Lecture Objectives:

1
Lecture Objectives

• 1) Discuss HW3 problems
• 2) Define Relaxation (example)
• 3) Define boundary conditions for CFD
• Model Boundary conditions

2
Residual calculation for CFD

• Residual for the cell
• RFijkFkijk-Fk-1ijk
• Total residual for the simulation domain
• RFtotalSRFijk
• Scaled (normalized) residual
• RFSRFijk/FF

iteration
cell position
Variable p,V,T,
For all cells
Flux of variable F used for normalization Vary
for different CFD software
3
Relaxation
Relaxation with iterative solvers When the
equations are nonlinear it can happen that you
get divergency in iterative procedure for
solving considered time step
divergence
variable
solution
convergence
Solution is Under-Relaxation YfY(n)(1-f)Y(n
-1) Y considered parameter , n iteration
, f relaxation factor For our example Yin
iteration 101fY(100)(1-f) Y(99) f 0-1
under-relaxation -stabilize the iteration f
1-2 over-relaxation - speed-up the
convergence
iteration
Value which is should be used for the next
iteration
Under-Relaxation is often required when you have
nonlinear equations!
4
Example of relaxation(example from homework 3
assignment)
Example Advection diffusion equation, 1-D,
steady-state, 4 nodes
1) Explicit format
4
3
1
2
2) Guess initial values
3)
Substitute and calculate
Substitute and calculate
4)
Substitute and calculate
.
5
Relaxation example in Excel
6
Boundary Conditions
CFD ACCURACY Depends on airflow in the vicinity
of Boundary conditions
1) At air supply device 2) In the vicinity
of occupant 3) At room surfaces

• Detailed modeling
• limited by
• computer power

7

• Define Boundary Conditions at
• Surfaces (wall functions)
• Velocity
• Temperature
• Concentration
• Inlets and outlets
• Diffusers and outlets
• Windows and cracks

8
Diffuser Types
Valve diffuser
swirl diffusers
ceiling diffuser
wall or ceiling
floor
9
Diffuser Types
Grill (side wall) diffusers
Linear diffusers
Vertical
Horizontal one side
10
Displacement ventilationdiffusers
11
Diffuser modeling
Momentum method

• Complex geometry - ?10-4m
• We can spend all our
• computing power for one small detail

12
Diffuser Modeling
Fine mesh or box
method for diffuser modeling
13
Diffuser modeling
High Aspiration diffuser
D
D
L
L
Jet through one opening only
14
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
15
Diffuser properties (ASHRAE)
20.4 ASHRAE method
Fig. 1 Airflow patterns of different diffusers
16
Examples in AirpakDiffusers Macro
17
Surface boundary conditionstemperatureand
velocity
18
Surface boundarieswall functions
Wall surface
Use wall functions to model the micro-flow in the
vicinity of surface Using relatively large mesh
(cell) size.
19
Surface boundary conditions and log-wall
functions
E is the integration constant and y is a length
scale
y- thickness of boundary layer
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 cell
Turbulent profile
Laminar sub-layer