Lean Flame Root Dynamics in a Gas Turbine Model Combustor

A swirl-stabilised flame close to blow-off conditions in a gas turbine model combustor is investigated using large eddy simulation. The sub-grid combustion is modelled using a presumed probability density function approach along with flamelets. Good comparisons between the computed and measured statistics are observed. This allows for a detailed investigation of the flame behaviour. Two distinct stages are noted for the flame behaviour. The flame has a steady and stable flame root anchored near the entrance to the burner, yielding a "V" shaped flame in Stage 1, and a transient lift-off event is observed in Stage 2. These two stages switch from one to the other, giving the unstable flame behaviour, as observed in the experimental studies. Further analysis of the simulations shows that large-scale scalar mixing plays a prominent role in the stabilisation of the flame and the entrainment of inflammable mixtures near the flame root location initiates the lift-off event.EPSRC DTP studentship (RG80792

Prediction of local extinctions in piloted jet flames with inhomogeneous inlets using unstrained flamelets

Multi-regime turbulent combustion modelling remains challenging and is explored with occurrence of local extinction in this study. A partially premixed model based on unstrained premixed flamelets is used in this work to investigate a piloted jet flame configuration with inhomogeneous inlets. Three different cases are simulated, which differ in the bulk mean velocity that amounts respectively to about 50\%, 70\% and 90\% of the blow off velocity measured experimentally. As the jet velocity approaches the blow off limit, local extinctions start to occur along the flame surface and thus these flames are challenging from a modelling prospective. Two different numerical approaches, involving scaled and unscaled progress variable respectively, are compared to elucidate their abilities and limitations to predict local extinctions and to deal with the three-stream problem at the pilot/coflow interface. The key modelling details for such predictions are indicated and discussed. LES results are systematically compared to two sets of experimental measurements available in the literature for the three flames. The differences observed in the two experimental datasets are also discussed with the help of LES results. Although both approaches show promising agreement for the flame statistics, the scaled progress variable approach better predicts the local extinctions. The unscaled approach shows to naturally handle the three-stream problem without additional treatment for the pilot/coflow interface, which is required for the scaled approach. Furthermore, computed scalar dissipation rate of mixture fraction is compared with the measurements showing good agreement for the conditions investigated. This further suggests that local extinctions can be predicted using unstrained flamelets if the correct scalar mixing and its dissipation are captured.EPSR

Fast computation of radar cross-section by fast multipole method in conjunction with lifting wavelet-like transform

The fast multipole method (FMM) in conjunction with the lifting wavelet-like transform scheme is proposed for the scattering analysis of differently shaped three-dimensional perfectly electrical conducting objects. As a flexible and efficient matrix compression technique, the proposed method can sparsify the aggregation matrix and disaggregation matrix in real time with compression ratio about 30%. The computational complexity and choice of proper wavelet are also discussed. Numerical simulation and complexity analysis have shown that the proposed method can speed up the aggregation and disaggregation steps of the FMM with lower memory requirements. © 2010 The Institution of Engineering and Technology.postprin

Adaptive frequency sweep analysis for electromagnetic problems using the Thiele interpolating continued fractions

A direct rational approximation method based on Thiele interpolating continued fractions theory is proposed for fast frequency sweep analysis of electromagnetic problems. And an adaptive algorithm is also formed. Compared with the conventional rational approximation method, the proposed method can get a rational approximation directly without a great number of matrix inverse computations and doesn't need to allocate much memory for high derivatives of the dense impedance matrix. Meanwhile, the computation of surface currents by continued fractions can be sped up as compared with the traditional rational approximation. Numerical simulations for broad band scattering analysis of different shaped objects are discussed to shown the effectiveness of the present method. © 2010 IEEE.published_or_final_versionThe 2nd International Conference on Education Technology and Computer (ICETC 2010), Shanghai, China, 22-24 June 2010. In Proceedings of 2nd ICETC, 2010, v. 5, p. 126-12

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

Effect of swirl on premixed flame response at high forcing amplitudes

The response of a lean premixed flame subjected to acoustic perturbations is a complex phenomenon that depends highly on the type of flame and the operating conditions. Swirl introduces additional complexities due to the azimuthal component of the flow. In this work, a bluff body stabilised burner is studied under non-swirling and highly swirling conditions by placing a removable axial swirl upstream of the burner. The influence of swirl is assessed in terms of the flame describing function which is the ratio of heat release rate fluctuations response to incoming velocity oscillations and the spatial flame dynamics at high forcing amplitudes. The effect of flame interaction with the wall on the flame response is also explored by considering an enclosure with a larger diameter. It is found that swirl can affect the non-linear characteristics of the flame at medium frequencies (Strouhal numbers around unity) by altering the flame roll-up mechanisms. This is related to the variation of the local swirl number in space and time. For Strouhal numbers that are considerably lower than unity, the effect of swirl is small due to the high convective wavelengths. The size of the enclosure can also change the flame response characteristics, specifically for large forcing frequencies. With a small enclosure, where the flame interacts with the wall, the flame break-up is more significant and the vortex formation is interrupted. This does not happen when the enclosure is enlarged and it can affect the non-linear behaviour of the flame

Geometry of reduced density matrices for symmetry-protected topological phases

© 2016 American Physical Society. In this paper, we study the geometry of reduced density matrices for states with symmetry-protected topological (SPT) order. We observe ruled surface structures on the boundary of the convex set of low-dimensional projections of the reduced density matrices. In order to signal the SPT order using ruled surfaces, it is important that we add a symmetry-breaking term to the boundary of the system - no ruled surface emerges in systems without a boundary or when we add a symmetry-breaking term representing a thermodynamic quantity. Although the ruled surfaces only appear in the thermodynamic limit where the ground-state degeneracy is exact, we analyze the precision of our numerical algorithm and show that a finite-system calculation suffices to reveal the ruled surface structures

Large Eddy Simulation of a dual swirl gas turbine combustor: Flame/flow structures and stabilisation under thermoacoustically stable and unstable conditions

A laboratory gas turbine model combustor with dual-swirler configuration is in- vestigated using Large Eddy Simulation (LES) with a flamelet subgrid combus- tion model. Two partially premixed methane/air flames with different equivalence ratio and thermal power are simulated: one stably burning with an elongated V- shape and another undergoing pronounced thermoacoustic oscillations exhibiting a flat shape. Additionally, both flames feature a hydrodynamic instability in the form of a precessing vortex core (PVC). Detailed comparisons between experi- mental and LES results show that the different flow and reaction zone structures in these two flames are reproduced well. The various flow dynamics resulting from the PVC and thermoacoustic oscillations are also captured accurately in the simulation. Further analyses on the lifted swirl flame stabilisation using phase averaged statistics at the PVC frequencies reveal that the PVC-induced stagnation points provide an anchoring mechanism for both the stable and unstable flames, although in the latter case large self-excited pressure oscillations are present. It is found that the PVC is significantly influenced by these oscillations, being axially stretched and compressed at high and low pressures, respectively. However, the formation of flame leading edge due to the PVC is robust during these unstable processes and the azimuthal movement of the leading point is found to be strongly correlated with the rotation of the PVC in both flames, further confirming the vital role of the PVC in the stabilisation process of these lifted swirl flames