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β =tan−1ψ−1 2 φ This equation is plotted in Fig. 3. Because the inlet blade angle of a radial-inflow turbine is zero (measured with the radial direction), the rotor inlet flow angle is numerically equal to the incidence angle. Considering the region of maximum efficiency in Fig. 1, it can be seen in Fig. 3 that this occurs at negative incidence. This is consistent with the common observation that radial turbines achieve their best efficiency when the incidence is negative (2). Zero incidence occurs at a stage loading coefficient of unity irrespective of the flow coefficient, and for stage loading coefficients greater than unity the incidence becomes positive. Positive incidence very quickly leads to separation of the flow from the blade suction surface and poor performance ensues. It would appear that in order to achieve higher stage loadings, therefore, the blades must be set, not in the radial direction, but curved forward to match a positive inlet flow angle, see Figs. 4a and 4b. Unfortunately this solution must be ruled out because it introduces a large degree of non-radial character into the blade sections near the inlet and greatly increases the blade stresses. However, radial sections can be maintained in a mixed flow turbine as illustrated in Fig. 4c. Such a solution, combining radial blade sections and forward curvature, introduces considerable lean into the blade geometry which, if taken too far, can cause manufacturing difficulties. The amount of lean depends on the cone angle at the inlet and the blade inlet angle, and the actual limit depends on the manufacturing process, but generally it is found that inlet blade angles up to 20–30° are acceptable. Figure 3 indicates that the maximum stage loading coefficient can be extended to about 1.15 by doing so. DESIGN OF A HIGHLY LOADED MIXED FLOW TURBINE A turbine was required to drive a compressor in order to achieve a high boost pressure ratio. The compressor design speed was fixed at 31,000 rpm and the target power output for the turbine was 670 kW. The application required an intensive cyclic duty, and based on fatigue tests on material specimens, the engine exhaust gas temperature, and experience of the likely levels of stress in the rotor, a maximum blade speed of 440 m/s was arrived at. This leads to a stage loading coefficient of 1.29 which is well in excess of anything achieved with a conventional radial-inflow turbine design. Many trial calculations using the mean line analysis described in (3) were made in order to obtain the best possible turbine efficiency within the limits of what was feasible, and the final result is shown in column A of Table 1. The rotor inlet relative flow angle is large and positive at 43.2°, and this rules out the use of radial section blades. A mixed flow turbine design was therefore selected. This choice also meant that the ratio of the exit tip to inlet tip radii could be increased to high values without introducing excessive shroud curvature. The specific speed of this application is quite low, and together these meant that the exducer tip radius was relatively unconstrained. The exducer hub radius however is limited by crowding of the blades, and it was anticipated that the blade hub thickness would be large to confer adequate strength. The design was then detailed and subjected to flow field and structural analyses. The flow field analysis was a three dimensional viscous analysis method that has been extensivelyPDF Image | HIGH BOOST TURBOCHARGERS radial and mixed flow turbines
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