Numerical Analysis of Unstable Flow in Last-Stage Blades of Steam Turbines

2006 ◽  
Author(s):  
J. C. Garci´a ◽  
J. Kubiak ◽  
F. Sierra ◽  
G. Gonza´lez ◽  
G. Urquiza
Keyword(s):  
Steady State ◽  
Pressure Field ◽  
Stokes Equations ◽  
Two Dimensions ◽  
Navier Stokes ◽  
Steam Turbines ◽  
Unstable Flow ◽  
Geometry Model ◽  
Last Stage ◽  
Exit Edge

As well known steam turbines are strongly affected because of vibrations. Unstable vibrations can appear together with steady-state vibrations. We present the results of numerical computations about unstable flow and its interaction on blades of steam turbines, which can lead to unstable modes of vibration. Unstable phenomena appear as a result of interaction of blades with the stream of steam flow where the pressure field provides the force. The analysis centers particularly in the last stage or L-0 of a 110 MW turbine. Navier-Stokes equations are resolved in two dimensions using a commercial program called Fluent based on finite-volume method. A 2-D geometry model was built in order to represent the dimensional aspects of the diaphragm as well as the rotor located in the last stage of the turbine. Periodic boundary conditions were applied to both sides of the blade with the purpose of simplifying the computation avoiding resolve for the whole wheel. The computations were conducted in both modes, steady state and time dependent. The results show the distribution of pressure fields as a function of the distance to the exit edge of the diaphragm blades. Also, the pressure and velocity fields are shown through contours along the flow channel between the diaphragm blades. The paper includes the time-dependence behavior of pressure field. A Fourier analysis is used to determine the characteristic frequencies of the system, based on numerical 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.

Instability and Sound Emission From a Flow Over a Curved Surface

1988 ◽  
Vol 110 (4) ◽  
pp. 538-544 ◽  
Author(s):  
L. Maestrello ◽  
P. Parikh ◽  
A. Bayliss
Keyword(s):  
Acoustic Waves ◽  
Acoustic Pressure ◽  
Pressure Field ◽  
Stokes Equations ◽  
Convex Surface ◽  
Two Dimensions ◽  
Navier Stokes ◽  
Sound Emission ◽  
Navier Stokes Equations ◽  
Linearized Euler Equations

The growth and decay of a wavepacket convecting in a boundary layer over a concave-convex surface is studied numerically using direct computations of the Navier-Stokes equations. The resulting sound radiation is computed using the linearized Euler equations with the pressure from the Navier-Stokes solution as a time-dependent boundary condition. It is shown that on the concave portion the amplitude of the wavepacket increases and its bandwidth broadens while on the convex portion some of the components in the packet are stabilized. The pressure field decays exponentially away from the surface and then algebraically exhibiting a decay characteristic of acoustic waves in two dimensions. The far field acoustic pressure exhibits a peak at a frequency corresponding to the inflow instability frequency.

A Sobolev gradient method for treating the steady-state incompressible Navier-Stokes equations

2013 ◽  
Vol 11 (4) ◽  
Author(s):  
Robert Renka
Keyword(s):  
Steady State ◽  
Stokes Equations ◽  
Numerical Test ◽  
Trust Region Method ◽  
Trust Region ◽  
Nonlinear Least Squares ◽  
Two Dimensions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Element Discretization

AbstractThe velocity-vorticity-pressure formulation of the steady-state incompressible Navier-Stokes equations in two dimensions is cast as a nonlinear least squares problem in which the functional is a weighted sum of squared residuals. A finite element discretization of the functional is minimized by a trust-region method in which the trustregion radius is defined by a Sobolev norm and the trust-region subproblems are solved by a dogleg method. Numerical test results show the method to be effective.

scholarly journals Modeling the 3-d flow around a cylinder using the SAS hybrid model

2014 ◽  
Vol 16 (5) ◽  
pp. 901-918 ◽  
Keyword(s):  
Turbulence Modeling ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Cross Flow ◽  
Numerical Code ◽  
Navier Stokes ◽  
Computational Domain ◽  
Mean Flow ◽  
Unstable Flow ◽  
Vortex Size

<div> <p>Three-dimensional calculations were performed to simulate the flow around a cylindrical vegetation element using the Scale Adaptive Simulation (SAS) model; commonly, this is the first step of the modeling of the flow through multiple vegetation elements. SAS solves the Reynolds Averaged Navier-Stokes equations in stable flow regions, while in regions with unstable flow it goes unsteady producing a resolved turbulent spectrum after reducing eddy viscosity according to the locally resolved vortex size represented by the von Karman length scale. A finite volume numerical code was used for the spatial discretisation of the rectangular computational domain with stream-wise, cross-flow and vertical dimensions equal to 30D, 11D and 1D, respectively, which was resolved with unstructured grids. Calculations were compared with experiments and Large Eddy Simulations (LES). Predicted overall flow parameters and mean flow velocities exhibited a very satisfactory agreement with experiments and LES, while the agreement of predicted turbulent stresses was satisfactory. Calculations showed that SAS is an efficient and relatively fast turbulence modeling approach, especially in relevant practical problems, in which the very high accuracy that can be achieved by LES at the expense of large computational times is not required.</p> </div> <p>&nbsp;</p>

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