Numerical Analysis of Fully Three-Dimensional Periodic Flows Through a Turbine Stage

1985 ◽  
Vol 107 (4) ◽  
pp. 945-952 ◽  
Author(s):  
M. Koya ◽  
S. Kotake
Keyword(s):  
Numerical Calculation ◽  
Three Dimensional ◽  
Time Dependent ◽  
Turbine Stage ◽  
Established Method ◽  
Periodic Flows ◽  
Time Space ◽  
Blade Row ◽  
Volume Method ◽  
Blade Row Interaction

Fully three-dimensional periodic flows through a turbine stage of stator and rotor are studied numerically by solving time-dependent three-dimensional Euler equations with the finite-volume method. The phase relation of stator and rotor flows and the related blade-row interaction are accounted for in the time-space domain. The established method of numerical calculation makes a practical contribution to predict actual turbine flows through a turbine stage of stator and rotor which have an arbitrary number of blades.

A Parametric Study of the Blade Row Interaction in a High Pressure Turbine Stage

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
G. Persico ◽  
P. Gaetani ◽  
C. Osnaghi
Keyword(s):  
High Pressure ◽  
Strong Dependence ◽  
Three Dimensional ◽  
Secondary Flows ◽  
Pressure Probe ◽  
Turbine Stage ◽  
Mixing Rate ◽  
Aerodynamic Pressure ◽  
Blade Row ◽  
Blade Row Interaction

An extensive experimental analysis on the subject of the unsteady periodic flow in a high subsonic high pressure (HP) turbine stage has been carried out at the Laboratorio di Fluidodinamica delle Macchine of the Politecnico di Milano (Italy). In this paper the aerodynamic blade row interaction in HP turbines, enforced by increasing the stator and rotor blade loading and by reducing the stator-rotor axial gap, is studied in detail. The time-averaged three-dimensional flowfield in the stator-rotor gap was investigated by means of a conventional five-hole probe for the nominal (0 deg) and highly positive (+22 deg) stator incidences. The evolution of the viscous flow structures downstream of the stator is presented to characterize the rotor incoming flow. The blade row interaction was evaluated on the basis of unsteady aerodynamic measurements at the rotor exit, performed with a fast-response aerodynamic pressure probe. Results show a strong dependence of the time-averaged and phase-resolved flowfield and of the stage performance on the stator incidence. The structure of the vortex-blade interaction changes significantly as the magnitude of the rotor-inlet vortices increases, and very different residual traces of the stator secondary flows are found downstream of the rotor. On the contrary, the increase in rotor loading enhances the unsteadiness in the rotor secondary flows but has a little effect on the vortex-vortex interaction. For the large axial gap, a reduction of stator-related effects at the rotor exit is encountered when the stator incidence is increased as a result of the different mixing rate within the cascade gap.

Characterization of Deterministic Correlations for a Turbine Stage: Part 1 — Time-Averaged Flow Analysis

1999 ◽  
Author(s):  
Fabien Bardoux ◽  
Francis Leboeuf ◽  
Cédric Dano ◽  
Clément Toussaint
Keyword(s):  
Flow Analysis ◽  
Time Dependent ◽  
Turbine Stage ◽  
Direct Computation ◽  
Correlation Models ◽  
Blade Row ◽  
Transonic Turbine ◽  
Physical Phenomena ◽  
Blade Row Interaction

This paper analyses the flow in a transonic turbine stage, using time-dependent numerical results. Unsteady blade-row interaction has repercussions on the time-averaged flow, which are represented by the so-called “deterministic correlations”. These correlations appear in the system of equations governing the time-averaged flow; they can be divided into four types with different physical meanings. Time-dependent results enable direct computation of these correlations in both rotor and stator frames of reference. The computed deterministic correlations are analysed in the paper, in order to bind them to physical phenomena and to evaluate their influence on the time-averaged flow field. This analysis is also intended to help assess the shortcomings of simple mixing-plane methods and more complex approaches using deterministic correlation models. While the first part focuses on one particular type of deterministic correlation, the so-called “spatial correlation”, the second part attempts a more detailed analysis of time-dependent results and gives some clues to the orders of magnitude of the four types of deterministic correlation. The conclusions should be taken with caution; they may partly depend on the present turbine configuration with a specified structure of unsteadiness and on the present turbulence model.

Calculation of the Three-Dimensional, Steady, Inviscid Flow in a Transonic Axial Turbine Stage

1985 ◽  
Vol 107 (2) ◽  
pp. 286-292 ◽  
Author(s):  
T. Arts
Keyword(s):  
Three Dimensional ◽  
Inviscid Flow ◽  
Turbine Stage ◽  
Axial Turbine ◽  
Absolute Flow ◽  
Cylindrical Coordinate ◽  
Blade Row ◽  
Time Marching ◽  
Finite Volume Approach ◽  
Blade Row Interaction

The aim of this paper is to develop an approach to compute the three-dimensional, rotational, adiabatic, inviscid flow of a perfect gas in a transonic axial turbine stage. The time-dependent Euler equations, expressed in a cylindrical coordinate system, are solved using a time-marching method and a finite volume approach. The absolute flow is calculated in the stator, whereas the relative flow is computed in the rotor. A time-averaged blade row interaction is assumed. The method is applied to a transonic single-stage turbine. The calculated results agree well with the measured performance and three-dimensional aspects of the flow appear clearly.

Effects of Off-Design Operating Conditions on the Blade Row Interaction in a HP Turbine Stage

2007 ◽  
Author(s):  
G. Persico ◽  
P. Gaetani ◽  
C. Osnaghi
Keyword(s):  
Flow Field ◽  
Strong Dependence ◽  
Secondary Flows ◽  
Operating Conditions ◽  
Pressure Probe ◽  
Turbine Stage ◽  
Mixing Rate ◽  
Aerodynamic Pressure ◽  
Blade Row ◽  
Blade Row Interaction

An extensive experimental analysis on the subject of the unsteady periodic flow in a highly subsonic HP turbine stage has been carried out at the Laboratorio di Fluidodinamica delle Macchine (LFM) of the Politecnico di Milano (Italy). In this paper the blade row interaction is progressively enforced by increasing the stator and rotor blade loading and by reducing the stator-rotor axial gap from 100% (very large to smooth the rotor inlet unsteadiness) to 35% (design configuration) of the stator axial chord. The time-averaged three-dimensional flow field in the stator-rotor gap was investigated by means of a conventional five-hole probe for the nominal (0°) and an highly positive (+22°) stator incidences. The evolution of the viscous flow structures downstream of the stator is presented to characterize the rotor incoming flow. The blade row interaction was evaluated on the basis of unsteady aerodynamic measurements at the rotor exit, performed with a fast-response aerodynamic pressure probe. Results show a strong dependence of the time-averaged and phase-resolved flow field and of the stage performance on the stator incidence. The structure of the vortex-blade interaction changes significantly as the magnitude of the rotor inlet vortices increases, and very different residual traces of the stator secondary flows are found downstream of the rotor. On the contrary, the increase of rotor loading enhances the unsteadiness in the rotor secondary flows but has a little effect on the vortex-vortex interaction. For the large axial gap, a reduction of stator-related effects at the rotor exit is encountered when the stator incidence is increased as a result of the different mixing rate within the cascade gap.

Interaction Effects in a Transonic Turbine Stage

2000 ◽  
Author(s):  
J. W. Barter ◽  
P. H. Vitt ◽  
J. P. Chen
Keyword(s):  
Analytical Techniques ◽  
Interaction Effects ◽  
Phase Lag ◽  
Turbine Stage ◽  
Reflected Waves ◽  
Blade Row ◽  
Transonic Turbine ◽  
Unsteady Loading ◽  
Unsteady Pressure Measurements ◽  
Blade Row Interaction

A 3D, viscous, time-accurate code has been used to predict the time-dependent flowfield in a transonic turbine stage. Two analytical techniques are used to understand the unsteady physics. One technique takes into account interaction effects associated with reflected waves bouncing between blade rows while the other neglects them. Both techniques model the exact blade counts using phase-lag boundary conditions. The analytical techniques are validated by comparing to unsteady pressure measurements which have been made on the vane and blade surfaces at midspan. The analytical results are then used to understand the importance of interaction effects when the blade rows are close-coupled and when they are more widely spaced. The results show that interaction effects must be taken into account in order to accurately predict the unsteady loading on the upstream blade row. However, for the downstream blade row, interaction effects are second order and do not routinely need to be taken into account in the design process.

scholarly journals Validation of a 4D Finite Volume Method for Blade Flutter

1996 ◽  
Author(s):  
Pieter Groth ◽  
Hans Mårtensson ◽  
Lars-Erik Eriksson
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Three Dimensional ◽  
Transfinite Interpolation ◽  
Time Space ◽  
Blade Flutter ◽  
Time Marching ◽  
External Flows ◽  
Nicolson Scheme ◽  
Volume Method

A finite volume method for blade flutter analyses, using moving grids is presented and partly validated. The method which solves the unsteady three-dimensional Euler equations is formulated in the four-dimensional time-space domain. An algebraic grid generation technique based on transfinite interpolation is used to move and deform the grid to conform to the blade motion. Fluxes are calculated using a third-order upwind-biased scheme. For time marching both an explicit three-stage Runge-Kutta scheme and a Crank-Nicolson scheme is used. Internal and external flows are calculated using the present method. Calculated results agree well with the corresponding experiments and with results obtained using other methods.

scholarly journals Penetration Grouting Mechanism of Time-Dependent Power-Law Fluid for Reinforcing Loose Gravel Soil

Minerals ◽  
2021 ◽  
Vol 11 (12) ◽  
pp. 1391
Author(s):  
Tingting Guo ◽  
Zhiwei Zhang ◽  
Zhiquan Yang ◽  
Yingyan Zhu ◽  
Yi Yang ◽  
...  
Keyword(s):  
Numerical Calculation ◽  
Numerical Simulations ◽  
Power Law ◽  
Three Dimensional ◽  
Time Dependent ◽  
Rheological Parameters ◽  
Power Law Fluid ◽  
Dependent Behavior ◽  
Gravel Soil ◽  
Penetration Grouting

The time-dependent behavior of power-law fluid has a significant influence on the grouting effects of reinforcing loose gravel soil. In this paper, based on basic rheological equations and the time-dependent behavior of rheological parameters (consistency coefficient and rheological index), rheological equations and penetration equations of time-dependent power-law fluid are proposed. Its penetration grouting diffusion mechanism for reinforcing loose gravel soil was then theoretically induced. A set of indoor experimental devices for simulating penetration grouting was designed to simulate the penetration grouting of power-law fluid with different time-dependent behaviors for reinforcing loose gravel soil. Then, relying on the COMSOL Multiphysics platform and Darcy’s law, three-dimensional numerical calculation programs for this mechanism were obtained using secondary-development programming technology. Thus, the numerical simulations of the penetration grouting process of power-law fluid with different time-dependent behaviors for reinforcing loose gravel soil were carried out. This theoretical mechanism was validated by comparing results from theoretical analyses, indoor experiments, and numerical simulations. Research results show that the three-dimensional numerical calculation programs can successfully simulate the penetration diffusion patterns of a time-dependent power-law fluid in loose gravel soil. The theoretical calculation values and numerical simulation values of the diffusion radius obtained from this mechanism are closer to indoor experimental values than those obtained from the penetration grouting diffusion theory of power-law fluid without considering time-dependent behavior. This mechanism can better reflect the penetration grouting diffusion laws of a power-law fluid in loose gravel soil than the theory, which can provide theoretical support and guidance for practical grouting construction.

Simulation of Rotor/Stator Interaction With a 4D Finite Volume Method

2002 ◽  
Author(s):  
Bjo¨rn Laumert ◽  
Hans Ma˚rtensson ◽  
Torsten H. Fransson
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Three Dimensional ◽  
Test Case ◽  
Pressure Distributions ◽  
Time Space ◽  
Rotor Stator Interaction ◽  
Pitch Ratio ◽  
Grid Nodes ◽  
Volume Method

A finite volume method for the computation of rotor/stator interaction for stages with arbitrary rotor/stator pitch ratios is presented and partly validated in this paper. The method which solves the unsteady three-dimensional Euler equations is formulated in the four-dimensional time-space domain. The method of time inclination is utilized to account for unequal pitchwise periodicity by distributing time co-ordinates at the grid nodes such that phase lagged boundary conditions can be employed. Calculated results show excellent agreement with the results of a reference solver for the validation test case. Furthermore the method was applied to the simulation of the unsteady flow field in a transonic test turbine stage with a stator/rotor pitch ratio of 1.875. The results were compared with measurements of the unsteady rotor blade pressure and a reference solver calculation where an approximate pitch ratio of 2.0 with a 6.7% scaled rotor geometry was employed. Both computational cases show satisfactory agreement with the experiments for both time averaged pressure distributions and pressure perturbation amplitudes.

A Three-Dimensional Linearized Euler Analysis of Classical Wake/Stator Interactions: Validation and Unsteady Response Predictions

2002 ◽  
Vol 1 (2) ◽  
pp. 137-163 ◽  
Author(s):  
D. Prasad ◽  
J.M. Verdon
Keyword(s):  
Three Dimensional ◽  
Phase Variation ◽  
Detailed Comparison ◽  
Numerical Results ◽  
Acoustic Response ◽  
Lifting Surface ◽  
Blade Row ◽  
Rotor Stator Interaction ◽  
Blade Row Interaction ◽  
Lifting Line

A comprehensive validation of the linearized Euler analysis, LINFLUX, for wake/blade row interaction is carried out. The flow configuration is that of the benchmark problem for rotor-stator interaction proposed at the Third Computational Aeroacoustics Workshop. It consists of an unstaggered, annular, flat-plate blade row excited by the vortical gusts associated with the wakes shed from an upstream rotor. The numerical results for the unsteady pressure responses of the stator are compared with semi-analytic lifting surface and lifting line solutions. The validation is first conducted for narrow-annulus flows, where the numerical results are shown to agree well with classical two-dimensional solutions over a range of frequencies. We then carry out a detailed comparison of the three-dimensional LINFLUX results with the lifting surface results of Namba and Schulten for a blade row with a hub-to-tip ratio of 0.5. This study encompasses gust excitation frequencies for which the stator responses vary from cut off to propagating, as well as gusts with varying degrees of spanwise variation. The numerical and semi-analytical analyses yield results for the stator pressure response, including the complex amplitudes of the propagating and least attenuated, evanescent, pressure modes that are in very good agreement. The effect of increasing the spanwise phase variation of the gust is generally, but not necessarily, to reduce the power associated with the acoustic response of the blade row. A comparison of the present numerical results with those obtained from a stripwise application of classical linear theory reveals that the latter approach can be erroneous and, therefore, of questionable applicability to realistic turbomachinery unsteady flows.

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