The ultra-low Reynolds number airfoil wake

Lift force and the near wake of an NACA 0012 airfoil were measured over the angle (α) of attack of 0°–90° and the chord Reynolds number (Re _c ), 5.3 × 10³–5.1 × 10⁴, with a view to understand thoroughly the near wake of the airfoil at low- to ultra-low Re _c . While the lift force is measured using a load cell, the detailed flow structure is captured using laser-Doppler anemometry, particle image velocimetry, and laser-induced fluorescence flow visualization. It has been found that the stall of an airfoil, characterized by a drop in the lift force, occurs at Re _c  ≥ 1.05 × 10⁴ but is absent at Re _c  = 5.3 × 10³. The observation is connected to the presence of the separation bubble at high Re _c but absence of the bubble at ultra-low Re _c , as evidenced in our wake measurements. The near-wake characteristics are examined and discussed in detail, including the vortex formation length, wake width, spanwise vorticity, wake bubble size, wavelength of K–H vortices, Strouhal numbers, and their dependence on α and Re _c .     

Dynamical deformation of a flat liquid–liquid interface

The passage of solid spheres through a liquid–liquid interface was experimentally investigated using a high-speed video and PIV (particle image velocimetry) system. Experiments were conducted in a square Plexiglas column of 0.1 m. The Newtonian Emkarox (HV45 50 and 65% wt) aqueous solutions were employed for the dense phase, while different silicone oils of different viscosity ranging from 10 to 100 mPa s were used as light phase. Experimental results quantitatively reveal the effect of the sphere’s size, interfacial tension and viscosity of both phases on the retaining time and the height of the liquid entrained behind the sphere. These data were combined with our previous results concerning the passage of a rising bubble through a liquid–liquid interface in order to propose a general relationship for the interface breakthrough for the wide range of Mo ₁/Mo ₂ ∈ [2 × 10⁻⁵–5 × 10⁴] and Re ₁/Re ₂ ∈ [2 × 10⁻³–5 × 10²].     

Study of airborne particles produced by normal impact of millimetric droplets onto a liquid film

The aim of this work is to carry out an experimental investigation into the generation of airborne microparticles when millimetric droplets of aqueous solutions impact onto a liquid film. Impact experiments using 3.9 mm diameter droplets were carried out for Weber numbers between 159 and 808, with a fixed Ohnesorge number of 2 × 10⁻³ and film parameters S _f (the ratio between the thickness of the liquid film h _film and the diameter of the impacting droplet d _i) between 0.3 and 1. Observed results show that the deposition/splashing threshold is independent of the parameter S _f in agreement with the data in the literature. The aerosol measurement results demonstrate the production of solid particles from the evaporation of secondary microdroplets with diameters less than 30 μm formed when splash occurs. The median diameter of these microdroplets is around 20 μm, corresponding to a value of d ₅₀/d _i = 5 × 10⁻³. Taken together, the results show that the mass and the number of particles emitted increase as the Weber number increases. Moreover, at a Weber number of 808, the results show that the mass and number of particles emitted increases as the parameter S _f decreases. In this case, the mean number of microdroplets emitted per impact is equal to 14 for S _f = 1 and equal to 76 for S _f = 0.3.     

Numerical modelling of film cooling with and without mist injection

Two-phase CFD calculations, using a Lagrangian model and commercial code Fluent 6.2.16, were employed to calculate the gas and droplet flows and film cooling effectiveness with and without mist on a flat plate. Two different three dimensional geometries are generated and the effects of the geometrical shape, size of droplets, mist concentration in the coolant flow and temperature of mainstream flow for different blowing ratios are studied. A cylindrical and laterally diffused hole with a streamwise angle of 30° and spanwise angle of 0° are used. The diameter of film cooling (d) hole, and the hole length to diameter ratio (L/d) for both of geometries are 10 mm and 4, respectively. Also the blowing ratio ranges from 1.0 to 2.0, and the mainstream Reynolds number based on the mainstream velocity and hole diameter (Re _d) is 6,219. The results are shown for different droplets diameters (1–10 μm), concentrations (1–5%) and mainstream temperatures (350–500 K). The centreline effectiveness and distribution of effectiveness on the surface of cooling wall are presented.     

Heat transfer from a surface fitted with rectangular blocks at different orientation angle

 An experimental investigation was carried out to study the enhancement of the heat transfer from a heated flat plate fitted with rectangular blocks of 1 × 2 × 2 cm³ dimensions in a channel flow as a function of Reynolds number (Re_h), spacing (S _y ) of blocks in the flow direction, and the block orientation angle (α) with respect to the main flow direction. The experiments were performed in a channel of 18 cm width and 10 cm height, with air as the working fluid. For fixed S _x =3.81 cm, which is the space between the blocks in transverse to the flow direction, the experimental ranges of the parameters were S _y =3.33–4.33 cm, α=0–45°, Re_h=7625–31550 based on the hydraulic diameter and the average velocity at the beginning of the test section in the channel. Correlations for Nusselt number were developed, and the ratios of heat transfer with blocks to those with no blocks were given. The results indicated that the heat transfer could be enhanced or reduced depending on the spacing between blocks, and the block orientation angle. The maximum heat transfer rate was obtained at the orientation angle of 45°. Received on 13 December 2000 / Published online: 29 November 2001     

Turbulent wall pressure fluctuation measurements on a towed model at high Reynolds numbers

Turbulent wall pressure fluctuation measurements were made in water on a towed model of length 129.8 (m) and diameter 3.8 (cm) for steady speeds from 6.2 (m/s) to 15.5 (m/s). The drag on the model was measured with a strut mounted load cell which provided estimates of the momentum thickness and friction velocity. Momentum thickness Reynolds numbers Re _θ varied from 4.8 × 10⁵ to 1.1 × 10⁶. The ratio of momentum thickness to viscous length scale is significantly greater than for flat plate cases at comparable Re _θ. The effectiveness of inner and outer velocity and length scales for collapsing the pressure spectra are discussed. The wavenumber–frequency spectra show a convective ridge at higher frequencies similar to flat plate boundary layers. At low frequencies, energy broad in wavenumber extends outside the convective ridge and acoustic cone, with no characteristic wave speed. Wall pressure cross-spectral levels scaled with similarity variables are shown to increase with increasing tow speed, and to follow decay constants consistent with flat plate cases. The convection velocities also display features similar to flat plate cases.     

Reynolds Number Effects on the Coherent Dynamics of the Turbulent Horseshoe Vortex System

The adverse pressure gradient induced by a surface-mounted obstacle in a turbulent boundary layer causes the approaching flow to separate and form a dynamically rich horseshoe vortex system (HSV) in the junction of the obstacle with the wall. The Reynolds number of the flow (Re) is one of the important parameters that control the rich coherent dynamics of the vortex, which are known to give rise to low-frequency, bimodal fluctuations of the velocity field (Devenport and Simpson, J Fluid Mech 210:23–55, 1990; Paik et al., Phys Fluids 19:045107, 2007). We carry out detached eddy simulations (DES) of the flow past a circular cylinder mounted on a rectangular channel for Re = 2.0 × 10⁴ and 3.9 × 10⁴ (Dargahi, Exp Fluids 8:1–12, 1989) in order to systematically investigate the effect of the Reynolds number on the HSV dynamics. The computed results are compared with each other and with previous experimental and computational results for a related junction flow at a much higher Reynolds number (Re = 1.15 × 10⁵) (Devenport and Simpson, J Fluid Mech 210:23–55, 1990; Paik et al., Phys Fluids 19:045107, 2007). The computed results reveal significant variations with Re in terms of the mean-flow quantities, turbulence statistics, and the coherent dynamics of the turbulent HSV. For Re = 2.0 × 10⁴ the HSV system consists of a large number of necklace-type vortices that are shed periodically at higher frequencies than those observed in the Re = 3.9 × 10⁴ case. For this latter case the number of large-scale vortical structures that comprise the instantaneous HSV system is reduced significantly and the flow dynamics becomes quasi-periodic. For both cases, we show that the instantaneous flowfields are dominated by eruptions of wall-generated vorticity associated with the growth of hairpin vortices that wrap around and disorganize the primary HSV system. The intensity and frequency of these eruptions, however, appears to diminish rapidly with decreasing Re. In the high Re case the HSV system consists of a single, highly energetic, large-scale necklace vortex that is aperiodically disorganized by the growth of the hairpin mode. Regardless of the Re, we find pockets in the junction region within which the histograms of velocity fluctuations are bimodal as has also been observed in several previous experimental studies.     

Supersonic leeside flow topology on delta wings revisited

The leeside vortex structures on delta wings with sharp leading edges were studied for supersonic flow at the Institute of Theoretical and Applied Mechanics of the Russian Academy of Sciences in Novosibirsk. The experiments were carried out with three wings with sweep angles of χ=68°, 73°, and 78° and parabolic profiles in the 0.6 × 0.6 m² test section of the blow-down wind tunnel T-313 of the institute. The test conditions were varied from Mach numbers M=2 to 4, unit Reynolds numbers from Re _l=26 × 10⁶ to 56 × 10⁶ m⁻¹, and angles of attack from α=0° to 22°. The results of the investigations revealed that for certain flow conditions shocks are formed above, below, and between the primary vortices. The experimental data were accurate enough to detect the onset of secondary and tertiary separation as well as other boundaries. The various flow regimes discussed in the literature were extended in several cases. The major findings are reported. Received: 6 September 1999/Accepted: 24 January 2000     

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.     

Transient natural convection cooling of a high Prandtl number fluid in a cubical cavity

This work presents a numerical analysis of the effects of thermal boundary conditions, fluid variable viscosity and wall conduction on transient laminar natural convection of a high Prandtl number (Pr=4×10⁴) fluid (Golden Syrup) in a cubical cavity. The simulations consider physical situations realizable at laboratory scale using a cavity with Plexiglas walls of 1 cm of thickness, and inside dimension of L=20 cm. The initial Rayleigh (Ra) number is 10⁶. The cavity is initially full of fluid at rest and at constant temperature (T _i =45°C) higher than the temperature of the walls (T _w =25°C). The time evolution of the flow patterns, the temperature contours, the mean temperature of the fluid and the Nusselt number (Nu) of eight different cases of cooling are presented and analyzed.     

Scalar dispersion in the near wake of a simplified model car

Experimental results on tracer gas diffusion within the near wake of a simplified model car (Ahmed model with a rear slant angle of 25°) are presented. Pollutant emission is simulated using heated air injected through a small pipe at one side of the model base. Fine cold wire thermometry is used to measure instantaneous temperature excess in the near wake. Characteristics of the temperature field over the Reynolds number range (1.3×10⁴<Re _L<7×10⁴) show strong differences as a result of transition in the wake at a critical Reynolds number Re _Lc=2.7×10⁴.     

Roughness induced forced convective laminar-transitional micropipe flow: energy and exergy analysis

Variable fluid property continuity, Navier–Stokes and energy equations are solved for roughness induced forced convective laminar-transitional flow in a micropipe. Influences of Reynolds number, heat flux and surface roughness, on the momentum-energy transport mechanisms and second-law of thermodynamics, are investigated for the ranges of Re = 1–2,000, Q = 5–100 W/m² and ε = 1–50 μm. Numerical investigations put forward that surface roughness accelerates transition with flatter velocity profiles and increased intermittency values (γ); such that a high roughness of ε = 50 μm resulted in transitional character at Re _tra = 450 with γ = 0.136. Normalized friction coefficient (C _f^*) values showed augmentation with Re, as the evaluated C _f^* are 1.006, 1.028 and 1.088 for Re = 100, 500 and 1,500, respectively, at ε = 1 μm, the corresponding values rise to C _f^* = 1.021, 1.116 and 1.350 at ε = 50 μm. Heat transfer rates are also recorded to rise with Re and ε; moreover the growing influence of ε on Nusselt number with Re is determined by the Nu _ε=50 μm/Nu _ε=1 μm ratios of 1.086, 1.168 and 1.259 at Re = 500, 1,000 and 1,500. Thermal volumetric entropy generation values decrease with Re and ε in heating; however the contrary is recorded for frictional volumetric entropy generation data, where the augmentations in are more considerable when compared with the decrease rates of      

Comparison of experimental data with results of some drying models for regularly shaped products

This paper presents an experimental and theoretical investigation of drying of moist slab, cylinder and spherical products to study dimensionless moisture content distributions and their comparisons. Experimental study includes the measurement of the moisture content distributions of slab and cylindrical carrot, slab and cylindrical pumpkin and spherical blueberry during drying at various temperatures (e.g., 30, 40, 50 and 60°C) at specific constant velocity (U = 1 m/s) and the relative humidity φ = 30%. In theoretical analysis, two moisture transfer models are used to determine drying process parameters (e.g., drying coefficient and lag factor) and moisture transfer parameters (e.g., moisture diffusivity and moisture transfer coefficient), and to calculate the dimensionless moisture content distributions. The calculated results are then compared with the experimental moisture data. A considerably high agreement is obtained between the calculations and experimental measurements for the cases considered. The effective diffusivity values were evaluated between 0.741 × 10⁻⁵ and 5.981 × 10⁻⁵ m²/h for slab products, 0.818 × 10⁻⁵ and 6.287 × 10⁻⁵ m²/h for cylindrical products and 1.213 × 10⁻⁷ and 7.589 × 10⁻⁷ m²/h spherical products using the Model-I and 0.316 × 10⁻⁵–5.072 × 10⁻⁵ m²/h for slab products, 0.580 × 10⁻⁵–9.587 × 10⁻⁵ m²/h for cylindrical products and 1.408 × 10⁻⁷–13.913 × 10⁻⁷ m²/h spherical products using the Model-II.     

Hypersonic interference heating in the vicinity of surface protuberances

The understanding of the behaviour of the flow around surface protuberances in hypersonic vehicles is developed and an engineering approach to predict the location and magnitude of the highest heat transfer rates in their vicinity is presented. To this end, an experimental investigation was performed in a hypersonic facility at freestream Mach numbers of 8.2 and 12.3 and Reynolds numbers ranging from Re _∞/m = 3.35 × 10⁶ to Re _∞/m = 9.35 × 10⁶. The effects of protuberance geometry, boundary layer state, freestream Reynolds number and freestream Mach numbers were assessed based on thin-film heat transfer measurements. Further understanding of the flowfield was obtained through oil-dot visualizations and high-speed schlieren videos. The local interference interaction was shown to be strongly 3-D and to be dominated by the incipient separation angle induced by the protuberance. In interactions in which the incoming boundary layer remains unseparated upstream of the protuberance, the highest heating occurs adjacent to the device. In interactions in which the incoming boundary layer is fully separated ahead of the protuberance, the highest heating generally occurs on the surface just upstream of it except for low-deflection protuberances under low Reynolds freestream flow conditions in which case the heat flux to the side is greater.     

On the Reynolds number scaling of vorticity production at no-slip walls during vortex-wall collisions

Recently, numerical studies revealed two different scaling regimes of the peak enstrophy Z and palinstrophy P during the collision of a dipole with a no-slip wall [Clercx and van Heijst, Phys. Rev. E 65, 066305, 2002]: Z μ Re^0.8{Z\propto{\rm Re}^{0.8}} and P μ Re^2.25{P\propto {\rm Re}^{2.25}} for 5 × 10² ≤ Re ≤ 2 × 10⁴ and Z μ Re^0.5{Z\propto{\rm Re}^{0.5}} and P μ Re^1.5{P\propto{\rm Re}^{1.5}} for Re ≥ 2 × 10⁴ (with Re based on the velocity and size of the dipole). A critical Reynolds number Re _c (here, Re_c ? 2×10⁴{{\rm Re}_c\approx 2\times 10^4}) is identified below which the interaction time of the dipole with the boundary layer depends on the kinematic viscosity ν. The oscillating plate as a boundary-layer problem can then be used to mimick the vortex-wall interaction and the following scaling relations are obtained: Z μ Re^3/4, P μ Re^9/4{Z\propto{\rm Re}^{3/4}, P\propto {\rm Re}^{9/4}} , and dP/dt μ Re^11/4{\propto {\rm Re}^{11/4}} in agreement with the numerically obtained scaling laws. For Re ≥ Re _c the interaction time of the dipole with the boundary layer becomes independent of the kinematic viscosity and, applying flat-plate boundary-layer theory, this yields: Z μ Re^1/2{Z\propto{\rm Re}^{1/2}} and P μ Re^3/2{P\propto {\rm Re}^{3/2}}.     

Uniaxial elongational behavior of poly(vinyl chloride) physical gel

A poly(vinyl chloride) (PVC,  M_w = 102×10³)(\mbox{PVC,}\;{\rm M}_{\rm w} =102\times 10^3) di-octyl phthalate (DOP) gel with PVC content of 20 wt.% was prepared by a solvent evaporation method. The dynamic viscoelsticity and elongational viscosity of the PVC/DOP gel were measured at various temperatures. The gel exhibited a typical sol–gel transition behavior with elevating temperature. The critical gel temperature (T_gel) characterized with a power–law relationship between the storage and loss moduli, G^′ and G^″, and frequency ω, G￠=G^￠￠/tan  ( np/2 ) μ wⁿ{G}^\prime={G}^{\prime\prime}{\rm /tan}\;\left( {{n}\pi {\rm /2}} \right)\propto \omega ^{n}, was observed to be 152°C. The elongational viscosity of the gel was measured below the T_gel. The gel exhibited strong strain hardening. Elongational viscosity against strain plot was independent of strain rate. This finding is different from the elongational viscosity behavior of linear polymer solutions and melts. The stress–strain relations were expressed by the neo-Hookean model at high temperature (135°C) near the T_gel. However, the stress–strain curves were deviated from the neo-Hookean model at smaller strain with decreasing temperature. These results indicated that this physical gel behaves as the neo-Hookean model at low cross-linking point, and is deviated from the neo-Hookean model with increasing of the PVC crystallites worked as the cross-linking junctions.     

Experimental investigation of mixed convection in a rectangular duct with a heated plate in the middle of cross section

The flow and heat transfer in an inclined and horizontal rectangular duct with a heated plate longitudinally mounted in the middle of cross section was experimentally investigated. The heated plate and rectangular duct were both made of highly conductive materials, and the heated plate was subjected to a uniform heat flux. The heat transfer processes through the test section were under various operating conditions: Pr ≈ 0.7, inclination angle ϕ = −60° to +60°, Reynolds number Re = 334–1,911, Grashof number Gr = 5.26 × 10²–5.78 × 10⁶. The experimental results showed that the average Nusselt number in the entrance region was 1.6–2 times as large as that in the fully developed region. The average Nusselt numbers and pressure drops increased with the Reynolds number. The average Nusselt numbers and pressure drops decreased with an increase in the inclination angle from −60° to +60° when the Reynolds number was less than 1,500. But when the Reynolds number increased to over about 1,800, the heat transfer coefficients and pressure drops were independent of inclination angles.     

Boundary layer structure of oscillatory open-channel shallow flows over smooth and rough beds

The boundary layer structure of oscillatory shallow open channel flows has been studied in a wide flume. Fluorescence solution was released at a porous rough bed through a diffuser covered by gravel of 0.5 cm grain size. A planar laser-induced fluorescence (PLIF) system was used to visualise the dye plumes in both vertical and horizontal planes for a qualitative understanding of the roles of large-scale flow structures in mass transport. A variety of tests were conducted for a range of oscillatory periods (30–240 s), water depths (3–16 cm) and velocity amplitudes (0.027–0.325 m/s), which cover a wide range of oscillatory flows with Reynolds numbers Re _a varied from 0.3 × 10⁴ (laminar) to 2.1 × 10⁶ (fully turbulent). For quantitative investigation, a novel technique, namely combined laser-induced fluorescence (LIF) and 2D laser Doppler velocimetry (LDV) (LIF/LDV), was developed and used to measure the velocity and solute concentration simultaneously in a vertical plane over 50 cycles. From the dye plumes revealed by the PLIF in transitional flows, there are different patterns of flow structure and solute transport with three representative stages of acceleration, deceleration and flow reversal. In the acceleration stage, turbulence was suppressed with dye layers adhering to the surface with little vertical mass transport. In the deceleration stage, flame-like turbulent structures occurred when turbulence generation was prominent. This was investigated quantitatively by recording the percentage occurrence of the adhered smooth layers per cycle. For those smooth bed cases with Re _a < 1.8 × 10⁵, the adhered smooth dye layers type of boundary layer occupied 100% of the oscillation period. Over a sufficiently high Re _a , a rough bed can generate fully turbulent oscillatory flows without the appearance of adhering dye layers. Between these two extremes, a transitional flow regime occurs in a wide range of flow conditions: Re _a > 2.7 × 10⁴ over the rough bed and Re _a > 8.3 × 10⁶ over a smooth bed.     

Streamwise evolution of an inclined cylinder wake

The streamwise evolution of an inclined circular cylinder wake was investigated by measuring all three velocity and vorticity components using an eight-hotwire vorticity probe in a wind tunnel at a Reynolds number Re_d of 7,200 based on free stream velocity (U _∞) and cylinder diameter (d). The measurements were conducted at four different inclination angles (α), namely 0°, 15°, 30°, and 45° and at three downstream locations, i.e., x/d = 10, 20, and 40 from the cylinder. At x/d = 10, the effects of α on the three coherent vorticity components are negligibly small for α ≤ 15°. When α increases further to 45°, the maximum of coherent spanwise vorticity reduces by about 50%, while that of the streamwise vorticity increases by about 70%. Similar results are found at x/d = 20, indicating the impaired spanwise vortices and the enhancement of the three-dimensionality of the wake with increasing α. The streamwise decay rate of the coherent spanwise vorticity is smaller for a larger α. This is because the streamwise spacing between the spanwise vortices is bigger for a larger α, resulting in a weak interaction between the vortices and hence slower decaying rate in the streamwise direction. For all tested α, the coherent contribution to [`(v<sup>2</sup>)] \overline{{v^{2}}} is remarkable at x/d = 10 and 20 and significantly larger than that to [`(u²)] \overline{{u^{2}}} and [`(w<sup>2</sup>)]. \overline{{w^{2}}}. This contribution to all three Reynolds normal stresses becomes negligibly small at x/d = 40. The coherent contribution to [`(u²)] \overline{{u^{2}}} and [`(v²)] \overline{{v^{2}}} decays slower as moving downstream for a larger α, consistent with the slow decay of the coherent spanwise vorticity for a larger α.