Turbulent flow of quadrangle mode in interdisk midplane between two shrouded co-rotating disks

Particle image velocimetry (PIV) was employed to study the flow patterns, time-averaged velocity field, and turbulence properties of the flow in the interdisk midplane between two shrouded co-rotating disks at the interdisk spacing to disk radius ratio S = 0.1 and rotating Reynolds number Re = 2.25 × 10⁵. A quadrangle core flow structure rotating at a frequency 75% of the disks’ rotating frequency was observed. The flow in the region outside the quadrangle core flow structure consisted of four cellular flow structures. Five characteristic flow regions—the hub-influenced region, solid-body rotation region, buffer region, vortex region, and shroud-influenced region—were identified in the flow field. Circumferential and radial turbulence intensities, Reynolds stresses, turbulence kinetic energy, correlation coefficients, as well as the Lagrangian integral time and length scales of turbulent fluctuations were analyzed and presented. Features of the turbulence properties were found to be closely related to the rotation motion of the inner and outer characteristic flow structures. The circumferential components of the turbulence properties exhibited local minima in the buffer region and maxima in the solid-body rotation and vortex regions, while the radial components of the turbulence intensity, turbulent normal stress, and Lagrangian integral turbulence time scale exhibited maximum values in the buffer region and relatively low values in the regions near the hub and the shroud.     

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.     

Scanning PIV investigation of the laminar separation bubble on a SD7003 airfoil

A laminar separation bubble occurs on the suction side of the SD7003 airfoil at an angle of attack α =  4–8° and a low Reynolds number less than 100,000, which brings about a significant adverse aerodynamic effect. The spatial and temporal structure of the laminar separation bubble was studied using the scanning PIV method at α =  4° and Re = 60,000 and 20,000. Of particular interest are the dynamic vortex behavior in transition process and the subsequent vortex evolution in the turbulent boundary layer. The flow was continuously sampled in a stack of parallel illuminated planes from two orthogonal views with a frequency of hundreds Hz, and PIV cross-correlation was performed to obtain the 2D velocity field in each plane. Results of both the single-sliced and the volumetric presentations of the laminar separation bubble reveal vortex shedding in transition near the reattachment region at Re = 60,000. In a relatively long distance vortices characterized by paired wall-normal vorticity packets retain their identities in the reattached turbulent boundary layer, though vortices interact through tearing, stretching and tilting. Compared with the restricted LSB at Re = 60,000, the flow at Re = 20,000 presents an earlier separation and a significantly increased reversed flow region followed by “huge” vortical structures.     

Phase-resolved PIV measurements of the flow between a pair of corotating disks in a cylindrical enclosure

This paper presents the measurements of the flow in the space between an enclosed corotating disk pair using particle image velocimetry (PIV) and laser doppler velocimetry (LDV). LDV gives the time history of velocity for time-domain analysis, while PIV provides the spatial distribution of the instantaneous velocity. A flow visualization technique displaying the concentration distribution of seeding particles was also employed to visualize the flow patterns. Experiments were conducted on the interdisk midplane with a Reynolds number of 5.25×10⁵. Based on the LDV measured rotating frequency of the vortices around the hub, the phase-resolved PIV measurements were achieved, and a rotating reference coordinate system was employed to represent the flow patterns. The phase-resolved measurements reveal that the circumferential flow velocity oscillates periodically in both the inner and outer regions but in opposite trends. Based on the phase averaged data, the contributions of the periodic and random motions to the Reynolds stresses were evaluated, and the spatial distributions of the periodic Reynolds stresses were displayed. It is found that, the local rotation of the fluid induced by the deformation of the inner region contribute to a significant portion of the momentum transport.     

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.     

Local measurements of turbulent angular momentum transport in circular Couette flow

We report on velocity fluctuations and the fluctuation-driven radial transport of angular momentum in turbulent circular Couette flow. Our apparatus is short (cylinder height to gap width ratio Γ ~ 2) and of relatively high wall curvature (ratio of cylinder radii η ~ 0.35). Fluctuation levels and the mean specific angular momentum are found to be roughly constant over radius, in accordance with previous studies featuring narrower gaps. Synchronized dual beam Laser Doppler Velocimetry (2D LDV) is used to directly measure the r − θ Reynolds stress component as a function of Reynolds number (Re), revealing approximate scalings in the non-dimensional angular momentum transport that confirm previous measurements of torque in similar flows. 2D LDV further allows for a decomposition of the turbulent transport to assess the relative roles of fluctuation intensity and r − θ cross-correlation. We find that the increasing angular momentum transport with Re is due to intensifying absolute fluctuation levels accompanied by a slightly weakening cross-correlation.     

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.     

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.     

Dual leading-edge vortex structure for flow over a simplified butterfly model

The dye visualization experiments show that a dual leading-edge vortex (LEV) structure exists on the suction side of a simplified butterfly model of Papilio ulysses at α = 8°−12°. Furthermore, the results of particle image velocimetry (PIV) measurement indicate that the axial velocity of the primary (outer) vortex core reaches the lower extreme value while a transition from a “wake-like” to a “jet-like” axial velocity profile occurs. The work reveals for the first time the existence of dual LEV structure on the butterfly-like forward-sweep wing configuration.     

Highly spatially resolving laser Doppler velocity measurements of the tip clearance flow inside a hard disk drive model

The flow in the tip clearance of a hard disk drive model has been investigated with laser Doppler techniques. The flow was driven by co-rotating disks inside a cylindrical enclosure in order to simulate a hard disk drive used for data storage devices. The main focus of the investigation was on the understanding of complex flow behavior in the narrow gap region between the disk tip and the outer shroud wall, which is supposed to be one of the causes of flow induced vibration of the disks. Experiments in the past have never been able to examine this region because of the lack of the spatial resolution of sensors in the highly three-dimensional flow in the region. In the present investigation, the flow velocity in the tip clearance region was measured with optical measurement techniques for the first time. The flow behaviors are investigated for four different conditions with two different gap widths and two different shapes of the shroud walls with and without ribs. The velocity measurements were taken both with conventional laser Doppler velocimetry and using a laser Doppler velocity profile sensor with a spatial resolution in the micrometer range. The circumferential velocity component was measured along the axial and radial directions. The steep gradients of the circumferential mean velocity in both directions were successfully captured with a high spatial resolution, which was achieved by the velocity profile sensor. From the supplementary investigations, the existence of vortex structures in the tip clearance region was confirmed with a dependence on the shroud gap width and the shroud shape. The interactions of the two boundary layers seem to be the source of the complex three-dimensional behaviors of the flow in this region.     

A rotating elliptic airfoil in fluid at rest and in a parallel freestream

This paper reports results of DPIV measurements on a two-dimensional elliptic airfoil rotating about its own axis of symmetry in a fluid at rest and in a parallel freestream. In the former case, we examined three rotating speeds (Re _c,Ω = 400, 1,000 and 2,000), and in the later case, four rotating speeds (Ro _c,Ω = 2.4, 1.2, 0.6 and 0.4), together with two freestream velocities (Re _c,u  = 200 and 1,000) and two starting configurations of the airfoil (i.e., chord parallel to (α ₀ = 0°) or normal (α ₀ = 90°) to the freestream). Results show that a rotating airfoil in a stationary fluid produces two distinct types of vortex structures depending on the Reynolds number. The first type occurs at the lowest Reynolds number (Re _c,Ω = 400), where vortices shed from the two edges or tips of the airfoil dissipated quickly, resulting in the airfoil rotating in a layer of diffused vorticity. The second type occurs at higher Reynolds numbers (i.e., Re _c,Ω = 1,000 and 2,000), where the corresponding vortices rotated together with the airfoil. Due to the vortex suction effect, the torque characteristics are likely to be heavily damped for the first type because of the rapidly subsiding vortex shedding, and more oscillatory for the second type due to persistent presence of tip vortices. In a parallel freestream, increasing the tip-speed ratio (V/U) of the airfoil (i.e., decreasing the Rossby number, Ro _c,Ω) transformed the flow topology from periodic vortex shedding at Ro _c,Ω = 2.4 to the generation of a “hovering vortex” at Ro _c,Ω = 0.6 and 0.4. The presence of the hovering vortex, which has not been reported in literature before, is likely to enhance the lift characteristics of the airfoil. Freestream Reynolds number is found to have minimal effect on the vortex formation and shedding process, although it enhances shear layer instability and produces more small-scale flow structures that affect the dynamics of the hovering vortex. Likewise, initial starting configuration of the airfoil, while affecting the flow transient during the initial phase of rotation, has insignificant effect on the overall flow topology. Unfortunately, technical constraint of our apparatus prevented us from carrying out complimentary force measurements; nevertheless, the results presented herein, which are more extensive than those computed by Lugt and Ohring (1977), will provide useful benchmark data, from which more advanced numerical calculations can be carried out to ascertain the corresponding force characteristics, particularly for those conditions with the presence of hovering vortex.     

On the formation of vortex rings and pairs

The axisymmetric vortex sheet model developed by Nitsche & Krasny (1994) has been extended to study the formation of vortex rings (pairs) at the edge of circular (2D) tube and opening. Computations based on this model are in good agreement with the experiments (Didden (1979) for circular tube and Auerbach (1987) for 2D tube and opening). Using this new model, evidences are provided to show that the main failure of the similarity theory (the false prediction of axial trajectory of vortex ring) is due to its ignorance of the self-induced ring velocity (mutual induction for vortex pair). We further reason why the similarity theory succeeds in its prediction of radial movement of vortex ring. The effects of various parameters such as turning angle α and piston speedU _p (t) on the formation of vortex ring are investigated. Numerical result shows that turning angle α has no effect on circulation shed τ. We also discuss Glezer (1988)'s summary on the influence ofU _p upon the shedding circulation, and finally give the variation of core distribution of vortex ring with α andU _p (t). The project is supported by National Natural Science Foundation of China and Doctoral Program of Institution of Higher Education     

Rheostructural studies of a discotic mesophase pitch at processing flow conditions

The flow-induced microstructure of a mesophase pitch was studied within custom-made dies for changing wall shear rates from 20 to 1,100 s^− 1, a flow scenario that is typically encountered during fiber spinning. The apparent viscosity values, measured at the nominal wall shear rates ranging from 500 to 2,500 s^− 1 using these dies, remain fairly constant. The microstructure was studied in two orthogonal sections: r–θ (cross section) and r–z (longitudinal mid plane). In these dies, the size of the microstructure gradually decreases toward the wall (to as low as a few micrometers), where shear rate is highest. Furthermore, as observed in the r–θ plane of the capillary, for a significant fraction of the cross section, discotic mesophase has a radial orientation. Thus, the directors of disc-like molecules were aligned in the vorticity (θ) direction. As confirmed from the microstructure in the r–z plane, most of the discotic molecules remain nominally in the flow plane. Orientation of the pitch molecules in the shear flow conditions is consistent with that observed in controlled low-shear rheometric experiments reported earlier. Microstructral investigation suggests that the radial orientation of carbon fibers obtained from a mesophase pitch originates during flow of pitch through the die.     

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.     

On Saint-Venant's Principle for a Homogeneous Elastic Arch-Like Region

In this paper, we consider a two-dimensional homogeneous isotropic elastic material state in the arch-like region a ≤ r ≤ b, 0 ≤ θ ≤ α, where (r, θ) denote plane polar coordinates. We assume that three of the edges r = a, r = b, θ = α are traction-free, while the edge θ = 0 is subjected to an (in plane) self-equilibrated load. We define an appropriate measure for the Airy stress function φ and then we establish a clear relationship with the Saint-Venant's principle on such regions. We introduce a cross-sectional integral function I(θ) which is shown to be a convex function and satisfies a second-order differential inequality. Consequently, we establish a version of the Saint-Venant principle for such a curvilinear strip, without requiring of any condition upon the dimensions of the arch-like region.     

Effects of a trapped vortex cell on a thick wing airfoil

The effects of a trapped vortex cell (TVC) on the aerodynamic performance of a NACA0024 wing model were investigated experimentally at Re = 10⁶ and 6.67×10⁵6.67\times 10^{5}. The static pressure distributions around the model and the wake velocity profiles were measured to obtain lift and drag coefficients, for both the clean airfoil and the controlled configurations. Suction was applied in the cavity region to stabilize the trapped vortex. For comparison, a classical boundary layer suction configuration was also tested. The drag coefficient curve of the TVC-controlled airfoil showed sharp discontinuities and bifurcative behavior, generating two drag modes. A strong influence of the angle of attack, the suction rate and the Reynolds number on the drag coefficient was observed. With respect to the clean airfoil, the control led to a drag reduction only if the suction was high enough. Compared to the classical boundary layer suction configuration, the drag reduction was higher for the same amount of suction only in a specific range of incidence, i.e., α = −2° to α = 6° and only for the higher Reynolds number. For all the other conditions, the classical boundary layer suction configuration gave better drag performances. Moderate increments of lift were observed for the TVC-controlled airfoil at low incidence, while a 20% lift enhancement was observed in the stall region with respect to the baseline. However, the same lift increments were also observed for the classical boundary layer suction configuration. Pressure fluctuation measurements in the cavity region suggested a very complex interaction of several flow features. The two drag modes were characterized by typical unsteady phenomena observed in rectangular cavity flows, namely the shear layer mode and the wake mode.     

Experimental investigations of a swirling jet in both stationary and rotating surroundings

The ‘plug’ flow emerging from a long rotating tube into a large stationary reservoir was used in the experimental investigation of swirling jets with Reynolds numbers, Re = 600, 1,000 and 2,000, and swirl numbers, S = ΩR/U, in the range 0–1.1, to cover flow regimes from the non-rotating jet to vortex breakdown. Here Ω is the nozzle rotation rate, R is the radius of the nozzle exit, and U is the mean mass axial velocity. The jet was more turbulent and eddies shed faster at larger Re. However the flow criticality and shear layer morphology remained unchanged with Re. After the introduction of sufficient rotation, co-rotating and counter-winding helical waves replaced vortex rings to become the dominant vortex structure. The winding direction of the vortex lines suggests that Kelvin–Helmholtz and generalized centrifugal instability dominated the shear layer. A quantitative visualization study has been carried out for cases where the reservoir was rotating independently with S _a  = Ω _a R/U = ±0.35, ±0.51 and ±0.70 at Re = 1,000 and 2000, where Ω _a is the rotation rate of the reservoir. The criterion for breakdown was found to be mainly dependent on the absolute swirl number of the jet, S. This critical swirl number was slightly different in stationary and counter-swirl surroundings but obviously smaller when the reservoir co-rotated, i.e. S _c  = 0.88, 0.85 and 0.70, respectively. These results suggest that the flow criticality depends mainly on the velocity distributions of the vortex core, while instabilities resulting from the swirl difference between the jet and its ambient seem to have only a secondary effect.     

The formation of vortex rings in a strongly forced round jet

The periodic formation of vortex rings in the developing region of a round jet subjected to high-amplitude acoustic forcing is investigated with High-Speed Particle Image Velocimetry. Harmonic velocity oscillations ranging from 20 to 120% of the mean exit velocity of the jet was achieved at several forcing frequencies determined by the acoustic response of the system. The time-resolved history of the formation process and circulation of the vortex rings are evaluated as a function of the forcing conditions. Overall, high-amplitude forcing causes the shear layers of the jet to breakup into a train of large-scale vortex rings, which share many of the features of starting jets. Features of the jet breakup such as the roll-up location and vortex size were found to be both amplitude and frequency dependent. A limiting time-scale of t/T ≈ 0.33 based on the normalized forcing period was found to restrict the growth of a vortex ring in terms of its circulation for any given arrangement of jet forcing conditions. In sinusoidally forced jets, this time-scale corresponds to a kinematic constraint where the translational velocity of the vortex ring exceeds the shear layer velocity that imposes pinch-off. This kinematic constraint results from the change in sign in the jet acceleration between t = 0 and t = 0.33T. However, some vortex rings were observed to pinch-off before t = 0.33T suggesting that they had acquired their maximum circulation. By invoking the slug model approximations and defining the slug parameters based on the experimentally obtained time- and length-scales, an analytical model based on the slug and ring energies revealed that the formation number for a sinusoidally forced jet is L/D ≈ 4 in agreement with the results of Gharib et al. (J Fluid Mech 360:121–140, 1998).     

Effects of magnetic field,porosity, and wall properties for anisotropically elastic multi-stenosis arteries on blood flow characteristics

A mathematical model for blood flow through an elastic artery with multistenosis under the effect of a magnetic field in a porous medium is presented. The considered arterial segment is simulated by an anisotropically elastic cylindrical tube filled with a viscous incompressible electrically conducting fluid representing blood. An artery with mild local narrowing in its lumen forming a stenosis is analyzed. The effects of arterial wall parameters represent viscoelastic stresses along the longitudinal and circumferential directions T _t and T _θ , respectively. The degree of anisotropy of the vessel wall γ, total mass of the vessel, and surrounding tissues M and contributions of the viscous and elastic constraints to the total tethering C and K respectively on resistance impedance, wall shear stress distribution, and radial and axial velocities are illustrated. Also, the effects of the stenosis shape m, the constant of permeability X, the Hartmann number H _α and the maximum height of the stenosis size δ on the fluid flow characteristics are investigated. The results show that the flow is appreciably influenced by surrounding connective tissues of the arterial wall motion, and the degree of anisotropy of the vessel wall plays an important role in determining the material of the artery. Further, the wall shear stress distribution increases with increasing T _t and γ while decreases with increasing T _θ , M, C, and K. Transmission of the wall shear stress distribution and resistance impedance at the wall surface through a tethered tube are substantially lower than those through a free tube, while the shearing stress distribution at the stenosis throat has inverse characteristic through totally tethered and free tubes. The trapping bolus increases in size toward the line center of the tube as the permeability constant X increases and decreases with the Hartmann number Ha increased. Finally, the trapping bolus appears, gradually in the case of non-symmetric stenosis, and disappears in the case of symmetric stenosis. The size of trapped bolus for the stream lines in a free isotropic tube (i.e., a tube initially unstressed) is smaller than those in a tethered tube.     

Some Reynolds number effects on two- and three-dimensional turbulent boundary layers

Experimental data for a two-dimensional (2-D) turbulent boundary layer (TBL) flow and a three-dimensional (3-D) pressure-driven TBL flow outside of a wing/body junction were obtained for an approach Reynolds number based on momentum thickness of Re _θ =23,200. The wing shape had a 3:2 elliptical nose, NACA 0020 profiled tail, and was mounted on a flat wall. Some Reynolds number effects are examined using fine spatial resolution (Δy ⁺=1.8) three-velocity-component laser-Doppler velocimeter measurements of mean velocities and Reynolds stresses at nine stations for Re _θ =23,200 and previously reported data for a much thinner boundary layer at Re _θ =5,940 for the same wing shape. In the 3-D boundary layers, while the stress profiles vary considerably along the flow due to deceleration, acceleration, and skewing, profiles of the parameter correlate well and over available Reynolds numbers. The measured static pressure variations on the flat wall are similar for the two Reynolds numbers, so the vorticity flux and the measured mean velocities scaled on wall variables agree closely near the wall. The stresses vary similarly for both cases, but with higher values in the outer region of the higher Re _θ case. The outer layer turbulence in the thicker high Reynolds number case behaves similarly to a rapid distortion of the flow, since stream-wise vortical effects from the wall have not diffused completely through the boundary layer at all measurement stations. Received: 9 June 2000/Accepted: 26 January 2001