scholarly journals Three Dimensional Unsteady Flow for an Oscillating Turbine Blade and the Influence of Tip Leakage

1998 ◽  
Author(s):  
D. L. Bell ◽  
L. He
Keyword(s):  
Unsteady Flow ◽  
Steady Flow ◽  
Turbine Blade ◽  
Test Data ◽  
Three Dimensional ◽  
Unsteady Aerodynamics ◽  
Blade Loading ◽  
Tip Leakage ◽  
Unsteady Pressure ◽  
Reduced Frequency

The results of two investigations, conducted on the aerodynamic response of a turbine blade oscillating in a three dimensional bending mode, are presented in this paper. The first is an experimental and computational study, designed to produce detailed three dimensional test cases for aeroelastic applications and examine the ability of a 3D time-marching Euler method to predict the relevant unsteady aerodynamics. Extensive blade surface unsteady pressure measurements were obtained for a range of reduced frequency, from a test facility with clearly defined boundary conditions, Bell & He (1997). The test data exhibits a significant three dimensional effect, whereby the amplitude of the unsteady pressure response at different spanwise positions is largely insensitive to the local bending amplitude. The inviscid numerical scheme successfully captured this behaviour, and a good qualitative and quantitative agreement with the test data was achieved for the full range of reduced frequency. In addition, the issue of linearity is addressed and both experimental and numerical tests demonstrate a linear behaviour of the unsteady aerodynamics. The second, an experimental investigation, considers the influence of tip leakage on the unsteady pressure response of an oscillating turbine blade. Results are provided for three tip clearances. The steady flow measurements show marked increases in the size and strength of the tip leakage vortex for the larger tip gaps and deviations in the blade loading towards the tip section. The changes in tip gap also caused distinct trends in the amplitude of the unsteady pressure at 90% span, which were consistent with those observed for steady flow blade loading. It is the authors opinion, that the existence of these trends in unsteady pressure warrants further investigation into the influence of tip leakage upon the local unsteady flow and aerodynamic damping.

Three-Dimensional Unsteady Flow for an Oscillating Turbine Blade and the Influence of Tip Leakage

1998 ◽  
Vol 122 (1) ◽  
pp. 93-101 ◽  
Author(s):  
D. L. Bell ◽  
L. He
Keyword(s):  
Unsteady Flow ◽  
Turbine Blade ◽  
Three Dimensional ◽  
Unsteady Aerodynamics ◽  
Tip Clearance ◽  
Computational Results ◽  
Blade Loading ◽  
Tip Leakage ◽  
Unsteady Pressure ◽  
Reduced Frequency

The results of two investigations, concerning the aerodynamic response of a turbine blade oscillating in a three-dimensional bending mode, are presented in this paper. The first is an experimental and computational study, designed to produce detailed three-dimensional test cases for aeroelastic applications and examine the ability of a three-dimensional time-marching Euler method to predict the relevant unsteady aerodynamics. Extensive blade surface unsteady pressure measurements were obtained over a range of reduced frequency from a test facility with clearly defined boundary conditions (Bell and He, 1997, ASME Paper No. 97-GT-105). The test data indicate a significant three-dimensional effect, whereby the amplitude of the unsteady pressure response at different spanwise locations is largely insensitive to the local bending amplitude. The computational results, which are the first to be supported by detailed three-dimensional test data, demonstrate the ability of the inviscid method to capture the three-dimensional behavior exhibited by the experimental measurements and a good level of quantitative agreement is achieved throughout the range of reduced frequency. Additional computational solutions, obtained through application of the strip methodology, reveal inadequacies in the conventional quasi-three-dimensional approach to the prediction of oscillating blade flows. The issue of linearity is also considered, and both experimental and computational results indicate a linear behavior of the unsteady aerodynamics. The second, an experimental investigation, addresses the influence of tip leakage upon the unsteady aerodynamic response of an oscillating turbine blade. Results are provided for three settings of tip clearance. The steady flow measurements show marked increases in the size and strength of the tip leakage vortex for the larger settings of tip clearance and deviations are present in the blade loading toward the tip section. The changes in tip clearance also caused distinct trends in the amplitude of the unsteady pressure at 90 percent span, which are observed to correspond with localized regions where the tip leakage flow had a discernible impact on the steady flow blade loading characteristic. The existence of these trends in the unsteady pressure response warrants further investigation into the influence of tip leakage on the local unsteady flow and aerodynamic damping. [S0889-504X(00)01101-6]

Structures and Dynamics Committee Best Paper of 1996 Award: Inlet Distortion Generated Forced Response of a Low-Aspect-Ratio Transonic Fan

1997 ◽  
Vol 119 (4) ◽  
pp. 665-676 ◽  
Author(s):  
S. R. Manwaring ◽  
D. C. Rabe ◽  
C. B. Lorence ◽  
A. R. Wadia
Keyword(s):  
Aspect Ratio ◽  
Steady Flow ◽  
Three Dimensional ◽  
Unsteady Aerodynamics ◽  
Forced Response ◽  
Navier Stokes ◽  
Surface Boundary ◽  
Unsteady Pressure ◽  
Low Aspect Ratio ◽  
Transonic Fan

This paper describes a portion of an experimental and computational program (ADLARF), which incorporates, for the first time, measurements of all aspects of the forced response of an airfoil row, i.e., the flow defect, the unsteady pressure loadings, and the vibratory response. The purpose of this portion was to extend the knowledge of the unsteady aerodynamics associated with a low-aspect-ratio transonic fan where the flow defects were generated by inlet distortions. Measurements of screen distortion patterns were obtained with total pressure rakes and casing static pressures. The unsteady pressure loadings on the blade were determined from high response pressure transducers. The resulting blade vibrations were measured with strain gages. The steady flow was analyzed using a three-dimensional Navier–Stokes solver while the unsteady flow was determined with a quasi-three-dimensional linearized Euler solver. Experimental results showed that the distortions had strong vortical, moderate entropic, and weak acoustic parts. The three-dimensional Navier–Stokes analyses showed that the steady flow is predominantly two-dimensional, with radially outward flow existing only in the blade surface boundary layers downstream of shocks and in the aft part of the suction surface. At near resonance conditions, the strain gage data showed blade-to-blade motion variations and thus, linearized unsteady Euler solutions showed poorer agreement with the unsteady loading data than comparisons at off-resonance speeds. Data analysis showed that entropic waves generated unsteady loadings comparable to vortical waves in the blade regions where shocks existed.

The Low Reduced Frequency Limit of Vibrating Airfoils: Part II — Numerical Experiments

2015 ◽  
Author(s):  
Almudena Vega ◽  
Roque Corral
Keyword(s):  
Stokes Equations ◽  
Unsteady Aerodynamics ◽  
Mean Value ◽  
Navier Stokes ◽  
Influence Coefficient ◽  
Navier Stokes Equations ◽  
Unsteady Pressure ◽  
Reduced Frequency ◽  
Influence Coefficients ◽  
Frequency Regime

This paper studies the unsteady aerodynamics of vibrating airfoils in the low reduced frequency regime with special emphasis in its impact on the scaling of the work per cycle curves using an asymptotic approach (Part I) and numerical simulations. A perturbation analysis of the linearized Navier-Stokes equations at low reduced frequency is presented and some conclusions are drawn (Part I of the corresponding paper). The first important result is that the loading of the airfoil plays an essential role in the trends of the phase and modulus of the unsteady pressure field caused by the vibration of the airfoil. For lightly loaded airfoils the unsteady pressure and the influence coefficients scale linearly with the reduced frequency whereas the phase departs from π/2 and changes linearly with the reduced frequency. As a consequence the work-per-cycle is proportional to the reduced frequency for any inter-blade phase angle and it is independent of its sign. For highly loaded airfoils the unsteady pressure modulus is fairly constant exhibiting only a small correction with the reduced frequency, while the phase departs from zero varies linearly with it. In this case only the mean value of the work-per-cycle scales linearly with the reduced frequency. This behavior is independent of the geometry of the airfoil and in first approximation of the mode-shape. For symmetric cascades the work-per-cycle scales linearly with the reduced frequency irrespectively of whether the airfoil is loaded or not. Simulations using a frequency domain linearized Navier-Stokes solver have been carried out on a low-pressure turbine airfoil section, the NACA0012 and NACA65 profiles and a flat plate operating at different flow conditions to show the generality and correctness of the analytical conclusions. Both the traveling-wave and influence coefficient formulations of the problem are used in combination to increase the understanding and explore the nature of the unsteady pressure perturbations.

scholarly journals Deterministic Stress Modeling of Hot Gas Segregation in a Turbine

1999 ◽  
Author(s):  
Judy Busby ◽  
Doug Sondak ◽  
Brent Staubach ◽  
Roger Davis
Keyword(s):  
Unsteady Flow ◽  
Steady Flow ◽  
Three Dimensional ◽  
Design Tool ◽  
Source Terms ◽  
Flow Equations ◽  
Flow Solution ◽  
Viscous Solution ◽  
Hot Streak ◽  
Gas Segregation

Simulation of unsteady viscous turbomachinery flowfields is presently impractical as a design tool due to the long run times required. Designers rely predominantly on steady-state simulations, but these simulations do not account for some of the important unsteady flow physics. Unsteady flow effects can be modeled as source terms in the steady flow equations. These source terms, referred to as Lumped Deterministic Stresses (LDS), can be used to drive steady flow solution procedures to reproduce the time-average of an unsteady flow solution. The goal of this work is to investigate the feasibility of using inviscid lumped deterministic stresses to model unsteady combustion hot streak migretion effects on the turbine blade tip and outer air seal heat loads. The LDS model is obtained from an unsteady inviscid calculation. The inviscid LDS model is then used with a steady viscous computation to simulate the time-averaged viscous solution. The feasibility of the inviscid LDS model is demonstrated on a single stage, three-dimensional, vane-blade turbine with a hot streak entering the vane passage at mid-pitch and mid-span. The steady viscous solution with the LDS model is compared to the time-averaged viscous, steady viscous and time-averaged inviscid computations. The LDS model reproduces the time-averaged viscous temperature distribution on the outer air seal to within 2.3%, while the steady viscous has an error of 8.4%, and the time-averaged inviscid calculation has an error of 17.2%. The solution using the LDS model is obtained at a cost in CPU time that is 26% of that required for a time-averaged viscous computation.

Time Accurate Euler Simulation of Interaction of Nozzle Wake and Secondary Flow With Rotor Blade in an Axial Turbine Stage Using Nonreflecting Boundary Conditions

1995 ◽  
Author(s):  
S. Fan ◽  
B. Lakshminarayana
Keyword(s):  
Flow Field ◽  
Boundary Conditions ◽  
Unsteady Flow ◽  
Secondary Flow ◽  
Rotor Blade ◽  
Three Dimensional ◽  
Computational Domain ◽  
Turbine Stage ◽  
Axial Turbine ◽  
Unsteady Pressure

The objective of this paper is to investigate the three dimensional unsteady flow interactions in a turbomachine stage. A three-dimensional time accurate Euler code has been developed using an explicit four-stage Runge-Kutta scheme. Three-dimensional unsteady non-reflecting boundary conditions are formulated at the inlet and at the outlet of the computational domain to remove the spurious numerical reflections. The three-dimensional code is first validated for 2-D and 3-D cascades with harmonic vortical inlet distortions. The effectiveness of non reflecting boundary conditions is demonstrated. The unsteady Euler solver is then used to simulate the propagation of nozzle wake and secondary flow through rotor and the resulting unsteady pressure field in an axial turbine stage. The three dimensional and time dependent propagation of nozzle wakes in the rotor blade row and the effects of nozzle secondary flow on the rotor unsteady surface pressure and passage flow field are studied. It was found that the unsteady flow field in the rotor is highly three-dimensional and the nozzle secondary flow has significant contribution to the unsteady pressure on the blade surfaces. Even though the steady flow at the midspan is nearly two-dimensional, the unsteady flow is 3-D and the unsteady pressure distribution can not by predicted by a 2-D analysis.

Unsteady Flow Behavior due to Breakdown of Tip Leakage Vortex in an Axial Compressor Rotor at Near-Stall Condition

2000 ◽  
Author(s):  
Masato Furukawa ◽  
Kazuhisa Saiki ◽  
Kazutoyo Yamada ◽  
Masahiro Inoue
Keyword(s):  
Unsteady Flow ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Surface Boundary ◽  
Pressure Side ◽  
Suction Surface ◽  
Tip Leakage Vortex ◽  
Tip Leakage ◽  
Pressure Surface ◽  
Compressor Rotor

The unsteady flow nature caused by the breakdown of the tip leakage vortex in an axial compressor rotor at near-stall conditions has been investigated by unsteady three-dimensional Navier-Stokes flow simulations. The simulations show that the spiral-type breakdown of the tip leakage vortex occurs inside the rotor passage at the near-stall conditions. Downstream of the breakdown onset, the tip leakage vortex twists and turns violently with time, thus interacting with the pressure surface of the adjacent blade. The motion of the vortex and its interaction with the pressure surface are cyclic. The vortex breakdown causes significant changes in the nature of the tip leakage vortex, which result in the anomalous phenomena in the time-averaged flow fields near the tip at the near-stall conditions: no rolling-up of the leakage vortex downstream of the rotor, disappearance of the casing wall pressure trough corresponding to the leakage vortex, large spread of the low-energy fluid accumulating on the pressure side, and large pressure fluctuation on the pressure side. As the flow rate is decreased, the movement of the tip leakage vortex due to its breakdown becomes so large that the leakage vortex interacts with the suction surface as well as the pressure one. The interaction with the suction surface gives rise to the three-dimensional separation of the suction surface boundary layer.

The Impact of Blade Loading and Unsteady Pressure Bifurcations on Low-Pressure Turbine Flutter Boundaries

2015 ◽  
Author(s):  
Joshua J. Waite ◽  
Robert E. Kielb
Keyword(s):  
Mode Shape ◽  
Pressure Ratio ◽  
Low Pressure ◽  
Forced Response ◽  
Blade Loading ◽  
Unsteady Pressure ◽  
Aerodynamic Damping ◽  
Low Pressure Turbine ◽  
Reduced Frequency ◽  
The Impact

The three major aeroelastic issues in the turbomachinery blades of jet engines and power turbines are forced response, non-synchronous vibrations, and flutter. Flutter primarily affects high-aspect ratio blades found in the fan, fore high-pressure compressor stages, and aft low-pressure turbine (LPT) stages as low natural frequencies and high axial velocities create smaller reduced frequencies. Often with LPT flutter analyses, physical insights are lost in the exhaustive quest for determining whether the aerodynamic damping is positive or negative. This paper underlines some well known causes of low-pressure turbine flutter in addition to one novel catalyst. In particular, an emphasis is placed on revealing how local aerodynamic damping contributions change as a function of unsteady (e.g. mode shape, reduced frequency) and steady (e.g. blade torque, pressure ratio) parameters. To this end, frequency domain RANS CFD analyses are used as computational wind tunnels to investigate how aerodynamic loading variations affect flutter boundaries. Preliminary results show clear trends between the aerodynamic work influence coefficients and variations in exit Mach number and back pressure, especially for torsional mode shapes affecting the passage throat. Additionally, visualizations of qualitative bifurcations in the unsteady pressure phases around the airfoil shed light on how local damping contributions evolve with steady loading. Final results indicate a sharp drop in aeroelastic stability near specific regions of the pressure ratio indicating a strong correlation between blade loading and flutter. Passage throat shock behavior is shown to be a controlling factor near the trailing edge, and like critical reduced frequency, this phenomenon is shown to be highly dependent on the vibratory mode shape.

The Low Reduced Frequency Limit of Vibrating Airfoils—Part I: Theoretical Analysis

2015 ◽  
Vol 138 (2) ◽  
Author(s):  
Roque Corral ◽  
Almudena Vega
Keyword(s):  
Stokes Equations ◽  
Order Approximation ◽  
Unsteady Aerodynamics ◽  
Mean Value ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Unsteady Pressure ◽  
Reduced Frequency ◽  
Influence Coefficients ◽  
Frequency Regime

This paper studies the unsteady aerodynamics of vibrating airfoils in the low reduced frequency regime with special emphasis on its impact on the scaling of the work-per-cycle curves, using an asymptotic approach. A perturbation analysis of the linearized Navier–Stokes equations for real modes at low reduced frequency is presented and some conclusions are drawn. The first important result is that the loading of the airfoil plays an essential role in the trends of the phase and modulus of the unsteady pressure caused by the vibration of the airfoil. For lightly loaded airfoils, the unsteady pressure and the influence coefficients (ICs) scale linearly with the reduced frequency whereas the phase departs from π/2 and changes linearly with the reduced frequency. As a consequence, the work-per-cycle scales linearly with the reduced frequency for any interblade phase angle (IBPA), and it is independent of its sign. For highly loaded airfoils, the unsteady pressure modulus is fairly constant exhibiting only a small correction with the reduced frequency, while the phase departs from zero and varies linearly with it. In this case, only the mean value of the work-per-cycle scales linearly with the reduced frequency. This behavior is independent of the geometry of the airfoil and the mode shape in first-order approximation in the reduced frequency. For symmetric cascades, the work-per-cycle scales linearly with the reduced frequency irrespective of whether the airfoil is loaded or not. These conclusions have been numerically confirmed in Part II of the paper.

Numerical Solutions for Unsteady Subsonic Vortical Flows Around Loaded Cascades

1993 ◽  
Vol 115 (4) ◽  
pp. 810-816 ◽  
Author(s):  
J. Fang ◽  
H. M. Atassi
Keyword(s):  
Flow Field ◽  
Unsteady Flow ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Frequency Range ◽  
Mean Flow ◽  
Vortical Flows ◽  
Unsteady Aerodynamic ◽  
Reduced Frequency ◽  
The Mean

A frequency domain linearized unsteady aerodynamic analysis is presented for three-dimensional unsteady vortical flows around a cascade of loaded airfoils. The analysis fully accounts for the distortion of the impinging vortical disturbances by the mean flow. The entire unsteady flow field is calculated in response to upstream three-dimensional harmonic disturbances. Numerical results are presented for two standard cascade configurations representing turbine and compressor bladings for a reduced frequency range from 0.1 to 5. Results show that the upstream gust conditions and blade sweep strongly affect the unsteady blade response.

Sign in / Sign up

Export Citation Format

Share Document