Research Papers: Gas Turbines: Structures and Dynamics

Nonsmooth Thermoelastic Simulations of Blade–Casing Contact Interactions

[+] Author and Article Information
Anders Thorin, Mathias Legrand

Structural Dynamics and Vibration Laboratory,
McGill University,
Montreal, QC H3A 0G4, Canada

Nicolas Guérin

École Centrale de Lyon,
Laboratoire de Tribologie et
Dynamique des Systèmes,
Écully 69130, France;
Safran Helicopter Engines,
Bordes 64511, France

Fabrice Thouverez

École Centrale de Lyon,
Laboratoire de Tribologie et Dynamique des
Écully 69130, France

Patricio Almeida

Safran Helicopter Engines,
Bordes 64511, France
e-mail: anders.thorin@mcgill.ca

1Corresponding author.

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received June 27, 2018; final manuscript received July 5, 2018; published online September 26, 2018. Editor: Jerzy T. Sawicki.

J. Eng. Gas Turbines Power 141(2), 022502 (Sep 26, 2018) (7 pages) Paper No: GTP-18-1384; doi: 10.1115/1.4040857 History: Received June 27, 2018; Revised July 05, 2018

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 Moreau–Jean nonsmooth integration scheme within an implicit θ-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.

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Fig. 1

Simplified finite element sector. Contact nodes [], constrained nodes [], and corresponding contact forces [].

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Fig. 2

Sensitivity to time-step in terms of radial displacement ur, temperature θ and normal contact force λ at node 4. Reference [], h = 10 − 4 s [] and h = 10 − 5 s [].

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Fig. 3

Close-up view of Fig. 2

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Fig. 4

Influence of time-step size. Reference [], h = 10 − 4 s [] and h = 10 − 5 s [].

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Fig. 5

Error as a function of the number of time-steps at contact node 4 for one second of simulation: ur [—], λ [--··] and θ [···]

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Fig. 6

Time histories for contact nodes 3 [] and 4 []

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Fig. 7

Time histories for contact nodes 3 [] and 4 [] without thermomechanical coupling

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Fig. 8

Comparison of time histories for node 4. Moreau–Jean [] and Carpenter [].

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Fig. 9

Close-up view of Fig. 8

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Fig. 10

Finite element model of simplified industrial compressor sector. Contact nodes [], constrained nodes []. Coloring refers to the radial displacement: (a) Positions at rest and (b) first flexural modeshape.

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Fig. 11

Time histories for node 1 with [] and without [] frictional heating

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Fig. 12

Time histories for node 1. Effect of excitation amplitude: forcing of 1 [] and 2 [] normalized amplitude.

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Fig. 13

Close-up view of Fig. 12

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Fig. 14

Contact simulation results for node 1. Carpenter algorithm [] and Moreau algorithm [] for h = 5 × 10−7 s.

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Fig. 15

Moreau–Jean's scheme sensitivity to time-step for node 1: h = 5 × 10−7 s [], 10−6 s [], 5 × 10−6 s [] and 10−5 s []

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Fig. 16

Computation times for a 1 s simulation. Carpenter algorithm [] versus Moreau–Jean algorithm [].



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