scholarly journals Solution of Particulate Viscous Flow in a Radial Inflow Turbine

1983 ◽  
Author(s):  
B. V. R. Vittal ◽  
W. Tabakoff
Keyword(s):  
Stokes Equations ◽  
Continuous Phase ◽  
Solid Particles ◽  
Rotor Blades ◽  
Field Analysis ◽  
Numerical Code ◽  
Navier Stokes ◽  
Stream Channels ◽  
Carrier Fluid ◽  
Radial Inflow Turbine

The presence of solid particles in turbomachinery flow affects the component performance as well as its life. The subject of particulated flows can be broadly divided into three parts, namely, particle trajectories, the effect of particles on the aerodynamics of flow and material erosion. The first two aspects are investigated in this paper taking into account the viscosity of the carrier fluid. The Lagrangian formulation is adopted for the particles, whereas the Eulerian approach is used for the continuous phase. The effect of particles is incorporated as interphase force terms in the fully incompressible stream function-vorticity form of the Navier-Stokes equations. The field analysis is based on the numerical integration of this equation over the rotor blade to blade stream channels. The numerical code used to solve the governing equations employs a nonorthogonal boundary fitted coordinate system that suits the most complicated blade geometries. The trajectories of the solid particles are determined including particle impacts with the blades. The particle rebounding velocity and direction after each impact is determined using semi-empirical correlations for the restitution ratios obtained experimentally. The method of analysis is applied to a radial inflow turbine. The effect of particles on the aerodynamics of the flow is studied by analyzing the fluid streamline pattern in the rotor blades with and without solid particles. The analysis is carried out for various particle concentrations.

A Study of the Viscous and Nonadiabatic Flow in Radial Turbines

1981 ◽  
Vol 103 (3) ◽  
pp. 481-489
Author(s):  
I. Khalil ◽  
W. Tabakoff
Keyword(s):  
Stokes Equations ◽  
Interaction Mechanism ◽  
Field Analysis ◽  
Numerical Code ◽  
Navier Stokes ◽  
Governing Equations ◽  
Stream Channels ◽  
Navier Stokes Equations ◽  
Separation Zones ◽  
Radial Turbines

A method for analyzing the viscous nonadiabatic flow within turbomachine rotors is presented. The field analysis is based upon the numerical integration of the incompressible Navier-Stokes equations together with the energy equation over the rotors blade-to-blade stream channels. The numerical code used to solve the governing equations employs a nonorthogonal boundary fitted coordinate system that suits the most complicated blade geometries. Effects of turbulence are modeled with two equations; one expressing the development of the turbulence kinetic energy and the other its dissipation rate. The method of analysis is applied to a radial inflow turbine. The solution obtained indicates the severity of the complex interaction mechanism that occurs between different flow regimes (i.e., boundary layers, recirculating eddies, separation zones, etc.). Comparison with nonviscous flow solutions tend to justify strongly the inadequacy of using the latter with standard boundary layer techniques to obtain viscous flow details within turbomachine rotors. Capabilities and limitations of the present method of analysis are discussed.

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.

Viscous Flow Analysis in Mixed Flow Rotors

1980 ◽  
Vol 102 (1) ◽  
pp. 193-201 ◽  
Author(s):  
I. Khalil ◽  
W. Tabakoff ◽  
A. Hamed
Keyword(s):  
Viscous Flow ◽  
Stokes Equations ◽  
Flow Analysis ◽  
Flow Characteristics ◽  
Laminar Flows ◽  
Operating Conditions ◽  
Field Analysis ◽  
Navier Stokes ◽  
Stream Channels ◽  
Wide Range

A method for analyzing the viscous flow through turbomachine rotors is presented. The field analysis is based on the solution of the full Navier-Stokes equations over the rotor blade-to-blade stream channels. An Alternating-Direction-Implicit method is employed to carry out the necessary numerical integration of the elliptic governing equations. The flow analysis may be applied to various types of turbomachine rotors. Preliminarily, only the case of laminar flows are considered in this paper. The flow characteristics within the rotors of a radial inflow turbine and a radial bladed compressor are investigated over a wide range of operating conditions. Excellent results are obtained when compared with existing experimental data. The method of this analysis is quite general and can deal with wide range of applications. Possible modification of the present study to deal with turbulent flow cases are also identified.

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.

Detached Eddy Simulation of Transonic Rotor Stall Flutter Using a Fully Coupled Fluid-Structure Interaction

2011 ◽  
Author(s):  
Hongsik Im ◽  
Xiangying Chen ◽  
Gecheng Zha
Keyword(s):  
Stokes Equations ◽  
Rotating Stall ◽  
Rotor Blades ◽  
Tip Clearance ◽  
Weno Scheme ◽  
Navier Stokes ◽  
Detached Eddy Simulation ◽  
Eddy Simulation ◽  
Stall Flutter ◽  
Fully Coupled

Detached eddy simulation of an aeroelastic self-excited instability, flutter in NASA Rotor 67 is conducted using a fully coupled fluid/structre interaction. Time accurate compressible 3D Navier-Stokes equations are solved with a system of 5 decoupled modal equations in a fully coupled manner. The 5th order WENO scheme for the inviscid flux and the 4th order central differencing for the viscous flux are used to accurately capture interactions between the flow and vibrating blades with the DES (detached eddy simulation) of turbulence. A moving mesh concept that can improve mesh quality over the rotor tip clearance was implemented. Flutter simulations were first conducted from choke to stall using 4 blade passages. Stall flutter initiated at rotating stall onset, grows dramatically with resonance. The frequency analysis shows that resonance occurs at the first mode of the rotor blade. Before stall, the predicted responses of rotor blades decayed with time, resulting in no flutter. Full annulus simulation at peak point verifies that one can use the multi-passage approach with periodic boundary for the flutter prediction.

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>

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.

Instability and Transition of a Plane Bubble Plume

2002 ◽  
Author(s):  
Ophe´lie Caballina ◽  
Eric Climent ◽  
Jan Dusˇek
Keyword(s):  
Stokes Equations ◽  
Fluid Layer ◽  
Fluid Velocity ◽  
Continuous Phase ◽  
Collective Effects ◽  
Recent Experimental Data ◽  
Fluid Viscosity ◽  
Bubble Plume ◽  
Carrier Fluid ◽  
Bubble Cloud

When bubbles are continuously released from a located source at the bottom of a fluid layer initially at rest, a plume is produced. The motion of the carrier fluid is initiated and driven by buoyancy of the bubble cloud. In the present study, a detailed analysis of the bubble plume transition is investigated. The continuous phase flow is obtained by direct numerical resolution of Navier-Stokes equations forced by the presence of bubbles. Collective effects induced by the presence of bubbles are modelled by a spatio-temporal distribution of momentum. Time evolution of the dispersed phase is solved by lagrangian tracking of all the bubbles. Focused on the description of plume transition, several configurations (plume widths, fluid viscosity, injection rate) are investigated. During the laminar ascension of the plume, fluid velocity profiles can be non-dimensionalised on a single auto-similar evolution. Dimensional analysis provides a prediction of the limit rising velocity of the plume top. This prediction has been confirmed by our numerical simulations. Furthermore, our first results point out the symmetry breaking induced by plume instability which appears beyond a critical transition height. Various data show that the Grashof number based on injection conditions is the key parameter to predict the transition of the plume. Our results agree very well with recent experimental data. Comparison with experiments on thermal plumes in air shows that the bubble plume is more unstable. This feature should be related to the lack of diffusion in the lagrangian transport of density gradient by the bubble cloud and to the slip velocity between the two phases.

scholarly journals Convective-diffusion model of particle deposition in modeling of building structures

2018 ◽  
Vol 251 ◽  
pp. 04008
Author(s):  
Vadim Akhmetov ◽  
Valentina Akhmetova
Keyword(s):  
Lateral Surface ◽  
Particle Deposition ◽  
Stokes Equations ◽  
Swirling Flow ◽  
Vortex Chamber ◽  
Solid Particles ◽  
Navier Stokes ◽  
Building Structures ◽  
Annular Slot ◽  
First Case

The problem of the motion of a swirling flow in a vortex chamber with particle deposition effects at the lateral surface is numerically investigated. Flowfields with formation of recirculation zones are analyzed on the basis of the Navier-Stokes equations. Two cases of the transport process for solid particles of different sizes with deposition on the lateral surface of the channel are studied (passive impurities are assumed). In the first case, the particles are injected into the peripheral part of the channel together with the swirling flow; in the second case, this process is performed through an annular slot without swirling. The results are compared with available experimental data and asymptotic solutions.

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.

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