A turbulent lifted slot-jet flame is studied using direct numerical simulation (DNS). A one-step chemistry model is employed with a mixture-fraction-dependent activation energy which can reproduce qualitatively the dependence of the laminar burning rate on the equivalence ratio that is typical of hydrocarbon fuels. The basic structure of the flame base is first examined and discussed in the context of earlier experimental studies of lifted flames. Several features previously observed in experiments are noted and clarified. Some other unobserved features are also noted. Comparison with previous DNS modelling of hydrogen flames reveals significant structural differences. The statistics of flow and relative edge-flame propagation velocity components conditioned on the leading edge locations are then examined. The results show that, on average, the streamwise flame propagation and streamwise flow balance, thus demonstrating that edge-flame propagation is the basic stabilisation mechanism. Fluctuations of the edge locations and net edge velocities are, however, significant. It is demonstrated that the edges tend to move in an essentially two-dimensional (2D) elliptical pattern (laterally outwards towards the oxidiser, then upstream, then inwards towards the fuel, then downstream again). It is proposed that this is due to the passage of large eddies, as outlined in Suet al.(Combust. Flame, vol. 144 (3), 2006, pp. 494–512). However, the mechanism is not entirely 2D, and out-of-plane motion is needed to explain how flames escape the high-velocity inner region of the jet. Finally, the time-averaged structure is examined. A budget of terms in the transport equation for the product mass fraction is used to understand the stabilisation from a time-averaged perspective. The result of this analysis is found to be consistent with the instantaneous perspective. The budget reveals a fundamentally 2D structure, involving transport in both the streamwise and transverse directions, as opposed to possible mechanisms involving a dominance of either one direction of transport. It features upstream transport balanced by entrainment into richer conditions, while on the rich side, upstream turbulent transport and entrainment from leaner conditions balance the streamwise convection.

The spatiotemporal dynamics of the coherent structures in an under-expanded supersonic impinging jet are studied using a spectral proper orthogonal decomposition technique. For this analysis, a large eddy simulation of an under-expanded supersonic impinging jet at a pressure ratio of 3.4 and a stand-off distance of 2 jet diameters at a Reynolds number of 50,000 is performed. The mean flow fields illustrate some striking features of this flow, such as an oblique shock, a stand-off shock, a Mach disk, and a recirculation bubble. The spectral proper orthogonal decomposition method is applied to time-resolved three-dimensional flow fields. The accumulative energy of modes within each azimuthal mode number reveals that the first three azimuthal modes contain most of the energy of the flow. The spectra of these azimuthal modes show that the flow exhibits a low-ranked behaviour with discrete frequencies at the optimal symmetric azimuthal mode while other two azimuthal modes have negligible contributions in this behaviour. Three peaks are observed in the spectra of the optimal symmetric azimuthal mode. The spatial fields of the streamwise velocity and pressure of these peaks show that the complex structures are consequences of the under-expansion, Mach disk, and the impingement. Strong hydrodynamic instabilities exist in the shear layer of the jet in the optimal azimuthal mode at each of these dominant frequencies. High-amplitude acoustic waves are also present in the near-field of the jet. These acoustic waves are strong at the nozzle lip, suggesting that a feedback loop linking these two processes exists for dominant frequencies in the optimal mode. High cross-spectrum density of near-field pressure fluctuations and streamwise velocity fluctuations near the nozzle lip at these frequencies confirms the hydro-acoustic coupling, which is necessary to close the feedback loop.

The receptivity of an under-expanded supersonic impinging jet flow at a sharp nozzle lip to acoustic impulse disturbances is investigated as a function of geometric and flow parameters. The under-expanded supersonic jets emanate from an infinite-lipped nozzle, i.e. the nozzle exit is a circular hole in a flat plate. Two specific cases have been investigated corresponding to nozzle-to-wall distances of from the jet centreline for acoustic disturbances of all azimuthal mode numbers.

Tomographic background-oriented schlieren (BOS) is used to measure three-dimensional instantaneous density fields in turbulent flows. Density gradients are related to the refractive index through the Gladstone-Dale relation. Based on path-integrated apparent displacements in a background pattern from path variations in light rays travelling through the flow, a tomographic reconstruction of the three-dimensional refractive index gradients can be obtained. A Poisson equation of the reconstructed gradients is solved to obtain the refractive index field. We examine four sources of measurement error: (i) defocus blurring; (ii) spatial averaging in the finite difference scheme for solving the Poisson equation; (iii) limited-view tomographic reconstruction; and (iv) displacement field noise. Synthetic BOS displacements are generated from the instantaneous density fields of a heated jet at a Reynolds number of 10 000 and jet exit centreline-to-ambient density ratio of 0.83 computed via DNS. Synthetic background displacements are produced by raytracing through the refractive index field obtained using the Gladstone-Dale relation. The virtual BOS setup consists of 15 cameras placed circumferentially around the jet axis, based on a proposed experimental setup. We show that defocus blurring has the greatest impact on the measurement accuracy, using the RMS and peak errors between the measured and true DNS fields as metrics; its impact is greatest in the transitional region and decreases steadily downstream. Sources (ii) and (iv) have marginal impact (for noise 15% of mean displacements). Three reconstruction methods are tested: (i) filtered back-projection (FBP); (ii) an algebraic reconstruction technique (ART); and (iii) sequential FBP-ART. ART and FBP-ART are similarly accurate, producing under half the errors of FBP, which suffers from significant reconstruction artefacts. The reconstruction error is modest compared to the impact of defocus blurring.