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Cpw water specific heat (J=Kg oC)
ra air mass density (Kg=m3)
Cpa air specific heat (J=Kg oC)
wr f wheel rotation factor (1 wr f 0)
n rotation speed of the wheel (10 rpm n 0 rpm)
´ As heat transfer surface area of one tube (m2)
U mean air velocity in the tube (m=s)
Tm(x; t) matrix temperature (
oC)
Ta(x; t) air temperature (
oC)
h convective heat transfer coefficient (W=m2 oK)
L wheel length (m)
Am cross sectional area of one tube of matrix (m2)
Aa cross sectional area of one tube for air (m2)
Km matrix thermal conductivity (W=m oK)
P exposion time (half of the period) (sec:)
Mm total matrix mass (Kg)
˙ ma air mass flow rate (Kg=h)
As heat transfer surface area on the supply or exhaust side (m2)
Cpm matrix specific heat (J=Kg oC)
C
r
Mm Cpm n
˙ ma Cpa
NTU h As
˙ ma Cpa
Cpc specific heat of the coil (J=Kg oC)
˙ mws supply water mass flow rate (Kg=h)
˙ mwt tertiary water mass flow rate (Kg=h)
mcw effective mass of the region of the coil at an average temperature
equal to outlet water temperature (Kg)
mca effective mass of the region of the coil at an average temperature
equal to outlet air temperature (Kg)
Cw Cpc mcw (J=oC)
Ca Cpc mca (J=oC)
N pump speed (rpm)
II. DYNAMIC MODELING
The HVAC system that will be considered consists of two
heat exchangers: an air-to-air heat exchanger and a water-
toair heat exchanger. In this section these components will
be described and their dynamic models will be developed.
Finally the overall nonlinear model of the HVAC system will
be linearized. This linear model will be used to design the
controller later.A. Air-to-air Heat Exchanger
The air-to-air heat exchanger is a rotary heat exchanger
in aluminium, with low pressure loss (shown in Fig. 1).
The rotor control comprises a gear motor with frequency
converter. Two fans are installed to produce the desired inlet
and outlet air flow.
1) Steady State Gain Determination: Here, it is supposed
that the ratio of the supply air flow to the return air flow is
one. Therefore, ht2 will be a function of air flow (qa), that is
the same for both supply and return air, and the rotation speed
of the wheel (n). In this context, results of testing the rotary
heat exchanger that was performed according to European
Standard for laboratory testing of air-to-air heat recovery
devices (EN 247, EN 305, EN 306, EN 307, EN 308) will
be used. According to results of the test, it is possible to
specify ht2 as a multiplication of two functions. Fig. 2 and 3
illustrate these functions [2]. Therefore, ht2 can be described
as following:2) Dynamic Behavior: Fig 4 shows an energy wheel oper-
ating in a counter flow arrangement. Under typical operating
conditions, warm air enters the tube during the supply part
of the cycle and transfers energy to the matrix. This energy
is then transferred from the matrix to the air during the
exhaust part of the cycle. The half plane of the matrix tube
is assumed impermeable and adiabatic and the bulk mean
temperatures of air are used in the model. The formulation
is therefore one dimensional and transient with space (x)
and time (t or q = w t) as the independent variables. The
governing equations for heat transfer (energy equations) in
energy wheel for air and matrix include energy storage,
convection, conduction based on the usual assumptions are
as fllows respectively:Equation (6) shows that air temperature (Ta) can be
assumed as the input for the matrix temperature (Tm) dif-
ferential equation. It means the matrix temperature as a
function of time (t) will perform as an output of the ordinary