Lecture Objectives

• Review wall functions• Discuss: Project 1, HW2, and HW3• Project topics

Surface boundary conditions and log-wall functions

)log(1*

2/1

EyyV

E is the integration constant and y* is a length scale

dydV

t

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*=(/Vt)

- von Karman's constant

2/1

tV

Friction velocityCorrection

K- turbulence model in boundary layer

dydV

t

y

1

2/3

Wall function for

Wall function for k

2kCt

Eddy viscosity

Wall shear stress

2/1

1C

k

V

) )/V(

log(1t

2/1

EyV

)

)/(

log(12/1

2/1

EyV

)log(1*

2/1

EyyV

HW2

• Problem 1

• Problem 2

• K- RNG vs. LES vs. DNS

DNS • Example from the previous project class

Boundary conditions !

LES vs. RANS• Examples form the ongoing project

Cough simulation

What do you see with RANS

What do you see with LESVelocity Vorticity

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) RANSSteady 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 getSteady 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

Comparison: Velocity

LES

RANS

Measurements

Comparison: Peak Velocity and Turbulence

13

Comparison: Cumulative Exposure

7 micron particles

HW3

• Questions?

Project 1

Airpak; How to : •Define occupancy zone•Zero diffusion •Refine mesh•Define isosurface•….

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