An inviscid model for vortex shedding from a deforming body

An inviscid vortex sheet model is developed in order to study the unsteady separated flow past a two-dimensional deforming body which moves with a prescribed motion in an otherwise quiescent fluid. Following Jones (J Fluid Mech 496, 405–441, 2003) the flow is assumed to comprise of a bound vortex sheet attached to the body and two separate vortex sheets originating at the edges. The complex conjugate velocity potential is expressed explicitly in terms of the bound vortex sheet strength and the edge circulations through a boundary integral representation. It is shown that Kelvin’s circulation theorem, along with the conditions of continuity of the normal velocity across the body and the boundedness of the velocity field, yields a coupled system of equations for the unknown bound vortex sheet strength and the edge circulations. A general numerical treatment is developed for the singular principal value integrals arising in the solution procedure. The model is validated against the results of Jones (J Fluid Mech 496, 405–441, 2003) for computations involving a rigid flat plate and is subsequently applied to the flapping foil experiments of Heathcote et al. (AIAA J, 42, 2196–2204, 2004) in order to predict the thrust coefficient. The utility of the model in simulating aquatic locomotion is also demonstrated, with vortex shedding suppressed at the leading edge of the swimming body.      

Flow past a plate with a moving surface

On the basis of a numerical solution of the unsteady Navier-Stokes equations, the flow past a finite plate with an upstream-moving surface is investigated. For the Reynolds numbers Re =10²−10⁴, the flow past the plate is analyzed as a function of the relative plate surface velocity. On the basis of this analysis a limiting mathematical model of the flow as Re → ∞ is proposed.     

Unsteady PTV velocity field past an airfoil solved with DNS: Part 1. Algorithm of hybrid simulation and hybrid velocity field at <Emphasis Type="Italic">Re</Emphasis> ≈ 10<Superscript>3</Superscript>

We develop a hybrid unsteady-flow simulation technique combining direct numerical simulation (DNS) and particle tracking velocimetry (PTV) and demonstrate its capabilities by investigating flows past an airfoil. We rectify instantaneous PTV velocity fields in a least-squares sense so that they satisfy the equation of continuity, and feed them to the DNS by equating the computational time step with the frame rate of the time-resolved PTV system. As a result, we can reconstruct unsteady velocity fields that satisfy the governing equations based on experimental data, with the resolution comparable to numerical simulation. In addition, unsteady pressure distribution can be solved simultaneously. In this study, particle velocities are acquired on a laser-light sheet in a water tunnel, and unsteady flow fields are reconstructed with the hybrid algorithm solving the incompressible Navier–Stokes equations in two dimensions. By performing the hybrid simulation, we investigate nominally two-dimensional flows past the NACA0012 airfoil at low Reynolds numbers. In part 1, we introduce the algorithm of the proposed technique and discuss the characteristics of hybrid velocity fields. In particular, we focus on a vortex shedding phenomenon under a deep stall condition (α = 15°) at Reynolds numbers of Re = 1000 and 1300, and compare the hybrid velocity fields with those computed with two-dimensional DNS. In part 2, the extension to higher Reynolds numbers is considered. The accuracy of the hybrid simulation is evaluated by comparing with independent experimental results at various angles of attack and Reynolds numbers up to Re = 10⁴. The capabilities of the hybrid simulation are also compared with two-dimensional unsteady Reynolds-Averaged Navier–Stokes (URANS) solutions in part 2. In the first part of these twin papers, we demonstrate that the hybrid velocity field approaches the PTV velocity field over time. We find that intensive alternate vortex shedding past the airfoil, which is predicted by the two-dimensional DNS, is substantially suppressed in the hybrid simulation and the resultant flow field is similar to the PTV velocity field, which is projection of the three-dimensional velocity field on the streamwise plane. We attempt to identify the motion that originates three-dimensional flow patterns by highlighting the deviation of the PTV velocity field from the two-dimensional governing equations at each snapshot. The results indicate that the intensive spots of the deviation appear in the regions in which three-dimensional instabilities are induced in the shear layer separated from the pressure side.     

Unsteady theory of the hydrofoil of finite span

A three-dimensional unsteady flow around the hydrofoil has been dealt with in this paper. Under the assumption of infinitesimal wave and thin hydrofoil, analytic solution of perturbation velocity potential induced by the unsteady flow of a hydrofoil which is simplified as a series of rectangular vortex rings is achieved and then the unsteady forces can be evaluated. The paper had been accepted by the X VI th International Congress of IUTAM, Lyngby, Denmark, Aug. 19–25, 1985.     

Unsteady filtration of a gas

The unsteady filtering flow of a gas described by the equations of motion proposed by Khristianovich in [1] is investigated. It is shown that for the gas flow in the pores a critical regime can develop when the reduced velocity (an analog of the Mach number in gas dynamics) is less than unity. The reduced velocity is the ratio of the flow velocity to the velocity of propagation of small filtering perturbations at a given point of the flow. St Petersburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 201–203, January–February, 1994.     

Dependence of the wake on inclination of a stationary cylinder

Three-dimensional vorticity in the wake of an inclined stationary circular cylinder was measured simultaneously using a multi-hot wire vorticity probe over a streamwise range of x/d = 10–40. The study aimed to examine the dependence of the wake characteristics on cylinder inclination angle α (=0°–45°). The validity of the independence principle (IP) for vortex shedding was also examined. It was found that the spanwise mean velocity which represents the three-dimensionality of the wake flow, increases monotonically with α. The root-mean-square (rms) values of the streamwise (u) and spanwise (w) velocities and the three vorticity components decrease significantly with the increase of α, whereas the transverse velocity (v) does not follow the same trend. The vortex shedding frequency decreases with the increase of α. The Strouhal number (St _N), obtained by using the velocity component normal to the cylinder axis, remains approximately a constant within the experimental uncertainty (±8%) when α is smaller than about 40°. The autocorrelation coefficients ρ _u and ρ _v of the u and v velocity signals show apparent periodicity for all inclination angles. With increasing α, ρ _u and ρ _v decrease and approach zero quickly. In contrast, the autocorrelation coefficient ρ _w of w increases with α in the near wake, implying an enhanced three-dimensionality of the wake.     

Unsteady supersonic flow around blunt bodies with detached shock wave

The numerical method of calculating the supersonic three-dimensional flow about blunt bodies with detached shock wave presented in [1–3] is applied to the case of unsteady flow. The formulation of the unsteady problem is analogous to that of [4], which assumes smallness of the unsteady disturbances.The paper presents some results of a study of the unsteady flow about blunt bodies over a wide range of variation of the Mach number M=1.50– and dimensionless oscillation frequency l/V=0–1.0. A comparison is made with the results obtained from the Newton theory.     

Experimental study of vortex structures in a hypersonic shock layer on a flat plate

The characteristics of travelling perturbations of density in a hypersonic shock layer on a flat plate for the Mach number M_∞=21 and unit Reynolds numberRe ₁=6·10⁵ m⁻¹ were experimentally studied by the method of electron-beam fluorescence. The perturbations were generated by interaction of the shock layer behind an oblique gas-dynamic whistle and the leading edge of the plate. The cases of unsteady and quasi-steady interaction were considered. In both cases, vortex disturbances of finite amplitude were generated. The measurements were performed at the fundamental frequency F=0.6·10⁻⁴ and at the harmonic; the streamwise phase velocities, the growth rates of the disturbances, and the angles of wave propagation were obtained. The measurement results are compared with some experimental data for subsonic flows, some particular results of the linear stability theory for compressible flows, and the results obtained on the basis of a simple model of the nonlinear stage of disturbance evolution in a hypersonic boundary layer. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 6, pp. 41–47, November–December, 1999.     

The Effect of Sweep-Angle Variation on the Turbulence Structure in a Separated,Three-Dimensional Flow

A three-dimensional separated flow behind a swept, backward-facing step is investigated by means of DNS for Re _H = C _∞ H/ν = 3000 with the purpose to identify changes in the statistical turbulence structure due to a variation of the sweep angle α from 0° up to 60°. With increasing sweep angle, the near-wall turbulence structure inside the separation bubble and downstream of reattachment changes due to the presence of an edge-parallel mean flow component W. Turbulence production due to the spanwise shear ∂W/∂y at the wall becomes significant and competes with the processes caused by impingement of the separated shear-layer. Changes due to a sweep angle variation can be interpreted in terms of two competing velocity scales which control the global budget of turbulent kinetic energy: the step-normal component U _∞ = C _∞cosα throughout the separated flow region and the velocity difference C _∞ across the entire shear-layer downstream of reattachment. As a consequence, the significance of history effects for the development into a two-dimensional boundary layer decreases with increasing sweep angle. For α ≥50°, near-wall streaks tend to form inside the separated flow region. Received 7 November 2000 and accepted 9 July 2002 Published online 3 December 2002 RID="*" ID="*" Part of this work was funded by the Deutsche Forschungsgemeinschaft within Sfb 557. Computer time was provided by the Konrad-Zuse Zentrum (ZIB), Berlin. Communicated by R.D. Moser     

Near-ground tornado-like vortex structure resolved by particle image velocimetry (PIV)

The near-ground flow structure of tornadoes is of utmost interest because it determines how and to what extent civil structures could get damaged in tornado events. We simulated tornado-like vortex flow at the swirl ratios of S = 0.03–0.3 (vane angle θ_v = 15°–60°), using a laboratory tornado simulator and investigated the near-ground-vortex structure by particle imaging velocimetry. Complicated near-ground flow was measured in two orthogonal views: horizontal planes at various elevations (z = 11, 26 and 53 mm above the ground) and the meridian plane. We observed two distinct vortex structures: a single-celled vortex at the lowest swirl ratio (S = 0.03, θ_v = 15°) and multiple suction vortices rotating around the primary vortex (two-celled vortex) at higher swirl ratios (S = 0.1–0.3, θ_v = 30°–60°). We quantified the effects of vortex wandering on the mean flow and found that vortex wandering was important and should be taken into account in the low swirl ratio case. The tangential velocity, as the dominant velocity component, has the peak value about three times that of the maximum radial velocity regardless of the swirl ratio. The maximum velocity variance is about twice at the high swirl ratio (θ_v = 45°) that at the low swirl ratio (θ_v = 15°), which is contributed significantly by the multiple small-scale secondary vortices. Here, the results show that not only the intensified mean flow but greatly enhanced turbulence occurs near the surface in the tornado-like vortex flow. The intensified mean flow and enhanced turbulence at the ground level, correlated with the ground-vortex interaction, may cause dramatic damage of the civil structures in tornadoes. This work provides detailed characterization of the tornado-like vortex structure, which has not been fully revealed in previous field studies and laboratory simulations. It would be helpful in improving the understanding of the interaction between the tornado-like vortex structure and the ground surface, ultimately leading to better predictions of tornado-induced wind loads on civil structures.     

Effect of streamwise structures on heat transfer in a hypersonic flow in a compression corner

Coefficients of heat transfer to the surface in a laminar hypersonic flow (M _∞ = 21) over plane and axisymmetric models with a compression corner are presented. These coefficients are measured by an infrared camera. The parameters varied in the experiments are the angle of the compression corner and the distance to the corner point. Characteristics of the flow with and without separation in the corner configuration are obtained. The measured results are compared with direct numerical simulations performed by solving the full unsteady Navier-Stokes equations. Experiments with controlled streamwise structures inserted into the flow are described. A substantial increase in the maximum values of the heat-transfer coefficient in the region of flow reattachment after developed laminar separation is demonstrated. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 112–120, July–August, 2009.     

Numerical modeling of the rotation of a solid body with a liquid-filled cavity having radial ribs

The boundary-value problem of unsteady vortex flow of a viscous incompressible fluid in a cylindrical vessel with radial ribs rotating at a variable angular velocity is solved using a finite-difference method. The results of the solution are used to calculate the motion of a system of a solid body and a cavity filled with a liquid. The results are compared with available experimental data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 135–139, March–April, 2007.     

The effects of acceleration in jets: kinematics of the near field vortices

Direct and large-eddy simulations (DNS/LES) of accelerating round jets are used to analyze the effects of acceleration on the kinematics of vortex rings in the near field of the jet (x/D < 12). The acceleration is obtained by increasing the nozzle jet velocity with time, in a previously established (steady) jet, and ends once the inlet jet velocity is equal to twice its initial value. Several acceleration rates (α = 0.02–0.6) and Reynolds numbers (Re _D = 500–20000) were simulated. Acceleration maps were used to make a detailed study of the kinematics of vortex rings in accelerating jets. One of the effects of the acceleration is to cause a number of new primary and secondary vortex merging events that are absent from steady jets. As the acceleration rate α increases, both the number of primary merging events between rings and the axial position where these take place decreases. The statistics for the speed of the starting ring that forms at the start of the acceleration phase for each simulation, agree well with the statistics for the “front” speed observed by Zhang and Johari (Phys Fluids 8:2185–2195, 1996). Acceleration maps and flow visualizations show that during the acceleration phase the near field coherent vortices become smaller and are formed at an higher frequency than in the steady jet, and their (mean) shedding frequency increases linearly with the acceleration rate. Finally, it was observed that the acceleration decreases the spreading rate of the jet, in agreement with previous experimental works.      

Receptivity of the boundary layer on a flat plate with a blunted leading edge to steady nonuniformity of the free stream

The flow past a flat plate with a blunted leading edge by a flow of a viscous incompressible fluid with a small spanwise-periodic, steady nonuniformity of the velocity profile is considered. Such a flow simulates the interaction of one type of vortex disturbances of a turbulent external flow with the boundary layer. The solution obtained predicts generation of strong disturbances in the boundary layer, which are similar to the streaky structure observed in the case of high free-stream turbulence. It is shown that the boundary-layer flow on blunted bodies is more sensitive to vortex disturbances than on a plate with a sharp leading edge. Central Aerohydrodynamic Institute, Zhukovskii, 140160. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 4, pp. 93–100, July–August, 2000.     

Special case of a traveling wave in one model of a multicomponent medium

The Kuropatenko model for a multicomponent medium whose components are polytropic gases is considered. It is assumed that, as x → ±∞, the multicomponent medium is in a homogeneous state with constant gas-dynamic parameters — velocity, pressure, and temperature. For the traveling wave flows, conditions similar to the Hugoniot conditions are obtained and used to uniquely determine the flow parameters for x → −∞ from the flow parameters x → +∞ and traveling wave velocity. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 39–47, July–August, 2009.     

Near-field tip vortex behind a swept wing model

The near-field flow structure of a tip vortex behind a sweptback and tapered NACA 0015 wing was investigated and compared with a rectangular wing at the same lift force and Re=1.81×10⁵. The tangential velocity decreased with the downstream distance while increased with the airfoil incidence. The core radius was about 3% of the root chord c _r, regardless of the downstream distance and α for α<8°. The core axial velocity was always wake-like. The core Γ_c and total Γ_o circulation of the tip vortex remained nearly constant up to x/c _r=3.5 and had a Γ_c/Γ_o ratio of 0.63. The total circulation of the tip vortex accounted for only about 40% of the bound root circulation Γ_b. For a rectangular wing, the axial flow exhibited islands of wake- and jet-like velocity distributions with Γ_c/Γ_o=0.75 and Γ_o/Γ_b=0.70. For the sweptback and tapered wing tested, the inner region of the tip vortex flow exhibited a self-similar behavior for x/c _r≥1.0. The lift force computed from the spanwise circulation distributions agreed well with the force-balance data. A large difference in the lift-induced drag was, however, observed between the wake integral method and the inviscid lifting-line theory.     

Measuring velocity fields in wind tunnels with holographic interferometry

This paper investigates the feasibility of using holographic interferometry in wind tunnel flows for measuring velocity fields rather than density or temperature fields. First results were obtained in a vortex street behind a cylinder at Re=190(U _∞=0.7 m/s). The light scattered from an illuminated fluid plane was holographically recorded twice with the same reference beam. Using a time interval of 10 μs, local fluid displacements smaller than a few microns were recorded. The holographic plate was placed in front and as close as possible to the fluid plane. The interferograms obtained from the hologram reconstruction give information about one velocity component, at 45° with the illuminated plane. The alignment of the cylinder axis with this 45° direction provided definite confirmation about the vortex street having a non-negligible axial velocity. The constant velocity fluid region has proven to be very useful for quantifying the velocity information contained in the interferogram. Received: 8 November 1999/Accepted: 14 March 2000     

Pulsatile flows in a lateral aneurysm anchored on a stented and curved parent vessel

We present particle tracking velocimetry measurements and flow visualization of pulsatile flow fields in a stented cerebrovascular lateral aneurysm model with a wide ostium anchored on a curved parent vessel. Among the stent parameters, the blocking ratioC _α ranging from 0% to 75% was selected to study its effect on the changes of intra-aneurysmal hemodynamics for the reference of minimally invasive endovascular aneurysm treatment. The Womersley number was 3.9 and the mean, peak, and minimal Reynolds numbers based on the bulk average velocity and diameter of the parent vessel were 600, 850, and 300, respectively. The results are characterized in terms of velocity vector field, coded streak images, region averaged velocity, vorticity, and wall shear stress. A critical range ofC _α related to the inflow location as well as the shape and number of intra-aneurysmal vortices is identified. The intra-aneurysmal flow activity, vortex strength, and wall shear stress are found to decrease with increasingC _α. Among theC _α examined,C _α=75% is the most favorable in attenuating the risk of aneurysmal rupture and promoting intra-aneurysmal thrombus.     

To formulating a nonlinear initial-boundary problem of an unsteady separated flow around an airfoil

A general formulation of a nonlinear initial-boundary problem of an unsteady separated flow around an airfoil by an ideal incompressible fluid is considered. The problem is formulated for a complex velocity. Conditions of shedding of vortex wakes from the airfoil are analyzed in detail. The proposed system of functional relations allows constructing algorithms for solving a wide class of problems of the wing theory. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 48–56, March–April, 2007.     

Pulsatile entrance flow in curved pipes: effect of various parameters

This paper presents the results of an experimental study on the developing pulsatile flow in curved pipes with a long, straight pipe upstream. In order to examine the dependence of flow-field development on the governing parameters, LDV measurements were conducted systematically for six cases of flow, where the Womersley number α was varied from 5.5 to 18, the mean Dean number D _m was 200 and 300, the flow rate ratio η was 0.5 and 1, and the curvature radius ratio Rc was 10 and 30. Peculiar flow phenomena, such as flow reversal for all values of α and a depression in the axial velocity profile for α = 10, were analyzed by decomposing the axial velocity into a time-mean and a varying component, as well as by obtaining the bias of their profiles. The velocity distributions abruptly change with the phase at turn angles Ω of 15–30°, corresponding to the nondimensional axial length z′ ≅ 1–2 from the bend entrance, and their development along the pipe axis is the most complicated for the flow at a moderate α of 10 and large η of 1. The entrance length in the case of pulsatile flow is shorter than that for steady flow with the same flow rate as the maximum pulsatile flow rate.