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