Ralf Blumenthal

• Technical University of Munich

Non-normal transient growth of energy is a feature encountered in many physical systems. Its observation is intimately related to the norm used to describe the system dynamics. For a multi-physics problem such as thermoacoustics, where a heat source is in feedback with acoustic waves and a flow field, the appropriate metric is an ongoing matter of...

The present study models a thermoacoustic system in the time domain where, in the limit of small amplitudes, the linear dynamics of a heat source is incorporated in terms of a distributed time lag response function. This approach allows for a description of the heat source that is richer than that in single time lag models such as the well-known n–...

Based on the analytical G-Equation model, the linear response of conical premixed flames to equivalence ratio fluctuations is derived analytically in the time domain. The resulting impulse response of the flame yields insight into the competing mechanisms of flame response. These are flame restoration and convection of the perturbing equivalence ra...

The present study develops an alternative perspective on the response of premixed flames to flow perturbations. In particular, the linear response of laminar premixed flames to velocity perturbations is examined in the time domain, and the corresponding impulse response functions are determined analytically. Different flame types and shapes as well...

Models for the analysis of thermoacoustic instabilities are conveniently formulated in the frequency domain. In this case one often faces the difficulty that the response behavior of some elements of the system is only known at real-valued frequencies, although the transfer behavior at complex-valued frequencies is required for the quantification o...

We show that the Kelvin-Helmholtz instability excited by a localized perturbation yields a self-similar wave. The instability of the mixing layer was first conceived by Helmholtz as the inevitable growth of any localized irregularity into a spiral, but the search and uncovering of the resulting self-similar evolution was hindered by the technical s...

A perturbation is induced at the sheared interface between a stream of liquid and a stream of gas. This initial perturbation then evolves as the response of inertia, viscosity and interfacial tension. We observe that the wave obtained by this procedure tends to a self-similar regime after a short transient. We describe the anatomy of this well-defi...