On flow separation and reattachment around a circular cylinder at critical Reynolds numbers

1989 ◽  
Vol 200 ◽  
pp. 149-171 ◽  
Author(s):  
H. Higuchi ◽  
H. J. Kim ◽  
C. Farell
Keyword(s):  
Boundary Layer ◽  
Flow Direction ◽  
Low Frequency ◽  
Reynolds Numbers ◽  
Circular Cylinders ◽  
Number Range ◽  
Critical Range ◽  
Flow Motion ◽  
Critical Reynolds Numbers ◽  
Layer Flow

An experimental investigation of the flow around smooth circular cylinders in the Reynolds number range 0.8 × 105 < Re < 2 × 105 is presented. Measured quantities include spectra, spanwise correlations and cross correlations of cylinder pressures and wake-velocity fluctuations, and low-frequency boundary-layer flow direction reversals near separation. The flow motion in the critical range is found to be characterized by intermittent, symmetric boundary-layer reattachments, occurring in cells with a well-defined spanwise structure, accompanying a significant decrease in drag coefficient and a weakening of the vortex shedding.

scholarly journals Investigation of the steady and unsteady forces acting on a pair of circular cylinders in crossflow up to ultra-high Reynolds numbers

2021 ◽  
Vol 62 (8) ◽  
Author(s):  
Günter Schewe ◽  
Nils Paul van Hinsberg ◽  
Markus Jacobs
Keyword(s):  
Power Spectra ◽  
Low Frequency ◽  
Reynolds Numbers ◽  
Circular Cylinders ◽  
Supercritical Regime ◽  
Unsteady Forces ◽  
Number Range ◽  
Single Cylinder ◽  
High Reynolds Numbers ◽  
High Reynolds

AbstractMeasurements of the steady and unsteady forces acting on a pair of circular cylinders in crossflow are performed from subcritical up to ultra-high Reynolds numbers. The two cylinders with equal diameters d are arranged inline at two centre-to-centre distances: S/d = 2.8 and 4. The trend of the drag curve for the upstream cylinder $$Cd_{1}$$ C d 1 (Re) at both distances is similar to that for a single circular cylinder. The development of the drag curves $$Cd_{2}$$ C d 2 (Re, S/d = 2.8, 4) of the downstream cylinder is inverse to that of the upstream cylinder. For both cylinder spacing values, the drag on the downstream cylinder is negative for subcritical Reynolds numbers, increases abruptly to positive values at the beginning of the supercritical regime, and shows a significant dip at transcritical Reynolds numbers. This drag inversion indicates that the critical distance Sc decreases sharply in the supercritical Reynolds number range. For S/d = 2.8 at Re$$\rightarrow$$ → 10$$^{7}$$ 7 , the downstream cylinder experiences once more a thrust force. The curve of the Strouhal number St(Re) of the downstream cylinder for S/d = 4 is very close to that of a single cylinder. For Reynolds numbers of Re$$\approx$$ ≈ 1$$\times$$ × 10$$^{6}$$ 6 - 7$$\times$$ × 10$$^{6}$$ 6 , the Strouhal numbers have nearly equal values of St$$\approx$$ ≈ 0.22 - 0.24 for both distances. This is followed by a branching. For Re$$\rightarrow$$ → 10$$^{7}$$ 7 and the case S/d = 2.8, the Strouhal numbers dip at St = 0.17. However, for S/d = 4, they increase up to St = 0.27. In the supercritical range, two peaks occur in the power spectra for the large distance S/d = 4. Based on a wavelet analysis, we can conclude that the low-frequency mode, which does not occur for a single cylinder, is an interference effect. Graphic abstract

Instability of the attachment line boundary layer in a supersonic swept flow

2021 ◽  
Vol 933 ◽  
Author(s):  
Alexander V. Fedorov ◽  
Ivan V. Egorov
Keyword(s):  
Boundary Layer ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Linear Instability ◽  
Navier Stokes ◽  
Mean Flow ◽  
Significant Drop ◽  
Critical Reynolds Numbers ◽  
Layer Flow ◽  
Attachment Line

Theoretical analysis of attachment-line instabilities is performed for supersonic swept flows using the compressible Hiemenz approximation for the mean flow and the successive approximation procedures for disturbances. The theoretical model captures the dominant attachment-line modes in wide ranges of the sweep Mach number ${M_e}$ and the wall temperature ratio. It is shown that these modes behave similar to the first and second Mack modes in the boundary layer flow. This similarity allows us to extrapolate the knowledge gained for Mack modes to the attachment-line instabilities. In particular, we find that at sufficiently large ${M_e}$ , the dominant attachment-line instability is associated with the synchronisation of slow and fast modes of acoustic nature. Point-by-point comparisons of the theoretical predictions with the experiments of Gaillard et al. (Exp. Fluids, vol. 26, 1999, pp. 169–176) demonstrate that at ${M_e} > 4$ , the theory captures a significant drop of the transition onset Reynolds number, which is below the contamination criterion of Poll $({R_\mathrm{\ast }} = 250)$ at ${M_e} > 6$ . This contradicts the generally accepted assumption that the attachment-line flow is stable for ${R_\mathrm{\ast }} \le 250$ . The theoretical critical Reynolds numbers lie well below the experimental transition-onset Reynolds numbers. Stability computations using the Navier–Stokes mean flow and accounting for the leading-edge curvature effect do not eliminate this discrepancy. Most likely, in the experiments of Gaillard et al., we face with an unknown effect that does not fit to the concept of transition arising from linear instability.

Two-dimensional global low-frequency oscillations in a separating boundary-layer flow

2008 ◽  
Vol 614 ◽  
pp. 315-327 ◽  
Author(s):  
UWE EHRENSTEIN ◽  
FRANÇOIS GALLAIRE
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Perturbation Analysis ◽  
Boundary Layer Flow ◽  
Stokes Equations ◽  
Low Frequency ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Optimal Perturbation ◽  
Layer Flow

A separated boundary-layer flow at the rear of a bump is considered. Two-dimensional equilibrium stationary states of the Navier–Stokes equations are determined using a nonlinear continuation procedure varying the bump height as well as the Reynolds number. A global instability analysis of the steady states is performed by computing two-dimensional temporal modes. The onset of instability is shown to be characterized by a family of modes with localized structures around the reattachment point becoming almost simultaneously unstable. The optimal perturbation analysis, by projecting the initial disturbance on the set of temporal eigenmodes, reveals that the non-normal modes are able to describe localized initial perturbations associated with the large transient energy growth. At larger time a global low-frequency oscillation is found, accompanied by a periodic regeneration of the flow perturbation inside the bubble, as the consequence of non-normal cancellation of modes. The initial condition provided by the optimal perturbation analysis is applied to Navier–Stokes time integration and is shown to trigger the nonlinear ‘flapping’ typical of separation bubbles. It is possible to follow the stationary equilibrium state on increasing the Reynolds number far beyond instability, ruling out for the present flow case the hypothesis of some authors that topological flow changes are responsible for the ‘flapping’.

A Model for High-Reynolds-Number Flow Past Rough-Walled Circular Cylinders

1977 ◽  
Vol 99 (3) ◽  
pp. 486-493 ◽  
Author(s):  
O. Gu¨ven ◽  
V. C. Patel ◽  
C. Farell
Keyword(s):  
Boundary Layer ◽  
Surface Roughness ◽  
Circular Cylinder ◽  
Turbulent Boundary Layer ◽  
Pressure Coefficient ◽  
Empirical Relation ◽  
Reynolds Numbers ◽  
Boundary Layer Separation ◽  
Circular Cylinders ◽  
Mean Flow

A simple analytical model for two-dimensional mean flow at very large Reynolds numbers around a circular cylinder with distributed roughness is presented and the results of the theory are compared with experiment. The theory uses the wake-source potential-flow model of Parkinson and Jandali together with an extension to the case of rough-walled circular cylinders of the Stratford-Townsend theory for turbulent boundary-layer separation. In addition, a semi-empirical relation between the base-pressure coefficient and the location of separation is used. Calculation of the boundary-layer development, needed as part of the theory, is accomplished using an integral method, taking into account the influence of surface roughness on the laminar boundary layer and transition as well as on the turbulent boundary layer. Good agreement with experiment is shown by the results of the theory. The significant effects of surface roughness on the mean-pressure distribution on a circular cylinder at large Reynolds numbers and the physical mechanisms giving rise to these effects are demonstrated by the model.

scholarly journals Assessment of inner–outer interactions in the urban boundary layer using a predictive model

2019 ◽  
Vol 875 ◽  
pp. 44-70 ◽  
Author(s):  
Karin Blackman ◽  
Laurent Perret ◽  
Romain Mathis
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Predictive Model ◽  
Boundary Layers ◽  
Large Scale ◽  
Reynolds Numbers ◽  
Limited Range ◽  
Rough Wall ◽  
Wall Boundary ◽  
Layer Flow

Urban-type rough-wall boundary layers developing over staggered cube arrays with plan area packing density, $\unicode[STIX]{x1D706}_{p}$, of 6.25 %, 25 % or 44.4 % have been studied at two Reynolds numbers within a wind tunnel using hot-wire anemometry (HWA). A fixed HWA probe is used to capture the outer-layer flow while a second moving probe is used to capture the inner-layer flow at 13 wall-normal positions between $1.25h$ and $4h$ where $h$ is the height of the roughness elements. The synchronized two-point HWA measurements are used to extract the near-canopy large-scale signal using spectral linear stochastic estimation and a predictive model is calibrated in each of the six measurement configurations. Analysis of the predictive model coefficients demonstrates that the canopy geometry has a significant influence on both the superposition and amplitude modulation. The universal signal, the signal that exists in the absence of any large-scale influence, is also modified as a result of local canopy geometry suggesting that although the nonlinear interactions within urban-type rough-wall boundary layers can be modelled using the predictive model as proposed by Mathis et al. (J. Fluid Mech., vol. 681, 2011, pp. 537–566), the model must be however calibrated for each type of canopy flow regime. The Reynolds number does not significantly affect any of the model coefficients, at least over the limited range of Reynolds numbers studied here. Finally, the predictive model is validated using a prediction of the near-canopy signal at a higher Reynolds number and a prediction using reference signals measured in different canopy geometries to run the model. Statistics up to the fourth order and spectra are accurately reproduced demonstrating the capability of the predictive model in an urban-type rough-wall boundary layer.

An approximate theory for the streaming motion past axisymmetric bodies at Reynolds numbers of from 1 to approximately 100

1977 ◽  
Vol 82 (3) ◽  
pp. 583-604 ◽  
Author(s):  
Michael S. Kolansky ◽  
Sheldon Weinbaum ◽  
Robert Pfeffer
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Reynolds Numbers ◽  
Bluff Bodies ◽  
Approximate Theory ◽  
Viscous Term ◽  
Number Range ◽  
Curvature Effects ◽  
Flow Past

In Weinbaum et al. (1976) a simple new pressure hypothesis is derived which enables one to take account of the displacement interaction, the geometrical change in streamline radius of curvature and centrifugal effects in the thick viscous layers surrounding two-dimensional bluff bodies in the intermediate Reynolds number range O(1) < Re < O(102) using conventional Prandtl boundary-layer equations. The new pressure hypothesis states that the streamwise pressure gradient as a function of distance from the forward stagnation point on the displacement body is equal to the wall pressure gradient as a function of distance along the original body. This hypothesis is shown to be equivalent to stretching the streamwise body co-ordinate in conventional first-order boundary-layer theory. The present investigation shows that the same pressure hypothesis applies for the intermediate Reynolds number flow past axisymmetric bluff bodies except that the viscous term in the conventional axisymmetric boundary-layer equation must also be modified for transverse curvature effects O(δ) in the divergence of the stress tensor. The approximate solutions presented for the location of separation and the detailed surface pressure and vorticity distribution for the flow past spheres, spheroids and paraboloids of revolution at various Reynolds numbers in the range O(1) < Re < O(102) are in good agreement with available numerical Navier–Stokes solutions.

Three-Dimensional Boundary-Layer Flow About an Ablating Slender Cone

1969 ◽  
Vol 91 (4) ◽  
pp. 632-648 ◽  
Author(s):  
T. K. Fannelop ◽  
P. C. Smith
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Cone Angle ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Boundary Layer Equations ◽  
Transverse Curvature ◽  
Dimensional Boundary ◽  
Layer Flow

A theoretical analysis is presented for three-dimensional laminar boundary-layer flow about slender conical vehicles including the effect of transverse surface curvature. The boundary-layer equations are solved by standard finite difference techniques. Numerical results are presented for hypersonic flow about a slender blunted cone. The influences of Reynolds number, cone angle, and mass transfer are studied for both symmetric flight and at angle-of-attack. The effects of transverse curvature are substantial at the low Reynolds numbers considered and are enhanced by blowing. The crossflow wall shear is largely unaffected by transverse curvature although the peak velocity is reduced. A simplified “channel flow” analogy is suggested for the crossflow near the wall.

On the force fluctuations acting on a circular cylinder in crossflow from subcritical up to transcritical Reynolds numbers

1983 ◽  
Vol 133 ◽  
pp. 265-285 ◽  
Author(s):  
Günter Schewe
Keyword(s):  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Dynamic Range ◽  
Reynolds Numbers ◽  
Band Spectrum ◽  
Transitional Region ◽  
Force Measurements ◽  
Unsteady Forces ◽  
Number Range ◽  
Critical Reynolds Numbers

Force measurements were conducted in a pressurized wind tunnel from subcritical up to transcritical Reynolds numbers 2.3 × 104[les ]Re[les ] 7.1 × 106without changing the experimental arrangement. The steady and unsteady forces were measured by means of a piezobalance, which features a high natural frequency, low interferences and a large dynamic range. In the critical Reynolds-number range, two discontinuous transitions were observed, which can be interpreted as bifurcations at two critical Reynolds numbers. In both cases, these transitions are accompanied by critical fluctuations, symmetry breaking (the occurrence of a steady lift) and hysteresis. In addition, both transitions were coupled with a drop of theCDvalue and a jump of the Strouhal number. Similar phenomena were observed in the upper transitional region between the super- and the transcritical Reynolds-number ranges. The transcritical range begins at aboutRe≈ 5 × 106, where a narrow-band spectrum is formed withSr(Re= 7.1 × 106) = 0.29.

Flow Characteristics around Circular Cylinders with a Normal Slit

2017 ◽  
Vol 379 ◽  
pp. 48-57 ◽  
Author(s):  
Cheng Hsiung Kuo ◽  
Hwa Wei Lin ◽  
Chih Tao Chai ◽  
Fred Cheng
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layer Flow ◽  
Rear Surface ◽  
Flow Characteristics ◽  
Boundary Layer Separation ◽  
Circular Cylinders ◽  
Flow Structures ◽  
Phase Lock ◽  
Layer Flow

Alterations of boundary layer separation along the upper-rear surface of a baseline and slit cylinder and the formation of a vortex in the near-wake are investigated by particle image velocimetry (PIV) at Reynolds number 1000. The slit ratio (S/D) is 0.3. The phase-lock flow structures are referred to the time-dependent volume flux at the slit exit and are achieved by the modified phase-averaged technique. The alterations and the evolution of boundary-layer flow along the upper-rear surface are demonstrated by the phase-lock flow structures. It is found that the alternate blowing and suction at the slit exit serves as a perturbation to the boundary layer near the shoulder of the slit cylinder leading to a significant delay of flow separation and the flow reattachment of boundary-layer flow along the upper-rear surface of the cylinder. After perturbation, the vortex street behind a slit cylinder is more organized and stronger than that behind a baseline cylinder at Reynolds number 1000.

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