1. Rotordynamic Forces Acting on a Centrifugal Open Impeller in Whirling Motion by Using Active Magnetic Bearing July 7, 2011 Eucass 2011 in St Petersburg Naoki Nagao 1, Masato Eguchi 2, Masaharu Uchiumi 1 and Yoshiki Yoshida 1 1 Japan Aerospace Exploration Agency 2 EBARA Corporation

2. Exordium: P. 2-4 Experimental methodology: P. 5-8 Experimental results: P. 9-13 Discussions: P. 14-17 Conclusions: P. 18-19 1 Outline

3. Exordium: P. 2-4 Experimental methodology: P. 5-8 Experimental results: P. 9-13 Discussions: P. 14-17 Conclusions: P. 18-19 2

4. Background H-IIA rocket The 1 st stage engine (LE-7A) The 2 nd stage engine (LE-5B) Engines of each stages Liquid oxygen turbopump (OTP) Liquid hydrogen turbopump (FTP) 3 Japan’s primary large-scale launch vehicle Turbopumps are required for high performance!

5. Rotordynamic coefficients M: Added mass C: Damping K: Stiffness Frequent troubles Modeling Shaft vibration analysis Optimum design of turbopump Objective Shaft vibration > Deficiency in performance 4 input reflect (Self-exited vibration) To suppress the self-exited vibrations and keep stable operation

6. Exordium: P. 2-4 Experimental methodology: P. 5-8 Experimental results: P. 9-13 Discussions: P. 14-17 Conclusions: P. 18-19 5

7. Experimental apparatus 800mm Casing Shaft Shaft rotation Whirling motion Ft Fn Rotordynamic Forces Experimented impeller Axial magnetic bearing Shaft Radial magnetic bearing Motor Flow Vibration mode 6 (EBARA Rotordynamic Test Stand) Translation Parallel Conical

8. Experimental object and condition Dynamic eccentricity Rotational frequency Tip clearance Flow rate ratio  N t Q/Qn [mm] [Hz] [mm] [-] 100, 150, 200 15, 20 0.4, 0.5, 0.6 0.6, 0.8, 1.0, 1.2 Whirl frequency ratio  [-]0.1-1.5 Vibration modeParallel FluidWater Impeller Vaned diffuser 250mm Experimental object Experimental condition Nominal condition in each parameters. 7

9. Definitions Impeller center Rotordynamic force effect at ： Restoring effect Casing center ： Inertia effect ： Damping effect ： Destabilizing effect Dimensionless rotordynamic force : Fluid density … (1) … (2) Dimensionless rotordynamic coefficients : Outlet radius of the impeller : Outlet blade height : Dimensionless direct added mass : Dimensionless cross-coupled added mass : Dimensionless direct damping : Dimensionless cross-coupled damping : Dimensionless direct stiffness : Dimensionless cross-coupled stiffness … (3) Destabilizing effect 8

10. Exordium: P. 2-4 Experimental methodology: P. 5-8 Experimental results: P. 9-13 Discussions: P. 14-17 Conclusions: P. 18-19 9

11. at various volumetric flow rate ratio “Q/Q n ” destabilizing effect in the all measured range fnfn ftft 10 Both f n and f t are enough small and stable. similar to typical shape of that acting on closed impellers They seem not to be affected by the flow rate.

12. at various dynamic eccentricity of the shaft “  ” 11 fnfn ftft different tendency from others nearly equal 0 There is threshold between 100 and 150μm. In actual operation the eccentricity is much smaller than 100μm, rotordynamic forces have little effect.

13. at various rotational frequency of the shaft “N” 12 fnfn ftft It may have to be cautious to normalize rotordynamic forces by rotational speed in this case. drastically different about the same Ｎ＝ Ω/2 π

14. at various tip clearance “t” 13 fnfn ftft increase with the tip clearance about the same t Casing Impeller brade

15. Exordium: P. 2-4 Experimental methodology: P. 5-8 Experimental results: P. 9-13 Discussions: P. 14-17 Conclusions: P. 18-19 14

16. Restoring effect Rotordynamic Coefficients NεtQ/QnMmCcKk 1200 200 0.50 0.6027-5.45.7330.913.6 0.8020-4.37.222-0.0164.1 1.0013-6.2109.9116.1 1.2011-4.29.39.88.86.4 100 1.00 6.9-0.692.9131.41.7 15013-0.0984.0139.65.8 200 0.4014-3.64.311124.4 0.6020-5.17.2166.35.7 9000.5012-7.9141.0256.0 |m| is not negligible smallpositive “K” (> 0) Destabilizing effect 15 Inertia effect

17. Direct stiffness “K” Hydrodynamics of Pumps C. E. Brennen  High Low Static pressure  Fluid velocity at tip clearance Closed impeller Open impeller Absence of front shroud Decrease of flow velocity at tip clearance Small Bernoulli effect Increase of “K” 16 decreases wall shear stress generates the leakage flow negative value

18. Cross-coupled added mass “m” In general (|m| is negligible) |m| is not negligible Destabilizing effect 0 0 |m| is enough large Minimum point of f t (Destabilizing at any time) 17 Linear expression The reason of this result is under review...

19. Exordium: P. 2-4 Experimental methodology: P. 5-8 Experimental results: P. 9-13 Discussions: P. 14-17 Conclusions: P. 18-19 18

20. Conclusions The experimental results and discussion can be summarized as follows: The tangential rotordynamic force “f t ” is small positive value in the all measured range which means that has destabilizing effect. The direct stiffness “K” is positive value in almost test condition. It seems that smaller Bernoulli effect because of absence of a front shroud makes “K” positive. The cross-coupled added mass “m” is not negligible small compared to the direct added mass “M”. This contributes that tangential rotordynamic force “f t ” is positive value in the all measured range. 19

21. Appendix

22. 21 Lomakin effect  High Low Static pressure L D 