Terminal velocities of clean and fully-contaminated drops in vertical pipes

Terminal velocities and shapes of drops rising through vertical pipes in clean and fully-contaminated systems are measured by using a high-speed video camera and an image processing method. Silicon oils and glycerol water solutions are used for the dispersed and continuous phases, respectively. Triton X-100 is used for surfactant. Clean and contaminated drops take either spherical, spheroidal or deformed spheroidal shapes when the diameter ratio λ is less than a critical value, λ_C, whereas they take bullet shapes for λ > λ_C (Taylor drops). The applicability of available drag and Froude number correlations is examined through comparisons with the measured data. Effects of surfactant on the shape and terminal velocity of a Taylor drop are also discussed based on the experimental data and interface tracking simulations. The conclusions obtained are as follows: (1) drag and Froude number correlations proposed so far give reasonable estimations of the terminal velocities of clean drops at any λ, (2) the terminal velocities of contaminated drops are well evaluated by making the viscosity ratio μ^* infinity in the drag correlation for clean drops in the viscous force dominant regime, (3) the effects of surfactant on the shape and terminal velocity of a Taylor drop become significant as the Eötvös number, Eo_D, decreases and μ^* increases, and (4) the reduction in surface tension due to the addition of surfactant would be the cause of the increase in the terminal velocity and elongation of a contaminated Taylor drop.     

Simulation of turbulent flows around a circular cylinder using nonlinear eddy-viscosity modelling: steady and oscillatory ambient flows

Steady incident flow past a circular cylinder for sub- to supercritical Reynolds number has been simulated as an unsteady Reynolds-averaged Navier–Stokes (RANS) equation problem using nonlinear eddy-viscosity modelling assuming two-dimensional flow. The model of Craft et al. (Int. J. Heat Fluid Flow 17 (1996) 108), with adjustment of the coefficients of the ‘cubic’ terms, predicts the drag crisis at a Reynolds number of about 2×10⁵ due to the onset of turbulence upstream of separation and associated changes in Strouhal number and separation positions. Slightly above this value, at critical Reynolds numbers, drag is overestimated because attached separation bubbles are not simulated. These do not occur at supercritical Reynolds numbers and drag coefficient, Strouhal number and separation positions are in approximate agreement with experimental measurements (which show considerable scatter). Fluctuating lift predictions are similar to sectional values measured experimentally for subcritical Reynolds numbers but corresponding measurements have not been made at supercritical Reynolds numbers. For oscillatory ambient flow, in-line forces, as defined by drag and inertia coefficients, have been compared with the experimental values of Sarpkaya (J. Fluid Mech. 165 (1986) 61) for values of the frequency parameter, β=D²/νT, equal to 1035 and 11240 and Keulegan–Carpenter numbers, KC=U₀T/D, between 0.2 and 15 (D is cylinder diameter, ν is kinematic viscosity, T is oscillation period, and U₀ is the amplitude of oscillating velocity). Variations with KC are qualitatively reproduced and magnitudes show best agreement when there is separation with a large-scale wake, for which the turbulence model is intended. Lift coefficients, frequency and transverse vortex shedding patterns for β=1035 are consistent with available experimental information for β≈250−500. For β=11240, it is predicted that separation is delayed due to more prominent turbulence effects, reducing drag and lift coefficients and causing the wake to be more in line with the flow direction than transverse to it. While these oscillatory flows are highly complex, attached separation bubbles are unlikely and the flows probably two dimensional.     

Optimization of Conical Wings in Hypersonic Flow

A method of calculation is presented to determine conical wing shapes that minimize the coefficient of (wave) drag, C _D, for a fixed coefficient of lift, C _L, in steady, hypersonic flow. An optimization problem is considered for the compressive flow underneath wings at a small angle of attack δ and at a high free-stream Mach number M _∞ so that hypersonic small-disturbance (HSD) theory applies. A figure of merit, F=C _D/C _L ^3/2, is computed for each wing using a finite volume discretization of the HSD equations. A set of design variables that determine the shape of the wing is defined and adjusted iteratively to find a shape that minimizes F for a given value of the hypersonic similarity parameter, H= (M _∞δ)⁻², and planform area. Wings with both attached and detached bow shocks are considered. Optimal wings are found for flat delta wings and for a family of caret wings. In the flat-wing case, the optima have detached bow shocks while in the caret-wing case, the optimum has an attached bow shock. An improved drag-to-lift performance is found using the optimization procedure for curved wing shapes. Several optimal designs are found, all with attached bow shocks. Numerical experiments are performed and suggest that these optima are unique. Received 1 May 1998 and accepted 14 October 1998     

Passive control of wake flow by two small control cylinders at Reynolds number 80

Passive control of the wake behind a circular cylinder in uniform flow is studied by numerical simulation at Re_D=80. Two small control cylinders are placed symmetrically along the separating shear layers at various stream locations. In the present study, the detailed flow mechanisms that lead to a significant reduction in the fluctuating lift but maintain the shedding vortex street are clearly revealed. When the stream locations lie within 0.8≤X_C/D≤3.0, the alternate shedding vortex street remains behind the control cylinders. In this case, the symmetric standing eddies immediately behind the main cylinder and the downstream delay of the shedding vortex street are the two primary mechanisms that lead to a 70–80% reduction of the fluctuating lift on the main cylinder. Furthermore, the total drag of all the cylinders still has a maximum 5% reduction. This benefit is primarily attributed to the significant reduction of the pressure drag on the main cylinder. Within X_C/D>3.0, the symmetry of the standing eddy breaks down and the staggered vortex street is similar to that behind a single cylinder at the same Reynolds number. In the latter case, the mean pressure drag and the fluctuating lift coefficients on the main cylinder will recover to the values of a single cylinder.     

The drag of three-dimensional rectangular cavities

Cavities and other surface cut-outs are present on aircraft in numerous forms, from cargo bays and landing gear housing to rivet depressions and panel handles. Although these surface imperfections make a significant contribution to the overall drag on an aircraft, relatively little is known about the flow mechanisms associated with cavities, particularly those which have a strongly three-dimensional geometry. The present work is a wind tunnel investigation of the drag forces and flow regimes associated with cavities having a 2:1 rectangular planform geometry. The effects of both the cavity depth and the flow incidence angle have been examined in terms of the overall cavity drag increment and the mean surface pressure distributions. The drag forces have been determined from both integrated pressures and direct force balance measurements. For the model normal to the flow direction the flow within the cavity was remarkably symmetrical in all the configurations examined. In most cases the cavity flow is dominated by a single large eddy. However, for cavities yawed to other incidence angles there is considerable flow asymmetry, with strong vorticity shedding and high drag in some cases, notably with depth/narrowest width ratio of 0.4–0.5 at 45–60° incidence. The present data correspond well with established results and extend the scope of information available for design purposes and for the development of numerical models.Nomenclature A _p planform area of model - C _D pressure drag coefficient (F _D /(A _p · q)) - C _D drag coefficient increase due to cavity (C _D – c_f) - c _f local skin friction coefficient - C _L pressure lift coefficient (F _L /(A _p · q)) - C _p mean surface pressure coefficient (P – P _s )/q) - F _D drag force - F _L lift force - h depth - L longest planform dimension of model - P surface pressure on model - P _s freestream static pressure - P _t freestream total pressure - q freestream dynamic pressure (P _t – P_s) - Re Reynolds number (U _R · W/v) - U _R freestream velocity - W narrowest planform dimension of model - Z vertical cartesian coordinate - incidence angle - kinematic viscosity     

Influence of cavitation on blade characteristics

An experimental study of flow around a blade with a modified NACA 4418 profile was conducted in a water tunnel that also enables control of the cavitation conditions within it. Pressure, lift force, drag force and pitching moment acting on the blade were measured for different blade angles and cavitation numbers, respectively. Relationships between these parameters were elaborated and some of them are presented here in dimensionless form. The analysis of results confirmed that cavitation changes the pressure distribution significantly. As a consequence, lift force and pitching moment are reduced, and the drag force is increased. When the cavitation cloud covers one side of the blade and the flow becomes more and more vaporous, the drag force also begins to decrease. The cavity length is increased by increasing the blade angle and by decreasing thé cavitation number.List of symbols A (m²) blade area,B ·L - B (m) blade width - C _D (–) drag coefficient,F _D /(p _d ·A) - C _L (–) lift coefficient,F _L /(P _d ·A) - C _M (–) pitching moment coefficient,M/(P _d ·A ·L) - C _p (–) pressure coefficient, (p-p _r )/p _d - F (N) force - L (m) blade length - M (Nm) pitching moment - p (Pa) local pressure on blade surface - p _d (Pa) dynamic pressure, ·V ²/2 - p _r (Pa) reference wall pressure at blade nose position if there would be no blade in the tunnel - p _v (Pa) vapor pressure - p ₁ (Pa) wall pressure 350 mm in front of thé blade axis - Re (–) Reynolds number,V ·L/v - V (m/s) mean velocity of flow in the tunnel - x (m) Cartesian coordinate along thé blade profile cord - x _c (m) cavity length,x-coordinate of cavity end - (°) blade angle - v (m²/s²) kinematic viscosity - (kg/m³) fluid density - (–) cavitation number, (p _r –p _v )/p _d - (°) angle of tangent to thé blade profile contour     

Effects of riblet bends on pipe flows

Four riblet bends were tested to investigate the effects of riblets on pipe flows including the secondary flow on the Reynolds numbers; Re _D =6×10³–4×10⁴. The pressure gradients on the smooth pipe downstream from the riblet bends were measured, and also the pressure losses of the bends only were measured. All riblet bends reduced the pressure gradient on the smooth pipe downstream from them, which means a drag reduction. Two of the riblet bends showed the maximum drag reduction of about 4 percent at Re _D = 6500; this reduction rate was significant considering the uncertainty of the present experiments. Since the pressure losses of these two riblet bends were almost identical to that of the smooth bend at Re _D = 6500, they could cause a net drag reduction of about 4 percent on the piping system including these bends at that Reynolds number. Furthermore, the velocity profiles measured by LDV indicated that the secondary flow becomes weaker downstream from the riblet bends when a drag reduction is recognized there.Nomenclature D pipe diameter - D ₀ the distance from the valley to the valley passing through the pipe center - H height of groove - P nondimensional static pressure (p/it/(U ₀ ² ):p is gauge pressure) - dP/dX nondimensional pressure gradient - Rc curvature of bend - Re _D Reynolds number based on bulk velocity and pipe diameter - s spacing of groove - U mean streamwise velocity along the horizontal diameter - U ₀ bulk velocity - V mean vertical velocity along the horizontal diameter - x streamwise direction along the pipe axis (see Fig. 1) - X nondimensionalx (=x/D) - y radial direction in the horizontal plane which is perpendicular to the plane including the bend (see Fig. 1) - yUV swirl intensity (nondimensional swirl intensity:yUV/(DU ₀ ² ))     

Viscoelasticity of a surfactant and its drag-reducing ability

There is considerable interest in the use of viscoelastic cationic surfactant-counterion mixtures in district heating and cooling systems to reduce pressure losses. A recent field test in a secondary system near Prague showed a 30+% reduction in pumping energy requirements.We have studied a number of commercial surfactants and we report here results of rheological, drag reduction and turbulence measurements on Arquad 18–50 (octadecyl trimethyl ammonium chloride (AR 18)) with an excess of sodium salicylate (NA). The concentration studied was 1.6 mM AR 18 and 4.0 mM NA which is about one third the concentration for excellent drag reduction in this surfactant's effective temperature range 30–90°C.Viscosity, , vs. shear rate,D, first normal stress difference,N ₁, vs. shear rate, drag reduction (as pressure drop,i=P/1) vs. average velocity,U _ave, in a 39.4 mm tube for AR 18, and turbulence intensity data for three drag reducing surfactants are reported.Of particular interest are the generally low turbulence intensities in all three directions which correspond to reduced heat, mass and momentum transfer rates compared to water, and the existence of large normal stress differences at 20°C for AR 18, a temperature at which no drag reduction occurs with this surfactant, indicating that normal stress effects do not correlate directly with drag reduction.The effect of time of pumping on increasing drag reduction demonstrates that this factor overwhelms the expected increase in drag reduction as temperature is raised from 18–19°C to 40.5°C.     

Effect of longitudinal riblets on the aerodynamic characteristics of a straight wing

The results of balance aerodynamic tests on model straight wings with smooth and ribbed surfaces at an angle of attack =–4°–12°, Mach number M=0.15–0.63, and Reynolds number Re=2.4·10⁶–3.5·10⁶ are discussed. The nondimensional riblet spacings ⁺, which determines the effect of the riblets on the turbulent friction drag, and the effect of riblets on the upper and/or lower surface of a straight wing on its drag, lift, and moment characteristics are estimated.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 33–38, March–April, 1995.     

The effect of support position and turbulence intensity on the flow near the surface of a sphere

The flow near the surface of a sphere was studied, using a flow visualization technique, for Reynolds numbers from about 4×10⁴ to 2.5×10⁵. It was concluded that the presence of a crossflow support substantially disturbed the flow near the surface of the sphere, especially at supercritical Reynolds numbers. Photographs of the flow patterns around spheres with crossflow supports, and with rear supports, have been presented. Also, measurements were made which show the way in which the turbulence intensity of the free stream influenced the angle of separation at various Reynolds numbers.

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Zusammenfassung Die Strömung nahe der Oberfläche einer Kugel wurde untersucht, indem die Stromlinien sichtbar gemacht wurden. Die Untersuchungen wurden durchgeführt für Reynoldszahlen von etwa 4×10⁴ bis 2,5×10⁵. Die Ergebnisse zeigten, daß die Anwesenheit einer Halterung quer zur Strömung diese in der Nähe der Kugeloberfläche wesentlich störte, besonders bei überkritischen Reynoldszahlen. Photographien des Strömungsverlaufes um die Kugel sowohl mit einer Halterung quer zur Stromrichtung als auch mit einer anderen hinter der Kugel werden gezeigt. Außerdem wurden Messungen durchgeführt, die zeigen, in welcher Weise die Intensität der Turbulenz der freien Strömung den Ablösungswinkel bei verschiedenen Reynoldszahlen beeinflußt.

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Nomenclature C _D drag coefficient (total drag/dynamic head × projected area) - C _Dc critical drag coefficient. IfC _D<D _Dc, the flow pattern is considered subcritical. - h distance (s. Fig. 1) - Nu Nusselt number - R radius of the sphere - Re Reynolds number - Re _c Reynolds number at whichC _D=C _Dc - Tu turbulence intensity component in the direction of the freestream flow - _s average angle from the stagnation point to the separation circle measured in the horizontal plane - _sc critical separation angle. If _s<_sc, the flow pattern is considered subcritical. In this investigation _sc 92°     

Diffusion of14C in dense saturated bentonite under steady-state conditions

Diffusion coefficients are critical parameters for predicting migration rates and fluxes of contaminants through clay-based barrier materials used in many waste containment strategies. Cabon-14 is present in high-level nuclear fuel waste and also in many low-level wastes such as those generated from some medical research activities. Diffusion coefficients were measured for¹⁴C (in the form of carbonate) in bentonite compacted to a series of dry bulk densities, _b, ranging from about 0.9 to 1.6 Mg/m³. The clay was saturated with a Na-Ca-Cl-dominated groundwater solution typical of those found deep in plutonic rock on the Canadian Shield. Both effective,D _e, and apparent,D _a, diffusion coefficients were determined.D _e is defined asD _{0 a} n _e, where D₀ is the diffusion coefficient in pure bulk water, _a the apparent tortuosity factor, andn _e the effective porosity available for diffusion; andD _a is defined asD _{0 a} n _e/(n _e + _b K _d ), where K_d is the solid/liquid distribution coefficient. BothD _e andD _a decrease with increasing _b:D _e values range from about 10×10^–12 m²/s at _b0.9 Mg/m³ to 0.6×10^–12 m²/s at 1.6 Mg/m³, andD _a values vary from approximately 40×10^–12 to 4×10^–12 m²/s over the same density range. The decrease inD _e andD _a is attributed to a decrease in both _a andn _e as _b increases. The data indicate thatn _e is <10% of the total solution-filled porosity of the clay at all densities.K _d values for¹⁴C with the clay range from about 0.3 to <0.1 m³/Mg; this indicates there is a small amount of¹⁴C sorbed on the clay and/or some¹⁴C is isotopically exchanged with¹²C in carbonate phases present in the clay. Finally, theD _e values for¹⁴C are lower than those of other diffusants — I^–, Cl^–, TcO₄ ^–, and Cs⁺ — that have been measured in this clay and pore-water solution. This is attributed to lower values for bothn _e andD ₀ for¹⁴C species relative to those of the other diffusants.     

Flow between parallel walls containing the lines of neutrally buoyant circular cylinders

The motions of a single and two lines of neutrally buoyant circular cylinders in fluid between flat parallel walls are numerically investigated over the range of the Reynolds number of 12 < Re < 96, the ratio of the diameter of the cylinder D_s to the channel width D of 0.25≤D_s/D≤0.5, and the ratio of the streamwise spacing of the cylinders L to the channel width of 0.75≤L/D≤2. The lattice Boltzmann method is used for computations of the fluid phase and the cylinders are moved according to Newton’s law of motion. The Segré–Silberberg effect is found for both a single and two lines of cylinders. It is also found that for two lines of cylinders with D_s/D=0.25 and L/D=1, the equilibrium positions of the two lines are arranged to be staggered with respect to each other in the flow direction. The effects of the Reynolds number Re, D_s/D, and L/D on the equilibrium position of the lines of cylinders and on the friction factor of the cylinder–fluid mixture are presented and discussed.     

Dynamics of Brownian particles in a turbulent channel flow

Turbulent channel flows with suspended particles are investigated by means of numerical simulations. The fluid velocity is computed by large eddy simulation. Motion of small graphite particles with diameter of 0.01–10 m, corresponding to the Schmidt number, Sc, of 2.87 × 10²–6.22 × 10⁶ and the particle relaxation time in wall unit, _p⁺, of 9.79 × 10^–5–4.51, is computed by Lagrangian particle tracking. Relation between the particle relaxation time and the computed deposition velocity is found to be in good agreement with an empirical relation. The statistics of the particle motion in the vicinity of the wall are studied. Clear differences are found in dynamical behavior of particles with different sizes. Medium size particles show a strong dependence on the structure of the fluid flow, while small and large particles are considerably less sensitive.     

The wake flow control behind a circular cylinder using ion wind

Active and passive flow control methods have been studied for decades, but there have been only a few studies of flow control methods using ion wind, which is the bulk motion of neutral molecules driven by locally ionized air from a corona discharge. This paper describes an experimental study of ion wind wake control behind a circular cylinder. The experimental conditions consisted of a range of electrohydrodynamic numbers—the ratio of an electrical body force to a fluid inertial force—from 0 to 2 and a range of Reynolds numbers from 4×10³ to 8×10³. Pressure distributions over the cylinder surface were measured and flow visualizations were carried out using a smoke-wire method. The flow visualizations confirmed that ion wind significantly affects the wake structure behind a circular cylinder, and that the pressure drag can be dramatically reduced by superimposing ion wind.List of symbols BR blockage ratio - C _d coefficient of the pressure drag - C _p coefficient of the surface pressure, 2(p–p ₀)/(U ₀ ²) - C _pb coefficient of the base surface pressure, 2(p _b–p ₀)/(U ₀ ²) - D diameter of the cylinder - D _P pressure drag - d _p diameter of particle - E the electric field - F _e Coulombian force (qE) - F _v viscous force - H wire-to-cylinder spacing - I total electric current (A) - L the axial length of cylinder (m) - N _EHD electrohydrodynamic number - p _b base pressure of cylinder at =180° - p ₀ reference static pressure at 10D upstream - q the charge on the particle - R radius of the cylinder - V applied voltage (kV) - U ₀ mean flow velocity (m/s) - ion mobility in air (m²/(s V)) - ₀ permittivity of free space - viscosity of fluid (kg/ms) - density of fluid (kg/m³) - installation angle of a wire electrode (°)     

Optimum rib size to enhance forced convection in a horizontal triangular duct with ribbed internal surfaces

The optimum rib size to enhance heat transfer had been proposed through an experimental investigation on the forced convection of a fully developed turbulent flow in an air-cooled horizontal equilateral triangular duct fabricated on its internal surfaces with uniformly spaced square ribs. Five different rib sizes (B) of 5 mm, 6 mm, 7 mm, 7.9 mm and 9 mm, respectively, were used in the present investigation, while the separation (S) between the center lines of two adjacent ribs was kept at a constant of 57 mm. The experimental triangular ducts were of the same axial length (L) of 1050 mm and the same hydraulic diameter (D) of 44 mm. Both the ducts and the ribs were fabricated with duralumin. For every experimental set-up, the entire inner wall of the duct was heated uniformly while the outer wall was thermally insulated. From the experimental results, a maximum average Nusselt number of the triangular duct was observed at the rib size of 7.9 mm (i.e. relative rib size ). Considering the pressure drop along the triangular duct, it was found to increase almost linearly with the rib size. Non-dimensional expressions had been developed for the determination of the average Nusselt number and the average friction factor of the equilateral triangular ducts with ribbed internal surfaces. The developed equations were valid for a wide range of Reynolds numbers of 4,000 < Re _D < 23,000 and relative rib sizes of under steady-state condition. A Inner surface area of the triangular duct [m²] - A _C Cross-sectional area of the triangular duct [m²] - B Side length of the square rib [mm] - C _P Specific heat at constant pressure [kJ·kg^–1·K^–1] - C ₁, C ₂, C ₃ Constant coefficients in Equations (10), (12) and (13), respectively - D Hydraulic diameter of the triangular duct [mm] - Electric power supplied to heat the triangular duct [W] - f Average friction factor - F View factor for thermal radiation from the duct ends to its surroundings - h Average convection heat transfer coefficient at the air/duct interface [W·m^–2 ·K^–1] - k Thermal conductivity of the air [W·m^–1 ·K^–1] - L Axial length of the triangular duct [mm] - Mass flow rate [kg·s^–1] - n ₁, n ₂, n ₃ Power indices in Equations (10), (12) and (13), respectively - Nu _D Average Nusselt number based on hydraulic diameter - P Fluid pressure [Pa] - Pr Prandtl number of the airflow - _c Steady-state forced convection from the triangular duct to the airflow [W] - _l Heat loss from external surfaces of the triangular duct assembly to the surroundings [W] - _r Radiation heat loss from both ends of the triangular duct to the surroundings [W] - Re _D Reynolds number of the airflow based on hydraulic diameter - S Uniform separation between the centre lines of two consecutive ribs [mm] - T Fluid temperature [K] - T _a Mean temperature of the airflow [K] - T _ai Inlet mean temperature of the airflow [K] - T _ao Outlet mean temperature of the airflow [K] - T _s Mean surface temperature of the triangular duct [K] - T Ambient temperature [K] - U Mean air velocity in the triangular duct [m·s^–1] - _r Mean surface-emissivity with respect to thermal radiation - Dynamic viscosity of the fluid [kg·m^–1·s^–1] - Kinematic viscosity of the airflow [m²·s^–1] - Density of the airflow [kg·m^–3] - Stefan-Boltzmann constant [W·m^–2·K^–4]     

Pulsating slurry flow in pipelines

An experimental study on pulsating turbulent flow of sand-water suspension was carried out. The objective was to investigate the effect of pulsating flow parameters, such as, frequency and amplitude on the critical velocity, the pressure drop per unit length of pipeline and hence the energy requirements for hydraulic transportation of a unit mass of solids. The apparatus was constructed as a closed loop of 11.4 m length and 3.3 cm inner diameter of steel tubing. Solid volumetric concentrations of up to 20% were used in turbulent flow at a mean Reynolds number of 33,000–82,000. Pulsation was generated using compressed air in a controlled pulsation unit. Frequencies of 0.1–1.0 Hz and amplitude ratios of up to 30% were used. Instantaneous pressure drop and flow rate curves were digitized to calculate the energy dissipation associated with pulsation. The critical velocity in pulsating flow was found to be less than that for the corresponding steady flow at the same volumetric concentration. Energy dissipation for pulsating flow was found to be a function of both frequency and amplitude of pulsation. A possible energy saving was indicated at frequencies of 0.4–0.8 Hz and moderate amplitudes ratios of less than 25%.List of symbols A cross-section area of the tube (m²) - C _D drag coefficient of sand particles - C _v volumetric concentration (%) - D inner diameter of test-section pipe (m) - F frequency (Hz) - f friction factor - g gravitational constant (m/s²) - J energy dissipation of suspension (W/m)/(kg/s) - J _p energy dissipation of pulsating suspension (W/m)/(kg/s) - J _s energy dissipation of steady component of suspension (W/m)/(kg/s) - J _w energy dissipation of pure water (W/m)/(kg/s) - L length of test-section (m) - m mass flow rate (kg/s) - P pressure drop in test-section (N/m²) - S specific gravity of sand - V instantaneous flow velocity (m/s) - V _c steady flow critical velocity (m/s) - V _cp pulsating flow critical velocity (m/s) - V _F settling velocity of particles (m/s) - V _s steady component of mean flow velocity (m/s) - dynamic viscosity (g/cm sec) - _m mean density of suspension (kg/m³) - angular velocity (rad/sec) - amplitude ratio (V — V _s)/V - nondimentional factor equal to - nondimentional factor equal to (V–V _s/V - NI nondimentional factor equal to (V ²C _d/g D(S – 1)) - Re Reynolds number (V ²C _d/C _v g D(S – 1))     

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.     

Measurement of the Coefficient of Transverse Dispersion in Flow Through Packed Beds for a Wide Range of Values of the Schmidt Number

Experimental values of the coefficient of transverse dispersion (D _T) were measured with the system 2-naphthol/water, over a range of temperatures between 293K and 373K, which corresponds to a range of values of viscosity () between 2.83×10^–4 Ns/m² and 1.01×10^–3 Ns/m² and of molecular diffusion coefficient (D _m) between 1.03×10^–9 m²/s and 5.49×10^–9 m²/s. Since the density () of water is close to 10³ kg/m³, the corresponding variation of the Schmidt number (Sc=/D _m) was in the range 1000 – 50. More than 200 experimental values of the transverse dispersion coefficient were obtained using beds of silica sand with average particle sizes (d) of 0.297 and 0.496mm, operated over a range of interstitial liquid velocities (u) between 0.1mm/s and 14mm/s and this gave a variation of the Reynolds number (Re=du/) between 0.01 and 3.5.Plots of the dimensionless coefficient of transverse dispersion (D _T/D _m) vs. the Peclet number (Pe_m=ud/D _m) based on molecular diffusion bring into evidence the influence of Sc on transverse dispersion. As the temperature is increased, the value of Sc decreases and the values of D _T/D _m gradually approach the line corresponding to gas behaviour (i.e. Sc 1), which is known to be well approximated by the equation D _T/D _m=1/+ud/12D _m, where is the tortuosity with regard to diffusion.     

Turbulent flows of solutions of surface-active substances

Not only polymers, but also some surface-active substances have the capacity to reduce the hydrodynamic resistance in the turbulent regime of a fluid. From the point of view of stability against mechanical destruction, the addition of surface-active substances has certain advantages over polymers; in particular, they are capable of recovering their hydrodynamic effectiveness having passed through pumps and local points of resistance [1]. The basic possibility of reducing drag by the addition of surface-active substances was demonstrated in [2–6]. It was later shown that a reduction in the drag of liquids could be achieved only by micelle-forming surface-active substances [5, 7], in solutions of which spherical and platelike micelles, respectively, are formed at the critical concentrationsC _m1 andC _m2 for micelle formation. The values ofC _m1 andC _m2 depend both on the molecular structure of the surface-active substances as well as on external factors such as the temperature, the presence in the solution of electrolytes, polar organic substances, and so forth. The connection established in [5, 7] between the reduction in the drag and the value ofC _m2 suggests that the reduction in the turbulent friction will also depend on the above factors. It is therefore possible to control processes of turbulent transfer in a fluid as well as the drag. However, this possibility has not been sufficiently studied. In [1–7], the influence of surface-active substances on the drag was investigated. First data on the velocity profiles in solutions of surface-active substances were given in [9, 10]; they are not sufficiently complete. In the present work, we made measurements of the velocity profiles and the turbulence intensity in solutions of surfaceactive substances, and we have calculated the generation of turbulence energy and the dissipation of the energy of the averaged motion. We have studied the influence of electrolytes and the temperature on the reduction in the drag and give the results of full-scale experiments.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 36–43, January–February, 1980.     

A field model interpretation of crack initiation and growth behavior in ferroelectric ceramics: change of poling direction and boundary condition

Strain energy density expressions are obtained from a field model that can qualitatively exhibit how the electrical and mechanical disturbances would affect the crack growth behavior in ferroelectric ceramics. Simplification is achieved by considering only three material constants to account for elastic, piezoelectric and dielectric effects. Cross interaction of electric field (or displacement) with mechanical stress (or strain) is identified with the piezoelectric effect; it occurs only when the pole is aligned normal to the crack. Switching of the pole axis by 90° and 180° is examined for possible connection with domain switching. Opposing crack growth behavior can be obtained when the specification of mechanical stress σ^∞ and electric field E^∞ or (σ^∞,E^∞) is replaced by strain ε^∞ and electric displacement D^∞ or (ε^∞,D^∞). Mixed conditions (σ^∞,D^∞) and (ε^∞,E^∞) are also considered. In general, crack growth is found to be larger when compared to that without the application of electric disturbances. This includes both the electric field and displacement. For the eight possible boundary conditions, crack growth retardation is identified only with (E_y^∞,σ_y^∞) for negative E_y^∞ and (D_y^∞,ε_y^∞) for positive D_y^∞ while the mechanical conditions σ_y^∞ or ε_y^∞ are not changed. Suitable combinations of the elastic, piezoelectric and dielectric material constants could also be made to suppress crack growth.