Turbulent Free Shear Flows

Tuesdays & Thursdays, 5:00-6:20 pm, DBH 1431

Prof. Dimitri Papamoschou
4214 Engineering Gateway
(949) 824-6590
dpapamos@uci.edu

Office hours: M 2:00-3:30 by appt.; W 2:00-3:30 open

WHAT THIS COURSE IS ABOUT

The course emphasizes the fundamental fluid dynamics of turbulent free shear flows with the aim of developing physics-based, common-sense tools for their prediction.  It encompasses a macroscopic (big-picture) view of turbulence designed to help the engineer  tackle the formidable challenge of predicting the behavior of turbulent flows in practical devices.  The flow in the above picture, for example, is a supersonic jet issuing from a rectangular nozzle.  The Reynolds number is about one million.  This is a flow of significance to jet engines, combustors, ejectors, even lasers. There is no "turbulence theory" that can predict this flow from first principles.   Exact computation is currently impossible and will remain so for the foreseeable future.  How can one predict (even approximately) this jet without resorting to an experiment for each flow/geometric condition?  How can we ensure that numerical computations, which are based on models, give answers that make physical sense? The answer lies in isolating the salient physics, developing simple analytical models, and combining this information with experimental data.   In this course we will focus on the link between the driver of turbulent motion in free shear flows, namely the instability wave, and the resulting non-linear, turbulent behavior.   We will establish similarity and scaling arguments for the growth of shear layers, jets, and wakes.  The effect of Mach number on those scaling laws will be included.  An overview of current technological problems involving turbulent free shear flows, including jet noise and scramjet mixing, will be presented.

PREREQUISITES

There are no strict prerequisites.  The course is open to all graduate students and even highly-qualified undergraduates. At a minimum, students attempting this course should have a good grasp of introductory graduate-level fluid mechanics and a basic knowledge of complex analysis, ordinary differential equations, and partial differential equations.   Knowledge of compressible flow is highly desirable. 

CATALOGUE DESCRIPTION

Practical and theoretical aspects of turbulent free shear flows commonly found in engineering practice. Instability characteristics, global scaling laws, mixing, and noise generation in incompressible and compressible shear layers, jets, and wakes. Kelvin-Helmholtz instability, dimensional arguments for growth rates, near- and far-field scaling laws, effect of convective Mach number, aeroacoustics of jets, Lighthill's analogy . Extensive review of archival literature.

COURSE OUTLINE (approximate)

Week 1: Overview of the turbulence problem. Basic statistical tools for describing turbulent quantities: mean, variance, skewness, autocorrelation, PDF, Fourier transform, spectrum.
(MS 2.1, 2.2, 2.3, 2.4)

Week 2: Reynolds-averaged equations and the closure problem.  Equation for the turbulent kinetic energy.  Concept of energy cascade. (MS 4.0-4.2)

Week 3: Linear instability analysis: vortex sheet (Kelvin-Helmholtz instability) (DR 4)

Week 4: Linear instability analysis: finite-thickness shear layer.   Rayleigh and Orr-Sommerfeld equations. (DR 21, 31.10)

Week 5: Connection of instability wave to coherent structure. Effects of velocity, density, and Mach number on growth rate.

Week 6: Dividing streamline and maximum shear stress in a shear layer.  Relation between shear stress, growth rate, and turbulent kinetic energy

Week 7: Scaling laws for jets.  Applications to aeroengines, ejectors, injectors

Week 8: Scaling laws for coflowing jets and wakes

Week 9: Overview of noise generation in turbulent jets: Lighthill theory, quadrupole noise, Mach wave emission, shock-cell noise.

Week 10: Mixing and combustion challenges in high-speed air-breathing propulsion.

COURSE MATERIALS

Although there are several excellelent books on turbulence, no single book is adequate for this course.  The course will be based mainly on lecture material with several books being used as reference. It is imperative that students attend all the lectures.  The books for this course are:

J. Mathieu and J. Scott, An Introduction to Turbulent Flow,  Cambridge University Press
A.A. Townsend, Structure of Turbulent Shear Flow,   Cambridge University Press
A.J. Smits and J.P. Dussauge, Turbulent Shear Layers in Supersonic Flow, AIP Press
P.G. Drazin and W.H. Reid, Hydrodynamic Stability, Cambridge Univ Press

All should be available at the bookstore. It is strongly recommended that students purchase the book by Mathieu & Scott, and consider seriously purchasing the other books, especially if they plan to do research in this field. The students are also encouraged to explore additional books on turbulence (such as Tennekes & Lumley and Hinze) and to read research papers on the subjects covered.  Many journals are now accessible on line, giving the student an opportunity to study recent developments.

COURSE CONDUCT

The performance of the students will be assessed on the following:

• Homework assignments, due every two weeks (40% of the grade)

• Term paper on a subject chosen by the student and approved by the instructor (30%)

• Final examination (30%)

NOTE:  Homewoks, term papers, and exams are individual efforts.   No collaborative efforts are acceptable.