scholarly journals Various approaches to determine active regions in an unstable global mode: application to transonic buffet

2019 ◽  
Vol 881 ◽  
pp. 617-647 ◽  
Author(s):  
Edoardo Paladini ◽  
Olivier Marquet ◽  
Denis Sipp ◽  
Jean-Christophe Robinet ◽  
Julien Dandois
Keyword(s):  
Boundary Layer ◽  
Flow Field ◽  
Stokes Equations ◽  
Active Regions ◽  
Physical Models ◽  
Computational Domain ◽  
Global Mode ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Transonic Buffet

The transonic flow field around a supercritical airfoil is investigated. The objective of the present paper is to enhance the understanding of the physical mechanics behind two-dimensional transonic buffet. The paper is composed of two parts. In the first part, a global stability analysis based on the linearized Reynolds-averaged Navier–Stokes equations is performed. A recently developed technique, based on the direct and adjoint unstable global modes, is used to compute the local contribution of the flow to the growth rate and angular frequency of the unstable global mode. The results allow us to identify which zones are directly responsible for the existence of the instability. The technique is firstly used for the vortex-shedding cylinder mode, as a validating case. In the second part, in order to confirm the results of the first part, a selective frequency damping method is locally used in some regions of the flow field. This method consists of applying a low-pass filter on selected zones of the computational domain in order to damp the fluctuations. It allows us to identify which zones are necessary for the persistence of the instability. The two different approaches give the same results: the shock foot is identified as the core of the instability; the shock and the boundary layer downstream of the shock are also necessary zones while damping the fluctuations on the lower surface of the airfoil; and outside the boundary layer between the shock and the trailing edge or above the supersonic zone does not suppress the shock oscillation. A discussion on the several physical models, proposed until now for the buffet phenomenon, and a new model are finally offered in the last section.

Effects of Inlet Distortion on the Flow Field in a Transonic Compressor Rotor

1996 ◽  
Author(s):  
Chunill Hah ◽  
Douglas C. Rabe ◽  
Thomas J. Sullivan ◽  
Aspi R. Wadia
Keyword(s):  
Boundary Layer ◽  
Flow Field ◽  
Viscous Flow ◽  
Total Pressure ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Aerodynamic Loss ◽  
Transonic Compressor ◽  
Inlet Distortion ◽  
Compressor Rotor

The effects of circumferential distortions in inlet total pressure on the flow field in a low-aspect-ratio, high-speed, high-pressure-ratio, transonic compressor rotor are investigated in this paper. The flow field was studied experimentally and numerically with and without inlet total pressure distortion. Total pressure distortion was created by screens mounted upstream from the rotor inlet. Circumferential distortions of 8 periods per revolution were investigated at two different rotor speeds. The unsteady blade surface pressures were measured with miniature pressure transducers mounted in the blade. The flow fields with and without inlet total pressure distortion were analyzed numerically by solving steady and unsteady forms of the Reynolds-averaged Navier-Stokes equations. Steady three-dimensional viscous flow calculations were performed for the flow without inlet distortion while unsteady three-dimensional viscous flow calculations were used for the flow with inlet distortion. For the time-accurate calculation, circumferential and radial variations of the inlet total pressure were used as a time-dependent inflow boundary condition. A second-order implicit scheme was used for the time integration. The experimental measurements and the numerical analysis are highly complementary for this study because of the extreme complexity of the flow field. The current investigation shows that inlet flow distortions travel through the rotor blade passage and are convected into the following stator. At a high rotor speed where the flow is transonic, the passage shock was found to oscillate by as much as 20% of the blade chord, and very strong interactions between the unsteady passage shock and the blade boundary layer were observed. This interaction increases the effective blockage of the passage, resulting in an increased aerodynamic loss and a reduced stall margin. The strong interaction between the passage shock and the blade boundary layer increases the peak aerodynamic loss by about one percent.

Large Eddy Simulation of Transitional Flow in a Compressor Cascade

2017 ◽  
Author(s):  
Syed Anjum Haider Rizvi ◽  
Joseph Mathew
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Separation Bubble ◽  
Transitional Flow ◽  
Transitional Region ◽  
Compressor Cascade ◽  
Suction Surface ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Large Eddy

At off-design conditions, when the blade Reynolds number is low, a significant part of the blade boundary layer can be transitional. Then, standard RANS models are unable to predict the flows correctly but explicit transition modeling provides some improvement. Since large eddy simulations (LES) are improvements on RANS, the performance of LES was examined by simulating a flow through a linear, compressor cascade for which experimental data are available — specifically at the Reynolds number of 210,000 based on blade chord when transition processes occur over a significant extent of the suction surface. The LES were performed with an explicit filtering approach, applying a low-pass filter to achieve sub-grid-scale modeling. Explicit 8th-order difference formulas were used to obtain high resolution spatial derivative terms. An O-grid was wrapped around the blade with suitable clustering for the boundary layer and regions of large changes along the blade. Turbulent in-flow was provided from a precursor simulation of homogeneous, isotropic turbulence. Two LES and a DNS were performed. The second LES refines the grid in the vicinity of the separation bubble on the suction surface, and along the span. Surface pressure distributions from all simulations agree closely with experiment, thus providing a much better prediction than even transition-sensitive RANS computations. Wall normal profiles of axial velocity and fluctuations also agree closely with experiment. Differences between LES and DNS are small, but the refined grid LES is closer to the DNS almost everywhere. This monotonic convergence, expected of the LES method used, demonstrates its reliability. The pressure surface undergoes transition almost immediately downstream of the leading edge. On the suction surface there are streaks as expected for freestream-turbulence-induced transition, but spots do not appear. Instead, a separating shear layer rolls up and breaks down to turbulence at re-attachment. Both LES capture this process. Skin friction distribution reveals the transition near the re-attachment to occur over an extended region, and subsequent relaxation is slower in the LES. The narrower transition zone in the DNS is indicative of the essential role of smaller scales during transition that should not be neglected in LES. Simulation data also reveal that an assumption of laminar kinetic energy transition models that Reynolds shear stress remains small in the pre-transitional region is supported. The remaining differences in the predictions of such models is thus likely to be the separation-induced transition which preempts the spot formation.

scholarly journals Speckle Observations of Solar Granulation

1994 ◽  
Vol 158 ◽  
pp. 398-400 ◽  
Author(s):  
C.R. de Boer ◽  
F. Kneer
Keyword(s):  
Transfer Function ◽  
Broad Band ◽  
Active Regions ◽  
Spectral Ratio ◽  
Speckle Interferometry ◽  
Frame Rate ◽  
Small Scale ◽  
Fourier Plane ◽  
Pass Filter ◽  
Low Pass Filter

Image reconstruction by means of speckle interferometry was successfully used to restore the intensity distribution of solar features and to investigate the morphology and dynamics of small-scale structures in active regions of the Sun. The observations were obtained with the Vacuum Tower Telescope (D = 70 cm, f = 46 m) at Observatorio del Teide, Tenerife, on May 17 and 20, 1991, from a plage region close to a sunspot near disc centre. Sequences of bursts consisting of 100 exposures were recorded with a broad-band filter centred at 550 nm (FWHM ≈ 10 nm, diffraction limit 0.2 arcsec). The pickup unit was a video CCD – system with an exposure time of 4 ms and a frame rate of three pictures per second. A description of the observing procedure and of the data handling can be found in de Boer et al. (1992). To obtain the complex Fourier phases speckle masking (Lohmann et al. 1983) was used. The speckle transfer function of the atmosphere was calculated indirectly using Korff's equation (1973). The Fried parameter r0 was estimated with the spectral ratio technique (von der Lühe 1984). This parameter was sometimes as large as 14 cm. With this the theoretical speckle transfer function could be determined for calculating the corrected Fourier amplitudes of the reconstruction. A new low pass filter, based on the reliability of each individual value in the Fourier plane, was applied to the amplitudes to suppress noise at high wavenumbers.

scholarly journals Time and Space Scales in the Tropical Cyclone Boundary Layer, and the Location of the Eyewall Updraft

2017 ◽  
Vol 74 (10) ◽  
pp. 3305-3323 ◽  
Author(s):  
Jeffrey D. Kepert
Keyword(s):  
Boundary Layer ◽  
Tropical Cyclone ◽  
Nonlinear Models ◽  
Vertical Motion ◽  
Oscillation Period ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Radial Profiles ◽  
Sinusoidal Oscillations ◽  
Tropical Cyclone Boundary Layer

Abstract The transient response of the tropical cyclone boundary layer is studied using linearized and nonlinear models, with particular focus on the frictionally forced vertical motion. The impulsively started, linearized tropical cyclone boundary layer is shown to adjust to its equilibrium solution via a series of decaying oscillations with the inertial period . In the nonlinear case, the oscillation period is slightly lengthened by inward advection of the slower-evolving flow from larger radii, but the oscillations decay more quickly. In an idealized cyclone with small sinusoidal oscillations superimposed on the gradient wind, the equilibrium nonlinear boundary layer acts as a low-pass filter with pass length scaling as , where is the 10-m frictional inflow. This filter is absent from the linearized boundary layer. The eyewall frictional updraft is similarly displaced inward of the radius of maximum winds (RMW) by a distance that scales with , owing to nonlinear overshoot of the inflowing air as it crosses the relatively sharp increase in I near the eyewall. This displacement is smaller (other things being equal) when the RMW is small, and greater when it is large, including in secondary eyewalls. The dependence of this distance on may explain, at least partially, why observed RMW are seldom less than 20 km, why storms with relatively peaked radial profiles of wind speed can intensify more rapidly, and why some secondary eyewalls initially contract rapidly with little intensification, then contract more slowly while intensifying.

Direct numerical simulation of a separated turbulent boundary layer

1998 ◽  
Vol 374 ◽  
pp. 379-405 ◽  
Author(s):  
Y. NA ◽  
P. MOIN
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Direct Numerical Simulation ◽  
Shear Layer ◽  
Stokes Equations ◽  
Pressure Fluctuations ◽  
Shear Stresses ◽  
Computational Domain

A separated turbulent boundary layer over a flat plate was investigated by direct numerical simulation of the incompressible Navier–Stokes equations. A suction-blowing velocity distribution was prescribed along the upper boundary of the computational domain to create an adverse-to-favourable pressure gradient that produces a closed separation bubble. The Reynolds number based on inlet free-stream velocity and momentum thickness is 300. Neither instantaneous detachment nor reattachment points are fixed in space but fluctuate significantly. The mean detachment and reattachment locations determined by three different definitions, i.e. (i) location of 50% forward flow fraction, (ii) mean dividing streamline (ψ=0), (iii) location of zero wall-shear stress (τw=0), are in good agreement. Instantaneous vorticity contours show that the turbulent structures emanating upstream of separation move upwards into the shear layer in the detachment region and then turn around the bubble. The locations of the maximum turbulence intensities as well as Reynolds shear stress occur in the middle of the shear layer. In the detached flow region, Reynolds shear stresses and their gradients are large away from the wall and thus the largest pressure fluctuations are in the middle of the shear layer. Iso-surfaces of negative pressure fluctuations which correspond to the core region of the vortices show that large-scale structures grow in the shear layer and agglomerate. They then impinge on the wall and subsequently convect downstream. The characteristic Strouhal number St=fδ*in/U0 associated with this motion ranges from 0.0025 to 0.01. The kinetic energy budget in the detachment region is very similar to that of a plane mixing layer.

scholarly journals Modal Analysis of a Laminar-Flow Airfoil under Buffet Conditions at Re = 500,000

2019 ◽  
Vol 104 (2-3) ◽  
pp. 509-532 ◽  
Author(s):  
Markus Zauner ◽  
Neil D. Sandham
Keyword(s):  
Boundary Layer ◽  
Laminar Flow ◽  
Prediction Models ◽  
Angle Of Attack ◽  
Dynamic Mode ◽  
Mean Flow ◽  
Global Mode ◽  
Moderate Reynolds Number ◽  
Shock Motion ◽  
Transonic Buffet

AbstractAn airfoil undergoing transonic buffet exhibits a complex combination of unsteady shock-wave and boundary-layer phenomena, for which prediction models are deficient. Recent approaches applying computational fluid mechanics methods using turbulence models seem promising, but are still unable to answer some fundamental questions on the detailed buffet mechanism. The present contribution is based on direct numerical simulations of a laminar flow airfoil undergoing transonic buffet at Mach number M = 0.7 and a moderate Reynolds number Re = 500, 000. At an angle of attack α = 4∘, a significant change of the boundary layer stability depending on the aerodynamic load of the airfoil is observed. Besides Kelvin Helmholtz instabilities, a global mode, showing the coupled acoustic and flow-separation dynamics, can be identified, in agreement with literature. These modes are also present in a dynamic mode decomposition (DMD) of the unsteady direct numerical solution. Furthermore, DMD picks up the buffet mode at a Strouhal number of St = 0.12 that agrees with experiments. The reconstruction of the flow fluctuations was found to be more complete and robust with the DMD analysis, compared to the global stability analysis of the mean flow. Raising the angle of attack from α = 3∘ to α = 4∘ leads to an increase in strength of DMD modes corresponding to type C shock motion. An important observation is that, in the present example, transonic buffet is not directly coupled with the shock motion.

scholarly journals On self-sustained oscillations in two-dimensional compressible flow over rectangular cavities

2002 ◽  
Vol 455 ◽  
pp. 315-346 ◽  
Author(s):  
CLARENCE W. ROWLEY ◽  
TIM COLONIUS ◽  
AMIT J. BASU
Keyword(s):  
Boundary Layer ◽  
Shear Layer ◽  
Stokes Equations ◽  
Boundary Layer Transition ◽  
Computational Domain ◽  
Two Dimensional ◽  
Mean Flow ◽  
Recirculating Flow ◽  
Layer Mode ◽  
Mach Numbers

Numerical simulations are used to investigate the resonant instabilities in two-dimensional flow past an open cavity. The compressible Navier–Stokes equations are solved directly (no turbulence model) for cavities with laminar boundary layers upstream. The computational domain is large enough to directly resolve a portion of the radiated acoustic field, which is shown to be in good visual agreement with schlieren photographs from experiments at several different Mach numbers. The results show a transition from a shear-layer mode, primarily for shorter cavities and lower Mach numbers, to a wake mode for longer cavities and higher Mach numbers. The shear-layer mode is characterized well by the acoustic feedback process described by Rossiter (1964), and disturbances in the shear layer compare well with predictions based on linear stability analysis of the Kelvin–Helmholtz mode. The wake mode is characterized instead by a large-scale vortex shedding with Strouhal number independent of Mach number. The wake mode oscillation is similar in many ways to that reported by Gharib & Roshko (1987) for incompressible flow with a laminar upstream boundary layer. Transition to wake mode occurs as the length and/or depth of the cavity becomes large compared to the upstream boundary-layer thickness, or as the Mach and/or Reynolds numbers are raised. Under these conditions, it is shown that the Kelvin–Helmholtz instability grows to sufficient strength that a strong recirculating flow is induced in the cavity. The resulting mean flow is similar to wake profiles that are absolutely unstable, and absolute instability may provide an explanation of the hydrodynamic feedback mechanism that leads to wake mode. Predictive criteria for the onset of shear-layer oscillations (from steady flow) and for the transition to wake mode are developed based on linear theory for amplification rates in the shear layer, and a simple model for the acoustic efficiency of edge scattering.

scholarly journals Numerical Investigation on the Effects of Vortex Shedding on Boundary Layer Unsteadiness

1970 ◽  
Vol 37 ◽  
pp. 33-39
Author(s):  
ABM Toufique Hasan ◽  
Dipak Kanti Das
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Finite Element ◽  
Flow Field ◽  
Flat Plate ◽  
Vortex Shedding ◽  
Stokes Equations ◽  
Number Range ◽  
Rotating Speed ◽  
Rotating Circular Cylinder

The interaction between an initially laminar boundary layer developed spatially on a flat plate under the influence of vortex shedding induced from a rotating circular cylinder has been simulated numerically. The rotational speed of the cylinder is varied to generate the vortex shedding of different intensities. Also the flat plate is kept at different positions from the cylinder. Due to asymmetry in the flow field, the present problem is governed by unsteady Navier-Stokes equations which are simulated numerically by finite element method. Computations are carried out for low Reynolds number range up to 1000. Instantaneous development of the flow field, unsteady boundary layer integral parameters, and wall skin friction are presented on different streamwise locations over the plate. From the computation, it is observed that the vortex shedding substantially affects the boundary layer development. The disturbed displacement and momentum thicknesses of the plate increase up to 1.6 times and 2.6 times of the undisturbed flow, respectively. Also the plate shape factor approaches a value of 1.5 which is typical for turbulent flow. This interaction strongly depends on the rotating speed of the cylinder, the relative positions of the cylinder and the plate and also on Reynolds number of the flow. Keywords: Vortex shedding, finite element, boundary layer, wall skin friction.doi:10.3329/jme.v37i0.817Journal of Mechanical Engineering Vol.37 June 2007, pp.33-39

scholarly journals Low-order stochastic modelling of low-frequency motions in reflected shock-wave/boundary-layer interactions

2011 ◽  
Vol 671 ◽  
pp. 417-465 ◽  
Author(s):  
EMILE TOUBER ◽  
NEIL D. SANDHAM
Keyword(s):  
Boundary Layer ◽  
Low Frequency ◽  
Intrinsic Property ◽  
Stochastic Modelling ◽  
Reflected Shock Wave ◽  
Present Contribution ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Reflected Shock ◽  
Wide Range

A combined numerical and analytical approach is used to study the low-frequency shock motions observed in shock/turbulent-boundary-layer interactions in the particular case of a shock-reflection configuration. Starting from an exact form of the momentum integral equation and guided by data from large-eddy simulations, a stochastic ordinary differential equation for the reflected-shock-foot low-frequency motions is derived. During the derivation a similarity hypothesis is verified for the streamwise evolution of boundary-layer thickness measures in the interaction zone. In its simplest form, the derived governing equation is mathematically equivalent to that postulated without proof by Plotkin (AIAA J., vol. 13, 1975, p. 1036). In the present contribution, all the terms in the equation are modelled, leading to a closed form of the system, which is then applied to a wide range of input parameters. The resulting map of the most energetic low-frequency motions is presented. It is found that while the mean boundary-layer properties are important in controlling the interaction size, they do not contribute significantly to the dynamics. Moreover, the frequency of the most energetic fluctuations is shown to be a robust feature, in agreement with earlier experimental observations. The model is proved capable of reproducing available low-frequency experimental and numerical wall-pressure spectra. The coupling between the shock and the boundary layer is found to be mathematically equivalent to a first-order low-pass filter. It is argued that the observed low-frequency unsteadiness in such interactions is not necessarily a property of the forcing, either from upstream or downstream of the shock, but an intrinsic property of the coupled system, whose response to white-noise forcing is in excellent agreement with actual spectra.

Effects of Inlet Distortion on the Flow Field in a Transonic Compressor Rotor

1998 ◽  
Vol 120 (2) ◽  
pp. 233-246 ◽  
Author(s):  
C. Hah ◽  
D. C. Rabe ◽  
T. J. Sullivan ◽  
A. R. Wadia
Keyword(s):  
Boundary Layer ◽  
Flow Field ◽  
Viscous Flow ◽  
Total Pressure ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Aerodynamic Loss ◽  
Transonic Compressor ◽  
Inlet Distortion ◽  
Compressor Rotor

The effects of circumferential distortions in inlet total pressure on the flow field in a low-aspect-ratio, high-speed, high-pressure-ratio, transonic compressor rotor are investigated in this paper. The flow field was studied experimentally and numerically with and without inlet total pressure distortion. Total pressure distortion was created by screens mounted upstream from the rotor inlet. Circumferential distortions of eight periods per revolution were investigated at two different rotor speeds. The unsteady blade surface pressures were measured with miniature pressure transducers mounted in the blade. The flow fields with and without inlet total pressure distortion were analyzed numerically by solving steady and unsteady forms of the Reynolds-averaged Navier–Stokes equations. Steady three-dimensional viscous flow calculations were performed for the flow without inlet distortion while unsteady three-dimensional viscous flow calculations were used for the flow with inlet distortion. For the time-accurate calculation, circumferential and radial variations of the inlet total pressure were used as a time-dependent inflow boundary condition. A second-order implicit scheme was used for the time integration. The experimental measurements and the numerical analysis are highly complementary for this study because of the extreme complexity of the flow field. The current investigation shows that inlet flow distortions travel through the rotor blade passage and are convected into the following stator. At a high rotor speed where the flow is transonic, the passage shock was found to oscillate by as much as 20 percent of the blade chord, and very strong interactions between the unsteady passage shock and the blade boundary layer were observed. This interaction increases the effective blockage of the passage, resulting in an increased aerodynamic loss and a reduced stall margin. The strong interaction between the passage shock and the blade boundary layer increases the peak aerodynamic loss by about one percent.

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