ASHRAE Journal - July 2023 - 60

TECHNICAL FEATURE
the " well-mixed " conditions
among all the rooms. It clearly
represents a limit case, when the
air recirculation rate is much
higher than the outdoor air
exchange (renewal) rate (rc >> rn).
Segregated Model
A big step forward in the
segregated model is retaining
physically segregated spaces;
the only connection among
different rooms is given by
the all-air ducted HVAC plant,
providing airflows with rn (h−1)
as the renewal rate and rc (h−1)
as the recirculation rate in each
room. Figure 4 shows a diagram of this model. The
diagram does not exactly reproduce the actual system
configuration, which generally involves recirculated
air being mixed with outdoor air to form supply
air before introduction into rooms. However, this
schematic makes it easier to understand how the
equations are derived and leads to the same result as
the actual situation regarding viral concentration in
the rooms.
Equation 4 refers to the concentration of infectious
quanta in the infected room, while Equation 5 refers
to that of the other rooms. All spaces are considered
perfectly mixed.
d I
d
C
t
=+ −+ C () C
V1
q*
d S
d
C
t
I
rc *
RI
rcN *
= −+R C rc N *
C ()C NS
where
CI
the infected room, quanta/m3
rc = air recirculation rate, h−1
CR
+−1 ¥ C
R = IS
NS
= volume concentration of infectious quanta in
= volume concentration of infectious quanta in
the recirculated air, quanta/m3
CS
= volume concentration of infectious quanta in
60
ASHRAE JOURNAL ashrae.o rg
J U LY 2023
rc * () C S
(4)
(5)
(6)
FIGURE 11 Concentration of infectious quanta in the corridor and service rooms.
susceptible individuals' rooms, quanta/m3
NS = total number of people involved (asymptomatic
infected individuals + susceptible individuals)
Including Equation 6 in the model yields a first-order
ordinary differential algebraic equation (ODAE) system
reducible to a symbolically solvable ordinary
differential equation (ODE) system, whose explicit
solution is omitted for the sake of brevity. The system
can be numerically solved by a code in a suitable computing
environment.
Figures 5a (for q = 40 quanta h−1) and 5b (for q = 120
quanta h−1) show the results of the application of the
segregated model in terms of the reproduction index
R* versus the total number of people involved NS.
The dependence of R* on both the fresh (outdoor) air
renewal volumetric airflow rate per person Qrn and
the air recirculation volumetric airflow rate per person
Qrc is evident in both figures.
Effect of Virus Removal/Inactivation in the Supply Duct
It is also possible to extend the segregated model
in order to account for the presence of filtration or
inactivation devices (high-efficiency mechanical or
electrostatic filters, UV-C irradiation, photocatalytic
oxidation, negative air ionization or other similar
technologies) in the air supply duct after the mixing
plenum. Assuming a removal/inactivation efficiency
ηf in the interval [0, 1], a multiplication factor of (1−
ηf) must be introduced in the CR formula in Equation
6. Figures 6, 7, 8 and 9 and Online Figure 2 show, for the
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