Application of Simplified Parametric Model to Estimate Fan Blade-Out Response

2018 ◽  
Author(s):  
Theodore S. Brockett ◽  
Jerzy T. Sawicki
Keyword(s):  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Engine Performance ◽  
Low Pressure ◽  
External Loading ◽  
System Response ◽  
Angular Rotation ◽  
Mass Eccentricity ◽  
Fan Blade ◽  
The Impact

A six-degree-of-freedom non-linear model is developed using Lagrange’s equation. The model is used to estimate transient fan-stage dynamic response during a fan-blade-out event in a turbo fan engine. The coupled degrees of freedom in the model include the fan whirl in the fan plane, the torsional response of the fan and low-pressure turbines (LPTs) about the engine centerline, the radial position of the released blade fragment, and the angular rotation of the trailing blade from its free state due to acceleration of the released blade. The released blade is assumed to slide radially outward along the trailing blade without friction. The external loading applied to the system includes fan imbalance, the remaining fan blades machining away the rub strip, rubbing of the blades with the fan case, and slowly-varying torques on the low pressure (LP) spool as engine performance degrades. The machining of the abradable imparts tangential loading on the fan blades as momentum is transferred to the liberated rub strip material. After application of the initial conditions including angular positions, angular velocities, released blade fragment position, and torsional wind-up, the governing equations are integrated forward in time from the instant the blade fragment is released. A reasonable match to test data is shown. Parameters affecting the fan-system response are varied to study the impact on fan peak lateral whirl amplitude, peak LP shaft torque, and peak loading on the trailing blade. It is found that the rub strip and mass eccentricity have the strongest influence on the LP shaft torsional loading. It is found that mass eccentricity has the largest influence on peak fan whirl. It is also found that released blade mass and attachment stiffness have the largest influence on the trailing blade loading.

Approximate Floquet Analysis of Parametrically Excited Multi-Degree-of-Freedom Systems With Application to Wind Turbines

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Gizem D. Acar ◽  
Brian F. Feeny
Keyword(s):  
Eigenvalue Problem ◽  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
System Response ◽  
Periodic Part ◽  
Mdof Systems ◽  
Floquet Modes ◽  
Problem Frequency ◽  
Exponential Part

General responses of multi-degrees-of-freedom (MDOF) systems with parametric stiffness are studied. A Floquet-type solution, which is a product between an exponential part and a periodic part, is assumed, and applying harmonic balance, an eigenvalue problem is found. Solving the eigenvalue problem, frequency content of the solution and response to arbitrary initial conditions are determined. Using the eigenvalues and the eigenvectors, the system response is written in terms of “Floquet modes,” which are nonsynchronous, contrary to linear modes. Studying the eigenvalues (i.e., characteristic exponents), stability of the solution is investigated. The approach is applied to MDOF systems, including an example of a three-blade wind turbine, where the equations of motion have parametric stiffness terms due to gravity. The analytical solutions are also compared to numerical simulations for verification.

Transient CFD Co-Simulation of a 3D Compressor Model in its 1D System Environment

2019 ◽  
Author(s):  
Andreas Spille-Kohoff ◽  
Farai Hetze ◽  
Bennie Du Toit
Keyword(s):  
Distribution System ◽  
Gas Flow ◽  
Cfd Simulation ◽  
Flow Direction ◽  
Low Pressure ◽  
System Response ◽  
Pressure Side ◽  
Time Step ◽  
The Impact ◽  
Transient Coupling

Abstract Rotary compressors such as screw compressors, roots blowers, and turbo compressors are used in industry to compress process gases, or as vacuum or backing pumps to evacuate vessels. Gas is sucked in at low-pressure side, transported and compressed by size-changing chambers (PD machines) or energy transmission from rotor to fluid (turbo machinery), and released at high-pressure side. In expanders or turbines, flow direction is from high to low pressure side to gain energy from pressurized gases. The 3D CFD simulation of such compressors/expanders is complex and time-consuming due to its transient nature and fine meshes to ensure a proper representation of radial and axial gaps in the range of some microns with machine dimensions up to meters. Due to this complexity, 3D CFD simulation should focus on the component, i.e. the compressor, and the attached overall system with vessels, valves, pipes, and consumers should be simulated in a 1D network or system simulation. Due to oscillations in the gas flow and interaction with the connected system a transient coupling is necessary. In this paper we show a 3D CFD simulation of a screw compressor using ANSYS CFX in a co-simulation with the 1D Flownex simulation environment of a network modelling the pressurized gas distribution. Whereas the 3D solver works on meshes with up to several million nodes in parallel on HPC systems, the 1D solver typically works serially on several thousand nodes that discretize the flow direction. The transient coupling is based on the exchange of variables at the boundaries of each simulation for every time step allowing for detailed analysis. The impact of the acoustic propagation of pressure fluctuations and the pulsating fluid flow provided by the compressor on the distribution system, and in return the effects of the system response on the compressor are evaluated. Furthermore transient scenarios such as start-up procedures or component failure will be shown.

scholarly journals The Impact of Realistic Casing Geometries and Clearances on Fan Blade Tip Aerodynamics

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
Alistair John ◽  
Ning Qin ◽  
Shahrokh Shahpar
Keyword(s):  
Engine Performance ◽  
Leading Edge ◽  
Tip Clearance ◽  
Blade Design ◽  
Engine Operation ◽  
Surface Method ◽  
Flow Features ◽  
Blade Tip ◽  
Fan Blade ◽  
The Impact

During engine operation, fan casing abradable liners are worn by the blade tip, resulting in the formation of trenches. This paper describes the influence of these trenches on the fan blade tip aerodynamics. A detailed understanding of the fan tip flow features for cropped and trenched clearances is first developed. A parametric model is then used to model trenches in the casing above the blade tip and varying blade tip positions. It is shown that increasing clearance via a trench reduces performance by less than increasing clearance through cropping the blade tip. A response surface method is then used to generate a model that can predict fan efficiency for a given set of clearance and trench parameters. This model can be used to influence fan blade design and understand engine performance degradation in service. It is shown that an efficiency benefit can be achieved by increasing the amount of tip rubbing, leading to a greater portion of the tip clearance sat within the trench. It is shown that the efficiency sensitivity to clearance is biased toward the leading edge (LE) for cropped tips and the trailing edge (TE) for trenches.

scholarly journals An Engine Research Program Focused on Low Pressure Turbine Aerodynamic Performance

2002 ◽  
Author(s):  
Raymond Castner ◽  
Santo Chiappetta ◽  
John Wyzykowski ◽  
John Adamczyk
Keyword(s):  
Reynolds Number ◽  
Cfd Simulation ◽  
State Of The Art ◽  
Engine Performance ◽  
Low Pressure ◽  
Low Pressure Turbine ◽  
Flow Capacity ◽  
Comprehensive Test ◽  
The Impact ◽  
Bypass Ratio

A comprehensive test program was performed in the Propulsion Systems Laboratory at the NASA Glenn Research Center, Cleveland Ohio using a highly instrumented Pratt and Whitney Canada PW 545 turbofan engine. A key objective of this program was the development of a high-altitude database on small, high-bypass ratio engine performance and operability. In particular, the program documents the impact of altitude (Reynolds number) on the aero-performance of the low-pressure turbine (fan turbine). A second objective was to assess the ability of a state-of-the-art CFD code to predict the effect of Reynolds number on the efficiency of the low-pressure turbine. CFD simulation performed prior and after the engine tests will be presented and discussed. Key findings are the ability of a state-of-the art CFD code to accurately predict the impact of Reynolds number on the efficiency and flow capacity of the low-pressure turbine. In addition the CFD simulations showed the turbulence intensity exiting the low-pressure turbine to be high (9%). The level is consistent with measurements taken within an engine.

Mechanically-Tunable Quantum Interference in Ferrocene-Based Single-Molecule Junctions

2020 ◽  
Author(s):  
María Camarasa-Gómez ◽  
Daniel Hernangómez-Pérez ◽  
Michael S. Inkpen ◽  
Giacomo Lovat ◽  
E-Dean Fung ◽  
...  
Keyword(s):  
Single Molecule ◽  
Quantum Interference ◽  
Degrees Of Freedom ◽  
Building Blocks ◽  
Ferrocene Derivative ◽  
Single Molecule Junctions ◽  
Molecule Junction ◽  
Single Molecule Junction ◽  
The Impact ◽  
D Orbitals

Ferrocenes are ubiquitous organometallic building blocks that comprise a Fe atom sandwiched between two cyclopentadienyl (Cp) rings that rotate freely at room temperature. Of widespread interest in fundamental studies and real-world applications, they have also attracted<br>some interest as functional elements of molecular-scale devices. Here we investigate the impact of<br>the configurational degrees of freedom of a ferrocene derivative on its single-molecule junction<br>conductance. Measurements indicate that the conductance of the ferrocene derivative, which is<br>suppressed by two orders of magnitude as compared to a fully conjugated analog, can be modulated<br>by altering the junction configuration. Ab initio transport calculations show that the low conductance is a consequence of destructive quantum interference effects that arise from the hybridization of metal-based d-orbitals and the ligand-based π-system. By rotating the Cp rings, the hybridization, and thus the quantum interference, can be mechanically controlled, resulting in a conductance modulation that is seen experimentally.<br>

scholarly journals On Kaufmann's theory of the impact of the pianoforte hammer

1920 ◽  
Vol 97 (682) ◽  
pp. 99-110 ◽  
Keyword(s):  
Initial Conditions ◽  
Practical Importance ◽  
Prima Facie ◽  
Point Of View ◽  
Infinite Length ◽  
Modes Of Vibration ◽  
Rigorous Treatment ◽  
The Subject ◽  
Set Up ◽  
The Impact

The theory of the vibrations of the pianoforte string put forward by Kaufmann in a well-known paper has figured prominently in recent discussions on the acoustics of this instrument. It proceeds on lines radically different from those adopted by Helmholtz in his classical treatment of the subject. While recognising that the elasticity of the pianoforte hammer is not a negligible factor, Kaufmann set out to simplify the mathematical analysis by ignoring its effect altogether, and treating the hammer as a particle possessing only inertia without spring. The motion of the string following the impact of the hammer is found from the initial conditions and from the functional solutions of the equation of wave-propagation on the string. On this basis he gave a rigorous treatment of two cases: (1) a particle impinging on a stretched string of infinite length, and (2) a particle impinging on the centre of a finite string, neither of which cases is of much interest from an acoustical point of view. The case of practical importance treated by him is that in which a particle impinges on the string near one end. For this case, he gave only an approximate theory from which the duration of contact, the motion of the point struck, and the form of the vibration-curves for various points of the string could be found. There can be no doubt of the importance of Kaufmann’s work, and it naturally becomes necessary to extend and revise his theory in various directions. In several respects, the theory awaits fuller development, especially as regards the harmonic analysis of the modes of vibration set up by impact, and the detailed discussion of the influence of the elasticity of the hammer and of varying velocities of impact. Apart from these points, the question arises whether the approximate method used by Kaufmann is sufficiently accurate for practical purposes, and whether it may be regarded as applicable when, as in the pianoforte, the point struck is distant one-eighth or one-ninth of the length of the string from one end. Kaufmann’s treatment is practically based on the assumption that the part of the string between the end and the point struck remains straight as long as the hammer and string remain in contact. Primâ facie , it is clear that this assumption would introduce error when the part of the string under reference is an appreciable fraction of the whole. For the effect of the impact would obviously be to excite the vibrations of this portion of the string, which continue so long as the hammer is in contact, and would also influence the mode of vibration of the string as a whole when the hammer loses contact. A mathematical theory which is not subject to this error, and which is applicable for any position of the striking point, thus seems called for.

scholarly journals A Rational Numerical Method for Simulation of Drop-Impact Dynamics of Oleo-Pneumatic Landing Gear

2021 ◽  
Vol 11 (9) ◽  
pp. 4136
Author(s):  
Rosario Pecora
Keyword(s):  
Numerical Method ◽  
Initial Conditions ◽  
Impact Load ◽  
Numerical Models ◽  
Landing Gear ◽  
Design Stage ◽  
Impact Dynamics ◽  
State Variables ◽  
Adopted Model ◽  
The Impact

Oleo-pneumatic landing gear is a complex mechanical system conceived to efficiently absorb and dissipate an aircraft’s kinetic energy at touchdown, thus reducing the impact load and acceleration transmitted to the airframe. Due to its significant influence on ground loads, this system is generally designed in parallel with the main structural components of the aircraft, such as the fuselage and wings. Robust numerical models for simulating landing gear impact dynamics are essential from the preliminary design stage in order to properly assess aircraft configuration and structural arrangements. Finite element (FE) analysis is a viable solution for supporting the design. However, regarding the oleo-pneumatic struts, FE-based simulation may become unpractical, since detailed models are required to obtain reliable results. Moreover, FE models could not be very versatile for accommodating the many design updates that usually occur at the beginning of the landing gear project or during the layout optimization process. In this work, a numerical method for simulating oleo-pneumatic landing gear drop dynamics is presented. To effectively support both the preliminary and advanced design of landing gear units, the proposed simulation approach rationally balances the level of sophistication of the adopted model with the need for accurate results. Although based on a formulation assuming only four state variables for the description of landing gear dynamics, the approach successfully accounts for all the relevant forces that arise during the drop and their influence on landing gear motion. A set of intercommunicating routines was implemented in MATLAB® environment to integrate the dynamic impact equations, starting from user-defined initial conditions and general parameters related to the geometric and structural configuration of the landing gear. The tool was then used to simulate a drop test of a reference landing gear, and the obtained results were successfully validated against available experimental data.

scholarly journals The halo model as a versatile tool to predict intrinsic alignments

2020 ◽  
Author(s):  
Maria Cristina Fortuna ◽  
Henk Hoekstra ◽  
Benjamin Joachimi ◽  
Harry Johnston ◽  
Nora Elisa Chisari ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Power Spectra ◽  
Stage Iv ◽  
Stage Iii ◽  
Radial Dependence ◽  
Additional Parameter ◽  
Small Scales ◽  
Cosmic Shear ◽  
Galaxy Populations ◽  
The Impact

Abstract Intrinsic alignments (IAs) of galaxies are an important contaminant for cosmic shear studies, but the modelling is complicated by the dependence of the signal on the source galaxy sample. In this paper, we use the halo model formalism to capture this diversity and examine its implications for Stage-III and Stage-IV cosmic shear surveys. We account for the different IA signatures at large and small scales, as well for the different contributions from central/satellite and red/blue galaxies, and we use realistic mocks to account for the characteristics of the galaxy populations as a function of redshift. We inform our model using the most recent observational findings: we include a luminosity dependence at both large and small scales and a radial dependence of the signal within the halo. We predict the impact of the total IA signal on the lensing angular power spectra, including the current uncertainties from the IA best-fits to illustrate the range of possible impact on the lensing signal: the lack of constraints for fainter galaxies is the main source of uncertainty for our predictions of the IA signal. We investigate how well effective models with limited degrees of freedom can account for the complexity of the IA signal. Although these lead to negligible biases for Stage-III surveys, we find that, for Stage-IV surveys, it is essential to at least include an additional parameter to capture the redshift dependence.

scholarly journals A Superfluid Perspective on Neutron Star Dynamics

Universe ◽  
2021 ◽  
Vol 7 (1) ◽  
pp. 17
Author(s):  
Nils Andersson
Keyword(s):  
Neutron Star ◽  
Degrees Of Freedom ◽  
Temperature Scale ◽  
Fluid System ◽  
Fluid Core ◽  
State Of Matter ◽  
Entrainment Effect ◽  
Neutron Component ◽  
The Impact

As mature neutron stars are cold (on the relevant temperature scale), one has to carefully consider the state of matter in their interior. The outer kilometre or so is expected to freeze to form an elastic crust of increasingly neutron-rich nuclei, coexisting with a superfluid neutron component, while the star’s fluid core contains a mixed superfluid/superconductor. The dynamics of the star depend heavily on the parameters associated with the different phases. The presence of superfluidity brings new degrees of freedom—in essence we are dealing with a complex multi-fluid system—and additional features: bulk rotation is supported by a dense array of quantised vortices, which introduce dissipation via mutual friction, and the motion of the superfluid is affected by the so-called entrainment effect. This brief survey provides an introduction to—along with a commentary on our current understanding of—these dynamical aspects, paying particular attention to the role of entrainment, and outlines the impact of superfluidity on neutron-star seismology.

scholarly journals Variation in human mobility and its impact on the risk of future COVID-19 outbreaks in Taiwan

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Meng-Chun Chang ◽  
Rebecca Kahn ◽  
Yu-An Li ◽  
Cheng-Sheng Lee ◽  
Caroline O. Buckee ◽  
...  
Keyword(s):  
Disease Surveillance ◽  
Initial Conditions ◽  
Human Mobility ◽  
Human Movement ◽  
Disease Spread ◽  
Spatial Spread ◽  
Movement Data ◽  
Intercity Travel ◽  
Travel Restrictions ◽  
The Impact

Abstract Background As COVID-19 continues to spread around the world, understanding how patterns of human mobility and connectivity affect outbreak dynamics, especially before outbreaks establish locally, is critical for informing response efforts. In Taiwan, most cases to date were imported or linked to imported cases. Methods In collaboration with Facebook Data for Good, we characterized changes in movement patterns in Taiwan since February 2020, and built metapopulation models that incorporate human movement data to identify the high risk areas of disease spread and assess the potential effects of local travel restrictions in Taiwan. Results We found that mobility changed with the number of local cases in Taiwan in the past few months. For each city, we identified the most highly connected areas that may serve as sources of importation during an outbreak. We showed that the risk of an outbreak in Taiwan is enhanced if initial infections occur around holidays. Intracity travel reductions have a higher impact on the risk of an outbreak than intercity travel reductions, while intercity travel reductions can narrow the scope of the outbreak and help target resources. The timing, duration, and level of travel reduction together determine the impact of travel reductions on the number of infections, and multiple combinations of these can result in similar impact. Conclusions To prepare for the potential spread within Taiwan, we utilized Facebook’s aggregated and anonymized movement and colocation data to identify cities with higher risk of infection and regional importation. We developed an interactive application that allows users to vary inputs and assumptions and shows the spatial spread of the disease and the impact of intercity and intracity travel reduction under different initial conditions. Our results can be used readily if local transmission occurs in Taiwan after relaxation of border control, providing important insights into future disease surveillance and policies for travel restrictions.

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