Reduced Order Modeling of a Bladed Rotor With Geometric Mistuning via Estimated Deviations in Mass and Stiffness Matrices

2011 ◽  
Author(s):  
Yasharth Bhartiya ◽  
Alok Sinha
Keyword(s):  
Reduced Order Modeling ◽  
Orthogonal Decomposition ◽  
Series Expansions ◽  
Computationally Efficient ◽  
Reduced Order ◽  
Stiffness Matrices ◽  
Taylor Series Expansions ◽  
Bladed Rotor ◽  
Proper Orthogonal ◽  
Further Development

This paper deals with further development of Modified Modal Domain Analysis (MMDA), which is a breakthrough method in the reduced order modeling of a bladed rotor with geometric mistuning. The main focus of this paper is to show that deviations in mass and stiffness matrices due to mistuning, estimated by Taylor series expansions in terms of independent Proper Orthogonal Decomposition variables representing geometric variations of blades, can be used for MMDA. This result has rendered Monte Carlo simulation of the response of a bladed rotor with geometric mistuning to be easy and computationally efficient.

Reduced Order Modeling of a Bladed Rotor With Geometric Mistuning Via Estimated Deviations in Mass and Stiffness Matrices

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Yasharth Bhartiya ◽  
Alok Sinha
Keyword(s):  
Reduced Order Modeling ◽  
Orthogonal Decomposition ◽  
Series Expansions ◽  
Computationally Efficient ◽  
Reduced Order ◽  
Stiffness Matrices ◽  
Taylor Series Expansions ◽  
Bladed Rotor ◽  
Proper Orthogonal ◽  
Further Development

This paper deals with further development of modified modal domain analysis (MMDA), which is a breakthrough method in the reduced order modeling of a bladed rotor with geometric mistuning. The main focus of this paper is to show that deviations in mass and stiffness matrices due to mistuning, estimated by Taylor series expansions in terms of independent proper orthogonal decomposition variables representing geometric variations of blades, can be used for MMDA. This result has rendered Monte Carlo simulation of the response of a bladed rotor with geometric mistuning to be easy and computationally efficient.

Reduced-Order Model of a Bladed Rotor With Geometric Mistuning

2007 ◽  
Author(s):  
Alok Sinha
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Coordinate Measurement ◽  
Coordinate Measurement Machine ◽  
Bladed Disk ◽  
Bladed Rotor ◽  
Proper Orthogonal

This paper deals with the development of an accurate reduced-order model of a bladed disk with geometric mistuning. The method is based on vibratory modes of various tuned systems and proper orthogonal decomposition of coordinate measurement machine (CMM) data on blade geometries. Results for an academic rotor are presented to establish the validity of the technique.

scholarly journals A Proper-Orthogonal Decomposition Variational Multiscale Approximation Method for a Generalized Oseen Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
John Paul Roop
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Incompressible Flows ◽  
Reduced Order Modeling ◽  
Orthogonal Decomposition ◽  
Qualitative Properties ◽  
Complex Flow ◽  
Reduced Order ◽  
Variational Multiscale ◽  
Oseen Problem ◽  
Proper Orthogonal

We introduce the variational multiscale (VMS) stabilization for the reduced-order modeling of incompressible flows. It is well known that the proper orthogonal decomposition (POD) technique in reduced-order modeling experiences numerical instability when applied to complex flow problems. In this case a POD discretization naturally separates out structures which corresponding to the energy cascade on large and small scales, in order, a VMS approach is natural. In this paper, we provide the mathematical background necessary for implementing VMS to a POD-Galerkin model of a generalized Oseen problem. We provide theoretical evidence which indicates the consistency of utilizing a VMS approach in the stabilization of reduced order flows. In addition we provide numerical experiments indicating that VMS improves fidelity in reproducing the qualitative properties of the flow.

Modified Modal Domain Analysis of a Bladed Rotor Using Coordinate Measurement Machine Data on Geometric Mistuning

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Vinod Vishwakarma ◽  
Alok Sinha ◽  
Yasharth Bhartiya ◽  
Jeffery M. Brown
Keyword(s):  
Natural Frequencies ◽  
Domain Analysis ◽  
Reduced Order Modeling ◽  
Forced Response ◽  
Mode Shapes ◽  
Reduced Order ◽  
Coordinate Measurement ◽  
Coordinate Measurement Machine ◽  
Bladed Rotor ◽  
Proper Orthogonal

Modified modal domain analysis (MMDA), a reduced order modeling technique, is applied to a geometrically mistuned integrally bladed rotor to obtain its natural frequencies, mode shapes, and forced response. The geometric mistuning of blades is described in terms of proper orthogonal decomposition (POD) of the coordinate measurement machine (CMM) data. Results from MMDA are compared to those from the full (360 deg) rotor Ansys model. It is found that the MMDA can accurately predict natural frequencies, mode shapes, and forced response. The effects of the number of POD features and the number of tuned modes used as bases for model reduction are examined. Results from frequency mistuning approaches, fundamental mistuning model (FMM) and subset of nominal modes (SNM), are also generated and compared to those from full (360 deg) rotor Ansys model. It is clearly seen that FMM and SNM are unable to yield accurate results whereas MMDA yields highly accurate results.

scholarly journals Investigation of the Effects of Length to Depth Ratio on Open Supersonic Cavities Using CFD and Proper Orthogonal Decomposition

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Ibrahim Yilmaz ◽  
Ece Ayli ◽  
Selin Aradag
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Stokes Equations ◽  
Reduced Order Modeling ◽  
Orthogonal Decomposition ◽  
Navier Stokes ◽  
Reduced Order ◽  
Modeling Approach ◽  
Depth Ratio ◽  
Minimum Number ◽  
Proper Orthogonal

Simulations of supersonic turbulent flow over an open rectangular cavity are performed to observe the effects of length to depth ratio (L/D) of the cavity on the flow structure. Two-dimensional compressible time-dependent Reynolds-averaged Navier-Stokes equations with k-ωturbulence model are solved. A reduced order modeling approach, Proper Orthogonal Decomposition (POD) method, is used to further analyze the flow. Results are obtained for cavities with severalL/Dratios at a Mach number of 1.5. Mostly, sound pressure levels (SPL) are used for comparison. After a reduced order modeling approach, the number of modes necessary to represent the systems is observed for each case. The necessary minimum number of modes to define the system increases as the flow becomes more complex with the increase in theL/Dratio. This study provides a basis for the control of flow over supersonic open cavities by providing a reduced order model for flow control, and it also gives an insight to cavity flow physics by comparing several simulation results with different length to depth ratios.

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