A detailed unsteady numerical simulation has been carried out to investigate the shock and unsteady flow in the low pressure (LP) rotor in a 1+1/2 counter-rotating turbine (vaneless counter-rotating turbine (VCRT)). Through analyzing the distribution of static pressure and Mach number etc. in the VCRT, it can be found that, when the outer-extending shock (OES) of high pressure (HP) rotor moving from one LP rotor leading edge into the next, the inflow condition of LP rotor will vary. In the process, there are two typical inflow conditions. One is subsonic, but sufficiently near 1.0, and the other is slightly above unity i.e. the OES impinges on the LP rotor leading edge. Such inflow conditions of LP rotor will result in two different shock systems at different time. When the OES impinges on the LP rotor leading edge, a bow shock appears upstream of the LP rotor, and a normal shock produces at roughly 70% axial chord on the suction surface of LP rotor, and between the bow shock and normal shock, a group of expansion waves exist. After the OES sweeps the LP rotor leading edge i.e. the inflow of LP rotor is subsonic, the bow shock upstream of the LP rotor disappears, and a normal shock, that is weaker than the above, produces at the same location, and in front of the normal shock, a group of expansion waves exist. This distribution of shock in the VCRT LP rotor is similar to that in a compressor double-circular-arc (DCA) airfoil cascade in the same inflow condition, but in the VCRT LP rotor, the shocks are confined to the suction surface side of passage and its intensity weaker. The reason of the difference of the shock systems between the VCRT and the DCA airfoil cascade is that in the cascade the flow is of pressurization while in the VCRT the flow is of decompression. When the wake of the HP rotor sweeps the LP rotor, the static pressure on the suction surface of LP rotor will fluctuate, and a variational lower pressure area appears on the suction surface, which will result in a clear adverse pressure gradient on the suction surface in the LP rotor.

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