Advanced Stability Analysis

Self-excited instabilities are important in many fields of science and technology. Examples from fluid dynamics include jet break-up and mixing, aerodynamic flutter, combustion instabilities, and thermo-hydraulic instabilities in nuclear reactors or concentrated solar power. It is the goal of stability analysis to predict whether a small perturbation to a system will grow (instability) or decay (stability). The conventional approach is to represent a perturbation as a superposition of eigenmodes, and to study the temporal development of each mode separately. If all modes are stable, the system is argued to be stable as well. However, it has been learned quite recently that this argument is not valid for systems with a non-normal evolution operator. Then the eigenmodes will be non-orthogonal, such that they can exchange energy among each other by interaction with the base flow, even in the linear limit of small perturbation amplitudes. Such non-normal behaviour can result in strong transient growth, which in combination with nonlinear effects may completely invalidate conventional modal analysis.

In the last decade, there has been a surge of activity in non-modal (also called non-normal) stability analysis within the applied maths community. Many applications are concerned with the stability of shear flows in simple geometries. Prof. Sujith has discovered that thermoacoustic interactions are governed by a non-normal operator, and has worked out in a series of break-through papers the possible implications for the stability of combustion systems. These investigations made use of simplistic model problems. We are currently working on investigating how important the effects of non-normality are for realistic combustor configurations. Then methods of non-modal stability analysis have to be developed to a point, where they can be used as design tools for technical applications. It is also important to establish solid, quantitative experimental evidence for non-normality in thermoacoustics.

Dr. Bruno Schuermans is a Rudolf Diesel Industry Fellow and currently Team Leader for Scientific Methods and Thermoacoustics at the Combustor Department at Alstom Ltd.’s Switzerland branch in Baden. He has joined the Focus Group Advanced Stability Analysis together with his host Prof. Thomas Sattelmayer from the Thermodynamics department.

Prof. R. I. Sujith is a Professor at the Department of Aerospace Engineering at the Indian Institute of Technology Madras. As a Hans Fischer Senior Fellow of the IAS (2010-2013), he has intensified his collaboration with Prof. Wolfgang Polifke of the Chair for Thermodynamics at TUM.

TUM-IAS funded doctoral candidates:
Ralf Blumenthal, Thermodynamics
Sebastian Bomberg, Thermodynamics
Tobias Hummel, Thermodynamics