scholarly journals Unsteady Rotor Dynamics in Cascade

1991 ◽  
Author(s):  
Yu-Tai Lee ◽  
Thomas W. Bein ◽  
Jin Zhang Feng ◽  
Charles L. Merkle
Keyword(s):  
Analytic Solution ◽  
Incompressible Flows ◽  
Piecewise Linear ◽  
Vortex Motion ◽  
Potential Effect ◽  
Time Step ◽  
Trailing Edge ◽  
Turbine Stator ◽  
Blade Row ◽  
Constant Source

A time-accurate potential-flow calculation method has been developed for unsteady incompressible flows through two-dimensional multi-blade-row linear cascades. The method represents the boundary surfaces by distributing piecewise linear-vortex and constant-source singularities on discrete panels. A local coordinate is assigned to each independently moving object. Blade-shed vorticity is traced at each time step. The unsteady Kutta condition applied is nonlinear and requires zero blade trailing-edge loading at each time. Its influence on the solutions depends on the blade trailing-edge shapes. Steady biplane and cascade solutions are presented and compared to exact solutions and experimental data. Unsteady solutions are validated with the Wagner function for an airfoil moving impulsively from rest and the Theodorsen function for an oscillating airfoil. The shed vortex motion and its interaction with blades are calculated and compared to an analytic solution. For multi-blade-row cascade, the potential effect between blade rows is predicted using steady and quasi unsteady calculations. The accuracy of the predictions is demonstrated using experimental results for a one-stage turbine stator-rotor.

Unsteady Rotor Dynamics in Cascade

1993 ◽  
Vol 115 (1) ◽  
pp. 85-93 ◽  
Author(s):  
Y. T. Lee ◽  
T. W. Bein ◽  
J. Feng ◽  
C. L. Merkle
Keyword(s):  
Analytic Solution ◽  
Incompressible Flows ◽  
Piecewise Linear ◽  
Vortex Motion ◽  
Potential Effect ◽  
Time Step ◽  
Trailing Edge ◽  
Turbine Stator ◽  
Blade Row ◽  
Constant Source

A time-accurate potential-flow calculation method has been developed for unsteady incompressible flows through two-dimensional multi-blade-row linear cascades. The method represents the boundary surfaces by distributing piecewise linear-vortex and constant-source singularities on discrete panels. A local coordinate is assigned to each independently moving object. Blade-shed vorticity is traced at each time step. The unsteady Kutta condition applied is nonlinear and requires zero blade trailing-edge loading at each time. Its influence on the solutions depends on the blade trailing-edge shapes. Steady biplane and cascade solutions are presented and compared to exact solutions and experimental data. Unsteady solutions are validated with the Wagner function for an airfoil moving impulsively from rest and the Theodorsen function for an oscillating airfoil. The shed vortex motion and its interaction with blades are calculated and compared to an analytic solution. For a multi-blade-row cascade, the potential effect between blade rows is predicted using steady and quasi-unsteady calculations. The accuracy of the predictions is demonstrated using experimental results for a one-stage turbine stator-rotor.

Perspective: Numerical Simulations of Wakes and Blade-Vortex Interaction

1994 ◽  
Vol 116 (1) ◽  
pp. 5-21 ◽  
Author(s):  
Dean T. Mook ◽  
Bonian Dong
Keyword(s):  
Incompressible Flows ◽  
Lower Surface ◽  
The Body ◽  
Spatial Density ◽  
Inviscid Fluid ◽  
Time Step ◽  
Trailing Edge ◽  
Blade Vortex Interaction ◽  
Attached Flow ◽  
Viscous Core

A method for simulating incompressible flows past airfoils and their wakes is described. Vorticity panels are used to represent the body, and vortex blobs (vortex points with their singularities removed) are used to represent the wake. The procedure can be applied to the simulation of completely attached flow past an oscillating airfoil. The rate at which vorticity is shed from the trailing edge of the airfoil into the wake is determined by simultaneously requiring the pressure along the upper and lower surface streamlines to approach the same value at the trailing edge and the circulation around both the airfoil and its wake to remain constant. The motion of the airfoil is discretized, and a vortex is shed from the trailing edge at each time step. The vortices are convected at the local velocity of fluid particles, a procedure that renders the pressure continuous in an inviscid fluid. When the vortices in the wake begin to separate they are split into more vortices, and when they begin to collect they are combined. The numerical simulation reveals that the wake, which is originally smooth, eventually coils, or wraps, around itself, primarily under the influence of the velocity it induces on itself, and forms regions of relatively concentrated vorticity. Although discrete vortices are used to represent the wake, the spatial density of the vortices is so high that the computed velocity profiles across a typical region of concentrated vorticity are quite smooth. Although the computed wake evolves in an entirely inviscid model of the flowfield, these profiles appear to have a viscous core. The computed spacing between the regions of concentrated vorticity in the wake and the circulations around them are in good agreement with the experimental results. As an application, a simulation of the interaction between vorticity in the oncoming stream and a stationary airfoil is also discussed.

Simulation of Vortex Shedding in a Turbine Stage

1999 ◽  
Vol 121 (3) ◽  
pp. 428-435 ◽  
Author(s):  
D. L. Sondak ◽  
D. J. Dorney
Keyword(s):  
Frequency Response ◽  
Vortex Shedding ◽  
Small Time ◽  
Turbine Stage ◽  
Time Step ◽  
Trailing Edge ◽  
Order Of Accuracy ◽  
Flow Simulations ◽  
Blade Row ◽  
Shedding Frequency

Vortex shedding in a turbomachine blade row is affected by the passing of blades in the adjacent downstream blade row, but these effects have not been examined in the literature. A series of flow simulations has been performed to study vortex shedding in a turbine stage, and to quantify the blade interaction effects on the unsteady pressure response. The numerical issues of spatial order of accuracy and the use of Newton subiterations were investigated first. Second-order spatial accuracy was shown to be inadequate to model the shedding frequency response and time-averaged base pressure accurately. For the small time step employed for temporal accuracy, Newton iterations were shown to be unnecessary. The effects of the adjacent blade row were examined by comparing the shedding frequency response for the stage simulations to the response for isolated cascades. The vane shedding was shown to occur exactly on a series of harmonics of the blade passing frequency for the stage case, compared to a single predominant frequency for the isolated cascade. Losses were also examined in the wake region. It was shown that close to the trailing edge, losses were mainly due to wake mixing. Farther downstream of the trailing edge, losses were predominantly due to the trailing edge shock wave.

Simulation of Vortex Shedding in a Turbine Stage

1998 ◽  
Author(s):  
Douglas L. Sondak ◽  
Daniel J. Dorney
Keyword(s):  
Frequency Response ◽  
Vortex Shedding ◽  
Small Time ◽  
Turbine Stage ◽  
Time Step ◽  
Trailing Edge ◽  
Order Of Accuracy ◽  
Flow Simulations ◽  
Blade Row ◽  
Shedding Frequency

Vortex shedding in a turbomachine blade row is affected by the passing of blades in the adjacent downstream blade row, but these effects have not been examined in the literature. A series of flow simulations has been performed to study vortex shedding in a turbine stage, and to quantify the blade interaction effects on the unsteady pressure response. The numerical issues of spatial order of accuracy and the use of Newton subiterations were first investigated. Second order spatial accuracy was shown to be inadequate to accurately model the shedding frequency response and time-averaged base pressure. For the small time step employed for temporal accuracy, Newton iterations were shown to be unnecessary. The effects of the adjacent blade row were examined by comparing the shedding frequency response for the stage simulations to the response for isolated cascades. The vane shedding was shown to occur exactly on a series of harmonics of the blade passing frequency for the stage case, compared to a single predominant frequency for the isolated cascade. Losses were also examined in the wake region. It was shown that close to the trailing edge, losses were mainly due to wake mixing. Farther downstream of the trailing edge, losses were predominantly due to the trailing edge shock wave.

scholarly journals Monolithic Solvers for Incompressible Two-Phase Flows at Large Density and Viscosity Ratios

2020 ◽  
Author(s):  
Mohamed EL OUAFA ◽  
stephane vincent ◽  
Vincent Le Chenadec
Keyword(s):  
Augmented Lagrangian ◽  
Incompressible Flows ◽  
Piecewise Linear ◽  
Staggered Grid ◽  
Interface Tracking ◽  
Two Phase Flows ◽  
Time Step ◽  
Two Phase ◽  
Flow Equations ◽  
Fully Coupled

In this paper, we investigate the accuracy and robustness of three classes of methods for solving two-phase incompressible flows on a staggered grid. Here, the unsteady two-phase flow equations are simulated by finite volumes and penalty methods using implicit and monolithic approaches (such as the augmented Lagrangian and the fully coupled methods), where all velocity components and pressure variables are solved simultaneously (as opposed to segregated methods). The interface tracking is performed with a Volume-of-Fluid (VOF) method, using the Piecewise Linear Interface Construction (PLIC) technique. The home code Fugu is used for implementing the various methods. Our target application is the simulation of two-phase flows at high density and viscosity ratios, which are known to be challenging to simulate. The resulting strategies of monolithic approaches will be proven to be considerably better suited for these two-phase cases, they also allow to use larger time step than segregated methods.

scholarly journals Monolithic Solvers for Incompressible Two-Phase Flows at Large Density and Viscosity Ratios

Fluids ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 23
Author(s):  
Mohamed El Ouafa ◽  
Stephane Vincent ◽  
Vincent Le Chenadec
Keyword(s):  
Augmented Lagrangian ◽  
Incompressible Flows ◽  
Piecewise Linear ◽  
Staggered Grid ◽  
Interface Tracking ◽  
Two Phase Flows ◽  
Time Step ◽  
Two Phase ◽  
Flow Equations ◽  
Fully Coupled

In this paper, we investigate the accuracy and robustness of three classes of methods for solving two-phase incompressible flows on a staggered grid. Here, the unsteady two-phase flow equations are simulated by finite volumes and penalty methods using implicit and monolithic approaches (such as the augmented Lagrangian and the fully coupled methods), where all velocity components and pressure variables are solved simultaneously (as opposed to segregated methods). The interface tracking is performed with a Volume-of-Fluid (VOF) method, using the Piecewise Linear Interface Construction (PLIC) technique. The home code Fugu is used for implementing the various methods. Our target application is the simulation of two-phase flows at high density and viscosity ratios, which are known to be challenging to simulate. The resulting strategies of monolithic approaches will be proven to be considerably better suited for these two-phase cases, they also allow to use larger time step than segregated methods.

Development of the Tip-Leakage Flow Downstream of a Planar Cascade of Turbine Blades: Vorticity Field

1989 ◽  
Author(s):  
M. Yaras ◽  
S. A. Sjolander
Keyword(s):  
Simple Model ◽  
Turbine Blades ◽  
Leakage Flow ◽  
Tip Leakage Flow ◽  
Vorticity Field ◽  
Trailing Edge ◽  
Tip Leakage ◽  
Blade Row ◽  
Axisymmetric Structure ◽  
Insight Into

The paper presents detailed measurements of the tip-leakage flow emerging from a planar cascade of turbine blades. Four clearances of from 1.5 to 5.5 percent of the blade chord are considered. Measurements were made at the trailing edge plane, and at two main planes 1.0 and 1.56 axial chord lengths downstream of the cascade. The results give insight into several aspects of the leakage flow including: the size and strength of the leakage vortex in relation to the size of the tip gap and the bound circulation of the blade; and the evolution of the components of vorticity as the vortex diffuses laterally downstream of the blade row. The vortex was found to have largely completed its roll-up into a nearly axisymmetric structure even at the trailing edge of the cascade. As a result, it was found that the vortex could be modelled surprisingly well with a simple model based on the diffusion of a line vortex.

scholarly journals An analytical and experimental investigation of aerofoil–turbulence interaction noise for plates with spanwise-varying leading edges

2019 ◽  
Vol 865 ◽  
pp. 137-168 ◽  
Author(s):  
Lorna J. Ayton ◽  
Paruchuri Chaitanya
Keyword(s):  
Noise Reduction ◽  
Analytic Solution ◽  
Piecewise Linear ◽  
Separation Of Variables ◽  
Leading Edge ◽  
Test Case ◽  
Far Field ◽  
Mean Flow ◽  
Flat Plates ◽  
Leading Edges

This paper presents an analytic solution for gust–aerofoil interaction noise for flat plates with spanwise-varying periodic leading edges in uniform mean flow. The solution is obtained by solving the linear inviscid equations via separation of variables and the Wiener–Hopf technique, and is suitable for calculating the far-field noise generated by any leading edge with a single-valued piecewise linear periodic spanwise geometry. Acoustic results for homogeneous isotropic turbulent flow are calculated by integrating the single-gust solution over a wavenumber spectrum. The far-sound pressure level is calculated for five test-case geometries; sawtooth serration, slitted $v$-root, slitted $u$-root, chopped peak and square wave, and compared to experimental measurements. Good agreement is seen over a range of frequencies and tip-to-root ratios (varying the sharpness of the serration). The analytic solution is then used to calculate the propagating pressure along the leading edge of the serration for fixed spanwise wavenumbers, i.e. only the contribution to the surface pressure which propagates to the far field. Using these results, two primary mechanisms for noise reduction are discussed; tip and root interference, and a redistribution of energy from cuton modes to cutoff modes. A secondary noise-reduction mechanism due to nonlinear features is also discussed and seen to be particularly important for leading edges with very narrow slits.

Numerical integration of the three-dimensional Navier-Stokes equations for incompressible flow

1969 ◽  
Vol 37 (4) ◽  
pp. 727-750 ◽  
Author(s):  
Gareth P. Williams
Keyword(s):  
Poisson Equation ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Wave Flow ◽  
Trigonometric Interpolation ◽  
Time Step ◽  
Navier Stokes Equations ◽  
The Poisson Equation

A method of numerically integrating the Navier-Stokes equations for certain three-dimensional incompressible flows is described. The technique is presented through application to the particular problem of describing thermal convection in a rotating annulus. The equations, in cylindrical polar co-ordinate form, are integrated with respect to time by a marching process, together with the solving of a Poisson equation for the pressure. A suitable form of the finite difference equations gives a computationally-stable long-term integration with reasonably faithful representation of the spatial and temporal characteristics of the flow.Trigonometric interpolation techniques provide accurate (discretely exact) solutions to the Poisson equation. By using an auxiliary algorithm for rapid evaluation of trigonometric transforms, the proportion of computation needed to solve the Poisson equation can be reduced to less than 25% of the total time needed to’ advance one time step. Computing on a UNIVAC 1108 machine, the flow can be advanced one time-step in 2 sec for a 14 × 14 × 14 grid upward to 96 sec for a 60 × 34 × 34 grid.As an example of the method, some features of a solution for steady wave flow in annulus convection are presented. The resemblance of this flow to the classical Eady wave is noted.

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