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.

References

References
1.
Jacquet-Richardet
,
G.
,
Torkhani
,
M.
,
Cartraud
,
P.
,
Thouverez
,
F.
,
Nouri-Baranger
,
T.
,
Herran
,
M.
,
Gibert
,
C.
,
Baguet
,
S.
,
Almeida
,
P.
, and
Peletan
,
L.
,
2013
, “
Rotor to Stator Contacts in Turbomachines. Review and Application
,”
Mech. Syst. Signal Process.
,
40
(
2
), pp.
401
420
.
2.
Parent
,
M.-O.
, and
Thouverez
,
F.
,
2016
, “
Phenomenological Model for Stability Analysis of Bladed Rotor-to-Stator Contacts
,”
16th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery
, Honolulu, HI, Apr. 10–15.https://hal.archives-ouvertes.fr/hal-01537643/document
3.
Carpenter
,
N. J.
,
Taylor
,
R. L.
, and
Katona
,
M. G.
,
1991
, “
Lagrange Constraints for Transient Finite Element Surface Contact
,”
Int. J. Numer. Methods Eng.
,
32
(
1
), pp.
103
128
.
4.
Legrand
,
M.
,
Pierre
,
C.
,
Cartraud
,
P.
, and
Lombard
,
J.-P.
,
2009
, “
Two-Dimensional Modeling of an Aircraft Engine Structural Bladed Disk-Casing Modal Interaction
,”
J. Sound Vib.
,
319
(
1–2
), pp.
366
391
.
5.
Stewart
,
D.
,
2000
, “
Rigid-Body Dynamics With Friction and Impact
,”
SIAM Rev.
,
42
(
1
), pp.
3
39
.
6.
Acary
,
V.
, and
Brogliato
,
B.
,
2008
,
Numerical Methods for Nonsmooth Dynamical Systems: Applications in Mechanics and Electronics
,
Springer
,
Berlin
.
7.
Almeida
,
P.
,
Gibert
,
C.
,
Thouverez
,
F.
,
Leblanc
,
X.
, and
Ousty
,
J.-P.
,
2014
, “
Experimental Analysis of Dynamic Interaction Between a Centrifugal Compressor and Its Casing
,”
ASME J. Turbomach.
,
137
(
3
), p. 031008.
8.
Shampine
,
L.
, and
Gear
,
C.
,
1979
, “
A User's View of Solving Stiff Ordinary Differential Equations
,”
SIAM Rev.
,
21
(
1
), pp.
1
17
.
9.
Glocker
,
C.
,
2006
, “
An Introduction to Impacts
,”
Nonsmooth Mechanics of Solids
(CISM International Centre for Mechanical Sciences Book Series, Vol.
485
),
Springer
,
Vienna, Austria
, pp.
45
101
.
10.
Ireman
,
P.
,
Klarbring
,
A.
, and
Strömberg
,
N.
,
2002
, “
Finite Element Algorithms for Thermoelastic Wear Problems
,”
Eur. J. Mech.-A/Solids
,
21
(
3
), pp.
423
440
.
11.
Legrand
,
M.
,
Batailly
,
A.
, and
Pierre
,
C.
,
2011
, “
Numerical Investigation of Abradable Coating Removal in Aircraft Engines Through Plastic Constitutive Law
,”
ASME J. Comput. Nonlinear Dyn.
,
7
(
1
), p.
011010
.
12.
Berthoul
,
B.
,
Batailly
,
A.
,
Legrand
,
M.
,
Stainier
,
L.
, and
Cartraud
,
P.
,
2015
, “
Abradable Coating Removal in Turbomachines: A Macroscopic Approach Accounting for Various Wear Mechanisms
,”
ASME
Paper No. GT2015-42500
.
13.
Moreau
,
J.-J.
,
1988
, “
Unilateral Contact and Dry Friction in Finite Freedom Dynamics
,”
Nonsmooth Mechanics and Applications
(International Centre for Mechanical Sciences Book Series, Vol.
302
),
Springer
,
Vienna, Austria
, pp.
1
82
.
14.
Jean
,
M.
,
1999
, “
The Non-Smooth Contact Dynamics Method
,”
Comput. Methods Appl. Mech. Eng.
,
177
(
3–4
), pp.
235
257
.
15.
Guérin
,
N.
,
Thorin
,
A.
,
Thouverez
,
F.
,
Legrand
,
M.
, and
Almeida
,
P.
,
2018
, “
Thermomechanical Model Reduction for Efficient Simulations of Rotor-Stator Contact Interaction
,”
ASME
Paper No. GT2018-75880.
You do not currently have access to this content.