Handbook of air conditioning and refrigeration / Shan K

18.52 CHAPTER EIGHTEEN
CFD Becomes More Popular
HVAC&R engineers traditionally conducted scale-model physical experiments to study air motion
and temperature distribution by maintaining similarity through a high Re number and an appropriate
Ar corresponding to the adopted scale. CFD was first developed in Europe and Japan. In the
late 1980s, ASHRAE organized a research project which thoroughly investigated many issues associated
with CFD simulation. In the late 1990s, CFD became more popular in the HVAC&R industry
for the determination of locations of supply outlets and return inlets, airflow patterns, air velocity
and temperature distributions, and contaminant concentration and removal in an HVAC&R system.
Baker et al. (1997) and Ladeinde and Neavon (1997) summarized the reasons for CFD’s popularity:
● CFD has the ability to establish firm quantitative data regarding air motion and can predict fluid
characteristics and pressure differentials to very low levels that are essentially impossible during
experiments.
● The cost of CFD is lower than that of scale-model experiments.
● Earlier CFD codes were developed on supercomputers. Today computing software is available for
simulations to be performed on personal computers.
● People are slowly getting over the fear of using CFD.
Reynolds-Averaged Navier-Stokes Equations
Numerical Methods
The mathematical expressions describing the basic space-time relationship between mass, velocity,
and temperature are expressed in partial differential equations called Navier-Stokes (NS) equations.
These equations may be only directly applied to laminar flow fields. Baker et al. (1997) pointed out
that CFD modeling based on NS equations requires a large number of assumptions and approximations.
These approximations are closely related to the CFD computing results.
For predicting turbulent flow, an approximation called Reynolds averaging (Ra) is used to
convert this time-unsteady flow to a mean velocity presentation. A principal assumption for CFD is
the turbulence closure model to govern the Reynolds-averaged Navier-Stokes partial differential
equations. The selected CFD has been a two-equation turbulent kinetic energy (TKE) model. The
TKE model assumes a fully turbulent flow existing everywhere for room airflow prediction. Actually,
at normal air change rates per hour, fully turbulent flow occurs only in supply ducts, air jets,
downstream of the edge of the obstacles. Elsewhere, the flow is more likely weakly turbulent and
actually time-unsteady. A quantitative measurement of the degree of turbulence of an airflow is the
turbulence Reynolds number (Re t ) which is defined as the ratio of the turbulence eddy viscosity to
the kinematic viscosity: Re t � v t /v. For laminar flow, Re t � 0, and for fully turbulent flow 50 �
Re t � 10 3 .
Because these Reynolds-averaged partial differential equations using the turbulence Reynold
number Re t are highly nonlinear, they are not solvable by explicit, analytical methods. In these
partial differential equations, the velocities u, v, w; and pressure p; temperature T; and some
scalar � are dependent variables to be calculated. Space displacements x, y, z and time t are independent
variables. Initial and boundary conditions must be specified. Numerical solution (approximate
methods) such as via the finite element and finite volume methods is more popular in CFD
simulation.
Ladeinde and Neavon (1997) illustrated the finite element procedure during the calculation
of airflow in a duct section. Figure 18.28a shows this duct section that contains an inlet and an
outlet. The interior of the duct that constitutes the region of airflow (domain of the CFD model)