An inverse design method for viscous flow in turbomachinery blading using a wall virtual movement

Figures & data

Figure 1. Cascade notation and computational domain.

Figure 2. Schematic of the wall movement.

Figure 3. Inverse design flow chart.

Figure 4. Mach contours for ONERA compressor cascade.

Table 1. ONERA cascade data and flow conditions.

Inlet flow angle	α1 = −39.8°
Exit low angle	α2 ∼ 16°
Cascade solidity	s/c = 0.299
Stagger angle	Γ = 0°
Reynolds number	Re = 10^6
Isentropic exit Mach number	M2is = 0.685

Figure 5. ONERA blade profiles.

Figure 6. Loading distributions for ONERA compressor cascade design.

Figure 7. Isentropic Mach number distributions for ONERA compressor cascade design.

Figure 8. Convergence history of ONERA compressor cascade design.

Table 2. DFVLR cascade data and flow conditions.

Inlet flow angle	α1 = 37.7°
Exit low angle	α2 ∼ −63°
Cascade solidity	s/c = 0.929
Stagger angle	Γ = 30.8°
Reynolds number	Re = 5 × 10^5
Isentropic exit Mach number	M2is = 0.61

Figure 9. Mach number contours for DFVLR turbine cascade.

Figure 10. Loading distributions for DFVLR turbine cascade redesigns.

Figure 11. Pressure distributions for DFVLR turbine cascade redesigns.

Figure 12. DFVLR turbine blade profiles.

Table 3. Aerodynamic characteristics of DFVLR turbine redesign.

	Original	Design 1	Design 2
ς	8.5%	5.3%	4.9%
CL	0.2145	0.2156	0.2150
p2/p1	1.197	1.201	1.196
	0.228	0.231	0.236

Table 4. NASA Rotor 67 data and flow conditions at midspan.

Inlet flow angle	α1 = 59.3°
Exit low angle	α2 ∼ 42°
Section solidity	s/c = 0.798
Stagger angle	Γ = 30.8°
Reynolds number	Re = 10^6
Isentropic exit Mach number	M2is = 0.73

Figure 13. Mach contours for Rotor 67 midspan blade section.

Figure 14. Loading distributions for Rotor 67 blade section redesign.

Figure 15. Pressure distributions for Rotor 67 midspan blade section redesign.

Figure 16. Rotor 67 midspan blade profiles.

Table 5. Aerodynamic characteristics of the redesigned Rotor 67.

	Original	Design	Δ [%]
ζ	10.4%	9.6%	0.8
Minlet	1.054	1.057	0.28
	0.2780	0.2781	0.04