1. Lecture Objectives
Finish with boundary conditions
Unsteady State Flow

2. 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

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

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

5. 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

6. Example of BC: Inlets or Diffusers (Various types)
Valve diffuser
swirl diffusers
ceiling diffuser
wall or ceiling
floor

7. Steady vs. Unsteady – State Flow
Example of velocity at specific point for different activities
door
walking
block
fan
20 s recuperation
60 s recuperation
Time (s)
Velocity (m/s)

8. Steady vs. Unsteady – State Flow
Example of temperature profile at two specific points for different activities

9. Unsteady-state (Transient) CFD simulations
Computationally very expensive
Steps
Identify the problem
Many problems do not require unsteady-state sim.
Identify equations which should be unsteady-state
Define the simulation period
Define the required time steps
Adjust other simulation parameters
turbulence model, mesh, convergence criteria, number of required iterations, etc.
Require substantial investigation for each problem

10. Computationally very expensive
Change of  in volume dxdydz In Time
Discretize equation
System of equation for each time step
ap and f are function of Dt
f is function of previous value for F x =
1) Solve the system using the simple algorithm
2) Change the boundary conditions
3) Update the coefficient
4) Solve the new system of equations A F

11. Simulation period and time step
Depends on the boundary condition of
considered phenomenon
Time step
Depends on the time scale
With too large time step quasi-steady-state simulation
Set of steady state simulations
(there is no link in-between previous and next time step)

12. Time period T and time step Dt
Uniform
Variable
Linear
Piecewise
User defined

13. Transient boundaries For unsteady-state airflow created by transient

14. Transient boundaries For unsteady-state airflow created by transient

15. Transient Calculation
Iterations in different time steps
Change of the variable in time

16. Steady-state, unsteady-state or quasi-steady-state
Examples
Airflow around the airplane
Airflow in the room
Airflow around the building
Injection of pollutant in experiment
Flow in the automobile engine cylinder
DNS simulation of flow in the boundary layer