Instabilities of Flows with and without Heat Transfer and Chemical Reactions
June 9, 2008 — June 13, 2008
Coordinator:
- Tapan K. Sengupta (Indian Institute of Technology, Kanpur, India)
Instabilities in flows are ubiquitous and remain as challenge to completely understand transition and turbulence. Topics considered here span from hydrodynamic to multi-physics problems involving heat transfer and chemical reactions. This course emphasizes roles of theoretical, computational and experimental approaches in advancing knowledge in the field, and is addressed to graduate students, researchers and practicing scientists and engineers in the fields of fluid dynamics, heat transfer including combustion, applied mathematics and physics.
Lectures cover materials from classical to newer developments- at advanced level. Classical topics covered are: (i) shear layer instabilities involving normal mode approach; (ii) methods of matched asymptotic expansions to obtain analytical solution; (iii) methods for nonparallel, weakly nonlinear theories; (iv) initial value approach and saddle point methods for large time evolution of wave-packets to understand absolute and convective instabilities. We will also use dynamical system approach for receptivity- incorporating input disturbances to calculate full response field. Receptivity study employing Bromwich contour integral allows exploring instability, without the need to restrict oneself to specifically spatial or temporal approaches, while looking at normal modes. This approach helps one obtain the full spatio-temporal response to understand instabilities, forerunners and spatio-temporal wave fronts. One is also exposed to the compound matrix method – a robust but easy to implement technique for solving stiff differential equations with applications in finding the eigen-spectrum, transient growth mechanism arising out of multi-mode interactions.
With advances in scientific computing, instability problems can now be studied without limiting assumptions. The participants will be introduced to Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) of instability problems and results related to nonlinear, nonparallel effects. We will discuss: (a) shear layer instability of attached flows; (b) mixed convection flow past vertical plate; (c) the nonlinear instability aspect of vortex shedding behind circular cylinder in the presence or absence of free stream turbulence, for assisting and opposing flows; (d) vortex-induced instability and bypass transition problems.
DNS methods are also used to study combustion instabilities for reacting and multi-phase flows. For this, the course covers: self-excited combustion instabilities vis-à-vis forced combustion modes; link between combustion instability and pollutants like NOX creation; flame stabilization; role of acoustics on reacting flows; DNS/LES of multi-phase flows, droplet clouds; closure models for evaporating droplets with real life applications in helicopter and aircraft engines.
The objective of the course is to provide the audience with tangible connections between stability concepts and what we see in experiments. An unique perspective is brought here to interpret stability theory via experiments, with focus on free shear flows, though important connections to wall bounded turbulent flows will be made.