Supercritical Reynolds Numbers Research Articles

Flow-Induced Vibration of Bluff Bodies. Evaluation of Turbulence-Induced Vibration of a Circular Cylinder in Supercritical Reynolds Number Flow.

Experiments have been conducted on turbulence-induced vibration of a circular cylinder in water flow with supercritical Reynolds number ranging from 3×105 to 3×106. Based on the power spectral density of cylinder vibrations measured at several Reynolds numbers, fluctuating force coefficients, Strouhal number and correlation length were evaluated. As a result, it was clarified that the prediction method based on the random vibration theory introducing the correlation length has sufficient margin for actual turbulence-induced response.

Flow-Induced Vibration of Bluff Bodies. Vortex-Induced Vibration of a Cantilever Circular Cylinder in Super-Critical Reynolds Number Flow and Its Suppression by Structure Damping.

Experimental validation of the design criteria for preventing the failure of a thermometer well by vortex-induced vibration is presented, clarifying the effects of Reynolds number and structure damping. An existing avoidance criterion for the vortex-induced vibration in the flow direction, which is given in terms of the reduced velocity Vr as Vr<1.0, has been developed based on the experimental data mainly in the sub-critical range. The applicability of this criterion in the super-critical range is examined in this paper based on the results of experiments performed in the Reynolds number region from 7.8×104 up to 1.1×106 at Vr=1.0. On the other hand, an existing suppression criterion of vortex-induced vibration in the flow direction is given in terms of the reduced damping Cn as Cn>1.2 (or 2.5) under the condition of Vr<3.3 in design guidelines. This criterion, however, has been proposed based on very limited available data The appropriateness of the suppression criterion is also examined in this paper based on the results of experiments in realistic thermometer well conditions, i.e. cantilever cylinders with varied structure damping in a pipe water flow. As a result, it becomes clear that Vr<1.0 is applicable in the super-critical range up to 1.1×106 and that the criteria of Vr<3.3 and Cn>1.2 are reasonably applicable to a cantilever cylinder in a pipe water flow.

Dispersive Stabilization of the Inverse Cascade for the Kolmogorov Flow

It is shown by perturbation techniques and numerical simulations that the inverse cascade of kink-antikink annihilations, characteristic of the Kolmogorov flow in the slightly supercritical Reynolds number regime, is halted by the dispersive action of Rossby waves in the beta-plane approximation. For beta tending to zero, the largest excited scale is proportional to the logarithm of one over beta and differs strongly from what is predicted by standard dimensional phenomenology which ignores depletion of nonlinearity.

Vortex-induced Vibrations of a Circular Cylinder in Cross Flow at Supercritical Reynolds Numbers.

Vortex-induced vibrations were measured for a circular cylinder subjected to a water cross flow at supercritical Reynolds numbers for a wide range of reduced velocities. Turbulence intensities were changed from 1% to 13% in order to investigate the effect of the Strouhal number on the region of synchronization by symmetrical and Karman vortex shedding. The reduced damping of the test cylinder was about 0.1 in water. The surface roughness of the cylinder was a mirror-polished surface. Strouhal number decreased from about 0.48 to 0.29 with increasing turbulence intensity. Synchronized vibrations were observed even at supercritical Reynolds numbers where fluctuating fluid force was small. Reduced velocities at which drag and lift direction lock-in by Karman vortex shedding were initiated decreased with increasing Strouhal number. When Strouhal number was about 0.29, the self-excited vibration in drag direction by symmetrical vortex shedding began at which the frequency ratio of Karman vortex shedding frequency to the natural frequency of cylinder was 0.32.

Vortex Shedding Characteristics from a Stationary Circular Cylinder in Cross Flow at Supercritical Reynolds Numbers.

Fluctuating lift and drag forces by Karman vortex shedding and pressure distributions around a stationary circular cylinder were measured in a water cross flow at supercritical Reynolds numbers. The surface roughness of the cylinder was a mirror-polished surface. Turbulence intensities of the incoming filow were changed from 1% to 13% in order to investigate the effect on vortex shedding characteristics. As the turbulence intensity increased in supercritical region, flow separation location of the boundary layer on the cylinder surface moved forward, Strouhal number decreased from about 0.48 to 0.29 and the fluctuating lift force by Karman vortex shedding increased.

Drag and Flow Characteristics around the Circular Cylinder with Grooves.

It is well-known the dimples on the surface of a golf ball increase in flying distance and the drag force of the pipe jumper that used as the conductor of the high-voltage transmission is decreased by the grooves on the surface of the pipe jumper. But it has not been clarified completely how dimples and grooves manipulate the flow. The final goal of our research is to make clear the drag reduction mechanism of grooves and dimples and the detailes of the related flow structures. As the first stage of this research, this paper deals with the influence of the depth of grooves on the cross-flow around a circular cylinder. Pressure distribution and drag and lift coefficients were measured in a uniform flow in the Reynolds number range of 8.6×103≤Re≤5×105. The Reynolds number regime was classified by the variation in the drag coefficient with Reynolds number. Pressure distributions and drag and lift coefficients showed the characteristic changes for subcritical, critical, and supercritical Reynolds number ranges, respectively. As the depth of grooves decreased, drag coefficient became lower, and the critical points shifted into the high Reynolds number range. Lift was generated in the range of critical Reynolds number, even though a circular cylinder was not rotating.

On interference between two circular cylinders at supercritical Reynolds number

Abstract The results of investigation of interference between two identical parallel circular cylinders carried out in a uniform smooth flow at supercritical Reynolds number (4.5 × 105), by means of pressure distribution measurement in wind-tunnel testing, are presented and discussed. The results show that the characteristics of interference are completely different with those at subcritical Reynolds number due to the difference of wake structure behind cylinders. The flow around two cylinders in tandem arrangement, which is somewhat like the case of subcritical Reynolds number, may be classified into two distinct regimes and four patterns of pressure distribution. On the other hand, two distinct regimes and three types of pressure patterns may be identified in side-by-side arrangement. The abrupt changes in pressure distributions on both cylinders were observed in the special case of two cylinders in staggered arrangement. In general, the significant effect of interference between two circular cylinders at supercritical Reynolds number is restricted to be within a rather small spacing ratio ( N d = 1.7), except for two cylinders in tandem arrangement and its vicinity.

Flow-history effect on higher modes in the spherical Couette system

Our flow-visualization and spectral studies of spherical Couette flow between two concentric spheres with only the inner sphere rotating for the clearance ratio (or gap ratio) 0.14 where the Taylor instability occurs have been pursued to systematically explore how and why a variety of wavenumbers and rotation frequencies of the non-axisymmetric periodic disturbances occurs at the same supercritical Reynolds number. The observed periodic disturbances constitute six kinds of disturbances: spiral TG (Taylor–Görtler) vortices, twists developing within toroidal TG vortices, both unmodulated and modulated waves travelling on the TG vortices, and both Stuart vortices and shear waves developing within the Ekman-type secondary flow. Development of these disturbances depends strongly on the flow mode at the initial Reynolds number (initial flow mode) and on the Reynolds-number evolution process approaching the final Reynolds number (acceleration rate and history of the Reynolds number). In our previous studies (Nakabayashi 1983; Nakabayashi &amp; Tsuchida 1988 a, b), we clarified the structures, wavenumbers and rotation frequencies of the periodic disturbances caused by a quasi-static increasing of the Reynolds number. In the present study, we consider how the characteristics of periodic disturbances depend on the following three factors: (i) the rate of increase of the Reynolds number; (ii) the number of toroidal vortices in an initial flow mode; and (iii) the quasi-static Reynolds-number history. The flow modes observed in the present study are all stable to small perturbations, and the transitions among the flow modes are reproducible.

Interference between wind loading on group of structures

This paper presents a brief review of the research on group effect done at the Peking University in the past several years. The aerodynamic characteristics of two circular cylinders in various arrangements at high subcritical and supercritical Reynolds numbers, of rectangular cylinders of different slenderness ratios as well as of several kinds of groups of cooling towers have been treated.

Supercritical Reynolds number experiments on a freely rotatable cylinder/splitter plate body

The behavior of a circular cylinder with attached splitter plate, under conditions where the entire cylinder/splitter plate body was free to rotate about the cylinder axis, has been studied experimentally as Reynolds number was increased through the critical value (laminar boundary layer separation replaced by turbulent boundary layer separation farther downstream). As in previous experiments (at lower Reynolds numbers), it was found that the plate did not align itself with the free stream, but instead rotated to some off-axis equilibrium angle, θ. For plates with splitter plate length, L, less than one cylinder diameter, D, θ dropped very quickly to some minimum value in the transitional Reynolds number range, then slowly increased toward some new supercritical value, which in all cases was smaller than that in the subcritical range. For cases with L/D≳1, however, in the transitional Reynolds number range, the splitter plate overshot the centerline and commenced oscillating between extremes on either side. At supercritical Reynolds numbers, for cases with L/D≤2, a new equilibrium angle eventually reestablished itself on one side or the other; but for cases with L/D≥2.5, the cylinder/splitter plate body continued to oscillate between extremes on either side, even at the highest Reynolds numbers tested.

Third-order upwind finite element solutions of high Reynolds number flows

A full upwind finite element scheme based on the Petrov-Galerkin formulation is presented for accurate solutions of high Reynolds number flows, and then a simplified finite scheme with third-order upwinding is developed in order to obtain a practical algorithm for numerical simulation, because structures of the full upwind finite element scheme are very complicated. Numerical dissipation added in the proposed upwind scheme is represented by high-order derivatives of flow velocities and pressure. Computational results for the subcritical and the supercritical Reynolds number flows around a circular cylinder and for flows around twin circular cylinders are shown to illustrate the effectiveness and robustness of the simplified upwind finite element scheme.

Two circular cylinders in high-turbulence flow at supercritical Reynolds number

Results of wind-tunnel study on time-mean pressure on two circular cylinders in various arrangements, as well as fluctuating pressure in some cases, in high-turbulence uniform flow (Iu = 10%) at supercritical Reynolds number (Re=6.5×105) are presented in this paper. The interference effects between two cylinders are different for different angles of incident wind and different gap ratios, though variations of magnitude of overall effect may not be large, except for very small gap ratios.

Heat transfer enhancement in a transitional channel flow

Flow modification by an array of spanwise eddy-promoters oriented normal to the flow direction is sometimes used to enhance the convective heat transfer rate from a heated wall. Here, we study the effect of such eddy-promoters on the heat transfer and dissipation in a fully-developed channel flow with one heated wall, in the laminar and transitional flow regimes. The experiment shows that flows with eddy-promoters result in a significant decrease in dissipation for a given heat transfer rate at all supercritical Reynolds numbers investigated. When the results are compared to other eddy-promoter geometries, they support a scale-matched destabilization method. The primary enhancement mechanism in the subcritical flows is travelling waves, but for supercritical flows vortex shedding is an equally important mechanism.

Linear stability of shear profiles and relation to the secondary instability of the Dean flow

Solutions of the Navier–Stokes equations for flow in a curved channel have previously been computed [Bottaro, J. Fluid Mech. 251, 627 (1993)] and the spatial development of the Dean flow is available at different supercritical Reynolds number. In this work the viscous instability of local longitudinal vortex structures (obtained from the nonlinear simulations) is investigated, with a focus toward the secondary instability of Dean vortices. Such a secondary instability takes the form of streamwise traveling waves. High-frequency waves are termed twisting waves, low frequency are defined undulating waves. Instead of performing analyses in which the basic flow in the cross section is two dimensional, significant shear profiles along y and z are considered as base flows at constant x before the establishment of a fully developed state. Thus one is able to discover that the twist instability is of shear type and is caused by inflectional spanwise profiles of the streamwise velocity component. Sinuous waves are always preferred to varicose waves, and the latter mode of instability is destabilized only at large Reynolds numbers. Undulating waves are related to normal profiles of the streamwise velocity; this type of secondary instability is of centrifugal origin. Results of the analyses for both types of waves are in good agreement with experiments.

Fluctuating pressure on two circular cylinders at high Reynolds numbers

In this paper the fluctuating pressure on two circular cylinders in a number of arrangements (including in tandem, side-by-side and staggered) subjected in a smooth cross flow are given at high subcritical Reynolds number (3.25 × 105) and supercritical Reynolds number (6.5 × 105) respectively. The results show that the interference effect on fluctuating pressure are weaker at supercritical Reynolds number than that at subcritical ones. In certain cases it may have very different features at these two Reynolds numbers.

Flow between eccentric rotating cylinders: Bifurcation and stability

The effect of cylinder eccentricity on Couette-Taylor transition is investigated here for flow between infinite rotating cylinders. The method of analysis is Fourier expansion of the conservation equations in the axial direction, followed by projection onto a polynomial subspace. Critical points of the solution, which are characterized by singularity of the Jacobian matrix, are located via parametric continuation. This computational scheme permits an extension of the DiPrima and Stuart results to higher values of the eccentricity ratio; it also makes it possible to move far from the critical point into the supercritical Reynolds number regime. The first bifurcation from Couette flow is found to be supercritical, while supercritical flow is shown to consist of regions of plane motion with recirculation, separating toroidal vortex regions. The domain of recirculating flow is asymmetric with respect to the line of centers, and on increasing the supercritical Reynolds number its axial dimension decreases while its radial dimension, in the plane separating the vortex cells, increases. The results established here for critical Reynolds number agree well with those of DiPrima and Stuart at eccentricities where their small perturbation solution is applicable, and there is good agreement with the experimental data of Vohr. The torque calculations compare favorably with the experimental data of Donnelly and Simon for the concentric case and with the data of Castle and Mobbs for non-zero eccentricity.

Three-dimensional dynamics and transition to turbulence in the wake of bluff objects

The wakes of bluff objects and in particular of circular cylinders are known to undergo a ‘fast’ transition, from a laminar two-dimensional state at Reynolds number 200 to a turbulent state at Reynolds number 400. The process has been documented in several experimental investigations, but the underlying physical mechanisms have remained largely unknown so far. In this paper, the transition process is investigated numerically, through direct simulation of the Navier—Stokes equations at representative Reynolds numbers, up to 500. A high-order time-accurate, mixed spectral/spectral element technique is used. It is shown that the wake first becomes three-dimensional, as a result of a secondary instability of the two-dimensional vortex street. This secondary instability appears at a Reynolds number close to 200. For slightly supercritical Reynolds numbers, a harmonic state develops, in which the flow oscillates at its fundamental frequency (Strouhal number) around a spanwise modulated time-average flow. In the near wake the modulation wavelength of the time-average flow is half of the spanwise wavelength of the perturbation flow, consistently with linear instability theory. The vortex filaments have a spanwise wavy shape in the near wake, and form rib-like structures further downstream. At higher Reynolds numbers the three-dimensional flow oscillation undergoes a period-doubling bifurcation, in which the flow alternates between two different states. Phase-space analysis of the flow shows that the basic limit cycle has branched into two connected limit cycles. In physical space the period doubling appears as the shedding of two distinct types of vortex filaments.Further increases of the Reynolds number result in a cascade of period-doubling bifurcations, which create a chaotic state in the flow at a Reynolds number of about 500. The flow is characterized by broadband power spectra, and the appearance of intermittent phenomena. It is concluded that the wake undergoes transition to turbulence following the period-doubling route.

Full scale measurements of wind force acting on a 200m concrete chimney, and the chimney's response

Full-scale measurements of wind pressures around a 200m concrete chimney and associated deflections and oscillations have been performed continuously since 1979. Records of strong typhoon and monsoon winds have been analysed and the characteristics of wind pressures and forces in the supercritical Reynolds number region have been obtained. As a result, alternative vortex shedding has been confirmed and it has been shown that the chimney deflects statically due to mean drag, and oscillates around its mean deflected position. Excellent across-wind oscillation due to fluctuating lift has also been confirmed.

Full scale measurements of wind force acting on a 200m concrete chimney, and the chimney's response

Full-scale measurements of wind pressures around a 200m concrete chimney and associated deflections and oscillations have been performed continuously since 1979. Records of strong typhoon and monsoon winds have been analysed and the characteristics of wind pressures and forces in the supercritical Reynolds number region have been obtained. As a result, alternative vortex shedding has been confirmed and it has been shown that the chimney deflects statically due to mean drag, and oscillates around its mean deflected position. Excellent across-wind oscillation due to fluctuating lift has also been confirmed.

Onset of three-dimensionality, equilibria, and early transition in flow over a backward-facing step

A numerical study of three-dimensional equilibria and transition to turbulence in flow over a backward-facing step is performed using direct numerical solution of the incompressible Navier-Stokes equations. The numerical method is a high-order-accurate mixed spectral/spectral-element method with efficient viscous outflow boundary conditions. The appearance of three-dimensionality in nominally two-dimensional geometries is investigated at representative Reynolds numbers ranging from the onset of three-dimensional bifurcation to later transitional stages. Strongly three-dimensional regions are identified through standard correlation coefficients and new three-dimensionality indices, as well as through instantaneous and time-average streamline patterns and vorticity contours. Our results indicate that onset of three-dimensionality occurs at the boundaries between the primary and secondary recirculating zones with the main channel flow, the latter being the most stable flow component. There is. therefore, strong secondary instability in the shear layers, mainly due to the one emanating from the step corner.The flow further downstream is excited through the action of the upstream shear layers acquiring a wavy form closely resembling Tollmien–Schlichting waves both spatially and temporally with a characteristic frequency f1; upstream, at the shear layer another incommensurate frequency, f2, is present. The two-frequency flow locks-in to a single frequency if external excitations are imposed at the inflow at a frequency close to f1 or f2; the smaller amplitude excitations, however, may cause a strong quasi-periodic response. Such excitations may significantly increase or decrease (by more than 20%) the length of the primary separation zone XR at lock-in or quasi-periodic states. The equilibrium states resulting from the secondary instability at supercritical Reynolds numbers produce a flow modulated in the spanwise direction, with corresponding variations in the reattachment location XR. While three-dimensionality explains partially the discrepancy between numerical predictions and experimental results on XR at higher Reynolds number Re, the main source of discrepancy is attributed to the inflow conditions, and in particular to external disturbances superimposed on the mean flow, the latter being the main reason also for the somewhat earlier transition found in laboratory experiments.