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.

Numerical Model of Liquid Film Formation and Breakup in Last Stage of a Low-Pressure Steam Turbine

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Pietro Rossi ◽  
Asad Raheem ◽  
Reza S. Abhari
Keyword(s):  
Steam Turbine ◽  
Stokes Equations ◽  
Low Pressure ◽  
Liquid Films ◽  
Operating Conditions ◽  
Rotor Blades ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Last Stage ◽  
The Impact

Formation of thin liquid films on steam turbine airfoils, particularly in last stages of low-pressure (LP) steam turbines, and their breakup into coarse droplets is of paramount importance to assess erosion of last stage rotor blades given by the impact of those droplets. An approach for this problem is presented in this paper: this includes deposition of liquid water mass and momentum, film mass and momentum conservation, trailing edge breakup and droplets Lagrangian tracking accounting for inertia and drag. The use of thickness-averaged two-dimensional (2D) equations in local body-fitted coordinates, derived from Navier–Stokes equations, makes the approach suitable for arbitrary curved blades and integration with three-dimensional (3D) computational fluid dynamics (CFD) simulations. The model is implemented in the in-house solver MULTI3, which uses Reynolds-averaged Navier–Stokes equations κ – ω model and steam tables for the steam phase and was previously modified to run on multi-GPU architecture. The method is applied to the last stage of a steam turbine in full and part load operating conditions to validate the model by comparison with time-averaged data from experiments conducted in the same conditions. Droplets impact pattern on rotor blades is also predicted and shown.

Numerical Modeling of Evolution of Boundary Between Incompressible Gas and Liquid in Two-Dimensional Region

2006 ◽  
Vol 4 ◽  
pp. 224-236
Author(s):  
A.S. Topolnikov
Keyword(s):  
Numerical Modeling ◽  
Interphase Boundary ◽  
Incompressible Liquid ◽  
Stokes Equations ◽  
Numerical Code ◽  
Navier Stokes ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Incompressible Media ◽  
Good Agreement

The paper is devoted to numerical modeling of Navier–Stokes equations for incompressible media in the case, when there exist gas and liquid inside the rectangular calculation region, which are separated by interphase boundary. The set of equations for incompressible liquid accounting for viscous, gravitational and surface (capillary) forces is solved by finite-difference scheme on the spaced grid, for description of interphase boundary the ideology of Level Set Method is used. By developed numerical code the set of hydrodynamic problems is solved, which describe the motion of two-phase incompressible media with interphase boundary. As a result of numerical simulation the solutions are obtained, which are in good agreement with existing analytical and experimental solutions.

scholarly journals Navier-Stokes Analysis of Unsteady Transonic Flows Through Gas Turbine Cascades With and Without Coolant Ejection

1997 ◽  
Author(s):  
T. Tanuma ◽  
N. Shibukawa ◽  
S. Yamamoto
Keyword(s):  
Gas Turbine ◽  
Stokes Equations ◽  
Viscous Flows ◽  
Navier Stokes ◽  
Implicit Time ◽  
Trailing Edge ◽  
Navier Stokes Equations ◽  
Time Marching ◽  
Turbine Cascades ◽  
Annular Cascade

An implicit time-marching higher-order accurate finite-difference method for solving the two-dimensional compressible Navier-Stokes equations was applied to the numerical analyses of steady and unsteady, subsonic and transonic viscous flows through gas turbine cascades with trailing edge coolant ejection. Annular cascade tests were carried out to verify the accuracy of the present analysis. The unsteady aerodynamic mechanisms associated with the interaction between the trailing edge vortices and shock waves and the effect of coolant ejection were evaluated with the present 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.

Numerical Simulation of the Cooling Process of Cubic Shells

2011 ◽  
Author(s):  
Manabu Okura ◽  
Kiyoaki Ono
Keyword(s):  
Heat Transfer ◽  
Stokes Equations ◽  
Temperature Fields ◽  
Numerical Code ◽  
Navier Stokes ◽  
Cooling Process ◽  
Air Velocity ◽  
Navier Stokes Equations ◽  
The Difference ◽  
The Heat Transfer Coefficient

In order to keep the environment in an air-conditioned room comfortable, it is important to anticipate the air velocity and temperature fields precisely. The numerical code, solving simultaneously the Navier-Stokes equations governing flow field inside and outside the room and the heat conduction equation applying to walls, are developed. The assumption that the heat transfer coefficient between the fluid and the surface of solids is not used. This code is applied to investigate the cooling process of a cubic shell. The computational results agree with the experimental results. We also investigated the same process of the cubic shells whose walls are internally or externally insulated. The difference of the amount of heat transfer will be discussed.

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.

A framework for optimising aspects of rotor blades

2011 ◽  
Vol 115 (1165) ◽  
pp. 147-161 ◽  
Author(s):  
C. S. Johnson ◽  
G. N. Barakos
Keyword(s):  
Objective Function ◽  
Stokes Equations ◽  
Rotor Blades ◽  
Navier Stokes ◽  
Computational Framework ◽  
Navier Stokes Equations ◽  
Theoretical Predictions ◽  
Artificial Neural ◽  
Optimisation Methods ◽  
Selection Of

AbstractThis work presents a computational framework for the optimisation of various aspects of rotor blades. The proposed method employs CFD combined with artificial neural networks, employed as metamodels, and optimisation methods based on genetic algorithms. To demonstrate this approach, two examples have been used, one is the optimal selection of 4- and 5-digit NACA aerofoils for rotor sections and the other is the optimisation of linear blade twist for rotors in hover. For each case, an objective function was created and the meta-model was subsequently used to evaluate this objective function during the optimisation process. The obtained results agree with real world design examples and theoretical predictions. For the selected cases, the artificial neural network was found to perform adequately though the results required a substantial amount of data for training. The genetic algorithm was found to be very effective in identifying a set of near-optimal parameters. The main CPU cost was associated with the population of the database necessary for the meta-models and this task required CFD computations based on the Reynolds-averaged Navier-Stokes equations. The framework is general enough to allow for several design or optimisation tasks to be carried out and it is based on open-source code made available by the authors.

scholarly journals Calculations of the Hydrodynamic Characteristics of a Ducted Propeller Operating in Oblique Flow

2017 ◽  
Vol 10 (20) ◽  
pp. 31
Author(s):  
Hassan Ghassemi ◽  
Sohrab Majdfar ◽  
Hamid Forouzan
Keyword(s):  
Stokes Equations ◽  
Open Water ◽  
Hydrodynamic Performance ◽  
Numerical Code ◽  
Navier Stokes ◽  
Hydrodynamic Characteristics ◽  
Navier Stokes Equations ◽  
Oblique Flow ◽  
Ducted Propeller ◽  
Acceptable Agreement

The purpose of this paper is to calculate the hydrodynamic performance of a ducted propeller (hereafter Duct_P) at oblique flows. e numerical code based on the solution of the Reynolds-averaged Navier– Stokes equations (RANSE) applies to the Kaplan propeller with 19A duct. e shear-stress transport (SST)-k-ω turbulence model is used for the present results. Open-water hydrodynamic results are compared with experimental data showing a relatively acceptable agreement. Two oblique flow angles selected to analyze in this paper are 10 and 20 degrees. Numerical results of the pressure distribution and hydrodynamic performance are presented and discussed. 

Development of Numerical Code to Predict Three-Dimensional Sand Erosion Phenomena

2003 ◽  
Author(s):  
Kuki Junichi ◽  
Kazuyuki Toda ◽  
Makoto Yamamoto
Keyword(s):  
Flow Field ◽  
Stokes Equations ◽  
Suspended Particle ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Numerical Code ◽  
Particle Collision ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Sand Erosion

This paper presents a numerical procedure to predict a three-dimensional sand erosion phenomenon and the interaction between the flow field and the eroded surface. To simulate this phenomenon, the turbulent flow field, the particle trajectory and the amount of erosion on the eroded wall are calculated repeatedly. In computations of the flow field, compressible Navier-Stokes equations and low-Reynolds-number type k–ε turbulence model are adopted. Assuming that the concentration of suspended particle is dilute, particle-particle collision and the influence of particle motions on the flow field are neglected. The Neilson-Gilchrist erosion model is used to estimate the weight loss due to erosion. To verify the developed code, two types of 90-degree bends are computed. The results show that the present procedure can reasonably reproduce the sand erosion process and the temporal change of both the flow field and the wall surface qualitatively.

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