Direction for High-Performance Supercritical CO₂ Centrifugal Compressor Design for Dry Cooled Supercritical CO₂ Brayton Cycle

Round 1

Reviewer 1 Report

This paper presents supercritical CO2 centrifugal compressor design and evaluation of backsweep angle on the performance. Several comments are listed below:

It seems that this study focused on 1-D method for centrifugal compressors. If so, detailed information of the model should be included, in particular loss models. CFD or experimental results should be included to validate the present model. The blue lines in Figures 4 and 5 are not clear to show the losses. Table 2, what do design conditions mean? Do these compressibility correspond to the temperature shown in Figure 12. What is the design condition for Figure 13? The authors stated that the compressor was for 10 MWe class power conversion system. What is the power and efficiency of different designs? More detailed information should be given for the compressor. There are some typos, e.g., the figure number and the descriptions are not corresponded. Please check carefully and revise.

Author Response

Dear reviewer.

Thank you for your thoughtful comments. It was very helpful to revise the manuscript. For your convenience, ‘C’ is marked for your comment while the answer to your comment is marked with ‘A’.

 

C1. It seems that this study focused on 1D method for centrifugal compressors. If so, detailed information of the model should be included, in particular loss models. CFD or experimental results should be included to validate the present model.

A1. Thank you for the comment. In the original manuscript, section 2.4. “Loss models selection” discusses the reviewer’s requested models as well as the validation results of the utilized model set with experimental data.

 

C2. The blue lines in Figures 4 and 5 are not clear to show the losses.

A2. Thank you for your comment. The loss models are empirical correlations for irreversibility estimation of turbomachinery. Typically, loss models can be categorized into internal losses and external losses. The internal loss is defined as how much the actual process is far from the isentropic process. It affects the efficiency as well as the pressure ratio of the compressor. The external loss is defined as the energy loss outside the main flow path. It is associated with minor flows leaking from the main flow through the compressor. These losses are complex but based on physical phenomena. Thus, authors schematized the flow inside the compressor using blue lines and tried to describe how the losses are generated. However, the authors agree with the reviewer that it is insufficient to use only Figures 4 and 5 to present the process. As a result, the description to supplement Figures 4 and 5 were added to paragraphs 2, 3 and 4 of 2.2 in the revised manuscript as below.

“Each loss mechanism of internal loss is as follows: 1. Incidence loss is derived from non-uniform incidence along the leading edge. It increases the relative velocity in the tangential component at the entrance and has the minimum loss at the optimum incidence angle. 2. Blade loading loss is the fluid momentum loss that is associated with blade surface boundary layer growth in decelerating flows. It is also related to flow separation in the impeller. 3. Skin friction loss is similar to enthalpy loss due to the wall friction of turbulent flow in a duct. However, it does not include the effect of blade surface boundary layers. 4. Clearance loss is defined as the loss due to the flow of fluid from the pressure surface of the blade to the suction surface. It is proportional to the ratio of tip clearance to blade height. Tip clearance is the gap between the rotating impeller and the stationary shroud. 5. Mixing loss is also known as wake-jet loss. It is derived from mixing of the high momentum fluid on the pressure side, namely jet, and the low momentum fluid on the suction side, namely wake. 6. Slip loss assumes that the flow cannot be perfectly guided by impeller blades. It causes the flow angle at the impeller exit leans to the opposite direction of the rotating direction. As a result, the tangential component of absolute velocity at impeller exit decreases as shown in Fig. 7.

Each loss mechanism of external loss is as follows: 1. Leakage loss occurs when the leakage flow of tip clearance is re-entered into the blade passage. 2. The recirculation loss is the enthalpy loss brought about the recirculation of low momentum fluid from the vaneless space back into the impeller flow path. 3. Disk friction loss is due to the wall friction between the back surface of the rotating impeller and the stationary surface.”

 

C3. Table 2, what do design conditions mean?

A3. Thank you for your comment. In this study, the recuperated Brayton cycle, as shown in Figure 2, was adopted for determining the compressor design condition. The recuperated Brayton cycle is a system with one compressor. Compressors are designed to meet the requirements of the cycle. One of the main objectives in this study is to confirm whether the inlet design condition of a compressor affects its performance. Therefore, in order to study the effect of inlet design condition on the compressor performance, five recuperated cycles were first designed to study five different compressors. The design conditions in Table 2 summarize compressor design conditions derived from cycle design for each case. Moreover, the additional description of the compressor design conditions were added to the second paragraph in section 2.5 as follows.

“The design conditions represent the inlet and outlet conditions for the compressor design derived from five different simple recuperated cycle designs. Since the variation of thermodynamic properties near the critical point depends on the compressibility factor, the compressibility factor was used as the representative value for the inlet condition. It is noted that the outlet pressure of all five compressors is all fixed at 20MPa when designing five different cycles studied in this paper.”

 

C4. Do these compressibility correspond to the temperature shown in Figure 12?

A4. Yes, those correspond to Figure 12. To prove that the compressibility factors in Figure 12 and Table 2 are consistent, temperature and pressure values are added to Table 2.

 

C5. What is the design condition for Figure 13?

A5. Thank you for the comment. The design conditions of Figure 13 is now added in section 2.5 as follows.

“Figure 13 is an example of an S-CO₂ compressor impeller after applying the design conditions of case 1 and the design parameters are summarized in Table 2.”

 

C6. The authors stated that the compressor was for 10MWe class power conversion system. What is the power and efficiency of different designs? More detailed information should be given for the compressor.

A6. Thank you for the comment. The power and efficiency of each case are added in Table 3 in the revised manuscript.

Typical compressor design procedures are as follows.

Step 1 – Cycle design. In this process, temperature, pressure and mass flow rate are determined.

Step 2 – Non-dimensional design. It is based on cycle design results and determines specific speed, rotational speed, compressor type (i.e. radial, axial and mixed) and the number of stage.

Step 3 – 1D mean stream-line design. It is based on results in step 2 and determines impeller and diffuser geometry are determined.

Step 4 – Detailed design. It determines the 3D flow path, shaft, seals, bearings and motors and so on.

This study includes up to the step 3 of the above and does not cover the detailed design. The results of Step 1 and 2 are summarized in section 2.5 and design conditions are summarized in Tables 2 and 3. The design parameters for the 1D mean stream-line design are summarized in section 2.5, design parameters in Table 2, and in section 3.1. The flow path of Figure 13 was generated using 1D design results. Bezier curves are used for the interpolation from inlet to outlet.

 

C7. There are some typos, e.g., the figure number and the descriptions are not corresponded. Please check carefully and revise.

A7. Thank you for your comment. It is now corrected

Author Response File: Author Response.docx

Reviewer 2 Report

Results figures and tendencies can be better explained

Author Response

Dear reviewer.

Thank you for your thoughtful comments. It was very helpful to revise the manuscript. For your convenience, ‘C’ is marked for your comment while the answer to your comment is marked with ‘A’.

 

C1. Results figures and tendencies can be better explained.

A1. Thank you for the comment. Firstly, as in the previous comment, the disagreement between descriptions and figure numbers in “Results” section hinders comprehension of this paper. The authors revised to match figures to descriptions in the revised version. Also, we tried to provide a better explanation of the results as below. The red part is a newly added discussion to the manuscript.
“Compressor performance was examined when the angle varied from 0 ^o to -77 ^o while using the design parameters summarized in Table 2. As shown in Fig. 14, the S-CO₂ centrifugal compressor showed the best efficiency at -70 ^o, which is larger than the typical design value for the air centrifugal compressor. Also, in all cases, the total to total efficiency tends to increase as its angle at the impeller exit increases. The S-CO₂ compressor has the best efficiency of 84% at the backsweep angle of - 70 ^o . It is an increase of about 3% in comparison with the recommended design region. Despite the rapid change in properties near the critical point, the compressor efficiency is insensitive to the change in the compressibility factor.
Due to the potential structural issue of the impeller in the low density fluids, such as air and helium, the backsweep angle is generally limited to -50 ^o. Fig. 15 explains why large backsweep angle involves high centrifugal stress level. The angle of absolute velocity leaving the impeller decreases as the backsweep angle increases when it operates under the same operating conditions. As a result, a higher peripheral speed is required as the backsweep angle to maintain identical outlet pressure and consequently it causes greater stresses. Fig. 16 summarizes the preliminary structural safety margin using the tip speed which is an important criterion for the centrifugal stress level. In spite that the safety margin decreases as the compressibility factor increases, an S-CO₂ compressor is generally less affected by the structural issues in all cases. The structural limit of centrifugal stress is set to be the same value of the air centrifugal compressor for the same design variables summarized in Table 2 and -50 ^o of backward sweep angle. Also, Fig. 17 supports why the S-CO₂ compressor has smaller centrifugal stress than the air compressor thermodynamically. S-CO₂ requires only a few hundredth of the enthalpy of air when it increases the same amount of pressure. It means that the work consumption for compression is significantly reduced when the S-CO₂ compressor increases the same amount of pressure compared to the air compressor. Thus, smaller tip speed is requires and this results is smaller centrifugal stress in the S-CO₂ compressor.
The adopted loss models do not cover irreversibility caused by shock wave because it assumes a centrifugal compressor is operating in the subsonic region. Since the speed of sound is substantially decreased near the critical point as shown in Fig. 18, a high Mach number may occur in low speed region. As aforementioned, the radius of an impeller increases as the backsweep angle at impeller exit increases. Thus, the relative Mach number needs to be checked whether it exceeds unity or not. Fig. 19 shows that the relative Mach numbers are under the subsonic region in all cases. It proves that the additional shock loss does not need to be included and the results of Fig. 14 are still valid. Also, because of the low Mach number in the S-CO₂ compressor, the variation of compressibility factor does not impact on its aerodynamic design in spite of its operation near the critical point where the compressibility factor change is substantial.
In order to understand the reason why the backsweep angle change affects the efficiency, the compressor loss distribution with varying angle was analyzed as shown in Figs. 20 to 23. It is again noted that the percentage of blade loading loss is minimized at -70 ^o which achieves the highest efficiency. Figure 20 shows the change in blade loading loss, clearance loss and mixing loss with increasing backsweep angle. All three losses are associated with the pressure loading on the blade. The blade loading loss is due to the flow separation resulting from the pressure load difference between the suction side and the pressure side. In this respect, the inclination of the blades to the radial direction reduces the pressure loading and it alleviates the secondary flow and the tip clearance flow. As the backsweep angle increases, less pressure loading per unit length on the blade is expected, which results in reducing the strength of the vortex at the blade tip. This means that the clearance loss decreases as the backsweep angle increases. Mixing loss is derived from mixing of the high momentum fluid on the pressure side and the low momentum fluid on the suction side. Decrease of pressure load means a reduction in difference of fluid momentum between pressure side and suction side, and the mixing loss decreases as the backsweep angle increases. This physical insight corresponds to the results of Fig. 20. Also, as the blade angle becomes more flat, the radius increases as shown in Fig. 24. This is because the pressure ratio of the compressor is assumed to be constant even if the backsweep angle changes. As the backsweep angle increases, smaller tangential component of absolute velocity is obtained. As a result, the diameter of the impeller is increased, as shown in Fig. 24, to maintain the same outlet pressure. Thus, as shown in Figs. 21 and 22, the skin friction loss, the leakage loss and the disk friction loss tend to increase because those are proportional to the impeller size. The compressor design is optimized to have the best efficiency as the backsweep angle changes. Therefore, the optimal incidence angle was chosen to minimize incidence loss, and consequently, as shown in Fig. 23, the incidence loss is always zero regardless of the change in the backsweep angle.
Fig. 25 shows effects of the off-design performance and the surge limit while backsweep angle varies. As shown in Fig. 15, if the mass flow rate decreases, the angle of relative velocity, W2, remains the same. On the other hand, the tangential component of the absolute velocity, Cw2, increases. Because the product of U2 and Cw2 has increased in comparison with the high mass flow rate condition, the work per unit of mass flow rate at the low mass flow rate condition has increased considerably. Thus, a backward sweep impeller can achieve higher pressure ratio as the mass flow rate is decreased. Also, this feature allows stable compressor operation in wider range because the surge limit is conservatively set as the point where the gradient of pressure ratio becomes zero.”

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

The authors have addressed all the comments and revised the manuscript accordingly. The paper can be accepted for publication on Applied Sciences.