Combined Effects of Both Axial Gap and Blade Count Ratio on the Unsteady Forces of a Steam Turbine Stage

2012 ◽  
Author(s):  
Tie Chen ◽  
Kush Patel ◽  
Peter Millington
Keyword(s):  
Linear Time ◽  
Harmonic Component ◽  
Correction Method ◽  
Combined Effects ◽  
Steam Turbines ◽  
Unsteady Forces ◽  
Count Ratio ◽  
Shape Correction ◽  
Time Marching ◽  
Harmonic Components

Rotating blades of steam turbines are subjected to unsteady forces due to the presence of both wakes and potential field from the upstream stationary blades. These forces are strongly influenced by both axial gap and blade count ratio. The combined effects of these parameters are studied for 120 scenarios covering the normal design space. The calculated unsteady forces are transformed into harmonic components using a Fourier transform. Each harmonic component is correlated to both axial gap and blade count ratio to provide guidance for preliminary blade design. This study uses an in-house non-linear time marching CFD code TF3D-VIB, which adopts a Shape Correction method to manage an arbitrary blade count ratio using a single passage. Consequently it is one-order more efficient than a conventional multiple passage method.

scholarly journals Three Dimensional Time-Marching Inviscid and Viscous Solutions for Unsteady Flows Around Vibrating Blades

1993 ◽  
Author(s):  
L. He ◽  
J. D. Denton
Keyword(s):  
Thin Layer ◽  
Stokes Equations ◽  
Linear Time ◽  
Correction Method ◽  
Navier Stokes ◽  
Finite Volume Scheme ◽  
Time Step ◽  
Blade Passage ◽  
Time Marching ◽  
Viscous Solutions

A 3-dimensional non-linear time-marching method of solving the thin-layer Navier-Stokes equations in a simplified form has been developed for blade flutter calculations. The discretization of the equations is made using the cell-vertex finite volume scheme in space and the 4-stage Runge-Kutta scheme in time. Calculations are carried out in a single-blade-passage domain and the phase-shifted periodic condition is implemented by using the shape correction method. The 3-D unsteady Euler solution is obtained at conditions of zero viscosity, and is validated against a well-established 3-D semi-analytical method. For viscous solutions, the time-step limitation on the explicit temporal discretization scheme is effectively relaxed by using a time-consistent two-grid time-marching technique. A transonic rotor blade passage flow (with tip-leakage) is calculated using the present 3-D unsteady viscous solution method. Calculated steady flow results agree well with the corresponding experiment and with other calculations. Calculated unsteady loadings due to oscillations of the rotor blades reveal some notable 3-D viscous flow features. The feasibility of solving the simplified thin-layer Navier-Stokes solver for oscillating blade flows at practical conditions is demonstrated.

Effects of Both Axial Gap and Blade Count Ratio on the Forced Response of a Steam Turbine Stage

2013 ◽  
Author(s):  
Tie Chen ◽  
John Rogerson ◽  
Kush Patel
Keyword(s):  
Steam Turbine ◽  
Dynamic Stress ◽  
Fluid Dynamic ◽  
Forced Response ◽  
Steam Turbines ◽  
Turbine Stage ◽  
Unsteady Forces ◽  
Count Ratio ◽  
Stress Prediction ◽  
Coupling Dynamic

Rotating blades of steam turbines are subjected to unsteady forces due to the presence of both wake and potential field from the adjacent stationary blade rows. The combined effects of both axial gap and blade count ratio on the unsteady forces have been demonstrated on a steam turbine stage. This study shows their effects on the forced response. Further investigations show their effects on stimulus, aero damping and frequency shift. This study uses a one-way coupling dynamic stress prediction tool, which integrates an in-house Computational Fluid Dynamic solver TF3D-VIB with a commercial Finite Element solver ABAQUS.

scholarly journals Mitigation Method of Slot Harmonic Cogging Torque Considering Unevenly Magnetized Permanent Magnets in PMSM

Energies ◽  
2019 ◽  
Vol 12 (20) ◽  
pp. 3887
Author(s):  
Jeong ◽  
Lee ◽  
Hur
Keyword(s):  
Permanent Magnet ◽  
Permanent Magnets ◽  
Permanent Magnet Synchronous Motor ◽  
Harmonic Component ◽  
Magnetic Flux Density ◽  
Element Analysis ◽  
Cogging Torque ◽  
Maxwell Stress Tensor ◽  
The Finite Element Analysis ◽  
Harmonic Components

This paper presents a mitigation method of slot harmonic cogging torque considering unevenly magnetized magnets in a permanent magnet synchronous motor. In previous studies, it has been confirmed that non-uniformly magnetized permanent magnets cause an unexpected increase of cogging torque because of additional slot harmonic components. However, these studies did not offer a countermeasure against it. First, in this study, the relationship between the residual magnetic flux density of the permanent magnet and the cogging torque is derived from the basic form of the Maxwell stress tensor equation. Second, the principle of the slot harmonic cogging torque generation is explained qualitatively, and the mitigation method of the slot harmonic component is proposed. Finally, the proposed method is verified with the finite element analysis and experimental results.

Advanced Calculation Flutter Procedure Developed for Ultra-Long Last Stage Blades for Steam Turbines

2019 ◽  
Author(s):  
Vaclav Slama ◽  
Bartolomej Rudas ◽  
Ales Macalka ◽  
Jiri Ira ◽  
Antonin Zivny
Keyword(s):  
Stokes Equations ◽  
Damping Ratio ◽  
Rotor Blades ◽  
Numerical Code ◽  
Navier Stokes ◽  
Steam Turbines ◽  
Navier Stokes Equations ◽  
Time Marching ◽  
Last Stage ◽  
The Time Domain

Abstract An advanced in-house procedure, which is based on a commercial numerical code, to predict a potential danger of unstalled flutter has been developed and validated. This procedure using a one way decoupled method and a full-scale time-marching 3D viscous model in order to obtain the solution of the Unsteady Reynolds-Averaged Navier-Stokes equations in the time domain thus calculate an aerodynamic work and a damping ratio is used as an essential tool for developing ultra-long last stage rotor blades in low pressure turbine parts for modern steam turbines with a large operating range and an enhanced efficiency. An example is shown on a development of the last stage blade for high backpressures.

Development of lateral interactions in the infant visual system

1992 ◽  
Vol 8 (1) ◽  
pp. 3-8 ◽  
Author(s):  
Samuel Sokol ◽  
Vance Zemon ◽  
Anne Moskowitz
Keyword(s):  
Visual System ◽  
Long Range ◽  
Short Range ◽  
Second Harmonic ◽  
Harmonic Component ◽  
Frequency Component ◽  
Human Infants ◽  
Long Range Interactions ◽  
Harmonic Components ◽  
Inhibitory Interactions

AbstractThe development of lateral inhibitory interactions in the infant visual system, as reflected by the visual-evoked potential (VEP), was studied using a radial, asymmetrical windmill-dartboard stimulus. This contrast-reversing stimulus generates VEP responses with a strong fundamental frequency component and an attenuated second harmonic component (relative to that obtained using a symmetrical stimulus). These two harmonic components reflect distinct phenomena, and appear to be the result of short-range (the fundamental) and long-range (attenuated second harmonic) lateral inhibitory interactions elicited by differential luminance-modulation of contiguous spatial regions. We studied the development of the short-and long-range interactions at 100% and 30% contrast in human infants using both VEP amplitude and phase measures. Attenuation of the second harmonic (long-range interactions) was adult-like by 8 weeks of age while the strength of the fundamental (short-range interactions) was adult-like by 20 weeks suggesting a differential development of long-range and short-range interactions. In contrast, corresponding phase data indicated significant immaturities at 20 weeks of age for both the short-and long-range components.

Unsteady Forces in Last Stage LP Steam Turbine Rotor Blades With Exhaust Hood

2016 ◽  
Author(s):  
Romuald Rzadkowski ◽  
Jan Surwiło ◽  
Leszek Kubitz ◽  
Piotr Lampart ◽  
Mariusz Szymaniak
Keyword(s):  
Numerical Study ◽  
Flow Analysis ◽  
Turbine Rotor ◽  
Rotor Blades ◽  
Steam Turbines ◽  
Exhaust Hood ◽  
Low Frequencies ◽  
Unsteady Forces ◽  
Relative Contribution ◽  
Last Stage

Several high vibration amplitude problems have been reported regarding the slender last stage blades of commercial LP steam turbines. This paper presents a numerical study of unsteady forces acting on rotor blades using ANSYS CFX. A 3D transonic viscous flow through the stator and rotor blades with an exhaust hood was modelled. The last stage was modelled as a full blade annulus, so that the axial, radial and circumferential distribution of flow patterns and blade forces could be examined. An unsteady flow analysis was conducted on a typically designed last stage and exhaust diffuser, with measured and calculated downstream static pressure distribution as the outlet boundary condition. The results showed that under off-design conditions, vortices occurred in the last stage and diffuser. Unsteady aerodynamic forces were found at high frequencies (stator passing frequencies) and low frequencies (generated from asymmetric pressure distributions behind the rotor), with the relative dominance of these forces/frequencies shifting as a function of radial span. An FFT analysis was carried out. Three sections were investigated: the hub, midspan and peripheral (tip) section. The steady pressure behind the rotor blade was compared with experimental results in the LP last stage behind the rotor blades and in a specified cross-section of the exhaust hood. The lower frequency unsteady forces had a higher relative contribution towards the tip of the blade.

Statistical Correlation Between the Crankshaft’s Speed Variation and Engine Performance—Part I: Theoretical Model

2003 ◽  
Vol 125 (3) ◽  
pp. 791-796 ◽  
Author(s):  
D. Taraza
Keyword(s):  
Statistical Model ◽  
Statistical Approach ◽  
Harmonic Component ◽  
Engine Performance ◽  
Statistical Correlation ◽  
Gas Pressure ◽  
Operating Conditions ◽  
Crank Angle ◽  
The Mean ◽  
Harmonic Components

The goal of this two-part paper is to develop a methodology using the variation of the measured crankshaft speed to calculate the mean indicated pressure (MIP) of a multicylinder engine and to detect cylinders that are lower contributors to the total engine output. Both the gas pressure torque and the crankshaft’s speed are, under steady-state operating conditions, periodic functions of the crank angle and may be expressed by Fourier series. For the lower harmonic orders, the dynamic response of the crankshaft approaches the response of a rigid body and that makes it is possible to establish correlations between the amplitudes and phases of the corresponding harmonic orders of the crankshaft’s speed and of the gas pressure torque. The inherent cycle-to-cycle variation in the operation of the cylinders requires a statistical approach to the problem. The first part of the paper introduces the statistical model for a harmonic component of the gas pressure torque and determines the correlation between the amplitudes and phases of the harmonic components of the gas pressure torque and the MIP of the engine. In the second part of the paper the statistical model is used to calculate the MIP and to detect deficient cylinders in the operation of a six-cylinder four-stroke diesel engine.

A Double-Passage Shape Correction Method for Predictions of Unsteady Flow and Aeroelasticity in Turbomachinery

2017 ◽  
Vol 9 (4) ◽  
pp. 839-860 ◽  
Author(s):  
Tongqing Guo ◽  
Di Zhou ◽  
Zhiliang Lu
Keyword(s):  
Unsteady Flow ◽  
Turbulent Flows ◽  
Fourier Coefficients ◽  
Three Dimensional ◽  
Correction Method ◽  
Solution Stability ◽  
Shape Correction ◽  
Flow Variables ◽  
Transonic Fan ◽  
Solution Accuracy

AbstractIn this paper, a double-passage shape correction (DPSC) method is presented for simulation of unsteady flows around vibrating blades and aeroelastic prediction. Based on the idea of phase-lagged boundary conditions, the shape correction method was proposed aimed at efficiently dealing with unsteady flow problems in turbomachinery. However, the original single-passage shape correction (SPSC) may show the disadvantage of slow convergence of unsteady solutions and even produce nonphysical oscillation. The reason is found to be related with the disturbances on the circumferential boundaries that can not be damped by numerical schemes. To overcome these difficulties, the DPSC method is adopted here, in which the Fourier coefficients are computed from flow variables at implicit boundaries instead of circumferential boundaries in the SPSC method. This treatment actually reduces the interaction between the calculation of Fourier coefficients and the update of flow variables. Therefore a faster convergence speed could be achieved and also the solution stability is improved. The present method is developed to be suitable for viscous and turbulent flows. And for real three-dimensional (3D) problems, the rotating effects are also considered. For validation, a 2D oscillating turbine cascade, a 3D oscillating flat plate cascade and a 3D practical transonic fan rotor are investigated. Comparisons with experimental data or other solutions and relevant discussions are presented in detail. Numerical results show that the solution accuracy of DPSC method is favorable and at least comparable to the SPSC method. However, fewer iteration cycles are needed to get a converged and stable unsteady solution, which greatly improves the computational efficiency.

Developing a Generalized Harmonic Balance Method for Accurate Identification of Crack Depth in a Continuous Shaft-Disc System

2015 ◽  
Author(s):  
Hamid Khorrami ◽  
Ramin Sedaghati ◽  
Subhash Rakheja
Keyword(s):  
Harmonic Balance ◽  
Crack Detection ◽  
Crack Depth ◽  
Harmonic Component ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Vibrational Properties ◽  
Accurate Identification ◽  
Harmonic Components ◽  
Generalized Harmonic Balance Method

In this work, the effect of a crack on the vibrational properties of a shaft-disc system has been studied applying a generalized harmonic balance method. In the reviewed literature, the reported methods to find the unbalance response of a continuous shaft-disc system provide only the first harmonic component of the response; whereas, the presented method gives the super-harmonic components as well. The shaft-disk system consists of a flexible shaft with a single rigid disc mounted on rigid short bearing supports. The shaft contains a transverse breathing crack (fatigue crack). The main concept for crack detection in vibration-based methods is basically the investigation of crack-induced changes in the selected vibrational properties. Shaft critical speeds and harmonic and super-harmonic components of the unbalance lateral response have been used as typical vibrational properties for crack detection in a rotating shaft system. A generalized harmonic balance method has been developed to efficiently investigate changes in vibrational properties due to the effect of crack properties, depth and location. The results of the developed analytical model have been compared with those obtained from the finite element model and close agreement has been observed.

Linkage Mechanisms With Cam-Integrated Joints for Controlled Harmonic Content of the Output Motion: Theory and Application

2007 ◽  
Vol 130 (1) ◽  
Author(s):  
L. Yuan ◽  
J. Rastegar ◽  
J. Zhang
Keyword(s):  
Closed Loop ◽  
Vibrational Excitation ◽  
High Harmonic ◽  
Harmonic Component ◽  
Linkage Mechanism ◽  
Mechanism Synthesis ◽  
Cam Mechanism ◽  
Harmonic Content ◽  
Harmonic Components ◽  
Four Bar Linkage

In a recent study, the authors presented a systematic method for the modification of the output motion of linkage mechanisms with closed-loop chains using cams positioned at one or more joints of the mechanism. In this paper, the method is applied to the design of a linkage mechanism with an integrated cam mechanism to eliminate high harmonic component of the output motion. The mechanism may be synthesized using any existing linkage mechanism synthesis technique. In the present study, a cam mechanism is synthesized to eliminate all high harmonic components of the output link motion of a four-bar linkage mechanism to illustrate the potentials of the present approach. The mechanism is then constructed and successfully tested. With the present method, selected ranges of high harmonic motions generated due to the mechanisms kinematics nonlinearity can be eliminated by integrating appropriately designed cams, thereby significantly reducing the potential vibrational excitation that the mechanism can impart on the overall system, including its own structure. Such systems should therefore be capable of operating at higher speeds and with increased precision.

Sign in / Sign up

Export Citation Format

Share Document