Study on E ﬀ ects of Inlet Resistance on the E ﬃ ciency of Scroll Expander in Micro-Compressed Air Energy Storage System

: As an important part of a micro-compressed air energy storage system, the scroll expander directly a ﬀ ects the e ﬃ ciency of the whole energy storage system. The e ﬀ ects of resistance on the e ﬃ ciency of scroll expander caused by inlet structure and size are discussed with theory analysis and experimental methods in this paper. Micro-compressed air energy storage system has aroused widespread attention because of its pollution-free, high ﬂexibility, in the community, remote areas power supply. Comprehensive experimental work with the selections of di ﬀ erent size and structure of the air inlet of the scroll expander was performed with the cutting angle of air inlet chamber of the scroll expander. The results of the experiments are discussed on how exergy e ﬃ ciency and inlet ﬂow of the scroll expander were a ﬀ ected resulting from the cutting angles dissected. The results show that a maximum value exists for exergy e ﬃ ciency of the scroll expander. Therefore, the exergy e ﬃ ciency of the scroll expander can be e ﬀ ectively improved by enlarging the air inlet port dimension and modifying the size of air chamber.


Introduction
Compressed Air Energy Storage (CAES) plays an important role in balancing the load and generation of power grid through peak shaving, load shifting, and valley filling to encourage renewable energy source integration [1]. The key components of a compressed air energy storage system are usually an expander/turbine, gas storage tank, compressor, etc., which determine the energy conversion efficiency of the CAES system. It is important to improve those components' efficiency for the whole system efficiency improvement. In this paper, the efficiency analysis of an expander is considered. Different expanders are used in CAES systems, such as piston expander, turbo expander, and scroll expander [2,3], among which scroll expanders are widely valued in the micro-compressed air storage systems for the applications in transport, simple structure exhaust recovery, black starting torque generation due to their low gas pressure requirements, and smooth and continuous working performance [4].
The study on how the inlet geometry changes affects the efficiency is hardly seen. To understand the influence of the inlet pressure and port size, it is necessary to conduct modeling and experimental study on the expanding process of a scroll expander [13]. The initial study was carried out through a prototype of scroll compression-expansion machine [14]. The authors of [14] found that the inlet structure (i.e., the rate of change of the inlet area) and the pressure loss of the scroll expander are the primary reason for change of energy conversion efficiency of the expander. Wu [15] confirmed that the structure of the air inlet is the main factor affecting energy conversion efficiency of the scroll expander. Compared with the circular air inlet hole, the opening characteristics of the waist-shaped air intake port can significantly improve the energy conversion efficiency.
To reduce the inlet resistance to air on the scroll expander, a mathematical model representing the relationship between the cutting angle of the head at the beginning of the intake chamber and the inlet size with the exergy efficiency is established in this paper. An experiment platform of compressed air energy storage system based on scroll expander is set up for accommodating this study. The influences of the inlet size and the cutting angle of the inlet chamber on the exergy efficiency of the scroll expander were tested with the new experimental platform.

Mathematical Model of a Scroll Expander
Scroll expander is a type of volumetric expander. The interior of the scroll expander is mainly composed of a pair of identical fixed and moving spirals with a phase difference mirrored with 180 • . Several pairs of closed crescent-shaped work chambers are formed by the mutual engagement of two scrolls. A diagram of the geometric structure of a scroll-type inertial vortex rotor with no wall thickness is shown in Figure 1. The moving scroll is represented by the red line; the fixed scroll is represented by the blue line; and the orbit of the moving scroll is represented by dotted black line. Compressed gas enters the expander from the air inlet, which is in the center of the fixed scroll. The moving scroll is pushed to rotate. Gas volume increases, and pressure energy is converted into the mechanical energy of the expander spindle. In this paper, the scroll line of a scroll expander is discussed as circular involute, as shown in Figure 2.   In Figure 1, α indicates the angle between the head of the moving scroll and the negative direction of the y-axis, and the current position of the expander is represented by α. If the initial position of the moving scroll head is (x 0 , y 0 ), the moving scroll vortex curve equation is: where ρ 0 is the base radius of the involute curve, ρ = ρ 0 + kϕ is the radius of the involute curve, k = dρ/dϕ determines the shape of the involute curve, ϕ is the unfolding angle of the moving scroll, ϕ ∈ (ϕ, ϕ end ), and ϕ end is the tangential angle of the end of the moving scroll, as shown in Figure 2.

Thermodynamic Modeling of Scroll Expander
According to the literature [15], the thermodynamic parameters of each chamber of the scroll expander can be known.
The gas mass flow through the expander inlet is [17,18]: where C d is flow coefficient [19], A s is the inlet cross-sectional area, T u is the upstream temperature of the air inlet, p u is the upstream gas pressure of the inlet, and f (p r ) is as follows: where p r is the ratio of the downstream to upstream gas pressure of the inlet. Assuming that the specific heat of air ratio γ = 1.4 and the gas constant is R, Finally, the thermodynamic model of intake process is obtained as follows: .
The expansion process model is: .

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The exhaust process model is: . .
where the subscripts c, s, and e represent the intake chamber, the expansion chamber, and the exhaust chamber, respectively. m is the gas quality, V is the chamber volume, X air represents the gas molar volume concentration, M air represents gas molar mass, h is the gas molar heat capacity, and c p is the specific heat capacity of the gas.

Exergy Efficiency Model of Scroll Expander
Exergy analysis not only considers the "quantity" of energy, but also combines the "quantity" and "quality" of energy. Compared with traditional energy analysis and entropy analysis, it reveals the transformation of "quantity" and "quality" in the process of energy transfer and conversion more profoundly.
Total driving torque of gas acting on moving scroll is [20]: where ρ i = p i /p s is the pressure ratio of the ith chamber pressure to the intake chamber pressure. The fluid motion parameters of various points in the internal flow field of the scroll expander are independent of time. Therefore, the gas flow in a scroll expander can be viewed as steady-state flow. The kinetic energy and position energy of the expander's inlet and outlet are neglected, thus the exergy of the unit mass compressed air is [21]: where h and h 0 represent the enthalpy of the unit mass compressed air and the enthalpy of the air in the ambient state, respectively. S and S 0 represent the entropy of the unit mass compressed air and the entropy of the air in the ambient state. Assume that the heat capacity is c p , the pressure of the compressed air is p, the temperature is T, the ambient temperature is T 0 , the atmospheric pressure is p 0 , and gas constant is R g . If air is considered as the ideal gas, then: Combining Equations (20) and (21) into Equation (19), the exergy of unit mass compressed air can be expressed as: Then exergy efficiency of scroll expander can be calculated by: where c p = 1.004 KJ/(kg·k), p 0 = 0.1 MPa, and T 0 = 303 K. e x1 and e x2 are, respectively, the exergy of the inlet gas and the exhaust gas, which can be calculated by Equation (22).
. m 1 and . m 2 represent the intake flow and the exhaust flow, which can be calculated by Equation (10).
To sum up, by substituting the geometric volume equation, thermodynamic equation, and kinetic equation of the scroll expander into the exergy efficiency equation of the expander, the relationship between the chamber volume and exergy efficiency can be obtained, and it can be seen that the cutting angle of the intake chamber and the size of the air inlet will affect the efficiency of the scroll expander.

Study on Experimental Performance of Scroll Expander
The above modeling shows that the exergy efficiency of the scroll expander for compressed air energy storage is related to inlet size and cutting angle. The compressed gas with a certain pressure enters into the intake chamber of the scroll expander through the inlet, which causes the throttle loss to a certain extent due to the throttle obstruction of the inlet and restricts the increase of the compressed gas flow rate. The existence of the head at the beginning of the intake chamber of the vortex disc has a certain blocking effect on the flow of compressed gas into the expander, which reduces the pressure energy used to drive the spindle of the expander to rotate. To further study the effect of the inlet size and the cutting angle on the efficiency of the expander, the following experiments were carried out.

Introduction of Experiment System
The scroll expander selected for this experiment was modified from the ATC-086 scroll compressor. The original compressor outlet valve was removed. The main structural parameters are shown in Table 1. The main equipment of the experiment platform includes air compressor, air tank, scroll expander, and magnetic powder brake. Measuring instruments are pressure regulator, temperature sensors, pressure sensors, flow sensors, torque and speed sensors, and data acquisition system. The instrument and equipment parameters are shown in Tables 2 and 3. The experiment platform for the compressed air energy storage system is shown in Figure 3. Air compressor, gas tank, scroll expander, and magnetic powder brake were connected one after the other to form the main body of the compressed air energy storage system. The working medium of the experiment platform was compressed air, which was produced by a low-pressure compressor and stored in the gas tank to reach the set pressure for the expander to do work.
In the energy release stage, the compressed air with a certain pressure enters the scroll expander to do work after being adjusted to a certain value through the pressure reducing valve. Compressed air enters the expander to expand, pushing the spindle to do work. The pressure sensor, flow sensor, and temperature sensor set in front of the expander measure the state parameters of the compressed air in the inlet of the expander. The torque and speed sensors collect the torque and speed of spindle. The magnetic powder brake at the end of the system, as the load of the system, converts the mechanical work transferred by the spindle into heat energy to consume the work generated by the expander. The compressed air is discharged from the exhaust outlet of the scroll expander. The sensor placed at the exhaust port of the expander measures the flow, pressure, and temperature of the discharged gas. Then, the exergy efficiency is calculated by substituting the measured inlet and outlet gas parameters into the formula derived above. During the experiment, the collection and preservation of all parameters were completed by data acquisition system dSPACE.

Research on Air Inlet Size of Scroll Expander
The air inlet opened in the fixed scroll baseplate is the only channel for compressed air to enter the expander. Air inlet size directly affects the amount of throttling loss of compressed air. To reduce the intake resistance, the influence of the size of the inlet of the scroll expander on its exergy efficiency was researched. The air inlet located at the center of the fixed scroll baseplate is expanded to different sizes. To ensure that the air inlet is not communicated with the chambers other than the air intake chamber, the maximum opening range of the air inlet is tangent to the beginning of the wrap, which is 14 mm, as shown in Figure 4. The original inlet diameter of the expander is 8 mm. Therefore, the inlet size of the expander is taken as 8, 10, 12, and 14 mm. The experiments were conducted separately. The effects of the inlet port size on the performance of scroll expander are shown in Figure 5. Figure 5a shows that, when the inlet pressure is 0.27 MPa, the exergy efficiency of the scroll expander is the highest. With the increasing of the intake pressure, the exergy efficiency gradually decreases, and the decreasing rate gradually decreases. When the inlet pressure is kept constant, the exergy efficiency of the scroll expander gradually increases as the inlet expands. When the inlet diameter of the scroll expander is expanded from 8 to 14 mm, the overall exergy efficiency of the scroll expander is increased by about 2%. Therefore, the exergy efficiency of the scroll expander can be improved effectively by expansion of the inlet size, especially when the intake pressure is below 0.3 MPa. When the inlet pressure is 0.27 MPa, the exergy efficiency can be increased by about 6%. When the inlet pressure is greater than 0.3 MPa, the effect of the inlet port size on the exergy efficiency of the expander is poor, only ranging from 1% to 2%. This is because of the limited expansion of the inlet port size. For the higher pressure, the smaller change in the size of the air intake has less effect on the intake air volume. In Figure 5b, with the increase of the air inlet, the air flow of the scroll expander generally increases. As the inlet pressure increases, the rate of increase continues to increase. When the inlet pressure is 0.8 MPa, the inlet flow of the expander increases by 33.3% compared with the original expander. This is mainly due to the expansion of the air inlet, so that the inlet resistance of the expander is reduced, the throttling loss is reduced, and the gas flow into the interior of the expander is increased. It can also be seen that the exergy efficiency is not a single value function of the inlet size.
These results indicate that the exergy efficiency of the scroll expander can be improved effectively by increasing size of the air inlet port. Therefore, the size of the inlet can be increased while ensuring it has no connection with the expansion chamber.

Research on Cutting Angle of Inlet Chamber of Scroll Expander
To research the influence of the intake chamber wall on the exergy efficiency of the scroll expander, the cutting angle of the intake chamber head of the scroll wall is, respectively, 45 • , 90 • , 135 • . . . 360 • resection, as shown in Figure 6. Some processed objects are shown in Figure 7.  The effects of the cutting angle of the scroll in the intake chamber on the exergy efficiency at different inlet pressures are shown in Figure 8, where, according to the effect of the air inlet size on exergy efficiency, the air inlet port size in the experiment is 14 mm. Figure 8a shows that the cutting angle has less effect on the exergy efficiency with the increase of the inlet pressure. When the inlet pressure is 0.28 MPa, the maximum exergy efficiency of the scroll expander is increased by about 8% at the angle of 180 • . When the inlet pressure is greater than 0.3 MPa, the exergy efficiency of the scroll expander decreases significantly with the increase of the inlet pressure, which is reduced from an increase of 8% to about 2%. This shows that the influence of the 180 • resection of the intake chamber head on the expansion exergy efficiency of the expander is more effective at the low pressure. When the intake pressure is between 0.3 and 0.4 MPa, the highest efficiency point of the expander is caused by 315 • cutting the head, the exergy efficiency of the expander is increased by about 12.5%, and the corresponding intake pressure is 0.32 MPa. This is caused by two reasons: (1) the same expander is used in this group of experiments, and after several times of dismantling and processing the leak of the expander is increased; and (2) the contact area at the wall end of the movable and fixed scroll is reduced, and the internal leakage is increased for the removal of the wall head of the intake chamber. When the inlet pressure is greater than 0.4 MPa, it can be clearly observed that the improvement rate of the exergy efficiency is greatly reduced, and the minimum increase is about 2%. Within this range of intake pressure, the most improvement of the exergy efficiency of the turbo-expander is caused by the 225 • angle of the wall head resection, which is increased by about 10%.
As shown in Figure 8b, with the increase of the cutting angle of the intake chamber head, the inlet flow of the expander increases continuously. When the inlet chamber is cut 180 • and the inlet air pressure of the expander is 0.2 MPa, the inlet flow of the expander increases by 35%. When the inlet chamber is cut 315 • and the inlet air pressure of the expander is 0.3-0.4 MPa, the inlet flow is increased by 50%. When the inlet chamber is cut 225 • and the inlet air pressure of the expander is greater than 0.4 MPa, the inlet flow of the expander increases by 30.3%.

Conclusions
The following conclusions can be drawn from the experiments on the influence of different inlet sizes and different cutting angles of the intake chamber wall on the exergy efficiency of the scroll expander: (1) The exergy efficiency of the scroll expander can be effectively increased by increasing the size of the air inlet, up to 6%. Therefore, the air inlet of the expander can be opened as large as possible and the air inlet is not communicated with other chambers than the air intake chamber. Resistance of the PMSG stator windings (ohm) P e The power consumed by the electrical load (W) P air The employed air power by the expander (W) h The special enthalpy of air (J/kg) η The discharging process energy efficiency η e+cold The overall discharging process energy efficiency considering of refrigerating P cold The cold air power supplied by the expander (W) Subscripts C,S The scroll expander's center and side chambers, respectively d,q The d,q axes for the PMSG modeling in,out The inlet and outlet of scroll expander Abbreviations CAES Compressed air energy storage PHS Pumped hydroelectric storage PMSG Permanent magnet synchronous