouhal numbers less than unity, fluctuations in pressure are the most significant source of the overall generation of unsteady entropy. However, at higher frequencies, mixture fraction fluctuations dominate the generation of entropy wave. The cut-off frequency for the generation of entropy wave is shown to depend not only on the thermal and hydrodynamic characteristics of the flame but also on the chemical properties of the downstream gases. It is further argued that the transfer function of entropy generation for a thin flame may feature an unrealistically high amplitude. This study shows that neglecting the chemical sources of an entropy wave can result in wrong predictions of the combustor acoustics and impede the suppression of combustion instabilities and noise.

Structure and stability characteristics of turbulent planar flames with inhomogeneous jet in a concentric flow slot burner

Turbulent flames with compositionally inhomogeneous mixtures are common in many combustion systems. Turbulent jet flames with a circular nozzle burner were used earlier to study the impact of inhomogeneous mixtures, and these studies showed that the nozzle radius affects the flame stability. Accordingly, planar turbulent flames with inhomogeneous turbulent jet are created in a concentric flow slot burner (CFSB) to avoid this effect in the present study. The stability characteristics, the mixing field structure, and the flame front structure were measured, and the correlations between stability and the mixing field structure were investigated. The mixture fraction field was measured in non-reacting jets at the nozzle exit using highly resolved Rayleigh scattering technique, and the flame front was measured in some selected turbulent flames using high-speed Planar Laser-Induced Fluorescence (PLIF) of OH technique. The data show strong correlations between flame stability and the range of mixture fraction fluctuations. The flames are highly stabilized within a mixing field environment with the range of fluctuation in mixture fraction close to the range of the flammability limits. The mixing field structure is also illustrated and discussed using a mixing regime diagram and showed that the scatter of the data of the different cases is consistent with the classified mixing regimes. Lean flames are stabilized in the current slot burner. The flame front structure topology varies consistently from thin, small curvature at the low level of turbulence and higher equivalence ratio to more wrinkled, larger curvature, but a thicker structure at a higher level of turbulence and lower equivalence ratio.

Coronal Electron Density Fluctuations Inferred from Akatsuki Spacecraft Radio Observations

Trans-coronal radio observations were taken during the 2011 observing campaign of the Akatsuki spacecraft through superior conjunction. The observed X-band (8.4 GHz) signals exhibit frequency fluctuations (FF) that are produced by temporal variations in electron density along the radio ray path. A two-component model for interpretation of the FF is proposed: FF scales largely with acoustic wave amplitude through the inner coronal regions where the sound speed dwarfs the solar wind outflow speed, while FF in the region of solar wind acceleration is dominated by the increased density oscillation frequency on the sensing path that results from bulk advection of the plasma inhomogeneities. An estimate of fractional electron density fluctuation is obtained from the mid-corona. A radial profile of slow solar wind speed is determined in the extended corona using mass-flux continuity principles. The coronal sonic point for slow solar wind is estimated to range from 4 to 5 solar radii from the heliocenter.

Thalamus is a common locus of reading, arithmetic, and IQ: Analysis of local intrinsic functional properties

Neuroimaging studies of basic achievement skills – reading and arithmetic – often control for the effect of IQ to identify unique neural correlates of each skill. This may underestimate possible effects of common factors between achievement and IQ measures on neuroimaging results. Here, we simultaneously examined achievement (reading and arithmetic) and IQ measures in young adults, aiming to identify MRI correlates of their common factors. Resting-state fMRI (rs-fMRI) data were analyzed using two metrics assessing local intrinsic functional properties; regional homogeneity (ReHo) and fractional amplitude low frequency fluctuation (fALFF), measuring local intrinsic functional connectivity and intrinsic functional activity, respectively. ReHo highlighted the thalamus/pulvinar (a subcortical region implied for selective attention) as a common locus for both achievement skills and IQ. More specifically, the higher the ReHo values, the lower the achievement and IQ scores. For fALFF, the left superior parietal lobule, part of the dorsal attention network, was positively associated with reading and IQ. Collectively, our results highlight attention-related regions, particularly the thalamus/pulvinar as a key region related to individual differences in performance on all the three measures. ReHo in the thalamus/pulvinar may serve as a tool to examine brain mechanisms underlying a comorbidity of reading and arithmetic difficulties, which could co-occur with weakness in general intellectual abilities.

Experimental investigation of the turbulent Schmidt number in supersonic film cooling with shock interaction

The interaction of an impinging shock and a supersonic helium cooling film is investigated experimentally by high-speed particle-image velocimetry. A laminar helium jet is tangentially injected into a turbulent air freestream at a freestream Mach number $Ma_\infty=2.45$. The helium cooling film is injected at a Mach number $Ma_i=1.30$ at a total temperature ratio $T_{0,i}/T_{0,\infty}=0.75$. A deflection $\beta=8\deg$ generates a shock that impinges upon the cooling film. A shock interaction case and a reference case without shock interaction are considered. The helium mass fraction fluctuations are measured and the turbulent mass flux as well as the turbulent Schmidt number are determined qualitatively. For comparison, large-eddy simulation (LES) results of a comparable flow configuration are used. The streamwise and wall-normal turbulent mass fluxes are in qualitative agreement with the LES data. The turbulent Schmidt number differs significantly from unity. Without shock interaction, the turbulent Schmidt number is in the range $0.5 \leq Sc_t \leq 1.5$ which is in agreement with the literature. With shock interaction, the turbulent Schmidt number varies drastically in the vicinity of the shock interaction. Thus, the experimental results confirm the numerical data showing a massively varying turbulent Schmidt number in supersonic film cooling flows, i.e., the standard assumption of a constant turbulent Schmidt number is valid neither without nor with shock interaction.

Experimental study of local solid volume fraction fluctuations in a liquid fluidized bed: Particles with a wide range of stokes numbers

In this study, the solid volume fraction fluctuations of different solid particles in a fluidized bed were measured using an Electrical Impedance Tomography system, which provides local fluctuation values. A wide range of particle Stokes numbers (122≤Stt≤3809) was tested by selecting specific particle sizes and densities. The results were compared with previous experimental studies. Since previous works measured only cross-sectional averages of the fluctuations, the local results of this study were spatially averaged for the comparison. The comparison showed an acceptable agreement in the level of RMS fluctuations. Importantly this study found that: (1) The strongest fluctuations always occurred at a narrow strip by the bed wall. Moving from the wall region towards the bed center, the magnitude of RMS fluctuations decreased. (2) The magnitude of local fluctuations was linked to the particle Stokes number (Stt), such that, at any given radial positions, the RMS fluctuations increased by increasing Stt. (3) Only limited agreement was observed among the trends of the measurements and the predictions of four existing mathematical and semiempirical models. The instantaneous local measurements conducted in this study are useful not only to examine currently available mathematical models, but they can also validate Computational Fluid Dynamics models of liquid fluidization.

Role of bubbling behaviour in segregation and mixing of binary gas-solids flow of particles with different density

Dynamics of segregation and mixing phenomena of binary gas-solids flow in fluidized beds is predominantly influenced by the bubbling behaviour. In the present work, we have investigated experimentally the effect of the local bubbling behaviour on the segregation and mixing phenomena of binary gas-solids flow with particles differing in density (of the same size) in a pseudo–2D rectangular fluidized bed. The bubbling characteristics were controlled using two different modes of air injection: uniform distributor and two-jet distributor under the same superficial gas velocity (UG). The local individual phase area fraction fluctuations of all the three phases were measured using the high-speed imaging. These measurements were further used to quantify the effects of bed composition, mode of air injection, and UG on the bubbling characteristics and eventually on the segregation/mixing behaviour. The present study shows that the use of the two-jet distributor led to an increase in the amplitude of the local gas-phase area fraction fluctuations in comparison to that of the uniform distributor and thus enhanced the mixing of the particles. Also, with an increase in the flotsam component in the mixture, due to increase in the bubble size and frequency, the bubble-induced mixing of the particles was enhanced further. The results reported here provide the understanding of the effect of local bubbling characteristics on the dynamics of segregation and mixing phenomena of binary mixtures with particles differing in density and also provide the much-needed database for validation of CFD-DEM and Eulerian multi-fluid CFD models.

Coherence properties of high-frequency wave field propagating through inhomogeneous ionosphere with anisotropic random irregularities of electron density: 1. Theoretical background

Rigorous analytic solution is constructed for the first of 2 s-order space position and frequency coherence function (which is alternatively also termed as symmetric) of the high-frequency wave field propagating through the stochastic transionospheric channel with the inhomogeneous layer of the background ionosphere and anisotropic fluctuations of the electron density in the approximation of the appropriate Markov equation. It is obtained employing the anisotropic parabolic model of the effective structure function of the fractional electron density fluctuations with two different scales along and across the Earth's magnetic field. The explicit analytic solution is presented, which is capable of describing the coherence properties of the field for any given inhomogeneous distribution of the electron density in the background ionosphere along a path of propagation. The procedure of calibrating the spatial scales of the anisotropic parabolic model of the electron density fluctuations along and across the Earth's magnetic field lines in order to provide the adequate solution to correspond to the realistic anisotropic inverse power law spectrum of the electron density fluctuations is presented in the companion paper.

Speed-adjustable atomic beam of metastable helium for precision measurement

A bright beam of metastable helium atoms is useful in various studies. Laser spectroscopy of helium in an atomic beam can provide a determination of the fine-structure constant and the nuclear charge radius, towards a test of quantum electrodynamics (QED). In these measurements, it is necessary to control not only the internal quantum state but also the translation motion of the helium atom. Here we present a setup producing an intense and speed-adjustable continuous beam of helium atoms. By using a combination of laser cooling, focusing, and deflection, helium atoms are prepared at the single quantum state of ${2}^{\phantom{\rule{0.16em}{0ex}}3}{S}_{1}$ ($m=0$), with a very narrow distribution of the longitudinal speed ($\ensuremath{\delta}{v}_{z}l\ifmmode\pm\else\textpm\fi{}4.5$ m/s). At the same time, we obtain a flux of $1.8\ifmmode\times\else\texttimes\fi{}{10}^{13}$ (atoms/s)/sr with a fractional fluctuation below 0.02%. The atomic-beam quality was investigated by laser spectroscopy, indicating a considerable improvement over those used in previous helium precision-spectroscopy measurements.

Magnetisation Processes in Geometrically Frustrated Spin Networks with Self-Assembled Cliques

Functional designs of nanostructured materials seek to exploit the potential of complex morphologies and disorder. In this context, the spin dynamics in disordered antiferromagnetic materials present a significant challenge due to induced geometric frustration. Here we analyse the processes of magnetisation reversal driven by an external field in generalised spin networks with higher-order connectivity and antiferromagnetic defects. Using the model in (Tadić et al. Arxiv:1912.02433), we grow nanonetworks with geometrically constrained self-assemblies of simplexes (cliques) of a given size n, and with probability p each simplex possesses a defect edge affecting its binding, leading to a tree-like pattern of defects. The Ising spins are attached to vertices and have ferromagnetic interactions, while antiferromagnetic couplings apply between pairs of spins along each defect edge. Thus, a defect edge induces frustrated triangles per n-clique participating in a larger-scale complex. We determine several topological, entropic, and graph-theoretic measures to characterise the structures of these assemblies. Further, we show how the sizes of simplexes building the aggregates with a given pattern of defects affects the magnetisation curves, the length of the domain walls and the shape of the hysteresis loop. The hysteresis shows a sequence of plateaus of fractional magnetisation and multiscale fluctuations in the passage between them. For fully antiferromagnetic interactions, the loop splits into two parts only in mono-disperse assemblies of cliques consisting of an odd number of vertices n. At the same time, remnant magnetisation occurs when n is even, and in poly-disperse assemblies of cliques in the range . These results shed light on spin dynamics in complex nanomagnetic assemblies in which geometric frustration arises in the interplay of higher-order connectivity and antiferromagnetic interactions.

Nature and magnitude of operating forces in a horizontal bend conveying gas-liquid slug flows

Operating forces and magnitude of loads from gas-liquid slug flows exerted on a horizontally orientated 90o bend are investigated. The distributed forces are either Newtonian, associated with the fluids motion or Configurational, inherent to the internal distributions of the phases. The forces are derived through the conventional balances of mass and linear momentum arising from the volume of fluid (VOF) description of gas-liquid flows. The study uses the integral form of the momentum balance to estimate the operating forces budget. Invoking dynamical time scales separation discloses the connection of the Lamb vector (vortex-force) to the local time rate of momentum. An interesting outcome being an explicit expression for Favre-Reynolds stress that reveals the contribution of void fraction fluctuations in the redistribution of the stress across the interface. Numerical simulations are performed to determine the magnitude of Newtonian loads on bend using a segmented domain technique to represent the fully established slug flow regime. The time-dependent traces of the relevant flow variables such as liquid hold-up, flow rates and resultant forces on the bend are recorded and analysed. Compared to the isotropic component, the deviatoric stresses are shown to have a marginal contribution to the total forces. It is also shown that loading cycles on bends are much higher than slugging cycles; this is an important feature for the structural integrity assessment of pipelines with bends.

Cavitation-Vortex-Pressure Fluctuation Interaction in a Centrifugal Pump Using Bubble Rotation Modified Cavitation Model Under Partial Load

Abstract Cavitation is a complicated phenomenon in the centrifugal pump. In this work, the improved unsteady calculation model based on bubble-rotation-based Zwart–Gerber–Belamri (BRZGB) cavitation model is used to investigate the cavitation-vortex-pressure fluctuation interaction in a centrifugal pump under partial load with experimental validation. Spatial–temporal evolution of cavitation can be classified into three stages: developing stage, shedding stage, and collapsing stage. The cavitation evolution period is found as 1/4T (T is impeller rotation period), corresponding to the frequency 4fi (fi is impeller rotation frequency). On the analysis of the relative vorticity transport equation, it is revealed that the cavity is stretched by the relative vortex stretching term (RVS) and developed by the relative vortex dilation term (RVD), and they have great influence on the cavity shedding. The peak value of pressure fluctuation intensity occurs near the vapor–liquid interface at cavity rear, and shifts downstream with the cavitation development. The hysteresis between the vapor volume fraction, vorticity, and pressure fluctuation is observed, and the variation of vapor volume fraction is the source of cavitation-vortex-pressure interaction.

Strain energy released by earthquake faulting with random slip components

SUMMARYThis study investigates the strain energy change caused by earthquake faulting. While conventional theories often assumed uniform stress change on the fault plane, this study supposed the slip fluctuation and non-uniform stress change on the fault. By using a stochastic modelling of the slip distribution, we represent the ensemble average of the strain energy change by using the power spectral density function of the slip fluctuation. This yields the following results. (1) When the initial stress is uniform and the earthquake contains a fluctuating slip distribution, the released strain energy is less than the one by an earthquake with the uniform stress change on the fault with the same seismic moment. (2) On the other hand, when the initial stress is fluctuating, the earthquake contains a fluctuating slip distribution, and the final stress is uniform, the released strain energy is more than the one by an earthquake with the uniform stress change on the fault. (3) The stress drop becomes large due to the fluctuating slip distribution from the viewpoint of the strain energy release. We derived the analytical solution of the stress change by using the power spectral density function of the random slip fluctuation. (4) The strain energy change is proportional to the seismic moment when ${\epsilon ^2}/a \propto {( {{M_0}} )^{ - 1/3}}$ (${\epsilon ^2}$ is the variance of the fractional slip fluctuation and $a$ is the correlation distance). (5) The energy balance gives the value of initial stress that is required for the earthquake generation. In order to generate an earthquake, the initial stress needs to be larger than the sum of half of the stress drop and the apparent stress. In other words, earthquakes having rich short-wavelength components in the slip distribution are not generated under a low initial stress level.

Biogas production enhancement using nanocomposites and its combustion characteristics in a concentric flow slot burner

Biogas combustion is a very essential topic for the development of many industrial combustion systems and engines. This fuel can replace current fossil fuels used in burners, engines, and many other applications. Understanding the combustion characteristics of this fuel and its stability in highly turbulent flames of practical interest is the aim of this work. The percentage of CO2 in Biogas varies between 25% and 45%, which affects the combustion stability and flame structure. The present work shows that the generation of Biogas is improved by adding Ni-Co-Ferrite or Ni-ferrite nano-additives. In this work, we selected 25 flames of mixtures of natural gas and CO2, where the ratio of CO2 varies from 0% to 40%. The flames are generated in a concentric flow slot burner that produces planar two-dimensional flames. The stability characteristics and the flame structure were investigated. The flame structure is presented in the form of temperature profiles in some selected flames using fine wire thermocouple measurements. The stability characteristics are illustrated for two limits of lifted flames and blow out. The production rate of Biogas can be increased by almost 30% using nano-additives of Ni-Co-Ferrite or Ni-ferrite. The data show that the stability of the flames is affected significantly for the 40% CO2 mixture. Therefore, it is recommended to keep CO2 percentage up to 30% for stable turbulent Biogas flames. On the other hand, partially premixed flames are highly stable for a certain level of mixture inhomogeneity at a mixing length ratio of L/D = 16. At this level, the mixture fraction fluctuations are expected to be within the flammability limits range based on previous investigations in round jet configuration.