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Near the tip, the blade camber is very slight, compared with the profile near the hub. In this region, the inlet Mach number is the highest (M=1.35) and most of the pressure rise here is caused by the shock. The shock wave is formed near the most convex part of the suction surface and is followed by strong diffusion near the trailing-edge.

In this case, the shock-boundary layer interaction at the tip is most intense and is enough to upset the boundary layer during diffusion and cause a region of separated flow (see figure 6.30).

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T r a i lin g E d g e : S m a ll R eg io n o f S e p a ra tio n

Figure 6.30: Relative Mach Number Contours and Velocity Vectors at the Tip: Original Blade

In adopting a completely fore-loaded design, the intent is to shift the shock towards the front where the boundary layer is still thin and less likely to separate. However, as the inlet Maeh number is already very high, this may cause stronger shock to develop at the front, incurring high losses. Ginder and Calvert (1987) encountered similar difficulties in the design of a civil aero-engine fan whose transonic aerodynamics are similar to that in rotor 67; they developed an optimization procedure to study and tackle the problem in a SI-S2 system.

In the current redesign, a high gradient is imposed on the prescribed blade loading distribution in the leading-edge region to accommodate the desired fore-loaded characteristic. However, the gradient has been limited so as to avoid a strong shock formation at the front.

The comparison of the redesigned and the original loading distribution near the tip along 80% blade height is given in figure 6.31. The steep slopes of the original loading distribution correspond approximately to the two ends of the passage shock, one on the pressure side and the other impinging on the suction surface of the blade. These are readily identified in the figure.

The effect of the redesign is also shown in the figure. From the Mach number contours of the new design, the passage shock has been relocated to the front as intended and without further aggravating its intensity. In fact, the shock is found to be milder especially on the suction surface where it is noticeably more diffused than that of the original.

These results reaffirm the effectiveness in using for transonic design; its peak

dm

position controls the shock location and the gradient directly determines its intensity of the formation. Here, the gentle slope of the middle section o f the prescribed distribution is seen to be directly responsible for the weakened suction end of the shock formation.

f O riginal Fan:

Along 80% Blade Height

A l o n g 8 0 % B l a d e H e i g h t w 1 5 0 0 E O r i g i n a l B l a d e R e d e s i g n e d B l a d e E 1000 5 0 0 - 5 0 0 20 6 0 8 0 1 0 0 Ax i il C h >rd F r o m L .E . D iffused Suction

R ede sig ned Fan: Along 80% Blade Height

Figure 6.31: Mass-Averaged Loading Distributions and Relative Mach Number Contours at 80% Blade Height: Original and Redesigned

A l o n g 8 0 % B l a d e H e i g h t

O r i g i n a l B l a d e R e d e s i g n e d B l a d e

Figure 6.32: Comparison o f Blade Profiles at 80% Blade Height: Original and Redesigned

Careful examination of the new blade section reveals that the suction side is actually slightly de-cambered (or negatively cambered) (see figure 6.32) and it is this concave shaping of the suction surface that provides precompression of the flow, leading to a more diffused (i.e. weaker) shock formation.

Cumpsty (1989) explains that the gradual compression along the suction surface may be thought of in two ways,

1) The curvature towards the tangential produces compression waves which may coalesce into a series o f weak oblique shocks; and

2) The cross-sectional area is decreased in the flow direction by this negative camber and this leads to a deceleration o f the supersonic flow.

The use of precompression in transonic designs was first described by Prince (1980) where an example of a rotor blade with a very pronounced decambered section giving a distinctive "S" shape was designed and tested. The successful application of negative camber along the suction surface was also reported by Ginder and Calvert (1987) to yield an improvement in the aerodynamic performance of the civil aero engine fan design. The fact that supersonic flow expands along a convex surface and compresses along a concave one has also been recognized by Casey (1994) as a basis on which optimization procedures may be performed on transonic fans.

T ra ilin g Edge: No S e p a ra tio n

Figure 6.33: Relative Mach Num ber Contours and Velocity Vectors at the Tip: Redesigned Blade

Along the tip section of the current design, an improvement is seen; the flow separation previously observed near the trailing-edge of the original blade has now disappeared (see velocity vectors in figure 6.33). This is a direct result of positioning the shock near the leading-edge since by doing so, not only is the shock moved to the region where the boundary layer is less susceptible to separation, there is also an adequate length for the boundary diffusion to take place gradually along the suction surface without separating the surface flow.