This work represents the initial steps in a wider project that aims to map out the sensitive areas in fuel injectors and combustion chambers. Direct numerical simulation (DNS) using a Low-Mach-number formulation of the Navier–Stokes equations is used to calculate direct-linear and adjoint global modes for axisymmetric low-density jets and lifted jet diffusion flames. The adjoint global modes provide a map of the most sensitive locations to open-loop external forcing and heating. For the jet flows considered here, the most sensitive region is at the inlet of the domain.

The sensitivity of the global-mode eigenvalues to force feedback and to heat and drag from a hot-wire is found using a general structural sensitivity framework. Force feedback can occur from a sensor-actuator in the flow or as a mechanism that drives global instability. For the lifted flames, the most sensitive areas lie between the inlet and flame base. In this region the jet is absolutely unstable, but the close proximity of the flame suppresses the global instability seen in the non-reacting case. The lifted flame is therefore particularly sensitive to outside disturbances in the non-reacting zone.

The DNS results are compared to a local analysis. The most absolutely unstable region for all the flows considered is at the inlet, with the wavemaker slightly downstream of the inlet. For lifted flames, the region of largest sensitivity to force feedback is near to the location of the wavemaker, but for the non-reacting jet this region is downstream of the wavemaker and outside of the pocket of absolute instability near the inlet.

Analysing the sensitivity of reacting and non-reacting variable-density shear flows using the low-Mach-number approximation has up until now not been done. By including reaction, a large forward step has been taken in applying these techniques to real fuel injectors.