Fixed Separation Points Research Articles

Unsteady forces on elongated bluff bodies

The aerodynamic shape of the bluff body plays a significant role in determining the unsteady drag force resulting from the three-dimensional (3D) distortion of approaching free-stream turbulence. This paper conducted pressure measurements of bluff bodies with four different cross sections (square, rectangular, circular, elliptic, with different aspect ratio δ = B/D, and B and D are the width and height of the cross section) to study the unsteady aerodynamic behavior of drag force, considering the influence of reduced dimension Lu/D (Lu is the longitudinal integral length scale). Generally, the body with a fixed separation point and a relatively small δ is more blunt, resulting in a higher drag coefficient, spectrum, and coherence than streamlined cross sections in turbulent flow compared to smooth flow. The aerodynamic shape significantly influences the high-frequency component of the one-wavenumber and two-dimensional aerodynamic admittance function (2D AAF). The greater the degree of bluntness of the model, the more pronounced the three-dimensional effect. As Lu/D increases, the drag coefficient and spanwise correlation of the model will both increase and approach the results of a smooth flow. Furthermore, the one-wavenumber AAF and 2D AAF increase at the high-frequency domain, and the 3D effect attenuates. This article proposes a 2D AAF model for modifying the distortion effect in wind tunnel tests.

A general solution for the water entry of an arbitrary curved wedge

ABSTRACT The present study proposes a general solution for the water entry of an arbitrary curved wedge with a constant speed. The solution is based on the assumption that the impact flow is an incompressible potential flow with negligible effects of gravity and surface tension. The slamming and transition stages of the water entry of the curved wedge are addressed theoretically. For the slamming stage, pressure and hydrodynamic force models are derived from a quasi self-similar assumption based on the wetted length and a similarity solution of the water entry of linear wedges. The solution can be applied to the water entry of linear and curved wedges, where the curvature effects are absorbed into the wetted length and the derivative of the wetted length with respect to the penetration depth. For the transition stage, where a fixed separation point of flow detachment is located at the knuckle of the wedge, a hydrodynamic force model is proposed by extending the transition stage model of the water entry of linear wedges to that of curved wedges. The present solution can quickly predict the pressure distributions and hydrodynamic forces for the water entry of curved wedges. The predictions are in good agreement with the experimental and numerical results for the slamming and transition stages.

Improvements for the DDES model with consideration of grid aspect ratio and coherent vortex structures

The delayed detached eddy simulation (DDES) model has achieved great success in simulations of massive separations, but has been found to significantly delay the Kelvin-Helmholtz (K-H) instability in weak separations due to the “grey area” problem. A new DDES model was proposed by considering the grid aspect ratio and local coherent vortex structures, named the DDES with an adaptive grid-scale and adaptive coefficient (DDES-AGAC). The DDES-AGAC model was examined in detail by computing four typical types of turbulent flows: fully attached turbulent boundary layer, massive separation, weakly unstable flow with a fixed separation point, and weak separation over a smooth surface due to pressure gradient. The results confirm the advantages of the new DDES-AGAC model over the standard DDES. It exhibits high efficiency and insensitivity to spanwise or circumferential grid spacing in flow simulations of quasi-three-dimensional flows. For the weakly unsteady separation, it helps to accelerate the rapid switch from Reynolds-averaged Navier-Stokes equations to large eddy simulation, unlock the K-H instability in the shear layer, and hence accurately resolve the turbulent structures, profiles of velocity and turbulent kinetic energy, and spectra in the separation regions. Furthermore, it does not result in a noticeable drag or skin friction reduction in the fully attached flow simulations. The DDES-AGAC model is expected to be widely used in simulations of engineering flows with separations.

Oscillation control and drag reduction for a low mass ratio cylinder with double splitter plates

A flow-induced vibration (FIV) investigation to realize oscillation control and drag reduction for an elastically mounted cylinder with double splitter plates (DSPs) attached was undertaken in a water tunnel at Reynolds number of 1100-7700. The length of the splitter plate is in a range of L∗ = 0-2.0 (L∗ = L/D, L is the plate length, D is the cylinder diameter). The intersection angle between two plates, δ, varies from 0°−90°. The dependence of oscillation characteristics, vortex evolution and drag force coefficients on L∗−δ is illustrated in detail. Four oscillation patterns are identified: VIV, combined VIV-galloping, separated VIV-galloping, and suppressed patterns. Under similar structural parameters, the device can perform well both in high and low mass ratio systems, which implies that mass ratio has little effect on the suppression efficiency of DSPs. Besides, the drag force coefficient is proportional to the vertical span of the plate tips, Lp, and the empirical formula is yielded. For Lp<1.3, both oscillation suppression and drag reduction can be attained. Flow visualization shows that the fixed separation points of shear layers resulting in the destructive vortex shedding in the downstream, which is responsible for the wake-stabilization in the downstream and FIV suppression.

The role of the separation point in streamwise vortex-induced vibrations

Structures in crossflow are susceptible to vortex-induced vibrations (VIV) when the vortex-shedding becomes synchronised with the structural vibration. Strategies to control VIV often include modifying the separation point on the cylinder surface, such as adding helical strakes, although there remains disagreement regarding the mechanism by which these work. We explore the role of the separation point on VIV acting in the streamwise (drag) direction, by performing high-speed Particle-Image Velocimetry (PIV) measurements of the wake and the structural displacement of a range of cylinders with different cross-sectional shapes, including circular (no fixed separation points), equilateral triangles (fixed separation points) and elliptical cylinders (which act as an intermediate case). None of the non-circular cylinders are found to exhibit VIV, despite having approximately the same experimental conditions (mass ratio, structural damping, Reynolds number range, etc.) as the circular cylinders, which undergo VIV. The phase-averaged PIV measurements of the near wake of the circular cylinder are used to calculate the separation angle throughout the shedding cycle for different wake modes, and it is shown that all the wake modes that are associated with VIV require a periodic movement of the separation point. In contrast, the variation in the separation angle was negligible for the von Kármán vortex street observed behind near-stationary circular cylinders and for all non-circular cylinders. The experiments illustrate the great sensitivity of the wake mode and streamwise VIV to modifications of the separation point and demonstrate that even a moderately elliptical cylinder (major to minor axis ratio of 1.54) is sufficient to completely suppress VIV.

Two-phase SPH simulation of vertical water entry of a two-dimensional structure

In view of the fact that the SPH model is easy to handle the flows with the free surface of large deformation, a 2-D flow induced by vertical water entry of a 2-D structure is simulated using the two-phase SPH model. The local pressure of the boundary particles is obtained by pressure of the fluid particles nearby through a modified kernel approximation. To evaluate the accuracy of the method, water entry of a 2-D symmetric wedge with fixed separation point of the free surface on the wedge surface is simulated. The pressure distribution of the wedge at the initial stage agrees well with the analytical results available. Evolution of the free surface and the air flow in the cavity induced by the water entry are obtained. A higher speed air jet is found at the neck of the cavity when the neck of the cavity becomes smaller. For the case of a horizontal cylinder entering the water with an unknown separation point of flow on the model surface, the early stage of the water entry is simulated for the rigid body with different density. Evolution of the free surface deformation of the half-buoyant cylinder and neutrally buoyant cylinder water entry is compared with the experimental data. The effects of the density ratio and Froude number on the pinch-off of the cavity are discussed. It is found that the pinch-off time remains almost constant for different density ratio and Froude number. Meanwhile, for a given Froude number, the dimensionless pinch-off depth and the location of the cylinder at the time of pinch-off increase with the density ratio. Further, for a given density ratio, these two parameters increase with the Froude number and, however, the relative cavity shape appears to be a self-similar shape when Fr ≥ 8.35.

The flow-induced vibration of an elliptical cross-section at varying angles of attack

This paper presents a study of the flow-induced vibration of an elliptical cross section at various angles of attack immersed in a free stream. The body is elastically-mounted and constrained to move only in the cross-stream direction. Two-dimensional direct numerical simulations are used to study the system response as a function of the spring stiffness and the angle of attack.The elliptical cross section used has an aspect ratio Γ=1.5. This aspect ratio is large enough so that the deformation from a circular cylinder is obvious, but not so large that the geometry is not related to the cylinder. Because of this, the impact of the symmetry of the system on the flow-induced vibration is studied without also introducing other complexities such as sharp corners or fixed separation points. The body is light with a mass ratio (body mass to displaced fluid mass) of one.The results show a surprisingly wide range of different flow regimes. For small angles (where the body is slightly streamlined) the flow behaviour is similar to that of a cylinder. However, for large angles, where the body is far from symmetric with respect to the wake centreline, the flow can be markedly different with distinct asymmetric modes, including one which is period-doubled. For angles where the body regains its symmetry (aligned across the flow and slightly bluff), an asymmetric mode continues to exist, apparently the result of a spontaneous symmetry breaking that is dependent on Reynolds number. Large-amplitude oscillations persist for very low stiffness or high reduced velocity, and this is explained in terms of the dependence of a critical mass on the angle of attack.

Steady-State Hydrodynamic Power Attenuation by Finned-Buoys

Results of experimental and computational fluid dynamics (CFD) studies conducted to compare the flow-energy-attenuating performances of two different buoy configurations are presented. A finned-body was experimentally studied in two orientations—one with a splitter and one in a 22.5 deg yaw orientation (with no splitter). The finned-buoy is designed for both wave and current attenuation; however, only the current application is discussed here. Scaled models were subjected to wind tunnel testing and CFD analyses. For this study, the steady-state drag coefficient (CD) is considered to be the performance measure. The CFD model is used to match the physical testing by utilizing the k–ω turbulence model. Reynolds numbers (based on the tip-to-tip fin diameter) approaching the drag crisis are used to evaluate the bodies of interest, both of which have an aspect ratio (draft-to-diameter) of 1.85. The finned-bodies do encounter a drag crisis (as commonly seen with a cylinder), since the fins cause the buoys to act as a bluff body. The flow structures around the bodies are examined and compared to those predicted by established theories. For the finned-body, the 22.5 deg yaw orientation is found to have a consistently higher drag than the splitter orientation. The drag enhancement is explained by two phenomena. The first is a low-pressure area located in pockets adjacent to the upstream fins. The second is the absence of the drag-crisis, due to fixed separation points at the fin tips for all Reynolds numbers.

Numerical Study on Plasma-Based Control of Flow over a Square Cylinder

Over the past decade, a lot of attention has been paid to plasma actuators because they are useful tools for flow control. Previous successes with plasma actuators include drag and noise reductions from a circular cylinder, one of representative bluff bodies, mainly through separation delay. However, to the best of authors’ knowledge, no attempt has been made to examine its capability to control square cylinder wake with fixed separation points. The purpose of this study is to numerically investigate whether or not the square cylinder wake can be controlled by means of plasma actuators. In particular, a linear plasma synthetic jet actuator is adopted and attached to the rear side of the cylinder. In this study, we use an immersed boundary method combined with an empirical plasma model for plasma-based flow control. The present method is second order accurate in time and space. Results show that the wake behind the square cylinder can be controlled effectively when the plasma-induced force is strong enough. With the plasma actuator on, the mean drag is reduced and the Karman vortex shedding is alleviated because the induced jet increases the base pressure and prevents the separating shear layers from interacting with each other.

An experimental investigation of the recirculation zone formed downstream of a forward facing step

An experimental investigation of the recirculation zone formed downstream of a forward facing step immersed in a turbulent boundary layer has been undertaken using particle image velocimetry. Bluff body flow is observed with the fixed separation point located at the leading edge of the step. The recirculation region dimensions are characterised over a range of Reynolds numbers (1400–19 000), with Re h based on the step height and the free stream velocity. Turbulent perturbations are produced in the free shear layer which develops between the recirculating flow close to the step and the free stream flow. Contour maps of amplification factor, streamwise perturbation velocity and Reynolds stresses are constructed, providing insight into optimal placement of structures within such topographical features. The mechanisms affecting the reattachment distance, namely the turbulent mixing within the boundary layer and the velocity deficit in the boundary layer, are discussed.

On continuation of inviscid vortex patches

Abstract This investigation concerns solutions of the steady-state Euler equations in two dimensions featuring finite area regions with constant vorticity embedded in a potential flow. Using elementary methods of the functional analysis we derive precise conditions under which such solutions can be uniquely continued with respect to their parameters, valid also in the presence of the Kutta condition concerning a fixed separation point. Our approach is based on the Implicit Function Theorem and perturbation equations derived using shape-differentiation methods. These theoretical results are illustrated with careful numerical computations carried out using the Steklov–Poincare method which show the existence of a global manifold of solutions connecting the point vortex and the Prandtl–Batchelor solution, each of which satisfies the Kutta condition.

Effects of Periodic Excitation on the Flow Around a D-Shaped Cylinder at Low Reynolds Numbers

The baseline and forced flow around a bluff body with semi-elliptical D-shape was investigated by solving the 2D Navier–Stokes equations at low Reynolds numbers. A D-shape rather than the canonic circular-cylinder was selected due to the fixed separation points in the latter, enabling to study a pure wake rather than boundary-layer control. The correlation between Strouhal and Reynolds numbers, the mean drag, the lift and drag oscillations vs. the Reynolds number and wake structure were investigated and compared to experimental and numerical data. Effects of open-loop forcing, resulting from the influence of zero-mass-flux actuators located at the fixed separation points, were studied at a Reynolds number of 150. Fluidic rather than body motion or volume forcing was selected due to applicability considerations. The motivation for the study was to quantify the changes in the flow field features, as captured by Proper Orthogonal Decomposition (POD) analysis, due to open-loop forcing, inside and outside the “lock-in” regime. This is done in order to evaluate the suitability of low-order-models based on POD modes of this changing flow field, for future feed-back flow control studies. The evolution of the natural and the excited vortices in the Karman wake were also investigated. The formation and convection regions of the vortex evolution were documented. It was found that the forcing causes an earlier detachment of the vortices from the boundary-layers, but does not affect their circulation or convection speeds. The results of the POD analysis of the near-wake flow show that the influence of the bluff body shape (“D”-shaped versus circular cylinder) on the baseline POD wake modes is small. It was found that the eigenfunctions (mode-shapes) of the POD velocity modes are less sensitive to slot excitation than the vorticity modes. As a result of the open-loop excitation, two types of mode-shape-change were observed: a mode can be exchanged with a lower-energy mode or shifted to a low energy level. In the latter case, the most energetic mode becomes the “actuator” mode. The evolution of one-slot excitation on still fluid (“Synthetic jet”) was studied and compared to published data and to “actuator” modes with external flow present. Based on the current findings, it is hypothesized that the cross-flow velocity POD modes are suitable for feedback control of wake flow using periodic excitation, due to their low sensitivity to the excitation as compared to the streamwise velocity or vorticity modes.

Generation and Suppression of a Karman Vortex Street by Negative Buoyancy in Wake from a Cylinder with Fixed Separation Points.

A wake from an elliptic cylinder with fixed separation points is analyzed numerically, and is clarified as follows : An isothermal Karman vortex street never occurs at Re<36, but a cooled Karman vortex street is generated by cooling a progressive wavy wake at 26≤ Re<36, where Re is the Reynolds number. The cooled Karman vortex street can be generated at smaller value of the absolute Richardson number in an elliptic cylinder wake than a circular cylinder wake. By cooling the Karman vortex street, a suppressed flow Is generated. Both the Karman vortex street and the suppressed flow have a double structure combined the motions due to both negative buoyancy and the forced flow. The dominant motion is due to the forced now at the Karman vortex street, and due to negative buoyancy for the suppressed flow. At the boundary between the Karman vortex street and the suppressed now, the dominant motion is exchanged, and the wake frequency and the mean Nusselt number decrease abruptly.

Effect of Fixed Separation Points on Wake Oscillation and Surface Character in Suppression of the Karman Vortex Street due to Positive Buoyancy from a Cylinder.

To elucidate an effect of fixed separation points on the wake oscillation and surface character in the suppression of the Karman vortex street due to positive buoyancy, a wake with positive buoyancy from a heated elliptic cylinder submerged in an upward air mainstream is calculated by numerical analysis. Numerical results agree well with the previous result for the isothermal wake, and show that separation points are exactly fixed with time and do not move by buoyancy. The critical Richardson number Ric is much larger than that in a circular cylinder wake. This means that the wake vorticity is larger and harder to disappear than that in the circular cylinder wake. With an increase of the Richardson number, the local Nusselt number and wall shear stress vary with time between separation points, and the mean Nusselt number decreases near Ric, which dose not occur in a circular cylinder wake.

A vortex method for separated flow around an airfoil with a detached spoiler

A discrete vortex method based on no-slip condition is developed for simulating unsteady separated flows around an airfoil with a detached spoiler. For flow separated at each sharp edge, such as the spoiler tips and the trailing edge of the airfoil, a vortex sheet is used to feed discrete vortices at each time step. The length, inclination and strength of each sheet is determined by the continuity equation, the momentum principle and a Kutta pressure condition such that the flow, net force and pressure difference across the vortex sheet are all zero. The separation on the airfoil upper surface is simulated by discrete vortices shed from a fixed separation point. The flow patterns behind a detached spoiler at different time steps are obtained and compared with those of the conventional spoiler. Reasonable agreements are found between the predicted pressure distributions and experimental measurements. The computed results show that base-venting changes the flow field around the spoiler and reduces the adverse effect in lift experienced by the airfoil when the spoiler undergoes a rapid deployment.

Entropy method for calculating separated-flow parameters

A variational method of calculating two-dimensional supersonic turbulent separated flows, based on the Prigogine principle (minimum entropy production), the relations of irreversible-process thermodynamics, and the integral energy equation of a viscous gas, is suggested. An application of this method is illustrated by an example of the calculations of the parameters of separated flows with a fixed separation point. The outer flow in the inviscid region is calculated by known methods.

Effects of splitter plates on the wake flow behind a bluff body

The effects of splitter plates on the wake behind a two-dimensional bluff body with fixed separation points has been experimentally studied for low Reynolds numbers between 0.35 x 103 and 1.15 x 103. A rectangular cylinder was chosen as a bluff body to have the location of the separation points fixed independent of the flow situation and the air velocity. Three sizes of splitter plates were used; these plates were mounted in the center plane of the cylinder at various distances downstream of the cylinder. Detailed measurements of shedding frequency, base pressure, coherence function, and correlation coefficient were obtained. The results indicate that splitter plates alter the manner of vortex formation in the wake causing a decrease in shedding frequency, an increase in base pressure, and a reduction in the overall drag by up to 50%. The effects of splitter plates on the wake-flow characteristics are discussed.

Calculation of the non-stationary aerodynamic characteristics of a body in the case of separated flow

The computerized simulation of three-dimensional separation flow past a poorly streamlined body with fixed separation points is considered. The problem is solved in the non-linear non-stationary statement for an ideal imcompressible fluid. The integrodifferential model for the flow is written, and the main points of the relevant numerical method are treated. Computational examples are given, and the results for the drag factor of a cube are compared with experimental data.