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

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

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Forces that affect the particle External forces Gravitation Brownian Thermophoretic Lift force Electrostatic 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. Lift force - lift due to shear Brownian force – creates random movement of particles - for sub-micron particles, Electrostatic – for charged particles

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

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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

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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

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Multiphase Flow Regimes Fluent user manual 2006

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

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

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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

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Natural Ventilation: Science Park, Gelsenkirchen, Germany

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

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Engineering Application Unlimited number of problems! For example:

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Human Exposure Airflow in the room vs. Airflow in vicinity of occupant - Course mesh - Simple geometry CO 2 distribution CO 2 sources Occupied zone

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

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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

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

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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

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