Some Applications of a Time-Linearized Euler Method to Flutter & Forced Response in Turbomachinery

Author(s):  
J. G. Marshall ◽  
M. B. Giles
Keyword(s):  
Author(s):  
J. G. Marshall ◽  
L. Xu ◽  
J. Denton ◽  
J. W. Chew

This paper presents a forced response prediction of 3 resonances in a low aspect ratio modern fan rotor and compares with other worker’s experimental data. The incoming disturbances are due to low engine-order inlet distortion from upstream screens. The resonances occur in the running range at 3 and 8 engine orders which cross low modes (flap, torsion and stripe) of the blade. The fan was tested with on-blade instrumentation at both on- and off-resonant conditions to establish the unsteady pressures due to known distortion patterns. The resulting steady and unsteady flow in the fan blade passages has been predicted by three methods, all three-dimensional. The first is a linearised unsteady Euler method; the second is a non-linear unsteady Navier-Stokes method; the third method uses a similar level of aerodynamic modelling as the second but also includes a coupled model of the structural dynamics. The predictions for the 3 methods are presented against the test data, and further insight into the problem is obtained through post-processing of the data. Predictions of the blade vibration response are also obtained. Overall the level of agreement between calculations and measurements is considered encouraging although further research is needed.


Author(s):  
G. Kahl

The Time Linearized Euler Method has proven to be a useful design tool, capable of predicting unsteady flows in turbomachinery within the accuracy required for engineering purposes while being fast enough for routine use in the design process. This paper first briefly describes the approach and its implementation in the current method. A range of applications of the method is described for flutter calculations in turbines and compressors with different levels of complexity such as chord wise bending, single or clustered airfoils, sub- or transonic flow. Farced response calculations are shown for airfoils passing through wakes and for a rotor operating in the pressure field of a downstream outlet guide vane. The results are presented as aerodynamic damping, unsteady work distributions and unsteady flowfield plots. Data shown includes information on boundary conditions, mesh size, computation time and convergence histories. The paper provides insight into an industry approach to modeling unsteady turbomachinery flows.


1992 ◽  
Vol 2 (4) ◽  
pp. 527-544
Author(s):  
Hsiao-Wei. D. Chiang ◽  
Sanford Fleeter
Keyword(s):  

2020 ◽  
Vol 48 (4) ◽  
pp. 287-314
Author(s):  
Yan Wang ◽  
Zhe Liu ◽  
Michael Kaliske ◽  
Yintao Wei

ABSTRACT The idea of intelligent tires is to develop a tire into an active perception component or a force sensor with an embedded microsensor, such as an accelerometer. A tire rolling kinematics model is necessary to link the acceleration measured with the tire body elastic deformation, based on which the tire forces can be identified. Although intelligent tires have attracted wide interest in recent years, a theoretical model for the rolling kinematics of acceleration fields is still lacking. Therefore, this paper focuses on an explicit formulation for the tire rolling kinematics of acceleration, thereby providing a foundation for the force identification algorithms for an accelerometer-based intelligent tire. The Lagrange–Euler method is used to describe the acceleration field and contact deformation of rolling contact structures. Then, the three-axis acceleration vectors can be expressed by coupling rigid body motion and elastic deformation. To obtain an analytical expression of the full tire deformation, a three-dimensional tire ring model is solved with the tire–road deformation as boundary conditions. After parameterizing the ring model for a radial tire, the developed method is applied and validated by comparing the calculated three-axis accelerations with those measured by the accelerometer. Based on the features of acceleration, especially the distinct peak values corresponding to the tire leading and trailing edges, an intelligent tire identification algorithm is established to predict the tire–road contact length and tire vertical load. A simulation and experiments are conducted to verify the accuracy of the estimation algorithm, the results of which demonstrate good agreement. The proposed model provides a solid theoretical foundation for an acceleration-based intelligent tire.


2021 ◽  
Vol 9 (7) ◽  
pp. 781
Author(s):  
Shi He ◽  
Aijun Wang

The numerical procedures for dynamic analysis of mooring lines in the time domain and frequency domain were developed in this work. The lumped mass method was used to model the mooring lines. In the time domain dynamic analysis, the modified Euler method was used to solve the motion equation of mooring lines. The dynamic analyses of mooring lines under horizontal, vertical, and combined harmonic excitations were carried out. The cases of single-component and multicomponent mooring lines under these excitations were studied, respectively. The case considering the seabed contact was also included. The program was validated by comparing with the results from commercial software, Orcaflex. For the frequency domain dynamic analysis, an improved frame invariant stochastic linearization method was applied to the nonlinear hydrodynamic drag term. The cases of single-component and multicomponent mooring lines were studied. The comparison of results shows that frequency domain results agree well with nonlinear time domain results.


2020 ◽  
Vol 20 (4) ◽  
pp. 717-725 ◽  
Author(s):  
Vidar Thomée

AbstractFor a spatially periodic convection-diffusion problem, we analyze a time stepping method based on Lie splitting of a spatially semidiscrete finite element solution on time steps of length k, using the backward Euler method for the diffusion part and a stabilized explicit forward Euler approximation on {m\geq 1} intervals of length {k/m} for the convection part. This complements earlier work on time splitting of the problem in a finite difference context.


Author(s):  
Bo Li ◽  
Xiaoting Rui ◽  
Guoping Wang ◽  
Jianshu Zhang ◽  
Qinbo Zhou

Dynamics analysis is currently a key technique to fully understand the dynamic characteristics of sophisticated mechanical systems because it is a prerequisite for dynamic design and control studies. In this study, a dynamics analysis problem for a multiple launch rocket system (MLRS) is developed. We particularly focus on the deductions of equations governing the motion of the MLRS without rockets by using a transfer matrix method for multibody systems and the motion of rockets via the Newton–Euler method. By combining the two equations, the differential equations of the MLRS are obtained. The complete process of the rockets’ ignition, movement in the barrels, airborne flight, and landing is numerically simulated via the Monte Carlo stochastic method. An experiment is implemented to validate the proposed model and the corresponding numerical results.


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