MECH 479: Computational Fluid Dynamics

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1 MECH 479: Computational Fluid Dynamics W. K. Bushe University of British Columbia Department of Mechanical Engineering

2 Today s To Do List Explain To Do List Discuss course outline Discuss basics of CFD Discuss some example applications

3 Outline Course Structure: 2 quizzes worth 15% of your grade (each) based on the lecture material. A project worth 20% of your grade (due at the final exam). Final (date TBA) worth 50% of your grade.

4 Text There is no text for this course. I ve never found one that I liked at least, enough to build lectures around. Three texts that you could read in if you really feel desperate to get more: Versteeg & Malalasekera, An Introduction of CFD Tu, Yeoh & Liu, CFD: A Practical Approach Pope, Turbulent Flows The last one is what I use for my graduate course in Turbulence (dense, highly mathematical, rigorous) and several lectures here are summarized therein.

Introduction of CFD Tu, Yeoh & Liu, CFD: A Practical Approach Pope, Turbulent Flows The last one is what I use for

5 Notes There is a web-site for this course: It can also be accessed through the department web-site (with considerable difficulty). The lecture notes will appear on that web site soon after each lecture; they appear in pdf format, so you need the Adobe Acrobat Reader (or Ghostview) to see them.

6 What is CFD? Computational (or Colourful ) Fluid Dynamics is the numerical solution of the governing equations for a fluid, usually in a modified form, applied over some domain of interest.

7 What flavours are available? There are three basic forms of the governing equations that are used for CFD; these lead to four different conventional solutions (which I refer to as different flavours ): DNS LES RANS others (including CNS) I ve put those in order of the quality of results you get; obviously, we d like to stay away from CNS. As we ll see later, DNS is only useful for laminar flows (except for the most basic, fundamental research purposes), and LES is still in its infancy, so RANS is what we ll talk about most here. Note: RANS and LES are only used for turbulent flows.

to as different flavours ): DNS LES RANS others (including CNS) I ve put those in order of the quality of results you get; obviously, we d like to

8 How does it work? Obviously, we ll be going into rather more detail about this, but the basic order of business is: define domain identify form of governing equations discretize equations on domain define initial and boundary conditions begin calculation

9 What do we mean by calculate? This depends on what flavour you re using. There are steadystate and unsteady varieties of CFD. Some of the flavours are intrisically one or the other (LES is always unsteady, for example). In the case of steady-state, you solve for a flow which does not evolve in time, in which case some of the terms in the governing equations should be zero. We can use a solution algorithm that finds that zero. In the case of unsteady methods, you simply integrate the governing equations in time from the initial condition.

In the case of steady-state, you solve for a flow which does not evolve in time, in which case some of the terms in the governing

10 What do we solve for? Ultimately, we wind up with the solution to the equations we ve been integrating or zeroing. This means we should wind up with a value for each of the scalar and vector fields at every point in the domain at some time (or at an infinite time in the case of a steady-state solution). That would be the information for which we solve. For turbulent flows, unless we re using DNS, we re solving for the average of the scalar fields; we ll discuss what this averaging process means later.

(or at an infinite time in the case of a steady-state solution). That would be the information for which we solve.

11 What do we use CFD for? We use CFD to answer some question (or questions). Knowing the velocity at every point in space at a given time is not (in general) intrinsically useful, except in a research context. We can (if we ve solved for the right information) use the fine-grained information available from CFD to calculate integral quantities. For example, you can use the pressure field to calculate the coefficient of lift on an airfoil. There, you only need the pressure at the points that are on the airfoil. That the majority of points in the domain are not actually on the airfoil is irrelevant; indeed, if we hadn t had those other points in the solution, the solution at the points in which we are interested would have been wrong.

We can (if we ve solved for the right information) use the fine-grained information available from CFD to calculate integral quantities.

12 Example Pratt & Whitney Canada uses an in-house CFD code to predict the flows inside of their gas turbines. What elements would they be simulating? Why?

13 Example Ford also uses CFD to predict flows. What flows would they be simulating and why?

14 CFD in Research Some people use CFD to do research directly others work on simulation in partnership with experiments. Examples: model validation physics of flows effects of turbulence

15 Research in CFD Conversely, there continues to be research in the development of improvements to CFD, in (among others): numerical methods mesh generation modelling

Module 6 Case Studies

Module 6 Case Studies 1 Lecture 6.1 A CFD Code for Turbomachinery Flows 2 Development of a CFD Code The lecture material in the previous Modules help the student to understand the domain knowledge required