1. Lecture Objectives:
Boundary Conditions
Project 1 (software)

2. Surface boundaries wall functions
Wall surface
Introduce velocity
temperature and concentration
Use wall functions to model the micro-flow in the vicinity of surface
Using relatively large mesh (cell) size.

3. Surface boundaries wall functions
Course mesh distribution in the vicinity of surface Y
Wall surface
Velocity in the first cell will depend on the distance y.

4. Surface boundary conditions and log-wall functions
E is the integration constant and
y* is a length scale
Friction velocity
u+=V/Vt
y*=(n/Vt)
y+=y/y*
k- von Karman's constant
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.
Surface cells
Turbulent profile
Laminar sub-layer

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

6. Modeling of Turbulent Viscosity in boundary layer
forced convection
natural convection

7. Temperature and concentration gradient in boundary layer
Depend on velocity field
Temperature
q=h(Ts-Tair)
Concentration
F=hc(Cs-Cair/m)
m=Dair/Ds
m- segregation coefficient
h = f(V) = f(k,e)
Tair Ts
Into source term
of energy equation
hC = f(V, material prop.)
Cair Cs

8. Project 1 Pat a) Numerical diffusion
The purpose of this project part is to analyze how mesh size and orientation affects
the accuracy of result.
outlet
inlet T1 T2
T1=30C
T2=20C
outlet
inlet
Pat b) Learn how to:
1) Model: geometry, heat sources, concentration sources, diffusers,
2) Select important simulation parameters
3) Generate appropriate mesh
4) Check the results
5) Present the results

9. AIRPAK Software

10. Example Modeling Problem
Office ventilation (tutorial 1 in handouts posted on the website)
Boundaries:
Geometry:

11. Temperature and concentration gradient in boundary layer
Depend on velocity field
Temperature
q=h(Ts-Tair)
Concentration
F=hc(Cs-Cair/m)
m=Dair/Ds
m- segregation coefficient
h = f(V) = f(k,e)
Tair Ts
Into source term
of energy equation
hC = f(V, material prop.)
Cair Cs

12. Inlets Diffuser Types Valve diffuser swirl diffusers ceiling diffuser
wall or ceiling
floor

13. Diffuser Types Grill (side wall) diffusers Linear diffusers Vertical
Horizontal one side

14. Displacement ventilation diffusers

15. Diffuser modeling Complex geometry - Δ~10-4m We can spend all our
momentum sources
Momentum method
Complex geometry - Δ~10-4m
We can spend all our
computing power for one small detail

16. Diffuser Modeling
Fine mesh or box method for diffuser modeling

17. Jet parameters A0 - effective area of the diffuser
V0 – initial jet velocity
X - distance from the diffuser
Vm – maximum jet velocity at
distance x from the diffuser
K – property of diffuser

18. Diffuser properties (ASHRAE)
Fig. 1 Airflow patterns of different diffusers

19. Project 1