Numerical Simulations of Unsteady Cascade Flows

1994 ◽  
Vol 116 (4) ◽  
pp. 665-675 ◽  
Author(s):  
D. J. Dorney ◽  
J. M. Verdon
Keyword(s):  
Numerical Simulations ◽  
Nonlinear Analysis ◽  
Unsteady Flows ◽  
Limited Range ◽  
Navier Stokes ◽  
Viscous Effects ◽  
Blade Vibration ◽  
Wide Range ◽  
Blade Row ◽  
Acoustic Excitations

A time-accurate Navier–Stokes analysis is needed for understanding the relative importance of nonlinear and viscous effects on the unsteady flows associated with turbomachinery blade vibration and blade-row noise generation. For this purpose an existing multi-blade-row Navier–Stokes analysis has been modified and applied to predict unsteady flows excited by entropic, vortical, and acoustic disturbances through isolated, two-dimensional blade rows. In particular, time-accurate, non-reflecting inflow and outflow conditions have been implemented to allow specification of vortical, entropic, and acoustic excitations at the inlet, and acoustic excitations at the exit, of a cascade. To evaluate the nonlinear analysis, inviscid and viscous numerical simulations were performed for benchmark unsteady flows and the predicted results were compared with analytical and numerical results based on linearized inviscid flow theory. For small-amplitude unsteady excitations, the unsteady pressure responses predicted with the nonlinear analysis show very good agreement, both in the field and along the blade surfaces, with linearized inviscid solutions. Based on a limited range of parametric studies, it was also found that the unsteady responses to inlet vortical and acoustic excitations are linear over a surprisingly wide range of excitation amplitudes, but acoustic excitations from downstream produce responses with significant nonlinear content.

scholarly journals Numerical Simulations of Unsteady Cascade Flows

1993 ◽  
Author(s):  
Daniel J. Dorney ◽  
Joseph M. Verdon
Keyword(s):  
Numerical Simulations ◽  
Nonlinear Analysis ◽  
Unsteady Flows ◽  
Limited Range ◽  
Navier Stokes ◽  
Viscous Effects ◽  
Blade Vibration ◽  
Wide Range ◽  
Blade Row ◽  
Acoustic Excitations

A time-accurate Navier-Stokes analysis is needed for understanding the relative importance of nonlinear and viscous effects on the unsteady flows associated with turbomachinery blade vibration and blade-row noise generation. For this purpose an existing multi-blade-row Navier-Stokes analysis has been modified and applied to predict unsteady flows excited by entropic, vortical, and acoustic disturbances through isolated, two-dimensional blade rows. In particular, time-accurate, nonreflecting inflow and outflow conditions have been implemented to allow specification of vortical, entropic, and acoustic excitations at the inlet, and acoustic excitations at the exit, of a cascade. To evaluate the nonlinear analysis, inviscid and viscous numerical simulations were performed for benchmark unsteady flows and the predicted results were compared with analytical and numerical results based on linearized inviscid flow theory. For small amplitude unsteady excitations, the unsteady pressure responses predicted with the nonlinear analysis show very good agreement, both in the field and along the blade surfaces, with linearized inviscid solutions. Based on a limited range of parametric studies, it was also found that the unsteady responses to inlet vortical and acoustic excitations are linear over a surprisingly wide range of excitation amplitudes, but acoustic excitations from downstream produce responses with significant nonlinear content.

scholarly journals Validation of a Nonlinear Unsteady Aerodynamic Simulator for Vibrating Blade Rows

1996 ◽  
Author(s):  
Timothy C. Ayer ◽  
Joseph M. Verdon
Keyword(s):  
Unsteady Flows ◽  
Harmonic Component ◽  
Navier Stokes ◽  
Viscous Effects ◽  
Accurate Analysis ◽  
Transonic Flows ◽  
Unsteady Aerodynamic ◽  
Unsteady Surface Pressure ◽  
Blade Flutter ◽  
Displacement Effects

A time-accurate Euler/Navier-Stokes analysis is applied to predict unsteady subsonic and transonic flows through a vibrating cascade. The intent is to validate this nonlinear analysis along with an existing linearized inviscid analysis via result comparisons for unsteady flows that are representative of those associated with blade flutter. The time-accurate analysis has also been applied to determine the relative importance of nonlinear and viscous effects on blade response. The subsonic results reveal a close agreement between inviscid and viscous unsteady blade loadings. Also, the unsteady surface pressure responses are essentially linear, and predicted quite accurately using a linearized inviscid analysis. For unsteady transonic flows, shocks and their motions cause significant nonlinear contributions to the local unsteady response. Viscous displacement effects tend to diminish shock strength and impulsive unsteady shock loads. For both subsonic and transonic flows, the energy transfer between the fluid and the structure is essentially captured by the first-harmonic component of the nonlinear unsteady solutions, but in transonic flows, the nonlinear first-harmonic and the linearized inviscid responses differ significantly in the vicinity of shocks.

Blade Row Interaction in a High-Pressure Steam Turbine

2003 ◽  
Vol 125 (1) ◽  
pp. 14-24 ◽  
Author(s):  
V. S. P. Chaluvadi ◽  
A. I. Kalfas ◽  
H. P. Hodson ◽  
H. Ohyama ◽  
E. Watanabe
Keyword(s):  
High Pressure ◽  
Flow Field ◽  
Numerical Simulations ◽  
Steam Turbine ◽  
Rotor Blade ◽  
Three Dimensional ◽  
Axial Flow ◽  
Navier Stokes ◽  
Flow Interaction ◽  
Blade Row

This paper presents a study of the three-dimensional flow field within the blade rows of a high-pressure axial flow steam turbine stage. Compound lean angles have been employed to achieve relatively low blade loading for hub and tip sections and so reduce the secondary losses. The flow field is investigated in a low-speed research turbine using pneumatic and hot-wire probes downstream of the blade row. Steady and unsteady numerical simulations were performed using structured 3-D Navier-Stokes solver to further understand the flow field. Agreement between the simulations and the measurements has been found. The unsteady measurements indicate that there is a significant effect of the stator flow interaction in the downstream rotor blade. The transport of the stator viscous flow through the rotor blade row is described. Unsteady numerical simulations were found to be successful in predicting accurately the flow near the secondary flow interaction regions compared to steady simulations. A method to calculate the unsteady loss generated inside the blade row was developed from the unsteady numerical simulations. The contribution of various regions in the blade to the unsteady loss generation was evaluated. This method can assist the designer in identifying and optimizing the features of the flow that are responsible for the majority of the unsteady loss production. An analytical model was developed to quantify this effect for the vortex transport inside the downstream blade.

A Nonlinear Numerical Simulator for Three-Dimensional Flows Through Vibrating Blade Rows

1998 ◽  
Author(s):  
H. Andrew Chuang ◽  
Joseph M. Verdon
Keyword(s):  
Three Dimensional ◽  
Unsteady Flows ◽  
Operating Characteristics ◽  
Blade Vibration ◽  
Subsonic Flows ◽  
Transonic Flows ◽  
Multi Stage ◽  
Blade Row ◽  
Blade Flutter ◽  
Numerical Simulator

The three-dimensional, multi-stage, unsteady, turbomachinery analysis, TURBO, has been extended to predict the aeroelastic and aeroacoustic response behaviors of a blade row operating within a cylindrical annular duct. In particular, a blade vibration capability has been incorporated so that the TURBO analysis can be applied over a solution domain that deforms with a vibratory blade motion. Also, unsteady far-field conditions have been implemented to render the computational inlet and exit boundaries transparent to outgoing unsteady disturbances and to allow for the prescription of incoming aerodynamic excitations. The modified TURBO analysis has been applied to predict unsteady subsonic and transonic flows. The intent is to partially validate this nonlinear analysis for blade flutter applications via numerical results for benchmark unsteady flows, and to demonstrate this analysis for a realistic fan rotor. For these purposes, we have considered unsteady subsonic flows through a 3D version of the 10th Standard Cascade and unsteady transonic flows through the first stage rotor of the NASA Lewis, Rotor 67 fan. Some general correlations between aeromechanical stabilities and fan operating characteristics will be presented.

Single-Passage Analysis of Unsteady Flows Around Vibrating Blades of a Transonic Fan Under Inlet Distortion

2002 ◽  
Vol 124 (2) ◽  
pp. 285-292 ◽  
Author(s):  
H. D. Li ◽  
L. He
Keyword(s):  
Computational Study ◽  
Three Dimensional ◽  
Unsteady Flows ◽  
Navier Stokes ◽  
Time Saving ◽  
Blade Vibration ◽  
Inlet Distortion ◽  
Single Passage ◽  
Flow Response ◽  
Transonic Fan

Computations of unsteady flows due to inlet distortion driven blade vibrations, characterized by long circumferential wavelengths, typically need to be carried out in multi-passage/whole-annulus domains. In the present work, a single-passage three-dimensional unsteady Navier-Stokes approach has been developed and applied to unsteady flows around vibrating blades of a transonic fan rotor (NASA Rotor-67) with inlet distortions. The phase-shifted periodic condition is applied using a Fourier series based method, “shape-correction,” which enables a single-passage solution to unsteady flows under influences of multiple disturbances with arbitrary interblade phase angles. The computational study of the transonic fan illustrates that unsteady flow response to an inlet distortion varies greatly depending on its circumferential wavelength. The response to a long wavelength (whole-annulus) distortion is strongly nonlinear with a significant departure of its time-averaged flow from the steady state, while that at a short wavelength (two passages) behaves largely in a linear manner. Nevertheless, unsteady pressures due to blade vibration, though noticeably different under different inlet distortions, show a linear behavior. Thus, the nonlinearity of the flow response to inlet distortion appears to influence the aerodynamic damping predominantly by means of changing the time-averaged flow. Good agreements between single-passage solutions and multi-passage solutions are obtained for all the conditions considered, which clearly demonstrates the validity of the phase-shifted periodicity at a transonic nonlinear distorted flow condition. For the present cases, typical CPU time saving by a factor of 5–10 is achieved by the single-passage solutions.

Validation of a Nonlinear Unsteady Aerodynamic Simulator for Vibrating Blade Rows

1998 ◽  
Vol 120 (1) ◽  
pp. 112-121 ◽  
Author(s):  
T. C. Ayer ◽  
J. M. Verdon
Keyword(s):  
Unsteady Flows ◽  
Harmonic Component ◽  
Navier Stokes ◽  
Viscous Effects ◽  
Accurate Analysis ◽  
Transonic Flows ◽  
Unsteady Aerodynamic ◽  
Unsteady Surface Pressure ◽  
Blade Flutter ◽  
Displacement Effects

A time-accurate Euler/Navier–Stokes analysis is applied to predict unsteady subsonic and transonic flows through a vibrating cascade. The intent is to validate this nonlinear analysis along with an existing linearized inviscid analysis via result comparisons for unsteady flows that are representative of those associated with blade flutter. The time-accurate analysis has also been applied to determine the relative importance of nonlinear and viscous effects on blade response. The subsonic results reveal a close agreement between inviscid and viscous unsteady blade loadings. Also, the unsteady surface pressure responses are essentially linear, and predicted quite accurately using a linearized inviscid analysis. For unsteady transonic flows, shocks and their motions cause significant nonlinear contributions to the local unsteady response. Viscous displacement effects tend to diminish shock strength and impulsive unsteady shock loads. For both subsonic and transonic flows, the energy transfer between the fluid and the structure is essentially captured by the first-harmonic component of the nonlinear unsteady solutions, but in transonic flows, the nonlinear first-harmonic and the linearized inviscid responses differ significantly in the vicinity of shocks.

A Nonlinear Numerical Simulator for Three-Dimensional Flows Through Vibrating Blade Rows

1999 ◽  
Vol 121 (2) ◽  
pp. 348-357 ◽  
Author(s):  
H. A. Chuang ◽  
J. M. Verdon
Keyword(s):  
Three Dimensional ◽  
Unsteady Flows ◽  
Operating Characteristics ◽  
Blade Vibration ◽  
Subsonic Flows ◽  
Transonic Flows ◽  
Aeroelastic Response ◽  
Blade Row ◽  
Dimensional Version ◽  
Blade Flutter

The three-dimensional, multistage, unsteady, turbomachinery analysis, TURBO, has been extended to predict the aeroelastic response of a blade row operating within a cylindrical annular duct. In particular, a blade vibration capability has been incorporated, so that the TURBO analysis can be applied over a solution domain that deforms with a vibratory blade motion. Also, unsteady far-field conditions have been implemented to render the computational inlet and exit boundaries transparent to outgoing unsteady disturbances and to allow for the prescription of incoming aerodynamic excitations. The modified TURBO analysis has been applied to predict unsteady subsonic and transonic flows. The intent is to validate this nonlinear analysis partially for blade flutter applications via numerical results for benchmark unsteady flows, and to demonstrate this analysis for a realistic fan rotor. For these purposes, we have considered unsteady subsonic flows through a three-dimensional version of the 10th Standard Cascade and unsteady transonic flows through the first-stage rotor of the NASA Lewis Rotor 67 fan. Some general correlations between aeromechanical stabilities and fan operating characteristics will be presented.

Numerical Simulation of the Effects of Rotor-Stator Spacing and Wake/Blade Count Ratio on Turbomachinery Unsteady Flows

1995 ◽  
Vol 117 (4) ◽  
pp. 639-646 ◽  
Author(s):  
W.-S. Yu ◽  
B. Lakshminarayana
Keyword(s):  
Incompressible Flows ◽  
Unsteady Flows ◽  
Loss Coefficient ◽  
Navier Stokes ◽  
Frequency Effect ◽  
Row Spacing ◽  
Rotor Wake ◽  
Count Ratio ◽  
Reduced Frequency ◽  
Blade Row

A two-dimensional time-accurate Navier-Stokes solver for incompressible flows is used to simulate the effects of the axial spacing between an upstream rotor and a stator, and the wake/blade count ratio on turbomachinery unsteady flows. The code uses a pressure-based method. A low-Reynolds number two-equation turbulence model is incorporated to account for the turbulence effect. By computing cases with different spacing between an upstream rotor wake and a stator, the effect of the spacing is simulated. Wake/blade count ratio effect is simulated by varying the number of rotor wakes in one stator passage at the computational inlet plane. Results on surface pressure, unsteady velocity vectors, blade boundary layer profiles, rotor wake decay and loss coefficient for all the cases are interpreted. It is found that the unsteadiness in the stator blade passage increases with a decrease in the blade row spacing and a decrease in the wake/blade count ratio. The reduced frequency effect is dominant in the wake/blade count ratio simulation. The time averaged loss coefficient increases with a decrease in the axial blade row spacing and an increase in the wake/blade count ratio.

SCALING OF FLUID RECOVERY FROM PERCOLATION FRACTALS

Fractals ◽  
1994 ◽  
Vol 02 (02) ◽  
pp. 269-272 ◽  
Author(s):  
IAN D WEDGWOOD ◽  
DONALD M MONRO
Keyword(s):  
Stokes Equations ◽  
Petroleum Reservoirs ◽  
Finite Difference Approximation ◽  
Navier Stokes ◽  
Difference Approximation ◽  
Viscous Effects ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Reservoir Models ◽  
Wide Range

We report on the recovery of fluid driven through percolation lattices across a range of scales using a finite difference approximation to the Navier-Stokes equation. This is important in the study of recovery from petroleum reservoirs, in which flow occurs over a wide range of scales, from the microscopic pores right up to the full reservoir. This variation of scale presents difficulties, since flow at the pore level is subject to predominantly viscous effects, whereas at the larger scales the viscous effects may become negligible in comparison with inertial effects. The Navier-Stokes equations may differ greatly with scale. Theoretical rock structures are created using percolation lattices and the flow properties of identical rock structures are then examined as a function of scale. The resultant recovery rates exhibit similarity across scale which would simplify the study of geological reservoir models.

On the Impact of Blade Count Reduction on Aerodynamic Performance and Loss Generation in a Three-Stage LP Turbine

2001 ◽  
Author(s):  
Jochen Gier ◽  
Sabine Ardey
Keyword(s):  
Low Pressure ◽  
Aerodynamic Performance ◽  
Point Of View ◽  
Navier Stokes ◽  
Viscous Effects ◽  
Local Flow ◽  
Wide Range ◽  
Separation Bubbles ◽  
Flow Phenomena ◽  
The Impact

Reducing the number of blades in low pressure turbines is a desirable option for decreasing total operation costs. From an aerodynamical point of view this directly leads to an increased blade load. However, increasing the blade load above a certain level results in viscous effects like separation bubbles and finally full separation. This becomes especially significant for aero engine turbines, which operate at high altitudes and thus low Reynolds numbers. The underlying local flow phenomena and the effect on the aerodynamic performance of such configurations are addressed in this paper. This investigation is based on a three-stage low pressure turbine typical for aero engines. Different setups are employed with different number of guide vanes in certain stages. Furthermore, the Reynolds number is varied within a wide range. These configurations are investigated numerically using a modern steady-state transitional Navier-Stokes solver and experimental results from the same turbine. Based on this information, a detailed analysis of the viscous flow phenomena is performed with focus on the influence of separation bubbles on the loss production after the transition. These results are discussed with respect to blade count reduction.

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