1. Introduction
A new climate regime, POST-2020, was agreed upon at the climate change conference held in Paris in December 2015. In order to implement this new climate system, all countries must strive to achieve their greenhouse gas reduction targets. To this end, many efforts are being made to develop clean energy worldwide. Representatively, there have been studies on the production and use of hydrogen energy. Recently, a full-scale study on the development of core technologies for hydrogen liquefaction plants began in South Korea.
A hydrogen liquefaction plant is a closed-loop system, and it consists of a compressor, heat exchanger, cold box, and expander. The expander is one of the core components in a cryogenic system. In the cryogenic expander, the working fluid is expanded under extremely low temperatures, e.g., below 93 K. Therefore, some of the parts, i.e., the rotor, shaft, and labyrinth seal, are operated under cryogenic conditions. In general, the cryogenic expander rotates at a high speed, from tens of thousands to hundreds of thousands of revolutions per minute, so rotordynamic stability is important.
The technologies required to develop the cryogenic expander are as follows: aerodynamic design technology with an expander loss model for cryogenic working fluids, seal and insulation technology, thermal stress analysis technology, high-speed oil-free bearing technology, clearance prediction and control technology, secondary flow stabilization technology, and expander power control technology. However, because of the information security of the industry, the introduction of these technologies in the literature or at conferences has been limited. However, it is possible to identify the latest technology trends and technical issues through the publications of a few companies that produce cryogenic expanders [
1,
2,
3].
There are several methods to exhaust the output power generated by the expander. First, a compressor is installed on the opposite side of the expander with the same shaft. It can be applied to compress the working fluid at the cryogenic system [
4]. This expander–compressor assembly is called a compander. When it is used as a compander, there is an advantage in that the high pressure required in the cryogenic system can be acquired from the compressor. However, there is a disadvantage in that the system operation is complicated.
Second, the power generated from the expander drives the brake compressor to exhaust energy [
5,
6,
7,
8]. Alternatively, there is a method of converting the power generated by the expander into heat energy using an eddy current breaker. It has an advantage in that the size of the system can be reduced and the control can be made simple. However, it dissipates the energy generated by the expander; therefore, it is not preferable for a large-capacity plant. Third, the expander rotates the generator, and electric power can be acquired from the generator. If the capacity of the expander is large enough, the application of a generator can be considered.
As described above, the method of utilizing expander energy can be determined by the characteristics of the cryogenic system. In this research, the brake compressor is connected to the expander so that the speed of the expander can be controlled by adjusting the compressor’s throttle valve.
Song et al. conducted blade optimization to reduce the swirl flow and cavitation in the draft tube of a cryogenic liquid turbine [
9]. Huang et al. investigated the effect of the blade loading distribution and blade lean angles on the cavitation in the draft tube of a cryogenic expander [
10]. However, there has been little research on the optimization of cryogenic expander efficiency.
To develop a highly efficient cryogenic system, it is necessary to increase the efficiency of the expander. In this paper, the optimization of an expander rotor was conducted to improve expander efficiency. The expander rotor rotates at tens of thousands of revolutions per minute under cryogenic conditions. However, there is no sufficient design modeling for an expander with cryogenic fluids. Therefore, careful decisions must be made on the shape factors that determine the efficiency of the expander.
In this study, the rotor blade meridional shape and blade angle were optimized to improve the expander efficiency. This can be used as a reference to design a high-efficiency cryogenic expander in the future.
2. Operation Conditions
In this study, cycle analysis was conducted to develop a high-efficiency hydrogen liquefaction system. Through the cycle analysis, the operating conditions of the component were determined. The target capacity of the hydrogen liquefaction system is condensing 0.5 tons of hydrogen per day.
Figure 1a shows a schematic of a 0.5-TPD class hydrogen liquefaction plant. The helium working fluid absorbs the cold heat of the vaporized nitrogen through a heat exchanger (Hx1), and by flowing through a sequence of heat exchangers and expanders, the temperature is lowered so that hydrogen can be liquefied. Hydrogen in the gaseous state is liquefied through heat exchangers Hx1−Hx4 and stored in a tank.
As shown in
Figure 1a, the system consists of two expanders, one compressor, and four heat exchangers. The expanders are connected in series. In this study, design and optimization were conducted for one of the expanders.
Figure 1b illustrates the temperature–entropy (T–s) diagram of the hydrogen liquefaction plant.
Table 1 shows the components in each process in the T–s diagram. A heat exchanger (process ④–⑤ in
Figure 1) is installed between Expander 1 and Expander 2. The expander that was studied in this research was Expander 1, which relates to processes ③–④ in the system.
Table 2 presents the operation conditions of the expanders. The considered expansion ratios of Expander 1 and Expander 2 were 1.6 and 3.69, respectively.
3. Expander Design
3.1. Preliminary Design
A preliminary design was performed to determine the rotational speed and diameter of the expander rotor. In the preliminary design, specific velocity and specific diameter analyses were conducted. The definitions of the specific velocity and specific diameter are as follows:
Table 3 shows the preliminary design results for Expander 1.
In the case of a centrifugal expander, the specific speed is generally selected between 0.5 and 0.6 in consideration of expander efficiency. However, in this study, the specific speed of the expander was selected as 0.392, considering rotordynamic performance. The design speed was 75,000 rpm. Through specific diameter analysis, it was estimated that the diameter of the rotor should be 53.77 mm.
In the case of the radial inflow expander, the relation of the specific speed
and the specific diameter
was
[
11]. Therefore, the specific diameter
was determined when the specific velocity
was chosen. For this reason, U_tip in
Table 3 is the same against the specific velocity
.
3.2. Meanline Design
Meanline design, which is also called one-dimensional design, was conducted based on the results of the preliminary design. Meanline design is a flow path design including the blade shape and flow angle. In this study, meanline design was conducted using ConceptsNREC Inc’s RITAL program. The Rodgers loss model was applied for the nozzle design, and the CETI passage loss model was applied for the rotor design.
Figure 2 shows the meanline shape of the expander. The designed expander consists of a volute, nozzle, and rotor. Generally, a volute is symmetric. However, in this research, an overhang-shaped volute was selected to shorten the shaft length and increase the assembly. Cho et al. compared losses according to the shape of volute [
12]. They conducted a CFD analysis of the loss in a circular volute and a rounded square volute. In this study, the volute shape was determined based on the fact that a circular volute has less loss than that of a rounded square volute. The major dimensions of the expander are shown in
Table 4. The designed tip clearance between the rotor and shroud was 0.3 mm.
The velocity triangles at the inlet and outlet of the rotor are shown in
Figure 3. In this study, the incidence angle was −26.74°, and the deviation angle was 22.8°.
Figure 4 shows the performance curves derived from the meanline design. They were plotted at 80% (60,000 rpm), 90% (67,500 rpm), and 100% (75,000 rpm) of the design speed.
Figure 4a shows the relation between the expansion ratio and mass flow rate.
Figure 4b shows the relation between the expansion ratio and efficiency. The efficiency from the meanline design was recalculated by reflecting the loss in the expander. It is defined as the ratio of the enthalpy difference and isentropic enthalpy difference between the inlet and outlet of the expander. It was verified that the target efficiency was satisfied at the design expansion ratio.
Figure 4c shows the relation between the expansion ratio and the power. Like the efficiency curve, the power from the meanline design was recalculated by reflecting the loss in the expander. Finally,
Figure 4d shows the relation between the expansion ratio and the expander outlet temperature. The cryogenic expander must satisfy the expander outlet temperature in the system requirements. As shown in the figure, the estimated expander outlet temperature meets the design temperature.
3.3. 3D Shape Generation
Based on the results of the meanline design, a three-dimensional expander geometry was generated to conduct the numerical analysis. The three-dimensional geometry was generated using AxCent program of ConceptsNREC.
Figure 5 shows the 3D shapes of the nozzle and rotor.
Considering the assembly of the expander, the length of the straight zones between the volute and nozzle inlet and between the nozzle and the rotor were determined. The trailing edge thickness was determined considering the blade manufacturer. The shape of the leading edge was rounded to prevent separation at the leading edge of the rotor.
3.4. Numerical Analysis
Numerical analysis was conducted using NUMECA’s FINE/Turbo program. As a turbulence model, the Spalart–Allmaras model, a one-equation model with excellent calculation efficiency, was applied to determine the exact properties of the boundary layer in the pressure gradient.
In order to increase the convergence of the calculation, the choice of boundary condition is important. In general, pressure, temperature, and flow rate are applied as boundary conditions in turbomachinery numerical analysis. Applicable pressure and temperature values are static and stagnation value. In addition, the applicable flow information is the mass flow rate and the velocity vector. In this study, numerical analysis was performed by analyzing the calculated result using the pressure condition as the main boundary condition. The applied boundary conditions were the inlet total pressure, inlet total temperature, velocity direction, turbulent viscosity, and outlet static pressure. To obtain the off-design point performance, the outlet static pressure was varied. The meanline design results were used for the flow angle information flowing into the nozzle inlet. That is, the absolute flow angle of the volute outlet was used as the nozzle inlet flow angle in the numerical analysis.
A mixing plane condition was applied between the nozzle outlet and the rotor inlet. Therefore, the average physical property value in the pitch direction was applied as the rotor inlet condition. In real operation conditions, the shape of the nozzle wake changes along with the rotor revolution, and to analyze it, unsteady calculations should be conducted. In this study, the focus was on efficiency improvement, and a steady calculation was conducted. The calculation was conducted for a single periodic passage.
To determine the appropriate number of grids, the efficiency according to the number of grids was analyzed. Efficiency was compared for the following number of grids: 199,079, 239,403, 345,415, 534,415, 1,088,147, and 1,332,851. When the number of grids was greater than 239,403, there was no significant change in efficiency. In this study, the number of grid cells in the calculation domain was 1,088,147.
Figure 6 shows the relationship of efficiency according to grid number to check grid independence. A hexa mesh was applied to generate a dense grid near the blade wall, and Y+ was set to 2.
The cryogenic expander design was conducted using the real gas properties of helium. To reduce the computation time during the numerical analysis, a property table of the working fluid was applied to the calculation. NUMECA’s TabGen was used to generate the data. TabGen creates a fluid property table in connection with NIST’s REFPROP, a program that provides fluid properties. Interpolation was performed based on the generated property table so that it could be used as a property value at a location necessary for numerical analysis.
Figure 7 shows the performance curves of the cryogenic expander derived from the numerical analysis. In the same way as for the meanline design results, the mass flow rate, efficiency, power, and outlet temperature were plotted against the expansion ratio at 80%, 90%, and 100% of the design speed. The efficiency and power from the numerical analysis were recalculated by taking into account the extra mechanical losses in the expander. The extra mechanical losses were the loss caused by the volute and the loss caused by the windage in the rotor back disk, and in this study, the losses were assumed to be 2% and 4%, respectively. The outlet temperature of the expander satisfies the temperature required by the system.
5. Conclusions
In this study, we introduced a design method for expanders for hydrogen liquefaction plants. Blade optimization was conducted to increase the expander efficiency. The capacity of the developed expander for a hydrogen liquefaction system is 0.5 tons of hydrogen liquefied per day. Based on the cycle analysis results of the hydrogen liquefaction system, the meridional and three-dimensional design of the expander were conducted. To improve the efficiency of the expander, the rotor blade meridional shape and blade angle were optimized. Through the optimization design, the blade height was increased between the blade leading edge and the trailing edge, and the distribution of the blade angle was rearranged smoothly. Finally, the optimized expander’s efficiency increased by 1.98% compared to that of the original model. To investigate the reason for this efficiency improvement, a flow analysis was conducted. The entropy distribution on the suction blade surface was smaller in the optimized model than that of the original model. Through the relative velocity distribution, it was found that the optimized model had a smoother main passage flow and smaller tip leakage flow than the original model. Due to the passage area of the optimized model, which is larger than the original model, the effect of the tip leakage flow on the main passage flow could be reduced. It was confirmed that the optimization of the blade β angle, rotor hub, and shroud meridional contour had an effect on improving the efficiency of the cryogenic expander. The efficiency optimization method in this paper can be used as a reference in designing high-efficiency cryogenic expanders in the future.