Boundary layer leading-edge receptivity to sound at incidence angles

2001 ◽  
Vol 444 ◽  
pp. 383-407 ◽  
Author(s):  
ERCAN ERTURK ◽  
THOMAS C. CORKE
Keyword(s):  
Acoustic Waves ◽  
Stokes Equations ◽  
Incidence Angle ◽  
Leading Edge ◽  
Quantitative Agreement ◽  
Navier Stokes ◽  
Angle Of Incidence ◽  
Sound Waves ◽  
Nose Radius ◽  
Navier Stokes Equations

The leading-edge receptivity to acoustic waves of two-dimensional parabolic bodies was investigated using a spatial solution of the Navier–Stokes equations in vorticity/streamfunction form in parabolic coordinates. The free stream is composed of a uniform flow with a superposed periodic velocity fluctuation of small amplitude. The method follows that of Haddad & Corke (1998) in which the solution for the basic flow and linearized perturbation flow are solved separately. We primarily investigated the effect of frequency and angle of incidence (−180° [les ] α2 [les ] 180°) of the acoustic waves on the leading-edge receptivity. The results at α2 = 0° were found to be in quantitative agreement with those of Haddad & Corke (1998), and substantiated the Strouhal number scaling based on the nose radius. The results with sound waves at angles of incidence agreed qualitatively with the analysis of Hammerton & Kerschen (1996). These included a maximum receptivity at α2 = 90°, and an asymmetric variation in the receptivity with sound incidence angle, with minima at angles which were slightly less than α2 = 0° and α2 = 180°.

Investigation of G4-73 Centrifugal Fan Airfoil Stall Characteristics

2011 ◽  
Vol 383-390 ◽  
pp. 4221-4226
Author(s):  
Song Ling Wang ◽  
Zhe Liu ◽  
Lei Zhang
Keyword(s):  
Stokes Equations ◽  
Incidence Angle ◽  
Leading Edge ◽  
Suction Side ◽  
Navier Stokes ◽  
Centrifugal Fan ◽  
Reliable Operation ◽  
Safe Operation ◽  
Navier Stokes Equations ◽  
Strong Vortex

It’s of great significance for safe and reliable operation of fan to research on the stall characteristics of the airfoil. The 2D non-compressible Reynolds-Averaged Navier-Stokes equations was built to simulate the flow around the airfoil of G4-73No.8D centrifugal fan, a detailed numerical simulation under different angles has been carried out which based on the Realizable turbulence model with Fluent. The numerical results show that the smaller of the flow rate, the bigger incidence angle is, when the incidence angle is bigger than the critical incidence angle, the suction side stall appears. According simulation the airfoil stall appears when the incidence angle is -28°, with the increasing of the negative incidence angle, the separation point gradually moves to the leading edge. There is a strong vortex which locates at suction side =0.5,the alternating stress on the blade which caused by vortex will make the blade fatigue. If the incidence angle is less than -20°,there is no flow separation, therefore, to ensure the safe operation of the fan, the incidence angle should be less than -20°.

scholarly journals The scattering of sound waves by a vortex: numerical simulations and analytical solutions

1994 ◽  
Vol 260 ◽  
pp. 271-298 ◽  
Author(s):  
Tim Colonius ◽  
Sanjiva K. Lele ◽  
Parviz Moin
Keyword(s):  
Boundary Conditions ◽  
Analytical Solutions ◽  
Acoustic Waves ◽  
Stokes Equations ◽  
Spatial Differentiation ◽  
Navier Stokes ◽  
Sound Waves ◽  
Navier Stokes Equations ◽  
Refraction Effect ◽  
Approximate Analytical Solutions

The scattering of plane sound waves by a vortex is investigated by solving the compressible Navier–-Stokes equations numerically, and analytically with asymptotic expansions. Numerical errors associated with discretization and boundary conditions are made small by using high-order-accurate spatial differentiation and time marching schemes along with accurate non-reflecting boundary conditions. The accuracy of computations of flow fields with acoustic waves of amplitude five orders of magnitude smaller than the hydrodynamic fluctuations is directly verified. The properties of the scattered field are examined in detail. The results reveal inadequacies in previous vortex scattering theories when the circulation of the vortex is non-zero and refraction by the slowly decaying vortex flow field is important. Approximate analytical solutions that account for the refraction effect are developed and found to be in good agreement with the computations and experiments.

Navier–Stokes Simulation of Transonic Blade-Vortex Interactions

1990 ◽  
Vol 112 (4) ◽  
pp. 501-509 ◽  
Author(s):  
N.-S. Liu ◽  
F. Davoudzadeh ◽  
W. R. Briley ◽  
S. J. Shamroth
Keyword(s):  
Acoustic Waves ◽  
Stokes Equations ◽  
Leading Edge ◽  
Lower Surface ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Load Variations ◽  
Vortex Interactions ◽  
Blade Vortex Interaction ◽  
Order Scheme

Transonic strong blade-vortex interaction is numerically analyzed by solving the unsteady 2-D Navier–Stokes equations using an iterative implicit second order scheme. The dominant processes during the interaction are the development of large transverse pressure gradients in the upper leading edge region and the development of disturbances at the root of the lower surface shock wave. As a result of this interaction, high pressure pulses are emitted from the leading edge, and acoustic waves are radiated from the lower surface in a region originally occupied by a supersonic pocket. In addition, severe load variations occur when the vortex is within one chord length of the blade.

Self-Sustained Oscillations With Tonal Sound Around a Backward-Facing Step With a Small Upstream Step

2007 ◽  
Author(s):  
H. Yokoyama ◽  
Y. Tsukamoto ◽  
C. Kato ◽  
A. Iida
Keyword(s):  
Acoustic Waves ◽  
Stokes Equations ◽  
Phase Relationship ◽  
Leading Edge ◽  
Navier Stokes ◽  
Backward Facing Step ◽  
Trailing Edge ◽  
Navier Stokes Equations ◽  
Acoustic Feedback ◽  
Sustained Oscillations

Self-sustained oscillations with acoustic feedback take place in a flow over a two-dimensional two-step configuration: a small forward-backward facing step, which we hereafter call “a bump”, and a relatively large backward-facing step (backstep). These oscillations can radiate intense tonal sound and fatigue nearby components of industrial products. We clarify the mechanism of these oscillations by directly solving the compressible Navier-Stokes equations. The results show that vortices are shed from the leading edge of the bump and acoustic waves are radiated when these vortices pass the trailing edge of the backstep. The propagated acoustic waves shed new vortices by stretching the vortex formed by the flow separation at the leading edge of the bump, and a feedback loop is formed. Moreover, we propose a formula for predicting the frequencies of the tonal sound based on the detailed investigation of the phase relationship between the vortices and the acoustic waves. Also, we investigate the flow conditions for these oscillations by changing the bump configurations. The results show that the oscillations strongly occur when the bump is sufficiently high and the trailing edge of the bump is sufficiently distant from the backstep.

Numerical Simulation of Clocking Effect on Wake Transportation and Interaction in a 1.5-Stage Axial Turbine

2010 ◽  
Author(s):  
Wei Li ◽  
Hua Ouyang ◽  
Zhao-hui Du
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Leading Edge ◽  
Navier Stokes ◽  
Maximum Efficiency ◽  
Suction Surface ◽  
Navier Stokes Equations ◽  
Pressure Surface ◽  
Turbine Efficiency ◽  
Small Influence

To give insight into the clocking effect and its influence on the wake transportation and its interaction, the unsteady three-dimensional flow through a 1.5-stage axial low pressure turbine is simulated numerically using a density-correction based, Reynolds-Averaged Navier-Stokes equations commercial CFD code. The 2nd stator clocking is applied over ten equal tangential positions. The results show that the harmonic blade number ratio is an important factor affecting the clocking effect. The clocking effect has a very small influence on the turbine efficiency in this investigation. The efficiency difference between the maximum and minimum configuration is nearly 0.1%. The maximum efficiency can be achieved when the 1st stator wake enters the 2nd stator passage near blade suction surface and its adjacent wake passes through the 2nd stator passage close to blade pressure surface. The minimum efficiency appears if the 1st stator wake impinges upon the leading edge of the 2nd stator and its adjacent wake of the 1st stator passed through the mid-channel in the 2nd stator.

scholarly journals Numerical Simulation of the Solar Granulation

1980 ◽  
Vol 58 ◽  
pp. 293-299
Author(s):  
Lawrence D. Cloutman
Keyword(s):  
Numerical Simulation ◽  
Numerical Solution ◽  
Stokes Equations ◽  
Solar Physics ◽  
Quantitative Agreement ◽  
Time Dependent ◽  
Navier Stokes ◽  
Vortex Rings ◽  
Solar Granulation ◽  
Navier Stokes Equations

AbstractThe solar granulation has been simulated by numerical solution of the multidimensional, time-dependent, nonlinear Navier-Stokes equations applied to the solar atmosphere. Granules may be explained as buoyantly rising bubbles created at the level where T = 8000 K, and which have collapsed into vortex rings. The calculation is in quantitative agreement with observations and has a number of implications for solar physics and convection theory.

Laminar incompressible flow past a semi-infinite flat plate

1967 ◽  
Vol 27 (4) ◽  
pp. 691-704 ◽  
Author(s):  
R. T. Davis
Keyword(s):  
Flat Plate ◽  
Incompressible Flow ◽  
Stokes Equations ◽  
Leading Edge ◽  
Navier Stokes ◽  
Local Similarity ◽  
Approximate Methods ◽  
Navier Stokes Equations ◽  
Flow Past

Laminar incompressible flow past a semi-infinite flat plate is examined by using the method of series truncation (or local similarity) on the full Navier-Stokes equations. The first and second truncations are calculated at points on the plate away from the leading edge, while only the first truncation is calculated at the leading edge. The solutions are compared with the results from other approximate methods.

scholarly journals Coriolis effect and the attachment of the leading edge vortex

2017 ◽  
Vol 820 ◽  
pp. 312-340 ◽  
Author(s):  
T. Jardin
Keyword(s):  
Stokes Equations ◽  
Leading Edge ◽  
Navier Stokes ◽  
Coriolis Effect ◽  
Viscous Effects ◽  
Navier Stokes Equations ◽  
Leading Edge Vortex ◽  
Edge Vortex ◽  
Vorticity Transport ◽  
Rotating Wing

The role of the Coriolis effect on the attachment of the leading edge vortex (LEV) is investigated. Toward that end, the Navier–Stokes equations are solved in the non-inertial reference frame of a high angle of attack $\unicode[STIX]{x1D6FC}$ rotating wing with the Coriolis term being artificially tuned. Reynolds numbers in the range $Re\in [100;750]$ are considered to identify the interplay between Coriolis and viscous effects. Similarly, artificial tuning of the centrifugal term is achieved to identify the interplay between Coriolis and centrifugal effects. It is shown that (i) the Coriolis effect is the key element in LEV stability for $Re>200$, (ii) viscous effects are the key element for $Re<200$ and (iii) centrifugal effects have a marginal role. The Coriolis effect is found to promote spanwise flow in the core and behind the LEV, which is known to promote outboard vorticity transport and presumably contributes to stabilizing the aft boundary layer. These mechanisms of LEV stabilization have increased authority as $\unicode[STIX]{x1D6FC}$ decreases.

scholarly journals Effect of Leading-Edge Bulges on Aerodynamic Characteristics of Bionic Wingsail

2021 ◽  
Author(s):  
Chen Li ◽  
Peiting Sun ◽  
Hongming Wang
Keyword(s):  
Stokes Equations ◽  
Lift Coefficient ◽  
Leading Edge ◽  
Aerodynamic Characteristics ◽  
Navier Stokes ◽  
Suction Surface ◽  
Ansys Fluent ◽  
Navier Stokes Equations ◽  
Extension Direction ◽  
Lift And Drag

The leading-edge bulges along the extension direction are designed on the marine wingsail. The height and the spanwise wavelength of the protuberances are 0.1c and 0.25c, respectively. At Reynolds number Re=5×105, the Reynolds Averaged Navier-Stokes equations are applied to the simulation of the wingsail with the bulges thanks to ANSYS Fluent finite-volume solver based on the SST K-ω models. The grid independence analysis is carried out with the lift and drag coefficients of the wingsail at AOA = 8° and AOA=20°. The results show that while the efficiency of the wingsail is reduced by devising the leading-edge bulges before stall, the bulges help to improve the lift coefficient of the wingsail when stalling. At AOA=22° under the action of the leading-edge tubercles, a convective vortex is formed on the suction surface of the modified wingsail, which reduces the flow loss. So the bulges of the wingsail can delay the stall.

Calculation of Transition in Adverse Pressure Gradient Flow by Conditioned Equations

1996 ◽  
Author(s):  
J. Steelant ◽  
E. Dick
Keyword(s):  
Pressure Gradient ◽  
Transport Equation ◽  
Stokes Equations ◽  
Growth Parameter ◽  
Gradient Flow ◽  
Leading Edge ◽  
Adverse Pressure Gradient ◽  
Transitional Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations

Conditionally averaged Navier-Stokes equations are used to describe transitional flow in adverse pressure gradient combined with a transport equation for the intermittency factor γ. A transport equation developped in earlier work has been modified to eliminate the use of a distance along a streamline. An extension of the correlations is proposed to determine the spot growth parameter in adverse pressure gradient. This approach is verified against flows over a flat plate with an elliptical leading edge.

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