Overview of FCU Case Study‌ Sample Clauses

Overview of FCU Case Study‌. The FCU example considers a system for heating a room by passing water from a heat pump through a coil, where heat is transferred to room air blown through the coil by a fan. The flow of air and water through the coil are controlled by the speed of the fan and the opening of a valve, respectively. The fan speed and valve setting are controlled by a software controller, the design of which is the focus of this case study. Heat transferred to the room is gradually lost over time through the walls of the room. Fig. 20 shows the overall layout of the FCU system. The water passing through the coil is heated by a heat pump to a constant temperature. We refer to the water leaving the heat pump as the leaving water temperature, LWT . The rate of heat transfer through the coil, Qin, is determined by the difference between LWT and the room air temperature, RAT , using the following equation, Qin = ϵ × fanSpeed × m˙ at × cair × (LWT — RAT ), (4) where • ϵ is a constant representing the effectiveness of the coil, • fanSpeed is the setting of the fan’s speed, ranging from 0 to 1, • m˙ at is the maximum air flow rate that the fan can produce, and • cair is the specific heat of air. The heat transfer, Qin, corresponds to the heat loss of water flowing through the coil. It is hence moreover related to the temperature EWT of the water entering the heat pump by the following equation, Qin = valveOpen × m˙ wt × cwater × (LWT — EWT ), (5) where • valveOpen is the setting of the valve, ranging from 0 to 1, • m˙ wt is the maximum water flow rate through the coil, and • cwater is the specific heat of water. In addition to the heat transfer through the coil, the room air temperature is also affected by heat lost through the wall, Qout . Such is determined by the difference between RAT and the surface temperature Tisurf of the wall on the inside of the room, and governed by the following equation: Qout = hair × Awall × (RAT — Tisurf ), (6) where • hair is the heat transfer coefficient for the air, and • Awall is the surface area of the wall. The overall rate of change in RAT is then determined using the following differential equation, d RAT dt = Qin — Qout ρair × cair × vair , (7) where • ρair is the density of air, • cair is, as above, the specific heat of air, and • vair is the volume of the air in the room. The equations presented above describe the movement of heat in the room. The movement of heat in the wall is described by the following pair of dif- ferential equations tha...
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