Active flow control for reduction of fluctuating aerodynamic forces of a blunt trailing edge profiled body

Vortex shedding in the wake of two-dimensional bluff bodies is usually accompanied by three dimensional instabilities. These instabilities result in streamwise and vertical vorticity components which occur at a certain spanwise wavelength. The spanwise wavelength of the instabilities (λ_Z) depends on several parameters, including profile geometry and Reynolds number. The objective of the present work is to study the three dimensional wake instabilities for a blunt trailing edge profiled body, comprised of an elliptical leading edge and a rectangular trailing edge, and to manipulate these instabilities to control the aerodynamic forces. Results of numerical simulations of flow around the body at Re(d) = 400, 600, and 1000, as well as planar Laser Induced Fluorescence (LIF) flow visualizations at Re(d) = 600 and 1000 are analyzed to determine the wake vorticity structure and λ_Z. Based on the findings of these analyses, an active flow control mechanism for attenuation of the fluctuating aerodynamic forces on the body is proposed. The flow control mechanism is comprised of a series of trailing edge injection ports distributed across the span, with a spacing equal to λ_Z. Injection of a secondary flow leads to amplification of the three dimensional instabilities and disorganization of the von Kármán vortex street. Numerical simulations indicate that the flow control mechanism can attenuate the fluctuating aerodynamic forces at lower Reynolds numbers (Re(d) = 400 and 600) where λ_Z is constant in time. However, the control mechanism loses its effectiveness at Re(d) = 1000, due to the temporal variations of λ_Z.     

Effect of interference on the pressure distribution on the ground plane around two low-rise prismatic bodies in tandem arrangement

In this paper the pressure distribution on the ground plane along the centre line of prismatic bodies with square cross section and height to width (h/b) ratio of 1 and 3 are presented when the bodies are in tandem arrangement. The dimensions used are typical of low-rise buildings. For bodies with h/b=1, the results indicate that when the gap between the bodies is small, it is the front body which influences the gap pressures. But for bodies with h/b=3, even at small gaps both the front and rear bodies influence the gap pressure distribution. An increase in the base pressure of the rear body compared to the no-interference case is observed. The interference effects are in general, stronger for the body with h/b=3 than for h/b=1. Flow visualisation results are presented which reveal the changes in the flow patterns that occur with interference. There is good correspondence between the pressure distribution results and the flow visualisation studies. The results presented are applicable to low-rise building aerodynamic problems with some limitations.Nomenclature b width of the body - C _pw (p–p _r)/1/2U _r ² , pressure coefficient on the ground - g gap between the bodies in tandem arrangement - h height of the body - I length of the body along the flow direction - p pressure at any point on the surface plate with the body - p _r pressure at the same point on the surface plate without the body - s distance from the leading edge of the surface plate to the front face of the body - U local velocity at a distance y from the ground - U _r free stream reference velocity - x coordinate along the flow direction - x coordinate along the centre line measured from the front face of the rear body - y vertical distance from the ground - density of air     

The Falkner–Skan Wedge Flows of Power-Law Fluids Embedded in a Porous Medium

The non-Darcy flow characteristics of power-law non-Newtonian fluids past a wedge embedded in a porous medium have been studied. The governing equations are converted to a system of first-order ordinary differential equations by means of a local similarity transformation and have been solved numerically, for a number of parameter combinations of wedge angle parameter m, power-law index of the non-Newtonian fluids n, first-order resistance A and second-order resistance B, using a fourth-order Runge–Kutta integration scheme with the Newton–Raphson shooting method. Velocity and shear stress at the body surface are presented for a range of the above parameters. These results are also compared with the corresponding flow problems for a Newtonian fluid. Numerical results show that for the case of the constant wedge angle and material parameter A, the local skin friction coefficient is lower for a dilatant fluid as compared with the pseudo-plastic or Newtonian fluids.     

Three‐dimensional numerical simulation of red blood cell motion in Poiseuille flows

An immersed boundary method based on an FEM has been successfully combined with an elastic spring network model for simulating the dynamical behavior of a red blood cell (RBC) in Poiseuille flows. This elastic spring network preserves the biconcave shape of the RBC in the sense that after the removal of the body force for driving the Poiseuille flow, the RBC with its typical parachute shape in a tube does restore its biconcave resting shape. As a benchmark test, the relationship between the deformation index and the capillary number of the RBCs flowing through a narrow cylindrical tube has been validated. For the migration properties of a single cell in a slit Poiseuille flow, a slipper shape accompanied by a cell membrane tank‐treading motion is obtained for Re , and the cell mass center is away from the center line of the channel due to its asymmetric slipper shape. For the lower Re ?0.0137, an RBC with almost undeformed biconcave shape has a tumbling motion. A transition from tumbling to tank‐treading happens at the Reynolds number between 0.0137 and 0.03. In slit Poiseuille flow, the RBC can also exhibit a rolling motion like a wheel during the migration when the cell is released in the fluid flow with φ = π/2 and θ = π/2 (see Figure 12 for the definition of φ and θ). The lower the Reynolds number, the longer the rolling motion lasts; but the equilibrium shape and position are independent from the cell initial position in the channel. Copyright © 2014 John Wiley & Sons, Ltd.     

Self-similar solution of the unsteady flow in the stagnation point region of a rotating sphere with a magnetic field

The unsteady flow and heat transfer of a viscous incompressible electrically conducting fluid in the forward stagnation point region of a rotating sphere in the presence of a magnetic field are investigated in this study. The unsteadiness in the flow field is caused by the velocity at the edge of the boundary layer and the angular velocity of the rotating sphere, both varying continuously with time. The system of ordinary differential equations governing the flow is solved numerically. For some particular cases, an analytical solution is also obtained. It is found that the surface shear stresses in x- and y-directions and the surface heat transfer increase with the acceleration, the magnetic and the rotation parameters whether the magnetic field is fixed relative to the fluid or body, except that the surface shear stress in x-direction and the surface heat transfer decrease with increasing the magnetic parameter when the magnetic field is fixed relative to the body. For a certain value of the acceleration parameter, the surface shear stress in the x-direction vanishes while the surface shear stress in the y-direction and the surface heat transfer remain finite. Also, below a certain value of the acceleration parameter, reverse flow occurs in the x-component of the velocity profile. Received on 18 May 1998     

A non-uniformly travelling shock-wave in an LMS-gas

In this paper an LMS-gas is considered. This is an ideal gas with constant specific heats but with a special entropy distribution, so that generalized Riemann invariants r* and s* exist. A flow with r* and s* constant has the property that the gas moves as a rigid body with a constant acceleration or deceleration. It is shown that a flow composed of two domains, in each of which r* and s* are constant, separated by a plane normal shock-wave is admitted by the Rankine-Hugoniot equations. The path of the shock-wave is calculated exactly and a reasonably realistic situation is suggested to generate this composite flow.     

Experimental study of flow patterns and regimes of condensation in horizontal three-dimensional micro-fin tubes

During condensation of R134a the flow patterns inside two three-dimensional (3-D) micro-fin tubes with different fin geometries were investigated. The flow patterns and their transitions were visibly observed and recorded. The experimental findings revealed the following results: a comparison of the condensation flow patterns in the 3-D micro-fin tubes with those in smooth tubes revealed no qualitative differences. The mist flow and the mist-annular flow that appeared in the smooth tube entrance region were not observed in 3-D micro-fin tubes. In the maps of the Mandhane flow regime and the Soliman flow regime, the area of annular flow region of the 3-D micro-fin tube extends towards lower Fr number range in the Soliman map and smaller vapor velocity range in the Mandhane map when compared with that of a smooth tube. The criterion of the flow regime transition between the annular flow and the wavy flow decreases from Fr=7 to Fr=2 in the Soliman flow regime map. However, no significant effect on the criterion for the plug flow transition was observed. The experimental data points of plug flow in the 3-D micro-fin tubes were also obtained in the same regime of smooth tube in Mandhane flow regime map. The Soliman flow regime map indicates the criterion for plug flow transition to be Fr=0.4.     

PIV measurements of flow past a confined cylinder

This study investigates the flow past a confined circular cylinder built into a narrow rectangular duct with a Reynolds number range of 1,500 ≤ Re _d ≤ 6,150, by employing the particle image velocimetry technique. In order to better explain the 3-D flow behaviour in the juncture regions of the lower and upper plates and the cylinder, respectively, as well as the dynamics of the horseshoe vortex system, both time-averaged and instantaneous flow data are presented for regions upstream and downstream of the cylinder. The size, intensity and interaction of the vortex systems vary substantially with the Reynolds number. Although the narrow rectangular duct with a single built-in cylinder is a geometrically symmetrical arrrangement, instantaneous flow data have revealed that the flow structures in both the lower and upper plate–cylinder junction regions are not symmetrical with respect to the centreline of the flow passage. The vortical flow structures obtained in side-view planes become dominant sometimes in the lower juncture region and sometimes in the upper juncture region in unsteady mode.     

Aerodynamics of intermittent bounds in flying birds

Flap-bounding is a common flight style in small birds in which flapping phases alternate with flexed-wing bounds. Body lift is predicted to be essential to making this flight style an aerodynamically attractive flight strategy. To elucidate the contributions of the body and tail to lift and drag during the flexed-wing bound phase, we used particle image velocimetry (PIV) and measured properties of the wake of zebra finch (Taeniopygia guttata, N = 5), flying at 6–10 m s⁻¹ in a variable speed wind tunnel as well as flow around taxidermically prepared specimens (N = 4) mounted on a sting instrumented with force transducers. For the specimens, we varied air velocity from 2 to 12 m s⁻¹ and body angle from −15° to 50°. The wake of bounding birds and mounted specimens consisted of a pair of counter-rotating vortices shed into the wake from the tail, with induced downwash in the sagittal plane and upwash in parasagittal planes lateral to the bird. This wake structure was present even when the tail was entirely removed. We observed good agreement between force measures derived from PIV and force transducers over the range of body angles typically used by zebra finch during forward flight. Body lift:drag (L:D) ratios averaged 1.4 in live birds and varied between 1 and 1.5 in specimens at body angles from 10° to 30°. Peak (L:D) ratio was the same in live birds and specimens (1.5) and was exhibited in specimens at body angles of 15° or 20°, consistent with the lower end of body angles utilized during bounds. Increasing flight velocity in live birds caused a decrease in C _L and C _D from maximum values of 1.19 and 0.95 during flight at 6 m s⁻¹ to minimum values of 0.70 and 0.54 during flight at 10 m s⁻¹. Consistent with delta-wing theory as applied to birds with a graduated-tail shape, trimming the tail to 0 and 50% of normal length reduced L:D ratios and extending tail length to 150% of normal increased L:D ratio. As downward induced velocity is present in the sagittal plane during upstroke of flapping flight, we hypothesize that body lift is produced during flapping phases. Future efforts to model the mechanics of intermittent flight should take into account that flap-bounding birds may support up to 20% of their weight even with their wings fully flexed.     

Suppression of force fluctuations in flow past an aerofoil

Force fluctuations on a solid body are associated with unsteadiness in the wake, e.g. vortex shedding. Therefore, the control of force fluctuations can be realised by suppressing the flow unsteadiness. A NACA0024 aerofoil closed with a round trailing edge is chosen to represent the solid body throughout this investigation, with the Reynolds number fixed at Re = 1000 and angle of attack α ≤ 15^o, at which the uncontrolled flow is two-dimensional. A linear optimal control is calculated by analysing the distribution of sensitivity of unsteadiness to control around the entire surface of the body. The nonlinear effects of the calculated control, which can be actuated through surface-normal suction and blowing across the surface of the aerofoil, are tested through two-dimensional direct numerical simulations. It is observed that a surface-normal velocity control with a maximum magnitude less than 8% of the free stream velocity completely suppresses unsteadiness at α = 10° with an overall drag reduction of 14% and a 138% increase of lift.     

Inviscid evolution of incompressible swirling flows in pipes: The dependence of the flow structure upon the inlet velocity field

This paper analyses the influence of the inlet swirl on the structure of incompressible inviscid flows in pipes. To that end, the inviscid evolution along a pipe of varying radius with a central body situated inside the pipe is studied for three different inlet swirling flows by solving the Bragg–Hawthorne equation both asymptotically and numerically. The downstream structure of the flow changes abruptly above certain threshold values of the swirl parameter (L). In particular, there exist a value L_r above which a near-wall region of flow reversal is formed downstream, and a critical value L_f above which the axial vortex flow breaks down. It is shown that the dependence upon the pipe geometry of these critical values of the swirl parameter varies strongly with the inlet azimuthal velocity profile considered. An excellent agreement between asymptotic and numerical results is found.     

Vortex shedding from a ring in shear flow

Vortex shedding from a bluff ring in a linear shear flow has been investigated experimentally. The shedding frequency, measured using a hot wire in various positions within the near wake of the ring, was found to be remarkably insensitive to a mean flow shear parameter, , defined by (d/U _o).U/y, where d is the mean ring diameter and U _o is the undisturbed upstream velocity on the ring axis; even for = 0.41, corresponding to a velocity variation of about ±24% across the outer ring diameter, the Strouhal number was only about 5% lower than in uniform flow. However, the strong axisymmetric shedding which dominates the flow for = 0 is significantly affected by shear. Indeed, spatial correlation measurements demonstrated that the shedding actually becomes anti-symmetric at the highest values of . The implication of these results is that vortex flowmeters constructed using a ring as the shedding body would be relatively unaffected by changes in the upstream mean flow profile.     

Laminar flow performance of a heated body in particle-laden water

The effects of small uniformly sized spherical particles seeded into the freestream flow of a water tunnel on the delayed transition of a heated laminar flow control body is examined experimentally. In separate trials, four different mean diameter particle seedings were added to the flow and the approach flow velocity was cycled from subcritical to supercritical conditions at three different body heating conditions. The transition Reynolds number based on the body arc length and the approach flow velocity decreases monotonically with increasing d/ ^*, where d is the particle diameter and ^* is the displacement thickness at a critical location. The location of initial turbulent spot formation defines the critical location, and, within the range of experimental conditions reported here, is independent of particle size, heating condition and the approach velocity. For the high unit Reynolds numbers considered (Re ^u 1.88 × 10⁷ per metre), there is no observed critical particle diameterbased Reynolds number threshold; all sizes of particles considered in the experiments (d = 37 to 218 m) have some effect on transition. In a second set of experiments, particles were injected into the laminar boundary layer from a small orifice located at the forward stagnation point. These injected particles have no observable effect on the laminar layer or transition, which suggests that the injected particles fail to produce wakes or vorticity within the laminar layer that may lead to turbulent spot production.Also with the Graduate Program in Acoustics, Penn State UniversityThis work has been supported by the Applied Research Laboratory of The Pennsylvania State University under contracts with the Office of Naval Research and the Naval Sea Systems Command. The authors are particularly indebted to Professor Ron Blackwelder and his colleagues for sharing their yet unpublished findings from particle-induced transition experiments being conducted at the University of Southern California.     

Flow over rectangular porous block in a fixed width channel: influence of porosity and aspect ratio

Flow over a rectangular porous block placed in a fixed width channel is considered and the influence of block aspect ratio on the heat transfer rate from the block is examined. A non-porous solid block is also accommodated to compare the effect of porosity on the flow field and heat transfer characteristics. Aspect ratio and the porosity of the block are varied in the simulations. A numerical scheme employing a control volume approach is considered when predicting the flow and temperature fields. The Reynolds number is selected to yield the mix convection situation in the flow field. It is found that the aspect ratio significantly influences Nu and Gr numbers, in which case increasing the aspect ratio enhances Nu while lowering Gr. Increasing porosity improves the heat transfer rates from the porous block, provided that at high aspect ratios, this situation ceases due to blockage effect of the body in the channel.     

Drag measurements on V-grooved surfaces on a body of revolution in axial flow

In water flows with velocities of up to 9 m/s the friction drag of a body of revolution in axial flow was investigated for dependence on the body surface structure. This was done for different types of riblet film fixed on the surface with the riblet direction aligned with the flow. The lateral spacing between the triangular shaped riblets varied between 0.033 mm and 0.152 mm. In all cases the riblet spacing was equal to the riblet height. For comparison a smooth reference film was used.Depending on the Reynolds number and the non-dimensional riblet spacings ⁺, a turbulent drag reduction of up to 9% could be achieved with riblets in comparison with the flow over a smooth surface.In the region of transition to turbulent flow and with non-dimensional riblet spacings ofs ⁺10–15 drag reductions of up to 13% were obtained. It is therefore conjectured, that in addition to hampering the near wall momentum exchange, the riblets can delay the development of initial turbulent structures in time and space.     

Motion of a small sphere in a nonhomogeneous flow of an incompressible liquid

We consider the motion of a small sphere in an arbitrary potential flow of an ideal liquid. For the general case we obtain an integral of the equations of motion and a particular solution. We find flows in which the force acting on the sphere is central. We also obtain exact solutions of the equations of motion of the sphere for the cases of stationary flows around a cylinder and around a body of revolution when the forces are noncentral. N. E. Zhukovskii [1] calculated the force acting on a fixed sphere in an arbitrary nonstationary flow. Kelvin [2] obtained the equations of motion of a sphere in a stationary flow of a liquid circulating through a hole in a solid. A formula for the force F, acting on a fixed small body of volume V in a stationary flow with speed v, was obtained by Taylor [3]: F = (T ₀ / v)Vv + 1/2_V v ² Here T₀ is the kinetic energy of an unbounded liquid in which a body moves with velocity v. This problem was solved in [3] through a direct integration of the pressure forces over the surface of the body in a flow defined by multipoles of the first and second orders at infinity.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 57–61, September–October, 1973.     

Investigation of flow mechanism of a robotic fish swimming by using flow visualization synchronized with hydrodynamic force measurement

When swimming in water by flapping its tail, a fish can overcome the drag from uniform flow and propel its body. The involved flow mechanism concerns 3-D and unsteady effects. This paper presents the investigation of the flow mechanism on the basis of a 3-D robotic fish model which has the typical geometry of body and tail with periodic flapping 2-freedom kinematical motion testing in the case of St = 0.78, Re = 6,600 and phase delay mode (φ = −75°), in which may have a greater or maximum propulsion (without consideration of the optimal efficiency). Using a special technique of dye visualization which can clearly show vortex sheet and vortices in detail and using the inner 3-component force balance and cable supporting system with the phase-lock technique, the 3-D flow structure visualized in the wake of fish and the hydrodynamic force measurement were synchronized and obtained. Under the mentioned flapping parameters, we found the key flow structure and its evolution, a pair of complex 3-D chain-shape vortex (S–H vortex-rings, S₁–H₁ and S₂–H₂, and their legs L₁ and L₂) flow structures, which attach the leading edge and the trailing edge, then shed, move downstream and outwards and distribute two anti-symmetric staggering arrays along with the wake of the fish model in different phase stages during the flapping period. It is different with in the case of St = 0.25–0.35. Its typical flow structure and evolution are described and the results prove that they are different from the viewpoints based on the investigation of 2-D cases. For precision of the dynamic force measurement, in this paper it was provided with the method and techniques by subtracting the inertial forces and the forces induced by buoyancy and gravity effect in water, etc. from original data measured. The evolution of the synchronized measuring forces directly matching with the flow structure was also described in this paper.     

Structure of the wake behind a cylinder in a fluid with a variable buoyancy frequency,studied with the help of echo sounding and optical observation

Acoustic sounding of the wake behind a circular cylinder and observation of the shadow pattern indicate that for a density gradient varying on distances of the order of the cylinder's vertical dimension two parametrically different vortex systems may coexist in the wake. In the particular case when the profile of the buoyancy frequency is symmetric and its axis coincides with the path along which the cylinder's axis travels, the vortex systems on both sides of the wake are nearly identical. However, if the axes do not coincide, then the structures of the upper and the lower parts of the wake are rather different.If the Froude number Fr=u/NR is based on the flow velocityu, the radius of the cylinderR, and the current value of the buoyancy frequencyN, then the observed flow pattern corresponds to known regime diagrams presented by several authors. In the present experimentsN was found using the characteristic periods of oscillation of the intensity of volume ultrasonic scattering.The vertical profiles of the coefficient of backscattering of ultrasound and the synchronous shadow flow patterns in the wake behind the body are subjected to simultaneous analysis.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 3–12, November–December, 1995.     

Three-dimensional darcian free convection near a stagnation point on an isothermal surface

The unsteady free convection boundary-layer flow in a fluid-saturated porous medium near a general three-dimensional stagnation point is considered. It is shown that the problem can be reduced to an equivalent two-dimensional problem by a simple transformation of variables. The form of solution then depends only on the sign of the quantity a + b, where a and b are the principal curvatures of the body at the stagnation point.     

Boundary Layers and KPP Fronts in a Cellular Flow

We study an eigenvalue problem associated with a reaction-diffusion-advection equation of the KPP type in a cellular flow. We obtain upper and lower bounds on the eigenvalues in the regime of a large flow amplitude A ≪ 1. It follows that the minimal pulsating traveling front speed c _*(A) satisfies the upper and lower bounds C ₁ A ^1/4≦ c _*(A)≦ C ₂ A ^1/4. Physically, the speed enhancement is related to the boundary layer structure of the associated eigenfunction – accordingly, we establish an “averaging along the streamlines” principle for the unique positive eigenfunction.