Reduced-Order Modeling and Experiment for Turbomachinery Stall Flutter

2002 ◽  
Author(s):  
George Scott Copeland ◽  
Gonzalo J. Rey
Keyword(s):  
Relative Sensitivity ◽  
Test Rig ◽  
Order Model ◽  
Reduced Order ◽  
System Parameters ◽  
Aeroelastic Model ◽  
Stall Flutter ◽  
Actuator Disk Modeling ◽  
Industry Experience ◽  
Good Agreement

A reduced-order model for stall flutter of turbomachinery is presented. The model is based on simplified physics (actuator disk modeling of bladerows, typical section aeroelastic model) and the measured steady performance characteristic. The model is not intended to be predictive, though it has been shown to be “tunable” to stability measurements of the test rig. The objective of the effort is to estimate the relative sensitivity of flutter damping to system parameters. It is found that predictions are in good agreement with measured test rig data and industry experience.

Design of a Kangaroo Inspired Hopping Robot for Unrestricted Locomotion and Controller Development

2019 ◽  
Author(s):  
Austin Curtis ◽  
James Mynderse ◽  
Hamid Vejdani
Keyword(s):  
Frequency Response ◽  
Three Dimensional ◽  
Reduced Order Model ◽  
Design Parameters ◽  
Order Model ◽  
Reduced Order ◽  
Gait Performance ◽  
System Parameters ◽  
Hopping Robot ◽  
The Relationship

Abstract Inspired by the agility and maneuverability of running kangaroos, a prototype robot was developed using a reduced order model to constrain the system. Both passive and active models were used to understand the relationship between system parameters and gait performance. A frequency response experiment was performed on the prototype to quantify the relationship between design parameters and system responses. Additionally, preliminary tail controllers were tested. Based on the results of the initial platform, a new robot was designed and built as a platform for the study of three dimensional hopping.

Multistage Blisk and Large Mistuning Modeling Using Fourier Constraint Modes and PRIME

2017 ◽  
Author(s):  
Eric Kurstak ◽  
Kiran D’Souza
Keyword(s):  
Expansion Method ◽  
Reduced Order Model ◽  
Order Model ◽  
Modal Expansion ◽  
Reduced Order ◽  
Modal Expansion Method ◽  
Multistage System ◽  
Computationally Expensive ◽  
First Time ◽  
Good Agreement

Current efforts to model multistage turbomachinery systems rely on calculating independent constraint modes for each degree of freedom on the boundary between stages. While this approach works, it is computationally expensive to calculate all the required constraint modes. This paper presents a new way to calculate a reduced set of constraint modes referred to as Fourier constraint modes (FCMs). These FCMs greatly reduce the number of computations required to construct a multistage reduced order model (ROM). The FCM method can also be integrated readily with the component mode mistuning method to handle small mistuning and the pristine rogue interface modal expansion method to handle large and/or geometric mistuning. These methods all use sector level models and calculations, which makes them very efficient. This paper demonstrates the efficiency of the FCM method on a multistage system that is tuned and, for the first time, creates a multistage ROM with large mistuning using only sector level quantities and calculations. The results of the multistage ROM for the tuned and large mistuning cases are compared with full finite element results and are found in good agreement.

Multistage Blisk and Large Mistuning Modeling Using Fourier Constraint Modes and PRIME

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Eric Kurstak ◽  
Kiran D'Souza
Keyword(s):  
Finite Element ◽  
Reduced Order Model ◽  
Degree Of Freedom ◽  
Order Model ◽  
Modal Expansion ◽  
Reduced Order ◽  
Multistage System ◽  
Computationally Expensive ◽  
First Time ◽  
Good Agreement

Current efforts to model multistage turbomachinery systems rely on calculating independent constraint modes for each degree-of-freedom (DOF) on the boundary between stages. While this approach works, it is computationally expensive to calculate all the required constraint modes. This paper presents a new way to calculate a reduced set of constraint modes referred to as Fourier constraint modes (FCMs). These FCMs greatly reduce the number of computations required to construct a multistage reduced order model (ROM). The FCM method can also be integrated readily with the component mode mistuning (CMM) method to handle small mistuning and the pristine rogue interface modal expansion (PRIME) method to handle large and/or geometric mistuning. These methods all use sector-level models and calculations, which make them very efficient. This paper demonstrates the efficiency of the FCM method on a multistage system that is tuned and, for the first time, creates a multistage ROM with large mistuning using only sector-level quantities and calculations. The results of the multistage ROM for the tuned and large mistuning cases are compared with full finite element results and are found in good agreement.

Validated Reduced Order Models for Simulating Trajectories of Bio-Inspired Artificial Micro-Swimmers

2010 ◽  
Author(s):  
Ahmet Fatih Tabak ◽  
Serhat Yesilyurt
Keyword(s):  
Rigid Body Dynamics ◽  
The Body ◽  
Reduced Order Model ◽  
Control Input ◽  
Body Frame ◽  
Order Model ◽  
Reduced Order ◽  
Resistive Force ◽  
Resistive Force Theory ◽  
Good Agreement

Autonomous micro-swimming robots can be utilized to perform specialized procedures such as in vitro or in vivo medical tasks as well as chemical surveillance or micro manipulation. Maneuverability of the robot is one of the requirements that ensure successful completion of its task. In micro fluidic environments, dynamic trajectories of active micro-swimming robots must be predicted reliably and the response of control inputs must be well-understood. In this work, a reduced-order model, which is based on the resistive force theory, is used to predict the transient, coupled rigid body dynamics and hydrodynamic behavior of bio-inspired artificial micro-swimmers. Conceptual design of the micro-swimmer is biologically inspired: it is composed of a body that carries a payload, control and actuation mechanisms, and a long flagellum either such as an inextensible whip like tail-actuator that deforms and propagates sinusoidal planar waves similar to spermatozoa, or of a rotating rigid helix similar to many bacteria, such as E. Coli. In the reduced-order model of the micro-swimmer, fluid’s resistance to the motion of the body and the tail are computed from resistive force theory, which breaks up the resistance coefficients to local normal and tangential components. Using rotational transformations between a fixed world frame, body frame and the local Frenet-Serret coordinates on the helical tail we obtain the full 6 degrees-of-freedom relationship between the resistive forces and torques and the linear and rotational motions of the swimmer. In the model, only the tail’s frequency (angular velocity for helical tail) is used as a control input in the dynamic equations of the micro-swimming robot. The reduced-order model is validated by means of direct observations of natural micro swimmers presented earlier in the literature and against; results show very good agreement. Three-dimensional, transient CFD simulations of a single degree of freedom swimmer is used to predict resistive force coefficients of a micro-swimmer with a spherical body and flexible tail actuator that uses traveling plane wave deformations for propulsion. Modified coefficients show a very good agreement between the predicted and actual time-dependent swimming speeds, as well as forces and torques along all axes.

A Mistuned Forced Response Analysis of an Embedded Compressor Blisk Using a Reduced Order Model

2018 ◽  
Author(s):  
Mauricio Gutierrez ◽  
Paul Petrie-Repar ◽  
Robert E. Kielb ◽  
Nicole L. Key
Keyword(s):  
Detailed Comparison ◽  
Forced Response ◽  
Reduced Order Model ◽  
Coupled Analysis ◽  
Response Analysis ◽  
Loading Conditions ◽  
Order Model ◽  
Reduced Order ◽  
Nominal Mode ◽  
Good Agreement

Accuracy when assessing mistuned forced response analyses is still a mayor concern. Since a full coupled analysis is still very computational expensive, several simplifications and reduced order models are carried out. The use of a reduction method, the assumptions and simplifications, generate different uncertainties that challenge the accuracy in the results. Experimental data are needed for validation and also to understand the propagation of these uncertainties. This paper shows a detailed mistuned forced response analysis of a compressor blisk. The blisk belongs to the Purdue Three-Stage (P3S) Compressor Research Facility. Two different stator-rotor-stator configurations of 38 and 44 upstream stator vanes are taken into consideration. Several loading conditions are analyzed at three different speed lines. A reduced order model known as subset nominal mode (SNM), has been used for all the analyses. This reduction takes as a basis a set of modes within a selected frequency spectrum. A detailed comparison between the predicted and measured results have been performed, showing a good agreement for the high loading conditions.

Developing a reduced order model from structural kinematic measurements of a flexible finite span wing in stall flutter

2017 ◽  
Vol 71 ◽  
pp. 56-69 ◽  
Author(s):  
Ethan C.E. Culler ◽  
Casey Fagley ◽  
Jürgen Seidel ◽  
Thomas E. McLaughlin ◽  
John A.N. Farnsworth
Keyword(s):  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Finite Span ◽  
Stall Flutter

Multifrequency Excitation of a Clamped-Clamped Microbeam

2015 ◽  
Author(s):  
Nizar R. Jaber ◽  
Abdallah Ramini ◽  
Mohammad Younis
Keyword(s):  
Natural Frequencies ◽  
Harmonic Excitation ◽  
Mode Shapes ◽  
Order Model ◽  
Reduced Order ◽  
Axial Forces ◽  
Electrically Actuated ◽  
Experimental Values ◽  
Good Agreement ◽  
Structural Layer

We present analytical and experimental investigation of an electrically actuated clamped-clamped microbeam under a two-source harmonic excitation. The first frequency is swept around the first mode of vibration where the second one is fixed. These microbeams are fabricated using polyimide as structural layer coated with nickel form top and chromium and gold layers from bottom. We demonstrate the excitation of additive and subtractive type resonance. We show that by properly tuning the frequency and the amplitude of the excitation force, the frequency bandwidth of the resonator is increased. Theoretically, we solved the eigenvalue problem for different axial forces to find the natural frequencies ratio that match the experimental values. Using Galerkin method, a reduced order model is derived to simulate the static and dynamic response of the device where using three symmetric mode shapes provided a good agreement with experimental data.

Design and Experimental Verification of Mistuning of a Supersonic Turbine Blisk

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
Pieter Groth ◽  
Hans Mårtensson ◽  
Clas Andersson
Keyword(s):  
Operating Conditions ◽  
Test Rig ◽  
Order Model ◽  
Unstable Region ◽  
Reduced Order ◽  
Flutter Boundary ◽  
Turbine Blisk ◽  
Random Patterns ◽  
System Mode

A rotor blisk of a supersonic space turbine has previously been designed to allow for free flutter to occur in an air test rig (Groth Mårtensson, and Edin, 2010, “Experimental and Computational Fluid Dynamics Based Determination of Flutter Limits in Supersonic Space Turbines,” 132(1), p. 011010). Flutter occurred at several operating conditions, and the flutter boundary for the test turbine was established. In this paper the rotor blisk is redesigned in order to inhibit flutter. The design strategy chosen is to introduce a mistuning concept. Based on aeroelastic analyses using a reduced order model a criterion for the required level of mistuning is established in order to stabilize the lower system modes. Proposals in literature suggest and analyze mistuning by varying blade mode frequencies in random patterns or by modifying blades in an odd-even pattern. Here a modification of sectors of the blisk is introduced in order to bring a sufficient split of the system mode frequencies. To verify that the redesigned blisk efficiently could inhibit flutter, an experiment similar to that in the work of Groth et al. is performed with the mistuned rotor blisk. By running the redesigned blisk at operating conditions deep into the unstable region of the tuned blisk, it is demonstrated that a relative low level of mistuning is sufficient to eliminate rotor flutter.

Initially Imperfect MEMS Microplates Under Electrostatic Actuation: Theory and Experiment

2016 ◽  
Author(s):  
Shahid Saghir ◽  
Mohammed L. Bellaredj ◽  
Mohammad I. Younis
Keyword(s):  
Building Blocks ◽  
Governing Equations ◽  
Flat Plates ◽  
Order Model ◽  
Micro Electro Mechanical Systems ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Harmonic Voltage ◽  
Static Behaviour ◽  
Good Agreement

Microplates are building blocks of many Micro-Electro-Mechanical Systems (MEMS). It is common for them to undergo imperfections due to residual stresses caused by the micro fabrication process. Such plates are essentially different from perfectly flat plates and cannot be modeled using the governing equations of flat plates. In this article, we adopt the governing equations of imperfect plates employing the modified von-Karman strains. These equations then are used to develop a Reduced Order Model based on the Galerkin procedure to simulate the static and dynamic behavior of an electrostatically actuated microplate. Also, microplates made of silicon nitride are fabricated and tested. First, the static behaviour of the microplate is investigated when applying a static voltage Vdc. To study the dynamic behaviour we apply a harmonic voltage, Vac, superimposed to Vdc. Simulation results show good agreement with the experimentally measured responses.

Design and Experimental Verification of Mistuning of a Supersonic Turbine Blisk

2008 ◽  
Author(s):  
Pieter Groth ◽  
Hans Ma˚rtensson ◽  
Clas Andersson
Keyword(s):  
Design Strategy ◽  
Operating Conditions ◽  
Test Rig ◽  
Order Model ◽  
Unstable Region ◽  
Reduced Order ◽  
Flutter Boundary ◽  
Turbine Blisk ◽  
Random Patterns ◽  
System Mode

A rotor blisk of a supersonic space turbine has previously been designed to allow for free flutter to occur in an air test rig [1]. Flutter occurred at several operating conditions and the flutter boundary for the test turbine was established. In this paper the rotor blisk is redesigned in order to inhibit flutter. The design strategy chosen is to introduce a mistuning concept. Based on aeroelastic analyses using a reduced order model (ROM) a criterion for the required level of mistuning is established in order to stabilize the lower system modes. Proposals in literature suggest and analyze mistuning by varying blade mode frequencies in random patterns or by modifying blades in an odd-even pattern. Here a modification of sectors of the blisk is introduced in order to bring a sufficient split of the system mode frequencies. To verify that the redesigned blisk efficiently could inhibit flutter an experiment similar to that in [1] is performed with the mistuned rotor blisk. By running the redesigned blisk at operating conditions deep in to the unstable region of the tuned blisk it is demonstrated that a relative low level of mistuning is sufficient to eliminate rotor flutter.

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