The students will initially learn the basics of Cartesian tensors and the index notation. A strong focus is placed on deriving and understanding the transport equations in three dimensions. These equations provide a generic basis for fluid mechanics, turbulence and heat transport. In continuum mechanics we will discuss the strain-rate tensor, the vorticity tensor and the vorticity vector. In connection to vorticity, the concept of irrotational flow, inviscid flow (i.e. zero viscosity) and potential flow will be introduced. The transport equation for the vorticity vector will be derived from Navier-Stokes equations
An introduction to potential flow will be given. A complex function is defined where the real part is the velocity potential and the imaginary part is the streamfunction. Exact solution to this complex function will be derived (flat plat boundary layer, stagnation flow, flow around a cylinder etc). These exact solution have many applications in real life such as Flettner rotors, looping in table tennis and freekicks in football.
In the larger part of the course the students will learn the basics of turbulent flow. Turbulence includes short-lived eddies of different size and frequency. The larger the Reynolds number, the larger the difference in size and frequency between the largest and the smallest eddies. This is the very reason why there is no computer large enough at which we can numerically solve the Navier-Stokes equations at high Reynolds number.
In the last part of the course we will work with the time-averaged Navier-Stokes equations. They include an unknown tensor -- the Reynolds stress tensor -- which must be modeled. We will derive the k-eps model which is the most common turbulence model in industry. The treatment of walls need special attention. There are two options, either wall functions or low-Reynolds number turbulence models. Both options will be discussed.