Rms Turbulent Velocity Research Articles

Numerical study of large-scale vorticity generation in shear-flow turbulence

Simulations of stochastically forced shear-flow turbulence in a shearing-periodic domain are used to study the spontaneous generation of large-scale flow patterns in the direction perpendicular to the plane of the shear. Based on an analysis of the resulting large-scale velocity correlations it is argued that the mechanism behind this phenomenon could be the mean-vorticity dynamo effect pioneered by Elperin, Kleeorin, and Rogachevskii [Phys. Rev. E 68, 016311 (2003)]. This effect is based on the anisotropy of the eddy viscosity tensor. One of its components may be able to replenish cross-stream mean flows by acting upon the streamwise component of the mean flow. Shear, in turn, closes the loop by acting upon the cross-stream mean flow to produce stronger streamwise mean flows. The diagonal component of the eddy viscosity is found to be of the order of the rms turbulent velocity divided by the wave number of the energy-carrying eddies.

Premixed turbulent flame front structure investigation by Rayleigh scattering in the thin reaction zone regime

Premixed turbulent flames of methane–air and propane–air stabilized on a bunsen type burner were studied using planar Rayleigh scattering and particle image velocimetry. The fuel–air equivalence ratio range was from lean 0.6 to stoichiometric for methane flames, and from 0.7 to stoichiometric for propane flames. The non-dimensional turbulence rms velocity, u′/ S L, covered a range from 3 to 24, corresponding to conditions of corrugated flamelets and thin reaction zones regimes. Flame front thickness increased slightly with increasing non-dimensional turbulence rms velocity in both methane and propane flames, although the flame thickening was more prominent in propane flames. The probability density function of curvature showed a Gaussian-like distribution at all turbulence intensities in both methane and propane flames, at all sections of the flame. The value of the term Dκ, the product of molecular diffusivity evaluated at reaction zone conditions and the flame front curvature, has been shown to be smaller than the magnitude of the laminar burning velocity. This finding questions the validity of extending the level set formulation, developed for corrugated flames region, into the thin reaction zone regime by increasing the local flame propagation by adding the term Dκ to laminar burning velocity.

Flame surface densities during spherical turbulent flame explosions

A novel way is presented of deriving the proportionality constant, k (mm−1), for flame surface density. This comprises simultaneous measurements, by Mie scattering, of mean reaction progress variable and the turbulent burning velocity, during explosions in a fan-stirred bomb. Mean effective laminar burning velocities at the wrinkled flame surface are derived theoretically from the distribution of flame stretch rates, the Markstein numbers, and the possible generation of localised flame instabilities and flame quenching. The changing radial profiles of flame surface density have been obtained, as flames accelerate in different propane-air explosions. The effective value of the rms turbulent velocity acting on the flame is derived from a newly developed power spectral density function. The values of k are similar to those found by researchers employing stationary turbulent flames, but the present work suggests dependencies of k upon Markstein number. Insights are obtained on the inter-relationship of k and turbulent burning phenomena. More research is required on the factors controlling the value of k, including its relationship to flame curvature.

Turbulent structures and budgets behind permeable ribs

Different rib geometries are traditionally used to improve heat transfer and enhance mixing in different industrial applications, i.e. heat exchangers, cooling passages of gas turbine blades and fuel elements of nuclear reactors, etc. Permeable ribs have been proposed in literature for passive control of the reattaching flow past surface mounted ribs leading to superior performance. The flow past different surface mounted permeable rib geometries, i.e. solid, slit, split-slit and inclined split-slit ribs have been investigated in this study. Both two components and stereo particle image velocimetry (PIV) have been used in streamwise and cross stream planes to study the underlying flow structures. The detailed turbulent statistics, i.e. mean and rms velocity, higher order moments, quadrant decomposition of turbulent shear stress producing motions, skewness and components of the turbulent kinetic energy budgets have been compared for different rib geometries. Coherent structures are identified based on the invariant of velocity gradient tensor invariant and wavelet transform. The skewness results demonstrate the intermittency of quadrant motions. The reattachment length of the inclined split-slit rib is lowest among all rib geometries. The average Reynolds stresses and the production of turbulent kinetic energy are highest for the inclined split-slit rib. The pressure transport calculated as residual of the turbulent kinetic energy budget equation is highest for the inclined split-slit rib. This is attributed to the smaller reattachment length leading to greater adverse pressure gradient for the inclined split-slit rib. The quadrant motions, turbulent fluxes, skewness and kinetic energy budgets at post reattachment region compares well with that of flat plate turbulent boundary layer from hot wire measurements in literature. Overall, this study demonstrates the effectiveness of PIV technique for the detailed turbulent structures characterization of complex flows.

DARRIEUS–LANDAU AND THERMO-ACOUSTIC INSTABILITIES IN CLOSED VESSEL EXPLOSIONS

Experiments involving a spherical explosion bomb are reported, in which Darrieus–Landau thermo-diffusive, D-L,T-D, flame instabilities interacted with primary and secondary, self-excited, thermo-acoustic oscillations. Explosions with central ignition demonstrated that rich i-octane and lean hydrogen-air mixtures generated strong pressure oscillations, a consequence of their negative Markstein numbers. Utilizing dual wall ignitions, the structures of high pressure flames were studied using appropriate optical techniques. The conditions that gave rise to the greatest increase in the rate of combustion were strong initial D-L,T-D, flame instabilities and a high rate of change of the heat release rate, sufficient to generate strong secondary pressure oscillations. These, in turn, generated Rayleigh-Taylor instabilities that further wrinkled the flames. The bomb was equipped with four fans which showed that an rms turbulent velocity in excess of about 0.6 m/s was sufficient to reduce, and almost eradicate, the effect of these instabilities on the flame speed.

The quenching of premixed turbulent flames of iso-octane, methane and hydrogen at high pressures

Experimental and theoretical studies are reported of turbulent flame quenching, with premixed flames of methane–air, iso-octane–air and hydrogen–air. Mixtures were exploded in a fan-stirred explosion bomb in which the rms turbulent velocity was varied by changes in fan speed. Influences of Markstein number, pressure up to 1.5 MPa, and Karlovitz stretch factor, K, were studied. It was found that the ratio of the positive stretch rate for extinction of the laminar flame to the rms turbulent strain rate was an important parameter. Probabilities of flame propagation, p f, from an initial kernel were measured. The conditions for probabilities of 0.8 and 0.2 were correlated in terms of the Karlovitz stretch factor and Markstein number. However, at a given p f, the theoretical probability, P bf, that the spectrum of stretch rates for a turbulent flame would support propagation, declined with increase in K. This theoretical probability assumed a positive flame stretch rate for quenching equal to that for the extinction of a steady-state laminar flame. Its declining value with K, at constant p f, was attributed, at least in part, to the inability of non-steady-state flamelets of the turbulent flame to respond to transient excursions of flame stretch rates to values in excess of those that extinguish laminar flames. Another possibility was that the highly convoluted flames were able to follow a route through regions of sufficiently low stretch rate to avoid extinctions.

Premixed flamelet modelling: Factors influencing the turbulent heat release rate source term and the turbulent burning velocity

A flamelet approach is adopted in a study of the factors affecting the volumetric heat release source term in turbulent combustion. This term is expressed as the product of an instability enhanced burning rate factor, P bi , and the mean volumetric heat release rate in an unstretched laminar flamelet of the mixture. Included in the expression for P bi are a pdf of the flame stretch rate and a flame stretch factor. Fractal considerations link the turbulent burning velocity normalised by the effective rms turbulent velocity to P bi . Evaluation of this last parameter focuses on problems of (i) the pdfs of the flame stretch rate, (ii) the effects of flame stretch rate on the burning rate, (iii) the effects of any flamelet instability on the burning rate, (iv) flamelet extinctions under positive and negative flame stretch rates, and (v) the effects of the unsteadiness of flame stretch rates. The Markstein number influences both the rate of burning and the possibility of flamelet instabilities developing which, through their ensuing wrinkling, increase the burning rate. The flame stretch factor is extended to embrace potential Darrieus–Landau thermo-diffusive flamelet instabilities. A major limitation is the insufficient understanding of the effects of negative stretch rates that might cause flame extinction. The influences of positive and negative Markstein numbers are considered separately. For the former, a computed theoretical relationship for turbulent burning velocity, normalised by the effective rms velocity, is developed which, although close to that measured experimentally, tends to be somewhat lower at the higher values of the Karlovitz stretch factor. This might be attributed to reduced flame extinction and reduced effective Markstein numbers when the increasingly nonsteady conditions reduce the ability of the flame to respond to changes in flame stretch rates. As the pressure increases, Markstein numbers decrease. For negative Markstein numbers the predicted values of P bi and turbulent burning velocity are significantly increased above the values for positive Markstein numbers. This is confirmed experimentally and these values are close to those predicted theoretically. The increased values are due to the greater stretch rate required for flame extinction, the increased burning rate at positive values of flame stretch rate, and, in some instances, the development of flame instabilities. At lower values of turbulence than those covered by these computations, burning velocities can be enhanced by flame instabilities, as they are with laminar flames, particularly at negative Markstein numbers.

VARIATION OF TURBULENT BURNING RATE OF METHANE, METHANOL, AND ISO-OCTANE AIR MIXTURES WITH EQUIVALENCE RATIO AT ELEVATED PRESSURE

ABSTRACT Turbulent burning velocities for premixed methane, methanol, and iso-octane/air mixtures have been experimentally determined for an rms turbulent velocity of 2 m/s and pressure of 0.5 MPa for a wide range of equivalence ratios. Turbulent burning velocity data were derived using high-speed schlieren photography and transient pressure recording; measurements were processed to yield a turbulent mass rate burning velocity, u tr. The consistency between the values derived using the two techniques, for all fuels for both fuel-lean and fuel-rich mixtures, was good. Laminar burning measurements were made at the same pressure, temperature, and equivalence ratios as the turbulent cases and laminar burning velocities and Markstein numbers were determined. The equivalence ratio (φ) for peak turbulent burning velocity proved not always coincident with that for laminar burning velocity for the same fuel; for iso-octane, the turbulent burning velocity unexpectedly remained high over the range φ = 1 to 2. The ratio of turbulent to laminar burning velocity proved remarkably high for very rich iso-octane/air and lean methane/air mixtures.

Turbulent Heating of Galaxy‐Cluster Plasmas

A number of studies suggest that turbulent heating plays an important role in the thermal balance of galaxy-cluster plasmas. In this paper, we construct a model of intracluster plasmas in which radiative cooling is balanced by heating from viscous dissipation of turbulent motions, turbulent diffusion of high-specific-entropy plasma into low-specific-entropy regions, and thermal conduction. We solve for the rms turbulent velocity u by setting Γ + Q + H = R throughout a cluster, where Γ, Q, and H are the heating rates from dissipation of turbulence, turbulent diffusion, and conduction, respectively, and R is the rate of radiative cooling. We account for the effects of buoyancy in our expression for the eddy diffusivity and neglect nonthermal pressure. We take the conductivity to be a fixed fraction (typically one-fifth) of the Spitzer value for a nonmagnetized plasma and the density and temperature to be given by analytical fits to published data. We set the dominant velocity length scale l equal to αr + l0, where α is a constant, r is distance from cluster center, and l0 = 0.5 kpc. For 0.05 0.5, although there are exceptions to this rule. For some values of α, we find that at some locations the heat flux from turbulent diffusion has positive divergence, so that turbulent diffusion locally cools the plasma. Buoyancy inhibits turbulent diffusion of heat in the radial direction to a degree that increases with increasing α. This leads to an increase in the computed value of u relative to models that neglect buoyancy; the magnitude of the increase is moderate for α = 0.5 and large for α > 1.

Effect of Developing Turbulence and Markstein Number on the Propagation of Flames in Methane-Air Premixture

In spark ignition engines, initial flame kernel is wrinkled by a progressively increasing bandwidth of turbulence length scales until eventually the size of the flame kernel is sufficient for it to experience the entire turbulence spectrum. In the present study, an effective rms turbulence velocity as a function of time, estimated by integrating the nondimensional power spectrum density (psd) function for isotropic turbulence, is utilized to analyze the statistical distribution of flame front curvatures and turbulent burning velocities of flames propagating in methane-air premixtures. The distributions of flame front curvatures show these to become more dispersed as the effective turbulence velocity increases, and result in increased burning of premixtures. A decrease in the Markstein number also results in a further increase in curvature dispersion and enhanced burning, in line with the flame stability analysis.

Thermal Conduction and Particle Transport in Strong Magnetohydrodynamic Turbulence, with Application to Galaxy Cluster Plasmas

Galaxy clusters possess turbulent magnetic fields with a dominant scale length lB ' 1 10 kpc. In the static magnetic field approximation, the thermal conductivityT for heat transport over distances 3 lB in clusters is '� SlB/LS(� e), whereS is the Spitzer thermal conductivity for a nonmagnetized plasma, the length LS(r0 )i s a characteristic distance that a pair of field lines separated by a distance r0 < lB at one location must be followed before they separate by a distance lB ,a nde is the electron gyroradius. We introduce an analytic Fokker-Planck model and a numerical Monte Carlo model of field-line separation in strong magnetohydrodynamic (MHD) turbulence to calculate LS(r0). We also determine LS(r0) using direct numerical simulations of MHD turbulence with zero mean magnetic field. All three approaches, like earlier models, predict that LS asymptotes to a value of order several lB as r0 is decreased toward ld in the large-lB/ld limit, where ld is the dissipation scale, which is taken to be the proton gyroradius. When the turbulence parameters used in the Fokker-Planck and Monte Carlo models are evaluated using direct numerical simulations, the Fokker-Planck model yields LSð� e Þ' 4:5lB and the Monte Carlo model yields LSð� e Þ' 6:5lB in the large-lB/ld limit. Extrapolating from our direct numerical simulations to the large-lB/ld limit, we find that LSð� e Þ' 5lB 10lB, implying thatT ' 0:1� S 0:2� S in galaxy clusters in the static field approximation. We also discuss the phenomenology of thermal conduction and particle diffusion in the presence of time-varying turbulent magnetic fields. Under the questionable assumption that turbulent re- sistivity completely reconnects field lines on the timescale lB/u ,w hereu is the rms turbulent velocity, we find that � T is enhanced by a moderate amount relative to the static field estimate for typical cluster conditions. Subject headings: galaxies: clusters: general — intergalactic medium — MHD — plasmas — turbulence

Particle Acceleration by Slow Modes in Strong Compressible Magnetohydrodynamic Turbulence, with Application to Solar Flares

Energetic particles that undergo strong pitch-angle scattering and diffuse through a plasma containing strong compressible MHD turbulence undergo diffusion in momentum space with diffusion coefficient Dp. If the rms turbulent velocity is of the order of the Alfven speed vA, the contribution to Dp from slow-mode eddies is (2p2vA/9l)[ln(lvA/D||) + 2γ - 3], where l is the outer scale of the turbulence, γ 0.577 is Euler's constant, and D|| is the spatial diffusion coefficient of energetic particles, which is assumed to satisfy D|| lvA. The energy spectrum of accelerated particles is derived for this value of Dp, taking into account Coulomb losses and particle escape from the acceleration region with an energy-independent escape time. Slow modes in the D|| lvA limit are an unlikely explanation for electron acceleration in solar flares to energies of 10-100 keV, because for solar flare conditions, the predicted acceleration times are too long, and the predicted energy spectra are too hard. The acceleration mechanism discussed in this paper could in principle explain the relatively hard spectra of gyrosynchrotron-emitting electrons in the 100-5000 keV range, but only if D|| lvA for such particles.

Turbulent burning velocity, burned gas distribution, and associated flame surface definition

Experimental studies of premixed, turbulent, gaseous explosion flames in a fan-stirred bomb are reported. The turbulence was uniform and isotropic, while changes in the rms turbulent velocity were achieved by changes in the speed of the fans. Central spark ignitions created mean spherical flame propagation. The spatial distributions of burned and unburned gases during the propagation were measured from the Mie scattering of tobacco smoke in a thin planar laser sheet. The plane was located just in front of the central spark gap and was generated by a copper vapor laser operating at a pulse rate of 4.5 kHz. High-speed schlieren images also were captured simultaneously. The distributions of the proportions of burned and unburned gases around circumferences were found for all radii at all stages of the explosion, and mean values of these proportions were derived as a function of the mean flame radius. The flame brush thickness increased with flame radius. The way the turbulent burning velocity is defined depends on the chosen associated flame radius. Various definitions are scrutinized and different flame radii presented, along with the associated turbulent burning velocities. Engulfment and mass turbulent burning velocities are compared. It is shown how the latter might conveniently be obtained from schlieren cine images. In a given explosion, the burning velocity increased with time and radius, as a consequence of the continual broadening of the effective spectrum of turbulence to which the flame was subjected. A decrease in the Markstein number of the mixture increased the turbulent burning velocity.

Modeling of maize starch explosions in a 12 m3 silo

This paper presents a 2-dimensional numerical model of Eulerian–Lagrangian multi-phase combustion flow to predict maize starch explosions in a 12 m3 silo. The flow field after ignition, flame propagation velocity and pressure development histories etc. during the explosion, are calculated. The data of non-uniform initial conditions including dust concentration, flow velocity and turbulent RMS velocity in the silo for this model are adopted from Hauert, Vogl and Radandt (1994) [Hauert, F., Vogl, A., Radandt, S. (1994). Measurement of turbulence and dust concentration in silos and vessels. 6th international colloquium on dust explosions (pp. 71–80), Shenyang, China, August 28–September 2, 1994.]. A simple concept of dust granule taking into consideration dust dispersion efficiency is proposed and introduced. The Lagrangian method is used to trace trajectories and granules, so it is easier to consider particle size distribution. The k−ε model is used to simulate the turbulence of the gas phase, and the particle's pulsation is modeled by random vector wind generated by the surrounding gas. In the combustion model, vaporization of water, volatilization of volatile, gas phase reaction and the particle's surface reaction are taken into account.

The influence of flow and turbulence on flame propagation through dust-air mixtures

Abstract Dust explosions are time-dependent flame propagation processes. Their description with “lumped parameter models” like the K St value are of limited validity only. More evidence of the process of flame propagation may be expected from an investigation of the flame velocity being composed by the laminar and turbulent velocities and the flow velocity. In the present paper the influences of the dust concentration and the flow velocity have been investigated by experiments in tube apparatus of three different diameters showing the dominating influence of the flow velocity and the turbulent rms velocity on the flame propagation. In addition, laminar and turbulent flame propagation has been investigated by an appropriate numerical model. Furthermore flow structures and particle distributions have been computed in a real size grain silo to assess the effects of possible explosions.

The optical interstellar spectrum of Vel (HD 81188) and a measurement of interstellar cloud turbulence

We present ultra-high resolution (R≈106>) observations of lines due to interstellar Na i D, Ca ii K, K i and Ti ii towards κ Vel (HD 81188). Five velocity components are identified in both Na i and Ca ii, and two in K i; an upper limit is recorded for Ti ii. The very high spectral resolution has enabled us to resolve fully the intrinsic interstellar line profiles, and thereby obtain reliable measurements of the velocity dispersion parameters (b-values) for all identified velocity components. By comparing the observed b-values for Na i and K i, which differ in mass by almost a factor of 2, it has been possible to derive the kinetic temperature (Tk) and line-of-sight rms turbulent velocity (vt) simultaneously for the two clouds identified in both elements. We obtain rigorous upper limits of 0.46 and 0.33 km s-1 for vt in these two clouds, which are definitely subsonic at the measured temperatures. The three-dimensional turbulent velocity (≡√ 3 ×vt) is also almost certainly subsonic for both components, although it might just exceed the isothermal sound speed if the kinetic temperatures were close to the lower limits permitted by the line-profile analysis.

Development of a Coherent Flamelet Model for a Spark-Ignited Turbulent Premixed Flame in a Closed Vessel

Three-dimensional calculations of turbulent combustion which include ignition, laminar and turbulent flame propagation and quenching at the wall are performed by the coherent flamelet model (CFM). The existing CFMs in the literature are tested and new forms are proposed. A mean stretch factor I 0 is introduced to consider the stretch and curvature effects of turbulence. Quenching at the wall is simulated by the simple wall flux model (SWFM) of the flame surface density. Two forms of the flame production term, CFM-1 and CFM-2, are tested to show the predictive capability of the CFM for turbulent burning velocity. CFM-1 has the flame production term given by the average rate of strain proposed by Cant et al. [20], while CFM-2 has the production term proportional to the rms turbulent velocity. It turns out that the turbulent burning velocity of CFM-2 is in reasonable agreement with the data of Checkel and Thomas and Bradley’s correlation with variation of the Karlovitz number, rms turbulent velocity, and integral length scale.

Dust cloud characterization and its influence on the pressure‐time‐history in silos

AbstractUsing VDI 3673 or NFPA guidelines for venting we distinguish between a homogeneous and inhomogeneous dust distribution in principle. Experiments were conducted in a 12 m3‐silo to measure the dust distribution, turbulence and the reduced explosion pressure using three different ways of generating the dust/air mixture: ring nozzles with pressurized dust chambers [1] (homogeneous distribution), [2] pneumatically fed vertically downwards [2] and tangentially [3]. Additionally, the dust feeding rate, the conveying velocity and the ignition position was changed. The reduction of the conveying velocity and therefore the decrease of the RMS turbulence velocity will cause a strong reduction of the explosion pressure and the pressure rate, respectively. The results show that the dust concentration in the pneumatically filled silo is inhomogeneous. However, the RMS turbulence velocity and the reduced explosion pressure for the homogeneous distribution and the vertical filling are of the same order. In comparison, the tangential feeding results in lower values. The calculations for the pneumatical vertical filling according to VDI 3673 guideline (inhomogeneous distribution) underestimate the resulting pressure for small vent areas, but the equations for the homogeneous distribution cover the experimental data.

Effects of Ingested Atmospheric Turbulence on Measured Tail Rotor Acoustics

Results from an outdoor hover test of a full-scale Lynx tail rotor are presented. The investigation was designed to further the understanding of the acoustics of an isolated tail rotor hovering out-of-ground effect in atmospheric turbulence, without the effects of the main rotor wake or other helicopter components. Measurements include simultaneous rotor performance, noise, inflow, and far-field atmospheric turbulence. Results with grid-generated inflow turbulence are also presented. The effects of turbulence ingestion on rotor noise are quantified. Turbulence ingestion noise is found to be the dominant noise mechanism at locations near the rotor axis. At these locations, the sound radiated by the hovering rotor increases with both increasing atmospheric wind speed and ingested rms turbulent velocity.

First results from the UHRF: ultra-high-resolution observations of atomic interstellar lines towards ζ Ophiuchi

We present ultra-high-resolution observations of optical interstellar lines towards zeta Oph obtained during the commissioning phase of the new Ultra-High-Resolution Facility (UHRF) at the AAT. The UHRF has achieved its design resolving power of R approximate to 10(6), and has very clearly resolved hyperfine splitting in three of the 11 identified Na I D-line velocity components towards zeta Oph. In addition, the intrinsic line profiles of the 3s-4p Na I doublet at 3302 Angstrom have been measured for the first time. 12 velocity components are identified in the interstellar Ca II K-line absorption profile, of which seven have definite velocity counterparts in the Na I profile. Three of the Na I velocity components have b-values which correspond to a gas temperature of about 200 K, for the case of pure thermal broadening. The strongest component in the sightline (-14.8 km s(-1)) was found to have a b-value of 0.6(-0.1)(+0.2) km s(-1), corresponding to a temperature of 500 K. If a true gas kinetic temperature of 54 K is assumed to apply to this component, from the H-2 rotational excitation temperature previously measured for the zeta Oph sightline, then the observed Na I and Fe I line profiles both imply an rms turbulent velocity of 0.4 km s(-1) within the cloud, just less than the local sound speed. The observed Ca II linewidths are all significantly larger than those of the corresponding Na I components. The Ca II components are interpreted as arising from warm neutral material (intercloud medium) surrounding cooler clouds, while half of the Na I components arise from cool clouds and half arise from warm intercloud material. The measured Na I/Ca II column density ratios, and the inferred temperatures, are consistent with a model in which calcium is heavily depleted on to grains in cool clouds but is restored to the gas phase by impact desorption in the warm intercloud medium.