1. Lecture Objectives Review wall functions Discuss: Project 1, HW2, and HW3 Project topics

2. Surface boundary conditions and log-wall functions E is the integration constant and y * is a length scale The assumption of ‘constant shear stress’ is used here. Constants k = 0.41 and E = 8.43 fit well to a range of boundary layer flows. y*=( / V t )  - von Karman's constant Friction velocity Correction

3. K-  turbulence model in boundary layer Wall function for  Wall function for k Eddy viscosity Wall shear stress V

4. HW2 Problem 1 Problem 2 K-  RNG vs. LES vs. DNS

5. DNS Example from the previous project class Boundary conditions !

6. LES vs. RANS Examples form the ongoing project

7. Cough simulation

8. What do you see with RANS

9. What do you see with LES Velocity Vorticity

10. Calculation time cost Modeling of unsteady cough and particle dispersion - period of 1 minute -mesh size: 500,000; particle #: 600,000; time step: 0.001s -Computers: 4 core 3.4 MHz 10 1) RANS Steady state calculation of background flow 3-6 hours Conversion to unsteady Calculation Time (2-5 day) Cough + particle injection (1s) Particle dispersion (60 s) 24-48 hours 6-12 hours Calculation Time (2-4 weeks) RANS to get Steady state background flow LES+part. inject (1s) LES+part. dispersion (60 s) LES calculation to get fully developed turbulent flow (calculation of 1500 seconds) 1~2 weeks 2-3 weeks 10 3-6 hours 2) LES

11. Comparison: Velocity LES RANS Measurements

12. Comparison: Peak Velocity and Turbulence

13. 13 Comparison: Cumulative Exposure 7 micron particles

14. HW3 Questions?

15. Project 1 Airpak; How to : Define occupancy zone Zero diffusion Refine mesh Define isosurface ….

16. Final project topics You will define the project topic Examples from previous years –Single side natural ventilation –Atrium ventilation - design problem –Rain water collection –Ventilation effectiveness – parametric study –Surface convection –Surface mass transfer