5.5 Optimal Profiling Examples

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The created profiling algorithms have allowed to design a series of profiles of turbine cascades.

As a starting (1O) was taken the standard profile P2 with a high aerodynamic quality. Wherein were accepted such flow conditions that ensure the smallest possible profile P2 (1O) losses: t = t/b=0.722, βb= 76°26′,β1 = 29°30′.

Retaining the basic, necessary for the machine profiling raw data:

with the help of the developed algorithms were obtained new profiles: 1MMC (for the geometric quality criteria – the minimum of maximum curvature) and 1MPL (the minimum of profile loss).

From technological considerations subsequently profile 1MMC contour was approximated by the radii (Fig. 5.4, 5.5, Table 5.2). Fig. 5.6–5.8 shows the distribution of the velocity and the parameter B (the Buri boundary layer separation criterion) along the contours of the original and newly created profiles.

The calculated profile loss ζpr values correspondingly are 3.35, 3.16 and 3.00%. Attention is drawn to the different law of the parameter B variation along the profiles contours. Apparently, the possibility of the boundary layer separation, or the intensity of its thickening (which leads to increased losses) must be judged not only by the maximum value of the parameter B, which (usually) achieved at cascade’s oblique cut, but also the character of its change within the channel prior bevel, particularly on the convex side of the profile.

For comparative testing of profiles 1O, 1MMC and 1MPL were chosen conditions of the original flow profile P2 (1O) which provide the smallest possible losses:t = t/b=0.722, βb= 76°26′.

All nominal dimensions of the experimental blades and cascades of considered profiles adopted respectively the same, namely a chord b = 42 mm; length of blade l = 120 mm; pitch t = 30.32 mm; channel throat a = 10.85 mm; the thickness of the trailing edge δ = = 0.66 mm. The stagger angles for the newly designed profiles 1MMK and 1MPP equaled stagger angle of the source profile 1O.





In the blades manufacture the profile was controlled by the working patterns. The template fit appears on the projector using the drawing profile contour 10 times increased relatively to the blade profile. When fit the profile by template contour clearance allowed not more than 0.04 mm. It should be noted that the difference in the contours of the most similar profiles 1O and 1MMC
reaches 0.6 mm, i.e. an order of magnitude greater of the blades manufacture tolerance. Particular attention was paid to ensure a predetermined trailing edge thickness. The admission to the size of the throat when building cascades was ± 0.03 mm. Effective angle downstream was β2e = arcsin a/t=20°55′.

The aim of the tests was to obtain comparative data on the profile losses factors ζsub>pr and exit flow angles β2 in the subsonic region, at the range of Mach numbers 0.3…0.65, and different inlet flow angles β1.

The comparability of the experimental results was ensured by making the blades and cascades in the same manner with the same requirements for precision and surface finish; cascade tests one the same test rig, using the same instrumentation and the measured data processing methods.

The main test was preceded by methodological tests. On expiration mode of Mach Msub>2T = 0.46, the measurements were carried out along the front of the cascade at different distances from the plane of output edges and in the three sections of the height of the blades. The values of certain kinetic energy loss factor ζsub>pr is calculated for the measurement intervals along the cascade front multiple of two, three and four steps of the blades. The results of such averages practically coincided, indicating that careful manufacture of blades and high quality cascades assembly.

As a result of preliminary tests it was found that the averaged energy losses in the flow behind cascade will stabilize at a distance from the 0.25b of the trailing edges. Thus for a layer thickness of 20% of the blades height, symmetrical about their middle, the flow is very close to the flat.

Final testing data of three experimental cascades were obtained by measurements on the middle section of the height of the blades at a distance equal to 0.285b from the trailing edges in the three-step interval.

Fig. 5.9 shows the experimental dependences of the cascade profile losses versus inlet flow angle β1 in the range of change from 26° to 41° at different Mach numbers ranging from 0.45 to 0.68, which corresponds to Reynolds numbers of Re = 3.9∙105 to Re = 5.75∙105 In these intervals profile losses curves of cascade made up of the original profile 1O, are located above the profile losses curve of newly designed cascade 1MMC. Both profiles have minimum profile loss at inlet flow angle β1 = 35°. The magnitude of profile loss in the second cascade of 0.3…0.4% less than the first substantially throughout the whole range of variation of the input flow angle β1 in the specified range of the Mach number values.

Wherein loss in each of the cascades 1O and 1MMC increasing against the minimum value of 0.8% in the case of 5° deviation of input flow from the optimum angle β1 = 35°. The minimum profile losses amount of the cascade, composed from the newly designed blades 1MMC, optimized for geometric quality criterion, is 2.2 %.

Profile losses of cascade, composed of profiles 1MPL, were slightly lower of cascades 1O and 1MMC at the nominal input flow angle β1 = 29°30′. With the inlet flow angle decreasing, 1MPL profile advantage slightly increases. However, at the inlet flow angles β1 >30° profile 1MPL is worse than others. It should be emphasized that this profile losses factor curve vs input flow angle β1 in the investigated range of Mach numbers has a minimum at the angle β1 29°30′, under which the profile 1MPL was designed.

Fig. 5.10 shows the dependence of the angles downstream the cascades β2 of the input flow angle β1 at different Mach numbers. The newly designed cascade 1MMC has the better match of the output flow angle β2 with the effective angle β2eff = arcsin a t value in the entire tested range. A similar pattern is observed for the cascade of 1MPL profiles within its region of advantages.


The other results of optimal profiling of cascades with converging and diffuser channels, as well as data of their experimental studies, can be found in [13].


The results obtained to build the turbine cascades of a minimum profile loss authenticate the proposed statement of the profiling problem. Of course, for such problems more correct to take as an objective function the integral loss, what is the most naturally achieved involving computational aerodynamics models.

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