Cross-coupled forces due to bladed components, bearings and seals can contribute to destabilizing a rotor system and are an important input to the rotordynamic design of turbomachinery. Alford (1965) developed a simple formula for describing the cross-coupled mechanism of an unshrouded axial turbine stage. The high flow radial inflow turbine studied here can exhibit similar characteristics due to its long stage length. In this work, a transient computational solution is developed to predict cross-coupling stiffness of an unshrouded turbo-expander. The three-dimensional computational fluid dynamics (CFD) model includes the flow path from the inlet guide vanes (IGV’s) to the exit of the radial inflow turbine. A 360 degree model of the flow path is used to simulate the turbine centered at its axis of rotation while the shroud is displaced a small distance from the axis of rotation. This offset simulates the uneven blade tip clearance that is present in a whirling rotor. Unsteady effects are included using a time-transient simulation while time-averaged forces acting on the turbine are used to calculate the cross-coupling aerodynamic coefficients. The rotordynamic coefficients calculated using this method are compared to both the Alford equation and formulations used for shrouded centrifugal compressor impellers.

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