Optimal Design of a Ljungström Turbine for ORC Power Plants: From a 2D model to a 3D CFD Validation
Round 1
Reviewer 1 Report
The authors design Ljungström type turbine considering five different organic working fluids. The turbine meanline design is based on Euler work equation and velocity triangles of turbine stages with design guidelines proposed by Kearton and Shepherd. Based on above-mentioned method, the authors propose a kinematic efficiency, which is used to optimize turbine using the meanline design. In addition, the authors investigate the effect of design parameters to the isentropic efficiency of the turbine with different loss models. CFD analysis of designed turbine’s first two stages are done and the results are compared to the meanline design predictions.
The article is well written and organized. However, there are some comments authors should address:
- Motivation of the article is not clear and should be clearly stated at the introduction.
- What is the novelty of the article?
- Validation of the developed mean line model should be presented.
- In line 15 what is @-T curve?
- In line 42, does low-T mean low temperature?
- In line 109 it is stated the all blades have same cross-section? What does it mean? Same shape, area etc?
- The units could be shown in Tables for better readability
- Line 141 (after fig. 8) starts with equation. Is there some text missing?
- Use creek letter at the axis in Figs 8, 9 and 10
- Give values of constraints when suitable in table 7.
- Specific speed could be added to Table 8.
- Reference (or short explanation) for equation 16. What is P in this equation? How much is the safety factor?
- What is regarded as manufacturing limit for the axial blade length?
- Show grid independency of CFD simulations
- Figure of grid(s) would be very illustrative
- It is not clearly stated but only first two stages were modelled. The authors should model the whole turbine or clearly state reasons not to do so.
- How fluid properties are calculated in CFD simulations?
- Comparison meanline results and CFD results is rather superficial. Analysis that is more thorough should be done.
- Fig 15 and analysis related to it should be given in the result part of the paper not in Conclusions.
- Conclusions are rather vague. What are the main findings of the study? What are the authors’ recommendations?
- Is the last sentence of the conclusions correct? Usually the longer the blade larger the wall friction losses.
Author Response
Point 1: Motivation of the article is not clear and should be clearly stated at the introduction.
Response 1: Introduction has been accordingly modified
Point 2: What is the novelty of the article?
Response 2: as clearly stated in the introduction for the range of power 20 – 70 kW the choice of the proper expander to be selected for a plant which use organic fluids as thermal vector is an open point for which a preferred choice is not yet defined. This article proposes an alternative solution to those already found in literature (i.e. scroll/screw expanders or radial in-flow and fixed-rotating radial out-flow turbines)
Point 3: Validation of the developed mean line model should be presented.
Response 3: As stated on page 9, the CFD simulations are intended to be the “validation” of the mean streamline calculations. For the geometry examined here, there are no experimental results to draw from.
Point 4: In line 15 what is @-T curve?
Response 4: Quite obviously a typo, corrected in the revised paper
Point 5: In line 42, does low-T mean low temperature?
Response 5: confirmed, it stands for low temperature thermal sources for which water use is not suitable because of its physical properties
Point 6: In line 109 it is stated the all blades have same cross-section? What does it mean? Same shape, area etc?
Response 6: yes, confirmed. These are rather standard assumptions, suggested in Reff 12 & 13
Point 7: The units could be shown in Tables for better readability
Response 7: Tables modified accordingly
Point 8: Line 141 (after fig. 8) starts with equation. Is there some text missing?
Response 8: Please refer to revised text
Point 9: Use creek letter at the axis in Figs 8, 9 and 10
Response 9: axes are now well identified by labels and scale
Point 10: Give values of constraints when suitable in table 7
Response 10: Done
Point 11: Specific speed could be added to Table 8.
Response 11: It is clear that the specific speed is reasonably relevant only for the inlet of the first blade row: the corresponding values have been added to Table 8
Point 12: Reference (or short explanation) for equation 16. What is P in this equation? How much is the safety factor?
Response 12: Eqtn. 16 is a super-standard formula used in the first-approximation sizing of a solid metal shaft. K is cubed because the formula has been solved here for d. K includes shape (grooves, splines…) and fatigue effects and thus leads to the adoption of a larger-than- theoretical diameter. In our work, K=1.3
Point 13: What is regarded as manufacturing limit for the axial blade length?
Response 13: This topic would require a separate study, not included in this paper. In this work, we assumed an axial length of 1,00 cm but this does not influence the validity of the paper since (as explained and supported by our calculations) the lower the blade length the higher the efficiency. As for the upper limit, the problem becomes very complex, because dynamic effects come into play (blade excited vibrations etc.), and is outside of the limits of this study.
Point 14: Validation of the developed mean line model should be presented.
Response 14: See response to Point 3 above
Point 15: Show grid independency of CFD simulations
Response 15: Figures of the mesh and relevant convergence of the results have been shown in Figures 13 and 14.
Point 16: Figure of grid(s) would be very illustrative
Response 16: With all due respect, we disagree with the Reviewer. In a purely academic sense, the idea that a visualization of the grid provides insight into the accuracy of the results is correct…but with 2.6 106 points, figures of grids are rather useless… to try to satisfy the Reviewer’s request though, and only for exemplary purposes, we have added two mesh details for the 2D simulation, which are easier to visualize
Point 17: It is not clearly stated but only first two stages were modelled. The authors should model the whole turbine or clearly state reasons not to do so
Response 17: The explanation is implicit in eqtn. 13: with the selected design specifications, nstages turned out (very conveniently indeed!) to be equal to 2
Point 18: How fluid properties are calculated in CFD simulations?
Response 18: ANSYS Fluent has an internal utility that allows for the specification of the fluid properties (there are also some “standard fluids” to choose from). For what the cycle calculations are concerned, they were executed in MATLAB, with fluid properties from a commercially available utility, COOLPROP (see page 2).
Point 19: Comparison meanline results and CFD results is rather superficial. Analysis that is more thorough should be done.
Response 19: The CFD simulation is intended to validate the meanline analysis. The idea here is obviously that of using the latter for a first sizing of the stages, and then perform the expensive CFD analysis to refine the results. This reflects our goal: to demonstrate that a simple meanline analysis ought not to be discarded as a preliminary design tool. The theoretical treatment developed on pages 6 through 8 (and the results displayed in figures 8 and 9) prove this point quite convincingly.
Point 20: Fig 15 and analysis related to it should be given in the result part of the paper not in Conclusions.
Response 20: Done (please in the revised version refer to Figure 17)
Point 21: Conclusions are rather vague. What are the main findings of the study? What are the authors’ recommendations?
Response 21: Conclusions were rewritten
Point 22: Is the last sentence of the conclusions correct? Usually the longer the blade larger the wall friction losses.
Response 22: It refers to the span-wise length: the longer the axial length of the blade, the more distant the counter rotating disks that provide endwall friction losses substantially higher than blade friction losses.
Reviewer 2 Report
Report
Optimal Design of a Ljungström Turbine for ORC Power 2 Plants: from a 2-D model to a 3-D CFD Validation by Coronetta and Sciubba
One of the main problems for more widespread applicability of ORC-s is the availability of well-applicable turbines. The Ljungström turbines can be a promising candidate, therefore a good CFD-based study can be great help for engineers.
Generally, the manuscript is well-written, the results are good and well-established, but there are a few minor and a few „medium” problems (I would not call it major one, but certainly needs some revision).
Minor ones:
- Figure 2: as I know, only diagrams with enthalpy axes are referred as Mollier-diagram
- Very few mis-types, like “…throughFigure…” in line 98 or “…throughTable…” in line 97.
- Automatic table and figure referencing causes some problems, like “…Tables Table 1 throughTable 5 present the thermodynamic properties of the considered fluids 97 at the relevant stations in the process; figures Figure 3 throughFigure 7…”, they should be corrected manually to “Tables from Table 1 through Table 5…”
- Probably also caused by this automatic referencing, some numbers or characters are bold, others are normal, for example in the previous sentence in Table 1 table is normal, 1 is bold, while in Table 5, the situation is reversed.
„Medium” problems:
- line 60-61 “…first, since the source is at low temperature, the fluid should have a low critical pressure…”. Well I am originally a Physicist with Physical Chemistry background, but I do not understand this part; please explain it (not just by citing other papers).
- The choice of colours of the figures is … well, quite terrible. Some of the lines can hardly be seen on the monitors and almost invisible in printed form. Light-yellow T-s diagram (figure 3) is not the best way for visualization. I would strongly advise to use darker colours and thicker lines
- Some of the chosen working fluids are dry ones. One of the reasons to choose dry working fluid is to avoid droplets upon expansion, without previously superheating the system (see for example Györke et al., Energy, 145 (2018) 288-300). Please, explain your choice to use superheating for example for R601, instead of varying the mass flows of heating oil and working fluid to reach higher evaporation temperature on a slightly higher pressure, then expand from point 5 (Fig. 4) without superheating; in this way the efficiency would be higher.
In general, the manuscript can be accepted after correcting these problems.
Author Response
Point 1: Minor ones:
Figure 2: as I know, only diagrams with enthalpy axes are referred as Mollier-diagram
Very few mis-types, like “…throughFigure…” in line 98 or “…throughTable…” in line 97.
Yes, we use the denomination “mollier” in a rather extended sense… hope this does not cause any substantial problems
Automatic table and figure referencing causes some problems, like “…Tables Table 1 throughTable 5 present the thermodynamic properties of the considered fluids 97 at the relevant stations in the process; figures Figure 3 throughFigure 7…”, they should be corrected manually to “Tables from Table 1 through Table 5…”
Corrected
Probably also caused by this automatic referencing, some numbers or characters are bold, others are normal, for example in the previous sentence in Table 1 table is normal, 1 is bold, while in Table 5, the situation is reversed.
Corrected
Point 2: „Medium” problems:
line 60-61 “…first, since the source is at low temperature, the fluid should have a low critical pressure…”. Well I am originally a Physicist with Physical Chemistry background, but I do not understand this part; please explain it (not just by citing other papers).
Low critical p is, for the fluids considered, combined with low critical T: what we mean is that the fluid ought to be able to substantially superheat even when in contact with a low-T heating source
The choice of colours of the figures is … well, quite terrible. Some of the lines can hardly be seen on the monitors and almost invisible in printed form. Light-yellow T-s diagram (figure 3) is not the best way for visualization. I would strongly advise to use darker colours and thicker lines
Agree. On the screen, the colours do not pose problems, but in a printed version it’s a different story. Corrected
Some of the chosen working fluids are dry ones. One of the reasons to choose dry working fluid is to avoid droplets upon expansion, without previously superheating the system (see for example Györke et al., Energy, 145 (2018) 288-300). Please, explain your choice to use superheating for example for R601, instead of varying the mass flows of heating oil and working fluid to reach higher evaporation temperature on a slightly higher pressure, then expand from point 5 (Fig. 4) without superheating; in this way the efficiency would be higher.
In general, the manuscript can be accepted after correcting these problems.
The mass and the T of the heating oil are fixed for comparison purposes, so that the Qin is the same for all cycles. The red curve (line) in figure 4 represents the oil temperature: the pinch point is necessarily located at the “cold” side.
Reviewer 3 Report
This is an interesting paper for the design of turbomachinery topic. It is well written and the methodology and results are clear. The research on this topic is important, devices for dispersed power generation systems are constantly being developed. This paper can be useful for the scientific and technical community. It would be an added value to the state of the knowledge related to such turbines. The paper can be recommended for publication.
Author Response
Point 1:
This is an interesting paper for the design of turbomachinery topic. It is well written and the methodology and results are clear. The research on this topic is important, devices for dispersed power generation systems are constantly being developed. This paper can be useful for the scientific and technical community. It would be an added value to the state of the knowledge related to such turbines. The paper can be recommended for publication.
Response 1: Many Thanks!
Round 2
Reviewer 2 Report
The manuscript has been improved and can be accepted now. Be aware, that automatic referencing till creating problems, like in line 277: „Error! Reference source not found”.
