Reduced-Order Modeling of Two-Sided Frictional Interfaces

2007 ◽  
Author(s):  
Jason D. Miller ◽  
D. Dane Quinn
Keyword(s):  
Modal Analysis ◽  
Computational Efficiency ◽  
Order Approximation ◽  
Reduced Order Modeling ◽  
Original Model ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Overall Response

We consider a model describing the behavior of a two-sided interface allowing for both elasticity and microslip of the joint. A reduced-order approximation of this system is developed based on a decomposition of the original model into an elastic chain and a dissipative component equivalent to a series-series Iwan chain. The Iwan chain is then solved using a quasi-static complementarity formulation while the order of the elastic chain is reduced using modal analysis. The computational efficiency of the resulting reduced-order model is significantly increased, while the overall response of the interface to realistic forcing conditions is maintained.

Reduced Order Modeling Based on Complex Nonlinear Modal Analysis and its Application to Bladed Disks With Shroud Contact

2013 ◽  
Author(s):  
Malte Krack ◽  
Lars Panning-von Scheidt ◽  
Jörg Wallaschek ◽  
Christian Siewert ◽  
Andreas Hartung
Keyword(s):  
Modal Analysis ◽  
Limit Cycle ◽  
Large Scale ◽  
Computational Effort ◽  
Reduced Order Modeling ◽  
Forced Response ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Nonlinear Modal Analysis

The design of bladed disks with contact interfaces typically requires analyses of the resonant forced response and flutter-induced limit cycle oscillations. The steady-state vibration behavior can efficiently be calculated using the Multi-Harmonic Balance method. The dimension of the arising algebraic systems of equations is essentially proportional to the number of harmonics and the number of degrees of freedom (DOFs) retained in the model. Extensive parametric studies necessary e.g. for robust design optimization are often not possible in practice due to the resulting computational effort. In this paper, a two-step nonlinear reduced order modeling approach is proposed. First, the autonomous nonlinear system is analyzed using a Complex Nonlinear Modal Analysis technique based on the work of Laxalde and Thouverez [1]. The methodology in [1] was refined by an exact condensation approach as well as analytical calculation of gradients in order to efficiently study localized nonlinearities in large-scale systems. Moreover, a continuation method was employed in order to predict nonlinear modal interactions. Modal properties such as eigenfrequency and modal damping are directly calculated with respect to the kinetic energy in the system. In a second step, a reduced order model is built based on the Single Nonlinear Resonant Mode theory. It is shown that linear damping and harmonic forcing can be superimposed. Moreover, similarity properties can be exploited to vary normal preload or gap values in contact interfaces. Thus, a large parameter space can be covered without the need for re-computation of nonlinear modal properties. The computational effort for evaluating the reduced order model is almost negligible since it contains a single DOF only, independent of the original system. The methodology is applied to both a simplified and a large-scale model of a bladed disk with shroud contact interfaces. In contrast to [1], the contact constraints account for variable normal load and lift-off in addition to dry friction. Forced response functions, backbone curves for varying normal preload and excitation level as well as flutter-induced limit cycle oscillations are analysed and compared to conventional methods. The limits of the proposed methodology are indicated and discussed.

scholarly journals Evolve Then Filter Regularization for Stochastic Reduced Order Modeling

2018 ◽  
Author(s):  
Xuping Xie ◽  
Feng Bao ◽  
Clayton G. Webster
Keyword(s):  
Stochastic Systems ◽  
Spatial Filter ◽  
Reduced Order Modeling ◽  
Reduced Order Model ◽  
Galerkin Projection ◽  
Order Model ◽  
Reduced Order ◽  
Stochastic Burgers Equation ◽  
Numerical Stabilization ◽  
Convection Dominated

In this paper, we introduce the evolve-then-filter (EF) regularization method for reduced order modeling of convection-dominated stochastic systems. The standard Galerkin projection reduced order model (G-ROM) yield numerical oscillations in a convection-dominated regime. The evolve-then-filter reduced order model (EF-ROM) aims at the numerical stabilization of the standard G-ROM, which uses explicit ROM spatial filter to regularize various terms in the reduced order model (ROM). Our numerical results based on a stochastic Burgers equation with linear multiplicative noise. It shows that the EF-ROM is significantly better results than G-ROM.

Reduced Order Modeling of Entrained Flow Solid Fuel Gasification

2009 ◽  
Author(s):  
Rory F. D. Monaghan ◽  
Mayank Kumar ◽  
Simcha L. Singer ◽  
Cheng Zhang ◽  
Ahmed F. Ghoniem
Keyword(s):  
Fluid Dynamics ◽  
Reduced Order Modeling ◽  
Combined Cycle ◽  
Reduced Order Model ◽  
Temperature Profiles ◽  
Order Model ◽  
External Temperature ◽  
Reduced Order ◽  
Entrained Flow ◽  
Entrained Flow Gasifiers

Reduced order models that accurately predict the operation of entrained flow gasifiers as components within integrated gasification combined cycle (IGCC) or polygeneration plants are essential for greater commercialization of gasification-based energy systems. A reduced order model, implemented in Aspen Custom Modeler, for entrained flow gasifiers that incorporates mixing and recirculation, rigorously calculated char properties, drying and devolatilization, chemical kinetics, simplified fluid dynamics, heat transfer, slag behavior and syngas cooling is presented. The model structure and submodels are described. Results are presented for the steady-state simulation of a two-metric-tonne-per-day (2 tpd) laboratory-scale Mitsubishi Heavy Industries (MHI) gasifier, fed by two different types of coal. Improvements over the state-of-the-art for reduced order modeling include the ability to incorporate realistic flow conditions and hence predict the gasifier internal and external temperature profiles, the ability to easily interface the model with plant-wide flowsheet models, and the flexibility to apply the same model to a variety of entrained flow gasifier designs. Model validation shows satisfactory agreement with measured values and computational fluid dynamics (CFD) results for syngas temperature profiles, syngas composition, carbon conversion, char flow rate, syngas heating value and cold gas efficiency. Analysis of the results shows the accuracy of the reduced order model to be similar to that of more detailed models that incorporate CFD. Next steps include the activation of pollutant chemistry and slag submodels, application of the reduced order model to other gasifier designs, parameter studies and uncertainty analysis of unknown and/or assumed physical and modeling parameters, and activation of dynamic simulation capability.

scholarly journals Time Stable Reduced Order Modeling by an Enhanced Reduced Order Basis of the Turbulent and Incompressible 3D Navier–Stokes Equations

2019 ◽  
Vol 24 (2) ◽  
pp. 45 ◽  
Author(s):  
Nissrine Akkari ◽  
Fabien Casenave ◽  
Vincent Moureau
Keyword(s):  
Stokes Equations ◽  
A Priori ◽  
Order Reduction ◽  
Reduced Order Modeling ◽  
Reduced Order Model ◽  
Navier Stokes ◽  
Reduced Basis ◽  
Order Model ◽  
Navier Stokes Equations ◽  
Reduced Order

In the following paper, we consider the problem of constructing a time stable reduced order model of the 3D turbulent and incompressible Navier–Stokes equations. The lack of stability associated with the order reduction methods of the Navier–Stokes equations is a well-known problem and, in general, it is very difficult to account for different scales of a turbulent flow in the same reduced space. To remedy this problem, we propose a new stabilization technique based on an a priori enrichment of the classical proper orthogonal decomposition (POD) modes with dissipative modes associated with the gradient of the velocity fields. The main idea is to be able to do an a priori analysis of different modes in order to arrange a POD basis in a different way, which is defined by the enforcement of the energetic dissipative modes within the first orders of the reduced order basis. This enables us to model the production and the dissipation of the turbulent kinetic energy (TKE) in a separate fashion within the high ranked new velocity modes, hence to ensure good stability of the reduced order model. We show the importance of this a priori enrichment of the reduced basis, on a typical aeronautical injector with Reynolds number of 45,000. We demonstrate the capacity of this order reduction technique to recover large scale features for very long integration times (25 ms in our case). Moreover, the reduced order modeling (ROM) exhibits periodic fluctuations with a period of 2 . 2 ms corresponding to the time scale of the precessing vortex core (PVC) associated with this test case. We will end this paper by giving some prospects on the use of this stable reduced model in order to perform time extrapolation, that could be a strategy to study the limit cycle of the PVC.

scholarly journals On error estimation for reduced-order modeling of linear non-parametric and parametric systems

2021 ◽  
Author(s):  
Lihong Feng ◽  
Peter Benner
Keyword(s):  
Reduced Order Modeling ◽  
Reduced Order Model ◽  
Error Estimator ◽  
Linear Dynamical System ◽  
Order Model ◽  
Reduced Order ◽  
Error Estimators ◽  
Theoretical Results ◽  
Parametric Systems ◽  
Better Than

Motivated by a recently proposed error estimator for the transfer function of the reduced-order model of a given linear dynamical system, we further develop more theoretical results in this work. Moreover, we propose several variants of the error estimator, and compare those variants with the existing ones both theoretically and numerically. It is shown that some of the proposed error estimators perform better than or equally well as the existing ones. All the error estimators considered can be easily extended to estimate the output error of reduced-order modeling for steady linear parametric systems.

Modal Analysis of Wake behind Stationary and Vibrating Cylinders

2020 ◽  
pp. 1-24
Author(s):  
Marek Janocha ◽  
Guang Yin ◽  
Muk Chen Ong
Keyword(s):  
Reynolds Number ◽  
Modal Analysis ◽  
Reduced Order Model ◽  
Dynamic Mode Decomposition ◽  
Navier Stokes ◽  
Dynamic Mode ◽  
Order Model ◽  
Reduced Order ◽  
Mode Decomposition ◽  
Sst Turbulence Model

Abstract The Dynamic Mode Decomposition (DMD) and Proper Orthogonal Decomposition (POD) are used to analyze the coherent structures of turbulent flow around vibrating isolated and piggyback cylinders configurations subjected to a uniform flow at a laminar Reynolds number (Re=200) and a upper transition Reynolds number (Re=3.6×106). Numerical simulations using two-dimensional URANS (Unsteady Reynolds Averaged Navier-Stokes) approach with the k-omega SST turbulence model are used to obtain the flow fields snapshots for the analysis. The wake flows behind the cylinders are decomposed into energy optimal modes (POD modes) and dynamical relevant modes (DMD modes). A reduced-order model for the flow is built based on the modal analysis. A comparison of POD and DMD is performed to characterize their special features. The present study provides new insights into the flow physics of fluid-structure interaction problem of two coupled cylinders. The characteristic vortex shedding frequencies and their harmonics are identified by DMD modes in all the investigated configurations. It is observed that for single cylinder configurations the most energetic and the most dynamically important mode is associated with the fundamental shedding frequency. For the stationary piggyback configuration, the gap flow between the cylinders appears to be a dominant flow feature as evidenced by leading DMD modes. The cylinder vibration increases significantly number of modes necessary to obtain a reduced order model (ROM) at given level of accuracy compared to respective stationary configurations.

scholarly journals A Reduction Methodology Using Free-Free Component Eigenmodes and Arnoldi Enrichment

2015 ◽  
Author(s):  
Hadrien Tournaire ◽  
Franck Renaud ◽  
Jean-Luc Dion
Keyword(s):  
Modal Analysis ◽  
Model Reduction ◽  
Reduction Method ◽  
Reduced Order Model ◽  
Reduced Model ◽  
Order Model ◽  
Reduced Order ◽  
Complex Problems

In order to perform faster simulations, the model reduction is nowadays used in industrial contexts to solve large and complex problems. However, the efficiency of such an approach is sometimes cut by the interface size of the reduced model and its reusability. In this article, we focus on the development of a reduction methodology for the build of modal analysis oriented and updatable reduced order model whose size is not linked to their contacting interface. In order to allow latter model readjusting, we impose the use of eigenmodes in the reduction basis. Eventually, the method introduced is coupled to an Arnoldi based enrichment algorithm in order to improve the accuracy of the reduced model produced. In the last section the proposed methodology is discussed and compared to the Craig and Bampton reduction method. During this comparison we observed that even when not enriched, our work enables us to recover the Craig and Bampton accuracy with partially updatable and smaller reduced order model.

A Study of Whole Joint Model Calibration Using Quasi-Static Modal Analysis

2020 ◽  
Vol 142 (5) ◽  
Author(s):  
David A. Najera-Flores ◽  
Robert J. Kuether
Keyword(s):  
Modal Analysis ◽  
Model Calibration ◽  
Computational Cost ◽  
Element Model ◽  
Calibration Method ◽  
Joint Model ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Joint Parameters

Abstract Small length and time scales resulting from high-fidelity frictional contact elements make long duration, low frequency simulations intractable. Alternative reduced order modeling approaches for structural dynamics models have been developed over the last several decades to approximate joint physics based on empirical or mathematical models within a whole joint model representation. The challenge with nonlinear constitutive elements based on empirical models is that the parameters must be calibrated to either experimental or simulation data. This research proposes a model calibration technique that identifies the joint parameters of a four-parameter Iwan element based on the nonlinear natural frequencies and damping ratios computed with quasi-static modal analysis (QSMA). The QSMA algorithm is applied to the full-order finite element model (FEM) to obtain reference data, and a genetic algorithm optimizes the joint parameters within a reduced order model (ROM) by minimizing the difference between the nonlinear modal characteristics for the modes of interest. The calibration method is demonstrated on a C-Beam bolted assembly and the resulting reduced order model is validated by comparing simulations of broadband, forced transient response. The resulting calibrated model captures the nonlinear, multimodal response at a significantly reduced computational cost and can be utilized for producing efficient models that do not have supporting experimental data for calibration.

Sign in / Sign up

Export Citation Format

Share Document