Insight Into Recompression Brayton Cycle

Nowadays, the demand for energy has increased significantly, which raises the attention of fossil energy reserves and environmental problems [1]. Carbon dioxide (CO₂) has been studied as a working fluid in power plants for years because of its favorable high efficiency [2] and environmental safety [3]. There are types of supercritical CO₂ power cycles [4], such as reheating cycle [5], intercooling cycle [5], recompression cycle [6], turbine split flow cycle [7], and few others are described in Refs. [4,8,9]. Mostly, recompression cycle, which was suggested by Feher [10] and Angelino [11], is considered as the most efficient layout of sCO₂. Since compression work around critical point is significantly lower in the sCO₂ cycle and only part of the flow goes through precooler, cycle efficiency increases [12]. Recompression Brayton cycle has been studied both in terrestrial and space applications [13] and proved to have better performances in industries such as bottoming cycles in multipurpose energy production [14], solar energy [15], and nuclear energy [16,17]. The performance of the recompression cycle has been analyzed previously, and its application in different areas has also been discussed recently. You et al. [18] studied the effects of recuperator effectiveness, pressure ratio, and split ratio on cycle performance such as efficiency, exergy efficiency, and energy effectiveness as a bottoming cycle coupled with lithium bromide (aq.) absorption cycle. They stated that combined pressure ratio of top and bottom cycles needs to be determined as well as optimum operating pressures of each layout. Sathish et al. [19] presented results for a 10 MWe with a compressor inlet temperature of 45 °C and discussed its optimal operation strategy. Singh and Mishra [20] presented energy- and exergy-based performance evaluation of a combined cycle of sCO₂ recompression cycle and organic Rankine cycle. Oh et al. [21] discussed an application of sCO₂ recompression cycle in electric thermal energy storage. The calculation for most articles is based on the iteration method in matlab, or using other commercial software like aspen plus, engineering equation solver (ees), which could only provide numerical solutions but not analytic results. Argon with constant specific heat has been used to understand the behavior of recompression cycles. This model provides the analytical solution of all temperatures in the cycle. Parameters such as minimum and maximum temperatures, compressor efficiency, turbine efficiency, and recuperator effectiveness have been chosen the same as those of sCO₂ recompression cycles. For these reasons, the focus has been on evaluating the effects of pressure ratio and split ratio on the performance of the cycle such as thermal efficiency and exergy efficiency.

In Sec. 2, power cycle model configuration is explained, and in Sec. 3, thermodynamics model has been introduced. In Sec. 4, mathematical model has been developed and equations for temperatures at each state have been derived. In Sec. 5, results have been presented as a function of pressure ratio at each split ratio. Conclusions have been stated in Sec. 6.

Recompression layout has nine energy conversion devices, including high temperature energy exchanger for energy input, low temperature recuperator (LTR), high temperature recuperators (HTR), a mixing chamber, main compressor, recompression compressor, a turbine, low temperature energy exchanger for transferring energy out of the system (precooler), and a single T-section to split mass flowrates between precooler and recompression. Low-pressure flow is split upon energy rejection at precooler and compressed to a low temperature recuperator at the main compressor. Split flow then mixes with recompressed fraction that is compressed from a parallel compressor into a high temperature side. These two flows then mix in a mixing chamber and enter a high temperature recuperator to recover energy from turbine output (Fig. 1).

Fundamentals of thermodynamics using balance equations have been used to determine the performance of the recompression cycle.

Energy balance has been simplified for different subsystems in the cycle.

Above equations along with Eqs. (15) and (16) have been used to determine thermal efficiency and exergy efficiency. Since the performance of the cycle depends mainly on pressure ratio across the compressors, an equation for optimum pressure ratio was developed. This was achieved by differentiating the equation for efficiency of the cycle with respect to pressure ratio and was set equal to zero.

Figure 2 shows total entropy generation in two recuperators at different split ratios as a function of recuperator effectiveness at a pressure ratio of 1.5. For higher split ratio overall irreversibility is greater in the recuperators. Lower split ratio is bounded with effectiveness of recuperator due to minimum temperature difference at LTR, T₅ ≤ T₁₀. As it can be seen at a constant effectiveness of recuperators, the lower split ratio results in less entropy production improving performance of the cycle.

The independent input variables in the system are minimum and maximum temperatures, effectiveness of low and high temperature recuperators, isentropic efficiencies of compressors and turbine, split and pressure ratios across the compressors and turbine. Dependent variables are temperatures at all states and performance of the power cycle such as thermal and exergy efficiencies. Parameters are $Tsource=800∘C$⁠, $Tenv=20∘C$⁠, $Tmin=25∘C$⁠, $Tmax=750∘C$⁠, effectiveness of low and high temperature recuperators, $εLTR=0.88$⁠, $εLTR=0.88$⁠, η_c = 0.89, η_t = 0.9, and c_p = 0.57 kJ/kg · K.

Figure 3 shows net work as a function of pressure ratio for three different splits. Cycle generates highest net work at a higher split ratio at which both energy input and energy rejection increase but increase of energy input is higher than energy rejection. Work required for compression is also lower due to lower fraction of split in recompressor. Moreover, net work increases with increasing pressure ratio up to a limit at which the maximum limit has been determined from entropy balance in HTR. This limit has been found for minimum split which yields the highest thermal-to-electric efficiency in the cycle.

Figure 4 shows cycle efficiency as a function of pressure ratio at three different split ratios. The highest efficiency has shown at a minimum split. Even a slight difference from the optimum drops the efficiency and at some pressure ratio split curves crosses and decreases in minimum split becomes greater. It can also be seen that optimum pressure ratio at minimum split ratio is smaller.

Figure 5 shows cycle exergy efficiency as a function of pressure ratio at three different split ratios. It has been observed that exergy efficiency decreases with increasing pressure ratio beyond the optimum pressure ratio.

Figure 6 indicates that increasing pressure ratio leads to a higher increment in energy input than that of net work. This explains the downward trend in cycle performance beyond the optimum pressure.

Figure 7 shows that ratio of total load, defined as amount of energy transferred from high temperature argon to low temperature argon, in recuperators to energy input to the cycle decreases with increasing pressure ratio and is almost independent of split ratio. The ratio of energy load in LTR is higher than HTR at all pressure ratios. At a constant pressure ratio, the load ratio is greater in LTR and smaller in HTR at a minimum split ratio. This implies that temperature difference around LTR is significantly higher than HTR so is irreversibility.

Figure 8 shows energy efficiency of the cycle as a function of pressure ratio at different turbine inlet temperatures. It can be seen when turbine inlet temperature increases, the efficiency increases significantly, which is consistent with other Brayton cycles. It also shows that there is an optimum pressure ratio which increases as turbine inlet temperature increases. This is consistent with the work of Hiller [22].

Figure 9 shows the relation between cycle optimum pressure ratio for maximum efficiency as a function of split ratio. For an ideal cycle, the relation is almost linear. As it can be seen, by increasing the split ratio the optimum pressure ratio (the pressure ratio for maximum cycle efficiency) also increases. This implies the cycle requires higher operating pressures by increasing the amount of flow sent to low temperature recuperator.

Recompression cycle depends mainly on factors such as effectiveness of recuperators, split ratio, turbine inlet temperature, and pressure ratio. In this work, we studied the effect of pressure ratio and split ratio on an ideal recompression Brayton cycle. Thermodynamics model was developed from energy and entropy balance equations resulting in a linear set of equations for temperatures at different states of the cycle. Temperatures at different states within the cycle have been calculated.

The following conclusions can be made:

1. Increasing effectiveness of recuperators decreases total entropy generation in the cycle.

2. Cycle net work increases as a function of pressure ratio.

3. Energy efficiency as well as exergy efficiency becomes maximum at optimum pressure ratio.

4. At the optimum pressure ratio, however, net work is not maximum.

5. Lower split ratio increases cycle energy efficiency at optimum pressure ratio.

6. Total energy recovery for all splits is almost equal but energy recovery at HTR is smaller at a minimum split and greater in LTR.

7. Cycle efficiency increases as turbine inlet temperature increases.

8. Optimum pressure ratio increases with increasing turbine inlet temperature.

There are no conflicts of interest. This article does not include research in which human participants were involved. Informed consent not applicable. This article does not include any research in which animal participants were involved.

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

e =

exergy

k =

specific heat ratio

q =

heat

s =

entropy

T =

temperature

$m˙$ =

mass flowrate

r_p =

pressure ratio

η =

efficiency of the cycle

e =

outlet

h =

enthalpy

i =

inlet

p =

pressure

t =

turbine

w =

work

x =

split ratio

c_p =

ideal gas constant specific heat

c1 =

main compressor

c2 =

recompression compressor

$ε$ =

recuperator effectiveness

$σ˙$ =

entropy production rate

HTR =

high temperature recuperator

LTR =

low temperature recuperator