Three-dimensional Bluff Bodies Research Articles

Direct numerical simulations of three-dimensional flows past obstacles with a vortex penalization method

A vortex method with penalization is proposed in order to simulate three-dimensional incompressible bluff body flows. This approach combines the robustness of vortex methods and the flexibility of penalization methods to impose boundary conditions on the obstacle. Far field boundary conditions are handled in a FFT-based Poisson solver. A validation of the proposed numerical method is carried out in the context of flow past a sphere and further simulations are performed in the more challenging case of flow past a hemisphere.

Numerical characterization of three-dimensional bluff body shear layer behaviour

Three-dimensional bluff body aerodynamics are pertinent across a broad range of engineering disciplines. In three-dimensional bluff body flows, shear layer behaviour has a primary influence on the surface pressure distributions and, therefore, the integrated forces and moments. There currently exists a significant gap in understanding of the flow around canonical three-dimensional bluff bodies such as rectangular prisms and short circular cylinders. High-fidelity numerical experiments using a hybrid turbulence closure that resolves large eddies in separated wakes close this gap and provide new insights into the unsteady behaviour of these bodies. A time-averaging technique that captures the mean shear layer behaviours in these unsteady turbulent flows is developed, and empirical characterizations are developed for important quantities, including the shear layer reattachment distance, the separation bubble pressure, the maximum reattachment pressure, and the stagnation point location. Many of these quantities are found to exhibit a universal behaviour that varies only with the incidence angle and face shape (flat or curved) when an appropriate normalization is applied.

Mean pressure distributions and reattachment lengths for roof-separation bubbles on low-rise buildings

Investigations of separated and reattaching flows near the leading edge of three-dimensional bluff bodies placed in turbulent boundary layers are important because of the large aerodynamic loads that these flows cause. Roofs of low-rise buildings are vulnerable to this kind of wind loading. Turbulence properties in the approaching boundary layer flow affect the pressure distributions and the mean size of the separation bubble formed on building surfaces. In this study, the effects of turbulence intensities and length scales in the incident boundary layer on the mean reattachment lengths and surface mean pressure distributions for low-rise building roofs are investigated. Particle Image Velocimetry measurements of the roof separation bubble, along with surface measurements, for a low-rise building model were taken for six different, upstream, boundary-layer conditions. Surface pressure measurements were taken for a second building model in similar upstream conditions. Along with these data, pressure data from the NIST aerodynamic database were used in the analysis. The mean size of the roof separation bubble is found to be unaffected by the turbulence length scales over the range tested, whereas turbulence intensity has a significant effect on reattachment lengths. The mean pressure distribution was found to be a function of both the mean reattachment length and the upstream turbulence intensity. A method of estimating the mean reattachment length on the roof of low-rise buildings from measured surface pressures and roof height turbulence intensity is proposed.

Turbulent wake past a three-dimensional blunt body. Part 2. Experimental sensitivity analysis

AbstractThe sensitivity of the flow around three-dimensional blunt geometry is investigated experimentally at Reynolds number $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}9.2\times 10^4$. Vertical and horizontal control cylinders are used to disturb the natural flow which is the superposition of two reflectional symmetry breaking states (see Part 1 of this study, Grandemange, Gohlke & Cadot, J. Fluid Mech., vol. 722, 2013b, pp. 51–84). When the perturbation breaks the symmetry of the set-up, it can select one of the two asymmetric topologies so that a mean side force is found. When the reflectional symmetry is preserved, some positions of horizontal and vertical control cylinders alter the natural bi-stability of the flow which may result in drag reduction. In addition, it is found that the horizontal perturbation affects the lift force especially when the top and bottom mixing layers are disturbed. The ability of the disturbances to suppress the bi-stable behaviour is discussed and, introducing a formalism of induced drag, a quantification of the impact on the drag of the cross-flow forces observed for the natural bi-stable wake is suggested. Finally, a general concept for a control strategy of separated flows past three-dimensional bluff bodies can be drawn up from these analyses.

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.

The wake of a two-dimensional ship in the low-speed limit: results for multi-cornered hulls

AbstractIn the Dagan & Tulin (J. Fluid Mech., vol. 51, 1972, pp. 529–543) model of ship waves, a blunt ship moving at low speeds can be modelled as a two-dimensional semi-infinite body. A central question for these reduced models is whether a particular ship design can minimize, or indeed eliminate, the wave resistance. In the previous part of our work (Trinhet al.,J. Fluid Mech., vol. 685, 2011, pp. 413–439), we demonstrated why a single corner can never be made waveless. In this accompanying paper, we continue our investigations with the study of more general piecewise-linear, or multi-cornered ships. By using exponential asymptotics, we demonstrate how the production of waves can be directly ascertained by the positions and angles of the corners. In particular, this theory answers the question raised by Farrow & Tuck (J. Austral. Math. Soc.B, vol. 36, 1995, pp. 424–437) as to why certain bulbous-like obstructions can minimize the production of waves. General results for wavelessness are given for a class of hulls, and numerical computations of the nonlinear ship-wave problem are used to confirm analytical predictions. Finally, we discuss open questions regarding hulls without corners and more general three-dimensional bluff bodies.

Reflectional symmetry breaking of the separated flow over three-dimensional bluff bodies

Experimental observation of a permanent reflectional symmetry breaking (RSB) is reported for a laminar three-dimensional wake. Based on flow visualizations, a first bifurcation from the trivial steady symmetric state to a steady RSB state is characterized at Re=340. The RSB state becomes unsteady after a second bifurcation at Re=410. It is found that this RSB regime is persistent at large Reynolds numbers and is responsible for a bistable turbulent wake.

Effect of blockage on the drag of a triangular cylinder

A method is presented to estimate the form drag and the base pressure on a triangular cylinder in the presence of blockage effect. The Strouhal number, which is found to increase with the flow constriction experimentally by Ramamurthy & Ng (1973), may be decoupled from the blockage effect when re-defined by using the velocity at flow separation and a theoretical wake width. By incorporating this wake width into the momentum equation by Maskell (1963) for the confined flow, a relationship between the form drag and the base pressure is derived. Independently, the experimental data of surface pressure from Ramamurthy & Lee (1973) are found to be independent of the blockage effect when expressed in terms of a modified pressure coefficient involving the pressure at separation. Using the potential flow model by Parkinson & Jandali (1970) and its subsequent development in Yeung & Parkinson (2000) for the unconfined flow, a linear relation between the pressure at separation and the form drag is formulated. By solving the two equations simultaneously with a specified blockage ratio and an apex angle of the triangular cylinder, the predictions of the drag and the base pressure are in reasonable agreement with experimental data. A new theoretical relationship for the Strouhal number, pressure drag coefficient and base pressure proposed in this study allows the confinement effect to be appropriately taken into consideration. The present approach may be extended to three-dimensional bluff bodies.

Reynolds-averaged Navier–Stokes simulations of unsteady separated flow using the k−ω−υ2 −f model

The objective of the present work is to evaluate the steady and unsteady Reynolds-averaged Navier–Stokes (RANS) approach turbulence model for separated flow applications. A υ2 − f model based on the standard k − ω model is employed and referred to as the k − ω − υ2 − f model. This model is validated by flow around two- and three-dimensional bluff bodies. The selected configurations are a single square cylinder, tandem square cylinders and cube. The flow predictions are discussed and compared with available experimental and numerical data. For these cases, none of the previously published numerical predictions obtained by steady-state RANS produced a good match with experimental data. Because these flow cases are inherently unsteady at high Reynolds numbers, unsteady RANS computations should be employed. It is found that the results obtained with this mode are in agreement with the available experimental and numerical data.

The interaction of an asymmetrical localised synthetic jet on a side-supported sphere

Abstract A localised synthetic jet offers promise of an optimum and cost-effective practical method of delaying separation and promoting reattachment in fluids with solid body interactions. The asymmetric flow that may result from its use may also be beneficial in improving the aerodynamic performance of a lifting body. There are insufficient studies of synthetic jets, particularly on three-dimensional bluff bodies that are more representative of complex flows in real situations. A comprehensive study on an 80 mm diameter sphere designed with localised synthetic jet orifices was, therefore, conducted in an 18 in×18 in open circuit closed test-section wind tunnel at a Reynolds number of 5×104. The coefficient of pressure distribution was measured by continuously varying the location of the synthetic jet and compared with the no synthetic jet condition. The three-dimensional effects on the flow over the sphere body are particularly made apparent through the growth and the effects of the boundary layer and the deviation from potential flow. Overall, the synthetic jet had the effect of delaying the separation point and extending it further downstream on the sphere surface concomitantly producing a significant reduction in drag, providing solid support to the viability of strategically located synthetic jet when higher lift or lower drag is desired. A surprising discovery was the ability of the synthetic jet to improve the flow at the junction of the sting support and sphere. This has promising implications in devising methods to reduce interference drag that are common in many practical applications such as near junctions between wing and the fuselage.

Reacting and Nonreacting Flowfields of a V-Gutter Stabilized Flame

Particle image velocimetry measurements have been performed to determine the flowfield around a confined V-gutter bluff body in both nonreacting and reacting environments. The incoming flow to the V-gutter bluff body is a vitiated mixture with secondary liquid fuel being injected upstream through a fuel spray bar to mimic realistic conditions. The measurements capture instantaneous and mean flow structures formed in the wake region of a three-dimensional bluff body. In addition to the flow structures, the mean velocity components, mean out-of-plane vorticity, and the turbulent kinetic energy have been compared between the nonreacting and reacting test cases. The results show significant differences in the instantaneous flow structures. The nonreacting case results in asymmetric shedding of large-scale vortical structures which span the entire wake region, whereas the reacting case results in both symmetric and asymmetric shedding of smaller scale vortical structures which are flattened out within the shear layer. A comparison of the mean velocity components clearly shows that the reacting case results in a larger region of reversed flow, experiences an acceleration of the freestream flow due to combustion, and results in a slower dissipation of the wake region.

Direct numerical simulation of turbulent flow around a wall-mounted cube: spatio-temporal evolution of large-scale vortices

Flow around a wall-mounted cube is an example of a turbulent flow around a three-dimensional bluff body attached to a surface. The main experimentally observed feature of this type of flow is the appearance of complex vortical structures, e.g. a horseshoe vortex originating in front of the body and enveloping it. The current paper is a follow-up to Yakhot, Liu & Nikitin (2006) in which we presented results of direct numerical simulation (DNS) of turbulent flow around a cube. Here, it is shown that unsteadiness of the considered flow is caused by inviscid–viscous interaction between the horseshoe vortex and the narrow band of positive vorticity attached to the surface in front of the cube. Details of the spatio-temporal evolution of large-scale vortical structures, including samples of long-term visualization and turbulence statistics, are presented. For the normal-to-the-wall velocity, in the vicinity of the cube's front face, the results reveal an anomalous probability distribution, namely, a bimodal distribution and one with high kurtosis.

Hydrodynamics of a particle impact on a wall

The problem of a particle impacting on a wall, a common phenomenon in particle-laden flows in the minerals and process industries, is investigated computationally using a spectral-element method with the grid adjusting to the movement of the particle towards the wall. Remeshing is required at regular intervals to avoid problems associated with mesh distortion and the constantly reducing maximum time-step associated with integration of the non-linear convective terms of the Navier–Stokes equations. Accurate interpolation between meshes is achieved using the same high-order interpolation employed by the spectral-element flow solver. This approach allows the full flow evolution to be followed from the initial approach, through impact and afterwards as the flow relaxes. The method is applied to the generic two-dimensional and three-dimensional bluff body geometries, the circular cylinder and the sphere. The principal case reported here is that of a particle colliding normally with a wall and sticking. For the circular cylinder, non-normal collisions are also considered. The impacts are studied for moderate Reynolds numbers up to approximately 1200. A cylindrical body impacting on a wall produces two vortices from its wake that convect away from the cylinder along the wall before stalling while lifting induced wall vorticity into the main flow. The situation for a sphere impact is similar, except in this case a vortex ring is formed from the wake vorticity. Again, secondary vorticity from the wall and particle plays a role. At higher Reynolds number, the secondary vorticity tends to form a semi-annular structure encircling the primary vortex core. At even higher Reynolds numbers, the secondary annular structure fragments into semi-discrete structures, which again encircle and orbit the primary core. Vorticity fields and passive tracer particles are used to characterize the interaction of the vortical structures. The evolution of the pressure and viscous drag coefficients during a collision are provided for a typical sphere impact. For a Reynolds number greater than approximately 1000 for a sphere and 400 for a cylinder, the primary vortex core produced by the impacting body undergoes a short-wavelength instability in the azimuthal/spanwise direction. Experimental visualisation using dye carried out in water is presented to validate the predictions.

Recent development of vortex method in incompressible viscous bluff body flows

Vortex methods have been alternative tools of finite element and finite difference methods for several decades. This paper presents a brief review of vortex method development in the last decades and introduces efficient vortex methods developed for high Reynolds number bluffbody flows and suitable for running on parallel computer architectures. Included in this study are particle strength exchange methods, core-spreading method, deterministic particle method and hybrid vortex methods. Combined with conservative methods, vortex methods can comprise the most available tools for simulations of three-dimensional complex bluff body flows at high Reynolds numbers.

Recent development of vortex method in incompressible viscous bluff body flows

Vortex methods have been alternative tools of finite element and finite difference methods for several decades. This paper presents a brief review of vortex method development in the last decades and introduces efficient vortex methods developed for high Reynolds number bluff body flows and suitable for running on parallel computer architectures. Included in this study are particle strength exchange methods, core-spreading method, deterministic particle method and hybrid vortex methods. Combined with conservative methods, vortex methods can comprise the most available tools for simulations of three-dimensional complex bluff body flows at high Reynolds numbers.

The orientation-averaged aspiration efficiency of IOM-like personal aerosol samplers mounted on bluff bodies.

This paper describes two sets of experiments that were intended to characterize the orientation-averaged aspiration efficiencies of IOM samplers mounted on rotating bluff bodies. IOM samplers were mounted on simplified, three-dimensional rectangular bluff bodies that were rotated horizontally at a constant rate. Orientation-averaged aspiration efficiencies (A360) were measured as a function of Stokes' number (St), velocity ratio (R) and dimension ratio (r). Aspiration efficiency (A) is the efficiency with which particles are transported from the ambient air into the body of a sampler, and A360 is A averaged over all orientations to the wind. St is a dimensionless variable that represents particle inertia, R is the ratio of the air velocity in the freestream and that at the plane of the sampler's entry orifice, and r is the ratio of the sampler's orifice diameter and the bluff body's width. The first set of experiments were instrumental in establishing a hierarchy of effects on orientation-averaged A. It was clear that compared to r, St had a much larger influence on A. It was also clear, however, that the effects of St were overpowered by the effects of R in many cases. As concluded in previous studies, R and St were considered the most important factors in determining A, even for A360. The second set of experiments investigated A360 of IOM samplers for a much wider range of r than examined in previous research. Two important observations were made from the experimental results. One was that the A360 of IOM samplers, as a function of St, did not change for an r-range of 0.066-0.4. This meant that an IOM sampler mounted on a near life-size mannequin would measure the same aerosol concentration as one not mounted on anything. The second observation was that the aspiration efficiency curve of the IOM sampler was close to the inhalability curve. This gave further evidence that the bluff body did not play a major role in influencing A360, as the IOM samplers, in these experiments, were either mounted on miniature bluff bodies or on nothing at all. These observations all suggest that it is quite possible to design and test personal samplers with desired sampling characteristics using protocols that do not require full-size mannequins, which greatly simplifies the development of new samplers.

Vortex Methods for Direct Numerical Simulation of Three-Dimensional Bluff Body Flows: Application to the Sphere at Re=300, 500, and 1000

Recent contributions to the 3-D vortex methods are presented. Following Cottet, the particles strength exchange (PSE) scheme for diffusion is modified in the vicinity of solid boundaries to avoid a spurious vorticity flux and to enforce a zero-normal component of vorticity during the convection/PSE step. The vortex sheet algorithm used to enforce the no-slip boundary condition through a vorticity flux at the boundary and the technique used to perform accurate redistributions in the presence of bodies of general geometry are extended from their 2-D counterpart. To perform simulations with nonuniform resolution, a mapping of the redistribution lattice is used. Computational efficiency is attained through the use of parallel tree codes based on multipole expansions of vortex particles and of vortex panels. The method is validated, by comparisons with other authors' results, on the flow past a sphere at Re=300. It is then applied to compute the flow at Re=500 and 1000.

Near-wake instabilities and vortex structures of three-dimensional bluff bodies: a review

Instabilities and vortical structure in the near wake of a sphere and a circular disk are reviewed, together with those of an elliptic disk and rectangular plate which have two length scales. The linear global instability analysis (J. Fluid Mech. 254 (1993) 323) yields critical Reynolds numbers of regular and Hopf bifurcations of the sphere wake, which are in excellent agreement with direct numerical simulations and experiments. The Strouhal number of shedding of hairpin-like vortices in the sphere wake is significantly dependent on Reynolds number, reflecting changes in the wake such as transition from laminar to turbulent wakes. The vortex structure at high Reynolds numbers still remains to be clarified. Two periodic components of velocity fluctuations are found in the wake of elliptic disks and rectangular plates, being likely to be caused by global instability in the near wake.

Buffeting for 2D and 3D sharp-edged bluff bodies

Aerodynamic buffeting is experimentally investigated for moderate Reynolds number, turbulent flows around two- and three-dimensional bluff bodies in tandem. Combining flow visualizations, surface pressure and velocity measurements, changes in aerodynamic loading and macroscale flow features are related. For large obstacle separations, it is found that when surface-mounted prisms are placed in thin boundary layers, loading and wake dynamics are similar to those found for cylinders suspended in free streams. However, important differences are identified for smaller gaps, which can be generally attributed to greater streamline curvature for three-dimensional configurations.

Time Resolved Torque of Three-Dimensional Rotating Bluff Bodies in a Cylindrical Tank

Torque measurements have been made on rotating three-dimensional bluff bodies in a cylindrical container from start-up to mean flow steady state. The flow is observed to pass through three distinct temporal regimes in the transient process. These regimes include a build-up period where the torque remains approximately constant, a decay period where the torque decreases, and a mean steady state where the mean torque remains at a constant level. Effects of body geometry, rotation rate, acceleration rate, and fluid height in the tank are quantified. The torque coefficient during the build-up and mean steady-state regimes is shown to be a function of Reynolds number and body geometry. A time scale marking the beginning of the decay period is presented in terms of the problem parameters. Over the range of parameters studied, the build-up, decay, and mean steady-state regimes are completely specified by the Reynolds number, geometric parameters, and decay time scale.