Rub Interactions of Flexible Casing Rotor Systems

1989 ◽  
Vol 111 (4) ◽  
pp. 652-658 ◽  
Author(s):  
F. K. Choy ◽  
J. Padovan ◽  
C. Batur
Keyword(s):  
Numerical Solutions ◽  
Spectral Characteristics ◽  
Integration Time ◽  
Sudden Increase ◽  
Time Step ◽  
Impeller Blade ◽  
Rotor Systems ◽  
Machine Failure ◽  
The Time Domain ◽  
Turbine Impeller

Rub interactions between a rotor assembly and its corresponding casing structure has long been one of the major causes for machine failure. Fracture/fatigue failures of turbine impeller blade components may even lead to catastrophic consequences. This paper presents a comprehensive analysis of a complex rotor-bearing-blade-casing system during component rub interactions. The modal method is used in this study. Orthonormal coupled rotor-casing modes are used to obtain accurate relative motion between rotor and casing. External base vibration input and the sudden increase of imbalance are used to simulate suddenly imposed adversed operating condition. Nonlinear turbine/impeller blade effects are included with the various stages of single/multiple blade participation. A variable integration time step procedure is introduced to insure both accuracy and efficiency in numerical solutions. The dynamic characteristics of the system are examined in both the time domain and the frequency domain using a numerical FFT procedure. Nonlinear bearing and seal forces are also included to enhance a better simulation of the operating system. Frequency components of the system spectral characteristics will be correlated with the localized rub excitations to enable rub signature analysis. A multibearing flexible casing rotor system will be used as an example. Conclusions will be drawn from the results of an extensive parametric study.

scholarly journals Numerical Analysis of Viscoelastic Rotating Beam with Variable Fractional Order Model Using Shifted Bernstein–Legendre Polynomial Collocation Algorithm

2021 ◽  
Vol 5 (1) ◽  
pp. 8
Author(s):  
Cundi Han ◽  
Yiming Chen ◽  
Da-Yan Liu ◽  
Driss Boutat
Keyword(s):  
Numerical Analysis ◽  
Fractional Order ◽  
Governing Equation ◽  
Numerical Solutions ◽  
Bernstein Polynomials ◽  
Matrix Product ◽  
Algebraic Equations ◽  
Rotating Beam ◽  
The Matrix ◽  
The Time Domain

This paper applies a numerical method of polynomial function approximation to the numerical analysis of variable fractional order viscoelastic rotating beam. First, the governing equation of the viscoelastic rotating beam is established based on the variable fractional model of the viscoelastic material. Second, shifted Bernstein polynomials and Legendre polynomials are used as basis functions to approximate the governing equation and the original equation is converted to matrix product form. Based on the configuration method, the matrix equation is further transformed into algebraic equations and numerical solutions of the governing equation are obtained directly in the time domain. Finally, the efficiency of the proposed algorithm is proved by analyzing the numerical solutions of the displacement of rotating beam under different loads.

scholarly journals Three-Dimensional Elastodynamic Analysis Employing Partially Discontinuous Boundary Elements

Algorithms ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 129
Author(s):  
Yuan Li ◽  
Ni Zhang ◽  
Yuejiao Gong ◽  
Wentao Mao ◽  
Shiguang Zhang
Keyword(s):  
Side Effect ◽  
Domain Boundary ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Integration Scheme ◽  
Computational Accuracy ◽  
Time Step ◽  
Corner Points ◽  
Discontinuous Elements ◽  
The Time Domain

Compared with continuous elements, discontinuous elements advance in processing the discontinuity of physical variables at corner points and discretized models with complex boundaries. However, the computational accuracy of discontinuous elements is sensitive to the positions of element nodes. To reduce the side effect of the node position on the results, this paper proposes employing partially discontinuous elements to compute the time-domain boundary integral equation of 3D elastodynamics. Using the partially discontinuous element, the nodes located at the corner points will be shrunk into the element, whereas the nodes at the non-corner points remain unchanged. As such, a discrete model that is continuous on surfaces and discontinuous between adjacent surfaces can be generated. First, we present a numerical integration scheme of the partially discontinuous element. For the singular integral, an improved element subdivision method is proposed to reduce the side effect of the time step on the integral accuracy. Then, the effectiveness of the proposed method is verified by two numerical examples. Meanwhile, we study the influence of the positions of the nodes on the stability and accuracy of the computation results by cases. Finally, the recommended value range of the inward shrink ratio of the element nodes is provided.

scholarly journals An Advance-Tracing Boundary Element Method in the Time Domain for Solving the Radiating Problem of an Arbitrary Obstacle Accelerating Randomly

2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Jui-Hsiang Kao
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Time Domain ◽  
Boundary Integral ◽  
Normal Velocity ◽  
Time Step ◽  
Random Acceleration ◽  
The Time Domain ◽  
First Time ◽  
Element Method

This research develops an Advance-Tracing Boundary Element Method in the time domain to calculate the waves that radiate from an immersed obstacle moving with random acceleration. The moving velocity of the immersed obstacle is multifrequency and is projected along the normal direction of every element on the obstacle. The projected normal velocity of every element is presented by the Fourier series and includes the advance-tracing time, which is equal to a quarter period of the moving velocity. The moving velocity is treated as a known boundary condition. The computing scheme is based on the boundary integral equation in the time domain, and the approach process is carried forward in a loop from the first time step to the last. At each time step, the radiated pressure on each element is updated until obtaining a convergent result. The Advance-Tracing Boundary Element Method is suitable for calculating the radiating problem from an arbitrary obstacle moving with random acceleration in the time domain and can be widely applied to the shape design of an immersed obstacle in order to attain security and confidentiality.

scholarly journals The Influence of an Integration Time Step on Dynamic Calculation of a Vehicle-Track-Bridge under High-Speed Railway

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 431
Author(s):  
Junjie Ye ◽  
Hao Sun
Keyword(s):  
High Speed ◽  
Coupled Model ◽  
Short Wave ◽  
Integration Time ◽  
Vertical Acceleration ◽  
Dynamic Calculation ◽  
Time Step ◽  
High Speed Railway ◽  
Track Irregularity ◽  
Track Bridge

In order to study the influence of an integration time step on dynamic calculation of a vehicle-track-bridge under high-speed railway, a vehicle-track-bridge (VTB) coupled model is established. The influence of the integration time step on calculation accuracy and calculation stability under different speeds or different track regularity states is studied. The influence of the track irregularity on the integration time step is further analyzed by using the spectral characteristic of sensitive wavelength. According to the results, the disparity among the effect of the integration time step on the calculation accuracy of the VTB coupled model at different speeds is very small. Higher speed requires a smaller integration time step to keep the calculation results stable. The effect of the integration time step on the calculation stability of the maximum vertical acceleration of each component at different speeds is somewhat different, and the mechanism of the effect of the integration time step on the calculation stability of the vehicle-track-bridge coupled system is that corresponding displacement at the integration time step is different. The calculation deviation of the maximum vertical acceleration of the car body, wheel-sets and bridge under the track short wave irregularity state are greatly increased compared with that without track irregularity. The maximum vertical acceleration of wheel-sets, rails, track slabs and the bridge under the track short wave irregularity state all show a significant declining trend. The larger the vibration frequency is, the smaller the range of integration time step is for dynamic calculation.

Advanced Weathervaning in Ice

2011 ◽  
Author(s):  
William Hidding ◽  
Guillaume Bonnaffoux ◽  
Mamoun Naciri
Keyword(s):  
Rapid Change ◽  
Ice Sheet ◽  
Model Tests ◽  
The Arctic ◽  
Mooring System ◽  
Sudden Increase ◽  
Time Step ◽  
Ice Loads ◽  
Level Ice ◽  
Drift Direction

The reported presence of one third of remaining fossil reserves in the Arctic has sparked a lot of interest from energy companies. This has raised the necessity of developing specific engineering tools to design safely and accurately arctic-compliant offshore structures. The mooring system design of a turret-moored vessel in ice-infested waters is a clear example of such a key engineering tool. In the arctic region, a turret-moored vessel shall be designed to face many ice features: level ice, ice ridges or even icebergs. Regarding specifically level ice, a turret-moored vessel will tend to align her heading (to weather vane) with the ice sheet drift direction in order to decrease the mooring loads applied by this ice sheet. For a vessel already embedded in an ice sheet, a rapid change in the ice drift direction will suddenly increase the ice loads before the weathervaning occurs. This sudden increase in mooring loads may be a governing event for the turret-mooring system and should therefore be understood and simulated properly to ensure a safe design. The paper presents ADWICE (Advanced Weathervaning in ICE), an engineering tool dedicated to the calculation of the weathervaning of ship-shaped vessels in level ice. In ADWICE, the ice load formulation relies on the Croasdale model. Ice loads are calculated and applied to the vessel quasi-statically at each time step. The software also updates the hull waterline contour at each time step in order to calculate precisely the locations of contact between the hull and the ice sheet. Model tests of a turret-moored vessel have been performed in an ice basin. Validation of the simulated response is performed by comparison with model tests results in terms of weathervaning time, maximum mooring loads, and vessel motions.

A Successive Merging and Condensation (SMAC) Method Applied to Transient Analysis of Multi-Shaft Rotor System

1993 ◽  
Author(s):  
Santosh Ratan ◽  
Jorge Rodriguez
Keyword(s):  
Transient Response ◽  
Transient Analysis ◽  
Rotor System ◽  
Time Step ◽  
Transient Dynamic Analysis ◽  
Numerical Examples ◽  
Linear Coupling ◽  
Rotor Systems ◽  
Coupling Constraints ◽  
Smac Method

Abstract A method for performing transient dynamic analysis of multi-shaft rotor system is proposed. The proposed methodology uses the reported Successive Merge and Condensation (SMAC) method [12] and a decoupling technique to decouple the shafts. Multi-shaft rotor systems are treated as systems of many independent single shaft rotor systems with external unknown coupling forces acting at the points of couplings. For each time step, first, the SMAC method is used to get the transient response in terms of the unknown coupling forces. This is followed by the application of the coupling constraints to calculate the coupling forces and, in turn, the response at the end of that time step. The proposed method preserves the efficiency advantages of the SMAC algorithm for single-shaft rotor system. Numerical examples to validate and illustrate the applicability of the method are given. The method is shown to be applicable to linear and non-linear coupling problems.

NUMERICAL SOLUTIONS OF 2D AND 3D SLAMMING PROBLEMS

2021 ◽  
Vol 153 (A2) ◽  
Author(s):  
Q Yang ◽  
W Qiu
Keyword(s):  
Free Surface ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Type Equation ◽  
The Body ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Highly Nonlinear ◽  
2D And 3D

Slamming forces on 2D and 3D bodies have been computed based on a CIP method. The highly nonlinear water entry problem governed by the Navier-Stokes equations was solved by a CIP based finite difference method on a fixed Cartesian grid. In the computation, a compact upwind scheme was employed for the advection calculations and a pressure-based algorithm was applied to treat the multiple phases. The free surface and the body boundaries were captured using density functions. For the pressure calculation, a Poisson-type equation was solved at each time step by the conjugate gradient iterative method. Validation studies were carried out for 2D wedges with various deadrise angles ranging from 0 to 60 degrees at constant vertical velocity. In the cases of wedges with small deadrise angles, the compressibility of air between the bottom of the wedge and the free surface was modelled. Studies were also extended to 3D bodies, such as a sphere, a cylinder and a catamaran, entering calm water. Computed pressures, free surface elevations and hydrodynamic forces were compared with experimental data and the numerical solutions by other methods.

scholarly journals MHDSTS: a new explicit numerical scheme for simulations of partially ionised solar plasma

2018 ◽  
Vol 615 ◽  
pp. A67 ◽  
Author(s):  
P. A. González-Morales ◽  
E. Khomenko ◽  
T. P. Downes ◽  
A. de Vicente
Keyword(s):  
Numerical Scheme ◽  
Operator Splitting ◽  
Conservation Equation ◽  
Ambipolar Diffusion ◽  
Point Of View ◽  
Integration Time ◽  
Solar Photosphere ◽  
Time Step ◽  
Diffusion Term ◽  
Fluid Approximation

The interaction of plasma with magnetic field in the partially ionised solar atmosphere is frequently modelled via a single-fluid approximation, which is valid for the case of a strongly coupled collisional media, such as solar photosphere and low chromosphere. Under the single-fluid formalism the main non-ideal effects are described by a series of extra terms in the generalised induction equation and in the energy conservation equation. These effects are: Ohmic diffusion, ambipolar diffusion, the Hall effect, and the Biermann battery effect. From the point of view of the numerical solution of the single-fluid equations, when ambipolar diffusion or Hall effects dominate can introduce severe restrictions on the integration time step and can compromise the stability of the numerical scheme. In this paper we introduce two numerical schemes to overcome those limitations. The first of them is known as super time-stepping (STS) and it is designed to overcome the limitations imposed when the ambipolar diffusion term is dominant. The second scheme is called the Hall diffusion scheme (HDS) and it is used when the Hall term becomes dominant. These two numerical techniques can be used together by applying Strang operator splitting. This paper describes the implementation of the STS and HDS schemes in the single-fluid code MANCHA3D. The validation for each of these schemes is provided by comparing the analytical solution with the numerical one for a suite of numerical tests.

Dynamic Co-Simulation Methods for Combined Transmission-Distribution System With Integration Time Step Impact on Convergence

2019 ◽  
Vol 34 (2) ◽  
pp. 1171-1181 ◽  
Author(s):  
Ramakrishnan Venkatraman ◽  
Siddhartha Kumar Khaitan ◽  
Venkataramana Ajjarapu
Keyword(s):  
Distribution System ◽  
Integration Time ◽  
Simulation Methods ◽  
Time Step

scholarly journals IL-GLOBO (1.0) – integrated Lagrangian particle model and Eulerian general circulation model GLOBO: development of the vertical diffusion module

2014 ◽  
Vol 7 (5) ◽  
pp. 2181-2191 ◽  
Author(s):  
D. Rossi ◽  
A. Maurizi
Keyword(s):  
General Circulation Model ◽  
General Circulation ◽  
Spline Interpolation ◽  
Circulation Model ◽  
Linear Interpolation ◽  
Computational Time ◽  
Integration Time ◽  
Particle Model ◽  
Vertical Diffusion ◽  
Time Step

Abstract. The development and validation of the vertical diffusion module of IL-GLOBO, a Lagrangian transport model coupled online with the Eulerian general circulation model GLOBO, is described. The module simulates the effects of turbulence on particle motion by means of a Lagrangian stochastic model (LSM) consistently with the turbulent diffusion equation used in GLOBO. The implemented LSM integrates particle trajectories, using the native σ-hybrid coordinates of the Eulerian component, and fulfils the well-mixed condition (WMC) in the general case of a variable density profile. The module is validated through a series of 1-D offline numerical experiments by assessing its accuracy in maintaining an initially well-mixed distribution in the vertical. A dynamical time-step selection algorithm with constraints related to the shape of the diffusion coefficient profile is developed and discussed. Finally, the skills of a linear interpolation and a modified Akima spline interpolation method are compared, showing that both satisfy the WMC with significant differences in computational time. A preliminary run of the fully integrated 3-D model confirms the result only for the Akima interpolation scheme while the linear interpolation does not satisfy the WMC with a reasonable choice of the minimum integration time step.

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