A Finite-Element Perturbation Approach to Fluid/Rotor Interaction in Turbomachinery Elements. Part 2: Application

1991 ◽  
Vol 113 (3) ◽  
pp. 362-367 ◽  
Author(s):  
E. A. Baskharone ◽  
S. J. Hensel
Keyword(s):  
Finite Element ◽  
Computational Models ◽  
Operation Mode ◽  
Analytical Data ◽  
Perturbation Approach ◽  
Rotordynamic Coefficients ◽  
Eccentric Rotor ◽  
Annular Seal ◽  
Circumferential Distribution ◽  
Flow Variables

A newly devised perturbation model for the fluid-induced vibration of turbomachinery rotating elements is used to compute the rotordynamic coefficients of an annular seal. First, the finite element-based solution of the flow field in the centered-rotor operation mode is verified and its grid dependency tested for different seal configurations. The rotordynamic behavior of a hydraulic seal with a clearance gap depth/length ratio of 0.01, as a representative case, is then analyzed under a cylindrical type of rotor whirl and several running speeds. The direct and cross-coupled rotordynamic coefficients dictating the rotor instability mechanism in this case are compared to experimental and analytical data, and the outcome is favorable. The numerical results are also used to discuss the validity of a common assumption in existing computational models in regard to the circumferential distribution of the perturbed flow variables in the eccentric rotor operation mode.

Interrelated Rotordynamic Effects of Cylindrical and Conical Whirl of Annular Seal Rotors

1991 ◽  
Vol 113 (3) ◽  
pp. 470-480 ◽  
Author(s):  
E. A. Baskharone ◽  
S. J. Hensel
Keyword(s):  
Finite Element ◽  
Flow Model ◽  
Computational Procedure ◽  
Rotordynamic Coefficients ◽  
Conical Whirl ◽  
Conical Rotor ◽  
Annular Seal ◽  
Rotor Surface ◽  
Flow Variables ◽  
Sample Case

A comprehensive approach for computing the dynamic coefficients of an annular seal is presented. The coefficients are partly those associated with a uniform lateral eccentricity mode of the rotor (known as the cylindrical whirl mode) and with an angular eccentricity (which gives rise to a conical whirl type). The rotor excitation effects in both cases are treated as interrelated by recognizing the fluid-exerted moments resulting from the lateral eccentricity and the net fluid force resulting from the angular eccentricity. In all cases, the rotor is assumed to undergo a whirling motion around the housing centerline. The computational procedure is a finite-element perturbation model in which the zeroth-order undisplaced-rotor flow solution in the clearance gap is obtained through a Petrov-Galerkin approach. Next, the rotor translational and angular eccentricities, considered to be infinitesimally small, are perceived to cause virtual distortions of varied magnitudes in the finite element assembly which occupies the clearance gap. Perturbations in the flow variables including, in particular, the rotor surface pressure, are then obtained by expanding the finite-element equations in terms of the rotor eccentricity components. The fluid-exerted forces and moments are in this case computed by integration over the rotor surface, and the full matrix of rotordynamic coefficients, in the end, obtained. The computational model is verified against a bulk-flow model for a sample case involving a straight annular seal. Choice of this sample model for validation was made on the basis that no other existing model has yet been expanded to account for the mutual interaction between the cylindrical and conical rotor whirl, which is under focus in this study.

Perturbed Flow Structure in an Annular Seal Due to Synchronous Whirl

1994 ◽  
Vol 116 (3) ◽  
pp. 564-569
Author(s):  
E. A. Baskharone
Keyword(s):  
Experimental Data ◽  
Finite Element ◽  
Flow Field ◽  
Operating Conditions ◽  
Clearance Ratio ◽  
Perturbation Model ◽  
Eccentric Rotor ◽  
Annular Seal ◽  
The Common ◽  
Good Agreement

This paper provides a thorough examination of the flow field resulting from synchronous whirl of an eccentric rotor in an annular seal under typical operating conditions. A new finite-element-based perturbation model is employed in the analysis, whereby perturbations in the flow thermophysical properties are attributed to virtual distortions in the rotor-to-housing finite element assembly. The numerical results are compared to a recent set of experimental data for a hydraulic seal with typical geometrical configurations and a synchronously whirling rotor. Despite the common perception that perturbation analyses are categorically confined to small rotor eccentricities, good agreement between the computed flow field and the experimental data is obtained for an eccentricity/clearance ratio of 50 percent. The agreement between the two sets of data is notably better at axial locations where the real-rig flow admission losses have diminished, and up to the seal discharge station. This attests to the accuracy of this untraditional and highly versatile perturbation model in predicting the rotordynamic characteristics of this and a wide variety of conceptually similar fluid/rotor interaction problems.

A Finite-Element Perturbation Approach to Fluid/Rotor Interaction in Turbomachinery Elements. Part 1: Theory

1991 ◽  
Vol 113 (3) ◽  
pp. 353-361 ◽  
Author(s):  
E. A. Baskharone ◽  
S. J. Hensel
Keyword(s):  
Finite Element ◽  
Companion Paper ◽  
General Term ◽  
Perturbation Approach ◽  
Fluid Forces ◽  
Annular Seal ◽  
Vibrational Characteristics ◽  
Seal Assembly ◽  
Discrete Finite Element ◽  
Small Deformations

The vibrational characteristics of a rotor that is in contact with a fluid in an annular clearance gap, as dictated by the fluid forces in the gap, are investigated. The “rotor” here is a general term that may refer to the shaft segment within the housing of an annular seal, on the simple end of the application spectrum, or the shroud-seal assembly in a shrouded-impeller stage of a turbomachine, on the complex end. The disturbance under consideration involves the axis of rotation, and includes a virtual lateral eccentricity, together with a whirling motion around the housing centerline. Uniqueness of the computational model stems from the manner in which the rotor eccentricity is physically perceived and subsequently incorporated. It is first established that the fluid reaction components arise from infinitesimally small deformations with varied magnitudes which are experienced by an assembly of finite elements in the rotor-to-housing gap as the gap becomes distorted due to the rotor virtual eccentricity. The idea is then cast into a perturbation model in which the perturbation equations emerge from the flow-governing equations in their discrete finite-element form as opposed to the differential form, which is traditionally the case. As a result, restrictions on the rotor-to-housing gap geometry, or the manner in which the rotor virtual eccentricity occurs are practically nonexisting. While the emphasis in this paper is on the theoretical model, a representative application of the model and assessment of the numerical results are the focus of a companion paper that is being published concurrently.

Using scaled FE solutions for an efficient coupled electromagnetic–thermal induction machine model

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Martin Marco Nell ◽  
Benedikt Groschup ◽  
Kay Hameyer
Keyword(s):  
Finite Element ◽  
Thermal Behavior ◽  
Fe Simulation ◽  
Operation Mode ◽  
Induction Machine ◽  
Optimization Procedure ◽  
Machine Model ◽  
Content Type ◽  
Thermal Network ◽  
Scaling Procedure

Purpose This paper aims to use a scaling approach to scale the solutions of a beforehand-simulated finite element (FE) solution of an induction machine (IM). The scaling procedure is coupled to an analytic three-node-lumped parameter thermal network (LPTN) model enabling the possibility to adjust the machine losses in the simulation to the actual calculated temperature. Design/methodology/approach The proposed scaling procedure of IMs allows the possibility to scale the solutions, particularly the losses, of a beforehand-performed FE simulation owing to temperature changes and therefore enables the possibility of a very general multiphysics approach by coupling the FE simulation results of the IM to a thermal model in a very fast and efficient way. The thermal capacities and resistances of the three-node thermal network model are parameterized by analytical formulations and an optimization procedure. For the parameterization of the model, temperature measurements of the IM operated in the 30-min short-time mode are used. Findings This approach allows an efficient calculation of the machine temperature under consideration of temperature-dependent losses. Using the proposed scaling procedure, the time to simulate the thermal behavior of an IM in a continuous operation mode is less than 5 s. The scaling procedure of IMs enables a rapid calculation of the thermal behavior using FE simulation data. Originality/value The approach uses a scaling procedure for the FE solutions of IMs, which results in the possibility to weakly couple a finite element method model and a LPTN model in a very efficient way.

Age Dependent and Anisotropic Material Properties of Immature Porcine Sclera

2013 ◽  
Author(s):  
Jami M. Saffioti ◽  
Brittany Coats
Keyword(s):  
Finite Element ◽  
Material Properties ◽  
Anisotropic Material ◽  
Computational Models ◽  
Fe Model ◽  
Ocular Tissues ◽  
Load Bearing ◽  
Anisotropic Properties ◽  
Age Dependent ◽  
Testing Protocols

Current finite element (FE) models of the pediatric eye are based on adult material properties [2,3]. To date, there are no data characterizing the age dependent material properties of ocular tissues. The sclera is a major load bearing tissue and an essential component to most computational models of the eye. In preparation for the development of a pediatric FE model, age-dependent and anisotropic properties of sclera were evaluated in newborn (3–5 days) and toddler (4 weeks) pigs. Data from this study will guide future testing protocols for human pediatric specimens.

scholarly journals Aspects of Uncertainty Analysis for Large Nonlinear Computational Models

2010 ◽  
Vol 24-25 ◽  
pp. 25-41 ◽  
Author(s):  
Keith Worden ◽  
W.E. Becker ◽  
Manuela Battipede ◽  
Cecilia Surace
Keyword(s):  
Finite Element ◽  
Monte Carlo ◽  
Computational Models ◽  
Element Model ◽  
Finite Element Models ◽  
Bayesian Algorithm ◽  
Basic Principles ◽  
Structure Interaction ◽  
Output Uncertainty ◽  
Input Uncertainties

This paper concerns the analysis of how uncertainty propagates through large computational models like finite element models. If a model is expensive to run, a Monte Carlo approach based on sampling over the possible model inputs will not be feasible, because the large number of model runs will be prohibitively expensive. Fortunately, an alternative to Monte Carlo is available in the form of the established Bayesian algorithm discussed here; this algorithm can provide information about uncertainty with many less model runs than Monte Carlo requires. The algorithm also provides information regarding sensitivity to the inputs i.e. the extent to which input uncertainties are responsible for output uncertainty. After describing the basic principles of the Bayesian approach, it is illustrated via two case studies: the first concerns a finite element model of a human heart valve and the second, an airship model incorporating fluid structure interaction.

AN ALGORITHM TO CALCULATE THE COMPONENTS OF ALL MUSCLE FORCES DURING EACH PHASES OF THE GAIT CYCLE, FOR THE PELVIC-FEMUR COMPLEX

2005 ◽  
Vol 05 (04) ◽  
pp. 539-548 ◽  
Author(s):  
SANTANU MAJUMDER ◽  
AMIT ROYCHOWDHURY ◽  
SUBRATA PAL
Keyword(s):  
Finite Element ◽  
Hip Joint ◽  
Computational Models ◽  
Gait Cycle ◽  
Muscle Force ◽  
Fe Analysis ◽  
Muscle Forces ◽  
Force Magnitude ◽  
Flexion Extension ◽  
Force Components

With the help of finite element (FE) computational models of femur, pelvis or hip joint to perform quasi-static stress analysis during the entire gait cycle, muscle force components (X, Y, Z) acting on the hip joint and pelvis are to be known. Most of the investigators have presented only the net muscle force magnitude during gait. However, for the FE software, either muscle force components (X, Y, Z) or three angles for the muscle line of action are required as input. No published algorithm (with flowchart) is readily available to calculate the required muscle force components for FE analysis. As the femur rotates about the hip center during gait, the lines of action for 27 muscle forces are also variable. To find out the variable lines of action and muscle force components (X, Y, Z) with directions, an algorithm was developed and presented here with detailed flowchart. We considered the varying angles of adduction/abduction, flexion/extension during gait. This computer program, obtainable from the first author, is able to calculate the muscle force components (X, Y, Z) as output, if the net magnitude of muscle force, hip joint orientations during gait and muscle origin and insertion coordinates are provided as input.

Natural Frequencies of Rectangular Membrane With Boundary Perturbation

1995 ◽  
Vol 1 (2) ◽  
pp. 139-144 ◽  
Author(s):  
Jamal A. Masad
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Galerkin Method ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Perturbation Approach ◽  
Boundary Perturbation ◽  
The Finite Element Method ◽  
Analytic Expression ◽  
Element Method

A perturbation approach, coupled with the adjoint concept, is used to derive an analytic expression for the natural frequencies of a nearly rectangular membrane. The method is applied for a rectangular membrane with a semicircle at one of the boundaries. The fundamental natural frequency results for this configuration are presented and compared with results from a finite-element method and results from an approximate Galerkin method. The agreement between the fundamental natural frequencies calculated with the perturbation approach and those calculated with the finite-element method improves as the radius of the semicircle decreases and as the semicircle location becomes more eccentric.

Modeling Beam–Solid Finite Element Interfaces: A Stabilized Formulation for Contact and Coupled Systems

2018 ◽  
Vol 10 (09) ◽  
pp. 1850094 ◽  
Author(s):  
Jorge A. Montero ◽  
Ghadir Haikal
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Computational Models ◽  
Solid Mechanics ◽  
Pressure Field ◽  
Coupled Systems ◽  
Weak Continuity ◽  
Finite Element Discretizations ◽  
Geometric Compatibility ◽  
Element Discretizations

A number of engineering applications involve contact with bodies modeled using specialized theories of solid mechanics like beams or shells. While computational models for contact in 2D and 3D solid mechanics have been extensively developed in the literature, problems involving contact with beams or shells have received less attention. When modeling contact between a solid body represented with beam or shell theory and a domain discretized with solid finite elements, the contact model faces the typical challenges of enforcing geometric compatibility and the transfer of a complete pressure field along the contact interface, with the added complications stemming from the different underlying mathematical formulations and finite element discretizations in the connecting domains. Resultant-based beam and shell theories do not provide direct estimates of surface tractions, therefore rendering the issue of pressure transfer on beam–solid and shell–solid interfaces more problematic. In the absence of specialized contact formulations for solid–beam and solid–shell interfaces, contact models have relied almost exclusively on the Node-To-Surface (NTS) geometric compatibility approach. This formulation suffers from well-known drawbacks, including instability, surface locking and incomplete pressure fields on the interface. The NTS approach, however, remains the method most readily applicable to contact with beam or shell elements among the vast variety of available methods for computational contact modeling using finite elements. The goal of this paper is to bridge the gap in the literature on coupling domains with beam and solid finite element discretizations. We propose an interface formulation for beam–solid interfaces that ensures the transfer of a complete pressure field while enforcing geometric compatibility using standard NTS constraints. The formulation uses a stabilization approach, based on a special form of the Discontinuous Galerkin method, to enforce weak continuity between the stress fields on the solid side of the interface, and the moment and shear resultants in the contacting beam. We show that the proposed formulation is a robust approach for satisfying compatibility constraints while ensuring the transfer of a complete pressure field on beam–solid finite element interfaces that can be used with bilinear and quadratic interpolations in the solid, and Euler or Timoshenko formulations for the beam.

Development of a Discrete Finite Element Cell Model

2007 ◽  
Author(s):  
Karen M. Coghlan ◽  
Patrick McGarry ◽  
Mohammad R. K. Mofrad ◽  
Peter E. McHugh
Keyword(s):  
Finite Element ◽  
Structural Properties ◽  
Continuum Mechanics ◽  
Cell Mechanics ◽  
Computational Models ◽  
Cell Model ◽  
Alternative Approach ◽  
Discrete Nature ◽  
Discrete Finite Element

Computational models have proven useful in the study of cell mechanics and mechanotransduction. While most finite element (FE) models of cells are commonly described in terms of the laws of continuum mechanics, a model that can accurately represent the microstructure of the filamentous network of the cytoskeleton would be required to relate mechanics to biology at the microscale level. An alternative approach to a continuum is presented here, whereby the discrete nature of the cytoskeleton of the cell is emphasized and the known structural properties of the cytoskeleton of the cell are utilized.

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