Previous numerical simulations have shown that vortex breakdown starts with the formation of a steady axisymmetric bubble and that an unsteady spiralling mode then develops on top of this. We investigate this spiral mode with a linear global stability analysis around the steady bubble and its wake. We obtain the linear direct and adjoint global modes of the linearized Navier-Stokes equations and overlap these to obtain the structural sensitivity of the spiral mode, which identifies the wavemaker region. We also identify regions of absolute instability with a local stability analysis. At moderate swirls, we find that the m = −1 azimuthal mode is the most unstable and that the wavemaker regions of the m = −1 mode lie around the bubble, which is absolutely unstable. The mode is most sensitive to feedback involving the radial and azimuthal components of momentum in the region just upstream of the bubble. To a lesser extent, the mode is also sensitive to feedback involving the axial component of momentum in regions of high shear around the bubble. At an intermediate swirl, in which the bubble and wake have similar absolute growth rates, other researchers have found that the wavemaker of the nonlinear global mode lies in the wake. We agree with their analysis but find that the regions around the bubble are more influential than the wake in determining the growth rate and frequency of the linear global mode. The results from this paper provide the first steps towards passive control strategies for spiral vortex breakdown.

We use direct numerical simulation (DNS) of the Navier-Stokes equations in the low-Mach-number limit to investigate the hydrodynamic instability of a lifted jet diffusion flame. We obtain steady solutions for flames using a finite rate reaction chemistry, and perform a linear global stability analysis around these steady flames. We calculate the direct and adjoint global modes and use these to identify the regions of the flow that are responsible for causing oscillations in lifted jet diffusion flames, and to identify how passive control strategies might be used to control these oscillations. We also apply a local stability analysis to identify the instability mechanisms that are active. We find that two axisymmetric modes are responsible for the oscillations. The first is a high-frequency mode with wavemaker in the jet shear layer in the premixing zone. The second is a low-frequency mode with wavemaker in the outer part of the shear layer in the flame. We find that both of these modes are most sensitive to feedback involving perturbations to the density and axial momentum. Using the local stability analysis, we find that the high-frequency mode is caused by a resonant mode in the premixing region, and that the low-frequency mode is caused by a region of local absolute instability in the flame, not by the interaction between resonant modes, as proposed in Nichols et al. (Phys. Fluids, vol. 21, 2009, article 015110). Our linear analysis shows that passive control of the low-frequency mode may be feasible because regions up to three diameters away from the fuel jet are moderately sensitive to steady control forces.

We investigate the flow over shallow cavities as a representative configuration for modelling small surface irregularities in wall-bounded shear flows. Due to the globally stable nature of the flow, we perform a frequency response analysis, which shows a significant potential for the amplification of disturbance kinetic energy by harmonic forcing within a certain frequency band. Shorter and more shallow cavities exhibit less amplified responses, while energy from the base flow can be extracted predominantly from forcing that impacts the cavity head-on. A structural sensitivity analysis, combined with a componentwise decomposition of the sensitivity tensor, reveals the regions of the flow that act most effectively as amplifiers. We find that the flow inside the cavity plays a negligible role, whereas boundary layer modifications immediately upstream and downstream of the cavity edges contribute significantly to the frequency response. The same regions constitute preferred locations for implementing active or passive control strategies to manipulate the frequency response of the flow.

Many studies have shown that low-density jets exhibit self-excited varicose oscillations. We use direct numerical simulation of the low Mach number Navier-Stokes equations to perform a linear global stability analysis of a helium jet at the threshold of onset of these oscillations. We calculate the direct and adjoint global modes and overlap these to obtain the structural sensitivity. We find that the structural sensitivity has high magnitudes in the shear layer downstream of the entrance plane, where the flow is absolutely unstable. We use the direct and adjoint global modes to calculate the effect of a control force on the growth rate and frequency of the unstable mode. We produce maps of the regions of the flow that are most sensitive to localized open loop steady forcing in the form of a body force and a heat source. We find that the most sensitive location for

Gradient-based optimization is used to reliably and optimally induce ignition in three examples of laminar non-premixed mixture configurations. Using time-integrated heat release as a cost functional, the non-convex optimization problem identified optimal energy source locations that coincide with the stoichiometric local mixture fraction surface for short optimization horizons, while for longer horizons, the hydrodynamics plays an increasingly important role and a balance between flow and chemistry features determines non-trivial optimal ignition locations. Rather than identifying a single optimal ignition location, the results of this study show that there may be several equally good ignition locations in a given flow configuration.