Spatio-Temporal Stability Analysis of Shear Flows

Spatio-Temporal Stability Analysis of Shear Flows: Using analytical and non-analytical approaches

Kumar, N.

Pinna, F. (mentor)
Groot, K.J. (mentor)
Pecnik, R. (mentor)

Mechanical, Maritime and Materials Engineering

Process and Energy

2016-10-14

A comprehensive understanding of the stability of shear flows is a fundamental problem in fluid mechanics and it has been a subject of both theoretical and practical interest in engineering research. A key aspect of these dynamic flows is the behaviour exhibited by the instabilities as it evolves from initial small perturbations of an equilibrium state, and may lead to fluctuations. In order to control these fluctuations, a study on the spatial and temporal evolution of the perturbations must be carried out. The objective of this thesis is to perform the spatio-temporal stability analysis on the plane, incompressible shear layers representing confined and unconfined shear flows. The analysis requires the estimation of the response of the flow to the initial perturbations for fixed values of relevant parameters. The numerical tools are developed for the low order piecewise linear profile approximations to the shear layers. The influence of typical flow features, like single and multiple shear dynamics, on the stability behaviour is studied and the convective/absolute instability boundary for various parameter combinations are identified. After validation for the analytical models, the numerical tools are extended to the non-analytical models. The analysis is then performed for higher order approximations of the experimental base flows in order to validate the results from the toolkit. A variation of the flow features and variables can change the stability behaviour of the shear flows. The single shear layer dynamics cannot contribute to absolute instability in the absence of a dispersive medium, like surface tension. The surface tension acts as a stabilising mechanism for perturbations of short wavelength. The multiple shear layer dynamics dictates that the unconfined jet or wake flow is more unstable than the single shear layer with equivalent parameter values, and that very high values of surface tension stabilises all perturbations. For confined jet or wake flows, the varicose mode perturbations are found to be highly absolutely unstable in the strongly confined dense inner flow limit. The temporal branches obtained from the toolkit match with the Linear Stability Theory (LST) results. This is a key result that allows the extension of the numerical tools developed for the low order analytical models to be applied to the non-analytical models obtained for higher order approximations of the experimental base flow.

instability
shear flow
dispersion relation
, local stability analysis
local stability analysis

http://resolver.tudelft.nl/uuid:d2ed7adf-45fe-4fde-af60-14671b5319ea

Student theses

master thesis

(c) 2016 Kumar, N.