Compressed air energy storage system: Effect of variable relative stator installation angle on nozzle governing turbine performance

The air storage pressure of compressed air energy storage system gradually decreases during the process of energy release, and a reasonable air distribution method for the turbine is required to make the turbine work efficiently in this process. In this paper, based on the single nozzle governing method, the effect of the variation of the full circumferential relative stator installation angle on the system performance improvement under the rated output work condition is investigated. It is shown that the specific work of the variable relative stator installation angle can be improved by up to 6.3 % relative to the design stator installation angle and up to 15.7 % relative to the throttle governing method under the base pressure of 10.0 MPa. With the same absence of throttling losses, the specific work of 3-nozzle inlets method is higher than that of 4-nozzle inlets method, and the turbine internal losses are reduced by 10.6 %. This study provides a theoretical basis for the design, optimization and operation control of nozzle governing turbines.


Introduction
With the benefits of high energy storage efficiency, extended storage cycle, big storage capacity, and relatively inexpensive investment, compressed air energy storage (CAES) has emerged as one of the most promising large-scale energy storage technologies [1,2].Air is compressed to a high pressure by a multi-stage compressor and stored in the air storage device throughout the CAES system's energy storage process.When the energy is released, the high-pressure air enters the multi-stage turbine to expand and produce electricity.The CAES system's overall effectiveness is directly impacted by the turbine's performance because it is one of its key components.The air pressure in the air storage device gradually drops during the energy release process.It is required to adopt an acceptable air distribution method for the turbine in order to make it operate effectively under varying inlet pressure (IP).At the moment, the two most common air distribution methods are nozzle governing (NG) and throttle governing (TG).
The system's efficiency is decreased by the TG method, which throttles the turbine's full circumferential air with high throttling losses.Each group of nozzles is managed by its own throttle valve (TV) when operating under NG circumstances.Similar to industrial steam turbine power plants, the mass flow rate of throttled air can be reduced while the total turbine efficiency increases by controlling the open degree and close of each TV [3].The flow field may worsen as a result of NG's ability to create inhomogeneities into the full circumferential or partial admission conditions.The turbine must generally run under rated output work (Woutput) operating conditions because it is the fundamental component of a CAES system for generating electricity.In order to increase the overall performance of the CAES system, it is crucial to analyze the turbine NG characteristics and performance improvement approaches for rated Woutput situations.
In contrast to the full circumferential inhomogeneous admission examined in this research, the existing literatures focus mostly on the analysis of partial admission features, which is the extreme example of NG.Initially, studies concentrated on the fundamental characteristics and flow loss processes of partial admission turbines [4,5].The flow channel structure [6,7], nozzle arrangement [8,9], and blade parameters [10,11] were determined to be the key elements impacting the performance of partial admission turbines.Researchers generally concurred that, in terms of flow channel structure, reducing the axial clearance between the nozzle and rotor within a suitable range can result in greater efficiency [12,13] and with decreasing mass flow rate, the efficiency and optimum speed ratio decline.Researchers generally concurred with the effect of the number of inlet nozzles that an increase in the number of inlet nozzles with the same partial admission degree will duplicate the admission losses and hence decrease turbine efficiency [14,15].Researchers have proposed that partial admission losses rise with increasing inlet arc spacing for the effect of inlet nozzle position [16,17].The impacts of blade solidity [18,19], aspect ratio [20,21], and nozzle outlet airflow angle [22,23] on partial admission turbine performance have been the main areas of research for blade parameters.Currently, the nozzle outlet airflow angle is typically controlled by altering the orientation of the nozzle alignment, but there hasn't been much investigation into controlling the airflow direction by altering the stator installation angle (SIA).
The system can be made to function smoothly under a variety of operating situations by using variable geometry turbines, which have good transient response characteristics and can be utilized to change the Woutput by altering the geometric area of the turbine inlet [24].One of the most popular forms of variable geometry turbine technology is the variable SIA method, which alters the operating conditions of the turbine to meet the Woutput requirements by varying the stator's open degree in order to manage the mass flow rate and outlet airflow angle.The stator needs to be fitted with a rotating shaft because of its controlled features.At the top and lower ends of the stator, a specific amount of space must be left to prevent friction between the stator and the hub and shroud.The existence of the clearance also causes leakage losses [25], which additionally rise with the bigger clearance [26].Hu [27] discovered that the performance of variable geometry turbines may be enhanced by the honeycomb seal structure's ability to efficiently restrict the leakage flow.The idea of a "stepped spherical endwall" was put forth by Gao et al. [28] and enables the stator's clearance to remain constant at various SIA while drastically lowering leakage losses.Researchers have also "split" the stator in addition to altering the SIA.Yang et al. discovered that by adopting a forward rotating stator design with a 10 % nozzle opening, the peak turbine efficiency could be raised by 13.5 % [29].The peak turbine efficiency may be successfully boosted by 8 % at a nozzle opening of 6 % thanks to their new split sliding stator suggestion [30].The downstream rotor's inlet will have a negative angle of attack when the stator is open, which will cause the flow separation of the pressure surface.This is revealed by an investigation of the flow field characteristics of the variable SIA.In contrast, when the stator is closed, the controlled stator will create a positive angle of attack at the downstream rotor's inlet, causing the suction surface to flow separately [31].Wang et al. [32] established the control strategy of SIA and fuel mass flow rate under maximum Woutput conditions based on the influence law of the SIA they had found.
From the current research, it can be seen that the aerodynamic parameters and flow field characteristics can be changed to effectively improve the performance of the turbine.The current research is primarily focused on the characteristics of the full circumferential SIA under partial admission conditions and the impact of the dynamic regulation process of the SIA on the performance of the turbine under full circumferential inlet conditions.There is little research on the NG characteristics for the variation of the total IP, and the influence law of the SIA under the NG conditions is even less well documented.Therefore, additional study is required in the following areas: (1) The NG characteristics of full circumferential IP variation.
(2) The influence mechanism of variable SIA under NG state.
(3) Optimization method of SIA for NG characteristics.Therefore, for an axial turbine in a CAES system, this article gives a full circumferential numerical simulation of NG.By changing the full circumferential SIA based on the single NG method, the nozzle IP regulation method corresponding to various SIA under rated Woutput conditions is obtained.Meanwhile, a theoretical foundation for the design, optimization, and operation control of the NG turbine is obtained, revealing the influence law of the variable SIA on the performance of the NG turbine.

Research objects
The research object is the axial turbine of the CAES system from the Institute of Engineering Thermophysics, Chinese Academy of Sciences.Figure 1 and Figure 2 depict the NG turbine's threedimensional model and NG method, respectively.The full circumferential nozzle stator and rotor, along with four chambers, make up the analyzed numerical model.The chamber is separated into four sections, NG1 through NG4, to reduce mixing losses brought on by the pressure difference between adjacent nozzles.Each nozzle corresponds to six stator flow channels.The primary design criteria for the axial turbine are presented in Table 1.When the full circumferential total IP reaches 7.0 MPa, the turbine is running at its rated capacity, producing 7820.0kW of Woutput and 81.3 kJ/kg of specific work (w).
The CAES system can store up to 10.0 MPa of air at a time.The air pressure in the storage device (base pressure, BP) is gradually decreased to the rated total IP of the axial turbine (7.0 MPa) during the energy release process.While the IP of the nozzles regulated in this process can be altered during operation by means of an independent TV, which can be regulated to any pressure less than the BP, the IP of the nozzles not regulated in this process is constant and the same as the BP.As a result, the open degree and close state of each TV may be regulated to manage the Woutput under various BPs, thus enhancing the CAES system's overall performance.[33] research that the system w is bigger with the single NG method.Because of this, only NG2 is used in this study as the regulated nozzle, and the other nozzles are either fully open or fully closed depending on the Woutput requirements.This study examines the impact of the variable SIA on the performance of the NG turbine during the energy release process by changing the full circumferential SIA in an effort to maximize the performance of the system based on NG.According to earlier studies, the stator throat area gradually shrinks and the mass flow rate drops when the stator is closed in comparison to the design state.It should be noted that the stator installation angle studied in this paper are all the variation values relative to the design installation angle, i.e., the relative stator installation angle (RSIA).
The turbine IP must be increased in order to fulfill the requirements for Woutput, which minimizes the regulated nozzle's throttling losses and boosts the system's w.As a result, only how the closed RSIA affects system performance in comparison to the design state is taken into account in this analysis.This study will only be conducted under the BP of 10.0 MPa in order to conserve space while examining the aerodynamic performance and flow field structure for various RSIAs.The similar method is used to investigate other BP.Only the position elements of different RSIAs should be considered when examining the influence law of variable RSIAs; as a result, the effects of the controlled mechanism and clearance on the flow field structure at both ends of the stator are ignored.It is significant to highlight that the studies in this paper are all carried out under rated Woutput conditions.

Numerical model
The ANSYS-CFX 2020 R1 solver is used to simulate a three-dimensional steady-state viscous compressible flow with the chamber, full circumferential nozzle stator, and rotor as the computational domain.The control equations are discretized and iteratively solved within several control bodies in the computational domain when using the ANSYS-CFX finite volume approach.A uniform total pressure, total temperature, and a mean static pressure condition are stated as the boundary conditions at the inlet and outlet, respectively.A no-slip condition is used, and it is assumed that all walls are adiabatic.The kω shear stress transfer (SST) turbulence model is utilized, which is better able to solve flow separation and inverse gradients in conventional turbomachinery.The "Frozen Rotor" stator to rotor interface is used.The physical parameters of the real air are generated by CFX-TASCFLOW.It should be noted that we utilize the mean static pressure at the first stage rotor's exit from the four-stage turbine as the first stage calculation's outlet boundary condition.
When the variations in total-to-total isentropic efficiency and total outlet temperature are less than 0.1 %, the model generated under design SIA satisfies the grid independence criteria at a grid cell number of 18.3 million.The grid for this numerical model is depicted in Figure 3.The more intricate chamber structure is represented by the tetrahedral unstructured grid, whilst the stator and rotor are represented by the structured grid.To satisfy the requirements of the turbulence model, the grid is refined near the wall surface.The y+ values for the chamber, stator and rotor hub, and blade surfaces are shown in Figure 4, where the RSIA is -7°, it can be seen that the average value of y+ is less than one.Moreover, the RSIA of the rest working conditions is greater than -7°.Therefore, the study satisfies the requirements of turbulence model.

Numerical method validation
A typical 1.5 stage Aachen turbine was used for the numerical method validation in order to confirm the reliability of the numerical method [34,35].The full circumferential computational grid model based on the experimental parameters is shown in Figure 5 (b), whereas Figure 5 (a) depicts the geometry of the Aachen turbine test rig.The model being studied shares the same boundary conditions and other settings with that in section 3.1.The distribution of total pressure along the spreading direction at the trailing edge of the first-stage stator, the first-stage rotor, and the second-stage stator was chosen as the study's object based on the grid-independent model, which contrasted the numerical values from the simulation with those discovered through experiment (Figure 6).The prediction errors of the flow field near the hub of the trailing edge of the first-stage rotor and the second-stage stator are large because the numerical model does not account for the effects of the stator and rotor axial clearance as well as the leakage loss of the wheel disk that existed in the experiments, but the overall distributions are essentially the same as those of the experiments.Therefore, the numerical method is determined to be appropriate for follow-up research.

Effect of RSIA on aerodynamic performance
The area of the stator flow channel changes in accordance with the RSIA deviation from the design value, which in turn impacts the variance in mass flow rate.The nozzle IP must be regulated in accordance with the system's rated Woutput.The nozzle IP for various RSIAs is shown in Table 2 under the BP of 10.0 MPa, where 0 MPa indicates that the NG1 inlet TV is completely closed.The BP under all conditions in this investigation is 10.0 MPa.Moreover, other BP situations are evaluated in the same manner as 10.0 MPa and not provided in this work.The primary aerodynamic parameter used to evaluate the performance of the CAES system turbine is the w, which stands for work capacity per unit mass flow rate of compressed air.The following are the expressions for w and Woutput : Where, w is the specific work of the system; hBP is the total enthalpy of the inlet air under the BP; hout is the total enthalpy of the air at the turbine outlet; Woutput is the output work of the system; and m is the total mass flow rate at the turbine outlet.7 (a) shows variation of each nozzle mass flow rate and total mass flow rate with variable RSIAs, where the 4-nozzle inlets and 3-nozzle inlets indicate the number of inlet nozzles as 4 and 3, respectively.It can be seen that the mass flow rate at the inlet of non-regulated nozzles (NG1, NG3 and NG4) shows an approximately linear increasing trend with the increase of RSIA.With the same number of inlet nozzles, the mass flow rate of the regulated nozzle (NG2) shows an approximately linear decreasing trend with the increase of RSIA, and the total flow rate shows an approximately linear increasing trend.When the number of inlet nozzles changed from 4 to 3, the total mass flow rate decreased significantly.Figure 7 (b) shows the increments of the total mass flow rate relative to the TG and the design SIA.When the RSIA is -3.6°, the total mass flow rate is the smallest, which is reduced by 13.3 % and 5.6 % compared with the TG and design SIA, respectively.It should be noted that the aerodynamic parameters of TG in this paper are obtained at the design SIA.Variation of mass flow rate with variable RSIAs.Figure 8 shows the variation of the w of the system with RSIA from -7° to 0°.It can be seen that for different number of inlet nozzles, the w tends to increase as the RSIA decreases.Overall, as the RSIA decreases, the w is higher than the design value.At the RSIA of -3.6°, there are only 3 inlet nozzles of the system and the inlet pressure is equal to the BP.The w at the RSIA of -3.6° is slightly higher than that at the RSIA of -7°, even though the 4 nozzles of the system are not throttled at the RSIA of -7° either.Compared with the TG, the w can be increased by up to 15.7 %.Meanwhile, compared with design SIA, the w can be increased by up to 6.3 %.Therefore, reducing the RSIA within a reasonable range can increase the w accordingly. .Variation of w with variable RSIAs.Figure 9 shows cross sections of the full circumferential stator outlet for different spanwise direction.Figure 10 shows the distribution of the full circumferential stator outlet Mach number in three spreading directions at different RSIAs.Overall, the average stator outlet Mach number gradually increases as the RSIA decreases, and when the RSIA is less than -3.6°, the corresponding stator outlet Mach number of the inlet nozzle has reached supersonic speeds.If the nozzle is non-admission or the inlet pressure is relatively low, its stator outlet Mach number is smaller near the hub and gradually increases from the hub to the shroud.The Mach number near the shroud already exceeds the Mach number at the stator outlet of the nozzles with higher inlet pressure because the mixing effect in the upstream high-pressure inlet nozzle is more pronounced in the downstream low-pressure region near the shroud.

Effect of RSIA on flow characteristics
Figure 12 shows the distribution of Mach number at stator outlet for different RSIAs.It can be seen that as the RSIA decreases, the average Mach number at the stator outlet shows an increasing trend.When the pressure difference between adjacent nozzles is large, the upstream high-pressure air will have a "push" effect on the downstream low-pressure air, so that the Mach number of the downstream lowpressure air increases, and even exceeds the Mach number of the high-pressure nozzle stator outlet.This "push" effect is more pronounced in the vicinity of the shroud.When the inlet pressure of the upstream nozzle is relatively low or non-admission, a localized high Mach number region is created at the junction with the downstream high-pressure nozzle.Figure 13 shows the static entropy distribution at the stator outlet for different RSIAs.It can be seen that as the RSIA decreases, the average static entropy at the stator outlet gradually decreases and the flow field tends to more uniform.This is because the number of inlet nozzles increases from three to four and the inlet pressure gradually converges to the BP.The high-pressure nozzles have a greater impact on the static entropy distribution in the downstream low-pressure or non-admission region, mainly concentrated near the shroud, which has similar characteristics to the Mach number distribution.Furthermore, the static entropy distribution at midspan (Figure 14) is analyzed for the four operating conditions mentioned above.It can be seen that the air from the high-pressure nozzle outlet expands downstream towards the low-pressure nozzle or the non-admission nozzle outlet, affecting the static entropy distribution at the low-pressure nozzle or non-admission nozzle outlet and their downstream rotor channel.As the RSIA decreases, the angle of attack of the rotor inlet tends to positive angle of attack.There is obvious flow separation at the suction side of the rotor, and the static entropy at the suction side rises significantly, but the average static entropy at the rotor outlet decreases gradually.Figure 15 gives the entropy increase in the chamber, stator, rotor and TV as the RSIA is varied from -7° to 0°.The chamber and stator are calculated together since the entropy increase in the chamber is very small.When the TV is not considered, the entropy increase in the rotor is the largest.For the same number of inlet nozzles, the entropy increase gradually decreases as the RSIA increases.However, when the effect of the TV is considered, the system entropy increase is higher for 4-nozzle inlets than for 3nozzle inlets.For the same number of inlet nozzles, a smaller RSIA corresponds to a lower entropy increase, i.e. the smallest total losses to the system.When the RSIA is -3.6°, the total losses of the system are minimized, which is consistent with the analysis of maximum w.Therefore, under the condition of satisfying the Woutput, a smaller number of nozzles should be chosen for air distribution, and the RSIA should be reduced appropriately so that the nozzle inlet pressure is equal to the BP as far as possible.If system losses are measured in terms of entropy increase, the 3-nozzle inlets method can reduce turbine internal losses by 10.6 % compared with the 4-nozzle inlets method for the same absence of throttling losses.

Conclusion
In this paper, full circumferential numerical simulations of nozzle governing (NG) are carried out for an axial turbine in a compressed air energy storage system.The influence of the relative stator installation angle (RSIA) on the performance of the NG turbine at rated output work is obtained, and the main conclusions are summarized as follows: (1) The specific work of the compressed air energy storage system can be effectively improved by adopting the nozzle governing method.For the same number of inlet nozzles, the specific work can be also increased appropriately when the RSIA is reduced within a certain range.
(2) For the top air storage pressure of 10.0 MPa, when the RSIA is -3.6°, the specific work of the system is maximum, which can be increased by up to 15.7 % compared with throttle governing, and by up to 6.3 % compared with the design stator installation angle.
(3) Under the condition of satisfying the output work, a smaller number of nozzles should be selected for air distribution and the RSIA should be reduced appropriately so that the nozzle inlet pressure is equal to the base pressure as far as possible.

Figure 1 .
Figure 1.NG method of axial turbine.Figure 2. 3D model of axial flow turbine with NG.

Figure 2 .
Figure 1.NG method of axial turbine.Figure 2. 3D model of axial flow turbine with NG.

Figure 7 .
Figure 7. Variation of mass flow rate with variable RSIAs.Figure8shows the variation of the w of the system with RSIA from -7° to 0°.It can be seen that for different number of inlet nozzles, the w tends to increase as the RSIA decreases.Overall, as the RSIA decreases, the w is higher than the design value.At the RSIA of -3.6°, there are only 3 inlet nozzles of the system and the inlet pressure is equal to the BP.The w at the RSIA of -3.6° is slightly higher than that at the RSIA of -7°, even though the 4 nozzles of the system are not throttled at the RSIA of -7° either.Compared with the TG, the w can be increased by up to 15.7 %.Meanwhile, compared with design SIA, the w can be increased by up to 6.3 %.Therefore, reducing the RSIA within a reasonable range can increase the w accordingly.
Figure 8. Variation of w with variable RSIAs.Figure9shows cross sections of the full circumferential stator outlet for different spanwise direction.Figure10shows the distribution of the full circumferential stator outlet Mach number in three spreading directions at different RSIAs.Overall, the average stator outlet Mach number gradually increases as the RSIA decreases, and when the RSIA is less than -3.6°, the corresponding stator outlet Mach number of the inlet nozzle has reached supersonic speeds.If the nozzle is non-admission or the inlet pressure is relatively low, its stator outlet Mach number is smaller near the hub and gradually increases from the hub to the shroud.The Mach number near the shroud already exceeds the Mach number at the stator outlet of the nozzles with higher inlet pressure because the mixing effect in the upstream high-pressure inlet nozzle is more pronounced in the downstream low-pressure region near the shroud.

Figure 9 .Figure 10 .
Figure 9. Cross sections of the full circumferential stator outlet for different spanwise direction.

Figure 11 Figure 11 .
Figure 10.Distribution of the Mach number at full circumferential stator outlet (BP: 10.0 MPa).Figure11shows the distribution of the full circumferential stator outlet air flow angle in three spreading directions at different RSIAs.It can be seen that the flow angle at the downstream of the junction with the high-pressure inlet nozzle and the non-admission nozzle shows negative values and backflow phenomenon occurs.As the RSIA decreases, the backflow area gradually reduces, but the

Figure 12 .
Distribution of Mach number at stator outlet for different RSIAs.

Figure 13 .
Distribution of static entropy at stator outlet for different RSIAs.

Figure 14 .
Figure 14.Distribution of static entropy at midspan under variable RSIAs.Figure15gives the entropy increase in the chamber, stator, rotor and TV as the RSIA is varied from -7° to 0°.The chamber and stator are calculated together since the entropy increase in the chamber is very small.When the TV is not considered, the entropy increase in the rotor is the largest.For the same number of inlet nozzles, the entropy increase gradually decreases as the RSIA increases.However, when the effect of the TV is considered, the system entropy increase is higher for 4-nozzle inlets than for 3nozzle inlets.For the same number of inlet nozzles, a smaller RSIA corresponds to a lower entropy increase, i.e. the smallest total losses to the system.When the RSIA is -3.6°, the total losses of the system are minimized, which is consistent with the analysis of maximum w.Therefore, under the condition of satisfying the Woutput, a smaller number of nozzles should be chosen for air distribution, and the RSIA should be reduced appropriately so that the nozzle inlet pressure is equal to the BP as far as possible.If system losses are measured in terms of entropy increase, the 3-nozzle inlets method can reduce turbine internal losses by 10.6 % compared with the 4-nozzle inlets method for the same absence of throttling losses.

Table 1 .
Main design parameters of axial turbine.Since only one nozzle is in the throttling state for each operating condition and the other nozzles are either fully open or fully closed, it is evident from Guan et al.'s

Table 2 .
NG method under the BP of 10.0 MPa.