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Chiller-Design1111111111111111.docxExecutive summary:
Table 1 below displays the sizing and dimensions for both the evaporator and condenser components of 1000 ton Direct Expansion chiller, along with the comparison with a commercially available water cooled chiller, designed in this report. The dimensions of these components fall in line with all specifications and parameters that were required in this problem statement. This report contains all necessary methodology, procedures, properties and calculations used in order to produce table 1 below:
Table 1: Direct Expansion Chiller dimensions
|
DX Chiller Dimension |
|||
|
|
Evaporator |
Condenser |
Commercial Water cooled chiller |
|
OD Tubes (mm) |
20 |
20 |
20 |
|
ID Tubes (mm) |
16 |
16 |
16 |
|
Tube ID Area (m2) |
0.3035 |
0.3035 |
0.3041 |
|
ID Shell (mm) |
1312.21 |
1315.73 |
1318.42 |
|
Pitch (mm) |
25 |
25 |
25 |
|
Clearance (mm) |
78 |
76 |
75 |
|
Tube Length (m) |
4.83 |
4.83 |
4.85 |
|
Tube Passes |
4 |
4 |
4 |
|
Number of tubes |
2226 |
2248 |
2235 |
|
Baffle Spacing (mm) |
262.44 |
263.15 |
263.04 |
Problem Statement:
Design a DX (direct expansion) chiller (evaporator and condenser) that provides 1000 tons of refrigeration to a chilled water system at 10oF delta T (CWR temperature = 55oF, CWS temperature = 45oF). The condenser rejects heat to a condenser water line connected to a cooling tower. Sizing the cooling tower is not a part of the design, but the condenser water leaves the condenser at 95oF and returns at 85oF.
Compare the dimensions you compute with dimensions of a commercially available water cooled chiller (include the comparisons in your report).
Select an appropriate refrigerant for the chiller (and justify your choice in your report). Assume the refrigerant leaves the evaporator as a saturated vapor and that it leaves the condenser as a saturated liquid. Route the refrigerant is routed through the tubes of the shell and tube heat exchanger.
Design Approach:
The DX Chiller condenser and evaporator are designed as shell and tube heat exchanger. The chiller is assumed to operate under an ideal refrigeration cycle; reversibilities within the components, frictional pressure drops, and heat loss to the surroundings are ignored. The condenser and evaporator are assumed to run at constant pressure, and the compression process is assumed to be isentropic. The overall heat transfer and the corresponding area were determined by using the log mean temperature difference method. The refrigerant used in this design is R134a as this is the best suitable refrigerant for water system.
The following formulas are used to determine the design of the given DX chiller.
The effectiveness of heat exchanger is given by the equations below:
E = (if mcCpc < mwCpw) (Eqn. 1)
E = (if mcCpc > mwCpw) (Eqn. 2)
qactual = E(mCp)min(T1 – t1) (Eqn. 3)
qmax = (mCp)min(T1 – t1) (Eqn. 4)
Q = mCpdT (Eqn. 5)
Tlm = (Eqn. 6)
R = (Eqn. 7)
S = (Eqn. 8)
Tm = FtTlm (Eqn. 9)
Q = UATm (Eqn. 10)
Db = do (Eqn. 11)
IB = (Eqn. 12)
Pt = 1.25*do (Eqn. 13)
As = (Eqn. 14)
de = (Pt2 – 0.917do2) (Eqn. 15)
For the condenser,
When
And when
For the evaporator,
(Eqn. 16)
Where,
E = Effectiveness
Q = Heat Transfer
m = mass flow rate
Cp = Specific heat
T = Warm fluid temperature
t = Cold fluid temperature
1 and 2 represents the inlet and outlet temperature
Tlm = Log mean temperature difference
Tm = True temperature difference
Ft = Temperature correction factor
A = Area of the unit (Heat exchanger)
U = overall heat transfer coefficient
Db = Bundle diameter
Nt = Number of tubes
do = Tube outside diameter
IB = Baffle spacing
Ds = Shell diameter (Db + Clearance)
Pt = Tube pitch
As = Cross flow area at shell equator
de = Shell side equivalent diameter
Gv = mass velocity of refrigerant (lbm/hr-ft2)
l = dynamic viscosity of the refrigerant as a fluid (lbm/hr-ft)
l = density of refrigerant as a fluid (lbm/ft3)
v = density of refrigerant as vapor (lbm/ft3)
Prl = Prandtl number of refrigerant
ifg = refrigerant enthalpy of vaporization (Btu/lbm)
Cp,l = Specific heat of refrigerant as a fluid (Btu/lbm-oF)
t = difference between refrigerant temperature and average water temperature (oF)
Kl = refrigerant thermal conductivity (Btu/hr-ft-oF)
C1 = 9 x 10-4 when Xe < 0.9, 8.2 x 10-3 when Xe > 1 (Xe = quality of refrigerant leaving the tube)
J = 778 (ft-lbf/Btu)
gc = 32.2 (lbm-ft/lbf-s2)
g = acceleration due to gravity (ft/s2)
L = Length of tube (ft)
n = 0.5 when xe < 0.9, 0.4 when xe > 1
By using the above equations, the value of Uo and Ao were calculated by making iterations so that the calculated Uo can be greater than the initially assumed Uo and thus the corresponding Ao is the actual area of the exchanger.
Results:
Prior to starting the design process of the Direct Expansion chiller, parameters were set in order to base our calculations around. By achieving the parameters in Table 2 below, our chiller met all design specifications that were stated in the problem statement.
Table 2: Thermodynamics Analysis of Chiller
|
Quantity |
Magnitude |
Units |
|
Evaporator Heat Transfer |
6506481.223 |
W |
|
Evaporator Water Flow Rate |
251.99 |
Kg/s |
|
Compressor Work |
5884606.7 |
W |
|
Refrigerant R134a Flow Rate |
1276.697829 |
Kg/s |
|
Condenser Heat Transfer |
6479097.42 |
W |
|
Temperature of R134 in Evaporator |
40 |
F |
|
Temperature of R134 in Condenser |
100 |
F |
|
Condenser Water Flow Rate |
251.99 |
Kg/s |
|
Enthalpy of R134 @Evaporator Exit |
257.699 |
KJ/Kg |
|
Enthalpy of R134 @Compressor Exit |
192.9701 |
KJ/Kg |
|
Enthalpy of R134 @Condenser Exit |
100.865 |
KJ/Kg |
|
Enthalpy of R134 @Evaporator Entrance |
100.865 |
KJ/Kg |
|
Liquid Saturation Enthalpy of R134a @ Low P |
17.27 |
KJ/kg |
|
Vapor Saturation Enthalpy of R134a @ Low P |
234.44 |
KJ/kg |
|
Liquid Saturation Enthalpy of R134a @ High P |
38.4234 |
KJ/kg |
|
Vapor Saturation Enthalpy of R134a @ High P |
244.452 |
KJ/kg |
Once the parameter were set, an EXCEL spreadsheet, consisting of the theoretical equations found in the design approach section, was created in order to calculate necessary values for designing both the evaporator and chiller components of the chiller. Through much trial and error, table 3 and 4 below were completed.
Table 3: Evaporator Design
|
Quantity |
Magnitude |
Units |
|
Refrigerant Properties |
|
|
|
Liquid Specific Heat |
0.198003 |
Btu/lb-F |
|
Liquid Thermal Conductivity |
0.007256 |
Btu/lb-hr-F |
|
Liquid Dynamic Viscosity |
0.03508 |
lb/hr-ft |
|
Vapor Dynamic Viscosity |
0.000326 |
lb/hr-ft |
|
Liquid Density |
0.683 |
lb/ft3 |
|
Vapor Density |
0.2774 |
lb/ft3 |
|
Water Properties |
|
|
|
Specific Heat |
0.0010032 |
Btu/lb-F |
|
Density |
62.1158 |
lb/ft3 |
|
Dynamic Viscosity |
1935.36 |
lb/hr-ft |
|
Kinematic Viscosity |
31.16 |
ft2/hr |
|
Thermal Diffusivity |
8.3464 |
ft3/lb-hr |
|
Prandtl Number |
3.733 |
|
|
Heat Transfer Coefficients |
|
|
|
Tube Side Nusselt Number |
1059479 |
|
|
Tube Side Prandtl Number |
0.9573 |
|
|
Tube Side Convection Coefficient |
145594.0832 |
Btu/hr-ft2-F |
|
Shell Side Nusselt Number |
1133.803 |
|
|
Shell Side Prandtl Number |
3.733 |
|
|
Shell Side Convection Coefficient |
136.178 |
Btu/hr-ft2-F |
|
Overall Heat Transfer Coefficient |
107.17 |
Btu/hr-ft2-F |
|
Evaporator Dimensions |
|
|
|
Shell Diameter |
1312.214 |
mm |
|
Inner Tube Diameter |
16 |
mm |
|
Outer Tube Diameter |
20 |
mm |
|
Tube Pitch (Indicate triangular or square by putting T or S next to the number) |
25 T |
mm |
|
Clearance |
78 |
mm |
|
Number of Baffles |
5 |
|
|
Baffle Spacing |
262.443 |
mm |
|
Number of Tube Passes |
4 |
|
|
Total Number of Tubes |
2226 |
|
|
Length of Tubes |
4.83 |
m |
|
Tube Velocity |
8388.931 |
ft/s |
|
Tube Reynolds Number (Based on Vapor) |
12609844 |
|
|
Shell Characteristic Velocity |
12.024 |
ft/s |
|
Shell Characteristic Area |
0.0688763 |
m2 |
|
Shell Reynolds Number |
73.35141 |
|
|
Equivalent Diameter |
14.201 |
mm |
|
Heat Transfer Surface Area |
675.46 |
m2 |
Table 4: Condenser Design
|
Quantity |
Magnitude |
Units |
|
Refrigerant Properties |
|
|
|
Liquid Specific Heat |
0.198003 |
Btu/lb-F |
|
Liquid Thermal Conductivity |
0.007256 |
Btu/lb-hr-F |
|
Liquid Dynamic Viscosity |
0.03508 |
lb/hr-ft |
|
Vapor Dynamic Viscosity |
0.000326 |
lb/hr-ft |
|
Liquid Density |
0.683 |
lb/ft3 |
|
Vapor Density |
0.2774 |
lb/ft3 |
|
Water Properties |
|
|
|
Specific Heat |
0.0010032 |
Btu/lb-F |
|
Density |
62.1158 |
lb/ft3 |
|
Dynamic Viscosity |
1935.36 |
lb/hr-ft |
|
Kinematic Viscosity |
31.16 |
ft2/hr |
|
Thermal Diffusivity |
8.3464 |
ft3/lb-hr |
|
Prandtl Number |
3.733 |
|
|
Heat Transfer Coefficients |
|
|
|
Tube Side Nusselt Number |
1050053 |
|
|
Tube Side Prandtl Number |
0.9573 |
|
|
Tube Side Convection Coefficient |
144298.7622 |
Btu/hr-ft2-F |
|
Shell Side Nusselt Number |
13.751 |
|
|
Shell Side Prandtl Number |
3.733 |
|
|
Shell Side Convection Coefficient |
135.452 |
Btu/hr-ft2-F |
|
Overall Heat Transfer Coefficient |
106.72 |
Btu/hr-ft2-F |
|
Condenser Dimensions |
|
|
|
Shell Diameter |
1315.73 |
mm |
|
Inner Tube Diameter |
16 |
mm |
|
Outer Tube Diameter |
20 |
mm |
|
Tube Pitch (Indicate triangular or square by putting T or S next to the number) |
25 T |
mm |
|
Clearance |
76 |
mm |
|
Number of Baffles |
5 |
|
|
Baffle Spacing |
263.15 |
mm |
|
Number of Tube Passes |
4 |
|
|
Total Number of Tubes |
2248 |
|
|
Length of Tubes |
4.83 |
m |
|
Tube Velocity |
8314.296 |
ft/s |
|
Tube Reynolds Number |
12497657 |
|
|
Shell Characteristic Velocity |
11.9594 |
ft/s |
|
Shell Characteristic Area |
0.06925 |
m2 |
|
Equivalent Diameter |
14.201 |
mm |
|
Shell Reynolds Number |
72.96 |
|
|
Heat Transfer Surface Area |
682.35 |
m2 |
Table 5 below displays some of the performance specifications for both the evaporator and condenser components of the designed DX chiller.
Table 5: Chiller Performance
|
|
Evaporator |
Condenser |
||
|
Effectiveness |
0.74977 |
|
0.79985 |
|
|
qmax |
29401.86 |
KW |
17632.65245 |
KW |
|
qactual |
22044.783 |
KW |
14103.58306 |
KW |
|
Inlet Temperature |
55 |
F |
95 |
F |
|
Outlet Temperature |
45 |
F |
85 |
F |
Conclusion:
The project was done in order to design a DX chiller having a capability of refrigerating 1000 ton of chilled water. For this purpose, both the evaporator and also the condenser have been designed. The results obtained from the calculations are in accordance with the practically working models. The table 3 given below includes the comparison between the calculated design and the practically used DX chiller. Thus at the end the designing of the chiller is completely in accordance with the practical values and the results thus obtained give a high degree of succession.
|
DX Chiller Dimension |
|||
|
|
Evaporator |
Condenser |
Commercial Water cooled chiller |
|
OD Tubes (mm) |
20 |
20 |
20 |
|
ID Tubes (mm) |
16 |
16 |
16 |
|
Tube ID Area (m2) |
0.3035 |
0.3035 |
0.3041 |
|
ID Shell (mm) |
1312.21 |
1315.73 |
1318.42 |
|
Pitch (mm) |
25 |
25 |
25 |
|
Clearance (mm) |
78 |
76 |
75 |
|
Tube Length (m) |
4.83 |
4.83 |
4.85 |
|
Tube Passes |
4 |
4 |
4 |
|
Number of tubes |
2226 |
2248 |
2235 |
|
Baffle Spacing (mm) |
262.44 |
263.15 |
263.04 |
Table 3: Chiller Dimensions
References:
1. Coulson and Richardson, “Chemical Engineering Design”, Vol. 6, Edition 4th.
2. Kern, “Process heat transfer”, vol. 4, Edition 4th.
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