A Navier–Stokes Analysis of the Stall Flutter Characteristics of the Buffum Cascade

2000 ◽  
Vol 122 (4) ◽  
pp. 769-776 ◽  
Author(s):  
Stefan Weber ◽  
Max F. Platzer
Keyword(s):  
Mach Number ◽  
Turbulence Modeling ◽  
Separation Bubble ◽  
Leading Edge ◽  
Navier Stokes ◽  
Implicit Time ◽  
Fully Implicit ◽  
High Incidence ◽  
Stall Flutter ◽  
Good Agreement

Numerical stall flutter prediction methods are much needed, as modern jet engines require blade designs close to the stability boundaries of the performance map. A Quasi-3D Navier–Stokes code is used to analyze the flow over the oscillating cascade designed and manufactured by Pratt & Whitney, and studied at the NASA Glenn Research Center by Buffum et al. The numerical method solves for the governing equations with a fully implicit time-marching technique in a single passage by making use of a direct-store, periodic boundary condition. For turbulence modeling, the Baldwin–Lomax model is used. To account for transition, the criterion to predict the onset location suggested by Baldwin and Lomax is incorporated. Buffum et al. investigated two incidence cases for three different Mach numbers. The low-incidence case at a Mach number of 0.5 exhibited the formation of small separation bubbles at reduced oscillation frequencies of 0.8 and 1.2. For this case the present approach yielded good agreement with the steady and oscillatory measurements. At high incidence at the same Mach number of 0.5 the measured steady-state pressure distribution and the separation bubble on the upper surface was also found in good agreement with the experiment. But computations for oscillations at high incidence failed to predict the negative damping contribution caused by the leading edge separation. [S0889-504X(00)01304-0]

A Navier-Stokes Analysis of the Stall Flutter Characteristics of the Buffum Cascade

2000 ◽  
Author(s):  
Stefan Weber ◽  
Max F. Platzer
Keyword(s):  
Mach Number ◽  
Turbulence Modeling ◽  
Separation Bubble ◽  
Leading Edge ◽  
Navier Stokes ◽  
Implicit Time ◽  
Fully Implicit ◽  
High Incidence ◽  
Stall Flutter ◽  
Good Agreement

Numerical stall flutter prediction methods are highly needed as modern jet engines require blade designs close to the stability boundaries of the performance map. A Quasi-3D Navier-Stokes code is used to analyze the flow over the oscillating cascade designed and manufactured by Pratt & Whitney, and studied at the NASA Glenn Research Center by Buffum et al. The numerical method solves for the governing equations with a fully implicit time-marching technique in a single passage by making use of a direct-store, periodic boundary condition. For turbulence modeling the Baldwin-Lomax model is used. To account for transition, the criterion to predict the onset location suggested by Baldwin and Lomax is incorporated. Buffum et al. investigated two incidence cases for three different Mach numbers. The low-incidence case at a Mach number of 0.5 exhibited the formation of small separation bubbles at reduced oscillation frequencies of 0.8 and 1.2. For this case the present approach yielded good agreement with the steady and oscillatory measurements. At high-incidence at the same Mach number of 0.5 the measured steady-state pressure distribution and the separation bubble on the upper surface was also found in good agreement with the experiment. But computations for oscillations at high-incidence failed to predict the negative damping contribution caused by the leading edge separation.

scholarly journals Boundary Layer and Navier-Stokes Analysis of a NASA Controlled-Diffusion Compressor Blade

1990 ◽  
Author(s):  
Y. K. Ho ◽  
G. J. Walker ◽  
P. Stow
Keyword(s):  
Boundary Layer ◽  
Turbulence Modeling ◽  
Separation Bubble ◽  
Leading Edge ◽  
Adverse Pressure Gradient ◽  
Compressor Blade ◽  
Navier Stokes ◽  
Laminar Separation ◽  
Controlled Diffusion ◽  
Pressure Distributions

Performance calculations for a NASA controlled-diffusion compressor blade have been carried out with a coupled inviscid-boundary layer code and a time-marching Navier-Stokes solver. Comparisons with experimental test data highlight and explain the strengths and limitations of both these computational methods. The boundary layer code gives good results at and near design conditions. Loss predictions however deteriorated at off-design incidences. This is mainly due to a problem with leading edge laminar separation bubble modelling; coupled with an inability of the calculations to grow the turbulent boundary layer at a correct rate in a strong adverse pressure gradient. Navier-Stokes loss predictions on the other hand are creditable throughout the whole incidence range, except at extreme positive incidence where turbulence modeling problems similar to those of the coupled boundary layer code are observed. The main drawback for the Navier-Stokes code is the slow rate of convergence for these low Mach number cases. Plans are currently under review to address this problem. Both codes give excellent predictions of the blade surface pressure distributions for all the cases considered.

Unsteady Aerodynamic Analysis of an Oscillating Cascade at Large Incidence

1999 ◽  
Author(s):  
Jong-Shang Liu ◽  
Durbha V. Murthy
Keyword(s):  
Mach Number ◽  
Fluid Dynamic ◽  
Leading Edge ◽  
Two Dimensional ◽  
Edge Region ◽  
Unsteady Aerodynamic ◽  
High Incidence ◽  
Flutter Analysis ◽  
High Mach ◽  
Good Agreement

The flutter analysis capability of the quasi-3D aeroelastic computational fluid dynamic (CFD) code UNSFLO is evaluated by comparing to unsteady pressure results in an oscillating cascade. The geometry is two-dimensional and the oscillation is well-controlled. Time unsteady UNSFLO results are compared with data at inlet Mach number from 0.2 to 0.8 with incidence 0° and 10°. Three reduced frequencies, 0.4, 0.8, and 1.2 with inter-blade phase angle of 180 degrees were tested. The calculated steady state loadings show good agreement with data at zero incidence. The correlations become worse for high incidence angles because of the separation. The calculated aerodynamic work capture the chordwise distribution except in the near leading edge region. The correlations become also worse for high incidence from the leading edge to midchord especially at high Mach number.

Numerical Modeling of Radiative and Reactive Flow Field Around a Blunt Body at Hypersonic Regimes

2010 ◽  
Author(s):  
Morteza Rahmanpour ◽  
Reza Ebrahimi ◽  
Mehrzad Shams
Keyword(s):  
Flow Field ◽  
Differential Equations ◽  
Heat Fluxes ◽  
Transitional Flow ◽  
Navier Stokes ◽  
Implicit Time ◽  
Discrete Ordinates ◽  
Two Dimensional ◽  
Fully Implicit ◽  
Time Marching

A numerical method for calculation of strong radiation for two-dimensional reactive air flow field is developed. The governing equations are taken to be two dimensional, compressible Reynolds-average Navier-Stokes and species transport equations. Also, radiation heat flux in energy equation is evaluated using a model of discrete ordinate method. The model used S4 approximation to reduce the governing system of integro-differential equations to coupled set of partial differential equations. A multiband model is used to construct absorption coefficients. Tangent slab approximation is assumed to determine the characteristic parameters needed in the Discrete Ordinates Method. The turbulent diffusion and heat fluxes are modeled by Baldwin and Lomax method. The flow solution is obtained with a fully implicit time marching method. A thermochemical nonequilibrium formulation appropriate to hypersonic transitional flow of air is presented. The method is compared with existing experimental results and good agreement is observed.

scholarly journals Unsteady Pressure Measurements on a Biconvex Airfoil in a Transonic Oscillating Cascade

1986 ◽  
Vol 108 (1) ◽  
pp. 53-59 ◽  
Author(s):  
L. M. Shaw ◽  
D. R. Boldman ◽  
A. E. Buggele ◽  
D. H. Buffum
Keyword(s):  
Mach Number ◽  
Incidence Angle ◽  
Dynamic Pressure ◽  
Leading Edge ◽  
Pressure Transducers ◽  
High Incidence ◽  
Shock Motion ◽  
Plate Analysis ◽  
Phase Angles ◽  
Unsteady Pressure Measurements

Flush-mounted dynamic pressure transducers were installed on the center airfoil of a transonic oscillating cascade to measure the unsteady aerodynamic response as nine airfoils were simultaneously driven to provide 1.2 deg of pitching motion about the midchord. Initial tests were performed at an incidence angle of 0.0 deg and a Mach number of 0.65 in order to obtain results in a shock-free compressible flow field. Subsequent tests were performed at an angle of attack of 7.0 deg and a Mach number of 0.80 in order to observe the surface pressure response with an oscillating shock near the leading edge of the airfoil. Results are presented for interblade phase angles of 90 and −90 deg and at blade oscillatory frequencies of 200 and 500 Hz (semichord reduced frequencies up to about 0.5 at a Mach number of 0.80). Results from the zero-incidence cascade are compared with a classical unsteady flat-plate analysis. Flow visualization results depicting the shock motion on the airfoils in the high-incidence cascade are discussed. The airfoil pressure data are tabulated.

A 3-D Thin Layer Navier-Stokes Code for Supersonic Laminar and Turbulent Flows

2002 ◽  
Author(s):  
Omid Abouali ◽  
Mohammad M. Alishahi ◽  
Homayoon Emdad ◽  
Goodarz Ahmadi
Keyword(s):  
Experimental Data ◽  
Shock Wave ◽  
Mach Number ◽  
Turbulent Flows ◽  
Turbulence Modeling ◽  
Cross Flow ◽  
Navier Stokes ◽  
Cross Sectional ◽  
Laminar And Turbulent Flows ◽  
Circumferential Pressure

A 3-D Thin Layer Navier-Stokes (TLNS) code for solving viscous supersonic flows is developed. The new code uses several numerical algorithms for space and time discretization together with appropriate turbulence modeling. Roe’s method is used for discretizing the convective terms and the central differencing scheme is employed for the viscous terms. An explicit time marching technique and a finite volume space discretization are used. The developed computational model can handle both laminar and turbulent flows. The Baldwin-Lomax model and Degani-Schiff modifications are used for turbulence modeling. The computational model is applied to a hypersonic laminar flow at Mach 7.95 around a cone at different incidence angles. The circumferential pressure distribution is compared with the experimental data. The cross-sectional Mach number contours are also presented. It is shown that in addition to the outer shock, a cross-flow shock wave is also present in the flow field. The cases of supersonic turbulent flows with Mach number 3 around a tangent-ogive with incidence angles of 6° and a secant-ogive with incidence angles of 10° are also studied. The circumferential pressure distributions are compared with the experimental data and the Euler code results and good agreement is obtained. The cross-sectional Mach number contours are also presented. It is shown that in this case also in addition to the outer shock, a cross-flow shock wave is also present at the incidence angle of 10°.

scholarly journals Turbulence Amplification with Incidence at the Leading Edge of a Compressor Cascade

1999 ◽  
Vol 5 (2) ◽  
pp. 89-98 ◽  
Author(s):  
Garth V. Hobson ◽  
Bryce E. Wakefield ◽  
William B. Roberts
Keyword(s):  
Separation Bubble ◽  
Leading Edge ◽  
Laser Doppler Velocimeter ◽  
Free Shear Layer ◽  
Compressor Cascade ◽  
Suction Surface ◽  
Flow Angle ◽  
Laminar Separation ◽  
High Incidence ◽  
High Turbulence

Detailed measurements, with a two-component laser-Doppler velocimeter and a thermal anemometer were made near the suction surface leading edge of controlled-diffusion airfoils in cascade. The Reynolds number was near 700,000, Mach number equal to 0.25, and freestream turbulence was at 1.5% ahead of the cascade.It was found that there was a localized region of high turbulence near the suction surface leading edge at high incidence. This turbulence amplification is thought to be due to the interaction of the free-shear layer with the freestream inlet turbulence. The presence of the local high turbulence affects the development of the short laminar separation bubble that forms very near the suction side leading edge of these blades. Calculations indicate that the local high levels of turbulence can cause rapid transition in the laminar bubble allowing it to reattach as a short “non-burst” type.The high turbulence, which can reach point values greater than 25% at high incidence, is the reason that leading edge laminar separation bubbles can reattach in the high pressure gradient regions near the leading edge. Two variations for inlet turbulence intensity were measured for this cascade. The first is the variation ofmaximum inlet turbulence with respect to inlet-flow angle; and the second is the variation of leading edge turbulence with respect to upstream distance from the leading edge of the blades.

On the Weis-Fogh mechanism of lift generation

1973 ◽  
Vol 60 (1) ◽  
pp. 1-17 ◽  
Author(s):  
M. J. Lighthill
Keyword(s):  
Stokes Equations ◽  
Separation Bubble ◽  
Three Dimensional ◽  
Leading Edge ◽  
The Body ◽  
Navier Stokes ◽  
Encarsia Formosa ◽  
Concentrated Force ◽  
Stagnation Points ◽  
Wing Tips

Weis-Fogh (1973) proposed a new mechanism of lift generation of fundamental interest. Surprisingly, it could work even in inviscid two-dimensional motions starting from rest, when Kelvin's theorem states that the total circulation round a body must vanish, but does not exclude the possibility that if the body breaks into two pieces then there may be equal and opposite circulations round them, each suitable for generating the lift required in the pieces’ subsequent motions! The ‘fling’ of two insect wings of chord c (figure 1) turning with angular velocity Ω generates irrotational motions associated with the sucking of air into the opening gap which are calculated in § 2 as involving circulations −0·69Ωc2 and + 0.69Ωc2 around the wings when their trailing edges, which are stagnation points of those irrotational motions, break apart (position (f)). Viscous modifications to this irrotational flow pattern by shedding of vorticity at the boundary generate (§ 3) a leading-edge separation bubble, and tend to increase slightly the total bound vorticity. Its role in a three-dimensional picture of the Weis-Fogh mechanism of lift generation, involving formation of trailing vortices at the wing tips, and including the case of a hovering insect like Encarsia formosa moving those tips in circular paths, is investigated in § 4. The paper ends with the comment that the far flow field of such very small hovering insects should take the form of the exact solution (Landau 1944; Squire 1951) of the Navier-Stokes equations for the effect of a concentrated force (the weight mg of the animal) acting on a fluid of kinematic viscosity v and density p, whenever the ratio mg/pv2 is small enough for that jet-type induced motion to be stable.

Wind-Related Heat Transfer Coefficient for Flat-Plate Solar Collectors

1987 ◽  
Vol 109 (2) ◽  
pp. 108-110 ◽  
Author(s):  
S. Shakerin
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Flat Plate ◽  
Separation Bubble ◽  
Convective Heat Transfer Coefficient ◽  
Leading Edge ◽  
The Heat Transfer Coefficient ◽  
Good Agreement

Experiments were performed to evaluate the convective heat transfer coefficient for a flat plate mounted in a wooden model of a roof of a building. The experiments were carried out in a closed-circuit wind tunnel and included parametric adjustments of the roof tilt and Reynolds number, based on the length of the plate. The roof tilt was set at 0, 30, 45, 60, and 90 degrees and the Reynolds number ranged from 58,000 to 250,000. A transient, one lump, thermal approach was used for heat transfer calculations. Due to a separation bubble at the leading edge of the model, i.e., the roof, at angles of attack of less than 40 degrees, the flow became turbulent after reattachment. This resulted in a higher heat transfer than previously reported in the literature. At higher angles of attack, the flow was not separated at the leading edge and remained laminar. The heat transfer coefficient for higher angles of attack, i.e., α > 40 deg, was found to be approximately independent of the angle of attack and in good agreement with the previously published results.

scholarly journals Numerical investigation of the effect of airfoil thickness on onset of dynamic stall

2019 ◽  
Vol 870 ◽  
pp. 870-900 ◽  
Author(s):  
Anupam Sharma ◽  
Miguel Visbal
Keyword(s):  
Reverse Flow ◽  
Separation Bubble ◽  
Time Integration ◽  
Angle Of Attack ◽  
Leading Edge ◽  
Flow Region ◽  
Dynamic Stall ◽  
Implicit Time ◽  
Gradual Change ◽  
Dynamic Simulations

Effect of airfoil thickness on onset of dynamic stall is investigated using large eddy simulations at chord-based Reynolds number of 200 000. Four symmetric NACA airfoils of thickness-to-chord ratios of 9 %, 12 %, 15 % and 18 % are studied. The three-dimensional Navier–Stokes solver, FDL3DI is used with a sixth-order compact finite difference scheme for spatial discretization, second-order implicit time integration and discriminating filters to remove unresolved wavenumbers. A constant-rate pitch-up manoeuver is studied with the pitching axis located at the airfoil quarter chord. Simulations are performed in two steps. In the first step, the airfoil is kept static at a prescribed angle of attack ($=4^{\circ }$). In the second step, a ramp function is used to smoothly increase the pitch rate from zero to the selected value and then the pitch rate is held constant until the angle of attack goes past the lift-stall point. The solver is verified against experiments for flow over a static NACA 0012 airfoil. Static simulation results of all airfoil geometries are also compared against XFOIL predictions with a generally favourable agreement. FDL3DI predicts two-stage transition for thin airfoils (9 % and 12 %), which is not observed in the XFOIL results. The dynamic simulations show that the onset of dynamic stall is marked by the bursting of the laminar separation bubble (LSB) in all the cases. However, for the thickest airfoil tested, the reverse flow region spreads over most of the airfoil and reaches the LSB location immediately before the LSB bursts and dynamic stall begins, suggesting that the stall could be triggered by the separated turbulent boundary layer. The results suggest that the boundary between different classifications of dynamic stall, particularly leading edge stall versus trailing edge stall, is blurred. The dynamic-stall onset mechanism changes gradually from one to the other with a gradual change in some parameters, in this case, airfoil thickness.

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