3D‐Flow structures behind a circular cylinder with hemispherical head geometry

An experimental investigation of the flow around a finite circular cylinder mounted on a flat plate, see fig. 1, is reported. The aspect ratio L/D (with length L and diameter D) of the cylinder model is 2.0. The focus of this study is toward examining the complex separated flow structures and wake properties. Velocity and turbulence measurements have been carried out with a three component Laser Doppler anemometer (LDA) at the Reynolds number Re_D = 2.0 · 10⁵. The experimental results show complex 3D fluid motions in the separated flow region. They are induced by the superposition of three main vortical flows.     

Numerical exploration of new features on three-dimensional transition of a cylinder wake

The three-dimensional transition of the wake flow behind a circular cylinder is studied in detail by direct numerical simulations using 3D incompressible N-S equations for Reynolds number ranging from 200 to 300. New features and vortex dynamics of the 3D transition of the wake are found and investigated. At Re = 200, the flow pattern is characterized by mode A instability. However, the spanwise characteristic length of the cylinder determines the transition features. Particularly for the specific spanwise characteristic length linear stable mode may dominate the wake in place of mode A and determine the spanwise phase difference of the primary vortices shedding. At Re = 250 and 300 it is found that the streamwise vortices evolve into a new type of mode’“dual vortex pair mode” downstream. The streamwise vortex structures switch among mode A, mode B and dual vortex pair mode from near wake to downstream wake. At Re = 250, an independent low frequency f _m in addition to the vortex shedding frequency f _s is identified. Frequency coupling between f _m and f _s occurs. These result in the irregularity of the temporal signals and become a key feature in the transition of the wake. Based on the formation analysis of the streamwise vorticity in the vicinity of cylinder, it is suggested that mode A is caused by the emergence of the spanwise velocity due to three dimensionality of the incoming flow past the cylinder. Energy distribution on various wave numbers and the frequency variation in the wake are also described.     

The Trailing Edge Problem For Mixed Convection Flow Past a Horizontal Plate

The influence of buoyancy onto the boundary‐layer flow past a horizontal plate aligned parallel to a uniform free stream is characterized by the buoyancy parameter K = Gr/Re^5/2 where Gr and Re are the Grashof and Reynolds number, respectively. An asymptotiy analysis of the complete flow field including potential flow, boundary layer, wake and interaction region is given for small buoyancy parameters and large Reynolds numbers in the distinguished limit KRe^1/4 = O(1). (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical study on viscoelastic fluid flow past a rigid body

Viscoelastic non-Newtonian fluids can be achieved by adding a small amount of polymer additives to a Newtonian fluid. In this paper, numerical simulations are used to investigate the influence of such polymer additives on the behavior of flow past a circular cylinder. A numerical method is proposed that discretizes the non-linear viscoelastic system on a uniform Cartesian grid, with a penalization method to model the presence of the cylinder. The drag of the cylinder and the flow behavior under the effect of different Reynolds numbers ($\mathrm{Re}$), Weissenberg numbers (Wi) and polymer viscosity ratios (ε) are studied. Numerical results show that different flow characteristics are exhibited in different parameter zones. The polymer viscosity ratio plays an important role at low Weissenberg and Reynolds numbers, but as the Reynolds and Weissenberg numbers increase, the influence of ε weakens. The drag force of the cylinder is mostly affected by the Reynolds and Weissenberg numbers. At low Reynolds numbers, the drag of the cylinder and the flow fields are only affected by a large value of Wi when the elastic forces are strong. Non-trivial drag reduction occurs only when there is vortex shedding in the wake flow, whereas drag enhancement happens when the vortex shedding is inhibited.     

Determining the limits of geometrical tortuosity from seepage flow calculations in porous media.

Recent investigations have found a distinct correlation of effective properties of porous media to sigmoidal functions, where one axis is the Reynolds number Re and the other is the effective property dependent of Re, Θ_i = S_i(Re). One of these properties is tortuosity. At very low Re (seepage flow), there is a characteristic value of tortuosity, and it is the upper horizontal asymptote of the sigmoidal function. With higher values of Re (transient flow) the tortuosity value decreases, until a lower asymptote is reached (turbulent flow). Estimations of this parameter have been limited to the low Reynolds regime in the study of porous media. The current state of the art presents different numerical measurements of tortuosity, such as skeletization, centroid binding, and arc length of streamlines. These are solutions for the low Re regime. So far, for high Re, only the arc length of stream lines has been used to calculate tortuosity. The present approach involves the simulation of fluid flow in large domains and high Re, which requires numerous resources, and often presents convergence problems. In response to this, we propose a geometrical method to estimate the limit of tortuosity of porous media at Re → ∞, from the streamlines calculated at low Re limit. We test our method by calculating the tortuosity limits in a fibrous porous media, and comparing the estimated values with numerical benchmark results. Ongoing work includes the geometric estimation of different intrinsic properties of porous media. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On critical reynolds numbers in plane channels with a sudden expansion at the entry

A method for the numerical solution of fluid dynamics equations is proposed. The evolution of the structure of the laminar flow with increasing Reynolds number and its behavior at the critical Reynolds number Re_cris analyzed. Various flow modes at Re = Re_cr are discussed.     

Vortex Generation in a Liquid Metal Duct Flow near a Magnetic Dipole

The generation of vortical structures by a strong magnetic dipole field in a liquid metal duct flow is studied by means of three-dimensional direct numerical simulations. The dipole is considered as the paradigm for a magnetic obstacle which will deviate the streamlines due to Lorentz forces which act on the fluid elements. Our model uses the quasi-static approximation applicable in the limit of small magnetic Reynolds numbers. The analysis covers the stationary flow regime at smaller flow Reynolds numbers Re as well as the fully time-dependent regimes at higher values with a turbulent flow in the wake of the magnetic obstacle. We present a systematic study of these two basic flow regimes on Re and the Hartmann number Ha, a measure of the strength of the magnetic dipole field. Furthermore, three orientations of the dipole are compared, the streamwise, spanwise and wall-normal ones. The most efficient generation of turbulence at a fixed distance above the duct occurs for the spanwise orientation in which we can observe the formation of Hartmann layers at the top plate. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Controlling chaos in a fluid flow past a movable cylinder

The model of a two-dimensional fluid flow past a cylinder is a relatively simple problem with a strong impact in many applied fields, such as aerodynamics or chemical sciences, although most of the involved physical mechanisms are not yet well known. This paper analyzes the fluid flow past a cylinder in a laminar regime with Reynolds number, Re, around 200, where two vortices appear behind the cylinder, by using an appropriate time-dependent stream function and applying non-linear dynamics techniques. The goal of the paper is to analyze under which circumstances the chaoticity in the wake of the cylinder might be modified, or even suppressed. And this has been achieved with the help of some indicators of the complexity of the trajectories for the cases of a rotating cylinder and an oscillating cylinder.     

Transition waves and nonlinear interactions in the near wake of a circular cylinder

Transition waves and interactions between two kinds of instability—vortex shedding and transition wave in the near wake of a circular cylinder in the Reynolds number range 3 000–10 000 are studied by a domain decomposition hybrid numerical method. Based on high resolution power spectral analyses for velocity new results on the Reynolds-number dependence of the transition wave frequency, i.e.f _t /f_s∼Re^0.87 are obtained. The new predictions are in good agreement with the experimental results of Wei and Smith but different from Braza s prediction and some early experimental resultsf _t/f_s∼Re ^0.5 given by Blooret al. The multi-interactions between two kinds of vortex are clearly visualized numerically. The strong nonlinear interactions between the two independent frequencies (f _t,f _s ) leading to spectra broadening to form the couplingmf _s +nf _t are predicted and analyzed numerically, and the characteristics of the transition are described. Longitudinal variations of the transition wave and its coupling are reported. Detailed mechanism of the flow transition in the near wake before occurrence of the thedimensional evolution is provided. Project supported by the National Natural Science Foundation of China, the LNM of Institute of Mechanics, and partially by the National Basic Research Project.     

DNS of a Turbulent Channel Flow with Streamwise Rotation - Study of the Reverse Effect of the Cross Flow

Modeling of rotating turbulent flows is a major issue in engineering applications. In this work a turbulent channel flow rotating about the streamwise direction is presented. The theory is based on the investigations of [3] employing Lie group analysis. It was found that a cross flow in spanwise direction is induced. A series of direct numerical simulations (DNS) has been conducted for both different rotation rates and different Reynolds numbers to validate the cross flow. In addition some new interesting effects were observed. The averaged profile ū₃ of the cross flow is formed like a ‘S’ that means it exhibits a triple zero-crossing which denotes regions of reverse flow. Alaso a reverse effect is seen which means that for small rotation rates up to Ro=10 the spanwise mean velocity profiles increase and at rotation number Ro=14 this effect appears to reverse. Both effects were observed at two different Reynolds numbers Re = 180 and Re = 270. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Streamwise oscillations of a cylinder beneath a free surface: Free surface effects on vortex formation modes

A computational study of a viscous incompressible two-fluid model with an oscillating cylinder is investigated at a Reynolds number of 200 and at a dimensionless displacement amplitude of A=0.13 and for the dimensionless forcing cylinder oscillation frequency-to-natural vortex shedding frequency ratios, f/f₀=1.5,2.5,3.5. Specifically, two-dimensional flow past a circular cylinder subject to forced in-line oscillations beneath a free surface is considered. The method is based on a finite volume discretization of the two-dimensional continuity and unsteady Navier-Stokes equations (when a solid body is present) on a fixed Cartesian grid. Two-fluid model based on improved volume-of-fluid method is used to discretize the free surface interface. The study focuses on the laminar asymmetric flow structure in the near wake region and lock-on phenomena at a Froude number of 0.2 and for the dimensionless cylinder submergence depths, h=0.25, 0.5 and 0.75. The equivorticity patterns and pressure distribution contours are used for the numerical flow visualization. The code validations in special cases show good comparisons with previous numerical results.     

Turbulent drag reduction at moderate Reynolds numbers via spanwise velocity waves

The question whether large turbulent drag reduction can be achieved at the high values of Re typical of applications is addressed. Answering such question, either by experiments or DNS, is obviously challenging. For DNS, the problem lies in the tremendous increase of the computational cost with Re, that has to be appreciated in view of the need of carrying out an entire parametric study at every Re, owing to the unknown location of the optimal forcing parameters. In this paper we limit ourselves to considering an open-loop technique based on spanwise forcing, the streamwise-traveling waves introduced by [1], and explore via Direct Numerical Simulations (DNS) how the drag reduction varies when the friction Reynolds number is increased from Re_τ = 200 to Re_τ = 2000. To achieve high Re while keeping the computational cost affordable, computational domains of reduced size are employed. We adopted special care to interpret results that are indeed still box-size dependent, as well as strategies to compute the random errors and give the results an error bar. Our results indicate that still R = 0.29 can be obtained at Re_τ = 2000 in the partial region of the parameter space studied. The maximum R is found to decrease as R ˜ Re_τ^−0.22 in the Reynolds range investigated. As most important outcome, we find that the sensitivity of R to Re becomes smaller when far from the low-Re optimum parameters: in this region, we suggest R ˜ Re_τ^−0.08. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

DNS and Lie group analysis of turbulent boundarly layer flow

Lie group approach is used to derive new scaling laws for zero-pressure gradient turbulent boundary layer flow. A direct numerical simulation of the flow at Reynolds number Re_θ = 2240 was performed for the verify theoretical results. Navier-Stokes equations were numerically solved using spectral method with up to 160 million grid points. The numerical simulation shows validity of the theoretical results. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of wall alignment in a very short rotating annulus

This paper reports numerical results of the study of effects of cylinders wall alignment in a small aspect ratio Taylor–Couette system. The investigation concerns bifurcations of steady vortical structures when the cylindrical walls defining the gap are not perfectly parallel. The imperfection is introduced by opening the outer fixed cylinder with a certain angle with regard to the vertical to form a tapered very short liquid column and keeping the inner rotating cylinder wall vertical. The numerical results obtained for the velocity components have revealed that bifurcation from a particular mode to another one occurs at a range of specific values of the inclination angle of the outer cylinder. The band width of the angle at which bifurcation occurred depended on the Reynolds number Re and was found to become narrower as Re increased. It is shown that geometrically broken symmetry can yield flow symmetry for specific combinations of geometrical and dynamical parameters.     

Comparison of the simplified and full MHD models for laminar incompressible flow past a circular cylinder

In the majority of research on incompressible magnetohydrodynamic (MHD) flows, the simplified model with the low magnetic Reynolds number assumption has been adopted because it reduces the number of equations to be solved. However, because the effect of flow on magnetic field is also neglected, the solutions of the simplified model may be different from those of the full model. As an example, the flow of an electrically conducting fluid past a circular cylinder under a magnetic field is investigated numerically using the simplified and full models in this paper. To solve the problems, two second-order compact finite difference algorithms based on the streamfunction-velocity formulation of the simplified model and the quasi-streamfunction-velocity formulation of the full model are developed respectively.Numerical simulations are carried out over a wide range of Hartmann number for steady-state laminar problems with both models. For the full model, magnetic Reynolds number (Re_m) is chosen from 0.01 to 10. The computed results show that solutions of the simplified MHD model are not exactly the same as those of the full MHD model for this flow problem in most cases even if Re_m in the full model is very low. Only in the special case that a strong external magnetic field is exerted perpendicular to the dominant flow direction, can the simplified MHD model be regarded as an approximation of the full MHD model with low Re_m.     

Singular perturbations for the exterior three-dimensional slow viscous flow problem

In this paper the rigorous justification of the formal asymptotic expansions constructed by the method of matched inner and outer expansions is established for the three-dimensional steady flow of a viscous, incompressible fluid past an arbitrary obstacle. The justification is based on the series representation of the solution to the Navier-Stokes equations due to Finn, and it involves the reductions of various exterior boundary value problems for the Stokes and Oseen equations to boundary integral equations of the first kind from which existence as well as asymptotic error estimates for the solutions are deduced. In particular, it is shown that the force exerted on the obstacle by the fluid admits the asymptotic representation F = A₀ + A₁Re + O(Re² ln Re⁻¹) as the Reynolds number Re → 0⁺, where the vectors A₀ and A₁ can be obtained from the method of matched inner and outer expansions.     

Numerical evaluation of the suppression effect of a free-to-rotate triangular fairing on the vortex-induced vibration of a circular cylinder

The suppression of vortex-induced vibration (VIV) of a circular cylinder with a free-to-rotate triangular fairing in the Reynolds number range of Re = 1100–6100 is numerically investigated using computational fluid dynamics. The unsteady Reynolds-averaged Navier–Stokes equations and the shear stress transport k–ω turbulence model coupled with an improved fourth-order Runge–Kutta method are used to solve the wake flow, the structure's vibration, and the fairing's rotation. The computational model is validated with the available experimental results for a cylinder with an attached short-tail fairing. The numerical results indicate that the triangular fairing has a positive role in suppressing vibration when it achieves a stable position deflected from the flow direction. The suppression effect is sensitive to the incoming flow velocity. The fairing shifts from a stable state to an unstable one when the flow velocity varies. Therefore, maintaining the hydrodynamic stability of the fairing is the key to achieving success in vibration suppression, and the stability is dependent on the characteristic length and the rotational friction. Although the strong flapping of the 70° triangular fairing excites a more vigorous vibration, it may be used as an amplifier of VIV for energy harvesting.     

Buoyancy-assisted flow of yield stress fluids past a cylinder: Effect of shape and channel confinement

The aiding-buoyancy mixed convection heat transfer in Bingham plastic fluids from an isothermal cylinder of elliptical and circular shape in a vertical adiabatic channel is numerically investigated. For a fixed shape of the elliptical cylinder E = 2 (ratio of major to minor axes), the effect of confinement is studied for three values of blockage ratio, B, defined as the ratio of the channel width to the circumference of the cylinder/π, as 6.5, 2.17 and 1.3. In order to delineate the role of cross-section of the cylinder, results are also presented here for a circular cylinder of the same heat transfer area as the elliptical cylinder. The results presented herein span the range of conditions as: Bingham number, 0 ≤ Bn ≤ 100, Reynolds number, 1 ≤ Re ≤ 40, and Prandtl number, 1 ≤ Pr ≤ 100 over the range of Richardson number Ri = 0 (pure forced convection) to Ri = 10. Extensive results on drag coefficient, local and surface averaged values of the Nusselt number and yield surfaces are presented herein to elucidate the combined effects of buoyancy, blockage ratio and fluid yield stress. The morphology of the yield surfaces shows that the unyielded plug regions formed upstream and downstream of the cylinder grow faster at low Reynolds numbers with the increasing yield stress effects under the weak buoyancy forces, i.e., small values of Grashof or Richardson number. The heat transfer enhancement is observed with the increasing channel-confinement due to the sharpening of the temperature gradients near the surface of the cylinder. The average Nusselt number shows a positive dependence on the Reynolds number, Prandtl number and Richardson number irrespective of the shape of the cylinder or the type of fluid. By employing the modified definitions of the dimensionless parameters (based on the two choices of the overall effective fluid velocity), predictive correlations have been established for estimating the value of the average Nusselt number in a new application.     

Forced convective flow and heat transfer past an unconfined blunt headed cylinder at different angles of incidence

In the present paper, a numerical investigation has been carried out to study the forced convective flow and heat transfer characteristics past a blunt-headed cylinder in crossflow. Employing air as an operating fluid, calculations are carried out for a range of Reynolds number (Re) from 40 to 160. The angle of incidence is varied in the range of 0^∘ ≤ α ≤ 180 ^∘. The thermofluid features of flow and heat transport are analysed in detail for different angles of incidence. To analyse the aerodynamic characteristics, several parameters such as drag and lift coefficients, moment coefficient, Strouhal number, recirculation length, and local time-averaged vorticity flux have been calculated. Furthermore, a stability analysis has been undertaken by using the Stuart Landau equation to enumerate the critical Reynolds number at each angle of incidence. Heat transfer characteristics are studied by computing local and time-averaged values of Nusselt numbers. When compared to a rectangular cylinder, a blunt-headed cylinder exhibits an enhanced heat transfer rate. In the end, an entropy generation analysis has been carried out to study the effects of Re and angle of incidence on the efficiency of thermofluid transport characteristics.     

High-Reynolds-number effects on turbulent scalings in compressible channel flow

The effect of the Reynolds number in a supersonic isothermal channel flow is studied using a direct numerical simulation (DNS). The bulk Mach number based on the wall temperature is 1.5, and the bulk Reynolds number is increased up to Re_τ ≈︁ 1000. The use of van Driest velocity transformation in the presence of heated walls has been questioned due to the poor accuracy at low Reynolds number. For this reason alternative transformations of the velocity profile and turbulence statistics have been proposed, as, for instance, semi-local scalings. We show that the van Driest transformation recovers its accuracy as the Reynolds number is increased. The Reynolds stresses collapse on the incompressible ones, when properly scaled with density, and very good agreement with the incompressible stresses is found in the outer layer. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)