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90 6 Radial turbine design for a micro-ORC test setup pressure, temperature, flow velocity, and Mach number in the nozzle before the oblique shock wave as well as the angle of the wake θ were used as the pre-shock state for the Hugoniot jump conditions for oblique shocks. CFD quantities are averaged over the noz- zle section at the trailing edge. The shock wave angle β1 from the trailing edge and the shock wave angle of the reflection from the long wall of the nozzle β2 were obtained ana- lytically and are presented in Table 6.6. The analytically solved shock wave and the wake positions are illustrated in Figure 6.13, and a comparison of the analytically solved shock wave directions and CFD results, for the stator design condition is presented in Figure 6.14. Table 6.6: Wake angles and analytically solved shock wave angles. Case θ β1 β2 design condition 80 % off-design 60 % off-design 8.5 30.3 23.9 12.1 32.9 24.0 16.2 35.9 24.7 Figure 6.13: Analytically solved oblique shock wave directions and wake directions at 60 % and 80 % off-design conditions and at design condition. The results obtained by using the analytical method for solving the direction of the oblique shock waves, agrees well with the results obtained by CFD showing similar behavior of the shock wave location hitting the longer wall of the nozzle moving upstream in off- design conditions. The difference between the results of the shock wave angles were estimated to be in the order of magnitude of 1-3 degrees when comparing the analytically solved results and the results obtained with CFD. 6.1.3 Rotor simulations Three different rotor geometries with different blade angle distributions representing dif- ferent meridional lengths of the flow passages but similar diameters, blade angles at thePDF Image | WORKING FLUID SELECTION AND DESIGN OF SMALL-SCALE WASTE HEAT RECOVERY SYSTEMS BASED ON ORGANIC RANKINE CYCLES
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