Scaling Concept for Axial Turbine Stages With Loosely Assembled Friction Bolts: The Linear Dynamic Assessment

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
J. Szwedowicz ◽  
Th. Secall-Wimmel ◽  
P. Dünck-Kerst ◽  
A. Sonnenschein ◽  
D. Regnery ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Dynamic Assessment ◽  
Steam Turbines ◽  
Fe Method ◽  
Stick Slip ◽  
Contact Conditions ◽  
Axial Turbine ◽  
Linear Dynamic ◽  
Air Jet ◽  
Resonance Frequencies

In the early 1980s, Siemens developed a last stage fast rotating condensation blading (SK) blade with strongly twisted and tapered profiles for industrial condensing steam turbines, which operate with variable speed under high steam mass flow and excessive condensing pressures. To suppress alternating stresses of the lowest blade resonances, conical friction bolts are loosely mounted at the upper parts of adjacent airfoils. Also, these bolts couple the rotating blades, since steam excitation is lower than the friction threshold force on the bolt contacts. These coupling and damping capabilities were proven experimentally for the smallest SK blade at the test rig of the real turbine. By considering the similar mechanical and aerodynamic characteristics based on the tested smallest airfoil, the entire SK-blade family has been scaled up for reliable utilization in more than 500 industrial turbines operating for diverse ranges of power and speed. A recent trend to very large compression units, like gas to liquids, acid terephtalic, or methanol plants, imposes a need for further enlargement of the SK-blade family and its friction bolt, whose mechanical properties have been proven experimentally for the smallest airfoil. In this paper, the mechanical capabilities of the smallest and large SK blades coupled by the bolts are verified by using the finite element (FE) method. The static analyses with friction sliding on airfoil interfaces and the linear dynamic behavior of tuned disk assemblies are considered. The FE mesh quality and the proper boundary conditions at the radial fork root are accomplished by getting good agreements between the computed and measured resonance frequencies of the large freestanding blade at standstill. The validated mesh refinement and root boundary conditions are used further in all numerical FE analyses. For the large SK-disk assembly under spin-pit conditions, the obtained FE results are in very good agreement with the experimental Campbell diagrams, which are measured with the three gauges that also identify the stick-slip and stuck bolt’s contact conditions. Concerning the gauge outputs and the FE steady-state blade resonances computed for the analytically determined air jet excitation, the experimental spin-pit results demonstrate that the bolts are mainly in stuck contact conditions. Only in very narrow frequency ranges around resonance peaks, microslips on the bolts occur due to the resonance amplification of blade vibrations. This is proven indirectly by comparison of the overall damping values evaluated from the blade resonances at standstill and in the spin pit. The described linear dynamic concept assesses properly static stresses and free vibrations of the scaled disk assembly with friction bolts. For the steam excitation, which generates dynamic contact reactions bigger than the friction threshold forces, the realistic blade responses need to be obtained from the blade simulation with friction (Szwedowicz, J., Secall-Wimmel, T., and Duenck-Kerst, P., 2007, “Damping Performance of Axial Turbine Stages With Loosely Assembled Friction Bolts; the Non-Linear Dynamic Assessment; Part II,” Proceedings of ASME Turbo Expo 2007, Montreal, Canada, May 14–17, ASME Paper No. GT2007-27506).

Scaling Concept for Axial Turbine Stages With Loosely Assembled Friction Bolts: The Linear Dynamic Assessment — Part I

2007 ◽  
Author(s):  
J. Szwedowicz ◽  
Th. Secall-Wimmel ◽  
P. Du¨nck-Kerst ◽  
A. Sonnenschein ◽  
D. Regnery ◽  
...  
Keyword(s):  
Dynamic Assessment ◽  
Aerodynamic Characteristics ◽  
Steam Turbines ◽  
Fe Method ◽  
Stick Slip ◽  
Contact Conditions ◽  
Linear Dynamic ◽  
Air Jet ◽  
Resonance Frequencies ◽  
Gas To Liquids

For industrial condensing steam turbines operating at variable speed, Siemens has developed a last stage SK-blade family in the early 80s. The principle goal was to design a robust blade profile for the highest reliability and a good performance, which allow the operation in resonances under high steam mass flow and excessive condensing pressures. To suppress resonance stresses through friction dissipation, loosely fitted conical bolts are applied to the upper part of adjacent airfoils. In the early 80s, these capabilities were experimentally investigated and validated for the smallest SK-blade at a set-up of the real turbine unit. The tapered and twisted geometry of the smallest SK-blade has been scaled under consideration of the similar mechanical and aerodynamic characteristics. The entire scaled-up SK-blade family has proved its reliability in more than 500 industrial turbine units arranged for different power and speeds. In the last years there could be seen a trend to very large compression units, like GTL (Gas to Liquids), PTA (Acid Terephtalic) or Methanol plants. Therefore, the SK-blade family has been extended to larger airfoils using the well established scale concept based on the smallest SK-unit. In this paper, the mechanical capabilities of the smallest and large SK-blades coupled by the bolts are verified by using the Finite Element (FE) Method. The static analyses with friction sliding on the bolts and the linear dynamic behaviour of tuned disc assemblies are considered. The FE mesh quality and the proper restraint conditions at the radial root are accomplished by getting good agreements between the computed and measured resonance frequencies of the large freestanding blade at standstill. The validated mesh refinement and root boundary conditions are used further in all numerical FE analyses. For the large SK-disc assembly under spin pit conditions, the obtained FE results are in very good agreement with the experimental Campbell diagram. The determined positions of the gauges allow for identifying either stick-slip or sticking contact conditions at the bolts. The experimental spin pit results show mainly sticking contact conditions at the bolts because of too weak air jet excitation. Only in very narrow frequency ranges around resonance peaks, micro-slips on the friction bolts occur due to the resonance amplification of blade vibrations. This is proved indirectly by the evaluated damping values for spin pit conditions, which are bigger than the damping magnitudes of the disc assembly at standstill, which was measured with hammer tests. This empirical statement is approved by the FE steady-state dynamic results for the analytically determined amplitudes of the air jet excitation. The obtained results show that the proposed linear dynamic concept can be successfully applied to the design process of the scaled turbine discs of different dimensions with loosely assembled friction bolts for assessment of maximum static stresses and free vibration behaviour. The scaling design criteria of the blades with friction bolts are confirmed fully for natural frequencies and excitation conditions, but their real responses depending on the excitation amplitudes need to be obtained from the non-linear dynamic simulation which is considered in paper GT2007-27506 (Szwedowicz et al., 2007).

Damping Performance of Axial Turbine Stages With Loosely Assembled Friction Bolts: The Nonlinear Dynamic Assessment

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
J. Szwedowicz ◽  
Th. Secall-Wimmel ◽  
P. Dünck-Kerst
Keyword(s):  
Nonlinear Dynamic ◽  
Dynamic Assessment ◽  
Contact Condition ◽  
Operating Conditions ◽  
Friction Forces ◽  
Axial Turbine ◽  
Resonance Frequencies ◽  
Wide Range ◽  
Dynamic Analyses ◽  
Nonlinear Dynamic Analyses

An entire family of twisted and tapered low pressure steam turbine fast rotating condensation blading (SK) blades with pinned radial root and loosely assembled conical bolts is designed by scaling the aerodynamic and mechanical properties of the smallest airfoil. For SK blades operating with variable speed, the friction bolts, mounted in the upper airfoil part, provide either damping or coupling capabilities for the blades with respect to resonance conditions. The damping and coupling performance have been proven experimentally in the test rig of the real turbine. The measurements of the smallest SK-disk assembly under different operating conditions have allowed us to understand the dynamic and damping behavior of the bolts that are either friction dampers or coupling devices for the vibrating blades depending on the excitation level. In this paper, nonlinear dynamic analyses of the smallest and large SK-turbine stage are performed and compared with the experimental data. The modal blade dynamics is defined by 30 complex finite element (FE) mode shapes of the freestanding blades coupled by the disk whereby the bolt’s motion is described by six rigid body modes. The sticking contact condition between the blades and bolts is represented by the normal and tangential contact stiffnesses. These values are firstly estimated analytically with Hertz’s formulas for the FE reaction forces and contact areas. More realistic contact stiffness values are obtained from the iterative process, in which the resonance frequencies are calculated with the steady-state simulations and compared to the FE nodal diameter curves for sticking contact conditions that meet the experimental frequencies very well (Szwedowicz, J. et al., 2007, “Scaling Concept for Axial Turbine Stages With Loosely Assembled Friction Bolts: The Linear Dynamic Assessment Part 1,” Proceedings of ASME Turbo Expo 2007, Montreal, Canada, May 14–17, ASME Paper No. GT2007-27502). In nonlinear simulations, in case of exceeding the sticking contact condition, the induced friction forces are linearized by the harmonic balance method. In this manner, the microslipping and sticking contact behavior at all contact points are calculated iteratively for the specified excitation amplitudes, friction coefficient, contact roughness, and aerodamping values that are known from the experiment. The computed results of the tuned smallest SK blades agree with the experimental resonance stresses of 12 measured blades. Differences between the computed and measured stresses are caused by mistuning, which was not quantified in the experiment. The nonlinear dynamic analyses provide evidence of good damping performance for the smallest and large SK blades with respect to a wide range of excitation forces, different friction coefficients, and various aerodynamic damping values. For the analyzed resonances of the eighth engine order, the scalability of damping performance is found for the SK blades of different sizes.

Boundary conditions and event scaling of granular stick-slip events

2009 ◽  
Author(s):  
Karen E. Daniels ◽  
Nicholas W. Hayman ◽  
Masami Nakagawa ◽  
Stefan Luding
Keyword(s):  
Boundary Conditions ◽  
Stick Slip

Experimental and Theoretical Nonlinear Dynamic Response of Intact and Cracked Bone-Like Specimens With Various Boundary Conditions

2007 ◽  
Vol 129 (5) ◽  
pp. 541-549 ◽  
Author(s):  
Erick Ogam ◽  
Armand Wirgin ◽  
Z. E. A. Fellah ◽  
Yongzhi Xu
Keyword(s):  
Boundary Conditions ◽  
Duffing Oscillator ◽  
Contact Friction ◽  
Nonlinear Dynamic Response ◽  
Various Boundary Conditions ◽  
Vibration Data ◽  
Element Simulation ◽  
Resonance Frequencies ◽  
Vibration Experiment ◽  
Freely Suspended

The potentiality of employing nonlinear vibrations as a method for the detection of osteoporosis in human bones is assessed. We show that if the boundary conditions (BC), relative to the connection of the specimen to its surroundings, are not taken into account, the method is apparently unable to differentiate between defects (whose detection is the purpose of the method) and nonrelevant features (related to the boundary conditions). A simple nonlinear vibration experiment is described which employs piezoelectric transducers (PZT) and two idealized long bones in the form of nominally-identical drinking glasses, one intact, but in friction contact with a support, and the second cracked, but freely-suspended in air. The nonlinear dynamics of these specimens is described by the Duffing oscillator model. The nonlinear parameters recovered from vibration data coupled to the linear phenomena of mode splitting and shifting of resonance frequencies, show that, despite the similar soft spring behavior of the two dynamic systems, a crack is distinguishable from a contact friction BC. The frequency response of the intact glass with contact friction BC is modeled using a direct steady state finite element simulation with contact friction.

scholarly journals Detailed Analysis of the Acoustic Mode Shapes of an Annular Combustion Chamber

1999 ◽  
Author(s):  
Günther Walz ◽  
Werner Krebs ◽  
Stefan Hoffmann ◽  
Hans Judith
Keyword(s):  
Boundary Conditions ◽  
Acoustic Mode ◽  
Mode Shapes ◽  
Maximum Deviation ◽  
Minor Importance ◽  
Velocity Of Sound ◽  
Fe Method ◽  
Shift Frequency ◽  
Space Dependence ◽  
Eigenfrequency Spectrum

To get a better understanding of the formation of thermoacoustic oscillations in an annular gasturbine combustor, an analysis of the acoustic eigenmodes has been conducted using the Finite Element (FE) method. The influence of different boundary conditions and a space dependent velocity of sound has been investigated. The boundary conditions actually define the eigenfrequency spectrum. Hence, it is crucial to know e.g. the burner impedance. In case of the combustion system without significant mixing air addition considered in this paper, the space dependence of the velocity of sound is of minor importance for the eigenfrequency spectrum leading to a maximum deviation of only 5% in the eigenvalues. It is demonstrated that the efficiency of the numerical eigenvalue analysis can be improved by making use of symmetry, by splitting the problem into several steps with alternate boundaries conditions, and by choosing the shift frequency ωs in the range of frequencies one is interested in.

Evaluation of Different Turbulence Models Applied in Turbopump’s Hydraulic Turbine

2021 ◽  
Author(s):  
Daniel Ferreira Corrêa Barbosa ◽  
Daniel da Silva Tonon ◽  
Luiz Henrique Lindquist Whitacker ◽  
Jesuino Takachi Tomita ◽  
Cleverson Bringhenti
Keyword(s):  
Boundary Conditions ◽  
Turbulence Model ◽  
Rotor Blade ◽  
Space Shuttle ◽  
Turbulence Models ◽  
Tip Clearance ◽  
Test Facility ◽  
Speed Ratio ◽  
Computational Domain ◽  
Axial Turbine

Abstract The aim of this work is an evaluation of different turbulence models applied in Computational Fluid Dynamics (CFD) techniques in the turbomachinery area, in this case, in an axial turbine stage used in turbopump (TP) application. The tip clearance region was considered in this study because it has a high influence in turbomachinery performance. In this region, due to its geometry and the relative movement between the rotor row and casing, there are losses associated with vortices and secondary flow making the flowfield even more turbulent and complex. Moreover, the flow that leaks in the tip region does not participate in the energy transfer between the fluid and rotor blades, degradating the machine efficiency and performance. In this work, the usual flat tip rotor blade geometry was considered. The modeling of turbulent flow based on Reynolds Averaged Navier-Stokes (RANS) equations predicts the variation of turbine operational characteristics that is sufficient for the present turbomachine and flow analysis. Therefore, the appropriate choice of the turbulence model for the study of a given flow is essential to obtain adequate results using numerical approximations. This comparison become important due to the fact that there is no general turbulence model for all engineering applications that has fluid and flow. The turbomachine considered in the present work, is the first stage of the hydraulic axial turbine used in the Low Pressure Oxidizer Turbopump (LPOTP) of the Space Shuttle Main Engine (SSME), considering the 3.0% tip clearance configuration relative to rotor blade height. The turbulence models evaluated in this work were the SST (Shear Stress Transport), the k-ε Standard and the k-ε RNG. The computational domain was discretized in several control volumes based on unstructured mesh. All the simulations were performed using the commercial software developed by ANSYS, CFX v15.0 (ANSYS). All numerical settings and how the boundary conditions were imposed at different surfaces are explained in the work. The boundary conditions settings follow the same rule used in the test facility and needs some attention during the simulations to vary the Blade-Jet-Speed ratio parameter adequately. The results from numerical simulations, were synthesized and compared with the experimental data published by National Aeronautics and Space Administration (NASA), in which the turbine efficiency and its jet velocity parameter are analyzed for each turbulence model result. The work fluid considered in this work was water, the same fluid used in the NASA test facility.

STUDYING THE CONTACT POINT AND INTERFACE MOVING IN A SINUSOIDAL TUBE WITH LATTICE BOLTZMANN METHOD

2001 ◽  
Vol 15 (09) ◽  
pp. 1287-1303 ◽  
Author(s):  
HAI-PING FANG ◽  
LE-WEN FAN ◽  
ZUO-WEI WANG ◽  
ZHI-FANG LIN ◽  
YUE-HONG QIAN
Keyword(s):  
Boundary Conditions ◽  
Contact Line ◽  
Lattice Boltzmann ◽  
Complex Geometry ◽  
Contact Point ◽  
Point Contact ◽  
Immiscible Fluids ◽  
Lattice Boltzmann Model ◽  
Stick Slip ◽  
Bounce Back

The multicomponent nonideal gas lattice Boltzmann model by Shan and Chen (S-C) is used to study the immiscible displacement in a sinusoidal tube. The movement of interface and the contact point (contact line in three-dimension) is studied. Due to the roughness of the boundary, the contact point shows "stick-slip" mechanics. The "stick-slip" effect decreases as the speed of the interface increases. For fluids that are non-wetting, the interface is almost perpendicular to the boundaries at most time, although its shapes at different position of the tube are rather different. When the tube becomes narrow, the interface turns a complex curves rather than remains simple menisci. The velocity is found to vary considerably between the neighbor nodes close to the contact point, consistent with the experimental observation that the velocity is multi-values on the contact line. Finally, the effect of three boundary conditions is discussed. The average speed is found different for different boundary conditions. The simple bounce-back rule makes the contact point move fastest. Both the simple bounce-back and the no-slip bounce-back rules are more sensitive to the roughness of the boundary in comparison with the half-way bounce-back rule. The simulation results suggest that the S-C model may be a promising tool in simulating the displacement behaviour of two immiscible fluids in complex geometry.

scholarly journals Artificial Finger Skin having Ridges and Distributed Tactile Sensors used for Grasp Force Control

2002 ◽  
Vol 14 (2) ◽  
pp. 140-146 ◽  
Author(s):  
Daisuke Yamada ◽  
◽  
Takashi Maeno ◽  
Yoji Yamada ◽  
Keyword(s):  
Reaction Force ◽  
Frictional Coefficient ◽  
Dynamic Contact ◽  
Fe Model ◽  
Tactile Sensors ◽  
Fe Method ◽  
Stick Slip ◽  
Grasping Force ◽  
Grasp Force ◽  
Finger Skin

An artificial elastic finger skin for robot fingers has been developed for controlling grasp force when weight and frictional coefficient of the grasped object are unknown. The elastic finger skin has ridges at the surface to divide the stick/slip area. It also has a pair of tactile sensors embedded per ridge similar to human fingertips. The surface of the whole finger is curved so that reaction force distributes. A Finite Element (FE) model of the elastic finger skin was made to conduct dynamic contact analysis using a FE method to design the elastic finger skin in detail. Then the elastic finger skin was made. We confirmed by calculation and experiment that incipient slippage of the ridge occurring near the edge of contact is detected. Then, grasp was controlled using the finger. Arbitrary objects were lifted by incipient slippage near the edge of contact. We found that artificial finger skin is useful for controlling grasping force when the weight and friction coefficient between the elastic finger skin and grasping object are unknown.

Pre-Stressed Stayed Steel Columns Non-Linear Dynamic Assessment

2011 ◽  
Author(s):  
R. R. De Araujo ◽  
P. C. G. Da S. Vellasco ◽  
J. G. S. Da Silva ◽  
L. R. O. De Lima ◽  
S. A. L. De Andrade ◽  
...  
Keyword(s):  
Dynamic Assessment ◽  
Steel Columns ◽  
Linear Dynamic ◽  
Non Linear

Vibration Analysis of Drug Delivery CNTs Using Transfer Matrix Method

2011 ◽  
Author(s):  
Anooshiravan Farshidianfar ◽  
Ali A. Ghassabi ◽  
Mohammad H. Farshidianfar ◽  
Mohammad Hoseinzadeh
Keyword(s):  
Boundary Conditions ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Equation Of Motion ◽  
Beam Model ◽  
Multi Wall Carbon Nanotubes ◽  
Resonance Frequencies ◽  
Euler Bernoulli Beam ◽  
Bernoulli Beam Model

The free vibration and instability of fluid-conveying multi-wall carbon nanotubes (MWCNTs) are studied based on an Euler-Bernoulli beam model. A theory based on the transfer matrix method (TMM) is presented. The validity of the theory was confirmed for MWCNTs with different boundary conditions. The effects of the fluid flow velocity were studied on MWCNTs with simply-supported and clamped boundary conditions. Furthermore, the effects of the CNTs’ thickness, radius and length were investigated on resonance frequencies. The CNT was found to posses certain frequency behaviors at different geometries. The effect of the damping corriolis term was studied in the equation of motion. Finally, a useful simplification is introduced in the equation of motion.

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