Lecture 1

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Lecture material will draw from these texts

Course Description

  • This course covers topics related to large-eddy simulation (LES), an advanced computational fluid dynamics (CFD) technique.
  • LES is quickly replacing traditional Reynolds Averaged Navier-Stokes (RANS) modeling as the method of choice for researchers and practitioners studying turbulent fluid flow phenomena in engineering and environmental problems.
  • LES explicitly solves for the larger scale turbulent motions that are highly dependent on boundary conditions, while using a turbulence model only for the smaller (and presumably more universal) motions.
  • This is a distinct advantage over traditional RANS models where the effects of turbulence on the flow field are entirely dependent on the turbulence parameterizations.

Course Objectives

  • Become familiar with the filtering concept in a turbulent flow and how the idea of scale separation forms the basis for LES.
  • Gain familiarity with the filtered forms of the conservation equations (e.g., mass, momentum, turbulent kinetic energy), how they are derived, and how the different terms in the equations can be interpreted.
  • Obtain a basic working knowledge of common subgrid-scale (SGS) parameterizations used in LES of turbulent flows.
  • Understand how to carry out a priori analysis of SGS models from experimental and Direct Numerical Simulation (DNS) data sets.
  • Understand common techniques for a posteriori evaluation of SGS models and what conditions are necessary and sufficient for a ``good’’ SGS model.
  • Become familiar with LES SGS models and techniques used in specific flow cases of interest (e.g., isotropic turbulence, high-Reynolds number boundary layers, turbulent reacting flows, etc.)

Course Outline

Assignments

Homework

Project #1

Project #2

Useful LES Books

Turbulence Intro

We can also define a signal by its individual statistics, which collectively describe the PDF. ~\\~\\ The mean (or expected) value of a random variable $U$ is given by: $$\langle U \rangle \equiv \int^{\infty}_{-\infty} Vf(V)dV$$ or in discrete form: $$\langle U \rangle \equiv \frac{1}{N} \sum^N_{i=1} V_i$$ The mean represents the probability-weighted sum of all possible values of $U$.