High-repetition rate measurements of temperature and thermal dissipation in a non-premixed turbulent jet flame

High-repetition rate laser Rayleigh scattering is used to study the temperature fluctuations, power spectra, gradients, and thermal dissipation rate characteristics of a non-premixed turbulent jet flame at a Reynolds number of 15,200. The radial temperature gradient is measured by a two-point technique, whereas the axial gradient is measured from the temperature time-series combined with Taylor’s hypothesis. The temperature power spectra along the jet centerline exhibit only a small inertial subrange, probably because of the low local Reynolds number (Re_δ ≈ 2000), although a larger inertial subrange is present in the spectra at off-centerline locations. Scaling the frequency by the estimated Batchelor frequency improves the collapse of the dissipation region of the spectra, but this collapse is not as good as is obtained in non-reacting jets. Probability density functions of the thermal dissipation are shown to deviate from lognormal in the low-dissipation portion of the distribution when only one component of the gradient is used. In contrast, nearly log-normal distributions are obtained along the centerline when both axial and radial components are included, even for locations where the axial gradient is not resolved. The thermal dissipation PDFs measured off the centerline deviate from log-normal owing to large-scale intermittency. At one-half the visible flame length, the radial profile of the mean thermal dissipation exhibits a peak off the centerline, whereas farther downstream the peak dissipation occurs on the centerline. The mean thermal dissipation on centerline is observed to increase linearly with downstream distance, reach a peak at the location of maximum mean centerline temperature, and then decrease for farther downstream locations. Many of these observed trends are not consistent with equivalent non-reacting turbulent jet measurements, and thus indicate the importance of understanding how heat release modifies the turbulence structure of jet flames.     

Spatial scales of extinction and dissipation in the near field of non-premixed turbulent jet flames

Simultaneous high-resolution Rayleigh scattering imaging and planar laser-induced fluorescence (PLIF) of OH are combined to measure the dissipative scales associated with thermal mixing and the structure and scales of extinguished regions of the reaction zone. Measurements are performed throughout the near field (x/d = 5, 10, 15, 20) of two turbulent, non-premixed methane/hydrogen/nitrogen jet flames with Re = 15,200 and 22,800 (flames DLR-A and DLR-B of the TNF workshop). Locally extinguished regions are identified by discontinuities in the OH layers, and the extinction hole sizes are measured. For each flame, the probability density function of the hole sizes is very similar throughout the entire near field, with the most likely hole size being 1.9 mm in DLR-A and 1.1 mm in DLR-B. Extinction events are equally probable at all measurement locations in DLR-A. In the DLR-B flame, there is a progression from frequent extinction close to the nozzle to more continuous reaction zones further downstream. The approximate instantaneous location of the stoichiometric contour is determined using the OH-PLIF images, enabling statistical analysis of dissipative scales conditioned on rich and lean conditions. The widths of the thin, elongated structures that dominate the thermal dissipation field are measured. Statistics of this microscale are qualitatively similar in both flames, with the higher Reynolds number producing smaller scales throughout the flow field. For dissipation layers in rich regions, the layer widths increase significantly with increasing temperature, while on the lean side the layer widths decrease with increasing temperature.     

Measurements of flame orientation and scalar dissipation in turbulent partially premixed methane flames

Three turbulent flames were studied using a new experimental facility developed at Sandia National Laboratories. Line imaging of Raman and Rayleigh scattering and CO laser-induced fluorescence (LIF) yielded information on all major species, temperature, mixture fraction, and a 1D surrogate measure of scalar dissipation. Simultaneously, crossed planar OH LIF imaging provided information on the instantaneous flame orientation, allowing estimation of the full 3D (flame-normal) scalar dissipation rate. The three flames studied were methane–air piloted jet flames (Sandia flames C, D, and E), which cover a range in Reynolds number from 13,400 to 33,600. The statistics of the instantaneous flame orientation are examined in the different flames, with the purpose of studying the prevailing kinematics of isoscalar contours. The 1D and 3D results for scalar dissipation rate are examined in detail, both in the form of conditional averages and in the form of probability density functions. The effect of overall strain and Reynolds number on flame suppression and eventual extinction is also investigated, by examining the doubly conditional statistics of temperature in the form of S-shaped curves. This latter analysis reveals that double conditioning of temperature on both mixture fraction and scalar dissipation does not collapse the data from these flames onto the same curve at low scalar dissipation rates, as might be expected from simple flamelet concepts.     

Turbulence/flame/wall interactions in non-premixed inclined slot-jet flames impinging at a wall using direct numerical simulation

In the present work, three-dimensional turbulent non-premixed oblique slot-jet flames impinging at a wall were investigated using direct numerical simulation (DNS). Two cases are considered with the Damköhler number (Da) of case A being twice that of case B. A 17 species and 73-step mechanism for methane combustion was employed in the simulations. It was found that flame extinction in case B is more prominent compared to case A. Reignition in the lower branch of combustion for case A occurs when the scalar dissipation rate relaxes, while no reignition occurs in the lower branch for case B due to excessive scalar dissipation rate. A method was proposed to identify the flame quenching edges of turbulent non-premixed flames in wall-bounded flows based on the intersections of mixture fraction and OH mass fraction iso-surfaces. The flame/wall interactions were examined in terms of the quenching distance and the wall heat flux along the quenching edges. There is essentially no flame/wall interaction in case B due to the extinction caused by excessive turbulent mixing. In contrast, significant interactions between flames and the wall are observed in case A. The quenching distance is found to be negatively correlated with wall heat flux as previously reported in turbulent premixed flames. The influence of chemical reactions and wall on flow topologies was identified. The FS/U and FC/U topologies are found near flame edges, and the NNN/U topology appears when reignition occurs. The vortex-dominant topologies, FC/U and FS/S, play an increasingly important role as the jet turbulence develops.     

An elementary model for the validation of flamelet approximations in non-premixed turbulent combustion

The fundamental soundness of three flamelet models for non-premixed turbulent combustion is examined on the basis of their performance in an idealized model problem that merges ideas from the laminar asymptotic theory for non-premixed flames and rigorous homogenization theory for the diffusion of a passive scalar. The overall flame configuration is stabilized by a mean gradient in the passive scalar: large Damköhler number asymptotics results are available for the laminar case to quantify the finite-rate effects that cause the flame to depart from its equilibrium state; the same results can also be used to incorporate higher-order corrections in the approximation of the reactive variables in terms of the passive scalar. The use of such flamelet approximations has been extended well beyond the laminar regime as they lie at the core of practical strategies to simulate non-premixed flames in the turbulent regime: the flamelet representation avoids the problem of turbulence closure for the reactive variables by replacing it by the presumably much simpler closure problem for a passive scalar. It is precisely the validity of this substitution outside the laminar regime that is addressed here in the idealized context of a class of small-scale periodic flows for which extensive rigorous results are available for the passive scalar statistics. Results for this simplified problem are reported here for significant wide ranges of Peclet and Damköhler numbers. Asymptotic convergence is observed in terms of the Damköhler number, with a convergence rate that is found to match the laminar predictions and appears relatively insensitive to the Peclet number. The passive scalar dissipation plays a key role in achieving higher-order corrections for the finite-rate case: replacing its pointwise value by an averaged value is convenient practically and can be rigorously motivated for the class of flows studied here, but while it does achieve an overall improvement over the lower-order equilibrium model, the simplification compromises the higher asymptotic convergence observed with the original finite-rate flamelet model with exact local dissipation.(Some figures in this article are in colour only in the electronic version; see www.iop.org)     

Statistics of the energy dissipation rate and local enstrophy in turbulent channel flow

Using high-resolution direct numerical simulations, the height and Reynolds number dependence of high-order statistics of the energy dissipation rate and local enstrophy are examined in incompressible, fully developed turbulent channel flow. The statistics are studied over a range of wall distances, spanning the viscous sublayer to the channel flow centerline, for friction Reynolds numbers Re_τ=180 and Re_τ=381. The high resolution of the simulations allows dissipation and enstrophy moments up to fourth order to be calculated. These moments show a dependence on wall distance, and Reynolds number effects are observed at the edge of the logarithmic layer. Conditional analyses based on locations of intense rotation are also carried out in order to determine the contribution of vortical structures to the dissipation and enstrophy moments. Our analysis shows that, for the simulation at the larger Reynolds number, small-scale fluctuations of both dissipation and enstrophy show relatively small variations for z⁺?100.     

Flame speed and self-similar propagation of expanding turbulent premixed flames

In this Letter we present turbulent flame speeds and their scaling from experimental measurements on constant-pressure, unity Lewis number expanding turbulent flames, propagating in nearly homogeneous isotropic turbulence in a dual-chamber, fan-stirred vessel. It is found that the normalized turbulent flame speed as a function of the average radius scales as a turbulent Reynolds number to the one-half power, where the average radius is the length scale and the thermal diffusivity is the transport property, thus showing self-similar propagation. Utilizing this dependence it is found that the turbulent flame speeds from the present expanding flames and those from the Bunsen geometry in the literature can be unified by a turbulent Reynolds number based on flame length scales using recent theoretical results obtained by spectral closure of the transformed G equation.     

Problems of predicting turbulent burning rates

Different approaches to the modelling of turbulent combustion first are reviewed briefly. A unified, stretched flamelet approach then is presented. With Reynolds stress modelling and a generalized probability density function (PDF) of strain rate, it enables a source term, in the form of a probability of burning function, P_b, to be expressed as a function of Markstein numbers and the Karlovitz stretch factor. When P_b is combined with some turbulent flame fractal considerations, an expression is obtained for the turbulent burning velocity. When it is combined with the profile of the unstretched laminar flame volumetric heat release rate plotted against the reaction progress variable and the PDF of the latter, an expression is obtained for the mean volumetric turbulent heat release rate. Through these relationships experimental values of turbulent burning velocity might be used to evaluate P_b and hence the CFD source term, the mean volumetric heat release rate.

Different theoretical expressions for the turbulent burning velocity, including the present one, are compared with experimental measurements. The differences between these are discussed and this is followed by a review of CFD applications of these flamelet concepts to premixed and non-premixed combustion. The various assumptions made in the course of the analyses are scrutinized in the light of recent direct numerical simulations of turbulent flames and the applications to the flames of laser diagnostics. Remaining problem areas include a sufficiently general combination of strain rate and flame curvature PDFs to give a single PDF of flame stretch rate, the nature of flame quenching under positive and negative stretch rates, flame responses to changing stretch rates and the effects of flame instabilities.     

The energy and dissipation of turbulent fluctuations of wind velocity and temperature in the boundary layer of the atmosphere

The relationships between the energy of small-scale turbulence and its dissipation rate are studied based on the data of long-term high-frequency measurements of temperature and wind velocity fluctuations in urban area. It is shown that the energy of wind velocity turbulent fluctuations is linearly related to the dissipation rate ɛ. The proportionality coefficient between turbulent kinetic energy (TKE) and ɛ is dimensional and does not depend on the stratification of the atmosphere, the Richardson number, or the Monin-Obukhov scale. Measurements in different seasons show that this coefficient can be related to the mean velocity of adiabatic motions (sound speed or air temperature), which enables one to select a more universal constant, γ. A linear relationship between the temperature fluctuations variance (the characteristic of the inner energy of turbulence) and their dissipation rate is also shown. The revealed proportionality is confirmed by measurements in urban and forest conditions, as well as in the surface layer over a flat desert terrain.     

Scalar length scales and spatial averaging effects in turbulent piloted methane/air jet flames

The effects of spatial averaging in measurements of scalar variance and scalar dissipation in three piloted methane/air jet flames (Sandia flames C, D, and E) are investigated. Line imaging of Raman scattering, Rayleigh scattering, and laser-induced CO fluorescence is applied to obtain simultaneous single-shot measurements of temperature, the mass fractions of all major species, and mixture fraction, ξ, along 7-mm segments. Spatial filters are applied to ensembles of instantaneous profiles to quantify effects of spatial averaging on the Favre mean and variance of mixture fraction and scalar dissipation at several locations in the three flames. The radial contribution to scalar dissipation, χ_r = 2D_ξ (∂ξ/∂r)², is calculated from the filtered instantaneous profiles. The variance of mixture fraction tends to decrease linearly with increasing filter width, while the mean and variance of scalar dissipation are observed to follow an exponential dependence. In each case, the observed functional dependence is used to extrapolate to zero filter width, yielding estimates of the “fully resolved” profiles of measured quantities. Length scales for resolution of scalar variance and scalar dissipation are also extracted from the spatial filtering analysis and compared with length scales obtained from spatial autocorrelations. These results provide new insights on the small scale structure of turbulent jet flames and on the spatial resolution requirements for measurements of scalar variance and scalar dissipation.     

Logarithmic corrections to scaling in turbulent thermal convection

We use a simplified model of turbulent convection to compute analytically heat transport in a horizontal layer heated from below, as a function of the Rayleigh and the Prandtl number. At low Reynolds numbers, when most of the dissipation comes from the mean flow, we recover power classical scaling regimes of the Nusselt versus Rayleigh number, with exponent 1/3 or 1/4. At larger Reynolds number, velocity and temperature fluctuations become non-negligible in the dissipation. In these regimes, there is no exact power law dependence the Nusselt versus Rayleigh or Prandtl. Instead, we obtain logarithmic corrections to the classical soft (exponent 1/3) or ultra-hard (exponent 1/2) regimes, in a way consistent with the most accurate experimental measurements available nowadays. This sets a need for the search of new measurable quantities that are less prone to dimensional theories.     

Extended local balance model of turbulence and couette-taylor flow

An extended local balance model of turbulence, based on a new transport equation for the dissipation rate with a negative diffusion coefficient, is presented. Analytical solutions for the mean velocity and the dissipation rate for the turbulent Couette-Taylor problem are derived. The dependence of torque on the Reynolds number is obtained. These solutions depend only on two constants k=0.4 and C=9.5 of the turbulent boundary layer and, within the limits of a narrow channel, are reduced to the well-known von Karman's solutions for planar Couette flow. Strange attractor behavior in this limit is also observed.     

Simultaneous multiple-line Raman/Rayleigh/LIF measurements in combustion

It is demonstrated that multiple 1D Raman scattering, Rayleigh scattering, and laser-induced fluorescence (LIF) measurements can be performed simultaneously. This can be used for quasi-2D (or quasi-3D) single-shot measurements of multiple species and the temperature in turbulent reacting and non-reacting flows. The technique has the potential to yield more precise information than most competitive planar imaging approaches in combustion. For example, it can be used to overcome Raman/LIF interference problems in technical flames. This is achieved by a new optical set-up that makes use of an imaging spectrograph combined with fiber optics. Received: 13 October 1999 / Revised version: 26 November 1999 / Published online: 27 January 2000     

Laser imaging system for determination of three-dimensional scalar gradients in turbulent flames

An imaging system for the measurement of three-dimensional (3D) scalar gradients in turbulent hydrocarbon flames is described. Combined line imaging of Raman scattering, Rayleigh scattering, and CO laser-induced fluorescence (LIF) allows for simultaneous single-shot line measurements of major species, temperature, mixture fraction, and a one-dimensional surrogate of scalar dissipation rate in hydrocarbon flames, while simultaneous use of two crossed, planar LIF measurements of OH allows for determination of instantaneous flame orientation. In this manner the full 3D scalar dissipation can be estimated in some regions of a turbulent flame on a single-shot basis.     

Temperature gradient spectra and temperature dissipation rate in a turbulent convective flow

Determining mixing coefficients in oceanographic flows relies on the form of temperature gradient spectra in turbulent water flows at large wavenumbers. Several recent investigations concluded that these spectra are best described by the functional form proposed by Kraichnan rather than by the Batchelor form, more commonly used in oceanography. In this study, we provide additional support for this conclusion using laboratory measurements of the temperature gradient spectra in a Rayleigh–Bénard convective cell, in order to avoid difficulties inherent in oceanographic field measurements. The range of Rayleigh numbers in experiments is between Ra = 3×10⁷ and Ra = 5×10⁹. In addition to a traditional method of traversing thermistors, a novel optical technique recently introduced for oceanic measurements was used to obtain the spectra; comparison between these two methods serves as a validation test for the new optical technique. The temperature measurements were also augmented by 2D particle image velocimetry (PIV) observations. The measured dependence of the Nusselt number on the Rayleigh number followed Nu ∝ Ra^0.29 at Pr = 6 and was consistent with the literature data. We observed the temperature dissipation rate to vary by an order of magnitude over a horizontal transect at Ra > 10⁹. The temperature dissipation spectra obtained by both methods were in agreement over the Ra interval considered. The location of the temperature dissipation peaks was also consistent with PIV measured energy dissipation rates. Our data suggest increasing importance of top/bottom boundaries for the momentum and the temperature dissipation with increasing Ra number. Applied to oceanic upper ocean convection, our results imply that most of the dissipation occurs close to the air–sea boundary. Thus, attempts to parameterise or measure air–sea turbulent convective fluxes have to reflect the dominant role of near boundary dissipation at large Ra.     

Stability characteristics and flowfields of turbulent non-premixed swirling flames

A simple, yet representative, burner geometry is used for the investigation of highly swirling turbulent unconfined, non-premixed, flames of natural gas. The burner configuration comprises a ceramic faced bluff-body with a central fuel jet. The bluff-body is surrounded by an annulus that delivers a swirling primary flow of air. The entire burner assembly is housed in a wind tunnel providing a secondary co-flowing stream of air. This hybrid bluff-body/swirl burner configuration stabilizes complex turbulent flames not unlike those found in practical combustors, yet is amenable to modelling because of its well-defined boundary conditions. Full stability characteristics including blow-off limits and comprehensive maps of flame shapes are presented for swirling flames of three different fuel mixtures: compressed natural gas (CNG), CNG–air (1:2 by volume) and CNG–H₂ (1:1 by volume).

It is found that with increased fuel flow, flame blow-off mode may change with swirl number, S_g. At low swirl, the flame remains stable at the base but blows off in the neck region further downstream. At higher swirl numbers, the flames peel off completely from the burner's base. Swirling CNG–air flames are distinct in that they only undergo base blow-off. In the low range of swirl number, increasing S_g causes limited improvement in the blow-off limits of the flames investigated and (for a few cases) can even lead to some deterioration over a small intermediate range of S_g. It is only above a certain threshold of swirl that significant improvements in blow-off limits appear. Six flames are selected for further detailed flowfield and composition measurements and these differ in the combination of swirl number, primary axial velocity through the annulus, U_s, and bulk fuel jet velocity, U_j. Only velocity field measurements are presented in this paper. A number of flow features are resolved in these flames, which resemble those already associated with non-reacting swirling flows of equivalent swirl obtained with the present burner configuration. Additionally, asymmetric flowfields inherent to some flames are revealed where the fluidic centreline of the flow (defined in the two-dimensional (U–W velocity pair) velocity field by the ?ω? = 0 tangential velocity contour), meanders strongly on either side of the geometric centreline downstream by about one bluff-body diameter. Flow structures revealed by the velocity data are correlated to flame shapes to yield a better understanding of how the velocity field influences the flames physical characteristics.     

A parallel solution – adaptive method for three-dimensional turbulent non-premixed combusting flows

A parallel adaptive mesh refinement (AMR) algorithm is proposed and applied to the prediction of steady turbulent non-premixed compressible combusting flows in three space dimensions. The parallel solution-adaptive algorithm solves the system of partial-differential equations governing turbulent compressible flows of reactive thermally perfect gaseous mixtures using a fully coupled finite-volume formulation on body-fitted multi-block hexahedral meshes. The compressible formulation adopted herein can readily accommodate large density variations and thermo-acoustic phenomena. A flexible block-based hierarchical data structure is used to maintain the connectivity of the solution blocks in the multi-block mesh and to facilitate automatic solution-directed mesh adaptation according to physics-based refinement criteria. For calculations of near-wall turbulence, an automatic near-wall treatment readily accommodates situations during adaptive mesh refinement where the mesh resolution may not be sufficient for directly calculating near-wall turbulence using the low-Reynolds-number formulation. Numerical results for turbulent diffusion flames, including cold- and hot-flow predictions for a bluff-body burner, are described and compared to available experimental data. The numerical results demonstrate the validity and potential of the parallel AMR approach for predicting fine-scale features of complex turbulent non-premixed flames.     

The effect of timescale variation in multiple mapping conditioning mixing of PDF calculations for Sandia Flame series D–F

A stochastic implementation of the multiple mapping conditioning (MMC) model has been used for the modelling of turbulence–chemistry interactions in a series of turbulent jet diffusion flames with varying degrees of local extinction (Sandia Flames D–F). The mapping function approximates the cumulative probability distribution of mixture fraction and the corresponding variance can be controlled by a standard implementation of the scalar mixing timescale. The conditional fluctuations are controlled by a minor dissipation timescale, τ_min. The results show a clear dependence of the conditional fluctuations on the choice of the minor timescale, and the appropriate value for turbulent jet flames is similar to values determined in related direct numerical simulation (DNS) studies of homogeneous turbulent reacting flows. The predictions of means and variances of temperature and species mass fractions are very good for all flames, indicating an appropriate modelling of the conditional variances. Further sensitivity studies with respect to particle number density demonstrate a relative insensitivity of the results to the particle number in the numerical solution procedure. Good results can be obtained with as few as 10 particles per cell, allowing for a computationally inexpensive implementation of a Monte Carlo/probability density function (PDF) method.