73157 - Applied Aerodynamics B

Learning outcomes

The student will be able to understand the physics of viscous fluid flows. By deriving and applying the fundamental equations of motion he/she will be able to describe (theoretically or numerically) the evolution of different viscous flow configurations in laminar, transitional and turbulent regime.

Course contents

1. THE FLUIDS AND THEIR MOTION Course introduction. Basic concepts of mechanics of fluids. The continuum hypothesis. The fluid particle. Kinematic, thermodynamic and transport properties of the fluid particle. The strain tensor. Viscosity and thermal conductivity. The Prandtl number 

2. THE NAVIER STOKES EQUATIONS The basic principles of the Mechanics of Fluids. Integral and differential formulation. The continuity equation. The transport theorem. The localization lemma. The momentum balance equation. Volume and surface forces. The surface stress. The Cauchy theorem. Real and Ideal fluid. The Pascal principle. The energy equation. The constitutive equations. The Navier-Stokes equations. The Euler equations. Equations for incompressible flow. Equation of irrotational flow. Generalised Bernoulli theorem. Fundamental equation of gasdynamics.

3. SOLUTIONS OF THE NAVIER STOKES EQUATIONS Non dimensional equations for incompressible flow. The steady solution in a plane duct (Poiseuille solution). Link between flow rate and pressure drop. The Couette solution. Basic concepts on the vectorial operators in non cartesian frame of reference. The equations of motion in cylindrical coordinates. The flow in axisymmetric ducts: the Hagen-Poiseuille flow. The Taylor-Couette flow.

4. THE BOUNDARY LAYER Weakly divergent flows: the boundary layer, jets and wakes. Non dimensional equations in weakly divergent problems. The Prandtl equations. Self-similar techniques for the solution of Prandtl equations. The flow on a flat-plate at zero angle of attack. The Blasius solution. Generalization of the Blasius solution. The Falkner-Skan solution. The flow in a plane convergent. Approximate solutions in general boundary layers. The Von Karman integral equation. The method of Pohlhausen. Main results and limits of the method.

5. HYDRODYNAMIC INSTABILITY AND TRANSITION Introduction. Definition of stability. Rayleigh and Orr-Sommerfeld equations. Normal mode hypothesis. Rayleigh inflection point criterion. Tollmien-Schlichting waves in channel and boundary layer flows. Eigenvalue problems. Solution of the Rayleigh equation for a piecewise liner profile (mixing layer). Transition prediction with the e-to-the-N-method. Qualitative effect of pressure gradient in boundary layer flows. Wind tunnel for transition research. Introduction to by-pass transition. Transient growth. Effects of free stream turbulence. Transition control a) through suction b) streak generation. Introduction to cross flow instability on wings and rotating disks. Centrifugal instability along curved surfaces. Effects of system rotation.

6. TURBULENCE Introduction. Dissipation in turbulent flows. Derivation of the Kolmogorov scales. Derivation of dissipation in pipe flow. Length scales and Reynolds number. Statistical methods, probability density distribution, mean, variance and higher moments. Sampling times needed for certain accuracy. Derivation of the RANS equations. Reynolds stresses. Derivation of the turbulent kinetic energy equation. Production, dissipation and transport terms. Example of turbulent flows. The 2D turbulent jet. The 2D turbulent wake. Wall bounded flows: turbulent channel flow. Turbulent boundary layers. The logarithmic velocity distribution. Wind tunnels for turbulent boundary layer research. The “Long Pipe” at CICLoPE. Wall shear stress measurements. Isotropic turbulence, Taylor scale, integral scale, correlation function. Kolmogorovs first and second hypothesis, The k-5/3 law. Spectral transfer. Wave number and frequency spectra. Taylors hypothesis of frozen turbulence.

Readings/Bibliography

Viscous fluid flow –  F. White  – Mc Graw Hill – ISBN 0070697124

Elements of Fluid Dynamics – G. Buresti – Imperial College Press

STABILITY and TURBULENCE - Lecture notes Prof. Alfredsson

Teaching methods

Lectures and exercises given by the docent. During the course, seminars and integrative courses, given by highly distinguished lecturers, can be organised. They will be focused on specific topics of advanced fluid dynamics. These arguments will be part of the program and can be the part of the final exam.

Assessment methods

The exam consists of a single session in which the student should answer a written test. The student must show a sufficient skill in writing down and commenting the mathematical and physical models as well as the different theoretical techniques.

Teaching tools

Blackboard and power point presentations.

Office hours

See the website of Per-Henrik Alfredsson