Application of the Modal Approach for Prediction of Forced Response Amplitudes for Fan Blades

2018 ◽  
Vol 141 (3) ◽  
Author(s):  
Franziska Eichner ◽  
Joachim Belz
Keyword(s):  
Energy Method ◽  
Stokes Equations ◽  
Resonant Mode ◽  
Forced Response ◽  
Navier Stokes ◽  
Vibrational Amplitude ◽  
Modal Approach ◽  
Blade Row ◽  
The Impact ◽  
Blade Row Interaction

Forced response is the main reason for high cycle fatigue in turbomachinery. Not all resonance points in the operating range can be avoided especially for low order excitation. For highly flexible carbon fiber reinforced polymer (CFRP) fans, an accurate calculation of vibration amplitudes is required. Forced response analyses were performed for blade row interaction and boundary layer ingestion (BLI). The resonance points considered were identified in the Campbell diagram. Forced response amplitudes were calculated using a modal approach and the results are compared to the widely used energy method. For the unsteady simulations, a time-based linearization of the unsteady Reynolds average Navier–Stokes equations were applied. If only the resonant mode was considered, the forced response amplitude from the modal approach was confirmed with the energy method. Thereby, forced response due to BLI showed higher vibration amplitudes than for blade row interaction. The impact of modes which are not in resonant to the total deformation were investigated by using the modal approach, which so far only considers one excitation order. A doubling of vibrational amplitude was shown in the case of blade row interaction for higher rotational speeds. The first and third modeshapes as well as modes with similar natural frequencies were identified as critical cases. The behavior in the vicinity of resonance shows high vibration amplitudes over a larger frequency range. This is also valid for high modes with many nodal diameters, which have a greater risk of critical strain.

Application of the Modal Approach for Prediction of Forced Response Amplitudes for Fan Blades

2018 ◽  
Author(s):  
Franziska Eichner ◽  
Joachim Belz
Keyword(s):  
Energy Method ◽  
Natural Frequencies ◽  
Resonant Mode ◽  
Forced Response ◽  
Vibrational Amplitude ◽  
Campbell Diagram ◽  
Modal Approach ◽  
Blade Row ◽  
The Impact ◽  
Blade Row Interaction

Forced response is the main reason for high cycle fatigue in turbomachinery. Not all resonance points in the operating range can be avoided especially for low order excitation. For highly flexible CFRP fans an accurate calculation of vibration amplitudes is required. Forced response analyses were performed for blade row interaction and boundary layer ingestion. The resonance points considered were identified in the Campbell diagram. Forced response amplitudes were calculated using a modal approach and results are compared to the widely used energy method. For the unsteady simulations a time-linearised URANS method was applied. If only the resonant mode was considered the forced response amplitude from the modal approach was confirmed with the energy method. Thereby forced response due to BLI showed higher vibration amplitudes than for blade row interaction. The impact of modes which are not in resonant to the total deformation were investigated by using the modal approach, which so far, only considers one excitation order. A doubling of vibrational amplitude was shown in the case of blade row interaction for higher rotational speeds. The first and third mode-shape as well as modes with similar natural frequencies were identified as critical cases. The behaviour in the vicinity of resonance shows high vibration amplitudes over a larger frequency range. This is also valid for high modes with many nodal diameters, which have a greater risk of critical strain.

Aerodynamic Origin of Rotor-Rotor Interaction Noise From Unducted Propulsors

2013 ◽  
Author(s):  
Florian Danner ◽  
Christofer Kendall-Torry ◽  
Hans-Peter Kau
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Propagation Characteristics ◽  
Propulsion Systems ◽  
Navier Stokes Equations ◽  
Pressure Distributions ◽  
Blade Row ◽  
Open Rotor ◽  
Blade Row Interaction ◽  
Insight Into

The sound arising from blade row interaction in open rotor propulsion systems is known to significantly contribute to overall noise emissions. The present paper therefore addresses the origination of rotor-rotor interaction noise from a pair of unducted counter-rotating fans. The focus is on the aerodynamic mechanisms that involve sound generation, in order to provide the physical understanding required to find noise-reducing means. Detailed insight into the underlying phenomena is provided on the basis of numerical simulations applying the unsteady Reynolds-averaged Navier-Stokes equations. The interaction mechanisms are identified by extracting the time-dependent disturbances of the flow field in the respective rotor relative frame of reference. Conclusions on the sources of interaction noise and potential noise-reducing means are drawn by evaluating polar directivities, blade surface pressure distributions and propagation characteristics.

Unsteady Forcing vs. Efficiency: The Effect of Clocking on a Transonic Industrial Compressor

2013 ◽  
Author(s):  
Florian Fruth ◽  
Damian M. Vogt ◽  
Ronnie Bladh ◽  
Torsten H. Fransson
Keyword(s):  
Stokes Equations ◽  
Leading Edge ◽  
Forced Response ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Transonic Compressor ◽  
Design Changes ◽  
Transient Simulations ◽  
Stator Blade ◽  
The Impact

A numerical investigation on the impact of clocking on the efficiency and the aerodynamic forcing of the first 1.5 stages of an industrial transonic compressor was conducted. Using unsteady 3D Navier-Stokes equations, seven clocking positions were calculated and analyzed. Efficiency changes due to clocking were up to 0.125%, whereas modal excitation changes up to 31.7%. However, no direct correlation between the parameters of efficiency, stimulus and modal excitation was found as reported by others. It was found that potential forced response risks can be reduced by clocking, resulting only in minor efficiency penalties. Assuming almost sinusoidal behavior of efficiency and stimulus changes, as found in this investigation, both parameters can be set into correlation by using an ellipse interpolation. Direct impact of design changes on efficiency and stimulus through clocking can be deducted from that graph and quick estimations about extrema be made using only 5–6 transient simulations. Results however also stress the importance of considering modal excitation when optimizing for aerodynamic forcing, for which the ellipse interpolation is not necessarily possible. Highest efficiency is achieved with the IGV wake impinging on the stator blade leading edge at mid-span. It was found however that this alone is not a sufficient criteria in case of inclined wakes, as wake impingement at different span positions leads to different efficiencies.

Analysis of Unsteady Blade Row Interaction Using Nonlinear Harmonic Approach

2000 ◽  
Author(s):  
T. Chen ◽  
P. Vasanthakumar ◽  
L. He
Keyword(s):  
Stokes Equations ◽  
Linear Time ◽  
Three Dimensional ◽  
Axial Flow ◽  
Interaction Effects ◽  
Navier Stokes ◽  
Linear Interaction ◽  
Blade Row ◽  
Non Linear ◽  
Blade Row Interaction

An efficient non-linear harmonic methodology has been developed for predicting unsteady blade row interaction effects in multistage axial flow compressors. Flow variables are decomposed into time averaged variables and unsteady perturbations, resulting in time averaged equations with deterministic stress terms depending on the unsteady perturbation. The non-linear interaction between the time averaged flow field and the unsteady perturbations are included by a simultaneous pseudotime integration approach, leading to a strongly coupled solution. The stator/rotor interface treatment follows a flux averaged characteristic based mixing plane approach and includes the deterministic stress terms due to upstream running potential disturbances and downstream running wakes, resulting in the continuous nature of all parameters across the interface. The basic computational methodology is applied to the three-dimensional Navier-Stokes equations and validated against several cases. Results show that this method is much more efficient than the non-linear time-marching methods while still modeling the nonlinear unsteady blade row interaction effects.

scholarly journals Navier-Stokes and Potential Calculations of Axial Spacing Effect on Vortical and Potential Disturbances and Gust Response in an Axial Compressor

1995 ◽  
Author(s):  
Meng-Hsuan Chung ◽  
Andrew M. Wo
Keyword(s):  
Lower Order ◽  
Spacing Effect ◽  
Axial Compressor ◽  
Interaction Effects ◽  
Moving Frame ◽  
Navier Stokes ◽  
Blade Row ◽  
Vortical Disturbance ◽  
Blade Row Interaction ◽  
Gust Response

The effect of blade row axial spacing on vortical and potential disturbances and gust response is studied for a compressor stator/rotor configuration near design and at high loadings using 2D incompressible Navier-Stokes and potential codes, both written for multistage calculations. First, vortical and potential disturbances downstream of the isolated stator in the moving frame are defined; these disturbances exclude blade row interaction effects. Then, vortical and potential disturbances for the stator/rotor configuration are calculated for axial gaps of 10%, 20%, and 30% chord. Results show that the potential disturbance is uncoupled; the potential disturbance calculated from the isolated stator configuration is a good approximation for that from the stator/rotor configuration for all three axial gaps. The vortical disturbance depends strongly on blade row interactions. Low order modes of vortical disturbance are of substantial magnitude and decay much more slowly downstream than do those of potential disturbance. Vortical disturbance decays linearly with increasing mode except very close to the stator trailing edge. For a small axial gap, lower order modes of both vortical and potential disturbances must be included to determine the rotor gust response.

Forced Response Assessment Using Modal Force Based Indicator Functions

2008 ◽  
Author(s):  
M. Vahdati ◽  
C. Breard ◽  
G. Simpson ◽  
M. Imregun
Keyword(s):  
Finite Element ◽  
Structural Model ◽  
Stokes Equations ◽  
Linear Time ◽  
Response Assessment ◽  
Element Model ◽  
Forced Response ◽  
Navier Stokes ◽  
Modal Force ◽  
Indicator Functions

This paper will focus on core-compressor forced response with the aim to develop two design criteria, the so-called chordwise cumulative modal force and heightwise cumulative force, to assess the potential severity of the vibration levels from the correlation between the unsteady pressure distribution on the blade’s surface and the structural modeshape. It is also possible to rank various blade designs since the proposed criterion is sensitive to changes in both unsteady aerodynamic loads and the vibration modeshapes. The proposed methodology was applied to a typical core-compressor forced response case for which measured data were available. The Reynolds-averaged Navier-Stokes equations were used to represent the flow in a non-linear time-accurate fashion on unstructured meshes of mixed elements. The structural model was based on a standard finite element representation from which the vibration modes were extracted. The blade flexibility was included in the model by coupling the finite element model to the unsteady flow model in a time-accurate fashion. A series of numerical experiments were conducted by altering the stator wake and using the proposed indicator functions to minimize the rotor response levels. It was shown that a fourfold response reduction was possible for a certain mode with only a minor modification of the blade.

Rotordynamic characterization of tilting-pad bearings with eight pads in vertical rotors

2021 ◽  
pp. 1-20
Author(s):  
David J Rondon ◽  
Gudeta Berhanu Benti ◽  
Jan-Olov Aidanpää ◽  
Rolf Gustavsson
Keyword(s):  
Stokes Equations ◽  
Forced Response ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Mean Values ◽  
Stationary Coordinate System ◽  
Tilting Pad ◽  
Tilting Pad Bearings ◽  
Stiffness And Damping

Abstract It has been documented that stiffness and damping for a four-pad bearing are dependent not only the magnitude of the load but also on the position of the rotor in the bearing. However, 8-pad bearings are not commonly employed on horizontal turbines, and the presence of several pads in the bearing will decisively affect the dynamics of the system. This paper evaluates the stiffness and damping coefficients of tilting-pad bearings with eight pads and explore the main frequencies acting on the forced response of a vertical rotor. The bearing properties were modeled as a function of eccentricity and position in the stationary coordinate system by Navier-Stokes equations whose results are taken from commercial software. The simulated unbalanced response is compared to experimental results; the changing position of the shaft produces a periodic stiffness and damping, which is dependent on the number of pads. Cross-coupled coefficients influence is discussed, showing that their absence makes an accurate model for the mean values. The results indicate that simulation of vertical rotors with 8-pad bearings can be simplified which allow more effective simulations and dynamic analysis.

scholarly journals Fluid-kinetic modelling for respiratory aerosols with variable size and temperature

2020 ◽  
Vol 67 ◽  
pp. 100-119 ◽  
Author(s):  
Laurent Boudin ◽  
Céline Grandmont ◽  
Bérénice Grec ◽  
Sébastien Martin ◽  
Amina Mecherbet ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Kinetic Modelling ◽  
Type Equation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Aerosol Dynamics ◽  
Convection Diffusion Equation ◽  
Time Marching ◽  
Branched Structure ◽  
The Impact

In this paper, we propose a coupled fluid-kinetic model taking into account the radius growth of aerosol particles due to humidity in the respiratory system. We aim to numerically investigate the impact of hygroscopic effects on the particle behaviour. The air flow is described by the incompressible Navier-Stokes equations, and the aerosol by a Vlasov-type equation involving the air humidity and temperature, both quantities satisfying a convection-diffusion equation with a source term. Conservations properties are checked and an explicit time-marching scheme is proposed. Twodimensional numerical simulations in a branched structure show the influence of the particle size variations on the aerosol dynamics.

scholarly journals Flow Pressure Behavior Downstream of Ski Jumps

Fluids ◽  
2020 ◽  
Vol 5 (4) ◽  
pp. 168 ◽  
Author(s):  
Agostino Lauria ◽  
Giancarlo Alfonsi ◽  
Ali Tafarojnoruz
Keyword(s):  
High Speed ◽  
Stokes Equations ◽  
Dynamic Pressure ◽  
Pressure Head ◽  
Navier Stokes ◽  
Maximum Pressure ◽  
Navier Stokes Equations ◽  
Free Jet ◽  
Jet Characteristics ◽  
The Impact

Ski jump spillways are frequently implemented to dissipate energy from high-speed flows. The general feature of this structure is to transform the spillway flow into a free jet up to a location where the impact of the jet creates a plunge pool, representing an area for potential erosion phenomena. In the present investigation, several tests with different ski jump bucket angles are executed numerically by means of the OpenFOAM® digital library, taking advantage of the Reynolds-averaged Navier–Stokes equations (RANS) approach. The results are compared to those obtained experimentally by other authors as related to the jet length and shape, obtaining physical insights into the jet characteristics. Particular attention is given to the maximum pressure head at the tailwater. Simple equations are proposed to predict the maximum dynamic pressure head acting on the tailwater, as dependent upon the Froude number, and the maximum pressure head on the bucket. Results of this study provide useful suggestions for the design of ski jump spillways in dam construction.

scholarly journals Development of An Integrated Numerical Model for Simulating Wave Interaction with Permeable Submerged Breakwaters Using Extended Navier–Stokes Equations

2020 ◽  
Vol 8 (2) ◽  
pp. 87 ◽  
Author(s):  
Paran Pourteimouri ◽  
Kourosh Hejazi
Keyword(s):  
Porous Medium ◽  
Wave Propagation ◽  
Numerical Model ◽  
Analytical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Stokes Wave ◽  
Navier Stokes Equations ◽  
Numerical Predictions ◽  
The Impact

An integrated two-dimensional vertical (2DV) model was developed to investigate wave interactions with permeable submerged breakwaters. The integrated model is capable of predicting the flow field in both surface water and porous media on the basis of the extended volume-averaged Reynolds-averaged Navier–Stokes equations (VARANS). The impact of porous medium was considered by the inclusion of the additional terms of drag and inertia forces into conventional Navier–Stokes equations. Finite volume method (FVM) in an arbitrary Lagrangian–Eulerian (ALE) formulation was adopted for discretization of the governing equations. Projection method was utilized to solve the unsteady incompressible extended Navier–Stokes equations. The time-dependent volume and surface porosities were calculated at each time step using the fraction of a grid open to water and the total porosity of porous medium. The numerical model was first verified against analytical solutions of small amplitude progressive Stokes wave and solitary wave propagation in the absence of a bottom-mounted barrier. Comparisons showed pleasing agreements between the numerical predictions and analytical solutions. The model was then further validated by comparing the numerical model results with the experimental measurements of wave propagation over a permeable submerged breakwater reported in the literature. Good agreements were obtained for the free surface elevations at various spatial and temporal scales, velocity fields around and inside the obstacle, as well as the velocity profiles.

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