Dynamic response of a rotating disk submerged and confined. Influence of the axial gap

In this paper, the natural frequencies and mode shapes of a rotating disk submerged and totally confined inside a rigid casing, have been obtained. These have been calculated analytically, numerically and experimentally for different axial gaps disk-casing. A simplified analytical model to analyse the dynamic response of a rotating disk submerged and confined, that has been used and validated in previous researches, is used in this case, generalised for arbitrary axial gaps disk-casing. To use this model, it is necessary to know the averaged rotating speed of the flow with respect to the disk. This parameter is obtained after an analytical discussion of the motion of the flow inside the casing where the disk rotates, and by means of CFD simulations for different axial positions of the disk. The natural frequencies of the rotating disk for the different axial confinements can be calculated following this method. A Finite Element Model has been built up to obtain the natural frequencies by means of computational simulation. The relative velocity of the flow with respect to the disk is also introduced in the simulation model in order to estimate the natural frequencies of the rotating disk. Experimental tests have been performed with a rotating disk test rig. A thin stainless steel disk (thickness of 8 mm, (h/r<5%) and mass of 7.6 kg) rotates inside a rigid casing. The position of the disk can be adjusted at several axial gaps disk-casing. A piezoelectric patch (PZT) attached on the rotating disk is used to excite the structure. Several miniature and submergible accelerometers have measured the response from the rotating frame. Excitation and measured signals are transmitted from the rotating to the stationary frame through a slip ring system. Experimental results are contrasted with the results obtained by the analytical and numerical model. Thereby, the influence of the axial gap disk-casing on the natural frequencies of a rotating disk totally confined and surrounded by a heavy fluid is determined.

[1]  Fabrice Thouverez,et al.  Rotor to stator contacts in turbomachines. Review and application , 2013 .

[2]  Chosei Okamura,et al.  VIBRATION OF ROTATING BLADED DISC EXCITED BY STATIONARY DISTRIBUTED FORCES , 1983 .

[3]  D. Dijkstra,et al.  The flow between two finite rotating disks enclosed by a cylinder , 1983, Journal of Fluid Mechanics.

[4]  Louis J. Durlofsky,et al.  On rotating disk flow , 1987, Journal of Fluid Mechanics.

[5]  Richard Vynne Southwell,et al.  On the free transverse vibrations of a uniform circular disc clamped at its centre; and on the effects of rotation , 1922 .

[6]  Hiroshi Tanaka,et al.  Vibration Behavior and Dynamic Stress of Runners of Very High Head Reversible Pump-turbines , 2011 .

[7]  Hideo Ohashi,et al.  Case Study of Pump Failure Due to Rotor-Stator Interaction , 1994 .

[8]  Wilfred Campbell,et al.  The Protection of Steam-Turbine Disk Wheels From Axial Vibration , 1924, Transactions of the American Society of Mechanical Engineers.

[9]  T. Naik,et al.  Dynamic response of a cantilever in liquid near a solid wall , 2003 .

[10]  Sébastien Poncet,et al.  Batchelor versus Stewartson flow structures in a rotor-stator cavity with throughflow , 2005 .

[11]  Eduard Egusquiza,et al.  Failure investigation of a large pump-turbine runner , 2012 .

[12]  T. Kármán.  Über laminare und turbulente Reibung , 1921 .

[13]  Bruno Mercier,et al.  On the response of a resonating plate in a liquid near a solid wall , 2007 .

[14]  Eduard Egusquiza,et al.  Capability of structural-acoustical FSI numerical model to predict natural frequencies of submerged structures with nearby rigid surfaces , 2012 .

[15]  J. C. Sun,et al.  Statistical energy analysis for complicated coupled system and its application in engineering , 2004 .

[16]  K. Stewartson.  On the flow between two rotating coaxial disks , 1953, Mathematical Proceedings of the Cambridge Philosophical Society.

[17]  Alexandre Presas,et al.  Influence of the rotation on the natural frequencies of a submerged-confined disk in water , 2015 .

[18]  Helmut F. Bauer,et al.  Transverse vibration and stability of spinning circular plates of constant thickness and different boundary conditions , 2007 .

[19]  G. Batchelor.  NOTE ON A CLASS OF SOLUTIONS OF THE NAVIER-STOKES EQUATIONS REPRESENTING STEADY ROTATIONALLY-SYMMETRIC FLOW , 1951 .

[20]  Horace Lamb,et al.  On the Vibrations of an Elastic Plate in Contact with Water , 1920 .

[21]  V. Shlyannikov,et al.  Fracture analysis of turbine disks and computational–experimental background of the operational decisions , 2001 .

[22]  Moon K. Kwak,et al.  Vibration of Circular Plates in Contact With Water , 1991 .

[23]  Yuji Kubota,et al.  Added Mass Effect on Disc Vibrating in Fluid , 1984 .

[24]  Kyeong-Hoon Jeong,et al.  Hydroelastic vibration of circular plates immersed in a liquid-filled container with free surface , 2013 .

[25]  Marco Amabili,et al.  FREE VIBRATIONS OF CIRCULAR PLATES COUPLED WITH LIQUIDS: REVISING THE LAMB PROBLEM , 1996 .

[26]  M. Amabili,et al.  EFFECT OF FINITE FLUID DEPTH ON THE HYDROELASTIC VIBRATIONS OF CIRCULAR AND ANNULAR PLATES , 1996 .

[27]  J. Lopez.  Flow between a stationary and a rotating disk shrouded by a co‐rotating cylinder , 1996 .

[28]  Horace Lamb,et al.  The vibrations of a spinning disk , 1921 .

[29]  Alexandre Presas,et al.  Experimental study on the added mass and damping of a disk submerged in a partially fluid-filled tank with small radial confinement , 2014 .

[30]  J. Hengstler.  Influence of the fluid-structure interaction on the vibrations of structures , 2013 .

[31]  Jintai Chung,et al.  Vibration analysis of a flexible rotating disk with angular misalignment , 2004 .

[32]  R. Blevins,et al.  Formulas for natural frequency and mode shape , 1984 .