A Parametric Blade Design Method for HighSpeed Axial Compressor
Abstract
:1. Introduction
 1.
 Flexibility
 2.
 Local adjustability
 
 Partial blade surface could be altered according to design needs while other parts of the airfoil are kept fixed, which is useful in blade optimizations.
 3.
 Usability
 
 The quantity of parameters is limited to a suitable level to make the method easy to use.
 
 The parameters have clear, intuitive effects on the blade geometry [24].
2. TwoDimensional Blade Airfoil Design
2.1. Airfoil Definition
2.2. Normalized Camber Angle Distribution ${f}_{1}\left(x\right)$
2.3. Normalized Thickness Distribution ${f}_{2}\left(x\right)$
3. From Airfoils to ThreeDimensional Blade Design
Stacking of Blade Element
4. Numerical Simulation Method Verification
5. Application Case: Efficient Transonic Axial Fan Design
5.1. Introduction of the Transonic Axial Fan System
5.2. Blade Design
5.3. Aerodynamic Performance
6. Conclusions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
$c$  Airfoil aerodynamic chord (mm), length of straightline connecting the origin point and terminal point of camberline 
$\dot{m}$  Mass flow rate $(\mathrm{kg}/\mathrm{s}$) 
$i$  Incidence angle, $i={\beta}_{1}{\beta}_{1\mathrm{m}}$ 
$\mathrm{k}$  Specific heat ratio, k = 1.4 
$p$  Static pressure (Pa) 
${p}_{\mathrm{r}}$  Static pressure ratio 
$r$  Radius (mm) 
${t}_{\mathrm{m}}$  Airfoil maximum relative thickness 
${t}_{\mathrm{LE}}$  Leading edge relative thickness 
${t}_{\mathrm{TE}}$  Trailing edge relative thickness 
$x$  Normalized coordinates in chordwise direction, $x=\xi /c$ 
$y$  Normalized coordinates in direction perpendicular to chordwise 
${y}_{\mathrm{c}}$  Centerline coordinates in direction perpendicular to chordwise 
$C$  Airfoil chord (mm) 
D  Diameter of blade passage inscribed circle 
DF  Diffusion factor, $DF=1{W}_{2}/{W}_{1}+\left({W}_{1}{W}_{2}\right)/\left(2\sigma {W}_{1}\right)$ for rotor; $DF=1{V}_{2}/{V}_{1}+\left({V}_{1}{V}_{2}\right)/\left(2\sigma {V}_{1}\right)$ for stator 
LE  Leading edge 
$\mathrm{M}a$  Mach number 
$N$  Relative rotating speed, the ratio of actual rotating speed to design rotating speed 
$P$  Total pressure (Pa) 
${P}_{\mathrm{m}}$  Maximum thickness chordwise location 
$R$  Blade relative height 
${R}_{\mathrm{P}}$  Total pressure recovery coefficient, ${R}_{\mathrm{P}}={P}_{2}/{P}_{1}$ 
$S$  Spacing (mm) 
$T$  Total temperature (K) 
TE  Trailing edge 
$X$  Axial coordinates (mm) 
$\overline{X}$  Normalized axial coordinates 
$Y$  Tangential coordinates (mm) 
$Z$  Radial coordinates (mm) 
$\delta $  Deviation angle (degree) 
$\beta $  Flow angle measured from axial direction (degree) 
${\beta}_{\mathrm{m}}$  Blade metal angle measured from axial direction (degree) 
${\beta}_{\mathrm{s}}$  Blade LE suction surface angle measured from axial direction (degree), ${\beta}_{\mathrm{s}}={\beta}_{\mathrm{m}}+{\mathsf{\delta}}_{\mathrm{LE}}$ 
$\epsilon $  Blade surface angle, the angle between surface tangent line and axial direction (degree) 
$\eta $  Adiabatic efficiency, $\eta =\left({\pi}^{\mathrm{k}1/\mathrm{k}}1\right)/\left(1{T}_{2}/{T}_{1}\right)$ 
$\theta $  Camber angle (degree) 
${\theta}_{0}$  Leading edge construction angle (degree) 
${\phi}_{R}$  Flow coefficient, ${\phi}_{R}={V}_{z}/{U}_{t}$ 
$\chi $  Suction surface incidence angle, $\chi ={\beta}_{1}{\beta}_{\mathrm{s}}$ 
${\psi}_{R}$  Load coefficient, ${\psi}_{R}=Lu/{U}_{t}^{2}$ 
$\xi $  Coordinates in chordwise direction (mm) 
$\pi $  Total pressure ratio, $\pi ={P}_{2}/{P}_{1}$ 
$\sigma $  Solidity, $\sigma =C/S$ 
$\Delta {S}_{1}$  Displacement distance of airfoil center of gravity for sweep 
$\Delta {S}_{2}$  Displacement distance of airfoil center of gravity for bow 
Subscripts
1  Inlet 
2  Outlet 
ax  Axial direction 
is  Isentropic 
C  Chocked 
D  Value at design work condition 
SG  Staggered 
Appendix A
Appendix A.1. The Derivation of SubFunction ${T}_{1}\left(x\right)$ and ${T}_{2}\left(x\right)$ from Basic Polynomial
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Strength Coefficient  Location Coefficient  Adjustable Coefficients  

$${S}_{1}$$

$${L}_{1}$$

$${A}_{1},{A}_{2}$$

$${B}_{1},{B}_{2},{B}_{3}$$

LE&TE Relative Thickness  Maxim. Thickness Location  Adjustable Coefficients  

$${t}_{\mathrm{LE}}$$

$${t}_{\mathrm{TE}}$$

$${P}_{\mathrm{m}}$$

$${V}_{1}$$

$${V}_{2}$$

$${V}_{3}$$

Topology Parameter  Grid 1  Grid 2  Grid 3  Grid 4 

Streamwise nodes  89  129  169  209 
Pitchwise nodes  69  81  101  113 
Pitchwise nodes across the Oblock  21  29  37  45 
Radial nodes  61  
Total nodes of mesh  1356 k  2008 k  2917 k  3828 k 
Flow Coefficient, ${\mathit{\phi}}_{\mathit{R}}$  Load Coefficient, ${\mathit{\psi}}_{\mathit{R}}$  

Stage 1  0.36  0.34 
Stage 2  0.50  0.32 
Stage 3  0.55  0.33 
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Shi, H. A Parametric Blade Design Method for HighSpeed Axial Compressor. Aerospace 2021, 8, 271. https://doi.org/10.3390/aerospace8090271
Shi H. A Parametric Blade Design Method for HighSpeed Axial Compressor. Aerospace. 2021; 8(9):271. https://doi.org/10.3390/aerospace8090271
Chicago/Turabian StyleShi, Hengtao. 2021. "A Parametric Blade Design Method for HighSpeed Axial Compressor" Aerospace 8, no. 9: 271. https://doi.org/10.3390/aerospace8090271