1. 14. Computational Fluid Dynamics
CH EN 374: Fluid Mechanics

2. Where We’ve Been 1rst Exam Period Microscopic (differential) balances:
Viscosity, shear stress
Hydrostatic pressure, pressure forces
Macroscopic (integral) materials balances:
Mass
Momentum (and force)
Energy
Microscopic (differential) balances:
Mass – continuity equation
Momentum (and force) – Navier-Stokes
NS Approximations and types of flow
Creeping (Stokes) flow
Inviscid flow
Boundary layers

3. Today Computational Fluid Dynamics (CFD)
Most CFD is performed using specific software packages that take time to learn
So we’re not going to do it ourselves in this class
Today I will introduce you to important CFD concepts

4. Computational Fluid Dynamics
Use numerical methods to solve the equations of motion:
Continuity
X-momentum
Y-momentum
Z-momentum
Four equations, 4 unknowns
( 𝑣 𝑥 , 𝑣 𝑦 , 𝑣 𝑧 , 𝑃)
What if heat transfer is important in our flow?
We might want to predict temperature, 𝑇
Any ideas about where we’d get another equation?

5. Advantages of CFD Example: Biomedical Engineering/Medicine Discuss:
Discuss:
What are some of the advantages of using CFD over only using experimental results?
Why is it important to also have experimental data?
How does this apply to areas other than medicine?

6. Algorithm Example
So ho does CFD solve problems we can’t solve analytically?
Divide flow into a grid of points 𝑖
𝑖+1
𝑖−1
𝑖− 1 2
𝑖+ 1 2

7. Algorithm Example 𝑖 𝑖+1 𝑖−1 𝑖− 1 2 𝑖+ 1 2
𝜕 2 𝑣 𝑥 𝜕 𝑥 2 𝑖 ≈ 𝜕 𝑣 𝑥 𝜕𝑥 𝑖+1/2 _ 𝜕 𝑣 𝑥 𝜕𝑥 𝑖−1/2 Δ𝑥
𝜕 𝑣 𝑥 𝜕𝑥 𝑖+1/2 ≈ 𝑣 𝑥 𝑖+1 − 𝑣 𝑥 𝑖 Δ𝑥
𝜕 𝑣 𝑥 𝜕𝑥 𝑖−1/2 ≈ 𝑣 𝑥 𝑖 − 𝑣 𝑥 𝑖−1 Δ𝑥
𝜕 2 𝑣 𝑥 𝜕 𝑥 2 𝑖 ≈ 𝑣 𝑥 𝑖+1 −2 𝑣 𝑥 𝑖 + 𝑣 𝑥 𝑖−1 Δ 𝑥 2

8. Algorithm Example 𝑖
𝑖+1
𝑖−1
𝑖− 1 2
𝑖+ 1 2
We have seen how to re-write NS terms as approximations of points on a grid
Based on what you know about numerical methods (263!) how would you describe what needs to happen next?

9. Grids Flow domain is divided into cells (a grid)
Boundary conditions must be the same when boundaries touch
Equation solved for each cell

10. Gridding/Meshing
What do you think the advantages and disadvantages of a finer grid (smaller cells) would be?

11. Boundary Conditions
Boundary conditions defined on outer edge of computational domain.
Types of boundary condition:
Wall
Inflow/outflow
Symmetry
Internal

12. Turbulent Flow Direct Numerical Simulation (DNS)
Directly calculates every tiny eddy from NS
What kind of grid do you think this requires?
What do you think the advantages/disadvantages of this would be?

13. Turbulent Flow Large Eddy Simulation (LES) NS for big eddies
Simpler model (an additional equation of motion) for smaller eddies
What do you think the advantages/disadvantages of this would be?

14. Results: Visualization Methods
Streamlines

15. Results: Visualization Methods
Contour Plots

16. Results: Visualization Methods
Vector Plots

17. Example Questions About CFD
Given this picture describes the results of a CFD simulation, name the visualization method.
Name some tradeoffs to consider when meshing a system for CFD.
Why are turbulent flows more difficult to simulate?

18. Examples! https://www.youtube.com/watch?v=hEsmlS6EGJw