Rms Turbulent Velocity Research Articles

Generation of Near-Equipartition Magnetic Fields in Turbulent Collisionless Plasmas.

The mechanisms that generate "seed" magnetic fields in our Universe and that amplify them throughout cosmic time remain poorly understood. By means of fully kinetic particle-in-cell simulations of turbulent, initially unmagnetized plasmas, we study the genesis of magnetic fields via the Weibel instability and follow their dynamo growth up to near-equipartition levels. In the kinematic stage of the dynamo, we find that the rms magnetic field strength grows exponentially with rate γ_{B}≃0.4u_{rms}/L, where L/2π is the driving scale and u_{rms} is the rms turbulent velocity. In the saturated stage, the magnetic field energy reaches about half of the turbulent kinetic energy. Here, magnetic field growth is balanced by dissipation via reconnection, as revealed by the appearance of plasmoid chains. At saturation, the integral-scale wave number of the magnetic spectrum approaches k_{int}≃12π/L. Our results show that turbulence-induced by, e.g., the gravitational buildup of galaxies and galaxy clusters-can magnetize collisionless plasmas with large-scale near-equipartition fields.

Turbulent Parameters in the Middle Atmosphere: Theoretical Estimates Deduced from a Gravity Wave–Resolving General Circulation Model

Abstract We present a scaling analysis for the stratified turbulent and small-scale turbulent regimes of atmospheric flow with emphasis on the mesosphere. We distinguish rotating-stratified macroturbulence turbulence (SMT), stratified turbulence (ST), and small-scale isotropic Kolmogorov turbulence (KT), and we specify the length and time scales and the characteristic velocities for these regimes. It is shown that the buoyancy scale (Lb) and the Ozmidov scale (Lo) are the main parameters that describe the transition from SMT to KT. We employ the buoyancy Reynolds number and horizontal Froude number to characterize ST and KT in the mesosphere. This theory is applied to simulation results from a high-resolution general circulation model with a Smagorinsky-type turbulent diffusion scheme for the subgrid-scale parameterization. The model allows us to derive the turbulent root-mean-square (rms) velocity in the KT regime. It is found that the turbulent RMS velocity has a single maximum in summer and a double maximum in winter months. The secondary maximum in the winter MLT we associate with a secondary gravity wave–breaking phenomenon. The turbulent rms velocity results from the model agree well with full correlation analyses based on MF-radar measurements. A new scaling for the mesoscale horizontal velocity based on the idea of direct energy cascade in mesoscales is proposed. The latter findings for mesoscale and small-scale characteristic velocities support the idea proposed in this research that mesoscale and small-scale dynamics in the mesosphere are governed by SMT, ST, and KT in the statistical average. Significance Statement Mesoscale dynamics in the middle atmosphere, which consists of atmospheric turbulence and gravity waves, remains a complex problem for atmospheric physics and climate studies. Due to its high nonlinearity, the mesoscale dynamics together with the small-scale turbulence is the primary source of uncertainties and biases in high-altitude general circulation models (GCM) in the middle atmosphere. We use the stratified turbulence theory and the gravity wave–resolving GCM to characterize different scaling regimes and to define various length, time, and velocity scales, that are relevant for the mesoscale and small-scale dynamical regimes. Our results highlight the importance of stratified turbulence in the mesosphere and lower-thermosphere region.

Smallest scale of wrinkles of a Huygens front in extremely strong turbulence.

By analyzing the statistically stationary stage of propagation of a Huygens front in homogeneous, isotropic, constant-density turbulence, a length scale l_{0} is introduced to characterize the smallest wrinkles on the front surface in the case of a low constant speed u_{0} of the front when compared to the Kolmogorov velocity u_{K}. The length scale is derived following a hypothesis of dynamical similarity that highlights a balance between (i) creation of a front area due to advection and (ii) destruction of the front area due to propagation. Consequently, the front speed is compared with the magnitude of the fluid velocity difference in two points separated by a distance smaller than the Kolmogorov length scale. Appropriateness of the smallest wrinkle scale is demonstrated by applying a fractal approach to evaluating the mean area of the instantaneous front surface. Since the scales of the smallest and larger wrinkles belong to different subranges (dissipation and inertial, respectively) of the Kolmogorov turbulence spectrum, the front is hypothesized to be a bifractal characterized by two different fractal dimensions in the two subranges. Both fractal dimensions are evaluated adapting the aforementioned hypothesis of dynamical similarity. Such a bifractal model yields a linear relation between the mean fluid consumption velocity, which is equal to the front speed u_{0} multiplied with a ratio of the mean area of the instantaneous front surface to the transverse projected area, and the rms turbulent velocity u^{'} even if a ratio of u_{0}/u^{'} tends to zero.

Passive Front Propagation in Intense Turbulence: Early Transient and Late Statistically Stationary Stages of the Front Area Evolution

The influence of statistically stationary, homogeneous isotropic turbulence (i) on the mean area of a passive front propagating in a constant-density fluid and, hence, (ii) on the mean fluid consumption velocity u¯T is explored, particularly in the case of an asymptotically high turbulent Reynolds number, and an asymptotically high ratio of the Kolmogorov velocity to a constant speed u0 of the front. First, a short early transient stage is analyzed by assuming that the front remains close to a material surface that coincides with the front at the initial instant. Therefore, similarly to a material surface, the front area grows exponentially with time. This stage, whose duration is much less than an integral time scale of the turbulent flow, is argued to come to an end once the volume of fluid consumed by the front is equal to the volume embraced due to the turbulent dispersion of the front. The mean fluid consumption velocity averaged over this stage is shown to be proportional to the rms turbulent velocity u′. Second, a late statistically stationary regime of the front evolution is studied. A new length scale characterizing the smallest wrinkles of the front surface is introduced. Since this length scale is smaller than the Kolmogorov length scale ηK under conditions of the present study, the front is hypothesized to be a bifractal with two different fractal dimensions for wrinkles larger and smaller than ηK. Finally, a simple scaling of u¯T∝u′ is obtained for this late stage as well.

Effective method of predicting confined pressure behavior under isotropic turbulence

Explosion pressure prediction is indispensable to ensure process safety against accidental gas explosions. This work is aimed at establishing a theoretical method for predicting confined methane-air explosion pressure under isotropic turbulence. The results indicated that the pressure rise rate becomes significantly increased by the existence of isotropic turbulence, which effect on peak value of explosion pressure is negligible. Among various models of turbulent burning velocity, the calculated pressure rise rate using Chiu model, Williams model and Liu model is relatively closer to experimental value. With the increase of turbulent integral length and RMS turbulent fluctuation velocity, the pressure rise rate becomes increased continuously. The influence of adiabatic compression and isothermal compression on pressure rise rate could be ignored. To predict explosion pressure in a more accurate way, the dynamic variation of turbulent integral length and RMS turbulent fluctuation velocity should be considered in the future.

Three dimensional measurements of surface areas and burning velocities of turbulent spherical flames

Measurements of 3D turbulent flame surface area and burnt gas were carried out for spherically expanding flames in different methane-air and hydrogen-air mixtures using a high frequency swinging laser sheet technique based on Mie scattering. The corresponding turbulent burning velocities were measured simultaneously using the rate of pressure rise, at turbulence rms velocities between 0.3 and 2.0 m/s. The ratio of turbulent burning velocity enhancement utm/ul to flame surface area enhancement A3D/a3D was measured as a function of turbulence rms velocity. For the methane-air flames, the turbulent burning velocity enhancement is close to that of the flame surface area enhancement. For the hydrogen-air flames, the former can exceed the latter by a factor of up to 6 at the largest values of turbulence rms velocity tested. The large discrepancy suggests that in the case of hydrogen-air flames, the measured rate of burning per unit flame area is significantly enhanced by the turbulence. For the reconstructed A3D/a3D, the corresponding A2D/a2D are also discussed.

Combustion-induced turbulent flow fields in premixed flames

Combustion-induced turbulence is studied in explosions of methane/air in a steel sphere with optical access. Rms turbulent velocities, u', created by four peripheral variable speed fans, were measured by Particle Image Velocimetry, PIV, which indicated near-uniform, isotropic turbulence, with small mean velocities. The gaseous expansion of a near-spherical propagating flame generated a radially outwards velocity of unburned mixture, the intensity of which depended upon the burning velocity and volume increase due to combustion. The study is to measure any extra turbulence created by this outwards velocity pulse. Only wave lengths less than the flame circumference can wrinkle the flame and increase the burning velocity, ut. Consequently the effective rms velocity at the flame front affecting its propagation, uk', is less than u'. Analysis shows, uk', to be a function of flame radius. The velocity pulse generated additional turbulence, enhancing uk'. This enhanced ut, giving further positive feedback. This higher rms value is designated as a spatial rms turbulent velocity, us'. PIV-measured gas velocities are resolved into a mean radial velocity, U-r and, us', with their radial profiles. These are derived from explosions at different equivalence ratios, pressures, and temperatures. At the radii at which ut are measured, us'/uk' is enhanced by the high rates of burning and volumetric expansion. This ratio attained a high value of 2.5, with stoichiometric CH4/air. Values of ut measured in explosions are higher than those measured in steady-state burners, attributable to the induced us', enhancing ut, in explosions, with no such effect in burners.

A Numerical Investigation of the Effects of Fuel Composition on the Minimum Ignition Energy for Homogeneous Biogas-Air Mixtures

The minimum ignition energy (MIE) requirements for ensuring successful thermal runaway and self-sustained flame propagation have been analysed for forced ignition of homogeneous stoichiometric biogas-air mixtures for a wide range of initial turbulence intensities and CO2 dilutions using three-dimensional Direct Numerical Simulations under decaying turbulence. The biogas is represented by a CH4 + CO2 mixture and a two-step chemical mechanism involving incomplete oxidation of CH4 to CO and H2O and an equilibrium between the CO oxidation and the CO2 dissociation has been used for simulating biogas-air combustion. It has been found that the MIE increases with increasing CO2 content in the biogas due to the detrimental effect of the CO2 dilution on the burning and heat release rates. The MIE for ensuring self-sustained flame propagation has been found to be greater than the MIE for ensuring only thermal runaway irrespective of its outcome for large root-mean-square (rms) values of turbulent velocity fluctuation, and the MIE values increase with increasing rms turbulent velocity for both cases. It has been found that the MIE values increase more steeply with increasing rms turbulent velocity beyond a critical turbulence intensity than in the case of smaller turbulence intensities. The variations of the normalised MIE (MIE normalised by the value for the quiescent laminar condition) with normalised turbulence intensity for biogas-air mixtures are found to be qualitatively similar to those obtained for the undiluted mixture. However, the critical turbulence intensity has been found to decrease with increasing CO2 dilution. It has been found that the normalised MIE for self-sustained flame propagation increases with increasing rms turbulent velocity following a power-law and the power-law exponent has been found not to vary much with the level of CO2 dilution. This behaviour has been explained using a scaling analysis and flame wrinkling statistics. The stochasticity of the ignition event has been analysed by using different realisations of statistically similar turbulent flow fields for the energy inputs corresponding to the MIE and it has been demonstrated that successful outcomes are obtained in most of the instances, justifying the accuracy of the MIE values identified by this analysis.

Bifractal nature of turbulent reaction waves at high Damköhler and Karlovitz numbers

Governing physical mechanisms of the influence of Kolmogorov turbulence on a reaction wave (e.g., a premixed flame) are often discussed by adopting (combustion) regime diagrams. While two limiting regimes associated with (i) a high Damköhler number Da, but a low Karlovitz number Ka, or (ii) a low Da, but a high Ka drew significant amount of attention, the third limiting regime associated with (iii) Da ≫ 1 and Ka ≫ 1 has yet been beyond the mainstream discussions in the literature. The present work aims at filling this knowledge gap by adapting the contemporary understanding of the fundamentals of the regimes (i) and (ii) in order to describe the basic features of the influence of intense turbulence on a reaction wave in the regime (iii). More specifically, in that regime, the entire turbulence spectrum is divided in two subranges: small-scale and large-scale eddies whose influence on the reaction wave is modeled similarly to the regimes (ii) and (i), respectively. Accordingly, the surface of the reaction wave is hypothesized to be a bifractal with two different fractal dimensions of Df = 8/3 and 7/3 at small and large scales, respectively. The boundary between the two ranges is found by equating the local eddy turn-over time to the laminar-wave time scale. Finally, a simple scaling of UT ∝ u′ is obtained for the turbulent consumption velocity at Da ≫ 1 and Ka ≫ 1. Here, u′ is the rms turbulent velocity.

Unsteady 3-D RANS simulations of dust explosion in a fan stirred explosion vessel using an open source code

Dust explosion is a constant threat to industries which deal with combustible powders such as woodworking, metal processing, food and feed, pharmaceuticals and additive industries. The current standards regarding dust explosion venting protecting systems, such as EN 14491 (2012) and NFPA 68 (2018), are based on empirical correlations and neglect effects due to complex geometry. Such a simplification may lead to failure in estimating explosion overpressure, thus, increasing risk for injuries and even fatalities at workplaces. Therefore, there is a strong need for a numerical tool for designing explosion protecting systems. This work aims at contributing to the development of such a tool by (i) implementing a premixed turbulent combustion model into OpenFOAM, (ii) verifying the implementation using benchmark analytical solutions, and (iii) validating the numerical platform against experimental data on cornflour dust explosion in a fan-stirred explosion vessel, obtained by Bradley et al. (1989a) under well-controlled laboratory conditions.For this purpose, the so-called Flame Speed Closure model of the influence of turbulence on premixed combustion is adapted and implemented into OpenFOAM. The implementation of the model is verified using exact and approximate analytical solutions for statistically one-dimensional planar and spherical turbulent flames, respectively. The developed numerical platform is applied to unsteady three-dimensional Reynolds Averaged Navier-Stokes simulations of the aforementioned experiments. The results show that the major trends, i.e. (i) a linear increase in an apparent turbulent flame speed St,b with an increase in the root mean square (rms) turbulent velocity u' and (ii) and an increase in St,b with an increase in the mean flame radius, are qualitatively predicted. Furthermore, the measured and computed dependencies of St,b(u') agree quantitatively under conditions of weak and moderate turbulence.

Self-similar propagation and turbulent burning velocity of CH4/H2/air expanding flames: Effect of Lewis number

In this study we clarify the role of differential diffusion characterized by effective Lewis number, Leeff, on the self-similar accelerative propagation and the associated turbulent burning velocity of turbulent expanding flames. The turbulent flame trajectories of the CH4/H2/air mixtures were measured using a newly developed large-scale, fan-stirred turbulent combustion chamber generating near-isotropic turbulence. It is found that the normalized turbulent propagation speed scales as the turbulent flame Reynolds number, ReT,f=(urms/SL)(〈r〉/lf), roughly to the one-half power for the stoichiometric CH4/H2 = 80/20 flames with unity Leeff (=1), where the average flame radius, 〈r〉, is the length scale and the thermal diffusivity, α=SLlf, is the transport property, SL and lf are the laminar burning velocity and flame thickness, and urms is the root-mean-square (rms) turbulent fluctuation velocity. The propagation of the fuel lean CH4/H2 = 20/80 flames with sub-unity Leeff (<1) is still self-similar, however, the normalized turbulent propagation speed is much higher and the power exponent is greater than 1/2 even though these two flames have almost the same laminar burning velocity, flame thickness with SL, lf and experience the similar turbulence perturbations. The stronger self-similar propagation of the Leeff < 1 flames is the consequences of the couple effects of the differential diffusion and the flame stretch on the local wrinkled flamelets within the turbulent flame brush. Based on the present experimental data, a modified possible general correlation for turbulent burning velocity is obtained in terms of the Leeff and ReT,f with differential diffusion consideration. This correlation is able to predict not only the present experimental data but also the previous turbulent burning velocities measured using both turbulent Bunsen flames and expanding flames at high pressures.

Topology and flame speeds of turbulent premixed flame kernels in supersonic flows

Premixed flame kernels exposed to a mean expanding supersonic channel flow are examined using experiments and large-eddy simulations. Four cases, spanning three Mach numbers and two equivalence ratios, are explored. Numerical results are processed similarly to and compared with experimental data. Accuracy is assessed by comparing the numerically resolved flow field, flame growth, and internal flame structure with experimental data. Evolution of the flame topology, ascertained using these combined studies, confirms that the flame kernel morphs into a reacting vortex ring upon interaction with the supersonic mean flow expansion. The vortex ring topology assessment shows potentially significant errors in the turbulent flame speed based on line of sight (LOS) measurements. Modifications to the flame speed to correct the error associated with line of sight measurements are proposed. Two turbulent flame speed scalings are investigated: one with the RMS turbulent velocity, u′, and the other with the vortex propagation velocity, UT. It is shown that u′ fails to collapse the flame speed data but UT scaling does collapse the data from all four cases and produces a nearly linear scaling regime. This finding suggests turbulence plays a secondary role to the hydrodynamic instability in this particular problem. The conditions for displacement and consumption speed equivalency are explored further and it is found that the nature of the diagnostic used (LOS, planar, volumetric) and the progress variable isocontour measured play important roles and should be considered during interpretation of experimental data.

A DNS Study of Sensitivity of Scaling Exponents for Premixed Turbulent Consumption Velocity to Transient Effects

3D Direct Numerical Simulations of propagation of a single-reaction wave in forced, statistically stationary, homogeneous, isotropic, and constant-density turbulence, which is not affected by the wave, are performed in order to investigate the influence of the wave development on scaling (power) exponents for the turbulent consumption velocity UT as a function of the rms turbulent velocity u′, laminar wave speed SL, and a ratio L11/δF of the longitudinal turbulence length scale L11 to the laminar wave thickness δF. Fifteen cases characterized by u′/SL = 0.5,1.0,2.0,5.0, or 10.0 and L11/δF = 2.1, 3.7, or 6.7 are studied. Obtained results show that, while UT is well and unambiguously defined in the considered simplest case of a statistically 1D planar turbulent reaction wave, the wave development can significantly change the scaling exponents. Moreover, the scaling exponents depend on a method used to compare values of UT, i.e., the scaling exponents found by processing the DNS data obtained at the same normalized wave-development time may be substantially different from the scaling exponents found by processing the DNS data obtained at the same normalized wave size. These results imply that the scaling exponents obtained from premixed turbulent flames of different configurations may be different not only due to the well-known effects of the mean-flame-brush curvature and the mean flow non-uniformities, but also due to the flame development, even if the different flames are at the same stage of their development. The emphasized transient effects can, at least in part, explain significant scatter of the scaling exponents obtained by various research groups in different experiments, thus, implying that the scatter in itself is not sufficient to reject the notion of turbulent burning velocity.

STURM: Resuspension mesocosms with realistic bottom shear stress and water column turbulence for benthic-pelagic coupling studies: Design and applications

Shear TUrbulence Resuspension Mesocosm (STURM) tanks, with high instantaneous bottom shear stress and realistic water column mixing in a single system, allow realistic benthic-pelagic coupling studies with sediment resuspension. The 1m3 tanks can be programmed to produce tidal or episodic sediment resuspension for extended time periods (e.g. 4weeks), over muddy sediments with a variety of benthic organisms. A resuspension paddle produces uniform bottom shear stress across the sediment surface while gently mixing a 1m deep overlying water column. The STURM tanks can be programmed to different magnitudes, frequencies, and durations of bottom shear stress (and thus resuspension) with proportional water column turbulence levels over a wide range of mixing settings for benthic-pelagic coupling experiments. Over ten STURM calibration settings, RMS turbulent velocity ranged from 0.26 to 4.52cms−1, energy dissipation rate from 0.0016 to 2.65cm2s−3, the average bottom shear stress from 0.0035 to 0.19Pa, and the instantaneous maximum bottom shear stress from 0.07 to 1.7Pa. We have performed four 4-week benthic-pelagic coupling ecosystem experiments with tidal resuspension and stepwise erosion experiments (both with and without infaunal bivalves), carried out experiments on oyster biodeposit resuspension, mimicked storms overlain on tidal resuspension, and studied the effects of varying frequency and duration of resuspension on sedimentary contaminant release. The large size of the tanks allows water quality and particle measurements using standard oceanographic instrumentation. The realistic scale and complexity of the contained ecosystems has revealed indirect feedbacks and responses that are not observable in smaller, less complex experimental systems.

Direct numerical simulation study of statistically stationary propagation of a reaction wave in homogeneous turbulence.

A three-dimensional (3D) direct numerical simulation (DNS) study of the propagation of a reaction wave in forced, constant-density, statistically stationary, homogeneous, isotropic turbulence is performed by solving Navier-Stokes and reaction-diffusion equations at various (from 0.5 to 10) ratios of the rms turbulent velocity U^{'} to the laminar wave speed, various (from 2.1 to 12.5) ratios of an integral length scale of the turbulence to the laminar wave thickness, and two Zeldovich numbers Ze=6.0 and 17.1. Accordingly, the Damköhler and Karlovitz numbers are varied from 0.2 to 25.1 and from 0.4 to 36.2, respectively. Contrary to an earlier DNS study of self-propagation of an infinitely thin front in statistically the same turbulence, the bending of dependencies of the mean wave speed on U^{'} is simulated in the case of a nonzero thickness of the local reaction wave. The bending effect is argued to be controlled by inefficiency of the smallest scale turbulent eddies in wrinkling the reaction-zone surface, because such small-scale wrinkles are rapidly smoothed out by molecular transport within the local reaction wave.

Does Density Ratio Significantly Affect Turbulent Flame Speed?

In order to experimentally study whether or not the density ratio σ substantially affects flame displacement speed at low and moderate turbulent intensities, two stoichiometric methane/oxygen/nitrogen mixtures characterized by the same laminar flame speed SL = 0.36 m/s, but substantially different σ were designed using (i) preheating from Tu = 298 to 423 K in order to increase SL, but to decrease σ, and (ii) dilution with nitrogen in order to further decrease σ and to reduce SL back to the initial value. As a result, the density ratio was reduced from 7.52 to 4.95. In both reference and preheated/diluted cases, direct images of statistically spherical laminar and turbulent flames that expanded after spark ignition in the center of a large 3D cruciform burner were recorded and processed in order to evaluate the mean flame radius bar {R}_{f}left (t right ) and flame displacement speed S_{t}=sigma ^{-1}{dbar {R}_{f}} left / right . {dt} with respect to unburned gas. The use of two counter-rotating fans and perforated plates for near-isotropic turbulence generation allowed us to vary the rms turbulent velocity u^{prime } by changing the fan frequency. In this study, u^{prime } was varied from 0.14 to 1.39 m/s. For each set of initial conditions (two different mixture compositions, two different temperatures Tu, and six different u^{prime }), five (respectively, three) statistically equivalent runs were performed in turbulent (respectively, laminar) environment. The obtained experimental data do not show any significant effect of the density ratio on St. Moreover, the flame displacement speeds measured at u′/SL = 0.4 are close to the laminar flame speeds in all investigated cases. These results imply, in particular, a minor effect of the density ratio on flame displacement speed in spark ignition engines and support simulations of the engine combustion using models that (i) do not allow for effects of the density ratio on St and (ii) have been validated against experimental data obtained under the room conditions, i.e. at higher σ.

Turbulent burning rates of gasoline components, Part 1 – Effect of fuel structure of C6 hydrocarbons

Measurements of laminar and turbulent burning velocities have been made for premixed hydrocarbon-air flames with six carbon atoms including unsaturated, branched and cyclic molecules. The seven different fuels studied were n-hexane, 1-hexene, 1-hexyne, 2,2 dimethyl butane, 2 methyl pentane (isohexane), cyclohexane and cyclohexene. The tests were performed in a constant volume, optically accessed spherical bomb, with the use of the schlieren technique and a high-speed camera. The deflagrations were initiated at elevated pressure and temperature of 0.5MPa and 360K, where burning velocity data is relatively sparse, under laminar and turbulent conditions with rms turbulent velocities of 2 and 6m/s and for equivalence ratios of 0.78–1.67. The primary objective of this work was to compare the turbulent burn rates of the different fuel–air mixtures; the laminar burning velocities were used to interpret the turbulent data. The ranking of the laminar burning velocity was overall found to be 1-hexyne>cyclohexene>1-hexene>cyclohexane>n-hexane>2-methyl pentane>2,2 dimethyl butane for the range of equivalence ratios tested. The ranking was found to be the same for the turbulent burn rate measurements, particularly so for the slowest and fastest fuels. As the rms turbulent velocity increased the relative differences between the fuels were found to generally increase for lean mixtures, remain similar around stoichiometric equivalence ratio and decrease for rich mixtures. This behaviour was linked to the sensitivity of turbulent flames to stretch and thermo-diffusive stability.

Turbulent burning rates of gasoline components, Part 2 – Effect of carbon number

Experimental measurements of turbulent and laminar burning velocities have been made for premixed hydrocarbon–air flames of straight chain molecules of increasing carbon number (from n-pentane to n-octane). Measurements were performed at 0.5MPa, 360K and rms turbulent velocities of 2 and 6m/s, for a range of equivalence ratios. The laminar burning velocities were used to interpret the turbulent data, but were also found to be broadly in line with those of previous workers. At lean conditions the turbulent burning velocity was measured to be similar between the four alkanes studied. However, at rich conditions there were notable differences between the turbulent burn rates of the fuels. The equivalence ratio of the mixtures at which the maximum burning velocities occurred in the turbulent flames was richer than that under laminar conditions. The equivalence ratio of the peak turbulent burning velocity was found to be a function of the carbon number of the fuel and the turbulent intensity and became gradually fuel rich with increases in each of these values.

THE EFFECT OF ANISOTROPIC VISCOSITY ON COLD FRONTS IN GALAXY CLUSTERS

Cold fronts -- contact discontinuities in the intracluster medium (ICM) of galaxy clusters -- should be disrupted by Kelvin-Helmholtz (K-H) instabilities due to the associated shear velocity. However, many observed cold fronts appear stable. This opens the possibility to place constraints on microphysical mechanisms that stabilize them, such as the ICM viscosity and/or magnetic fields. We performed exploratory high-resolution simulations of cold fronts arising from subsonic gas sloshing in cluster cores using the grid-based Athena MHD code, comparing the effects of isotropic Spitzer and anisotropic Braginskii viscosity (expected in a magnetized plasma). Magnetized simulations with full Braginskii viscosity or isotropic Spitzer viscosity reduced by a factor f ~ 0.1 are both in qualitative agreement with observations in terms of suppressing K-H instabilities. The RMS velocity of turbulence within the sloshing region is only modestly reduced by Braginskii viscosity. We also performed unmagnetized simulations with and without viscosity and find that magnetic fields have a substantial effect on the appearance of the cold fronts, even if the initial field is weak and the viscosity is the same. This suggests that determining the dominant suppression mechanism of a given cold front from X-ray observations (e.g. viscosity or magnetic fields) by comparison with simulations is not straightforward. Finally, we performed simulations including anisotropic thermal conduction, and find that including Braginskii viscosity in these simulations does not significant affect the evolution of cold fronts; they are rapidly smeared out by thermal conduction, as in the inviscid case.

A direct numerical simulation study of vorticity transformation in weakly turbulent premixed flames

Database obtained earlier in 3D Direct Numerical Simulations (DNS) of statistically stationary, 1D, planar turbulent flames characterized by three different density ratios σ is processed in order to investigate vorticity transformation in premixed combustion under conditions of moderately weak turbulence (rms turbulent velocity and laminar flame speed are roughly equal to one another). In cases H and M characterized by σ = 7.53 and 5.0, respectively, anisotropic generation of vorticity within the flame brush is reported. In order to study physical mechanisms that control this phenomenon, various terms in vorticity and enstrophy balance equations are analyzed, with both mean terms and terms conditioned on a particular value c of the combustion progress variable being addressed. Results indicate an important role played by baroclinic torque and dilatation in transformation of average vorticity and enstrophy within both flamelets and flame brush. Besides these widely recognized physical mechanisms, two other effects are documented. First, viscous stresses redistribute enstrophy within flamelets, but play a minor role in the balance of the mean enstrophy \documentclass[12pt]{minimal}\begin{document}$\overline{\Omega }$\end{document}Ω¯ within turbulent flame brush. Second, negative correlation \documentclass[12pt]{minimal}\begin{document}$\overline{\mathbf {u}^{\prime } \cdot \nabla \Omega ^{\prime }}$\end{document}u′·∇Ω′¯ between fluctuations in velocity u and enstrophy gradient contributes substantially to an increase in the mean \documentclass[12pt]{minimal}\begin{document}$\overline{\Omega }$\end{document}Ω¯ within turbulent flame brush. This negative correlation is mainly controlled by the positive correlation between fluctuations in the enstrophy and dilatation and, therefore, dilatation fluctuations substantially reduce the damping effect of the mean dilatation on the vorticity and enstrophy fields. In case L characterized by σ = 2.5, these effects are weakly pronounced and \documentclass[12pt]{minimal}\begin{document}$\overline{\Omega }$\end{document}Ω¯ is reduced mainly due to viscosity. Under conditions of the present DNS, vortex stretching plays a minor role in the balance of vorticity and enstrophy within turbulent flame brush in all three cases.