Full three-dimensional investigation of structural contact interactions in turbomachines

Abstract Minimizing the operating clearance between rotating bladed-disks and stationary surrounding casings is a primary concern in the design of modern turbomachines since it may advantageously affect their energy efficiency. This technical choice possibly leads to interactions between elastic structural components through direct unilateral contact and dry friction, events which are now accepted as normal operating conditions. Subsequent nonlinear dynamical behaviors of such systems are commonly investigated with simplified academic models mainly due to theoretical difficulties and numerical challenges involved in non-smooth large-scale realistic models. In this context, the present paper introduces an adaptation of a full three-dimensional contact strategy for the prediction of potentially damaging motions that would imply highly demanding computational efforts for the targeted aerospace application in an industrial context. It combines a smoothing procedure including bicubic B-spline patches together with a Lagrange multiplier based contact strategy within an explicit time-marching integration procedure preferred for its versatility. The proposed algorithm is first compared on a benchmark configuration against the more elaborated bi-potential formulation and the commercial software Ansys. The consistency of the provided results and the low energy fluctuations of the introduced approach underlines its reliable numerical properties. A case study featuring blade-tip/casing contact on industrial finite element models is then proposed: it incorporates component mode synthesis and the developed three-dimensional contact algorithm for investigating structural interactions occurring within a turbomachine compressor stage. Both time results and frequency-domain analysis emphasize the practical use of such a numerical tool: detection of severe operating conditions and critical rotational velocities, time-dependent maps of stresses acting within the structures, parameter studies and blade design tests.

[1]  T. G. Carne,et al.  Combined experimental/analytical modeling using component mode synthesis , 1984 .

[2]  Thomas J. R. Hughes,et al.  Stability, convergence and growth and decay of energy of the average acceleration method in nonlinear structural dynamics , 1976 .

[3]  R. Taylor,et al.  Lagrange constraints for transient finite element surface contact , 1991 .

[4]  Hyojin Kim,et al.  Crack evaluation of the fourth stage blade in a low-pressure steam turbine , 2011 .

[5]  Benoît Magnain,et al.  Développement d'algorithmes et d'un code de calcul pour l'étude des problèmes de l'impact et du choc , 2006 .

[6]  Philippe G. Ciarlet,et al.  The finite element method for elliptic problems , 2002, Classics in applied mathematics.

[7]  Herbert A. Mang,et al.  Algorithmic stabilization of FE analyses of 2D frictional contact problems with large slip , 2003 .

[8]  Stability , 1973 .

[9]  Analysis of an energy-conserving time integration algorithm , 1989 .

[10]  T. Laursen,et al.  A framework for development of surface smoothing procedures in large deformation frictional contact analysis , 2001 .

[11]  Michel Raous,et al.  Consistent time discretization for a dynamical frictional contact problem and complementarity techniques , 1998 .

[12]  Michael Ortiz,et al.  A note on energy conservation and stability of nonlinear time-stepping algorithms , 1986 .

[13]  M. Bampton,et al.  Coupling of substructures for dynamic analyses. , 1968 .

[14]  C. D. Boor B(asic)-Spline Basics. , 1986 .

[15]  P. Wriggers,et al.  Smooth C1‐interpolations for two‐dimensional frictional contact problems , 2001 .

[16]  J. Peraire,et al.  A variationally consistent mesh adaptation method for triangular elements in explicit Lagrangian dynamics , 2010 .

[17]  A. Batailly,et al.  Simulation de l'interaction rotor/stator pour des turbo-machines aéronautiques en configuration non-accidentelle , 2008 .

[18]  M. Wierzbińska,et al.  Fracture analysis of compressor blade of a helicopter engine , 2009 .

[19]  Peter Wriggers,et al.  Contact treatment in isogeometric analysis with NURBS , 2011 .

[20]  Dominique Chamoret,et al.  New smoothing procedures in contact mechanics , 2004 .

[21]  M L Kaplan,et al.  Energy-conserving impact algorithm for the heel-strike phase of gait. , 2000, Journal of biomechanics.

[22]  A. Curnier,et al.  A finite element method for a class of contact-impact problems , 1976 .

[23]  A. F. Emery,et al.  An experimental investigation of temperatures due to rubbing at the blade-seal interface in an aircraft compressor , 1983 .

[24]  Shaker A. Meguid,et al.  On the modelling of smooth contact surfaces using cubic splines , 2001 .

[25]  J. C. Simo,et al.  Exact energy-momentum conserving algorithms and symplectic schemes for nonlinear dynamics , 1992 .

[26]  Jean-Michel Cros,et al.  The bi-potential method applied to the modeling of dynamic problems with friction , 2005 .

[27]  José J. Muñoz,et al.  Modelling unilateral frictionless contact using the null-space method and cubic B-Spline interpolation , 2008 .

[28]  Michael G. Dunn,et al.  Experimental Results From Controlled Blade Tip/Shroud Rubs at Engine Speed , 2007 .

[29]  T. Hughes,et al.  Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement , 2005 .

[30]  Fulei Chu,et al.  Stiffening effect of the rotor during the rotor-to-stator rub in a rotating machine , 2007 .

[31]  E. Poursaeidi,et al.  Fatigue crack growth simulation in a generator fan blade , 2009 .

[32]  J. Arora,et al.  Multiplier methods for engineering optimization , 1991 .

[33]  T. Laursen Computational Contact and Impact Mechanics , 2003 .

[34]  Young-Ha Hwang,et al.  Analysis of a J69-T-25 engine turbine blade fracture , 2002 .

[35]  J. Bonet,et al.  A Variationally Consistent Mesh Adaptation Method for Explicit Lagrangian Dynamics , 2007 .

[36]  Arnaud Sternchüss,et al.  On the reduction of quasi-cyclic disk models with variable rotation speeds , 2006 .

[37]  Laurent Stainier,et al.  Simulation of crashworthiness problems with improved contact algorithms for implicit time integration , 2006 .

[38]  John A. Evans,et al.  Isogeometric analysis using T-splines , 2010 .

[39]  A. P,et al.  Mechanical Vibrations , 1948, Nature.

[40]  B. Barsky End conditions and boundary conditions for uniform B-spline curve and surface representations☆ , 1982 .

[41]  Christophe Pierre,et al.  Two-dimensional modeling of an aircraft engine structural bladed disk-casing modal interaction , 2009 .

[42]  Etienne Arnoult,et al.  Modelisation numerique et approche experimentale du contact en dynamique : application au contact aubes/carter de turboreacteur , 2000 .

[43]  Christophe Pierre,et al.  Assessment of reduced models for the detection of modal interaction through rotor stator contacts , 2010 .

[44]  J. C. Simo,et al.  An augmented lagrangian treatment of contact problems involving friction , 1992 .

[45]  F. Armero,et al.  Formulation and analysis of conserving algorithms for frictionless dynamic contact/impact problems , 1998 .