Lecture Objectives

1. Lecture Objectives • Finish with modeling of PM • Discuss • Advance discretization • Specific class of problems • Discuss the CFD software

2. Two basic approaches for modeling of particle dynamics • Lagrangian Model • particle tracking • For each particle ma=SF • Eulerian Model • Multiphase flow (fluid and particles) • Set of two systems of equations

3. Forces that affect the particle External forces Electrostatic Thermophoretic Gravitation Lift force Brownian Brownian force – creates random movement of particles - for sub-micron particles, Lift force - lift due to shear Electrostatic – for charged particles Thermophoretic Force Small particles suspended in a gas that has a temperature gradient are exposed to a force in the direction opposite to that of the gradient. This phenomenon is known as thermophoresis.

4. Algorithm for CFD and particle tracking Unsteady state airflow Steady state airflow Airflow (u,v,w) for time step  Airflow (u,v,w) Steady state Injection of particles Injection of particles Particle distribution for time step  Particle distribution for time step  Airflow (u,v,w) for time step + Particle distribution for time step + Particle distribution for time step + Particle distribution for time step +2 ….. ….. One way coupling Case 1 when airflow is not affected by particle flow Case 2 particle dynamics affects the airflow Two way coupling

5. Eulerian Model • Solve several sets of NS equations • Define the boundary conditions in-between phases Multiphase/Mixture Model • Mixture model • Secondary phase can be granular • Applicable for solid-fluid simulations • Granular physics • Solve total granular pressure to momentum equation • Use Solids viscosity for dispersed solid phase • Density difference should be small. • Useful mainly for liquid-solids multiphase systems There are models applicable for particles in the air

6. Multiphase flow Multiphase flow can be classified in the following regimes: • gas-liquid or liquid-liquid flows • gas-solid flows • particle-laden flow: discrete solid particles in a continuous gas • pneumatic transport: flow pattern depends on factors such as solid loading, Reynolds numbers, and particle properties. Typical patterns are slug flow, packed beds, and homogeneous flow. • fluidized beds: consist of a vertical cylinder containing particles where gas is introduced through a distributor. • liquid-solid flows • three-phase flows

7. Multiphase Flow Regimes Fluent user manual 2006

8. Advection equation 1-D, steady-state Dx Dx P E W Dx Vx>0 1) Upwind scheme: Vx<0 2) Central differencing scheme: 3) Hybrid of upwind and central differencing scheme Higher order differencing scheme: Quadratic upwind differencing Scheme (QUICK) N+1 N+2 N-1 N N-2 P WW E EE W We need to find coefficients aP, aW, aE, aWW, aEE,

9. Quadratic upwind differencing Scheme (QUICK) Coefficients: Advection coefficient: Source: Diffusion coefficients : For advection only:

10. Challenging Problem:Application of CFD in a large space - The geometry should present correct geometry around large openings - The ratio between the total flow area and the floor area should be the same as in full scale - Air supply and return openings should be defined in a coarse grid sufficient for momentum and energy flow predictions The result will define global air and energy flow between zones but accuracy is insufficient for an analysis of the detail air velocity distribution in the zones. EXAMPLE: Five-Story Parking Garage Ventilation Multi-space building Course grid model properties www.airpak.fluent.com

12. Natural Ventilation:Science Park, Gelsenkirchen, Germany

13. Detail air velocity distribution in room Detail description of geometry Simple Description of Interior Furnishings can be described as A volume with additional pres- sure drop in the momentum Equations:

14. Engineering Application Unlimited number of problems! For example: http://www.ansys.com/products/airpak/solutions.asp?name=p1 http://www.cd-adapco.com/applications/building.html

15. - Simple geometry - Course mesh CO2 sources Occupied zone Human Exposure Airflow in the room vs. Airflow in vicinity of occupant CO2 distribution

16. Simulation of an occupant Detailed geometry: Good for local convection coefficient calculation at the skin Effect of breathing an movement decrease accuracy

17. Different level of geometry details • Avaraged geometry can be used for global effects • Simple geometry can be used for semi-global effects • Detailed geometry should be used for local effects • Conclusions from geometry analysis (Peter Nielsen) • Semi-global effect • Differences in geometry have a small influence on • velocity, temperature distribution, contaminant distribution • far from the manikin • Local effect • Differences in geometry have an effect on velocity and • concentration distribution close to a person and exposure of • a person

18. We Often Need Experimental Validation Room with nonuniform temporal and spatial distribution of particles (for example smoke) Validation results for 0.74 m S1 CFD model Monitoring Position S1 Monitoring Position S2 S2 Pollution Source active 2 minutes Experiment

19. Examples of CFD application in Indoor environment research Some hot topics • Particle Transport in a boundary layer • Surface Chemistry • Air and particle flow in lung • Various analyses of fluid flow in building components and HVAC systems