Comparison of Model Order Reduction Methods in Thermoacoustic Stability Analysis

Model order reduction can play a pivotal role in reducing the cost of repeated computations of large thermoacoustic models required for comprehensive stability analysis and optimization. In this proof-of-concept study, acoustic wave propagation is modeled with a 1D network approach, while acoustic-flame interactions are modeled by a flame transfer function. Three reduction techniques are applied to the acoustic subsystem: firstly modal truncation based on preserving the acoustic eigenmodes, and then two approaches that strive to preserve the input-output transfer behavior of the acoustic subsystem, i.e., truncated balanced realization and iterative rational Krylov algorithm. After reduction, the reduced-order models (ROMs) are coupled with the flame transfer function. Results show that the coupled reduced system from modal truncation accurately captures thermoacoustic cavity modes with weak influence of the flame, but fails for cavity modes strongly influenced by the flame as well as for intrinsic thermoacoustic modes. On the contrary, the coupled ROMs generated with the other two methods accurately predict all types of modes. It is concluded that reduction techniques based on preserving transfer behavior are more suitable for thermoacoustic stability analysis.

Comparison of Model Order Reduction Methods in Thermoacoustic Stability Analysis

Model order reduction can play a pivotal role in reducing the cost of repeated computations of large thermoacoustic models required for comprehensive stability analysis and optimization. In this proof-of-concept study, acoustic wave propagation is modeled with a 1D network approach, while acoustic-flame interactions are modeled by a flame transfer function. Three reduction techniques are applied to the acoustic subsystem: firstly modal truncation based on preserving the acoustic eigenmodes, and then two approaches that strive to preserve the input-output transfer behavior of the acoustic subsystem, i.e., truncated balanced realization and iterative rational Krylov algorithm. After reduction, the reduced-order models (ROMs) are coupled with the flame transfer function. Results show that the coupled reduced system from modal truncation accurately captures thermoacoustic cavity modes with weak influence of the flame, but fails for cavity modes strongly influenced by the flame as well as for intrinsic thermoacoustic modes. On the contrary, the coupled ROMs generated with the other two methods accurately predict all types of modes. It is concluded that reduction techniques based on preserving transfer behavior are more suitable for thermoacoustic stability analysis.

Investigating the influence of connecting constraint properties and modeling parameters on vehicle dynamic responses

This paper presents a detailed investigation about the effect of structural damping and modal truncation number on vehicle dynamic characteristics. Finite element method and experimental method are applied to research vehicle’s dynamic response. According to the real vehicle’s structure, the dynamic simulation model of vehicle is established by the substructure modeling method. In order to research the influence of different variables on vehicle’s dynamic responses, the control variable method is adopted. In other words, the parameters of structural damping and mode truncation number are changed respectively. Comparing the dynamic response results, the influence rules of structural damping and mode truncation number on dynamic responses are obtained. Results show that the dynamic responses of vehicle changes significantly with the change of structural damping and mode truncation number. The studying results provide important significance for the determination of parameters. As well as, the correctness and reliability of the analysis results are verified by the experimental method.

Damping of coupled bending-torsion beam vibrations by a two-dof tmd with analogous coupling

Coupled bending-torsion vibrations of a beam with a single cross-section axis of symmetry are mitigated by a two-degree-of-freedom (dof) tuned mass damper with a coupling analogous to that of the beam. By modal truncation a four-degree-of-freedom model is derived for tmd tuning. Because of the analogous tmd properties, a stiffness tuning formula identical to that for the classic tuned mass damper secures inverse relations between all four undamped natural frequencies. Expressions for the tmd damping are subsequently found by a numerical search, which maximizes the smallest of the four damping ratios, resulting in equal damping in three of the four modes. The two-dof coupled tmd is finally assessed by numerical root locus and frequency response analysis for a full flexible beam.

Breaking the Kolmogorov Barrier in Model Reduction of Fluid Flows

Turbulence modeling has been always a challenge, given the degree of underlying spatial and temporal complexity. In this paper, we propose the use of a partitioned reduced order modeling (ROM) approach for efficient and effective approximation of turbulent flows. A piecewise linear subspace is tailored to capture the fine flow details in addition to the larger scales. We test the partitioned ROM for a decaying two-dimensional (2D) turbulent flow, known as 2D Kraichnan turbulence. The flow is initiated using an array of random vortices, corresponding to an arbitrary energy spectrum. We show that partitioning produces more accurate and stable results than standard ROM based on a global application of modal decomposition techniques. We also demonstrate the predictive capability of partitioned ROM through an energy spectrum analysis, where the recovered energy spectrum significantly converges to the full order model’s statistics with increased partitioning. Although the proposed approach incurs increased memory requirements to store the local basis functions for each partition, we emphasize that it permits the construction of more compact ROMs (i.e., of smaller dimension) with comparable accuracy, which in turn significantly reduces the online computational burden. Therefore, we consider that partitioning acts as a converter which reduces the cost of online deployment at the expense of offline and memory costs. Finally, we investigate the application of closure modeling to account for the effects of modal truncation on ROM dynamics. We illustrate that closure techniques can help to stabilize the results in the inertial range, but over-stabilization might take place in the dissipative range.

Dynamics Analysis of the Rigid-Flexible Coupling Lifting Comprehensive Mechanism for a Rotary Dobby

This paper addresses the problem of dynamics analysis of the rigid-flexible coupling lifting comprehensive mechanism for a rotary dobby, which is the important part of the loom. To provide a physical model basis for a precise dynamics model, the finite element method was used to discretize the bending arm of the rotary dobby effectively. Combining with the modal synthesis techniques, the dynamic model of the bending arm was established by using Kane’s formulation, and it laid a foundation for analyzing the dynamic performance of the heald frame. By comparing virtual prototype simulation results with the numerical calculation results of the bending arm, the correctness of this model was verified. Based on the established dynamic model, the modal truncation method is used to simplify the dynamic model; in addition, the influence of parameters such as the speed of the dobby, the warp tension, the movement distance of the heald frame, and the thickness of the bending arm on the dynamic characteristics of the heald frame was analyzed. Last, the sensitivity analysis (SA) method is used to analyze the effects of each parameter. The results show that it is appropriate to select the first four modes to calculate, and increasing the speed greatly or increasing the warp tension, the shedding performance is obviously worse, while the shedding performance of the loom can be optimized by reducing the shedding range or increasing the thickness of the bending arm.