Nonsmooth Thermoelastic Simulations of Blade–Casing Contact Interactions

Abstract

In turbomachinery, it is well known that tighter operating clearances improve the efficiency. However, this leads to unwanted potential unilateral and frictional contact occurrences between the rotating (blades) and stationary components (casings) together with attendant thermal excitations. Unilateral contact induces discontinuities in the velocity at impact times, hence the terminology nonsmooth dynamics. Current modeling strategies of rotor-stator interactions are either based on regularizing penalty methods or on explicit time-marching methods derived from Carpenter's forward Lagrange multiplier method. Regularization introduces an artificial time scale in the formulation corresponding to numerical stiffness which is not desirable. Carpenter's scheme has been successfully applied to turbomachinery industrial models in the sole mechanical framework, but faces serious stability issues when dealing with the additional heat equation.This work overcomes the above issues by using the MoreauJean nonsmooth integration scheme within an implicit Â-method. This numerical scheme is based on a mathematically sound description of the contact dynamics by means of measure differential inclusions and enjoys attractive features. The procedure is unconditionally stable opening doors to quick preliminary simulations with time-steps one hundred times larger than with previous algorithms. It can also deal with strongly coupled thermomechanical problems.

Thermomechanical Model Reduction for Efficient Simulations of Rotor-Stator Contact Interaction

“…A validation analysis is now conducted through comparison with other existing methods. Unless stated otherwise, results are presented for a time step h D 10 5 s as in the companion paper [17] and m u D 10.…”

“…The penalty approach is known to induce numerical stiffness [21,22,1]. The forward Lagrange multiplier method relies on an explicit scheme which suffers from stability limitations, especially coping with a thermomechanical model [17]. However, a robust numerical method dedicated to nonsmooth problems, namely, the Moreau-Jean scheme [22], is employed in the present work.…”

“…Again, the numerical method employed to enforce the contact conditions are detailed in [17]. Results are provided for boundary node 3.…”

“…However, a robust numerical method dedicated to nonsmooth problems, namely, the Moreau-Jean scheme [22], is employed in the present work. Its description is detailed in a companion paper [17]. Contact conditions are incorporated via a signed gap function g.u/.…”

“…As for the reduction process, the simulation of thermomechanical contact problems poses modeling and solving issues. The robust treatment of unilateral contact conditions inspired by numerical methods developed in nonsmooth dynamics is detailed in a companion paper [17]. The model of interest is first introduced (section 1), then the reduction methodology is described (section 2).…”