Study on one-dimensional performance prediction of multi-stage axial turbine based on the blade height

Ke-wen Xu; Ze Yuan; Zhao-lin Li; Guo-qiang Yue

doi:10.1515/tjj-2023-0058

Article

Study on one-dimensional performance prediction of multi-stage axial turbine based on the blade height

Ke-wen Xu , Ze Yuan , Zhao-lin Li and Guo-qiang Yue

Published/Copyright: August 31, 2023

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From the journal International Journal of Turbo & Jet-Engines Volume 41 Issue 3

Abstract

As turbine operating conditions change, the blade height and tip clearance undergo continuous alterations due to the combined effects of thermal stress, aerodynamic forces and centrifugal forces, subsequently influencing the turbine performance. To take this effect into account in turbine performance prediction, this study considers the influence of fluid-heat-structure coupling on blade height and tip clearance and establishes a one-dimensional comprehensive prediction method for multi-stage axial turbine performance considering blade height. When compared with experimental results from a four-stage axial turbine, by considering the fluid-thermal-solid coupling effects, the average relative error in total pressure ratio prediction is reduced from 3.76 % to 1.99 % and the average relative error in total temperature ratio prediction is reduced from 2.03 % to 1.26 %. Compared with the traditional flow prediction method, the prediction results of turbine characteristics considering blade height and tip clearance changes in this paper are closer to the experimental results.

Keywords: blade height; fluid-thermal-solid coupling; multi-stage axial turbine; performance prediction; tip clearance

Corresponding author: Guo-qiang Yue, Turbomachines Laboratory, Department of Power and Energy Engineering, Harbin Engineering University, Harbin, 150000, China, E-mail: yuegq@hrbeu.edu.cn

Acknowledgment

The authors wish to thank the support of the National Science and Technology Major Project (No. 2019-Ⅰ-0007-0007).

Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Research funding: None declared.
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

Nomenclature

A: area [m²]
a: coefficient of linear expansion [−]
b: chord [m]
c: absolute velocity [m/s]
c _p: constant pressure specific heat [J/(kg K)]
c _v: constant volume specific heat [J/(kg K)]
D: diameter [m]
E: elastic modulus [Pa]
F: force [N]
G: mass flow rate [kg/s]
H: stator or rotor height [m]
h: coefficient of convective heat transfer [W/(m² K)]
k: heat ratio coefficient [−]
K _P: specific heat at constant pressure [−]
l: radial deflection [mm]
M _a: mach number [−]
N: rotating speed of rotor [rpm]
o: throat width [mm]
P: pressure [Pa]
q: reduced flow [−]
Q: heat [kJ]
R: radius [m]
Rg: gas constant [−]
s: pitch [mm]
T: temperature [K]
u: convected velocity [m/s]
w: relative velocity [m/s]
Y _AMDCKO: total loss coefficient for blade row in AMDCKO loss system [−]
Y _P: profile loss coefficient [−]
Y _S: secondary loss coefficient [−]
Y _shock: component of profile loss coefficient due to leading edge shock [−]
Y _TE: trailing edge loss multiplier [−]
Y _TL: tip clearance loss coefficient [−]

Greek letters

α _m: mean gas angle defined in equation [°]
β: relative flow angle [°]
β _k: stator and rotor metal angle [°]
∆T: temperature difference [K]
∆E _TE: trailing edge K.E. loss coefficient [−]
ε: strain [mm]
ε _θ ′: thermal strain [mm]
ε _θ ″: aerodynamic strain [mm]
η: efficiency [−]
λ ₀: turbine inlet velocity coefficient [−]
λ _c: absolute velocity coefficient [−]
λ _w: relative velocity coefficient [−]
λ _u: linear velocity coefficient [−]
μ: poisson ratio [−]
π: turbine expansion ratio [−]
ρ: density [kg/m³]
σ: stress [Pa]
τ: turbine temperature ratio [−]
τ′: tip clearance of blade [mm]
φ: stator speed coefficient [−]
ψ: rotor speed coefficient [−]
χ _AR: aspect ratio function [−]
χ _i: aeriation coefficient of profile loss with incidence for typical turbine [−]
χ _Re: reynolds number correction factor [−]
ω: angular speed [rad/s]

Superscript

*: stagnation parameter

Subscript

a: inside the casing
b: outside casing
c: inner side of turbine disc
cf: centrifugal force
cr: critical state
d: outside of turbine disc
e: blade root
f: blade tip
i: mixture component
in: inlet
j: number of sections
rot: rotor
st: stator
out: outlet
0: inlet of stator blade
1: outlet of stator blade
2: outlet of rotor blade
r: radial
t: circumferential
p: centrifugal force at any blade section
pl: plastic stress of section
cold: cold tip clearance of blade
blade: radial displacement of blade tip
casing: radial displacement of casing inner diameter
disc: radial displacement of disc outer diameter

References

1. Bai, CJ, Wang, WC. Review of computational and experimental approaches to analysis of aerodynamic performance in horizontal-axis wind turbines. Renew Sustain Energy Rev 2016;63:506–19. https://doi.org/10.1016/j.rser.2016.05.078.Search in Google Scholar

2. Van Eck, H, Van der Spuy, SJ, Von Backstrom. Development of a one-dimensional code for the initial design of a micro gas turbine mixed flow compressor stage. Int J Turbo Jet Engines 2022; Early Access. https://doi.org/10.1515/tjj-2022-0008.Search in Google Scholar

3. Gao, J, Zheng, Q, Niu, XY, Yue, GQ. Aerothermal characteristics of a transonic tip flow in a turbine cascade with tip clearance variations. Appl Therm Eng 2016;107:271–83. https://doi.org/10.1016/j.applthermaleng.2016.06.155.Search in Google Scholar

4. Ainley, DG, Mathieson, G. A method of performance estimation for axial-flow turbines. British ARC R&M;2974:1951.Search in Google Scholar

5. Dunham, J, Came, PM. Improvements to the ainley-mathieson method of turbine performance prediction. ASME J Eng Gas Turbines Power 1970;92:252–6. https://doi.org/10.1115/1.3445349.Search in Google Scholar

6. Kacker, SC, Okapuu, U. A mean line prediction method for axial flow turbine efficiency. ASME J Eng Gas Turb Power 1982;104:111–9. https://doi.org/10.1115/1.3227240.Search in Google Scholar

7. Glassman, AJ. Design geometry and design/off-design performance computer codes for compressors and turbines. Cleveland: Lewis Research Center; 1995. NASA/CR198433 (in American).Search in Google Scholar

8. Teia, L. New insight into aspect ratio’s effect on secondary losses of turbine blades. ASME J Turbomach 2019;11:141–69. https://doi.org/10.1115/1.4044079.Search in Google Scholar

9. Liu, YM, Patrick, H, ZhengpingZ, Frank, B. A reliable update of the ainley and mathieson profile and secondary correlations. Int J Turbo Propul Power 2022;7:14. https://doi.org/10.3390/ijtpp7020014.Search in Google Scholar

10. Juangphanich, PC, Maesschalck, C, Paniagua, G. From conceptual 1-D design towards full 3-D optimization of a highly loaded turbine stage. Texas: AIAA Paper; 2017. No. 2017-0110.10.2514/6.2017-0110Search in Google Scholar

11. Min, LY, Hendrick, P, Zou, Z. Statistical and computational evaluation of empirical axial turbine correlations in design of centrifugal turbines. ASME J Turbomach 2022;144:041002.10.1115/1.4052525Search in Google Scholar

12. Agromayor, R, Müller, B, Nord, LO. One-dimensional annular diffuser model for preliminary turbomachinery design. Int J Turbomach Propuls Power 2019;4:31. https://doi.org/10.3390/ijtpp4030031.Search in Google Scholar

13. Agromayor, R, Nord, LO. Preliminary design and optimization of axial turbines accounting for diffuser performance. Int J Turbomach Propuls Power 2019;4:32. https://doi.org/10.3390/ijtpp4030032.Search in Google Scholar

14. Chiong, MS, Rajoo, S, Romagnoli, A, Costall, AW, Martinez-Botas, RF. Integration of meanline and one-dimensional methods for prediction of pulsating performance of a turbocharger turbine. Energy Convers Manag 2014;81:270–81. https://doi.org/10.1016/j.enconman.2014.01.043.Search in Google Scholar

15. Liu, XH, Jin, DH, Gui, XG. Investigation and verification of the aerodynamic performance of a fan/booster with through-flow method. J Therm Sci 2018;27:103–10. https://doi.org/10.1007/s11630-018-0990-7.Search in Google Scholar

16. Gu, CW, Li, HB, Yin, S. Development of an aero-thermal coupled through-flow method for cooled turbines. Sci China Technol Sci 2015;58:2060–71. https://doi.org/10.1007/s11431-015-5941-x.Search in Google Scholar

17. Chaibakhsh, A, Amirkhani, S. A simulation model for transient behaviour of heavy-duty gas turbines. Appl Therm Eng 2018;132:115–27. https://doi.org/10.1016/j.applthermaleng.2017.12.077.Search in Google Scholar

18. Wang, BT, Song, ZY, Zou, WZ, Yang, H, Wen, M, Zhou, K, et al.. Rapid performance prediction model of axial turbine with coupling one-dimensional inverse design and direct analysis. Aero Sci Technol 2022;130:107828. https://doi.org/10.1016/j.ast.2022.107828.Search in Google Scholar

19. Xiang, H, Chen, J, Cheng, J, Song, X. Blade number selection for a splittered mixed-flow compressor impeller using improved loss model. Int J Turbo Jet Engines 2022;39:549–64. https://doi.org/10.1515/tjj-2020-0008.Search in Google Scholar

20. XiaomeiG, Chongyang, J, Heng, Q, Zuchao, Z. The influence of tip clearance on the performance of a high-speed inducer centrifugal pump under different flow rates conditions. Processes 2023;11:239. https://doi.org/10.3390/pr11010239.Search in Google Scholar

21. Hennecke, DK, Trappmann, K. Turbine tip clearance control in gas turbine engine. NASA 1983;N83-29254.Search in Google Scholar

22. Decastro, JA, Melcher, KJ. A study on the requirements for fast active turbine tip clearance control systems. Florida: AIAA Paper; 2004. No. 2004-4176.10.2514/6.2004-4176Search in Google Scholar

23. Javier, A, Kypuros, PD, Rodrigo, C, Afredo, M. Improved temperature dynamic model of turbine subcomponents for facilitation of generalized tip clearance control. In: NASA. Texas A & M University; 2004, NAG3-2587.Search in Google Scholar

24. Merkler, R, Staudacher, S, Schölch, M, Schulte, H. Description of thermal effects in aero engi nes by matrices. New York: ISABE2005-1071, 2005 (in American).Search in Google Scholar

25. Merkler, R, Staudacher, S, Schlch, M, Schulte, H, Schmidt, KJ. Simulation of clearance changes and mechanical stresses in transient gas turbine operation by a matrix method. Arizona: AIAA Paper; 2005. No. 2005-4022.10.2514/6.2005-4022Search in Google Scholar

26. Qi, WK, Chen, W. Tip clearance numerical analysis of an aero-engine HPT. J Nanjing Univ Aeronaut Astronaut 2003;35:63–7.Search in Google Scholar

27. Qi, XM, Pu, Y, Zhun, JH. 3-D numerical analysis of the tip clearance of an aero-engine high pressure turbine. J Aero Power 2008;23:904–8.Search in Google Scholar

28. Khalil, KM, Mahmoud, S, Al-Dadah, RK. Experimental and numerical investigation of blade height effects on micro-scale axial turbines performance using compressed air open cycle. Energy 2020;211:118660. https://doi.org/10.1016/j.energy.2020.118660.Search in Google Scholar

29. Yang, H, Chen, J, Pang, X. Wind turbine optimization for minimum cost of energy in low wind speed areas considering blade length and hub height. Appl Sci 2018;8:1202. https://doi.org/10.3390/app8071202.Search in Google Scholar

30. Khustochka, O, Yepifanov, S, Zelenskyi, R, Przysowa, R. Estimation of performance parameters of turbine engine components using experimental data in parametric uncertainty conditions. Aerospace 2020;7:6. https://doi.org/10.3390/aerospace7010006.Search in Google Scholar

31. Liu, H, Zeng, Z, Guo, K. Numerical analysis on hydrogen swirl combustion and flow characteristics of a micro gas turbine combustor with axial air/fuel staged technology. Appl Therm Eng 2023;219:119460. https://doi.org/10.1016/j.applthermaleng.2022.119460.Search in Google Scholar

32. Rathod, UH, Kulkarni, V, Saha, UK. On the application of machine learning in savonius wind turbine technology: an estimation of turbine performance using artificial neural network and genetic expression programming. ASME J Energ Resour 2022;144:061301. https://doi.org/10.1115/1.4051736.Search in Google Scholar

33. Casati, E, Vitale, S, Pini, M, Persico, G, Colonna, P. Centrifugal turbines for mini-organic rankine cycle power systems. ASME J Eng Gas Turb Power 2014;136:122607. https://doi.org/10.1115/1.4027904.Search in Google Scholar

Received: 2023-07-11

Accepted: 2023-07-12

Published Online: 2023-08-31

Published in Print: 2024-08-27

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Articles in the same Issue

https://doi.org/10.1515/tjj-2023-0058

Keywords for this article

blade height; fluid-thermal-solid coupling; multi-stage axial turbine; performance prediction; tip clearance