HVAC SYSTEMS - HFT Stuttgart

this differential equation has the form:
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CHAPTER 02
dT col , m ( t )
= a − b ⋅T
col , ( t )
(2.2.1-14)
dt
C eff
m
Considering the initial condition: Tcol,m(0) = Tcol,m,0 the solution of this equation
is:
b ⋅t
b ⋅t
− ⎛
− ⎞
C eff
C eff
e ⎜b
⋅T
col m a e a ⎟
, , 0 + ⋅ −
⎜
⎟
T col m t =
⎝
⎠
, ( )
(2.2.1-15)
b
The collector outlet temperature is then calculated from equation 2.2.1-11. The
dynamic model has been programmed in FORTRAN as INSEL block. To
compare the efficiency of the static model and of the dynamic one node model
an INSEL model has been developed with varying solar radiation and on / off
switching of the collector mass flow. The results are shown in Fig. 2.2.
Temperature / °C
140
120
100
80
60
40
20
Solar Solare radiation Einstrahlung / W [W/m²/10] m² x 10-1 Solar Solare radiation Einstrahlung / W [W/m²/10] m² x 10-1 W m -2 x 10 -1
Collector Kollektormassenstrom
mass flow
Collector Austrittstemperatur outlet temperature quasi dynamisches
Modell dynamic DIN one EN node 12975 model
Collector outlet Austrittstemperatur
temperature
advanced dynamisches dynamic one Modell node model
0
0 500 1000 1500 2000 2500 3000 3500 4000 4500
Time in s
Fig. 2-2: Comparison of the performance of a static and a one
node dynamic collector model
The difference between the static model and the dynamic one node model is
clearly visible. The static model increases immediately to the steady state outlet
temperature as soon as solar irradiation is on the collector plane and drops
immediately down to the collector inlet temperature as soon the solar radiation
#01
#02
#03
#04
#05
#06
#07
Collector mean
Austrittstemperatur
Collector outlet
temperatures
temperature statisches Modell static
model