Modelling of turbulent lifted jet flames using flamelets: a priori assessment and a posteriori validation

This study focuses on the modelling of turbulent lifted jet flames using flamelets and presumed PDF approach with interests on both flame lift-off height and flame brush structure. First, flamelet models used to capture contributions from premixed and non-premixed modes to the partially premixed combustion in the lifted jet flame are assessed using a Direct Numerical Simulation (DNS) data for turbulent lifted hydrogen jet flame. The joint PDFs of mixture fraction, Z, and progress variable, c, including their statistical correlation are obtained using a copula method, which is also validated using the DNS data. The statistically independent PDFs are found to be generally inadequate to represent the joint PDFs from the DNS data. The effects of Z-c correlation and contribution from non-premixed combustion mode on the flame lift-off height are studied systematically by including one effect at a time in the simulations used for a posteriori validation. A simple model including the effects of chemical kinetics and scalar dissipation rate is suggested and used for non-premixed combustion contributions. The results clearly show that both Z-c correlation and non-premixed combustion effects are required in the premixed flamelets approach to get a good agreement with the measured flame lift-off heights as function of jet velocity. The flame brush structure reported in earlier experimental studies is also captured reasonably well for various axial positions. It seems that the flame stabilisation is influenced by both premixed and non-premixed combustion modes, and their mutual influences.A part of this work involving DNS data analysis was performed under the collaborative program on turbulent combustion modelling between Cambridge University and JAXA. The financial support from Mitsubishi Heavy Industries, Ltd, Takasago, Japan, is gratefully acknowledged.This is an Accepted Manuscript of an article published by Taylor & Francis in Combustion Theory and Modelling on 4 April 2014, available online: http://wwww.tandfonline.com/10.1080/13647830.2014.898409

Investigation of flame stretch in turbulent lifted jet flame

DNS data of a laboratory-scale turbulent lifted hydrogen jet flame has been analysed to show that this flame has mixed mode combustion not only at the flame base but also in downstream locations. The mixed mode combustion is observed in instantaneous structures as in earlier studies and in averaged structure, in which the predominant mode is found to be premixed combustion with varying equivalence ratio. The nonpremixed combustion in the averaged structure is observed only in a narrow region at the edge of the jet shear layer. The analyses of flame stretch show large probability for negative flame stretch leading to negative surface averaged flame stretch. The displacement speed-curvature correlation is observed to be negative contributing to the negative flame stretch and partial premixing resulting from jet entrainment acts to reduce the negative correlation. The contribution of turbulent straining to the flame stretch is observed to be negative when the scalar gradient aligns with the most extensive principal strain rate. The physics behind the negative flame stretch resulting from turbulent straining is discussed and elucidated through a simple analysis of the flame surface density transport equation.The authors are grateful for the inspiring discussion with Prof. K.N.C. Bray, and financial support from Mitsubishi Heavy Industries (MHI) is gratefully acknowledged. A part of this work is performed under the collaborative research between Cambridge University and JAXA.This is an Accepted Manuscript of an article published by Taylor & Francis in Combustion Science and Technology on 24 February 2014, available online: http://wwww.tandfonline.com/10.1080/00102202.2013.877335

Identifying network communities with a high resolution

Community structure is an important property of complex networks. An automatic discovery of such structure is a fundamental task in many disciplines, including sociology, biology, engineering, and computer science. Recently, several community discovery algorithms have been proposed based on the optimization of a quantity called modularity (Q). However, the problem of modularity optimization is NP-hard, and the existing approaches often suffer from prohibitively long running time or poor quality. Furthermore, it has been recently pointed out that algorithms based on optimizing Q will have a resolution limit, i.e., communities below a certain scale may not be detected. In this research, we first propose an efficient heuristic algorithm, Qcut, which combines spectral graph partitioning and local search to optimize Q. Using both synthetic and real networks, we show that Qcut can find higher modularities and is more scalable than the existing algorithms. Furthermore, using Qcut as an essential component, we propose a recursive algorithm, HQcut, to solve the resolution limit problem. We show that HQcut can successfully detect communities at a much finer scale and with a higher accuracy than the existing algorithms. Finally, we apply Qcut and HQcut to study a protein-protein interaction network, and show that the combination of the two algorithms can reveal interesting biological results that may be otherwise undetectable.Comment: 14 pages, 5 figures. 1 supplemental file at http://cic.cs.wustl.edu/qcut/supplemental.pd

Simulation of turbulent lifted methane jet flames: Effects of air-dilution and transient flame propagation

Turbulent lifted methane jet flames with various air-dilution levels and a range of inlet velocities are simulated. A partially premixed combustion model based on premixed flamelets with presumed joint Probability Density Function (PDF) is used. The joint PDF is obtained using a copula to include the statistical correlation between mixture fraction, Z, and progress variable, c. The non-premixed combustion effect is included using a simple algebraic model. Both steady and unsteady RANS simulations are performed. The steady simulations show that the computed lift-off heights agree well with measured values for a wide range of jet velocities and air-dilution level. Both of the Z-c correlation and non-premixed combustion effects are found to be important to get the correct lift-off height. Their individual and combined effects are analysed systematically. The unsteady RANS results indicate that multi-stage flame development, namely the initial expansion, flame brush development, its propagation and final stabilisation, is captured reasonably well in simulations. The various stages of temporal evolution of the flame brush edge is captured well and the agreement with experimental measurements is good.The supports of Cambridge Overseas Trust and China Scholarship Council are acknowledged by ZC. SR and NS acknowledge the support of MHI, Takasago, Japan.This is the accepted manuscript. The final version will be available from Elsevier at: http://www.sciencedirect.com/science/article/pii/S001021801400279X

Large Eddy Simulation of flame edge evolution in a spark-ignited methane-air jet

The unsteady evolution of lifted methane–air jet flames following spark ignition is computed using Large Eddy Simulation (LES). A presumed joint Probability Density Function (PDF) approach is used for the sub-grid combustion modelling accounting for both premixed and non-premixed mode contributions. Two flames, one with high and another with low jet velocities are investigated and the computed temporal variation of flame leading point agrees quite well with the measured data for both the transient evolution and final lift-off height. The joint PDF of the axial and radial stabilisation locations shows that these locations are correlated with the jet exit velocity. The flame leading point evolution in the three-dimensional physical space is visualised using its trajectory, starting from the ignition location to the final lift-off height. A $\textit{spiral}$-shaped path is observed for both velocity cases showing different flame propagation behaviours at different heights from the jet exit. These observations are explained on a physical basis.Cambridge Overseas TrustsThis is the author accepted manuscript. The final version is available from Elsevier via http://dx.doi.org/10.1016/j.proci.2016.06.02

Computation of Forced Premixed Flames Dynamics

Bluff body stabilised turbulent premixed flames subject to inlet velocity oscillation over a wide range of forcing frequency and amplitude are simulated using a flamelet-based combustion model. Two sets of detailed chemical kinetic schemes are used to model combustion chemistry. It is observed that the computed dynamics of forced flames agree reasonably well with experimental measurements. The flame elongation and shortening at a frequency of 40 Hz and strong flame-vortex interaction at a higher frequency of 160 Hz are captured well in the computations. The global flame describing function extracted from the computational results shows a linear response at 40 Hz and a nonlinear behaviour at 160 Hz as observed in the experiments. The nonlinear response is due to vortex roll-up and its subsequent shedding. The quantitative agreement of the computed flame describing function (FDF) with experimental measurement is uniformly good over a wide range of forcing frequency and amplitude. Some influence of chemical kinetics on the FDFs is observed, which mainly stems from the difference in laminar burning velocity and spatial heat release rate distribution.The support of Mitsubishi Heavy Industries, Takasago, Japan is acknowledged gratefully.This is the author accepted manuscript. The final version is available from Taylor & Francis via http://dx.doi.org/10.1080/00102202.2016.117411

X-ray and multi-epoch optical/UV investigations of BAL to non-BAL quasar transformations

We report on an X-ray and optical/UV study of eight Broad Absorption Line (BAL) to non-BAL transforming quasars at $z\,\approx\,$1.7-2.2 over 0.29-4.95 rest-frame years with at least three spectroscopic epochs for each quasar from the SDSS, BOSS, $Gemini$, and ARC 3.5-m telescopes. New $Chandra$ observations obtained for these objects show their values of $\alpha_{\rm ox}$ and $\Delta{\alpha}_{\rm ox}$, as well as their spectral energy distributions, are consistent with those of non-BAL quasars. Moreover, our targets have X-ray spectral shapes that are, on average, consistent with weakened absorption with an effective power-law photon index of $\Gamma_{\rm eff}\,=\,1.69^{+0.25}_{-0.25}$. The newer $Gemini$ and ARC 3.5-m spectra reveal that the BAL troughs have remained absent since the BOSS observations where the BAL disappearance was discovered. The X-ray and optical/UV results in tandem are consistent with at least the X-ray absorbing material moving out of the line-of-sight, leaving an X-ray unabsorbed non-BAL quasar. The UV absorber might have become more highly ionized (in a shielding-gas scenario) or also moved out of the line-of-sight (in a wind-clumping scenario).Comment: 14 pages, 5 figures, Accepted for publication in MNRA

Simulation of premixed combustion with varying equivalence ratio in gas turbine combustor

RANS simulation of a gas turbine combustor with complex geometry is performed. The turbulence is modelled using a two-equation approach. The scalar mixing and combustion is modelled using a flamelet based approach for partially premixed combustion. In this approach transport equations to described scalar mixing and reacting fields and their statistical interactions are solved along with standard conservation equations. The boundary conditions are specified using measured values. The computed spatial variations of averaged temperature and dry mole fractions of various scalars, including CO and NOx, compared quite well with measured values. The results of this combustion model are compared to the eddy-dissipation-concept (EDC) model commonly used for gas turbine combustion calculation and this comparison showed that the results of partially premixed combustion model is improved considerably.This is the author accepted manuscript. The final version is available from the American Institute of Aeronautics and Astronautics via http://dx.doi.org/10.2514/1.B3551

A priori investigation of subgrid correlation of mixture fraction and progress variable in partially premixed flames

Subgrid correlation of mixture fraction, Z, and progress variable, c, is investigated using Direct Numerical Simulation (DNS) data of a hydrogen lifted jet flame. Joint subgrid behaviour of these two scalars are obtained using a Gaussian-type filter for a broad range of filter sizes. Joint probability density function (JPDF) constructed using single-snapshot DNS data is compared qualitatively with that computed using two independent β-PDFs and a copula method. Strong negative correlation observed at different streamwise locations in the flame is well captured by the copula method. The subgrid contribution to the Z-c correlation becomes important if the filter is of the size of laminar flame thickness or larger. A priori assessment for the filtered reaction rate using flamelet approach with independent β-PDFs and correlated JPDF is then performed. The comparison with the DNS data shows that both models provide reasonably good results for a range of filter sizes. However, the reaction rate computed using copula JPDF is found to have a better agreement with the DNS data for large filter sizes because the subgrid Z-c correlation effect is included