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Lecture Objectives: Boundary Conditions Project 1 (software)
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Surface boundaries wall functions
Wall surface Introduce velocity temperature and concentration Use wall functions to model the micro-flow in the vicinity of surface Using relatively large mesh (cell) size.
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Surface boundaries wall functions
Course mesh distribution in the vicinity of surface Y Wall surface Velocity in the first cell will depend on the distance y.
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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
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K-e turbulence model in boundary layer
Wall shear stress Eddy viscosity V Wall function for e Wall function for k
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Modeling of Turbulent Viscosity in boundary layer
forced convection natural convection
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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
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Project 1 Pat a) Numerical diffusion
The purpose of this project part is to analyze how mesh size and orientation affects the accuracy of result. outlet inlet T1 T2 T1=30C T2=20C outlet inlet Pat b) Learn how to: 1) Model: geometry, heat sources, concentration sources, diffusers, 2) Select important simulation parameters 3) Generate appropriate mesh 4) Check the results 5) Present the results
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AIRPAK Software
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Example Modeling Problem
Office ventilation (tutorial 1 in handouts posted on the website) Boundaries: Geometry:
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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
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Inlets Diffuser Types Valve diffuser swirl diffusers ceiling diffuser
wall or ceiling floor
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Diffuser Types Grill (side wall) diffusers Linear diffusers Vertical
Horizontal one side
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Displacement ventilation diffusers
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Diffuser modeling Complex geometry - Δ~10-4m We can spend all our
momentum sources Momentum method Complex geometry - Δ~10-4m We can spend all our computing power for one small detail
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Diffuser Modeling Fine mesh or box method for diffuser modeling
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Jet parameters A0 - effective area of the diffuser
V0 – initial jet velocity X - distance from the diffuser Vm – maximum jet velocity at distance x from the diffuser K – property of diffuser
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Diffuser properties (ASHRAE)
Fig. 1 Airflow patterns of different diffusers
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Project 1
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