Lecture Objectives:
• Learn about
• Plumbing System Modeling
–HW3
• Cooling tower modeling
• Chiller modeling
HW2 & HW3
40 ft
20 ft
20 ft
5 ft
30 ft
200 ft
30 ft
200 ft
40 ft
10 ton
20 ft
5 ft
5 ft
5 ft
5 ft
5 ft
30 ft
10 ft
10 ft
30 ft
10 ft
10 ft
10 ton
HW1 – Design
HW3 – Modeling
Cooling Tower Performance Curve
R
TCTR
Outdoor
WBT
TCTS
from chiller
to chiller
Temperature difference:
TCTS
R= TCTR -TCTS
Most important variable is
wet bulb temperature
TCTS = f( WBToutdoor air , TCTR , cooling tower properties)
or for a specific cooling tower type
T
= f( WBT
, R)
WBT
Cooling Tower Model
Model which predict tower-leaving water temperature (TCTS) for arbitrary
entering water temperature (TCTR) and outdoor air wet bulb temperature (WBT)
Temperature difference:
R= TCTR -TCTS
Model:
TCTS  a4  b4 WBT  c4 WBT 2  [d4  e4 WBT  f 4 WBT 2 ]  R  [ g 4  h4 WBT  i4 WBT 2 ]  R 2
For HW 3b:
You will need to find coefficient a4, b4, c4, d4, e4, f4, g4, h4, and i4 based on the
graph from the previous slide and two variable function fitting procedure
Two variable function fitting
(example for a variable sped pump)
Function fitting for a chiller
q = f (condensing and evaporating T)
200
q[kW]
25 C
35 C
45 C
150
100
50
0
0
6
2
4
6
Tevaporator [C]
8
10
Modeling of Water Cooled Chiller
(COP=Qcooling/Pelectric)
Chiller model:
COP= f(TCWS , TCTS , Qcooling , chiller properties)
Modeling of Water Cooled Chiller
Chiller model:
Chiller data:
QNOMINAL nominal cooling power,
PNOMINAL electric consumption for QNOMINAL
Available capacity as function of evaporator and condenser temperature
Cooling water supply
Cooling tower supply
2
2
CPATF  a1  b1  TCW S  c1  TCW
S  d1  TCTS  e1  TCTS  f1  TCW S  TCTS
Full load efficiency as function of condenser and evaporator temperature
2
2
EIRFT  a2  b2  TCW S  c2  TCW

d

T

e

T
S
2
CTS
2
CTS  f 2  TCW S  TCTS
Efficiency as function of percentage of load
EIRFPLR  a3  b3  PLR  c3  PLR
Part load: PLR 
Q( )
QNOMINAL  CAPFT
The consumed electric power [KW] under any condition of load
P  PNOMINAL  CPFT  EIRFT  EIRFPL
The coefiecnt of performance under any condition
COP( ) 
Q( )
P( )
Reading: http://apps1.eere.energy.gov/buildings/energyplus/pdfs/engineeringreference.pdf page 597.
Combining Chiller and Cooling
Tower Models
P  PNOMINAL  CPFT  EIRFT  EIRFPL
Function of TCTS
3 equations from previous slide
Add your equation for TCTS
TCTS  a4  b4 WBT  c4 WBT 2  [d4  e4 WBT  f 4 WBT 2 ]  R  [ g 4  h4 WBT  i4 WBT 2 ]  R 2
→ 4 equation with 4 unknowns
(you will need to calculate R based on water flow in the cooling tower loop)
Merging Two Models
Temperature difference:
R= TCTR -TCTS
Model:
TCTS  a4  b4 WBT  c4 WBT 2  [d4  e4 WBT  f 4 WBT 2 ]  R  [ g 4  h4 WBT  i4 WBT 2 ]  R 2
Link between the chiller and tower models is the Q released on the condenser:
Q condenser = Qcooling + Pcompressor ) - First law of Thermodynamics
Q condenser = (mcp)water form tower (TCTR-TCTS)
m cooling tower is given - property of a tower
TCTR= TCTS - Q condenser / (mcp)water
Finally: Find P() or COP( ) 
Q( )
P( )
The only fixed variable is TCWS = 5C (38F) and Pnominal and Qnominal for a chiller (defined
in nominal operation condition: TCST and TCSW);
Based on Q() and WBT you can find P() and COP().
Low Order Building Modeling
Measured data
or
Detailed modeling
Find Q() = f (DBT)
For HW3a (variable sped pump
efficiency) you will need Q()
Yearly based analysis:
You will need Q() for 365 days x 24 hours
Use simple molded below and the Syracuse TMY weather file posted in the
course handout section
20
Q [ton]
16
12
8
Q=--27.48+0.5152*t
4
Q=-0.45 +0.0448*t
0
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90
t [F]