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

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

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

Veröffentlicht/Copyright: 31. August 2023

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Aus der Zeitschrift International Journal of Turbo & Jet-Engines Band 41 Heft 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

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Received: 2023-07-11

Accepted: 2023-07-12

Published Online: 2023-08-31

Published in Print: 2024-08-27

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

Schlagwörter für diesen Artikel

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