Tri-generation cascade of s-CO₂ Brayton-Rankine-absorption chiller cycles for WHRS in zero-emission marine systems

2.1 Integrated Hybrid Cycle Configuration Description

Figure 2 provides the structural illustration for the hierarchy energy-management strategy adopted in this study. The overall system integrates an s-CO₂ Brayton topping cycle, a steam Rankine bottoming cycle (SRC) and an absorption refrigeration system (ABS) arranged in a three-tier temperature cascade. The figure clarifies the energy flow direction and the hierarchical heat-grade matching from the high-temperature exhaust gas stream to the medium and low-temperature streams. To ensure transparent and reproducible thermodynamic molding, Figure 3 demonstrates the integrated cascade configuration, specifying the interconnections and thermodynamic interfaces for heat-transfer duties, pressure losses as well as energy balances.

Figure 2:

The s-CO2 Brayton-SRC-ABS energy hierarchy

Figure 3:

The integrated waste-heat cascade and ABS cooling system

The heat and mass balance principles serve as the foundation for the invention, which is logically energy hierarchy management:

• - Tier I: Working in the highest-grade heat (800-1000K), from the SOFC-GT or nuclear reactors exhaust drives the Brayton loop. The working fluid s-CO₂ streams continuously within a closed circle, maximizing energy and exergy efficiency as well as eliminating the thermal energy extraction to the surrounding environment.
• - Tier II: Operating in the medium-grade heat from 500K to 600K, the steam Rankine turbine converts the upper exhaust gas after Brayton turbine to govern the middle cycle.
• - Tier III: Working under the lowest-grade heat from 370K to 400K, in which the middle cycle exhaust gas has been transferred to the ABS, supplying cold energy for onboard demands and chilling storage purposes.

The heating and cooling integration commences a new era of thermodynamic principle applications in marine engineering due to a considerable improvement of overall energy and exergy efficiency.

2.2 Thermodynamic Modeling

The proposed design has been divided into three main tiers with the combination of Braton cycle recovering the waste heat from the 700^oC thermal waste source, while the second layer presenting the possibility to utilize the waste heat from 150-250^oC and the bottoming cycle recovering the low-grade heat from 80-100^oC. By integrating three different thermal cycles together, the waste heat source can be efficiently utilized. The integrated system was modelled as a unified thermodynamic framework combining a closed CO₂ Brayton cycle, dual recuperators, a HRSG-Rankine loop, and an absorption chiller. Each subsystem was defined using energy balance and NTU - ε correlations. Parametric tables allowed the adjustment of variables such as T₃, PR, NTU_HTR, and HRSG pinch. In this study, the system is formulated as an analytical thermodynamic model based on coupled mass/energy and exergy balances, together with UA-NTU heat-exchanger relations. The resulting state-point equations are solved in MATLAB using an iterative convergence routine, which also enables automated parametric sweeps of key design and operating variables. The modeling framework develops analytical energy and exergy balancing equations with real-fluid thermodynamics evaluation and process-level validation using Aspen HYSYS V12.1 software. The mathematical calculations support the consistent modeling of s-CO₂ Brayton, SRC, and LiBr-H₂O absorption cooling within thermodynamic simulation conditions.

Figure 4:

Three-tier sCO2-RC-ABS cascade T-s diagram

To build up the computational consistency, steady-state operational and one-dimensional flow conditions are assumed for the subsystems. First, the pressure drop ratio has been calculated at 3% within pipeline system and heat exchangers while the kinetic and potential energy differences are ignored. The unified analysis of power and cooling generation is governing and enabling by an energy and exergy balancing as well as the UA-NTU heat-transfer modeling. The working fluid CO₂ thermodynamic characteristics are calculated under Helmholtz energy equation close to the critical point at 304.13K and 7.38 MPa. Component efficiencies are based on typical marine-scale turbomachinery with turbine energy efficiency is 0.9, compressor efficiency is 0.85 and compact heat exchanger efficiency is 0.9. For any component i such as turbine, compressor, heat exchanger, or pump, the steady-state energy balance is written under the first law of thermodynamics:

Where $$ {\dot{W}}_i$$ is the shaft work (kW), $$ \dot{m}$$ is the mass flow rate (kg/h), h is the specific enthalpy (kJ.kg^-1). The compressor and turbine are investigated under the isentropic efficiencies:

In which, the subscript s denotes the isentropic state. The compressor and turbine work outputs are calculated by Equation (3):

Regarding the CO₂ stream, the amount of total heat transferred to the HRSG is measured:

While the steam-side balance is:

High-temperature exhaust gases from the SOFC-GT subsystem are supplied to the s-CO₂ Brayton cycle, which then sends recovered heat to the steam Rankine loop via the HRSG. The Rankine condenser rejects residual thermal energy to power the ABS chiller, creating a chilled stream at 260K suitable for storing LNG or ammonia.

To minimize energy losses, each subsystem is thermally coupled to provide a closed-loop tri-generation configuration. The dual recuperators and the HRSG have been governed by the Thermodynamics law and modeled through the UA-NTU calculation to investigate the fluctuations of supercritical CO₂ working fluid. This method couples the overall heat-transfer coefficient (UA) and effectiveness (ε) to the logarithmic mean and variable heat capacities:

Where UA is the overall heat-transfer conductance (W.K-1); C_min and C_max are the minimum and maximum heat capacity rates and $$ C_r=\frac{C_{min}}{C_{max}}$$. By comparing analytical UA-NTU predictions with ASPEN HYSYS calculated heat exchanger duties, the method offers a rigorous validation basis. The LiBr-H₂O absorption chiller uses Rankine condenser heat Q_gen to transfer the cold energy for LNG tank or ammonia storage with the fixed evaporator temperature at T_evap= 260K, the coefficient of performance is:

This stage enables sub-zero thermal management, serving cryogenic storage of low flashpoint fuels. Building upon the general steady-state formulation above, the present work isolates the Brayton-Rankine-ABS thermodynamic subsystem to evaluate its independent performance without the SOFC primary source. In this configuration, the external heat input to the Brayton heater represents the available high-temperature energy from any upstream prime mover (e.g., SOFC, nuclear reactor, or gas-turbine exhaust), whereas the subsequent Rankine and absorption stages recover the medium- and low-grade heat in cascade. The same first-law and UA-NTU relations introduced in Equation (1) – Equation (9) are retained, while the fuel-based chemical-exergy expressions are omitted. Accordingly, the following section develops explicit component-level relations (compressor, turbine, recuperators, HRSG, and ABS) and defines the system energy and exergy efficiencies within a self-contained Brayton-Rankine-ABS framework.

2.3 Integrated Modelling Assumptions

Based on the energy-balance formulation described in the previous section, the integrated configuration couples a closed supercritical CO₂ Brayton cycle (topping) with a single-pressure steam Rankine bottoming cycle and a LiBr-H₂O absorption refrigeration system(ABS). The methodology follows Mubashir et al. [19], in which energy and exergy balances are applied to each subsystem linked through cascading heat recovery. Main simulations are assumed as below:

• • Steady-state, potential and kinetic energies neglected.
• • Real-fluid thermodynamic properties of CO₂ are used in all cycle calculations, and no constant c_p ideal gas approximation is applied in the final performance evaluation
• • Pressure drop ratio is 3% [20][21]
• • Counter-flow heat exchangers solved via NTU - ε
• • Fluid equilibrium at each component boundary.

To ensure realistic and safe operation, several design limits were imposed prior to the thermodynamic evaluation. The minimum temperature difference in the recuperators prevents numerical divergence in the NTU - ε model and ensures feasible counter-flow heat transfer. The HRSG pinch point was fixed at 8K to limit excessive surface area and pressure drop, while the Brayton turbine inlet temperature was restricted to be smaller than 900K due to material constraints. These constraints were applied in all subsequent simulations and parametric analyses.

Compression: state 1- 2

Expansion: state 3- 4

Dual recuperators (LTR & HTR)

HRSG and Rankine Cycle

Gas-side heat balance

Steam-side enthalpy relations

Absorption chiller system (ABS)

Energy and exergy efficiencies

To determine the best design zones for maritime operation, sensitivity analysis on pressure ratio, turbine inlet temperature, and recuperator NTU are carried out. A paramount contribution is carrying out a hybrid multi-platform validation procedure that integrates analytical modeling and process-level simulation in a single thermodynamic environment. The remarkable contribution is governing by the energy and exergy conservation principles aligning with the process simulated in Aspen HYSYS simulator, thus supporting the validation of the multi-tiered design. Additionally, the introduced configuration examines the deployment of Brayton-Rankine-ABS integration, resulting in a modeling technique that is both thermodynamically conservation and operationally capable opportunity.

Off-design modeling assumptions

Exhaust gas mass flow scaling at full load with L is engine load (L ∈ {50, 75, 100} and $$ {\dot{m}}_{100}$$ is the exhaust gas mass flow at 100% load.

Exhaust gas temperature derating is defined as in Equation (30).

where k_r = 100K= 100K, yielding T_EXG,75= 948K, and T_EXG,50= 923K

To present hydraulic losses, pressure losses were simulated under a segment-level lumped allowance approach. The pressure drop is prescribed as a fixed fraction of the local inlet pressure:

The outlet pressure is defined

A parametric sweep was conducted over f_PD ∈ {0.01,0.03,0.05} to quantify the impact of plausible hydraulic-loss uncertainty on the key performance indicators.

3.1 Integrated System Thermodynamics Performance Analysis

The proposed Brayton-steam Rankine-ABS configuration indicates a considerable thermodynamic enhancement over the stand-alone Brayton or SOFC-GT system. This demonstrates a substantial improvement in thermodynamic performance compared to the conventional marine combined cycles as illustrated in Table 1.

Table 1:

Subsystem energy and exergy analysis

As the system-level energy efficiency reported, about 32.0% is evaluated according to Equation (27) and therefore includes both net electric power and the equivalent primary-energy saving associated with the 13.19 kW of cooling. The total system power output accounted for 34.93 kW, which is sufficiently supplied for onboard demanding energies and served as the extra electric as well as thermal supplying source for heating, accommodation hot water providing, and lubricant oil heating. Overall energy and exergy efficiencies reach 32.0% and 49.2%, representing a 13% improvement over the conventional Brayton baseline from 19% to 32%. The results have validated with the previous study [22].

The topping s-CO₂ Brayton subsystem generates a net power output of 28.58 kW from a total heat input of 150.4 kW, illustrating an energy efficiency of 18.99% and an exergy efficiency η_ex,B= 29.2%. The dual-recuperator Brayton cycle effectively leads to the turbine exhaust temperature growth for efficient heat recovery in the immediate layer, while the ABS chiller utilizes the upper exhaust gas then converts to useful cooling as the thermodynamic characteristics. The s-CO₂ Brayton cycle energy efficiency is significantly affected by the imposed turbine temperature inlet limit (TIT less than 973K) and the finite temperature approaches in the dual recuperators. However, the first cycle recovers an extremely high temperature from the given exhaust gas flow from turbine or recuperator outlet. This heat source is thermodynamically well-matched with the downstream Rankine cycle and thus acts as the principal exergy carrier within the tri-generation design. The exhaust gas exiting the turbine (T4r = 707K) is utilized as the prime heat supplying source for the HRSG in the bottoming Rankine cycle.

The intermediate Rankine cycle operates as a relatively simple single pressure bottoming component. In which, steam vapor is generated thanks to the HRSG generator (HRSG) at a boiler pressure of 2 MPa and condenser pressure of 10 kPa, with a steam turbine efficiency of 0.75. The HRSG extracts 29.91 kW of recovered heat from the Brayton exhaust. The LiBr-H₂O absorption chiller recovers 80% of the Rankine condenser heat (fabs= 0.8), in which ABS can efficiently deploy the lowest grade heat that rejecting from the Rankine condenser. With a coefficient of performance (COPabs= 0.7), the system delivers 13.19 kW of cooling ability at the boiling temperature of 260K and a generator source temperature of approximately 580K. Although the exergy efficiency of this low-temperature subsystem is lower than that of the power cycles, the cooling capacity is sufficient to support sub-ambient services such as fuel pre-cooling, boil-off reduction in LNG or ammonia tanks, or refrigerated cargo, thereby converting residual thermal losses into operationally valuable refrigeration. By efficiently converting low-temperature waste heat into usable refrigeration, this step improves system utilization overall. The steam generated passing by the SRC turbine, in the next stage producing 6.35 kW of net power. The Rankine subsystem exhibits a cycle efficiency of approximately 21.3% and exergy efficiency of 33.3%, contributing about 18% of the total electrical output.

The exergy distribution among subsystems clarifies their respective roles in exergy recovery. Despite the Brayton cycle being the primary source of mechanical power, the bottoming units account for a substantial fraction of the useful exergy. As shown in Figure 5, the Rankine cycle exhibits the highest exergy efficiency (33.3%), whereas the Brayton and ABS subsystems reach 29.2% and 16.4%, respectively. The Rankine, Brayton, and ABS subsystems contribute roughly 42%, 37%, and 21% of the total recovered exergy. These numbers show that the cascaded Rankine and ABS stages together recover a significant portion of the available exergy that would otherwise be destroyed or rejected, even though the topmost s-CO₂ Brayton cycle serves as the primary driving power. This distribution indicates that, although the topping cycle provides the main driving potential, the cascaded bottoming stages collectively recover the majority of exergy that would otherwise be destroyed or rejected, emphasizing that system-level design is more effective than isolated optimization of the topping cycle alone.

Figure 5:

Three-tiered Brayton-SRC-ABS exergy efficiency

3.2 Design-Parameter Sensitivity and Optimization

The influence of key design and operating parameters on the system energy efficiency of the tri-generation system is examined through a parametric sensitivity analysis stage. The analysis considered several key parameters such as Brayton pressure ratio, the minimum temperature difference in the recuperators and the overall heat transfer conductance expressed via the number of transfer units (NTU) for the dual recuperators. Over the investigated range, the total energy efficiency η_en,tot increases almost linearly with PR, reflecting higher specific work and a higher mean temperature of heat addition in the Brayton cycle as PR rises. The figures for the minimum temperature difference (ΔT_min), the overall heat-transfer conductance of the recuperators, and pressure ratio have been investigated under different layers with the aim of examining the maximized margins of system overall energy efficiency as illustrated in Figure 6.

Figure 6:

Parametric sensitivity analysis

However, as illustrated in Figure 7, this gain is accompanied by a rise in irreversibility associated with increased compression work and larger temperature differences in the recuperators at off-design points. Consequently, there exists a practical PR window in which the total system energy value is significantly enhanced while the marginal penalty in exergy destruction and mechanical complexity remains acceptable for marine applications. Similarly, an increase in recuperator NTU (for both LTR and HTR) improves the internal temperature matching of the s-CO₂ streams, leading to a higher preheat level at the Brayton heater inlet and a lower exhaust temperature entering the HRSG. This simultaneously increases Brayton-cycle efficiency and the quality of heat supplied to the Rankine system. The results indicate that η_en,tot is sensitive to NTU in the low-to-moderate range but exhibits diminishing returns as NTU becomes large, where the effectiveness approaches its asymptotic limit while heat-exchanged area, cost, and pressure drop continue to increase.

Figure 7:

Trade-off between design PR and irreversibility

As demonstrated in Figure 7, at PR= 3.5, the overall energy accounts for 32% total energy. Beyond this point, the additional compressor work offsets turbine expansion benefits. Exergy analysis indicates 45%, 32%, and 23% destruction in the Brayton, Rankine, and ABS subsystems, respectively. This confirms that recuperator enhancement remains the primary pathway for efficiency improvement and quality of the heat supplied to the Rankine system. It is indicated that total energy is sensitive to NTU in the low-to-moderate heat range, but as NTU increases, its effectiveness approaches its asymptotic limit, whereas the heat exchanger size and pressure drop continue to rise. High irreversibility and poor utilization of low-grade heat are main elements limiting the waste heat recovery potential of conventional diesel and LNG-fueled vessels.

When interpreted in a marine context, these findings have direct practical implications. The three-tier architecture aligns naturally with the temperature hierarchy of typical shipboard energy streams: high-temperature exhaust from a prime mover (SOFC, gas turbine, or nuclear reactor) is processed in the s-CO₂ Brayton cycle; medium-temperature heat is recovered in the steam Rankine cycle; and low-grade heat is converted into useful cooling in the ABS chiller. The compactness of s-CO₂ turbomachinery and printed-circuit-type heat exchangers facilitates integration in space- and weight-constrained engine rooms, whereas the Rankine and ABS modules can be implemented as modular skids interfacing with existing exhaust-gas and cooling-water circuits. The 13.19 kW of cooling produced by the ABS at 260K can be flexibly allocated to accommodation HVAC, refrigerated cargo, or cryogenic fuel services, thereby reducing the operating hours of conventional electrically driven chillers and auxiliary compressors.

3.3 Robustness under Operating-Condition Variations

Marine waste-heat recovery systems are predominantly clustered around part-load conditions due to engine load fluctuations and installation-dependent hydraulic losses in heat exchangers and piping. To capture off-design operation, the exhaust gas boundary conditions are parameterized as a function of engine load. The engine load is set at 50%, 75%, and 100% and for each load case, the resulting performance trends are analyzed to identify whether power and cooling outputs remain within an acceptable range for practical deployment.

In addition, the overall pressure-drop ratio necessitates due to uncertainty in hydraulic losses which can further shift the operating point. Thus, the changes in net power output and absorption cooling capacity, referenced to the baseline, define the off-design performance envelope and support the selection of resilient setpoints. Table 2 shows near-linear scaling with engine load as $$ {\dot{m}}_{EXG}$$ doubles from 6000 to 12000 kg/h, T_EXG increases slightly from 923K to 973K, the W_net,total rises from 17.47 to 34.93 kW. The power split remains essentially constant, indicating 82% Brayton, 18% Rankine while ABS cooling increases from 6.6 to 13.19 kW.

Table 2:

Engine-load sensitivity analysis

As demonstrated in Table 3, the pressure-drop sweep (1-5%) indicates that cycle performance is weakly sensitive to the assumed uniform hydraulic-loss margin. Increasing the loss factor increases the imposed drops (ΔP_Shell in the range of 60-300 kPa; ΔP_tube in the range of 20-100 kPa) and lowers net output from 36.33 kW (1%) to 33.57 kW (5%). Importantly, the 3% baseline lies near the center of this band: relative to 3% (34.93 kW), net power changes by only +4.01% (pressure drop 1%) and -3.89% (pressure drop 5%), and efficiency overall decreases modestly from 32.9% to 32%. This bounded response shows that the key conclusions are not artifacts of the pressure-drop assumption; rather, ΔP mainly shifts absolute KPIs without altering trends. Therefore, adopting ΔP = 3% is a reasonable and conservative screening-level allowance representing aggregated exchanger/piping/minor losses under concept-design uncertainty.

Table 3:

Net power vs pressure-drop sensitivity analysis

Author Contributions

Conceptualization, T.T.H To, H.K Kang; Methodology, T.T.H To; Software, T.T.H To; Formal Analysis, T.T.H To; Investigation, T.T.H To; Resources, T.T.H To, C. Lee; Data Curation T.T.H To, C. Lee; Writing-Original Draft Preparation, T.T.H To; Writing-Review & Editing, T.T.H To, H.K Kang; Visualization, T.T.H To, C. Lee; Supervision, H.K Kang; Project Administration, H.K Kang; Funding Acquisition, H.K Kang.