Supercritical Reynolds Numbers Research Articles

Development of a new Lagrangian vortex method for evaluating effects of surfaces roughness

Abstract The main contribution of this paper is to develop a new methodology to include effects of surface roughness on aerodynamic of bodies. The numerical approach simulates the mechanism of vortex shedding of a rough circular cylinder in the subcritical flow regime ( R e = 1 0 5 ) using a mesh-free vortex method. The local turbulence effects are considered during the vorticity diffusion process; as consequence a connection between the larger scales and the smaller ones is made by eddy viscosity. The eddy viscosity computation is necessary for each Lamb vortex element that constructs the Karman vortex street; it is also the way employed to make feasible the purposed surface roughness model. Simultaneous measurements of the spanwise-integrated unsteady aerodynamic forces and time averaged local surface pressures on a two-dimensional rough circular cylinder are investigated aiming to reach supercritical Reynolds number flow patterns from subcritical flows. It is shown that the surface roughness model captures successfully the drag crisis in a qualitative way.

Aerodynamic characteristics of a rounded-corner square cylinder in shear flow at subcritical and supercritical Reynolds numbers

Shear-inflow effects on flows past a rounded-corner square cylinder is investigated when Reynolds number (Re) increases from subcritical regimes (Re=2.2×104) to supercritical regimes (Re=1.0×106), with a focus on the latter Re in this study. The dimensionless shear parameter K ranges from 0 to 1.0. Results show that shear inflows have different effects on the aerodynamic characteristics of the cylinder in two Re regimes, and generally shear effects are smaller when Re is in the supercritical region. Specifically, mean and r.m.s pressure distributions remain in the same shapes under all shear inflows tested at supercritical Re; however they witness strong dependency on K at subcritical Re. Moreover, the directions of mean lifts at supercritical Re are opposite to those at subcritical Re. Correspondingly, the mean flow patterns observed in the uniform flow are overall preserved in shear flows at the supercritical Re: the free stream flows along the cross section and separates from the trailing corners on both sides of the cylinder, despite of the existence of small-degree asymmetry in the near-wake. However, the flow patterns are significantly changed at the subcritical Re by the sufficiently high shear inflows: the shear layer in suspension tends to reattach on the side wall of the high-velocity side and eventually separates from the trailing edge while the other on the low-velocity side becomes farther from the side wall. It results in the near-wake forming along an axis rotated in the clockwise direction from the horizontal axis, being opposite to the anticlockwise direction at supercritical Re. The mechanism for Re effects is further explored. The preservation of overall flow pattern at supercritical Re even under the strong shear effects is suggested mainly due to the greater favorable pressure gradient and the induced greater velocity acceleration before flow separation on the low-velocity side.

Global instability in a laminar boundary layer perturbed by an isolated roughness element

Roughness-induced boundary-layer instabilities are investigated by means of hot-film anemometry in a water channel to provide experimental evidence of a global instability. It is shown that the roughness wake dynamics depends on extrinsic disturbances (amplifier) at subcritical Reynolds numbers, whereas intrinsic, self-sustained oscillations (wavemaker) are suspected at supercritical Reynolds numbers. The critical Reynolds number, therefore, separates between two different instability mechanisms. Furthermore, the critical Reynolds number from recent theoretical results is successfully confirmed in this experiment, supporting the physical relevance of 3-d global stability theory.

Numerical Investigation of the Flow Past a Rotating Golf Ball and Its Comparison with a Rotating Smooth Sphere

Large-eddy simulations are conducted for a rotating golf ball and a rotating smooth sphere at a constant rotational speed at the subcritical, critical and supercritical Reynolds numbers. A negative lift force is generated in the critical regime for both models, whereas positive lift forces are generated in the subcritical and supercritical regimes. Detailed analysis on the flow separations on different sides of the models reveals the mechanism of the negative Magnus effect. Further investigation of the unsteady aerodynamics reveals the effect of rotating motion on the development of lateral forces and wake flow structures. It is found that the rotating motion helps to stabilize the resultant lateral forces for both models especially in the supercritical regime.

Dimensionless, fluid-independent equations for heat and momentum transfer in supercritical fluids

This study shows that the thermo-hydraulic behavior of several supercritical fluids are nearly identical when their thermophysical properties are non-dimensionalized with adequate fluid-dependent scaling constants. Hence, the transport equations are shown to be solvable as a function of dimensionless numbers (e.g., supercritical Reynolds number), from which the solution to other fluids can be scaled, a possibility only available for constant-property fluids thus far. The fluid-specific scaling coefficients are determined by squared-error minimization for triatomic fluids for various thermodynamic states near the critical point. The proposed non-dimensionalization is demonstrated by showing that the temperature and velocity fields, and their respective gradients, of supercritical CO2 flowing inside a heated-wall channel are nearly identical whether the transport equations are solved with the actual equation of state of CO2 or with dimensionless properties scaled from water. Finally, the fluid-specific scaling constants are shown to be determinable by closed-form expressions.

Investigation of drag crisis phenomenon using CFD methods

When fluid flow passes a cylinder, the drag crisis phenomenon occurs between the sub-critical and the super-critical Reynolds numbers. The focus of the present studies was on the numerical prediction of the drag crisis based on CFD methods. In this work, block structured meshes with refined grids near the cylinder surface and in the downstream were employed. Both 2D and 3D simulations were performed using various turbulence models, including the SST k−ω model, the k−ϵ model, the SST with LCTM, the DES model, and the LES model. In the convergence studies, the effects of the grid size, the time step, the first grid size and the aspect ratio (for 3D simulations) on the solutions were examined. The errors due to spatial and time discretizations were quantified according to a V&V procedure. Validation studies were carried out for various Reynolds numbers between Re=6.31×104 and 7.57×105. The averaged drag force, the RMS of lift force and the Strouhal number were compared with experimental data. The studies indicated that standard 2D and 3D RANS methods were inadequate to capture the drag crisis phenomenon. The LES method however has the potential to address the problem.

Topology of three-dimensional steady cellular flow in a two-sided anti-parallel lid-driven cavity

The structure of the incompressible steady three-dimensional flow in a two-sided anti-symmetrically lid-driven cavity is investigated for an aspect ratio $\unicode[STIX]{x1D6E4}=1.7$ and spanwise-periodic boundary conditions. Flow fields are computed by solving the Navier–Stokes equations with a fully spectral method on $128^{3}$ grid points utilizing second-order asymptotic solutions near the singular corners. The supercritical flow arises in the form of steady rectangular convection cells within which the flow is point symmetric with respect to the cell centre. Global streamline chaos occupying the whole domain is found immediately above the threshold to three-dimensional flow. Beyond a certain Reynolds number the chaotic sea recedes from the interior, giving way to regular islands. The regular Kolmogorov–Arnold–Moser tori grow with increasing Reynolds number before they shrink again to eventually vanish completely. The global chaos at onset is traced back to the existence of one hyperbolic and two elliptic periodic lines in the basic flow. The singular points of the three-dimensional flow which emerge from the periodic lines quickly change such that, for a wide range of supercritical Reynolds number, each periodic convection cell houses a double spiralling-in saddle focus in its centre, a spiralling-out saddle focus on each of the two cell boundaries and two types of saddle limit cycle on the walls. A representative analysis for $\mathit{Re}=500$ shows chaotic streamlines to be due to chaotic tangling of the two-dimensional stable manifold of the central spiralling-in saddle focus and the two-dimensional unstable manifold of the central wall limit cycle. Embedded Kolmogorov–Arnold–Moser tori and the associated closed streamlines are computed for several supercritical Reynolds numbers owing to their importance for particle transport.

Cellular flow in a partially filled rotating drum: regular and chaotic advection

The topology of the incompressible steady three-dimensional flow in a partially filled cylindrical rotating drum, infinitely extended along its axis, is investigated numerically for a ratio of pool depth to radius of 0.2. In the limit of vanishing Froude and capillary numbers, the liquid–gas interface remains flat and the two-dimensional flow becomes unstable to steady three-dimensional convection cells. The Lagrangian transport in the cellular flow is organised by periodic spiralling-in and spiralling-out saddle foci, and by saddle limit cycles. Chaotic advection is caused by a breakup of a degenerate heteroclinic connection between the two saddle foci when the flow becomes three-dimensional. On increasing the Reynolds number, chaotic streamlines invade the cells from the cell boundary and from the interior along the broken heteroclinic connection. This trend is made evident by computing the Kolmogorov–Arnold–Moser tori for five supercritical Reynolds numbers.

Fluctuating wind pressure distribution around full-scale cooling towers

At present, external wind pressure description around cooling towers in various loading Codes is based on full-scale measurement data. The data has been collected during 1960s–1990s for hyperbolic cooling towers with heights of about 90m~120m, and focus has been usually on the average wind pressure distribution. In fact, modern cooling towers taller than 165m show sensitivity to wind-induced effects under strong wind excitation. The performance of these flexible structures is closely related to the fluctuating wind action in the atmospheric boundary layer. Modeling of these features is underscored by the difficulty in matching supercritical Reynolds number in boundary layer wind tunnels. Accordingly, it has been difficult to accurately establish a relationship between fluctuating pressures on the surface of a cooling tower to inflow conditions. This has caused a bottleneck for enhancements in the state of wind resistant structural design of larger cooling towers. In view of this difficulty, high Reynolds number flows were simulated in the wind tunnel using scaled model with a combination of surface roughness elements to establish a relationship between the inflow turbulence intensity and pressure fluctuations. This was supplemented by a validation using data from long-term measurements of wind pressure around a 166.68m cooling tower. Wind tunnel experiments were in a general agreement with full-scale observations which offered a relationship between the fluctuating wind pressure distribution and the incoming turbulence intensity at supercritical Reynolds number conditions (Re≥4×10E7).

Dynamics of a thin film flowing down a heated wall with finite thermal diffusivity

Consider the dynamics of a thin film flowing down a heated substrate. The substrate heating generates a temperature distribution on the free surface, which in turn induces surface-tension gradients and corresponding thermocapillary stresses that affect the free surface and therefore the fluid flow. We study here the effect of finite substrate thermal diffusivity on the film dynamics. Linear stability analysis of the full Navier-Stokes and heat transport equations indicates if the substrate diffusivity is sufficiently small, the film becomes unstable at a finite wavelength and at a Reynolds number smaller than that predicted in the long-wavelength limit. This property is captured in a reduced-order system of equations derived using a weighted-residual integral-boundary-layer method. This reduced-order model is also used to compute the bifurcation diagrams of solution branches connecting the trivial flat film to travelingwaves including solitary pulses. The effect of finite diffusivity is to separate a simultaneous Hopf-transcritical bifurcation into its individual component bifurcations. The appropriate Hopf bifurcation then connects only to the solution branch of negative-hump pulses, with wave speed less than the linear wave speed, while the branch of positive-single-hump pulses merges with the branch of positive-two-hump pulses at a supercritical Reynolds number. In the regime where finite-wavelength instability occurs, there exists a Hopf-bifurcation pair connected by a branch of periodic solutions, whose period cannot be increased indefinitely. Numerical simulation of the reduced-order system shows the development of a train of coherent structures, each of which resembles a stationary positive-hump pulse, and, in the regime of finite-wavelength instability, wavelength selection and saturation to periodic traveling waves.

Application of the γ-Re θ Transition Model to Simulations of the Flow Past a Circular Cylinder

Based on the finite volume method, the flow past a two-dimensional circular cylinder at a critical Reynolds number (Re = 8.5 × 105) was simulated using the Navier-Stokes equations and the γ-Reθ transition model coupled with the SST k − ω turbulence model (hereinafter abbreviated as γ-Reθ model). Considering the effect of free-stream turbulence intensity decay, the SST k − ω turbulence model was modified according to the ambient source term method proposed by Spalart and Rumsey, and then the modified SST k − ω turbulence model is coupled with the γ-Reθ transition model (hereinafter abbreviated as γ-Reθ-SR model). The flow past a circular cylinder at different inlet turbulence intensities were simulated by the γ-Reθ-SR model. At last, the flow past a circular cylinder at subcritical, critical and supercritical Reynolds numbers were each simulated by the γ-Reθ-SR model, and the three flow states were analyzed. It was found that compared with the SST k − ω turbulence model, the γ-Reθ model could simulate the transition of laminar to turbulent, resulting in better consistency with experimental result. Compared with the γ-Reθ model, for relatively high inlet turbulence intensities, the γ-Reθ-SR model could better simulate the flow past a circular cylinder; however the improvement almost diminished for relatively low inlet turbulence intensities The γ-Reθ-SR model could well simulate the flow past a circular cylinder at subcritical, critical and supercritical Reynolds numbers.

Large-eddy simulation of the flow past a circular cylinder at sub- to super-critical Reynolds numbers

Large-eddy simulation of turbulent flow past a circular cylinder at sub- to super-critical Reynolds numbers is performed using a high-fidelity orthogonal curvilinear grid solver. Verification studies investigate the effects of grid resolution, aspect ratio and convection scheme. Monotonic convergence is achieved in grid convergence studies. Validation studies use all available experimental benchmark data. Although the grids are relatively large and fine enough for sufficiently resolved turbulence near the cylinder, the grid uncertainties are large indicating the need for even finer grids. Large aspect ratio is required for sub-critical Reynolds number cases, whereas small aspect ratio is sufficient for critical and super-critical Reynolds number cases. All the experimental trends were predicted with reasonable accuracy, in consideration the large facility bias, age of most of the data, and differences between experimental and computational setup in particular free stream turbulence and roughness. The largest errors were for under prediction of turbulence separation.

An innovative open boundary treatment for incompressible SPH

SummaryAn innovative inflow/outflow boundary treatment has been proposed to be used in smoothed particle hydrodynamics (SPH). Among other strategies, it involves the use of extended regions at open boundary sections and a procedure to enforce the mass continuity constraint, as well as to minimize outflow reflections. This methodology has been coupled with a modified ‘particle shifting’ algorithm, so that the robustness of the method could be ensured at high Reynolds number regimes. Confined flow around a square cylinder with an open outflow has been selected as the flow problem to analyze the performance of the new method. Detailed comparisons with data available in the literature for a variety of mesh‐based methods have been made for two different values of the blockage ratio β, namely for β = 1/4 and 1/8, and a range of supercritical Reynolds numbers. The results obtained with the present implementation of truly incompressible SPH have demonstrated numerical accuracy comparable with that of other methods, as well as the success of the open boundary treatment. A direct comparison with previously published SPH results for a distinct blockage ratio, namely for β = 1/5, has also revealed that a major improvement has been achieved by the use of the method described in this paper. Copyright © 2015 John Wiley & Sons, Ltd.

On the flow past a circular cylinder from critical to super-critical Reynolds numbers: Wake topology and vortex shedding

Large-eddy simulations (LES) of the flow past a circular cylinder are used to investigate the flow topology and the vortex shedding process at Reynolds numbers Re=2.5×105-8.5×105. This range encompasses both the critical and super-critical regimes. As the flow enters the critical regime, major changes occur which affect the flow configuration. Asymmetries in the flow are found in the critical regime, whereas the wake recovers its symmetry and stabilizes in the super-critical regime. Wake characteristic lengths are measured and compared between the different Reynolds numbers. It is shown that the super-critical regime is characterised by a plateau in the drag coefficient at about CD≈0.22, and a quasi-stable wake which has a non-dimensional width of dw/D≈0.4. The periodic nature of the flow is analysed by means of measurements of the unsteady drag and lift coefficients. Power spectra of the lift fluctuations are computed. Wake vortex shedding is found to occur for both regimes investigated, although a jump in frequencies is observed when the flow enters the super-critical regime. In this regime, non-dimensional vortex-shedding frequency is almost constant and equal to St=fvsD/Uref≈0.44. The analysis also shows a steep decrease in the fluctuating lift when entering the super-critical regime. The combined analysis of both wake topology and vortex shedding complements the physical picture of a stable and highly coherent flow in the super-critical regime.

Analysis of stratospheric lighter-than-air vehicle's aerodynamic characteristics based on large eddy simulation

Flowing over stratospheric lighter-than-air vehicle( SLV) with spherical capsule shape at supercritical Reynolds number were simulated by using large eddy simulation( LES) method. Meanwhile,the results at different sphere spacing were analyzed and compared so that the influence of different sphere spacing on stratospheric lighter-than-air vehicle's aerodynamic characteristics was obtained. Compared with the results of the experiments,the calculations of time-average drag coefficients agreed well with Achenbach's experimental results in the single sphere. The method was verified accurate on the analysis of flow over spheres at supercritical Reynolds number. The drag coefficients of the two spheres at different sphere spacing and frequency spectrum were studied. With the increase of the upstream and downstream spheres 'spacing,the whole drags increased first,then decreased,and the the dominant frequencies of upstream sphere decreased.The upstream and downstream spheres had the same dominant frequency of vibration when the spheres' spacing were G = 1. 5D and G = 2D. With the increasing of G,the interaction between the two spheres and the influence of upstream sphere's trailing vortex to downstream sphere's trailing vortex waned.

Enstrophy-based proper orthogonal decomposition for reduced-order modeling of flow past a cylinder.

Here proper orthogonal decomposition (POD) modal decomposition are performed for flow past a circular cylinder at supercritical Reynolds numbers by projecting this onto instability modes. The important task of modeling a cylinder wake by Stuart-Landau (SL) and the Stuart-Landau-Eckhaus (SLE) equation for instability modes is discussed, with the latter shown to be more consistent with multimodal pictures of POD and instability modes. The difficult task of finding the coefficients of the SLE equation is reported by taking a least squares approach for the reduced order model (ROM). The important aspect of the ROM is the choice of initial condition for the developed SLE equations, as these are stiff ordinary differential equations which are very sensitive to the choice of initial conditions. An accurate representation of enstrophy-based POD also reveals the presence of modes which occur in isolation (in comparison to modes that come in pairs) and the traditional approach of treating instability modes by SL or SLE equations does not work directly, which also reveals higher frequency variations. Quantifying effects of this mode by time-averaged Navier-Stokes equation (NSE) fail to show the variation of the phase of these isolated time-varying modes and this is captured here using direct numerical simulation (DNS) data by a multitime scale approach. A reconstructed 3-mode ROM solution and the disturbance vorticity from DNS match globally in the flow. The agreement between 3-mode SLE reconstruction and DNS also proves the consistency of the proposed method and helps explain the physical nature of the ensuing Hopf bifurcation following an instability.

Optimal wavepackets in streamwise corner flow

AbstractThe global non-modal stability of the flow in a right-angled streamwise corner is investigated. Spatially confined linear optimal initial conditions and responses are obtained by use of direct-adjoint looping. Two base states are considered, the classical self-similar solution for a zero streamwise pressure gradient, and a modified solution that mimics leading-edge effects commonly observed in experimental studies. The latter solution is obtained in a reverse engineering fashion from published measurement data. Prior to the global analysis, a classical local linear stability and sensitivity analysis of both base states is conducted. It is found that the base-flow modification drastically reduces the critical Reynolds number through an inviscid mechanism, the so-called corner mode. A survey of the geometry of the two base states confirms that the modification greatly aggravates the inflectional nature of the flow. Global optimals are calculated for subcritical and supercritical Reynolds numbers, and for two finite optimization times. The optimal initial conditions are found to be self-confined in the spanwise directions, and symmetric with respect to the corner bisector. They evolve into streaks or streamwise modulated wavepackets, depending on the base state. Substantial transient growth caused by the Orr mechanism and the lift-up effect is observed.

Numerical Study of Flow over Sphere at Supercritical Reynolds Numbers

Numerical study of flow over sphere at supercritical Reynolds numbers by SST equations model and DES method based on SST model has been done. The simulation on Re = 9.4×105,1.88×106,2.82×106were given. Compared with the Results of experiments, the calculations of drag coefficients at Re=1.88×106、2.82×106agreed well with Achenbach’s results. The trailing vortex structure was shown through the identification method of three dimensional flow field. It had a good agreement with Taneda’s results. The time histories and spectrum characteristics of the drag and the lateral force were investigated by the transient mothod.

Aerodynamics of a golf ball with grooves

In this study, we investigate the aerodynamics of our newly designed golf ball that does not have dimples but grooves on its surface. The smooth part of its surface is approximately 1.7 times that of a golf ball with dimples. We directly measure the drag and lift forces on two versions of this golf ball in the ranges of real golf-ball velocity and rotational speed, and compare them with those of smooth and dimpled balls. At zero spin, the drag coefficient of our balls shows a rapid fall-off at a Reynolds number similar to that of a dimpled ball and maintains nearly a constant value (lower by 50% than that of smooth ball) at higher Reynolds numbers. At non-zero spin, the lift-to-drag ratio of one version of our ball is higher by 5%–20% in the supercritical Reynolds number regime than that of a dimpled ball, but it is lower otherwise. With the measured drag and lift forces, we predict the trajectories of our balls and compare them to those of smooth and dimpled balls for the same initial conditions. The flight distances of our balls are larger by 148%–202% than that of smooth ball and shorter by 6%–10% than that of a dimpled ball.

Wavelet-based adaptive simulations of three-dimensional flow past a square cylinder

AbstractThe wavelet-based eddy capturing approach is extended to three-dimensional bluff body flows, where the flow geometry is enforced through Brinkman volume penalization. The wavelet-collocation/volume-penalization combined method is applied to the simulation of vortex shedding flow behind an isolated stationary prism with square cross-section. Wavelet-based direct numerical simulation is conducted at low supercritical Reynolds number, where the wake develops fundamental three-dimensional flow structures, while wavelet-based adaptive large-eddy simulation supplied with the one-equation localized dynamic kinetic-energy-based model is performed at moderately high Reynolds number. The present results are in general agreement with experimental findings and numerical solutions provided by classical non-adaptive methods. This study demonstrates that the proposed hybrid methodology for modelling bluff body flows is feasible, accurate and efficient.