Study on heat transfer and pressure drop characteristics in marine S-CO 2 power cycle hybrid heat exchangers

. The S-CO 2 power cycle has the advantages of compact structure and high energy density, which can be used to recover the waste heat of ship exhaust, thus improving the energy efficiency of ships and reducing emissions. The hybrid heat exchangers with etched plates and fins can be used as the heat transfer device of S-CO 2 and exhaust, its heat transfer and pressure drop characteristics have a great influence on S-CO 2 power cycle performance. In this study, a CFD model of the hybrid heat exchangers was established. The effects of different exhaust inlet temperatures, inlet mass flow rates and inlet pressures on the heat transfer and the pressure drop characteristics were analyzed by Fluent. The results show that the inlet temperatures and inlet mass flow rates of exhaust have a great influence on the heat transfer characteristics of the hybrid heat exchanger. The inlet mass flow rates and inlet pressures of exhaust have a great influence on the pressure drop characteristics of the hybrid heat exchangers. In the design of the hybrid heat exchangers, the status of the exhaust need to be considered to ensure efficient operation of the heat exchangers. The study can provide guidance for the design of the hybrid heat exchangers.


Introduction
The application of S-CO 2 power cycle in ship waste heat recovery can reduce fuel consumption and protect the environment. The S-CO 2 power cycle uses CO 2 in the supercritical state as the working medium to convert the thermal energy of the heat source into mechanical energy. S-CO 2 is suitable for thermodynamics cycles due to its good fluidity, high heat transfer efficiency, low compressibility and chemical stability [1]. Due to the limited space inside the ship, the requirements for the volume of equipments are strict. Compared with Rankine cycle, S-CO 2 power cycle has the advantages of small size and high energy conversion efficiency, so it has advantages in application on ships. Combs et al. [2] of Massachusetts Institute of Technology have done research on the use of S-CO 2 power cycle in the recovery of exhaust heat from naval ships in the 1970s. Echogen Power Systems [3] designed the commercial S-CO 2 generator set EPS100, confirming the feasibility of a megawatt S-CO 2 generator set.
In the S-CO 2 power cycle where nuclear energy and solar energy are heat sources, the heat source fluid is relatively clean, so the heat exchangers are mainly printed circuit heat exchangers (PCHEs) [4]. The ship exhaust is complex, and the tar and particulate matter are likely to cause blockage of the PCHEs channel, making it unable to work properly. Conventional plate-fin heat exchangers (PFHEs) and shell-and-tube heat exchangers are difficult to meet the compactness requirements and withstand the high pressure of S-CO 2 . The hybrid heat exchangers with etched plates and fins through diffusion welding are an effective solution for marine S-CO 2 power cycle heat exchangers. The fluid in the etched channels is S-CO 2 , and the fluid in the fin channels is the exhaust.
At present, there are few studies on the heat transfer and pressure drop characteristics of marine S-CO 2 power cycle hybrid heat exchangers, but many studies have been carried out on PCHEs and PFHEs. The research on PCHEs and PFHEs mainly focuses on two aspects: to research the variation of convection heat transfer coefficient and fanning drag coefficient with operating conditions and geometry parameters of channels [5][6]; optimize the design of the local structure and overall size to obtain a balance between greater heat exchange and smaller pressure drop [7][8].
The exhaust characteristics of marine low-speed twostroke diesel engines are mainly reflected in temperatures, pressures and mass flow rates changing with the loads of the diesel engines. In this study, a CFD model of the hybrid heat exchanger was established, and then the effects of the exhaust inlet temperatures, the mass flow rates, and the pressures on the heat transfer and pressure drop characteristics of the hybrid heat exchangers were analyzed. Finally, some conclusions have been drawn regarding the influence of diesel engine exhaust characteristics on the heat transfer and pressure drop characteristics of hybrid heat exchangers.

Model and numerical simulation
The core of the hybrid heat exchanger is mainly diffusion welded by fins, etched plates and baffles. In this study, a hybrid heat exchanger is designed, and the periodic unit is shown in Figure 1. The thickness of the fin is 0.6 mm, the height of the fin channel is 3.4 mm, and the width of the channel is 2.4 mm. The etched plate has a thickness of 2 mm and the semicircle channel has a diameter of 2 mm, a pitch of 3 mm. The thickness of the baffle is 1 mm. The length of the numerical model is 300mm, where the length divided by the hydraulic diameter is greater than 65, and the influence of the inlet section can be ignored. Due to the complex composition of diesel exhaust, it is not easy to calibrate with accurate physical parameters, and the air thermal physical properties is very close to the diesel exhaust, so air is used to represent diesel exhaust. The material of the fluid in the fin channels is air, the fluid in the etched channels is S-CO 2 , and the solid material is steel. The turbulence model used is SST K-omega turbulence models. The top and bottom of the model are translational boundary conditions, and the left and right are adiabatic boundary conditions. The calculation satisfies conservation of mass, momentum, and energy and the residuals of K and omega are set to the 10 -8 . The independence of grid division is demonstrated first, and a grid that can meet the calculation accuracy and economic efficiency is obtained, as shown in Figure 1. Then, it was found that Type A and Type B are basically the same in calculating the heat transfer and pressure drop of the hybrid heat exchanger, and can be replaced with each other. In this study, Type B fins are selected for calculation.

Results and discussion
The exhaust characteristics of marine low-speed twostroke diesel engines change with diesel engine loads, and the changes in exhaust characteristics are reflected in temperatures, mass flow rates and pressures. The effects of temperatures, mass flow rates and pressures on the heat transfer and pressure drop characteristics of hybrid heat exchangers were studied separately.

Effect of different air inlet temperatures
Set the S-CO 2 inlet temperature to 600 K, change the air inlet temperature from 620 K to 700 K, and the step size is 20 K. The pressure of the air is 0.4 MPa, and the pressure of S-CO 2 is 15 MPa. The mass flow rate of air is 0.0006 kg/s, and the mass flow rate of S-CO 2 is 0.0006 kg/s. As shown in Fig 2 and Fig 3, the heat transfer and pressure drop characteristics were obtained. As the air inlet temperature increases linearly, the total heat transfer rate also increases linearly. However, the convection heat transfer coefficients of air and S-CO 2 remain basically unchanged. For every 20 K increase in air inlet temperature, the total heat transfer rate increases by 7.32 W. The convection heat transfer coefficient of air is about 485 W/m 2 -K, and the convection heat transfer coefficient of S-CO 2 is about 2355 W/m 2 -K. With the increase of the air inlet temperature, the pressure drop between the fin channel and the etched channel slightly increases, but f basically remains unchanged. The f of the air in the fin channel is about 0.35, which is higher than 0.28 of the S-CO 2 in the etched channel.

Conclusion
In this study, a CFD model of the hybrid heat exchanger was established. The effects of different exhaust inlet temperatures, mass flow rates, and pressures on the heat transfer and pressure drop characteristics were analyzed. The main conclusions are as follows: 1) The temperature change of the exhaust will significantly affect the total heat transfer rate, and has little effect on the convection heat transfer coefficient and pressure drop characteristics.
2) The increase in exhaust mass flow rates can enhance the heat transfer characteristics on the fin channel, but the pressure drop also increases significantly.
3) When the exhaust temperature and mass flow rate are constant, the pressures has little effect on the heat transfer characteristics. The pressure drop of the fin channel decreases with the increase of the exhaust inlet pressure, and the pressure drop on the etched channel is basically unchanged.