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.     

Numerical analysis of entropy generation in a turbulent diffusion flame

Thermodynamic irreversibilities generated by the combustion process are evaluated and analyzed numerically. The numerical simulation is performed for a reference case study for which experimental data are available in the literature: diffusion flame properties in a common burner configuration are studied by the Fluent software with the standard k–ε turbulence model and two-step chemical reaction. The study quantifies the contribution of each mechanism to entropy generation, i.e., friction, heat conduction, species diffusion, and chemical reaction. The chemical reaction and heat conduction are found to be the major sources of entropy production. Preheating of air reduces thermodynamic irreversibilities within the combustor.     

LIF-LII measurements in a turbulent gas-jet flame

 Detection of soot by laser-induced incandescence (LII) and fuel-rich (PAH containing) regions by laser-induced fluorescence (LIF) is demonstrated in a turbulent, Re=2500, ethylene gas-jet diffusion flame. Simultaneous combined LIF–LII images allow identification of regions containing PAH or soot and their relative spatial relationship. Separate LII images confirm the identity of the soot containing regions shown in the LIF–LII images. Variations in the size, structure, spatial location and intensity of the PAH and soot containing regions are shown qualitatively in the images and quantified through histograms of image intensities and spatial extents. Received: 9 September 1996/Accepted: 4 February 1997     

Schlieren measurement of turbulent structure in a diffusion flame

The regular and random mixing structures in a turbulent diffusion flame were investigated using the quantitative, dynamic crossed-beam schlieren method. Evidence was found close to the nozzle relating to the vortexlike structure of eddies surrounding the central fuel jet flow. The observations also make possible resolution of turbulent intensity, scales, convection, and spectra within the diffusion flame without the use of seeding or intrusion of measuring probes. It is found that length scales and other turbulence parameters in the diffusion flame progressively revert to values similar to those expected and observed in scalar passive mixing as the combustion reaction intensity reduces with axial distance from the nozzle system.     

Measurement of velocity-temperature correlations in a turbulent diffusion flame

The paper reports on the nonintrusive, simultaneous measurement of velocity and temperature fluctuations in a turbulent jet diffusion flame. Velocity fluctuations were measured using laser Doppler anemometry (LDA), whereas coherent anti-Stokes Raman spectroscopy (CARS) was used for temperature measurements. The simultaneous measurements were affected by both density bias and velocity bias because the LDA imposed a form of biased sampling on the CARS. The measured velocity-temperature correlation coefficients indicated that the gradient-diffusion hypothesis is reasonably accurate for the radial direction. However, for the axial direction the gradient diffusion hypothesis is accurate only in the central region of the flame, while countergradient diffusion is found in the outer region.     

Tomographic PIV measurements in a turbulent lifted jet flame

Measurements of instantaneous volumetric flow fields are required for an improved understanding of turbulent flames. In non-reacting flows, tomographic particle image velocimetry (TPIV) is an established method for three-dimensional (3D) flow measurements. In flames, the reconstruction of the particles location becomes challenging due to a locally varying index of refraction causing beam-steering. This work presents TPIV measurements within a turbulent lifted non-premixed methane jet flame. Solid seeding particles were used to provide the 3D flow field in the vicinity of the flame base, including unburned and burned regions. Four cameras were arranged in a horizontal plane around the jet flame. Following an iterative volumetric self-calibration procedure, the remaining disparity caused by the flame was less than 0.2 pixels. Comparisons with conventional two-component PIV in terms of mean and rms values provided additional confidence in the TPIV measurements.     

Propagation rate and limits of existence of a turbulent flame

In a theoretical study of turbulent burning it is usually assumed that the average rate of the chemical reaction (heat release) is determined only by the average temperature. Ya. B. Zel'dovich [1] and later T. Karman [2] noted the necessity of taking into account the effect of temperature pulsations on the reaction rate. A quantitative estimate of this effect on the reaction rate constant is given in [3]. A critical analysis of various approaches to the theoretical study of turbulent flames is given in the reviews [4, 5]. In the present article, it is shown that, taking the pulsation component of the temperature and concentration into account, the average rate of the chemical reaction depends on the gradient of the mean temperature and the scale of the turbulent pulsations. The case, where a first-order reaction takes place in the flame is studied in detail. Existence and uniqueness theorems which determine the limits of the propagation of flames are proven. Quantitative rules for the propagation rate, limit, and structure of a turbulent flame front are analyzed with respect to the results of a numerical calculation of a series of variants. Dimensional interpolation equations are presented for the total propagation rate of a flame.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 65–76, May–June, 1972.     

Thermal-field structure of a non-premixed turbulent flame formed in a strong pressure-gradient flow

Statistical characteristics of a non-premixed turbulent flame formed in a curved-rectangular duct and spatio-temporal structures of the thermal field were investigated experimentally. The flame was much affected by a strong pressure gradient in the radial direction of the duct curvature, which caused strong gradient diffusion in turbulent heat transfer on the inner-wall side of the flame and, in contrast, counter-gradient heat transfer on the outer-wall side. Two-point correlation measurement of temperature fields revealed that, in the strong gradient diffusion region, a spatial thermal pattern generated by turbulent mixing of high- and low-temperature fluid parcels was advected downstream with little diffusion. In contrast, the pattern was attenuated and diffused rapidly in the counter-gradient diffusion region. These results accurately correspond to the generation mechanism of the counter-gradient heat transport so far observed in stably stratified turbulent flows.     

Mathematical theory of the stationary propagation velocity of a fine-scale turbulent flame

A boundary-value problem in the theory of propagation of a fine-scale turbulent flame is investigated, taking into account the influence of temperature and concentration pulsations on the magnitude of the heat liberation rate. In contrast to [1], the case when a second-order reaction proceeds in the flame is examined in detail. Conditions are found for the existence of a turbulent flame; the structure of the flame front is studied by a computational method. A change in the progress of the reaction is disclosed near the propagation limits.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 109–114, July–August, 1973.     

Efficient retrieval of the thermo‐acoustic flame transfer function from a linearized CFD simulation of a turbulent flame

The stability of thermo‐acoustic pressure oscillations in a lean premixed methane‐fired generic gas turbine combustor is investigated. A key element in predicting the acoustically unstable operating conditions of the combustor is the flame transfer function. This function represents the dynamic relationship between a fluctuation in the combustor inlet conditions and the flame's acoustic response. A transient numerical experiment involving spectral analysis in computational fluid dynamics (CFD) is usually conducted to predict the flame transfer function. An important drawback of this spectral method application to numerical simulations is the required computational effort. A much faster and more accurate method to calculate the transfer function is derived in this paper by using a most important basic assumption: the fluctuations must be small enough for the system to behave linear. This alternative method, which is called the linear coefficient method, uses a linear representation of the unsteady equations describing the CFD problem. This linearization is applied around a steady‐state solution of the problem, where it can consequently describe the dynamics of the system. Finally, the flame transfer function can be calculated from this linear representation. The advantage of this approach is that one only needs a steady‐state solution and linearization of the unsteady equations for calculating a dynamic transfer function, i.e. no time‐consuming transient simulations are necessary anymore. Nevertheless, as a consequence of the large number of degrees of freedom in a CFD problem, an extra order reduction step needs to be performed prior to calculating the transfer function from the linear representation. Still, the linear coefficient method shows a significant gain in both speed and accuracy when calculating the transfer function from the linear representation as compared to a spectral analysis‐based calculation. Hence, this method gives a major improvement to the application of the flame transfer function as a thermo‐acoustic design tool. Copyright © 2007 John Wiley & Sons, Ltd.     

CH double-pulsed PLIF measurement in turbulent premixed flame

The flame displacement speeds in turbulent premixed flames have been measured directly by the CH double-pulsed planar laser-induced fluorescence (PLIF). The CH double-pulsed PLIF systems consist of two independent conventional CH PLIF measurement systems and laser beams from each laser system are led to same optical pass using the difference of polarization. The highly time-resolved measurements are conducted in relatively high Reynolds number turbulent premixed flames on a swirl-stabilized combustor. Since the time interval of the successive CH PLIF can be selected to any optimum value for the purpose intended, both of the large scale dynamics and local displacement of the flame front can be discussed. By selecting an appropriate time interval (100–200 μs), deformations of the flame front are captured clearly. Successive CH fluorescence images reveal the burning/generating process of the unburned mixtures or the handgrip structures in burnt gas, which have been predicted by three-dimensional direct numerical simulations of turbulent premixed flames. To evaluate the local flame displacement speed directly from the successive CH images, a flame front identification scheme and a displacement vector evaluation scheme are developed. Direct measurements of flame displacement speed are conducted by selecting a minute time interval (≈30 μs) for different Reynolds number (Re _λ = 63.1–115.0). Local flame displacement speeds coincide well for different Reynolds number cases. Furthermore, comparisons of the mean flame displacement speed and the mean fluid velocity show that the convection in the turbulent flames will affect the flame displacement speed for high Reynolds number flames.     

Direct Numerical Simulation of a Gaussian acoustic wave interaction with a turbulent premixed flame

The interaction of a Gaussian negative pulse with a H₂/O₂/N₂ turbulent premixed flame is examined using Direct Numerical Simulation (DNS). Transport properties and chemical kinetics are described in a very detailed manner. An extended nonlinear local Rayleigh's criterion, for laminar as well as turbulent, premixed or nonpremixed flames, is proposed. Situations in which amplification or attenuation occur are listed. Calculations of a turbulent flame are then carried out with and without an acoustic wave and results are recorded at the same time. The influence of acoustic wave/turbulent flame interaction is obtained by a simple difference. It is shown that longitudinal and transverse velocity components are perturbed by the turbulent flame. Moreover, the vorticity induced by the acoustic wave is observed to be weak. Finally, Rayleigh's criterion shows that wave amplification occurs punctually. To cite this article: A. Laverdant, D. Thévenin, C. R. Mecanique 333 (2005).     

Influence of strain rate on a premixed turbulent flame stabilized in a stagnating flow

In order to describe the influence of strain rate on the behaviour and on the characteristics of premixed turbulent combustion, a methane-air flame stabilized by a stagnation plate is studied experimentally. The plate is set at a fixed distance from the nozzle and the strain is varied by changing the exit velocity at the nozzle. At low strain rates, the evolution of profiles of mean axial velocity along the centreline agrees with classical results, and these results are used to characterise the flame. The variation of these characteristics with parameters such as plate temperature, equivalence ratio and strain rate is investigated. At the highest strain rates, the shape of the axial velocity profiles along the stagnation line is modified. This change emphasises a critical strain rate K _C that has to be considered as well as the extinction strain rate K _EX. Measurements also demonstrate the existence of a virtual stagnation point that moves towards the plate as the strain rate increases. The axial and transverse fluctuating components of the velocity are analyzed along the centreline and very close to the wall. The results show the importance of the critical strain rate K _C , which is linked to a drastic change in the evolution of the axial and transverse velocity fluctuations. Received: 15 January 1998/Accepted: 7 February 1999     

Finite element solution of an enclosed turbulent diffusion flame

A finite element formulation of enclosed turbulent diffusion flames is presented. A primitive variables approach is preferred in the analysis. A mixed interpolation is employed for the velocity and pressure. In the solution of the Navier-Stokes equations, a segregated formulation is adopted, where the pressure discretization equation is obtained directly from the discretized continuity equation, considering the velocity-pressure relationships in the discretized momentum equations. The state of turbulence is defined by a κ–? model. Near solid boundaries, a wall function approach is employed. The combustion rates are estimated using the eddy dissipation concept. The expensive direct treatment of the integrodifferential equations of radiation is avoided by employing the moment method, which allows the derivation of an approximate local field equation for the radiation intensity. The proposed finite element model is verified by investigating a technical turbulent diffusion flame of semi-industrial size, and comparing the results with experiments and finite difference predictions.     

Numerical simulation of methane-air turbulent jet flame using a new second-order moment model

A new second-order moment model for turbulent combustion is applied in the simulation of methane-air turbulent jet flame. The predicted results are compared with the experimental results and with those predicted using the wellknown EBU-Arrhenius model and the original second-order moment model. The comparison shows the advantage of the new model that it requires almost the same computational storage and time as that of the original second-order moment model, but its modeling results are in better agreement with experiments than those using other models. Hence, the new second-order moment model is promising in modeling turbulent combustion with NO_x formation with finite reaction rate for engineering application. The project sponsored by the Foundation for Doctorate Thesis of Tsinghua University, and the National Key Project in 1999–2004 sponsored by the Ministry of Science and Technology of China     

管内均相湍流燃烧加速的数值模拟

通过均相流体模型、湍流k 模型和EBU(EddyBreak Up) Arrhenius燃烧模型 ,选用Simple格式对管中戊烷和空气的燃烧实例进行了数值求解。其结果反映了燃烧导致的爆炸过程中管内流场各参数的变化规律 ,揭示了管内燃烧、流动、湍流之间的正反馈耦合关系 ,并与实验结果和相关数值结果基本相符。     

Large eddy simulation of a turbulent flame using tabulated chemistry with a novel multivariate PDF

ABSTRACT

A novel, efficient method to account for multivariate probability density functions (PDFs) in the context of the flamelet generated manifolds (FGM) approach in a large eddy simulation (LES) framework is presented and discussed. It consists of applying the ‘Correlation Set by Simulated Annealing (CSSA)’ algorithm on univariate samples of each control variable to recombine them into multivariate samples in joint space, while accounting for the needed covariances. This is done on the fly and on a cell-by-cell basis. Thereby, the assumption of statistical independence of the control variables has been relaxed. The PDF is represented in a discrete manner and the integration is replaced through ensemble averaging. Consequently, the shape of the PDF no longer appears in the look-up table. The algorithm has been validated in the context of LES calculations of two configurations. Compared to a conventional pre-integrated FGM approach, the required CPU time has increased only modestly.     

Digital speckle correlation for strain measurement by image analysis

This paper is concerned with small strain measurement utilizing the numerical processing of digital images. The proposed method has its theoretical basis in digital signal analysis and, from a methodological point of view, it can be considered as an extension to digital images of the wellknown white light speckle photography technique. That conventional method is based on the analysis of photographic plates that are exposed twice (before and after the specimen deformation) with the image of a random speckle pattern that has been previously printed on the test piece surface. The digital speckle correlation advantages consist of requiring a very simple specimen preparation and, mainly, of allowing the strain field computation just by numerical elaboration of the acquired images. In this paper, the theoretical basis of the technique and some valuable improvements to the known analogous methodologies are presented. Finally, test results for an application of digital speckle correlation are shown and advantages and disadvantages of the technique are elaborated. In addition, further developments in this area are discussed.     

High-resolution imaging of dissipative structures in a turbulent jet flame with laser Rayleigh scattering

High-resolution 2-D imaging of laser Rayleigh scattering is used to measure the detailed structure of the thermal dissipation field in a turbulent non-premixed CH₄/H₂/N₂ jet flame. Measurements are performed in the near field (x/d = 5–20) of the flame where the primary combustion reactions interact with the turbulent flow. The contributions of both the axial and radial gradients to the mean thermal dissipation are determined from the 2-D dissipation measurements. The relative contributions of the two components vary significantly with radial position. The dissipation field exhibits thin layers of high dissipation. Noise suppression by adaptive smoothing enables accurate determination of the dissipation-layer widths from single-shot measurements. Probability density functions (PDF) of the dissipation-layer widths conditioned on temperature are approximately log-normal distributions. The conditional layer width PDFs are self-similar functions with the layer widths scaling with temperature to the 0.75 power. The high signal-to-noise ratio of the Rayleigh scattering images coupled with an interlacing technique for noise suppression enable fully resolved measurements of the mean power spectral density (PSD) of the temperature gradients. These spectra are used to determine the turbulence microscales by measuring a cutoff wavelength, λ _C , at 2% of the peak PSD. The Batchelor scale is estimated from λ _C , and the results are compared with estimates from scaling laws in non-reacting flows. At x/d = 20, the different approaches to determining the Batchelor scale are comparable on the jet centerline. However, the estimates from non-reacting flow scaling laws are significantly less accurate in off-centerline regions and at locations closer to the nozzle exit. Throughout the near field of the jet flame, the measured ratio of a characteristic dissipation-layer width to the local Batchelor scale is larger than values previously reported for the far field of non-reacting flows.