Supercritical Reynolds Numbers Research Articles

Hydrodynamic properties of propellers with large blade-area ratio and truncated blade in free water

In the literature exist data about the hydrodynamic characteristics of propulsion systems, which include a duct and a fixed-pitch propeller with a truncated blade shape (Kaplan propeller), which has a relatively small blade-area ratio of 0.55. Usual such propellers has a very high loading coefficient, which entails the need to increase propellers blade-area ratio in order to prevent the occurrence of developed cavitation. The article presents the results of the first stage of research, which included testing a series of four-blade truncated propellers with a blade-area ratio 1.0 in free water. The tests were carried out in the towing tank of Admiral Makarov State University of Maritime and Inland Shipping on experimental installation, which include a special hydrodynamic stand. A series of tested propellers were 3D printed from PET-G plastic. A preliminary assessment showed that the chosen diameter of the models will ensure the achievement of supercritical Reynolds numbers at a rotation frequency of about 20 s–1. However, during the tests, it was found that the rotational speed must be increased to 30 s–1, which, in turn, led to a reduction in the test program due to the regime limitations of the experimental equipment. Nevertheless, the analysis of the test results made it possible to build a “hull” and “machinary” diagrams according to the Papmel form. An assessment of the strength of the models was carried out, which showed that the stresses arising in the root of the blade are significantly less than the allowable ones. The obtained results expand the design possibilities of Kaplan propellers with water-jet propulsion units, as well as a part of the “propeller-nozzle” propulsion complex.

Floquet stability analysis of pulsatile flow in toroidal pipes

The linear temporal stability of the fully developed pulsatile flow in a torus with high curvature is investigated using Floquet theory. The baseflow is computed via a Newton-Raphson iteration in frequency space to obtain basic states at supercritical Reynolds numbers in the steady case for two curvatures, δ=0.1 and 0.3, exhibiting structurally different linear instabilities for the steady flow. The addition of a pulsatile component is found to be overall stabilizing over a wide range of pulsation amplitudes, in particular for high values of curvature. The pulsatile flows are found to be at most transiently stable with large intracyclic growth rate variations even at small pulsation amplitudes. While these growth rates are likely insufficient to trigger an abrupt transition at the parameters in this work, the trends indicate that this is indeed likely for higher pulsation amplitudes, similar to pulsatile flow in straight pipes. At the edge of the considered parameter range, subharmonic eigenvalue orbits in the local spectrum of the time-periodic operator, recently found in pulsating channel flow, have been confirmed also for pulsatile flow in toroidal pipes, underlining the generality of this phenomenon. Published by the American Physical Society 2024

Simulation of the flow past a circular cylinder from sub-critical to super-critical Reynolds numbers using an intermittency-based hybrid model

In this work, we investigate the prediction of the flow around a circular cylinder from sub-critical to super-critical Reynolds numbers using a hybrid approach which combines a dynamic variational multiscale (DVMS) large-eddy simulation (LES) model and a transitional RANS model. In the proposed hybrid approach, the variational multiscale model, aiming to limit the effects of the subgrid-scale (SGS) model to the smallest resolved scales, is combined with the dynamic procedure which provides a tuning of the SGS dissipation in space and time. For representing laminar to turbulent boundary layer transition, the equations of the RANS part of the hybrid approach are completed with a transition model based on an intermittency transport equation. Results are compared to those of other numerical simulations in the literature and with experimental data. They highlight the overall good prediction capabilities of the proposed hybrid strategy for the simulation of such massively separated flows, even with the use of coarse meshes. In particular, the intermittency-based hybrid model was found to be able to predict the drag crisis of a circular cylinder, as well as the sharp increase in vortex shedding frequency, unlike the equivalent hybrid approach when no laminar-turbulent transition model is introduced.

Resolvent and dynamic mode analysis of flow past a square cylinder at subcritical Reynolds numbers

Flow-induced vibration (FIV) of bluff bodies can occur at subcritical Reynolds numbers (i.e., below the Re of the vortex shedding from fixed bodies). To analyze the mechanism of this subcritical FIV phenomenon, resolvent and dynamic mode analyses are introduced in this work. For laminar flow past a square cylinder, both resolvent and dynamic modes are extracted and investigated. The results indicate that the dominant dynamic mode decomposition mode and the leading response mode are similar. Both modes lead to vortex shedding at supercritical Reynolds numbers, and they vanish below Re = 19 along with the dominant forcing mode. In addition, the first and second resolvent gains separate near the characteristic flow frequency and overlap at Re = 19, indicating the disappearance of the first-order resolvent mode. The disappearance of these critical modes indicates the lowest Reynolds number of FIV instability for flow past a square cylinder.

Large Eddy Simulation of Flow and Separation Bubbles Around a Circular Cylinder from Sub-critical to Super-critical Reynolds Numbers

Large Eddy Simulation of Flow and Separation Bubbles Around a Circular Cylinder from Sub-critical to Super-critical Reynolds Numbers

Quantifying parameter ranges for high fidelity simulations for prescribed accuracy by Lax–Wendroff method

Explicit second order central difference (CD2) based Lax–Wendroff (LW) method is evaluated for large eddy simulation here, using global spectral analysis (GSA) for its ability to compute fluid flows up to a specified accuracy. While the LW method has been analyzed for numerical stability in the past, rigorous quantification for performing accurate simulations including error dynamics has not been reported before. This is addressed here by determining optimal numerical parameters for prescribed accuracies based on the GSA of 2D convection–diffusion equation (CDE), which is the main focus of the present research. First, two LW methods are reported based on the application of the method for convection and both convection and diffusion operators, respectively, with the latter also having third derivative dispersive and fourth order diffusion terms. Using GSA, the optimal scheme is determined by comparing the two schemes for accuracy. The accuracy of GSA for wave propagation is also demonstrated by the validation of the q-waves determined from the analysis with the numerical simulations of 2D CDE. Finally, motivated by a one-to-one correspondence of the Navier–Stokes equation with the linear CDE established in “Effects of numerical anti-diffusion in closed unsteady flows governed by two-dimensional Navier–Stokes equation- (Suman et al., 2020)”, optimal simulation parameters are determined for the accuracy in representing physical diffusion of the scheme and validated using simulations of the canonical lid-driven cavity problem for a sub- and a super-critical Reynolds number.

Numerical Study on the Flow Past Three Cylinders in Equilateral-Triangular Arrangement at Re = 3 × 106

One of the most common systems in engineering problems is the multi-column system in the form of an equilateral-triangular arrangement. This study used three-dimensional numerical simulations to investigate the flow around three cylinders in this arrangement at the super-critical Reynolds number Re=3×106, concentrating on the influence on the spacing ratio (L/D) among cylinders. The instantaneous vortex structures, Strouhal numbers, fluid force coefficients, and pressure distributions are analyzed thoroughly. The present study demonstrated that fluid dynamics is sensitive to L/D, by which five different flow patterns are classified, namely single bluff body flow (L/D≤1.1), deflected gap flow (1.2≤L/D≤1.4), anti-phase flow (1.5≤L/D≤2.3), in-phase flow (2.5≤L/D<3.5), and co-shedding flow (L/D≥3.5). Critical bounds are identified by significant transitions in the flow structure, discontinuous drop and jump of St, and force coefficients.

Insensitivity of a turbulent laser-plasma dynamo to initial conditions

It has recently been demonstrated experimentally that a turbulent plasma created by the collision of two inhomogeneous, asymmetric, weakly magnetized, laser-produced plasma jets can generate strong stochastic magnetic fields via the small-scale turbulent dynamo mechanism, provided the magnetic Reynolds number of the plasma is sufficiently large. In this paper, we compare such a plasma with one arising from two pre-magnetized plasma jets whose creation is identical save for the addition of a strong external magnetic field imposed by a pulsed magnetic field generator. We investigate the differences between the two turbulent systems using a Thomson-scattering diagnostic, x-ray self-emission imaging, and proton radiography. The Thomson-scattering spectra and x-ray images suggest that the external magnetic field has a limited effect on the plasma dynamics in the experiment. Although the external magnetic field induces collimation of the flows in the colliding plasma jets and although the initial strengths of the magnetic fields arising from the interaction between the colliding jets are significantly larger as a result of the external field, the energies and morphologies of the stochastic magnetic fields post-amplification are indistinguishable. We conclude that, for turbulent laser-plasmas with supercritical magnetic Reynolds numbers, the dynamo-amplified magnetic fields are determined by the turbulent dynamics rather than the seed fields or modest changes in the initial flow dynamics of the plasma, a finding consistent with theoretical expectations and simulations of turbulent dynamos.

Efficient measurement of hydrodynamic coefficients for vibrating cylinders at supercritical Reynolds numbers

Free-response Vortex-Induced Vibration (VIV) tests were conducted on a 6.233 m long cylinder with a diameter of 0.325 m. The cylinder was allowed to vibrate in the cross-flow direction and towed at Reynolds numbers varying from 200,000 to 700,000. Rather than conducting hundreds of individual tests at discrete values of reduced velocity, the free-response was measured while continuously varying the towing speed in a manner that ensures quasi-steady response. These ‘ramp-tests’ not only yielded response data corresponding to continuously varying reduced velocity, but also yielded observations of the hysteresis effects associated with increasing or decreasing flow speed. The results from the carefully conducted ‘ramp-tests’ are compared with steady towing speed results to confirm their validity. The cylinder’s free-response was controlled by systematically varying the external electro-mechanical damping. Lift and added mass coefficients at supercritical Reynolds numbers were extracted using the known relationships between cylinder response and hydrodynamic loading. Contour plots of lift and added mass coefficients are presented as a function of dimensionless response amplitude and reduced velocity. Stationary cylinder drag coefficients were also efficiently acquired using the ramp testing technique. These results are presented and compared with the VIV amplified drag coefficients.

On the Characteristics of the Super-Critical Wake behind a Circular Cylinder

The flow topology of the wake behind a circular cylinder at the super-critical Reynolds number of Re=7.2×105 is investigated by means of large eddy simulations. In spite of the many research works on circular cylinders, there are no studies concerning the main characteristics and topology of the near wake in the super-critical regime. Thus, the present work attempts to fill the gap in the literature and contribute to the analysis of both the unsteady wake and the turbulent statistics of the flow. It is found that although the wake is symmetric and preserves similar traits to those observed in the sub-critical regime, such as the typical two-lobed configuration in the vortex formation zone, important differences are also observed. Owing to the delayed separation of the flow and the transition to turbulence in the attached boundary layer, Reynolds stresses peak in the detached shear layers close to the separation point. The unsteady mean flow is also investigated, and topological critical points are identified in the vortex formation zone and the near wake. Finally, time-frequency analysis is performed by means of wavelets. The study shows that in addition to the vortex shedding frequency, the inception of instabilities that trigger transition to turbulence occurs intermittently in the attached boundary layer and is registered as a phenomenon of variable intensity in time.

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

Measurements 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}(Re) at both distances is similar to that for a single circular cylinder. The development of the drag curves Cd_{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 Rerightarrow 10^{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 Reapprox 1times10^{6} - 7times10^{6}, the Strouhal numbers have nearly equal values of Stapprox 0.22 - 0.24 for both distances. This is followed by a branching. For Rerightarrow 10^{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

Effect of cable surface characteristics and flow turbulence on the aerodynamic behaviour of stay cables in dry conditions

This article describes a wind-tunnel study to evaluate the aerodynamic behaviour of stay cables of a bridge with various surface geometries in dry conditions. Nine cable models were fabricated and tested. Aerodynamic forces acting on the static models were measured for different wind speeds, cable-wind angles and cable axial rotation angles, in smooth and turbulent flow. The aerodynamic forces of bare, round cable models with different roughness levels were used as a baseline to compare the aerodynamic loading of the cables with surface geometry features. A comprehensive database of existing and emerging cable geometries in a wide range of flow conditions and cable-wind angles was generated. The trends exhibited by models with geometric features are similar to results available in the open literature. The aerodynamic drag coefficient was largely affected by the presence of cable surface geometry. The model with helical strakes had the lowest drag coefficient throughout the range of Reynolds numbers that was evaluated. It was observed that turbulence had a similar effect on all models, resulting in a reduction of the drag coefficient at lower Reynolds numbers and an earlier increase in drag that is associated with the supercritical Reynolds number regime. The presence of turbulent flow resulted in higher drag coefficients at high Reynolds numbers. An important secondary finding was that models fabricated with the Selective Laser Sintering (SLS) technique have a higher surface roughness than high-density polyethylene (HDPE) stay cable sleeves but when printed, they have a similar surface roughness.

Transitional Flow Dynamics Behind a Micro-Ramp

Micro-ramps are popular passive flow control devices which can delay flow separation by re-energising the lower portion of the boundary layer. We compute the laminar base flow, the instantaneous transitional flow, and the mean flow around a micro-ramp immersed in a quasi-incompressible boundary layer at supercritical roughness Reynolds number. Results of our Direct Numerical Simulations (DNS) are compared with results of BiLocal stability analysis on the DNS base flow and independent tomographic Particle Image Velocimetry (tomo-PIV) experiments. We analyse relevant flow structures developing in the micro-ramp wake and assess their role in the micro-ramp functionality, i.e., in increasing the near-wall momentum. The main flow feature of the base flow is a pair of streamwise counter-rotating vortices induced by the micro-ramp, the so-called primary vortex pair. In the instantaneous transitional flow, the primary vortex pair breaks up into large-scale hairpin vortices, which arise due to linear varicose instability of the base flow, and unsteady secondary vortices develop. Instantaneous vortical structures obtained by DNS and experiments are in good agreement. Matching linear disturbance growth rates from DNS and linear stability analysis are obtained until eight micro-ramp heights downstream of the micro-ramp. For the setup considered in this article, we show that the working principle of the micro-ramp is different from that of classical vortex generators; we find that transitional perturbations are more efficient in increasing the near-wall momentum in the mean flow than the laminar primary vortices in the base flow.

Maximal Speed of Underwater Locomotion

Background. An increasing interest in unmanned underwater vehicles continues to draw attention to swimming in aquatic animals. Their high speed continues to surprise researchers. In particular, the high dolphin speed caused a series of attempts to explain its paradox, which continues to this day. Some researchers believe that even rigid bodies, shaped like water animals, provide an attached flow pattern, as opposed to the widespread view of the inevitable separation. The possible explanation may be in the perfect body form, which provides an attached flow pattern (without boundary layer separation). Elongated unseparated shapes can not only reduce the pressure drag but also delay the laminar-to-turbulent transition in the boundary layer, significantly reducing the friction drag. Thus, the highest possible swimming speeds are expected in aquatic animals. Objective. We will try to prove that the low drag and the high speed of aquatic animals can only be ensured by their unseparated shape (as a rigid body), neglecting flexibility and compliance. Methods. We will use: a) shape calculations of special bodies of revolution with negative pressure gradients near the tail similar to fish trunks with the use of the developed before approach; b) the known drag estimations of such shapes for laminar and turbulent cases; c) the swimming power balance and the theory of ideal propeller; d) statistical analysis of available data about the length, the speed and the aspect ratio of aquatic animals. Results. The swimming speed of most aquatic animals is proportional to the length of the body in power 7/9. The exception is whale locomotion that occurs in turbulent mode at supercritical Reynolds numbers. Conclusions. The perfect body shapes of most aquatic animals provide an attached laminar flow pattern. Estimated maximum speeds for laminar and turbulent cases show that the special shaped unseparated hulls can greatly increase the speed of underwater vehicles and SWATH ships. Further increase in speed can be achieved by using supercavitation and greater than animal capacity-efficiency.

On the flow around two circular cylinders in tandem arrangement at high Reynolds numbers

The flows around two tandem circular cylinders in the subcritical and supercritical flow regimes are studied through three-dimensional numerical simulations. Different spacing ratios L/D (where L is the center-to-center distance between the two cylinders with D being the diameter of the cylinders) from 2.0 to 5.0 is considered. The instantaneous flow structures, pressure distributions and hydrodynamic forces on two tandem cylinders are analyzed at subcritical (Re=2.2×104) and supercritical (Re=3.0×106) Reynolds numbers. The present numerical solutions demonstrated that at the two Re, for L/D<3.5, the shear layer from the upstream cylinder reattaches on the surface of the downstream cylinder and vortex street is only formed behind the downstream cylinder, while the shear layer from the upstream cylinder rolls up alternately for L/D≥3.5, and vortex shedding occurs from both upstream and downstream cylinders. Compared with the flow characteristics at Re=2.2×104, for Re=3.0×106, the flow separation positions on the upstream cylinder move backward and the width of the wake behind the upstream cylinder becomes narrower, which leads to forward movement of the reattachment position. At the supercritical Reynolds number, the mean drag and fluctuating lift coefficients of the upstream cylinder are nearly independent of L/D while the sharp increase of force coefficients of the downstream cylinder occurs for L/D=3.5. Comparing to the case at the subcritical Reynolds number, higher vortex-shedding frequencies from the upstream and downstream cylinders are identified. It is also revealed that the slope of the best fit line for φ (the phase lag of the fluctuating lift force between two cylinders) and L/D increases at the supercritical Reynolds number. In addition, for L/D=2.5, the mean drag coefficients of the upstream cylinder decrease sharply for Re>1.0×105, while those of the downstream cylinder rise slightly with the growing Re. Moreover, the fluctuating lift coefficients of the upstream cylinder are almost independent of Re, but those of downstream cylinder drop as Re increases.

Experiments on a Flettner rotor at critical and supercritical Reynolds numbers

The Flettner rotor is attracting increasing attention as a viable technology for wind-assisted ship propulsion. Nonetheless, the influence of the Reynolds number on the aerodynamic performance of rotating cylinders is still unclear and under debate. The present study deals with a series of wind-tunnel experiments on a large-scale Flettner rotor in which the forces and pressures acting on the cylinder were measured for Reynolds numbers as large as Re=1.0⋅106. The rotating cylinder used in the experimental campaign had a diameter of 1.0 m and span of 3.73 m. The results indicate that the lift coefficient is only affected by the Reynolds number in the critical flow region and below velocity ratio k=2.5. Conversely, in the velocity ratio range 1<k≤2.5, the drag coefficient is markedly influenced by the Reynolds number over the entire range of flow conditions analyzed. The power coefficient scales with the cube of the tangential velocity and it appears to be insensitive to the Reynolds number or whether the cylinder is spun in an air stream or in still air.

Numerical simulation of electrically conducting jet flow in a straight duct under longitudinal homogeneous magnetic field

Spatial evolution of electrically conducting jet flow at a supercritical Reynolds number, entering a duct filled with the liquid of the same physical properties, is studied by direct numerical simulations for the case of a streamwise uniform magnetic field. In contrast to the case of a transverse field, here the jet mean velocity does not interact with the streamwise field, and only the turbulent fluctuations of the flow are influenced and suppressed by the field. In this case, the jet saves its energy and has a tendency to spread at much larger distances. Therefore, one interesting and important property of this setup is the flow stabilization, i.e., transition to turbulence can be largely delayed due to the stabilizing effect of the magnetic field. This occurs in the presence of moderate magnetic fields. At strong magnetic fields, the second instability evolves—the jet profile becomes unsteady due to the traveling waves, which propagate along the jet while not interacting with the field. These traveling waves are generated by the interaction of secondary radial flows and magnetic field.

Application and optimization of drag reduction characteristics on the flow around a partial grooved cylinder by using the response surface method

ABSTRACTIt is well known that drag reduction occurs when the flow is passing by a grooved circular cylinder at certain Reynolds numbers, which has been used as a powerful energy saving method in a broad range of circumstances. However, a challenge here is how to evaluate the combined effects of depth, width and location of a given triangular groove set covering half of the cylindrical surface area. A useful approach to quantitatively analyze the influence of these different factors on drag reduction using the response surface methodology is described here. The flow characteristics, including drag coefficient, flow velocity, turbulent kinetic energy and vorticity, were calculated by numerical simulation. The results showed a great drag reduction effect under the legitimate set of groove structure parameters at a super-critical Reynolds number providing a base for optimization process in various engineering applications. The drag reduction mechanism found from this research could extend to other cases and should provide insights into engineering applications like car grilles.

Giant drag reduction on Leidenfrost spheres evaluated from extended free-fall trajectories

Vapor layer sustained on the surface of a heated sphere, by the means of the Leidenfrost effect, can dramatically reduce the hydrodynamic drag on a sphere due to an early drag crisis transition. Here we investigate the vapor layer effect on the free fall of heated metallic spheres in a fluorocarbon liquid, FC-72 (perfluorohexane), employing two tall liquid tanks: a 3 m tall 14 cm wide tank and a 2 m tall 20 × 20 cm cross-section tank with a heater device. These tanks are significantly larger than the tanks used in prior studies. We use high-speed video camera recordings to track extended fall trajectories and to compare the drag on room-temperature no-vapor-layer spheres to that of heated Leidenfrost vapor-layer spheres. Analysis of the extended free-fall trajectories and acceleration, based on the sphere dynamic equation of motion, enables the accurate evaluation of the vapor-layers-induced drag reduction, without the need for extrapolation. We demonstrate that the drag on the Leidenfrost sphere in FC-72, can be as low as CD = 0.04 ± 0.01, or an order of magnitude lower than the values for the no vapor layer spheres in the subcritical Reynolds number range. This drag reduction extends into the supercritical Reynolds number range. The analysis method developed herein, to describe the sphere trajectories, can be applied in other related studies. Results of this study are expected to stimulate the development on energy saving drag-reduction technologies based on lubricating gas layers.

The vortex-induced forces on a multi-column platform in current at high Reynolds numbers

The unsteady vortex-induced forces on a multi-column platform in current from subcritical up to supercritical Reynolds numbers have been investigated using three-dimensional numerical simulations. Two different current incidences, 0[Formula: see text] and 45[Formula: see text], are considered. The results show that for 0[Formula: see text] current incidence, the mean streamwise force coefficients [Formula: see text] increase with the rise of [Formula: see text] when [Formula: see text], while they grow slightly when [Formula: see text]. For 45[Formula: see text] current incidence, a decrease of streamwise force with increasing [Formula: see text] is observed. Similar to a single cylinder, the fluctuating transverse force coefficients [Formula: see text] of the multi-column platform drop at [Formula: see text] for 0[Formula: see text] and 45[Formula: see text] current incidences. In addition, it is found that for 0[Formula: see text] current incidence, the [Formula: see text] values of the downstream columns are much larger than those of the upstream columns, while for 45[Formula: see text] current incidence, the [Formula: see text] values of each column are similar. Furthermore, the results of correlations between the forces on each column and total forces indicates that for 0[Formula: see text] current incidence, the fluctuating transverse forces on the downstream columns are mainly responsible for the total fluctuating transverse force on the multi-column platform.