scholarly journals Determination of Aerodynamic Damping at High Reduced Frequencies

2018 ◽  
Author(s):  
Minghao Pan ◽  
Paul Petrie-Repar ◽  
Hans Mårtensson ◽  
Tianrui Sun ◽  
Tobias Gezork
Keyword(s):  
Acoustic Resonance ◽  
Forced Response ◽  
Economic Consequences ◽  
Navier Stokes ◽  
Flow Solver ◽  
Aerodynamic Damping ◽  
Acoustic Modes ◽  
Reduced Frequency ◽  
Standard Configuration

In turbomachines, forced response of blades is blade vibrations due to external aerodynamic excitations and it can lead to blade failures which can have fatal or severe economic consequences. The estimation of the level of vibration due to forced response is dependent on the determination of aerodynamic damping. The most critical cases for forced response occur at high reduced frequencies. This paper investigates the determination of aerodynamic damping at high reduced frequencies. The aerodynamic damping was calculated by a linearized Navier-Stokes flow solver with exact 3D non-reflecting boundary conditions. The method was validated using Standard Configuration 8, a two-dimensional flat plate. Good agreement with the reference data at reduced frequency 2.0 was achieved and grid converged solutions with reduced frequency up to 16.0 were obtained. It was concluded that at least 20 cells per wavelength is required. A 3D profile was also investigated: an aeroelastic turbine rig (AETR) which is a subsonic turbine case. In the AETR case, the first bending mode with reduced frequency 2.0 was studied. The 3D acoustic modes were calculated at the far-fields and the propagating amplitude was plotted as a function of circumferential mode index and radial order. This plot identified six acoustic resonance points which included two points corresponding to the first radial modes. The aerodynamic damping as a function of nodal diameter was also calculated and plotted. There were six distinct peaks which occurred in the damping curve and these peaks correspond to the six resonance points. This demonstrates for the first time that acoustic resonances due to higher order radial acoustic modes can affect the aerodynamic damping at high reduced frequencies.

Analytical Maps of Aerodynamic Damping as a Function of Operating Condition for a Compressor Profile

2006 ◽  
Author(s):  
Paul J. Petrie-Repar ◽  
Andrew McGhee ◽  
Peter A. Jacobs ◽  
Rowan Gollan
Keyword(s):  
Inviscid Flow ◽  
Operating Conditions ◽  
Navier Stokes ◽  
Compressor Cascade ◽  
Operating Condition ◽  
Flow Solver ◽  
Aerodynamic Damping ◽  
Wide Range ◽  
Contour Plots ◽  
Standard Configuration

In this paper, analytical maps of aerodynamic damping for a two-dimensional compressor cascade (Standard Configuration 10) are presented. The maps are shown as contour plots of the aerodynamic damping as a function of operating condition. The aerodynamic dampings were calculated by a linearized Navier-Stokes flow solver. The flutter boundaries over a wide range of operating conditions are clearly shown on the damping maps and were found to be strongly dependent on the mode frequency and the mode shape. Extremely low values of negative aerodynamic damping were predicted for some off-design operating conditions where flow separation occurred. A damping map was also constructed based on inviscid flow simulations. There were differences in the viscous and inviscid flutter boundaries particularly at off-design inflow angles. The extremely low values of negative aerodynamic damping were only predicted by the viscous simulations and not the inviscid simulations.

Physical Understanding and Sensitivities of Low Pressure Turbine Flutter

2014 ◽  
Vol 137 (1) ◽  
Author(s):  
Joshua J. Waite ◽  
Robert E. Kielb
Keyword(s):  
Dynamic Pressure ◽  
Acoustic Resonance ◽  
Low Pressure ◽  
Navier Stokes ◽  
Low Pressure Turbine ◽  
Reduced Frequency ◽  
Influence Coefficients ◽  
Standard Configuration ◽  
Physical Phenomena ◽  
Phase Angles

Successful, efficient turbine design requires a thorough understanding of the underlying physical phenomena. This paper investigates the flutter phenomenon of low pressure turbine (LPT) blades seen in aircraft engines and power turbines. Computational fluid dynamics (CFD) analysis will be conducted in a two-dimensional (2D) sense using a frequency domain Reynolds-averaged Navier—Stokes (RANS) solver on a publicly available LPT airfoil geometry: École Polytechnique Fédérale De Lausanne (EPFL's) Standard Configuration 4. An emphasis is placed on revealing the underlying physics behind the threatening LPT flutter mechanism. To this end, flutter sensitivity analysis is conducted on three key parameters: reduced frequency, mode shape, and Mach number. Additionally, exact 2D acoustic resonance interblade phase angles (IBPAs) are analytically predicted as a function of reduced frequency. Made evident via damping versus IBPA plots, the CFD model successfully captures the theoretical acoustic resonance predictions. Studies of the decay of unsteady aerodynamic influence coefficients away from a reference blade are also presented. The influence coefficients provide key insights to the harmonic content of the unsteady pressure field. Finally, this work explores methods of normalizing the work per cycle by the exit dynamic pressure.

Forced Response Analysis of a Transonic Fan

2012 ◽  
Author(s):  
Parthasarathy Vasanthakumar ◽  
Paul-Benjamin Ebel
Keyword(s):  
Finite Element ◽  
Flow Field ◽  
Forced Response ◽  
Navier Stokes ◽  
Response Analysis ◽  
Aerodynamic Damping ◽  
Forcing Function ◽  
Transonic Fan ◽  
Work Done ◽  
Highly Loaded

The forced response of turbomachinery blades is a primary source of high cycle fatigue (HCF) failure. This paper deals with the computational prediction of blade forced response of a transonic fan stage that consists of a highly loaded rotor along with a tandem stator. In the case of a transonic fan, the forced response of the rotor due to the downstream stator assumes significance because of the transonic flow field. The objective of the present work is to determine the forced response of the rotor induced as a result of the unsteady flow field due to the downstream stator vanes. Three dimensional, Navier-Stokes flow solver TRACE is used to numerically analyse the forced response of the fan. A total of 11 resonant crossings as identified in the Campbell diagram are examined and the corresponding modeshapes are obtained from finite element modal analysis. The interaction between fluid and structure is dealt with in a loosely coupled manner based on the assumption of linear aerodynamic damping. The aerodynamic forcing is obtained by a nonlinear unsteady Navier-Stokes computation and the aerodynamic damping is obtained by a time-linearized Navier-Stokes computation. The forced response solution is obtained by the energy method allowing calculations to be performed directly in physical space. Using the modal forcing and damping, the forced response amplitude can be directly computed at the resonance crossings. For forced response solution, the equilibrium amplitude is reached when the work done on the blade by the external forcing function is equal to the work done by the system damping (aerodynamic and structural) force. A comprehensive analysis of unsteady aerodynamic forces on the rotor blade surface as a result of forced response of a highly loaded transonic fan is carried out. In addition, the correspondence between the location of high stress zones identified from the finite element analysis and the regions of high modal force identified from the CFD analysis is also discussed.

A Navier–Stokes Analysis of Airfoils in Oscillating Transonic Cascades for the Prediction of Aerodynamic Damping

1997 ◽  
Vol 119 (1) ◽  
pp. 77-84 ◽  
Author(s):  
R. S. Abhari ◽  
M. Giles
Keyword(s):  
Numerical Study ◽  
Three Dimensional ◽  
Outer Region ◽  
Navier Stokes ◽  
Compressor Cascade ◽  
Time Step ◽  
Aerodynamic Damping ◽  
Transonic Compressor ◽  
Standard Configuration ◽  
The Impact

An unsteady, compressible, two-dimensional, thin shear layer Navier–Stokes solver is modified to predict the motion-dependent unsteady flow around oscillating airfoils in a cascade. A quasi-three-dimensional formulations is used to account for the stream-wise variation of streamtube height. The code uses Ni’s Lax–Wendroff algorithm in the outer region, an implicit ADI method in the inner region, conservative coupling at the interface, and the Baldwin–Lomax turbulence model. The computational mesh consists of an O-grid around each blade plus an unstructured outer grid of quadrilateral or triangular cells. The unstructured computational grid was adapted to the flow to better resolve shocks and wakes. Motion of each airfoil was simulated at each time step by stretching and compressing the mesh within the O-grid. This imposed motion consists of harmonic solid body translation in two directions and rotation, combined with the correct interblade phase angles. The validity of the code is illustrated by comparing its predictions to a number of test cases, including an axially oscillating flat plate in laminar flow, the Aeroelasticity of Turbomachines Symposium Fourth Standard Configuration (a transonic turbine cascade), and the Seventh Standard Configuration (a transonic compressor cascade). The overall comparison between the predictions and the test data is reasonably good. A numerical study on a generic transonic compressor rotor was performed in which the impact of varying the amplitude of the airfoil oscillation on the normalized predicted magnitude and phase of the unsteady pressure around the airfoil was studied. It was observed that for this transonic compressor, the nondimensional aerodynamic damping was influenced by the amplitude of the oscillation.

The Impact of Blade Loading and Unsteady Pressure Bifurcations on Low-Pressure Turbine Flutter Boundaries

2015 ◽  
Author(s):  
Joshua J. Waite ◽  
Robert E. Kielb
Keyword(s):  
Mode Shape ◽  
Pressure Ratio ◽  
Low Pressure ◽  
Forced Response ◽  
Blade Loading ◽  
Unsteady Pressure ◽  
Aerodynamic Damping ◽  
Low Pressure Turbine ◽  
Reduced Frequency ◽  
The Impact

The three major aeroelastic issues in the turbomachinery blades of jet engines and power turbines are forced response, non-synchronous vibrations, and flutter. Flutter primarily affects high-aspect ratio blades found in the fan, fore high-pressure compressor stages, and aft low-pressure turbine (LPT) stages as low natural frequencies and high axial velocities create smaller reduced frequencies. Often with LPT flutter analyses, physical insights are lost in the exhaustive quest for determining whether the aerodynamic damping is positive or negative. This paper underlines some well known causes of low-pressure turbine flutter in addition to one novel catalyst. In particular, an emphasis is placed on revealing how local aerodynamic damping contributions change as a function of unsteady (e.g. mode shape, reduced frequency) and steady (e.g. blade torque, pressure ratio) parameters. To this end, frequency domain RANS CFD analyses are used as computational wind tunnels to investigate how aerodynamic loading variations affect flutter boundaries. Preliminary results show clear trends between the aerodynamic work influence coefficients and variations in exit Mach number and back pressure, especially for torsional mode shapes affecting the passage throat. Additionally, visualizations of qualitative bifurcations in the unsteady pressure phases around the airfoil shed light on how local damping contributions evolve with steady loading. Final results indicate a sharp drop in aeroelastic stability near specific regions of the pressure ratio indicating a strong correlation between blade loading and flutter. Passage throat shock behavior is shown to be a controlling factor near the trailing edge, and like critical reduced frequency, this phenomenon is shown to be highly dependent on the vibratory mode shape.

Blade Aerodynamic Damping Variation With Rotor-Stator Gap: A Computational Study Using Single-Passage Approach

2003 ◽  
Vol 127 (3) ◽  
pp. 573-579 ◽  
Author(s):  
H. D Li ◽  
L. He
Keyword(s):  
Computational Study ◽  
Three Dimensional ◽  
Forced Response ◽  
Navier Stokes ◽  
Aerodynamic Damping ◽  
Transonic Compressor ◽  
Single Passage ◽  
Finite Volume Discretization ◽  
Shape Correction ◽  
Gap Spacing

One of the outstanding issues in turbomachinery aeromechanic analysis is the intrarow interaction effects. The present work is aimed at a systematic examination of rotor-stator gap effects on blade aerodynamic damping by using a three-dimensional (3D) time-domain single-passage Navier-Stokes solver. The method is based on the upwind finite volume discretization and the single-passage shape-correction approach with enhanced accuracy and efficiency for unsteady transonic flows prediction. A significant speedup (by a factor of 20) over to a conventional whole annulus solution has been achieved. A parametric study with different rotor-stator gaps (56%–216% rotor tip chord) for a 3D transonic compressor stage illustrates that the reflection from an adjacent stator row can change rotor aerodynamic damping by up to 100% depending on the intrarow gap spacing. Furthermore, this rotor aerodamping dependency on the intrarow gap seems also to be affected by the number of stator blades. The predicted nonmonotonic relationship between the rotor blade aerodynamic damping and the gap spacing suggests the existence of an optimum gap regarding rotor flutter stability and/or forced response stress levels.

scholarly journals Computation of Aerodynamic Damping for Flutter Analysis of a Transonic Fan

2011 ◽  
Author(s):  
Parthasarathy Vasanthakumar
Keyword(s):  
Phase Angle ◽  
Stokes Equations ◽  
Mode Shapes ◽  
Navier Stokes ◽  
Aerodynamic Load ◽  
Exchange Method ◽  
Flow Solver ◽  
Aerodynamic Damping ◽  
Transonic Fan ◽  
Operating Points

This paper describes the computational analysis of aerodynamic damping for prediction of flutter characteristics of a transonic fan stage that consists of a highly loaded rotor along with a tandem stator. Three dimensional, linearized Navier-Stokes flow solver TRACE is used to numerically analyse the flutter stability of the fan. The linear flow solver enables the modeling of a single blade passage to simulate the desired inter-blade phase angle. The unsteady aerodynamic load on a vibrating blade is obtained by solving the unsteady Navier-Stokes equations on a dynamically deforming grid and the energy exchange method is used to calculate the aerodynamic damping. The calculation of aerodynamic damping for the prediction of flutter characteristics of the fan rotor is carried out with and without considering the influence of the disk. The blade mode shapes from finite element modal analysis are obtained accordingly and the flutter calculations are carried out for three blade vibration modes at the design speed and at part speeds for all possible inter-blade phase angles. Two operating points, one on the working line and the other near stall are investigated at every rotational speed. Different aspects that affect the aerodynamic damping behaviour like part speed operation, variation in unsteady blade surface pressure fluctuation between operating points on the working line and at near stall and the corresponding variation in aerodynamic work, inter-blade phase angle etc., are described. This analysis primarily focuses on the variations in aerodynamic damping of the fan with and without the influence of the disk. In addition, influence and effect of shock wave on the aerodynamic damping is also discussed.

Blade Aerodynamic Damping Variation With Rotor-Stator Gap: A Computational Study Using Single-Passage Approach

2003 ◽  
Author(s):  
H. D. Li ◽  
L. He
Keyword(s):  
Computational Study ◽  
Forced Response ◽  
Navier Stokes ◽  
Aerodynamic Damping ◽  
Transonic Compressor ◽  
Single Passage ◽  
Finite Volume Discretization ◽  
Shape Correction ◽  
Speed Up ◽  
Stator Blade

One of the outstanding issues in turbomachinery aeromechanic analysis is the intra-row interaction effects. The present work is aimed at a systematic examination of rotorstator gap effects on blade aerodynamic damping by using a 3D time-domain single-passage Navier-Stokes solver. The method is based on the upwind finite volume discretization (AUSMD/V) and the single-passage Shape-Correction approach with enhanced accuracy and efficiency for unsteady transonic flows prediction. A significant speed up (by a factor of 20) over to a conventional whole annulus solution has been achieved. A parametric study with different rotor-stator gaps (56%–216% chord) for a 3D transonic compressor stage illustrates that the reflection from an adjacent stator row can change rotor aerodynamic damping by up to 100%. It is shown that this intra-row interference effect on the rotor aero-damping can be qualitatively altered by changing the number of stator blades. Thus, the stator blade count could be considered as a useful aeromechanical control/design parameter. Furthermore, the predicted non-monotonic relationship between the rotor blade aerodynamic damping and the gap distance suggests the existence of an optimum gap regarding rotor flutter stability and/or forced response stress levels.

Physical Understanding and Sensitivities of LPT Flutter

2014 ◽  
Author(s):  
Joshua J. Waite ◽  
Robert E. Kielb
Keyword(s):  
Dynamic Pressure ◽  
Acoustic Resonance ◽  
Two Dimensional ◽  
Low Pressure Turbine ◽  
Reduced Frequency ◽  
Influence Coefficients ◽  
Standard Configuration ◽  
Turbine Design ◽  
Physical Phenomena ◽  
Phase Angles

Successful, efficient turbine design requires a thorough understanding of the underlying physical phenomena. This paper investigates the flutter phenomenon of low pressure turbine (LPT) blades seen in aircraft engines and power turbines. CFD analysis will be conducted in a two-dimensional sense using a frequency domain RANS solver on a publicly available LPT airfoil geometry: EPFL’s Standard Configuration 4. An emphasis is placed on revealing the underlying physics behind the threatening LPT flutter mechanism. To this end, flutter sensitivity analysis is conducted on three key parameters: reduced frequency, mode shape, and Mach number. Additionally, exact two-dimensional acoustic resonance inter-blade phase angles (IBPAs) are analytically predicted as a function of reduced frequency. Made evident via damping vs. IBPA plots, the CFD model successfully captures the theoretical acoustic resonance predictions. Studies of the decay of unsteady aerodynamic influence coefficients away from a reference blade are also presented. The influence coefficients provide key insights to the harmonic content of the unsteady pressure field. Finally, this work explores methods of normalizing the work per cycle by the exit dynamic pressure.

Computation of Modal Aerodynamic Damping Using CFD

2003 ◽  
Author(s):  
F. Bertagnolio ◽  
M. Gaunaa ◽  
N. N. So̸rensen ◽  
M. Hansen ◽  
F. Rasmussen
Keyword(s):  
Wind Turbine ◽  
Structural Model ◽  
Turbine Rotor ◽  
Dynamic Stall ◽  
Navier Stokes ◽  
Test Cases ◽  
Flow Solver ◽  
Aerodynamic Damping ◽  
Semi Empirical ◽  
Wind Turbine Rotor

This work focuses on the numerical evaluation of aerodynamic damping for a wind turbine rotor. A finite beam element code is used to describe the structure. Two types of aerodynamic models are compared. Firstly, two engineering semi-empirical dynamic stall models implemented in the structural code for modelling the aerodynamic forces are applied. Secondly, a Navier-Stokes flow solver has been coupled to the structural model. Test cases involving a two-bladed wind turbine rotor are computed. The aerodynamic damping is determined for the two first eigenmodes of the structure. A comparison study of the results highlights the discrepancies between the different models.

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