1. Lecture Objectives Review for exam Discuss midterm project
Course overview
Example questions from previous exams
Discuss midterm project

2. Course Masterial Review
Navier-Stokes equations and RANS
Turbulence modeling
Discretization and equation solver
Boundary conditions
Numerical properties

3. Conservation Equations Navier Stokes Equations

4. Reynolds Averaged Navier Stokes equations
Continuity: 1)
Momentum: 2) 3) 4)
Similar is for STy and STx
4 equations 5 unknowns → We need to model

5. Modeling of Turbulent Viscosity
Fluid property – often called laminar viscosity
Flow property – turbulent viscosity
MVM: Mean velocity models
TKEM: Turbulent kinetic energy equation models
Additional models:
LES: Large Eddy simulation models
RSM: Reynolds stress models

6. Discretization and equation solver
SIMPLE algorithm
Discretization of RANS
Guess p*
p=p*
Step1: solve V* from momentum equations
Step2: introduce correction P’ and express V = V* + f(P’)
Step3: substitute V into continuity equation solve P’ and then V
Step4: Solve T , k , e equations no
Converged
(residual check)
yes
end

7. Boundary Conditions Surfaces (wall functions) Inlets and outlets
Velocity
Temperature
Concentration
Inlets and outlets
Supply diffusers and
Outlets
Surface cell
Velocity profile
Laminar sub-layer
momentum sources

8. Numerical properties that affect the solutions
Grid distribution
- Grid dependent/independent solution
Differencing scheme
- Numerical diffusion
Convergence
- Residual and Number of iterations
Stability
- Relaxation
Tests the solution
- Check the conservation of mass, concentration, and energy

9. Exam Open book, open notes 90 minutes 30% of your final grade
Comprehensive
Several short problems and
Several questions
Examples are posted on the course website !

10. Example of short questions (yes no or very short answer)
Reynolds stresses describe the property of fluid or flow?
What is the difference between the shear stresses and Reynolds stresses?
Is the relaxation is necessary for the system of linear equations?
Is the SIMPLE algorithm explicit method for solving of system of equations?
Why do we use QUICK discretization scheme?
How many Reynolds stresses we have in two dimensional flow?

11. Explanation questions
Describe the difference between explicit and implicit method. Which are the advantages and disadvantages of both?
Explain how the dispersion of contaminant in the boundary layer depends on velocity field.
Describe how the temperature field affects the airflow. Identify the term in conservation equation that link energy and velocity equation, and describe which assumption we used to get this term.

12. IAQ parameters Number of ACH quantitative indicator
ACH - for total air
- for fresh air
Ventilation effectiveness
qualitative indicator
takes into account air distribution in the space
Exposure
takes into account air distribution and source position and intensity

13. IAQ parameters Age-of-air air-change effectiveness (EV)
Specific Contaminant Concentration
contaminant removal effectiveness e

14. Single value IAQ indicators Ev and ε
Contaminant removal effectiveness (e)
concentration at exhaust
average contaminant concentration
Contamination level
2. Air-change efficiency (Ev)
shortest time for replacing the air
average of local values of age of air
Air freshness

15. Air-change efficiency (Ev)
Depends only on airflow pattern in a room
We need to calculate age of air (t)
Average time of exchange
What is the age of air at the exhaust?
Type of flow
Perfect mixing
Piston (unidirectional) flow
Flow with stagnation and short-circuiting flow

16. Air exchange efficiency for characteristic room ventilation flow types
Flow pattern
Air-change
efficiency
Comparison with average time of exchange
Unidirectional flow
1 - 2
tn < texc < 2tn
Perfect mixing 1
texc = tn
Short Circuiting
0 - 1
texc > tn

17. Contaminant removal effectiveness (e)
Depends on:
position of a contaminant source
Airflow in the room
Questions
1) Is the concentration of pollutant in the room with stratified flow larger or smaller that the concentration with perfect mixing?
2) How to find the concentration at exhaust of the room?

18. Differences and similarities of Ev and e
Depending on the
source position:
- similar or
- completely different
air quality
Ev = 0.41
e = 0.19
e = 2.20