LES of Low to High Turbulent Combustion in an Elevated Pressure Environment

A subgrid scale flame surface density combustion model for the Large Eddy Simulation (LES) of premixed combustion is derived and validated. The model is based on fractal characteristics of the flame surface, assuming a self similar wrinkling of the flame between smallest and largest wrinkling length scales. Experimental and direct numerical simulation databases as well as theoretical models are used to derive a model for the fractal parameters, namely the cut-off lengths and the fractal dimension suitable in the LES context. The combustion model is designed with the intent to simulate low as well as high Reynolds number premixed turbulent flame propagation and with a focus on correct scaling with pressure. The combustion model is validated by simulations of turbulent Bunsen flames with methane and propane fuel at pressure levels between 0.1 MPa and 2 MPa and at turbulence levels of $0 < u^{\prime }/s_{L}^{0} < 11$ , conditions typical for spark ignition engines. The predicted turbulent flame speed is in a very good agreement with the experimental data and a smooth transition from resolved flame wrinkling to fully modelled, nearly subgrid-only wrinkling is realized. Evaluating the influence of mesh resolution shows a predicted mean flame surface and turbulent flame speed independent of mesh resolution for cases with 9–86 % resolved flame surface. Additional simulations of a highly turbulent jet flame at 0.1 MPa and 0.5 MPa and the comparison with experimental data in terms of flame shape, velocity field and turbulent fluctuations validates the model also at conditions typical for gas turbines.     

An experimental study to determine fractal parameters for lean premixed flames

 In this study the fractal parameters of a lean, premixed methane-air flame were determined over a range of turbulence conditions. The focus of the present work was to improve the experimental technique so as to resolve the inner cutoff scale, the outer cutoff scale, and the fractal dimension. By adjusting the flow velocity through a set of three interchangeable grids in a steady-flow combustion tunnel, a range of turbulence intensities and scales was obtained within the test section. The integral scale varied from 2.5 to 5.5 mm and the turbulence intensity varied from 0.5 to 3.8 times the laminar burning velocity, while the equivalence ratio of the fuel–air mixture was 0.60. The flame was stabilized inside a 51 mm square, open-ended test section by means of a small, centrally-located, pilot burner. A 60 mm ×45 mm cross section of the flame was visualized by means of an argon-ion laser sheet and titanium dioxide seeding, and was recorded on high-sensitivity black and white film by a 35 mm camera using a shutter speed of 1/8000 s. The film negatives were digitized at 60 pixels/mm, equivalent to a resolution of 12 pixels/mm (83 μm per pixel) on the scale of the flame. Using commercially available software, the images were analyzed to identify the position of the flame front; custom software was used to determine the fractal dimension and the inner and outer cutoff scales of the turbulent flame. In the range of conditions reported in this paper, it was observed that the fractal dimension increased with turbulence level but the values were approximately 5% lower than those reported by others. The inner cutoff scale was found to increase with decreasing turbulence, thus confirming an earlier hypothesis about the smoothing effect of flame propagation at low turbulence levels. The outer cutoff scale varied from 11 to 16 mm and its value tended to decrease with increasing turbulence level. Received: 8 August 1995 / Accepted: 1 July 1996     

Resolution Requirements in Stochastic Field Simulation of Turbulent Premixed Flames

The spatial resolution requirements of the Stochastic Fields probability density function approach are investigated in the context of turbulent premixed combustion simulation. The Stochastic Fields approach is an attractive way to implement a transported Probability Density Function modelling framework into Large Eddy Simulations of turbulent combustion. In premixed combustion LES, the numerical grid should resolve flame-like structures that arise from solution of the Stochastic Fields equation. Through analysis of Stochastic Fields simulations of a freely-propagating planar turbulent premixed flame, it is shown that the flame-like structures in the Stochastic Fields simulations can be orders of magnitude narrower than the LES filter length scale. The under-resolution is worst for low Karlovitz number combustion, where the thickness of the Stochastic Fields flame structures is on the order of the laminar flame thickness. The effect of resolution on LES predictions is then assessed by performing LES of a laboratory Bunsen flame and comparing the effect of refining the grid spacing and filter length scale independently. The usual practice of setting the LES filter length scale equal to grid spacing leads to severe under-resolution and numerical thickening of the flame, and to substantial error in the turbulent flame speed. The numerical resolution required for accurate solution of the Stochastic Fields equations is prohibitive for many practical applications involving high-pressure premixed combustion. This motivates development of a Thickened Stochastic Fields approach (Picciani et al. Flow Turbul. Combust. X, YYY (2018) in order to ensure the numerical accuracy of Stochastic Fields simulations.     

Topology of turbulent premixed flame fronts resolved by simultaneous planar imaging of LIPF of OH radical and rayleigh scattering

 Planar images of Rayleigh scattering and laser-induced predissociative OH-fluorescence (OH-LIPF) have been obtained simultaneously in turbulent premixed jet flames on a single-shot basis. The geometric structure of temperature and OH isocontours were extracted for fractal analysis. A power-law fractal behavior can be identified in the ensemble-averaged flame length measure. It was found that the inner and outer cut-off scales of OH contours are larger than those of the iso-temperature contours; while the OH images show comparatively smaller fractal dimensions. The joint-pdf ’s between flame temperature and OH LIPF signals at different heights are also derived to evaluate the flame stretch effect on local flame structure. Comparison of image pairs near the extinction limit suggests that Rayleigh thermometry is more adequate to characterize the fine-scale flame front wrinkling in highly stretched turbulent premixed flames. Received: 12 September 1997/Accepted: 19 May 1998     

Stationary modes of combustion in a fine-scale turbulent stream

The majority of models of the turbulent combustion of gases are based mainly on intuitive concepts concerning the processes occurring in the flame. The characteristics of a turbulent flame are estimated from considerations of dimensionality and similarity. A detailed review of works on turbulent combustion is given in [1]. Problems on the calculation of the combustion rate in a turbulent stream as a proper value of the equations of heat and mass transfer and of the corresponding boundary conditions have recently been raised. Here too one must rest on assumptions of a semiempirical nature, which in large measure is connected with the inadequate level of development of turbulence theory. In the present work the equation of propagation of the zone of chemical reactions in the stream is averaged statistically by analogy with studies of turbulent flows. Correct averaging is possible at scales of hydrodynamic disturbances smaller than the flame thickness (fine-scale turbulence). The temperature pulsations are related with the size of the heat flux using the theory of mixing lengths. The main influence is specific to effects arising during averaging of the heat release function. Two stationary modes, distinguished by the normal propagation velocity ₁, are isolated within the framework of the Cauchy problem with a given initial mixture temperature and zero heat flux in the burned gas. A heat conduction mode occurs with a stream velocity > ₁ and an induction mode with < ₁. An expression is found for ₁ which reflects the principal effects in the flame and which in the limit coincides with the equation of Zel'dovich and Frank-Kamenetskii for a laminar flame. In those cases when the distorting effect of the heat release function is small, the turbulence affects the combustion rate through mechanisms of intensification of transport processes.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 118–124, September–October, 1973.     

The Problems of the Turbulent Burning Velocity

The paper reviews the practical problems in measuring a turbulent burning velocity that gives the mass rate of burning. These largely centre on identifying an appropriate flame surface to associate with the turbulent burning velocity, u _t , and the density of the unburned mixture. Such a flame surface has been identified, in terms of the mean reaction progress variable, $\bar {c}$ , for explosive flame propagation in a fan-stirred bomb. Measurement of $\bar {c}$ makes possible an estimation of the flame surface density, ??, from the relationship ${\it \Sigma} =k\bar {c}\left( {1-\bar {c}} \right)$ . It is shown that in such explosions, mass rates of burning derived from the measured total flame surface area agreed well with those found from the measured turbulent burning velocity. Flamelet considerations identify appropriate dimensionless correlating parameters for u _t . As a result, correlations of turbulent burning velocity divided by the effective rms turbulent velocity, are plotted against the turbulent Karlovitz stretch factor, K, for different values of the Markstein number for flame strain rate, Ma_sr. These plots cover a wide range of variables, including pressure and fuels, and are indicative of different regimes of turbulent combustion. At the lower values of K, there is some evidence of increases in u _t and k due to high-frequency flame surface wrinkling arising from flame instabilities. These increase as Ma_sr becomes more negative. It is found from the developed value of the mean flame surface density throughout the flame brush that, to a first approximation, an increase in u _t for a given mixture is accompanied by a proportional increase in the volume of the brush. The analysis shows that the volume fraction of the turbulent flame brush that is reacting is quite small.     

Spatial resolution of PIV for the measurement of turbulence

Recent technological advancements have made the use of particle image velocimetry (PIV) more widespread for studying turbulent flows over a wide range of scales. Although PIV does not threaten to make obsolete more mature techniques, such as hot-wire anemometry (HWA), it is justifiably becoming an increasingly important tool for turbulence research. This paper assesses the ability of PIV to resolve all relevant scales in a classical turbulent flow, namely grid turbulence, via a comparison with theoretical predictions as well as HWA measurements. Particular attention is given to the statistical convergence of mean turbulent quantities and the spatial resolution of PIV. An analytical method is developed to quantify and correct for the effect of the finite spatial resolution of PIV measurements. While the present uncorrected PIV results largely underestimate the mean turbulent kinetic energy and energy dissipation rate, the corrected measurements agree to a close approximation with the HWA data. The transport equation for the second-order structure function in grid turbulence is used to establish the range of scales affected by the limited resolution. The results show that PIV, due to the geometry of its sensing domain, must meet slightly more stringent requirements in terms of resolution, compared with HWA, in order to provide reliable measurements in turbulence.

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A method to simultaneously image two-dimensional mixture fraction, scalar dissipation rate, temperature and fuel consumption rate fields in a turbulent non-premixed jet flame

A new imaging technique was developed that provides two-dimensional images of the mixture fraction (ξ), scalar dissipation rate (χ), temperature (T), and fuel consumption rate in a turbulent non-premixed jet flame. The new method is based on “seeding” nitric oxide (NO) into a particular carbon monoxide–air flame in which it remains passive. It is first demonstrated that the mass fraction of NO is a conserved scalar in the present carbon monoxide–air flame configuration, using both laminar flame calibration experiments and computations with full chemistry. Simultaneous planar laser-induced fluorescence (PLIF) and planar Rayleigh scattering temperature imaging allow a quantitative determination of the local NO mass fraction and hence mixture fraction in the turbulent jet flame. The instantaneous mixture fraction fields in conjunction with the local temperature fields are then used to determine quantitative scalar dissipation rate fields. Advantages of the present technique include an improved signal-to-noise ratio over previous Raman scattering techniques, improved accuracy near the stoichiometric contour because simplifying chemistry assumptions are not required, and the ability to measure ξ and χ in flames experiencing localized extinction. However, the method of measuring ξ based on the passive NO is restricted to dry carbon monoxide–air flames due to the well-controlled flame chemistry. Sample imaging results for ξ, χ, T, and are presented that show high levels of signal-to-noise while resolving the smallest mixing scales of the turbulent flowfield. The application, accuracy, and limitations of the present technique are discussed.     

Fractal analysis of turbulent premixed flame surface

The fractal-like character of the laminar flamelet surface in turbulent premixed combustion of lean methane/air mixtures was studied by using the laser tomography technique to visualize the instantaneous flame surface in the two-dimensional section cut by the laser sheet. The fractal analysis of the surface revealed that the surface actually exhibits a self-similarity behavior in a narrow range of scale, and the value of fractal dimension can be defined. The inner cutoff scale was the laminar flame thickness, while the outer cutoff scale was the flame size. The fractal dimension was found to depend on the orientation of the section, and to increase towards downstream. It is suggested that the observed fractal-like character is not directly connected to approach flow turbulence, but should represent certain aspects of the flamelet itself.     

Particle image velocimetry with optical flow

 An optical Flow technique based on the use of Dynamic Programming has been applied to Particle Image Velocimetry thus yielding a significant increase in the accuracy and spatial resolution of the velocity field. Results are presented for calibrated synthetic sequences of images and for sequences of real images taken for a thermally driven flow of water with a freezing front. The accuracy remains better than 0.5 pixel/frame for tested two-image sequences and 0.2 pixel/frame for four-image sequences, even with a 10% added noise level and allowing 10% of particles of appear or disappear. A velocity vector is obtained for every pixel of the image. Received: 18 July 1997/Accepted: 5 December 1997     

Measurements of ensemble averaged flame dynamics using spatially resolved analysis

When applying flame sheet models to predict the dynamics of turbulent flames, it is common to model turbulence using ensemble averaging of the velocity. Measurements of the flame dynamics were made to support use this type of methodology, by measuring the dynamic volume of the flame using phase averaged images of the CH^∗ chemiluminescence. The dynamics agreed with the common behavior described in the literature, namely frequency scaling according to Strouhal number based on flow convective timescales. However, slightly different timescales were observed for the response magnitude and phase, indicating the possibility of different scaling mechanisms at work between these phenomena. The flame heat release rate dynamics were found to be identical to the dynamic response of the flame volume to inlet velocity perturbations, suggesting a simple proportionality between heat release rate and the flame volume. This result supports the use of ensemble averaging for modeling of the turbulent velocity for predictions of flame dynamics.     

Scalar interfaces in digital images of turbulent flows

A scalar interface is defined as the surface separating the scalar-marked regions of a turbulent flow from the rest. The problem of determining the two-dimensional intersections of scalar interfaces is examined, taking as a specific example digital images of an axisymmetric jet visualized by laser-induced fluorescence. The usefulness of gradient and Laplacian techniques for this purpose is assessed, and it is shown that setting a proper threshold on the pixel intensity works well if the signal/noise ratio is high. Two methods of determining the proper threshold are presented, and the results are discussed. As one application of the technique, the fractal dimension of the scalar interface is calculated.     

Role of Buoyancy on Instabilities and Structure of Transitional Gas Jet Diffusion Flames

Transitional jet diffusion flames provide the link between dynamics of laminar and turbulent flames. In this study, instabilities and their interaction with the flow structure are explored in a transitional jet diffusion flame, with focus on isolating buoyancy effects. Experiments are conducted in hydrogen flames with fuel jet Reynolds number of up to 2,200 and average jet velocity of up to 54 m/s. Since the fuel jet is laminar at the injector exit, the transition from laminar to turbulent flame occurs by the hydrodynamic instabilities in the shear layer of fuel jet. The instabilities and the flow structures are visualized and quantified by the rainbow schlieren deflectometry technique coupled with a high-speed imaging system. The schlieren images acquired at 2,000 frames per second allowed exposure time of 23 μs with spatial resolution of 0.4 mm. Results identify a hitherto unknown secondary instability in the flame surface, provide explanation for the observed intermittency in the breakpoint length, show coherent vortical structures downstream of the flame breakpoint, and illustrate gradual breakdown of coherent structures into small-scale random structures in the far field turbulent region.     

Effect of metachronal phasing on the pumping efficiency of oscillating plate arrays

An aqueous solution of sodium iodide and zinc iodide is proposed as a fluid that matches the refractive index of a solid manufactured by rapid prototyping. This enabled optical measurements in single-phase flow through porous structures. Experiments were also done with an organic index-matching fluid (anisole) in porous structures of different dimensions. To compare experiments with different viscosities and dimensions, we employed Reynolds similarity to deduce the scaling laws. One of the target quantities of our investigation was the dissipation rate of turbulent kinetic energy. Different models for the dissipation rate estimation were evaluated by comparing isotropy ratios. As in many other studies also, our experiments were not capable of resolving the velocity field down to the Kolmogorov length scale, and therefore, the dissipation rate has to be considered as underestimated. This is visible in experiments of different relative resolutions. However, being near the Kolmogorov scale allows estimating a reproducible, yet underestimated spatial distribution of dissipation rate inside the porous structure. Based on these results, the $k-\varepsilon$ model was used to estimate the turbulent diffusivity. Comparing it to the dispersion coefficient obtained in the same porous structure, we conclude that even at $Re_p=500$ the turbulent diffusivity makes up only a small part of mass transfer in axial direction. The main part is therefore attributed to Taylor dispersion.     

Spatial resolution effects on the measurement of scalar variance and scalar gradient in turbulent nonpremixed jet flames

The effect of spatial averaging is important for scalar gradient measurements in turbulent nonpremixed flames, especially when the local dissipation length scale is small. Line imaging of Raman, Rayleigh and CO-LIF is used to investigate the effects of experimental resolution on the scalar variance and radial gradient in the near field of turbulent nonpremixed CH₄/H₂/N₂ jet flames at Reynolds numbers of 15,200 and 22,800 (DLR-A and B) and in piloted CH₄/air jet flames at Reynolds numbers of 13,400, 22,400 and 33,600 (Sandia flames C/D/E). The finite spatial resolution effects are studied by applying the Box filter with varying filter widths. The resulting resolution curves for both scalar variance and mean squared-gradient follow nearly the same trends as theoretical curves calculated from the model turbulence kinetic energy spectrum of Pope. The observed collapse of resolution curves of mean squared-gradient for nearly all studied cases implies the shape of the dissipation spectrum is approximately universal. Fluid transport properties are shown to have no effect on the dissipation resolution curve, which implies that the dissipation length scale inferred from the square gradient is equivalent to the length scale for the scalar dissipation rate, which includes the diffusion coefficient. With the Box filter, the required spatial resolution to resolve 98% of the mean dissipation rate is about one−two times of the dissipation cutoff length scale (analogous to the Batchelor scale in turbulent isothermal flows). The effects of resolution on the variances of mixture fraction, temperature, and the inverted Rayleigh signal are also compared. The ratio of the filtered variance to the true variance is shown to depend nearly linearly on the probe resolution. The inverted Rayleigh scattering signal can be used to study the resolution effect on temperature variance even when the Rayleigh scattering cross section is not constant. The experimental results also indicate that these laboratory scale turbulent jet flames have small effective Reynolds numbers, such that there is some direct interaction of the large (energy containing) and small (dissipative) scalar length scales, especially for the near field case at x/d = 7.5 of the piloted Sandia flames C/D/E.     

A-priori testing of an eddy viscosity model for the density-weighted subgrid scale stress tensor in turbulent premixed flames

In this study, we report on the direct measurement of the density-weighted subgrid scale (SGS) stress tensor in turbulent premixed flames. In large-eddy simulations (LES), this unresolved tensor is typically modelled using eddy viscosity approaches. Additionally to the direct measurement, we provide a pure experimentally based a-priori test of the commonly used eddy viscosity model suggested by Smagorinsky. For two turbulent premixed V-shaped methane–air flames, a statistical analysis is presented where the correlation between the directly measured SGS stress tensor and the eddy viscosity model following Smagorinsky is tested. The measurement strategy is based on the application of a dual-plane stereo-PIV technique which enables the measurement of the 3D flow field in two parallel planes. This allows the determination of velocities as well as velocity gradients in all three directions. Here, a vector resolution of 118 μm was achieved. For a priori testing, the data are subjected to a spatial filtering procedure that reproduces the application of the filter function in LES. The calculation of velocity gradients is performed after the application of this spatial averaging. Additionally to the velocity field, the flame front position is deduced from the clearly observable step in the tracer particle number density between burnt and unburnt regions of the flame. This facilitates the direct single-shot-based evaluation of all components of the density-weighted SGS stress tensor. Additionally, the model expressions related to these terms can be determined, which is done in this first study for the static Smagorinsky model. With that, the instantaneous local comparison between directly measured stress terms and modelled terms is possible, based on the instantaneous local evaluation procedure. The measurement procedure is described, and first results are presented and discussed. They show a rather poor performance of the static form of the Smagorinsky model (with fixed Smagorinsky constant). Our future aims are to use the directly measured SGS data for the a-priori comparison with more advanced models.     

Imaging of premixed flames in microgravity

A laser schlieren system which uses video recording and digital images analysis has been developed and applied successfully to microgravity combustion experiments performed in a drop-tower. The optical system and the experiment are installed within a small package which is subjected to free-fall. The images are recorded on video tape and are digitized and analyzed by a computer-controlled image processor. The experimental results include laminar and turbulent premixed conical flames in microgravity, normal positive gravity (upward), and reverse gravity (downward). The procedures to extract frequency information from the digitized images are described. Many gross features of the effects of gravity on premixed conical flames are found. Flames that ignite easily in normal gravity fail to ignite in microgravity. Buoyancy driven instabilities associated with an interface formed between the hot products and the cold surrounding air is the mechanism through which gravity influences premixed laminar and turbulent flames. In normal gravity, this causes the flame to flicker. In reverse gravity, -g, and microgravity, g, the interface is stable and flame flickering ceases. The flickering frequencies of +g flames vary with changing upstream boundary conditions. The absence of flame flickering in g suggest that g flames would be less sensitive to these changes.This work is supported by NASA Microgravity Sciences and Applications Divisions under contract No. C-32000-R through the U.S. Department of Energy Contract No. DE-AC03-76F00098. Technical support is provided by NASA Lewis Research Center. Project Scientist is Dr. Karen J. Weiland. The authors would like to acknowledge Dr. Liming Zhou for his contribution to early testing of the schlieren system, and to Mr. Gray Hubbard for writing the image analysis software     

CCD Recording method for cross-correlation PIV development in unstationary high speed flow

Up to now, the use of CCD cameras, for cross-correlation development in Particle Image Velocimetry (PIV), is reduced to relatively slow flows. An original storage method of two images on the two half frames of a video camera permits now to decrease the interval between exposures (10 s). Therefore, it is possible to study high speed flows. Applications are shown of a jet and a turbulent flame propagation.