Component 801: Room Model by HVACSIM+
General Description
The room model has been described in reference [1], and is loosely
based on reference [2]. The model considers the air mass, an interior mass,
and a wall mass. No modeling of the building shell is attempted, and heat
flows are treated as inputs to the model.
The air mass is artificially divided into two parts: a fully mixed
part near the ventilation supply, and a piston flow part near the ventilation
exhaust. The fraction of the air mass in these two parts is adjustable. Each
part of the air mass exchanges heat with tow kinds of room mass: an interior
mass and a wall mass. the temperature of each room mass is assumed to be
uniform. Two heat flows are also defined: a heat flow into the wall mass,
representing conduction through the walls, and a direct heat flow into the
fully mixed air mass, representing internal gains.
Nomenclature
Ca - specific heat of air
CI - specific heat of interior mass
Cw - specific heat of wall mass
f - fraction of air mass which is fully mixed
HI - heat transfer coefficient times area of interior mass
Hw - heat transfer coefficient times area of wall mass
MI - interior mass
Mw - wall mass
QI - heat flow due to internal gains
Qw - conduction heat flow into wall mass
Tai - ventilation air inlet temperature
Tao - exhaust air temperature
TI - interior mass temperature
Tm - temperature of fully mixed portion of air mass
Tp - temperature of piston flow portion of air mass
Tr - average room air temperature
Tw - wall mass temperature
V - volume of room air mass
w - mass flow rate of ventilation air
p - density of air
Mathematical Description
The fully mixed air mass temperature is given by the following
equation:
(f*p*V*Ca)*d(Tm)/dt = QI + w*Ca*(Tai - Tm) +
f*Hw*(Tw - Tm) + f*HI*(TI - Tm)
The piston flow part of the air mass exchanges heat with the interior mass and
the wall mass as it moves through the room according to the following equation:
w*L*Ca*d(Tp(x))/dx = (1 - f)*[Hw*(Tw - Tp(x)) + HI*(TI - Tp(x))]
where L is the total distance moved by the air mass. The solution to this
equation is:
Tp(x) = Ts - (Ts - Tm)*exp(-ax/L)
where
Ts = (Hw*Tw + HI*TI) / (Hw + HI)
a = [(Hw + HI) / (w*Ca)]*(1 - f)
and Tp(x) is the temperature of the air as a function of the distance traveled.
The spatial average air mass temperature is approximately given by:
d(Tbar,p)/dt = [w*(Tbar,s - Tbar,p)] / [p*V*(1 - f)]
where
Ts = Ts - (Ts - Tm)*[(1 - exp(-a)) / a]
The room mass temperatures are given by the following equations:
Mw*Cw*d(Tw)/dt = Qw + Hw*(Tr - Tw)
MI*CI*d(TI)/dt = HI*(Tr - TI)
Tr = f*Tm + (1 - f)*Tbar,p
The exhaust air temperature is equal to the temperature of the piston flow
portion of the air mass at x=L:
Tao = Ts - (Ts - Tm)*exp(-a)
A transport delay is applied to the exhaust air temperature using the utility
subroutine DELAY with a delay time equal to the flush time for the piston flow
fraction of the room volume.
Component 801 Configuration
Inputs Description
1 w - mass flow rate of ventilation air
2 Tai - ventilation air inlet temperature
3 Tm - temperature of fully mixed portion of air mass
4 Tw - wall mass temperature
5 TI - interior mass temperature
6 Tbar,p - spatial average temperature of the piston flow
portion of the air mass
7 Qw - conduction heat flow into wall mass
8 QI - heat flow due to internal gains
Outputs Description
1 Tm - temperature of fully mixed portion of air mass
2 Tw - wall mass temperature
3 TI - interior mass temperature
4 Tbar,p - spatial average temperature of the piston flow
portion of the air mass
5 Tr - average room air temperature
6 Tao - exhaust air temperature
Parameters Description
1 V - volume of room air mass
2 Mw*Cw - thermal capacitance of walls
3 MI*CI - thermal capacitance of interior mass
4 Hw - heat transfer coefficient times area for the
wall mass
5 HI - heat transfer coefficient times area for the
interior mass
6 f - fraction of the air mass which is fully mixed
Reference:
1. Hill, C.R. "Simulation of a multizone air handler." ASHRAE
Transactions, Vol. 91 (1985).
2. Borresen, B.A. "Thermal room models for control analysis." ASHRAE
Transactions, Vol. 87, part 2, 1981.
3. HVACSIM+ Building Systems and Equipment Simulation Program Reference
Manual (NBSIR 84-2996)
Daniel R. Clark
United States Department of Commerce
National Institute of Standards and Technology
Gaithersburg, Maryland 20899-0001