The schematic diagram of the power plant is presented in
Figure 1. As can be observed, the power plant consisted of four basic components, including the heater, the turbine, the cooling tower, and the pump. Moreover, there were four processes regarding the thermodynamic cycle of the working fluid in the system, among which, in process 1–2, the condensed fluid was pumped into the high pressure state; in process 2–3, the working fluid experienced phase transition and changed into the high temperature and high pressure supercritical state in the heater; in process 3–4, the supercritical fluid was expanded to produce power in the turbine; and in process 4–1, the working fluid was cooled in the cooling tower. Here, the NDDCT was selected as the condenser, which could cool the working fluid with no water loss and almost no parasitic power consumption [
27].
Figure 3 presents the critical pressure and critical temperature for the CO
2/R161 mixtures with various mass fractions [
28]. Clearly, the critical temperature of the mixtures was increased with the increase in the mass fraction of R161. Meanwhile, the critical pressure of the mixtures was decreased, which rendered a lower TRC operation pressure than that of tCO
2, and laid the foundation for the practical application of TRC using CO
2 mixtures.
2.2. Mathematical Model
The equations for the system components were based on the first law of thermodynamics. The National Institute of Standards and Technology (NIST) REFPROP program [
29] was used for physical properties of CO
2/R161 mixture.
The heat exchanger in the cooling tower was made up of bundles with the same structural and functional characteristics. It can be seen in
Figure 4 that each bundle was composed of 10 finned tubes arranged in five rows. Meanwhile, the working fluid would enter the bundle through the left side of the fifth row in the finned tubes and leave the bundle at the right side of the first row in the finned tubes. Then, the air would cool the working fluid by flowing from the bottom to the top of the bundle. The calculation for the heat exchanger model is also presented in
Figure 4. Generally, the traditional method of heat exchanger modeling is only valid for a working fluid with constant properties. In this study, the nodal approach was adopted in designing the heat exchanger, in which each row of the heat exchanger bundles was divided into 24 sections, as if a number of small heat exchangers were connected in series.
The heat balance equation between CO
2 mixture and air was as follows,
where
QCt is the heat emission of the cooling tower (W),
hCO2 represents the enthalpy of CO
2 (J·kg
−1), while
i and
o stand for the inlet and outlet of the working fluid, respectively, and
Cp,air indicates the average heat capacity of air (J·kg
−1·K
−1).
Additionally, the product of the heat transfer area and the overall heat transfer coefficient (UA) of the heat exchanger could be obtained through the logarithmic mean temperature difference (LMTD), as displayed below.
where
U is the thermal conductivity of the system (W·m
−2·K
−1),
A stands for the area of heat transfer (m
2),
FT indicates the correction factor of LMTD (which amends the counter current flow as the cross-flow), and
represents the logarithmic mean temperature (K), which can be calculated as follows,
when the working fluid experienced counter current flow in the heat exchanger,
,
.
On the other hand, the condenser could be divided into the superheated single-phase region and the two-phase region based on the working fluid state at the turbine outlet. For the single-phase region of the CO
2 mixture, the Krasnoshchekov–Petukhov correlation [
30,
31] was employed,
where
U represents the heat transfer coefficient and
D suggests the inner diameter of the tube.
The following correlation [
32] was used for the two-phase region of the CO
2 mixture.
where
g represents acceleration due to gravity,
and
are the densities of liquid and vapor working fluid, and
is the modified latent heat of vaporization.
The heat transfer coefficient at the air side [
22] was calculated as follows,
where
ha is the air side heat transfer coefficient,
Aa stands for the air side heat transfer area, and Re
a indicates the Reynolds number of air. Moreover, the characteristic length of Re
a was deemed as the equivalent circular diameter of the air flow passage, which was 1.7 × 10
−2 m for this particular heat exchanger.
The structure chart of the NDDCT and the distribution diagram of air side resistance are displayed in
Figure 5 and
Figure 6, respectively. Clearly, the NDDCT consisted of the tower support columns, the heat exchanger bundles, the hyperbolic-type tower shell, and the sensors.
The ventilation equation represents the balance equation between the buoyancy with the result of air heating and the air pressure loss in the NDDCT, as shown below:
where
is the air pressure at state 1 in
Figure 1 (Pa),
suggests the air temperature at state 1 (K),
H3 represents the distance between the heat exchanger bundles bottom and the ground (m),
H4 indicates the distance between the top of the heat exchanger bundles and the ground (m),
H5 is the distance between the tower outlet and the ground (m),
stands for the air temperature at state 4 (K),
ma is indicative of the air flow (kg·s
−1),
is the face area of the heat exchanger bundle bottom (m
2),
signifies the average air density of the heat exchanger bundles (kg·m
−3),
A5 denotes the outlet area of the cooling tower (m
2),
represents the outlet air density of cooling tower (kg·m
−3), and
K indicates the coefficients of air loss in the NDDCT. More details are presented in
Table 2.
The specified parameters for the design of the NDDCT are listed in
Table 3. The design flow of the NDDCT was built on the parameter iteration according to the energy conservation equation and the ventilation equation. Typically, the minimum
was 5.00 K. The detailed data for the heat exchanger are listed in
Table 4.