Lecture Objectives Ventilation Effectiveness, Thermal Comfort, and other CFD results representation Surface Radiation Models Particle modeling

Thermal comfort Temperature and relative humidity

Thermal comfort Velocity Can create draft Draft is related to air temperature, air velocity, and turbulence intensity.

Thermal comfort Mean radiant temperature potential problems Asymmetry Warm ceiling (----) Cool wall (---) Cool ceiling (--) Warm wall (-)

Prediction of thermal comfort Predicted Mean Vote (PMV) + 3 hot + 2 warm + 1 slightly warm PMV = 0 neutral -1 slightly cool -2 cool -3 cold PMV = [0.303 exp ( -0.036 M ) + 0.028 ] L L - Thermal load on the body L = Internal heat production – heat loss to the actual environment L = M - W - [( Csk + Rsk + Esk ) + ( Cres + Eres )] Predicted Percentage Dissatisfied (PPD) PPD = 100 - 95 exp [ - (0.03353 PMV4 + 0.2179 PMV2)] Empirical correlations Ole Fanger Further Details: ANSI/ASHRAE standard 55, ISO standard 7730

Surface Radiation Models Combined with CFD Example: Heat transfer through a window Cavity: CFD Domain

Particulate matters (PM) Properties Size, density, liquid, solid, combination, … Sources Airborne, infiltration, resuspension, ventilation,… Sinks Deposition, filtration, ventilation (dilution),… Distribution - Uniform and nonuniform Human exposure

Properties ASHRAE Transaction 2004

Particle size distribution ASHRAE Transaction 2004 Ventilation system affect the PM concentration in indoor environment !

Modeling of PM: We need to say something about 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 dune flow, 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

Multiphase Flow Regimes Fluent user manual 2006

Two basic approaches for modeling of particle dynamics PM Modeling 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

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

Lagrangian Model particle tracking A trajectory of the particle in the vicinity of the spherical collector is governed by the Newton’s equation m∙a=SF Forces that affect the particle (rVvolume) particle ∙dvx/dt=SFx (rVvolume) particle ∙dvy/dt=SFy (rVvolume) particle ∙dvz/dt=SFz System of equation for each particle Solution is velocity and direction of each particle

Lagrangian Model particle tracking Basic equations - momentum equation based on Newton's second law Drag force due to the friction between particle and air - dp is the particle's diameter, - p is the particle density, - up and u are the particle and fluid instantaneous velocities in the i direction, - Fe represents the external forces (for example gravity force). This equation is solved at each time step for every particle. The particle position xi of each particle are obtained using the following equation: For finite time step

Forces that affect the particle The drag force is the most significant force and it depends on Particle and fluid velocities Reynolds number defined for particle fluid velocity difference Drag coefficient:        a1, a2,a3 are constants that apply to smooth spherical particles or for non spherical particles: b1, b2,b3, b4 are constants that take into account non-spherical shape of particles

Forces that affect the particle For sub-micron particles Stokes drag law: Velocities of air and particle Where m is fluid viscosity and dp is particle diamete> Ce is the Cunningham correction factor: l is the molecular mean free path. Overall: Drag force depends on the flow parameters such as Reynolds number, turbulence level,…

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.

Algorithm for CFD and particle tracking Steady state airflow Unsteady state airflow Airflow (u,v,w) Airflow (u,v,w) for time step  Steady state Injection of particles Injection of particles Particle distribution for time step  Particle distribution for time step  Particle distribution for time step + Airflow (u,v,w) for time step + Particle distribution for time step +2 Particle distribution 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

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