12 Appendi x C: Heat exchanger performance characteristics
12.1 INTER-COOLER CHARACTER ISTICS
As stated in Chapter 5, the inter-cooler's performance is regulated by geometrical dimensions and the inter-relationship between these dimensions. Inter-cooler characteristic parameters will be evaluated over a range of the geometric dimensions: shell
diameter[^^,,,,],
tube insidediameter[^^[,,^]
tube outsidediameter[^^,,^^,],
the number of tubes[n] and the length [L] of the inter-cooler.12.1.1 Inter-cooler efficiency
The effect of the geometric parameters on the inter-cooler efficiency can now be investigated.
Shell length [m]
Figure 12.1: Inter-cooler efficiency as a function of shell length.
Figure 12.1 shows that the inter-cooler efficiency increases with an increase in shell length, but the curve flattens at high length values. This indicates that there is an optimal shell length;
thereafter increasing the shell length no longer improves the inter-cooler efficiency. Enhancing the efficiency more than 90% by lengthening the heat exchanger is not feasible as a huge extension in length will only result in a small rise in efficiency. For this reason, a lower limit for the length of the inter-cooler is set to the minimum limit of 0.9444 m.
The conceptual design for development 121
of a micro gas turbine generator.
Appendix C: Heat exchanger performance characteristics
-7I - 7
0.2 0.3 0.4 0.5 0.6 0.7
Shell diameter [m]
Figure 12.2: Inter-cooler efficiency as a function of shell diameter.
The inter-cooler's efficiency is also influenced by the shell diameter as seen in Figure 12.2, showing that an increase in shell diameter will result in a small increase in efficiency, as the cross- sectional heat transfer and the number of tubes increase. This implies that an increase in the shell diameter greater than 0.5389 m will not result in an increase of inter-cooler efficiency.
Figure 12.3 illustrates that an increase in the tube outer diameter leads to a decrease in efficiency.
By increasing the tube outer diameter, the number of tubes decreases and the total heat transfer area decreases. The maximum tube diameter is limited to 0.015 m, as the efficiency tends to drop below the accepted level of 90% for larger diameters.
12.1.2 Inter-cooler pressure losses
The work needed to overcome fluid friction in the heat exchanger can be represented by the pressure loss over the heat exchanger. In the TCIR cycle only the gas side's pressure losses are calculated, but the coolant side is important for the auxiliary design.
Pressure drop of the fluid through the inter-cooler is limited to 1% of the inlet pressure.
Figure 12.4: Inter-cooler pressure-loss as a function of shell length.
In this configuration the length of the shell has little effect on the pressure loss of the gas side, but has a significant influence on the coolant side of heat exchanger. In order to minimize the pressure loss in the coolant side it is essential that the minimum length of the inter-cooler is limited to 1.389 m. By inspection of Figure 12.5 it is possible to limit the minimum shell diameter to 0.344m, due to the pressure loss considerations of both the hot and the cold stream.
7 , 6 -
- 5 -
-
82
4 -- E!
:
V) 3 -2 2 -
1 -
0 T
0 0.1 0.2 0.3 0.4 0.5
Shell diameter [m]
---
Figure 12.5: Inter-cooler pressure-loss as a function of shell diameter.
DeltaP-coolant
\ D-o[tube] = 0.01 27 m
\
\
\
\
\
\
\
\
'\ '. -- - -
DeRaP-gas
---_
--I
The conceptual design for development of a micro gas turbine generator.
0 0.5 1 1.5 2 2.5 3
Shell length [m]
Appendix C: Heat exchanger performance characteristics
Tube outside diameter [m]
Figure 12.6: Inter-cooler pressure-loss as a function of tube outside diameter.
The maximum allowable pressure loss across the cooler is limited to 1% of the inlet pressure of the fluid. Figure 12.6 shows that a lower limit is needed when considering the dimensions of the tubes in order to limit the pressure loss experienced by the coolant. The minimum tube diameter that will result in a maximum pressure loss of 1 % is equal to 0.01 1 m.
A limitation set previously, [ D,,[,e,l 10.03m ] (the effect the tube diameter has on the cooler's efficiency) still holds true for pressure losses and is the upper limit and is not affected by the pressure loss limitation of 1 %.
12.1.3 Inter-cooler limits an results
The geometrical parameters were evaluated against the effects on efficiency and pressure loss and resulted in the following limitations:
1 . 5 1 L S l . 9 Dshell 2 0.3444 0.01 1 I D
,,,,,,,
S 0.03A relationship between D<,[,?]and D,,, exists. The relationship between these two parameters is calculated from the cross sectional area of the inter-cooler.
Ashe//
' .
Ao[f&e.r 1 Eq 5.12 thus:%
( ~ ; h e / I) '
' ( ~ ~ [ I u b ~ ~ 1)%
By introducing a constant k 5 1 :
An illustration of this relation can be seen in Figure 12.8.
Shell diameter [m]
Figure 12.8: Illustration of the relation between D,che,l
,
D,,[Iubel.
All of these limitations have been considered and calculated in a simulation written to simulate and heat exchanger with this inter-cooler's characteristics. The results are as follows:
Geometric dimensions:
Inter-cooler length [L]: 1.5 m Inter-cooler shell diameter [Dshell] : 0.4 m Inter-cooler tube
diameter[^,,,,^]
: 12,7 mmNumber of tunes [n]: 508 Intercooler characteristics:
Efficiency [77i,
]
: 82 % Real heat transfer [Q]: 43 kW Maximum heat transfer [Q,,,]: 47 kW Inter-cooler boundary conditions for the gas side:Inlet pressure: 180 kPa
Inlet temperature: 97 "C
Exit pressure: 179.85 kPa
Exit pressure: 28 "C
Pressure loss: 0.15 %
Inter-cooler boundary conditions on the coolant side:
Inlet pressure: 300 kPa
Inlet temperature: 20 "C The conceptual design for development
of a micro gas turbine generator.
Appendix C: Heat exchanger performance characteristics
Exit pressure: 295.66 kPa
Exit temperature: 27 "C
Pressure loss: 1.44 %
Figure 12.9 shows the axial temperature distribution through the inter-cooler with the given geometric limitations. Note that the gas enters at increment 0, and exits at increment 10, while the coolant (water) enters at 10 and exits at increment 1, thus cross-flow heat exchanger.
0 2 4 6 8 10 12
Increments
Figure 12.9: The axial temperature distribution of the inter-cooler.