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Ventilation Design Handbook on Animal Research Facilities Using Static Microisolators 
5.2 Description of Mathematical Model 
5.2.1 Governing Equations 
The generic form of the governing equations, shown by equation 5.1, can be expanded to form 
the three fundamental conservation laws that comprise the Navier-Stokes equations. These are 
the conservation of mass: 
3p apt/,. 
dt dx i 
= 0 
(5.2) 
the conservation of momentum: 
ML + ±( pUiU \ = _iL + A 
dt dx, ' dx ; dx: 
H 
dJL 
d XJ , 
+ 8i(p~Po) 
(5.3) 
and the conservation of thermal energy: 
ap h a / \ a 
ar + a7< pu ' w > = ar 
£ 
+ 
dP 
dt 
(5.4) 
These equations describe the behavior of fluids under both laminar and turbulent flow conditions. 
When calculating the flow in the built environment, one of the most important physical effects is 
that of turbulence. 
5.2.2 Turbulence Modeling 
For this project, an established and reliable approach to turbulence modeling is required to 
achieve the large number of calculations necessary for analysis of the many configurations. This 
section provides some background on the different approaches to modeling turbulence. 
To model a turbulent flow, the temporal terms of equations 5.2, 5.3, and 5.4 would have to have 
a time step (dt) small enough to capture all turbulent fluctuations on even the smallest time 
scales. The same applies to all physical dimensions of the control volume cells (dxd terms. They 
would have to be as small as that known as the Kolmogarov scale, which decreases nonlinearly 
with an increase in Reynolds number. 
