scholarly journals Dynamic response of vertical shaft Pelton turbine unit for forced vibration

2021 ◽  
Vol 4 (1) ◽  
pp. 34-41
Author(s):  
Raman Koirala ◽  
Mahesh Chandra Luitel
Keyword(s):  
Forced Vibration ◽  
Turbine Unit ◽  
Research Work ◽  
Water Jet ◽  
Forced Response ◽  
Pelton Turbine ◽  
Mode Amplitude ◽  
Ansys Simulation ◽  
Mathematical Mode ◽  
Forcing Function

This research work was carried out to model the excitation force imparted by water jet in the form of Fourier series and determine the forced response of Pelton turbine unite of Khulelhani-I hydropower analytically by developing mathematical mode. Amplitude of forced vibration form analytical was compared with simulation result. The mathematical model was developed by calculating the kinetic energy of disk and potential energy of both disk and shaft. Hamilton’s principle was used to determine equation of motion and then Galerkin method was used to determine response of the system. Fourier analysis was done to obtain the function in its exact form. The developed methodologies were followed to find the analytical solution of Kulekhani-I unit of 3100 kW rated at 600rpm. A rigid disk (runner and bucket assembly) was situated along end of flexible shaft with fixed support at the shaft. First five Fourier components are to be considered in analysis for meaningful representation of forcing function. The amplitude of vibration of Pelton turbine unit with single nozzle in Y-direction (the direction of water jet) obtained by analytical method was closed with that obtained from the ANSYS simulation.

Blade Forcing Function and Aerodynamic Work Measurements in a High Speed Centrifugal Compressor With Inlet Distortion

2009 ◽  
Author(s):  
Albert Kammerer ◽  
Reza S. Abhari
Keyword(s):  
Failure Modes ◽  
Pressure Sensors ◽  
Forced Response ◽  
Blade Surface ◽  
Centrifugal Compressors ◽  
Flow Distortion ◽  
Unsteady Pressure ◽  
Inlet Distortion ◽  
Forcing Function ◽  
Work Distribution

Centrifugal compressors operating at varying rotational speeds, such as in helicopters or turbochargers, can experience forced response failure modes. The response of the compressors can be triggered by aerodynamic flow non-uniformities, such as with diffuser-impeller interaction or with inlet distortions. The work presented here addresses experimental investigations of forced response in centrifugal compressors with inlet distortions. This research is part of an ongoing effort to develop related experimental techniques and to provide data for validation of computational tools. In this work measurements of blade surface pressure and aerodynamic work distribution were addressed. A series of pressure sensors were designed and installed on rotating impeller blades and simultaneous measurements with blade-mounted strain gauges were performed under engine representative conditions. To the best knowledge of the authors, this is the first publication which presents comprehensive experimental unsteady pressure measurements during forced response for highspeed radial compressors. Experimental data were obtained for both resonance and off-resonance conditions with uniquely tailored inlet distortion. This paper covers aspects relating to the design of fast response pressure sensors and their installation on thin impeller blades. Additionally, sensor properties are outlined with a focus on calibration and measurement uncertainty estimations. The second part of this paper presents unsteady pressure results taken for a number of inlet distortion cases. It will be shown that the intended excitation order due to inlet flow distortion is of comparable magnitude to the second and third harmonics which are consistently observed in all measurements. Finally, an experimental method will be outlined that enables the measurement aerodynamic work on the blade surface during resonant crossing. This approach quantifies the energy exchange between the blade and the flow in terms of cyclic work along the blade surface. The phase angle between the unsteady pressure and the blade movement will be shown to determine the direction of energy transfer between the blade and the fluid.

Forced Response Sensitivity of a Mistuned Rotor From an Embedded Compressor Stage

2015 ◽  
Author(s):  
Fanny M. Besem ◽  
Robert E. Kielb ◽  
Nicole L. Key
Keyword(s):  
Experimental Data ◽  
Forced Response ◽  
Symmetric System ◽  
Response Analysis ◽  
Cfd Simulations ◽  
Forcing Function ◽  
Wear And Tear ◽  
The Individual ◽  
The Impact ◽  
Interblade Phase Angle

The frequency mistuning that occurs due to manufacturing variations and wear and tear of the blades can have a significant effect on the flutter and forced response behavior of a blade row. Similarly, asymmetries in the aerodynamic or excitation forces can tremendously affect the blade responses. When conducting CFD simulations, all blades are assumed to be tuned (i.e. to have the same natural frequency) and the aerodynamic forces are assumed to be the same on each blade except for a shift in interblade phase angle. The blades are thus predicted to vibrate at the same amplitude. However, when the system is mistuned or when asymmetries are present, some blades can vibrate with a much higher amplitude than the tuned, symmetric system. In this research, we first conduct a deterministic forced response analysis of a mistuned rotor and compare the results to experimental data from a compressor rig. It is shown that tuned CFD results cannot be compared directly with experimental data because of the impact of frequency mistuning on forced response predictions. Moreover, the individual impact of frequency, aerodynamic, and forcing function perturbations on the predictions is assessed, leading to the conclusion that a mistuned system has to be studied probabilistically. Finally, all perturbations are combined and Monte-Carlo simulations are conducted to obtain the range of blade response amplitudes that a designer could expect.

scholarly journals Forced Vibration in Cutting Process considering the Nonlinear Curvature and Inertia of a Rotating Composite Cutter Bar

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Yongsheng Ren ◽  
Donghui Yao
Keyword(s):  
Cutting Force ◽  
Forced Vibration ◽  
Multiple Scales ◽  
Damping Ratio ◽  
Three Dimensional ◽  
Forced Response ◽  
Cutting Process ◽  
Response Curves ◽  
Rotating Speed ◽  
Cutting System

Forced vibration of the cutting system with a three-dimensional composite cutter bar is investigated. The composite cutter bar is simplified as a rotating cantilever shaft which is subjected to a cutting force including regenerative delay effects and harmonic exciting items. The nonlinear curvature and inertia of the cutter bar are taken into account based on inextensible assumption. The effects of the moment of inertia, gyroscopic effect, and internal and external damping are also considered, but shear deformation is neglected. Equation of motion is derived based on Hamiltonʼs extended principle and discretized by the Galerkin method. The analytical solutions of the steady-state response of the cutting system are constructed by using the method of multiple scales. The response of the cutting system is studied for primary and superharmonic resonances. The effects of length-to-diameter ratio, damping ratio, cutting force coefficients, ply angle, rotating speed, and internal and external damping are investigated. The results show that nonlinear curvature and inertia imposed a significant effect on the dynamic behavior of the cutting process. The equivalent nonlinearity of the cutting system shows hard spring characteristics. Multiple solutions and jumping phenomenon of typical Duffing system are found in forced response curves.

Structural and Aerodynamic Influences to Airfoil Forced Response: Does a Thicker Airfoil Have Reduced Vibratory Response?

1993 ◽  
Author(s):  
Spiros Tatakis ◽  
Richard J. Stockton
Keyword(s):  
Endurance Limit ◽  
Low Frequency ◽  
Element Model ◽  
Forced Response ◽  
Modal Parameter ◽  
Forcing Function ◽  
Vibratory Response ◽  
Aerodynamic Parameters ◽  
Forcing Mechanisms ◽  
Modal Stress

The influence of airfoil geometric and aerodynamic parameters on the vibratory response of low frequency modes subjected to low order excitations was investigated. The predicted vibratory response of a thicker airfoil was compared to the response of a baseline thickness design. Two types of forcing mechanisms were analyzed. It was found that force-controlled response, that may originate from mechanical input or surge, can be managed by increasing the airfoil thickness and providing sufficient margin below the endurance limit of the material. Velocity-controlled response, mainly from aerodynamic interactions, depend on the airfoil excitation placement. The aerodynamic forcing function and damping were determined using flat plate unsteady aerodynamic solutions integrated with an MSC/NASTRAN structural finite element model of the airfoil. Thickening appears to reduce blade response in a velocity-controlled situation provided the modal stress has been reduced by the thickening. However, the response reduction is greater for the force-controlled situation. The modal parameter model provides a quick assessment of either possibility.

Hydro Francis Runner Stability and Forced Response Calculations

2019 ◽  
Author(s):  
Charles Seeley ◽  
Sunil Patil ◽  
Andy Madden ◽  
Stuart Connell ◽  
Gwenael Hauet ◽  
...  
Keyword(s):  
Large Scale ◽  
Forced Response ◽  
Operating Conditions ◽  
Mode Shapes ◽  
Symmetric Model ◽  
Validation Data ◽  
Fea Model ◽  
Forcing Function ◽  
Cyclic Symmetric ◽  
Work Done

Abstract Hydroelectric power generation accounts for 7% of the total world electric energy production. Francis turbines are often employed in large-scale hydro projects and represent 60% of the total installed base. Outputs up to 800 MW are available and efficiencies of 95% are common. Cost, performance, and design cycle time are factors that continue to drive new designs as well as retrofits. This motivates the development of more sophisticated analysis tools to better assess runner performance earlier in the design phase. The focus of this paper is to demonstrate high fidelity and time-efficient runner damping and forced response calculations based on one-way fluid-structure interaction (FSI) using loosely coupled commercial finite element analysis (FEA) and computational fluid dynamics (CFD) codes. The runner damping is evaluated based on the work done by the fluid on the runner. The calculation of the work first involves determining the runner mode shapes and natural frequencies using a cyclic symmetric FEA model with structural elements to represent the runner hardware, and acoustic fluid elements to represent the mass loading effect of the fluid. The mode shapes are then used in a transient CFD calculation to determine the damping which represents the work done by the fluid on the runner. Positive damping represents stability from flutter perspective while negative damping represents unstable operating conditions. A transient CFD calculation was performed on a runner to obtain engine order forcing function from upstream stationary vanes. This unsteady forcing function was mapped to the FEA model. Care is taken to account for the proper inter-blade phase angle on the cyclic symmetric model. The hydraulic damping from flutter calculations was also provided as input to the forced response. The forced response is then determined using this equivalent proportional damping and modal superposition of the FEA model that includes both the structural and acoustic elements. Results of the developed analysis procedure are presented based on the Tokke runner, that has been the basis of several studies through the Norwegian HydroPower Center. Unique features of the workflow and modeling approaches are discussed in detail. Benefits and challenges for both the FEA model and the CFD model are discussed. The importance of the hydraulic damping, that is traditionally ignored in previous analysis is discussed as well. No validation data is available for the forced response, so this paper is focused on the methodology for the calculations.

Unsteady Computational Fluid Dynamics Investigation on Inlet Distortion in a Centrifugal Compressor

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
Armin Zemp ◽  
Albert Kammerer ◽  
Reza S. Abhari
Keyword(s):  
Centrifugal Compressor ◽  
Temporal Evolution ◽  
Flow Distribution ◽  
Forced Response ◽  
Inlet Section ◽  
Flow Distortion ◽  
Inlet Flow ◽  
Inlet Distortion ◽  
Forcing Function ◽  
Unsteady Fluid

Blade failure in turbomachinery is frequently caused by an excessive resonant response. Forced response of the blades originates from unsteady fluid structure interactions as conditioned in the inlet section by duct bends, struts, or inlet guide vanes. This paper presents the computational part of a research effort that focuses on the blade forced response in a centrifugal compressor. Unsteady fluid flow simulations are used to quantify the forcing function acting on the compressor blades due to inlet flow distortion. The measured inlet flow distribution is applied as inlet boundary conditions in the computation. The unsteady investigation provided the temporal evolution of the distorted flow through the compressor. The time-resolved blade pressure distribution showed the temporal evolution of the dynamic load on the blade surface caused by the inlet distortion. The results suggest that the forcing function is most sensitive in the leading edge region due to inlet angle variations. Toward the impeller stability line the increase in incidence caused separation on the suction side of the main blade and therefore considerably altered the amplitude and the phase angle of the unsteadiness. The investigation of the effect of idealizing the inlet flow distribution on the forcing function showed an increase in the peak amplitude of approximately 30% compared with the actual inlet flow distribution.

scholarly journals An Investigation of Abrasive Water Jet Machining on Graphite/Glass/Epoxy Composite

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Deepak Doreswamy ◽  
Basavanna Shivamurthy ◽  
Devineni Anjaiah ◽  
N. Yagnesh Sharma
Keyword(s):  
Process Parameters ◽  
Feed Rate ◽  
Epoxy Composite ◽  
Research Work ◽  
Water Jet ◽  
Kerf Width ◽  
Machining Parameters ◽  
Operating Pressure ◽  
Abrasive Water Jet ◽  
Glass Fiber Reinforced

In the present research work, the effect of abrasive water jet (AWJ) machining parameters such as jet operating pressure, feed rate, standoff distance (SOD), and concentration of abrasive on kerf width produced on graphite filled glass fiber reinforced epoxy composite is investigated. Experiments were conducted based on Taguchi’s L27 orthogonal arrays and the process parameters were optimized to obtain small kerf. The main as well as interaction effects of the process parameters were analyzed using the analysis of variance (ANOVA) and regression models were developed to predict kerf width. The results show that the operating pressure, the SOD, and the feed rate are found to be significantly affecting the top kerf width and their contribution to kerf width is 24.72%, 12.38%, and 52.16%, respectively. Further, morphological study is made using scanning electron microscope (SEM) on the samples that were machined at optimized process parameters. It was observed that AWJ machined surfaces were free from delamination at optimized process parameters.

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.

Blade Forcing Function and Aerodynamic Work Measurements in a High Speed Centrifugal Compressor With Inlet Distortion

2010 ◽  
Vol 132 (9) ◽  
Author(s):  
Albert Kammerer ◽  
Reza S. Abhari
Keyword(s):  
High Speed ◽  
Pressure Sensors ◽  
Forced Response ◽  
Blade Surface ◽  
Centrifugal Compressors ◽  
Flow Distortion ◽  
Unsteady Pressure ◽  
Inlet Distortion ◽  
Forcing Function ◽  
Work Distribution

Centrifugal compressors operating at varying rotational speeds, such as in helicopters or turbochargers, can experience forced response failure modes. The response of the compressors can be triggered by aerodynamic flow nonuniformities such as with diffuser-impeller interaction or with inlet distortions. The work presented here addresses experimental investigations of forced response in centrifugal compressors with inlet distortions. This research is part of an ongoing effort to develop related experimental techniques and to provide data for validation of computational tools. In this work, measurements of blade surface pressure and aerodynamic work distribution were addressed. A series of pressure sensors were designed and installed on rotating impeller blades and simultaneous measurements with blade-mounted strain gauges were performed under engine representative conditions. To the best knowledge of the authors, this is the first publication, which presents comprehensive experimental unsteady pressure measurements during forced response, for high-speed radial compressors. The experimental data were obtained for both resonance and off-resonance conditions with uniquely tailored inlet distortion. This paper covers aspects relating to the design of fast response pressure sensors and their installation on thin impeller blades. Additionally, sensor properties are outlined with a focus on calibration and measurement uncertainty estimations. The second part of this paper presents unsteady pressure results taken for a number of inlet distortion cases. It will be shown that the intended excitation order due to inlet flow distortion is of comparable magnitude to the second and third harmonics, which are consistently observed in all measurements. Finally, an experimental method will be outlined that enables the measurement of aerodynamic work on the blade surface during resonant crossing. This approach quantifies the energy exchange between the blade and the flow in terms of cyclic work along the blade surface. The phase angle between the unsteady pressure and the blade movement will be shown to determine the direction of energy transfer.

scholarly journals A Study on Fluid Self-Excited Flutter and Forced Response of Turbomachinery Rotor Blade

2014 ◽  
Vol 2014 ◽  
pp. 1-20 ◽  
Author(s):  
Chih-Neng Hsu
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Power Plants ◽  
Single Mode ◽  
Element Model ◽  
Forced Response ◽  
Structural Dynamic ◽  
Turbine Engine ◽  
Forcing Function ◽  
Structural Dynamic Characteristics

Complex mode and single mode approach analyses are individually developed to predict blade flutter and forced response. These analyses provide a system approach for predicting potential aeroelastic problems of blades. The flow field properties of a blade are analyzed as aero input and combined with a finite element model to calculate the unsteady aero damping of the blade surface. Forcing function generators, including inlet and distortions, are provided to calculate the forced response of turbomachinery blading. The structural dynamic characteristics are obtained based on the blade mode shape obtained by using the finite element model. These approaches can provide turbine engine manufacturers, cogenerators, gas turbine generators, microturbine generators, and engine manufacturers with an analysis system to remedy existing flutter and forced response methods. The findings of this study can be widely applied to fans, compressors, energy turbine power plants, electricity, and cost saving analyses.

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