scholarly journals Nonsmooth Thermoelastic Simulations of Blade–Casing Contact Interactions

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Anders Thorin ◽  
Nicolas Guérin ◽  
Mathias Legrand ◽  
Fabrice Thouverez ◽  
Patricio Almeida
Keyword(s):  
Numerical Scheme ◽  
Frictional Contact ◽  
Unilateral Contact ◽  
Contact Dynamics ◽  
Nonsmooth Dynamics ◽  
Integration Scheme ◽  
Strongly Coupled ◽  
Measure Differential Inclusions ◽  
Time Marching ◽  
Stability Issues

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.

scholarly journals Nonsmooth Thermoelastic Simulations of Blade-Casing Contact Interactions

2018 ◽  
Author(s):  
Anders Thorin ◽  
Nicolas Guérin ◽  
Mathias Legrand ◽  
Fabrice Thouverez ◽  
Patricio Almeida
Keyword(s):  
Numerical Scheme ◽  
Frictional Contact ◽  
Unilateral Contact ◽  
Contact Dynamics ◽  
Nonsmooth Dynamics ◽  
Integration Scheme ◽  
Strongly Coupled ◽  
Measure Differential Inclusions ◽  
Time Marching ◽  
Stability Issues

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.

Effects of Wheel-Shaft-Fluid Coupling and Local Wheel Deformations on the Global Behavior of Shaft Lines

2002 ◽  
Vol 124 (4) ◽  
pp. 953-957 ◽  
Author(s):  
D. Lornage ◽  
E. Chatelet ◽  
G. Jacquet-Richardet
Keyword(s):  
Three Dimensional ◽  
Fluid Film ◽  
Global Behavior ◽  
Three Dimensional Model ◽  
Fluid Films ◽  
Strongly Coupled ◽  
Proposed Model ◽  
Structural Deformations ◽  
Time Marching ◽  
Fluid Coupling

Rotating parts of turbomachines are generally studied using different uncoupled approaches. For example, the dynamic behavior of shafts and wheels are considered independently and the influence of the surrounding fluid is often taken into account in an approximate way. These approaches, while often sufficiently accurate, are questionable when wheel-shaft coupling is observed or when fluid elements are strongly coupled with local structural deformations (leakage flow between wheel and casing, fluid bearings mounted on a thin-walled shaft, etc.). The approach proposed is a step toward a global model of shaft lines. The whole flexible wheel-shaft assembly and the influence of specific fluid film elements are considered in a fully three-dimensional model. In this paper, the proposed model is first presented and then applied to a simple disk-shaft assembly coupled with a fluid film clustered between the disk and a rigid casing. The finite element method is used together with a modal reduction for the structural analysis. As thin fluid films are considered, the Reynolds equation is solved using finite differences in order to obtain the pressure field. Data are transferred between structural and fluid meshes using a general method based on an interfacing grid concept. The equations governing the whole system are solved within a time-marching procedure. The results obtained show significant influence of specific three-dimensional features such as disk-shaft coupling and local disk deformations on global behavior.

scholarly journals Simulation of Wire Bonding Process Using Explicit Fem with Ale Remeshing Technology

2019 ◽  
Vol 36 (1) ◽  
pp. 47-54
Author(s):  
C. C. Yang ◽  
Y. F. Su ◽  
Steven Y. Liang ◽  
K. N. Chiang
Keyword(s):  
Time Integration ◽  
Wire Bonding ◽  
Bonding Process ◽  
Integration Scheme ◽  
Arbitrary Lagrangian Eulerian ◽  
Cracking Behavior ◽  
Free Air ◽  
Time Integration Scheme ◽  
Time Marching ◽  
The Wire

ABSTRACTThermosonic wire bonding is a common fabrication process for connecting devices in electronic packaging. However, when the free air ball (FAB) is compressed onto the I/O pad of the chip during bonding procedure, chip cracking may occur if the contact pressure is too large. This study proposes an effective simulation technique that can predict the wire ball geometry after bonding in an accurate range. The contact force obtained in the simulation can be used for possible die cracking behavior evaluation. The simulation in this study used the explicit time integration scheme to deal with the time marching problem, and the second-order precision arbitrary Lagrangian-Eulerian (ALE) algorithm was used to deal with the large deformation of the wire ball during the bonding process. In addition, the equilibrium smoothing algorithm in LS-DYNA can make the contact behavior and geometry of the bonding wire almost the same as the experiment, which can also significantly reduce the distortion of the mesh geometry after remeshing.

scholarly journals Unsplit complex frequency-shifted PML implementation using auxiliary differential equations for seismic wave modeling

Geophysics ◽  
2010 ◽  
Vol 75 (4) ◽  
pp. T141-T154 ◽  
Author(s):  
Wei Zhang ◽  
Yang Shen
Keyword(s):  
Free Surface ◽  
Finite Difference ◽  
Differential Equations ◽  
Seismic Wave ◽  
Numerical Scheme ◽  
Complex Frequency ◽  
Order Accuracy ◽  
First Order ◽  
Time Marching ◽  
Interior Domain

The complex-frequency-shifted perfectly matched layer (CFS-PML) technique can efficiently absorb near-grazing incident waves. In seismic wave modeling, CFS-PML has been implemented by the first-order-accuracy convolutional PML technique or second-order-accuracy recursive convolution PML technique. Both use different algorithms than the numerical scheme for the interior domain to update auxiliary memory variables in the PML and thus cannot be used directly with higher-order time-marching schemes. We work with an unsplit-field CFS-PML implementation using auxiliary differential equations (ADEs) to update the auxiliary memory variables. This ADE CFS-PML results in complete first-order differential equations. Thus, the numerical scheme for the interior domain can be used to solve ADE CFS-PML equations. We have implemented ADE CFS-PML in the finite-difference time-domain method and in anonstaggered-grid finite-difference method with the fourth-order Runge-Kutta scheme, demonstrating its straightforward implementation in different numerical time-marching schemes. We have also theoretically analyzed the role of the scalingfactor of CFS-PML; it transforms the PML to a transversely isotropic material, reducing the effective wave speed normal to the PML layer and bending the wavefront toward the normal direction of the PML layer. Our numerical tests indicate that the optimal value reduces the points per dominant wavelength at the outermost boundary to three, about half the value required by the numerical scheme. We also have found that the PML equations should be derived taking the free-surface boundary condition into account in finite-difference methods. Otherwise, the free surface in the PML layer causes instability or ineffective absorption of surface waves. Tests show that we can use a narrow-slice mesh with ADE CFS-PML to simulate full wave propagation efficiently in models with complex structure.

scholarly journals Probing into frictional contact dynamics by ultrasound and electrical simulations

2014 ◽  
Vol 1 (1) ◽  
pp. 943012
Author(s):  
Changshan Jin ◽  
Mei Jin ◽  
Duc Pham
Keyword(s):  
Frictional Contact ◽  
Contact Dynamics

The Influence of Initial Residual Stress State on the Steady State Behaviour of Cyclically Loaded Coupled Contacts

2011 ◽  
Author(s):  
Robert Flicek ◽  
Daniele Dini ◽  
David A. Hills
Keyword(s):  
Residual Stress ◽  
Frictional Contact ◽  
Contact Problems ◽  
Coupled Problems ◽  
Strongly Coupled ◽  
Initial Residual Stress ◽  
Residual Stress State ◽  
Initial Load ◽  
State Behaviour ◽  
Steady State Behaviour

The Melan’s shakedown theorem applies to uncoupled frictional contact problems, but is known formally not to apply in the case of coupled contacts. In this paper we look at two example coupled problems (one very strongly coupled) in detail and show that, in fact, for these specific cases, shakedown does occur for a range of initial load states.

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

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Nicolas Guérin ◽  
Anders Thorin ◽  
Fabrice Thouverez ◽  
Mathias Legrand ◽  
Patricio Almeida
Keyword(s):  
Krylov Subspace ◽  
Frictional Contact ◽  
Recent Literature ◽  
Unilateral Contact ◽  
Reduction Technique ◽  
Thermomechanical Coupling ◽  
Reduced Order Models ◽  
Thermomechanical Model ◽  
Reduced Order ◽  
Prediction Tools

Turbomachinery rotor–stator unilateral contact induced interactions play a growing role in lifecycle analysis and thus motivate the use of accurate numerical prediction tools. Recent literature confirmed by ongoing in-house experiments have shown the importance of thermomechanical coupling effects in such interactions. However, most available (possibly reduced-order) models are restricted to the sole mechanical aspects. This work describes a reduction technique of thermomechanical models involving unilateral contact and frictional contact occurrences between rotor and stator components. The proposed methodology is grounded on Guyan and Craig–Bampton methods for the reduction of the structural dynamics in conjunction with Krylov subspace techniques, and specifically the Craig–Hale approach, for the reduction of the thermal equations. The method has the capability to drastically reduce the size of the model while preserving accuracy. It stands as a reliable strategy to perform simulations of thermomechanical models with localized mechanical and thermal loads.

Time-Marching Analysis of Steady Transonic Flow in Turbomachinery Cascades Using the Hopscotch Method

1983 ◽  
Vol 105 (2) ◽  
pp. 272-279 ◽  
Author(s):  
R. A. Delaney
Keyword(s):  
Experimental Data ◽  
Euler Equations ◽  
Transonic Flow ◽  
Numerical Scheme ◽  
Curvilinear Coordinates ◽  
Two Dimensional ◽  
Analysis Method ◽  
Time Marching ◽  
Turbine Cascades ◽  
Turbomachinery Cascades

A rapid, time-marching, numerical scheme based on the hopscotch method is presented for solution of steady, two-dimensional, transonic flow in turbomachinery cascades. The scheme is applied to the strong-conservation form of the unsteady Euler equations written in arbitrary curvilinear coordinates. Cascade solutions are obtained on an orthogonal, body-centered coordinate system. Numerical solution results for two turbine cascades are presented and compared with experimental data to demonstrate the accuracy and computational efficiency of the analysis method.

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