PIV studies of coherent structures generated at the end of a stack of parallel plates in a standing wave acoustic field

Oscillating flow near the end of a stack of parallel plates placed in a standing wave resonator is investigated using particle image velocimetry (PIV). The Reynolds number, Re _d , based on the plate thickness and the velocity amplitude at the entrance to the stack, is controlled by varying the acoustic excitation (so-called drive ratio) and by using two configurations of the stacks. As the Reynolds number changes, a range of distinct flow patterns is reported for the fluid being ejected from the stack. Symmetrical and asymmetrical vortex shedding phenomena are shown and two distinct modes of generating “vortex streets” are identified.     

Geometrical properties of the vorticity vector derived using large-eddy simulation

In this paper, the geometrical properties of the resolved vorticity vector derived from large-eddy simulation are investigated using a statistical method. Numerical tests have been performed based on a turbulent Couette channel flow using three different dynamic linear and nonlinear subgrid-scale stress models. The geometrical properties of have a significant impact on various physical quantities and processes of the flow. To demonstrate, we examined helicity and helical structure, the attitude of with respect to the eigenframes of the resolved strain rate tensor and negative subgrid-scale stress tensor -τ_ij, enstrophy generation, and local vortex stretching and compression. It is observed that the presence of the wall has a strong anisotropic influence on the alignment patterns between and the eigenvectors of , and between and the resolved vortex stretching vector. Some interesting wall-limiting geometrical alignment patterns and probability density distributions in the form of Dirac delta functions associated with these alignment patterns are reported. To quantify the subgrid-scale modelling effects, the attitude of with respect to the eigenframe of -τ_ij is studied, and the geometrical alignment between and the Euler axis is also investigated. The Euler axis and angle for describing the relative rotation between the eigenframes of -τ_ij and are natural invariants of the rotation matrix, and are found to be effective for characterizing a subgrid-scale stress model and for quantifying the associated subgrid-scale modelling effects on the geometrical properties of .     

Integration approach of the Couette inverse problem of powder type self-compacting concrete in a wide-gap concentric cylinder rheometer

For powder type self-compacting concrete (SCC) mixes, commonly used in Belgium, a shear thickening (Herschel–Bulkley) flow behaviour of the fresh mixes is quite often observed.A longstanding problem in rheometry is the so-called “Couette inverse problem”, where one tries to derive the flow curve from the torque measurements T(N) in a (wide-gap) concentric cylinder (Couette) rheometer, with T the torque registered at the inner, stationary cylinder and N the rotational velocity of the outer, rotating, cylinder.In this paper, the Couette inverse problem is approached by means of the integration method in order to convert T(N) into for a wide-gap (R_o/R_i = 1.45) concentric cylinder rheometer. The approach consists in the decoupling of the flow resistance and the power-law flow behaviour after exceeding the flow resistance. The integration approach is validated by experimental verification with different powder type SCC mixtures. By means of illustration, the results of one limestone powder type SCC mixture with different superplasticizer contents are shown in this paper.     

Bifurcation analysis of an arch structure with parametric and forced excitation

The subharmonic bifurcation and universal unfolding problems are discussed for an arch structure with parametric and forced excitation in this paper. The amplitude–frequency curve and some dynamical behavior have been shown for this class of problems by Liu et al. Here, by means of singularity theory, in the case of strict 1:2 internal resonance, the bifurcation behavior of the amplitude with respect to a parameter (which is related to the amplitude of the live load imposed on the arch structures) is studied. The results indicate that it is a high codimensional bifurcation problem with codimension 5, and the universal unfolding is given. From the mechanical background, 20 forms of two parameter unfoldings with some constraints are studied. The transition sets in the parameter plane and the bifurcation diagrams are plotted. The results obtained in this paper present some new dynamic buckling patterns and abundant bifurcation phenomena.     

Analysing flow and heat transfer of a viscoelastic fluid over a semi-infinite horizontal moving flat plate

This paper presents a numerical study of the flow and heat transfer of an incompressible homogeneous second grade type fluid above a flat plate moving with constant velocity U. Such a viscoelastic fluid is at rest and the motion is created by the sheet. The effects of the non-Newtonian nature of the fluid are governed by the local Deborah number K (the ratio between the relaxation time of the fluid and the characteristic time of the flow). When , a new analytical solution for this flow is presented and the effects of fluid's elasticity on flow characteristics, dimensionless stream function and its derivatives are analysed in a wide domain of K. A novel result of the analysis is that a change in the flow solution's behaviour occurs when the dimensionless stream function at the edge of the boundary layer, f_∞, equals 1.0. It is found that velocity at a point decreases with increase in the elasticity of the fluid and, as expected, the amount of fluid entrained diminishes when the effects of fluid's elasticity are augmented. In our heat transfer analyses we assume that the surface temperature has a power-law variation. Two cases are studied, namely, (i) the sheet with prescribed surface temperature (PST case) and (ii) the sheet with prescribed heat flux (PHF case). Local similarity heat-transfer solutions are given for PST case when s=2 (the wall temperature parameter) whereas when a similarity solution takes place in the case of prescribed wall heat flux. The numerical results obtained are fairly in good agreement with the aforementioned analytical ones.     

Collision operator including large-angle scattering for moderately coupled plasma

A new approach has been developed to treat the large-angle as well as the small-angle binary collisions in high temperature and high density plasmas when the test particle distribution function f_α is even function about the test velocity and the relations of the mass and the velocity between the test particles and the field particles are satisfied with m_αm_β (such as electron–ion collision or Lorentz-gas model) and . With the approach, the Boltzmann collision operator is derived to be suitable for the plasma considered as weakly coupled (Coulomb logarithm ) and moderately coupled , i.e., for the electron–ion coupling constant Γ_ei<0.1. The modified collision operator has a direct and practical connection to the Rosenbluth potentials, the new reduced electron–ion collision operator differs from the original Fokker–Planck operator for Coulomb collisions by terms of order . Moreover, some calculations of relaxation rate and transport properties are given for new reduced electron–ion collision operator that shows corrections.     

Chaotic diffusion in steady wavy vortex flow—Dependence on wave state and correlation with Eulerian symmetry measures

The dimensionless effective axial diffusion coefficient, D_z, calculated from particle trajectories in steady wavy vortex flow in a narrow gap Taylor-Couette system, has been determined as a function of Reynolds number (R=Re/Re_c), axial wavelength (λ_z), and the number of azimuthal waves (m). Two regimes of Reynolds number were found: (i) when R<3.5, D_z has a complex and sometimes multi-modal dependence on Reynolds number; (ii) when R>3.5, D_z decreases monotonically.Eulerian quantities measuring the departure from rotational symmetry, ?_θ, and flexion-free flow, ?_ν, were calculated. The space-averaged quantities and were found to have, unlike D_z, a simple unimodal dependence on R. In the low R regime the correlation between D_z and ?_θ?_ν was complicated and was attributed to variations in the spatial distribution of the wavy disturbance occurring in this range of R. In the large R regime, however, the correlation simplified to for all wave states, and this was attributed to the growth of an integrable vortex core and the concentration of the wavy disturbance into narrow regions near the outflow and inflow jets.A reservoir model of a wavy vortex was used to determine the rate of escape across the outflow and inflow boundaries, the size of the ‘escape basins’ (associated with escape across the outflow and inflow boundaries), and the size of the trapping region in the vortex core. In the low R regime after the breakup of all KAM tori, the outflow basin (γ_O) is larger than the inflow basin (γ_I), and both γ_O and γ_I are (approximately) independent of R. In the large R regime, with increasing Reynolds number the trapping region grows, the outflow basin decreases, and the inflow basin shows a slight increase. This implies that the growth of the integrable core occurs at the expense of the outflow escape basin. Finally, it is shown that the variation of the weighted escape rates (γ_Or_O,γ_Ir_I) with Reynolds number was in excellent qualitative agreement with the variation of .     

Dissipative spectral transfers of turbulent plasma pulsations

We discuss the excitation of low-frequency (^s _em_e/m_i) acoustic vibrations by a beam of transverse (rf) waves. It is found that under certain conditions the dispersion (and not simply the excitation increment) of the low-frequency acoustic vibrations is uniquely connected with the rf wave energy density.Translated from Zhurnal Prikladnoi Mekhaniki Tekhnicheskoi Fiziki, Vol. 10, No. 6, pp. 23–29, November–December, 1969.The estimates from (4.5) can be obtained similarly.     

Free- and forced-convection film condensation from a horizontal elliptic tube with a vertical plate and horizontal tube as special cases

A simple mathematical model is developed for the study of the mixed-convection film condensation with downward flowing vapors onto a horizontal elliptic tube. Analytical analysis for both the local condensate film thickness and heat transfer characteristics under simultaneous effects of interfacial vapor shear and pressure gradient has been performed by adopting a unified geometry parameter, eccentricity e. The present results for two limit cases, e = 0 (circular tube) and e = 1.0 (vertical plate) are in an excellent agreement with the earlier works. For very slow vapor flow, the present result for dimensionless mean heat transfer coefficient reduces to the same form as in the earlier works, , whose value is 0.728 for e = 0 and 0.943 for e = 1.0. As for very fast vapor flow, the dimensionless mean heat transfer coefficient, increase with increasing eccentricity under the effects of pressure gradient caused by potential flow and surface tension.     

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))     

Flow visualization of the elastic Taylor-Couette instability in Boger fluids

Flow visualization is performed on an elastically-dominated instability in several similar Boger fluids in Taylor-Couette flow. The onset and evolution of secondary flow are observed over a range of shear rates using reflective mica platelet seeding. Sequences of ambiently and sheet-illuminated images were digitally processed. Rotation of the inner cylinder was ramped from rest to its final value over a time on the order of a polymer relaxation time. Dilute solutions of high molecular weight polyisobutylene in oligomeric polybutene manifest a flow transition at a Deborah number, De _s = _s 1.5 with a Taylor number of 0.00022 in a cell with dimensionless gap ratio = 0.0963. At this transition, simple azimuthal shearing is replaced by steady, roughly square, axisymmetric counter-rotating vortices grossly similar to the well-known Taylor vortex flow that is observed at De _s = 0, Ta = 3612. At De _s = 3.75, Ta = 0.0014, an axisymmetric oscillatory secondary flow develops initially but is replaced by the steady vortices. At De _s = 7.5, Ta = 0.0054, the oscillatory and vortex flow coexist and possess an irregular cellular cross-section. A wide span of growth rates is observed: the ratio of onset to polymer relaxation time ranges from 170000 at De _s = 1.5 to O(10) at De _s > 5. The role of inertia was explored through changing the solvent viscosity. A transition similar to the one that occurs at De _s = 3.75, Ta = 0.0014, from the base azimuthal shearing flow to axisymmetric vortices, was also observed with a much lower viscosity fluid at De _s = 3.3, Ta = 74.     

Investigations on the flow through a staggered tube bundle at Reynolds numbers up toRe=107

In a range of Reynolds numbers 10⁵<Re<10⁷ investigations were made on the flow through a staggered heat exchanger model consisting of five rows. The surfaces of the tubes were polished. The transversal pitch of the tube arrangement wasa=s _t/D=2.0, the longitudinal oneb=s _l/D=1.4. The distribution of the local static pressure and skin friction was experimentally determined around the tubes in several positions of the bundle. Furthermore the total pressure drop p was measured.Results: 1. The dependency of the total pressure coefficient uponRe-number is caused by a shifting of the separation point of the boundary layer. At the criticalRe-numberRe _crit=5×10⁵ the coefficient shows a minimum. The beginning of the supercritical range is indicated by an intermediate maximum of the -distribution atRe=2×10⁶. 2. From the local quantities the momentum loss of each row can be computed. Regarding the pressure drop the entrance effect is restricted to the first row. The coinciding values of the 2., 3. and 4. row represent the pressure drop curve for a heat exchanger consisting of large number of rows. 3. The percentage of the friction drag was determined to have a maximal value of 5%. It diminishes with increasingRe-number down to 0.7% atRe=10⁷. 4. The comparison of the actual results with those of other authors shows, that an increase of the roughness height of the tube surface causes smaller values of criticalRe-numbers. At the same time a rise in was observed in the supercriticalRe-range. In the subcritical flow régime the influence of roughnesses is negligible.

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Zusammenfassung Im Bereich der Reynoldszahl 10⁵<Re<10⁷ wurde die Strömung durch ein fünfreihiges versetztes Rohrbündel mit der Querteilunga=s _t/D=2,0 und der Längsteilungb=s _l/D=1,4 untersucht. Die Rohroberflächen des Wärmetauschermodells waren poliert. Es wurden der örtliche statische Druck sowie die Verteilung der lokalen Wandschub-spannung als Funktion des Umfangswinkels in verschiedenen Positionen des Bündels gemessen. Ferner wurde der Druckabfall p über das gesamte Bündel bestimmt.Ergebnisse: 1. DieRe-Abhängigkeit des Gesamtdruckbeiwertes wird durch ein Wandern des Ablösepunktes der Grenzschicht bewirkt. BeiRe=5×10⁵ ergibt sich im -Verlauf ein Minimum. Ein Zwischenmaximum beiRe=2×10⁶ deutet an, daß der überkritische Strömungszustand erreicht ist. 2. Aus den örtlichen Meßwerten läßt sich durch Integration der Druckverlustanteil der einzelnen Rohrreihen berechnen. Daraus ersieht man, daß der Einlaufvorgang bezüglich des Druckverlustes auf die erste Reihe beschränkt bleibt. Die zusammenfallenden Werte der 2., 3. und 4. Reihe ergeben die Grenzkurve für den -Verlauf eines Bündels mit hohen Rohrreihenzahlen. 3. Der Reibungsanteil am Gesamtwiderstand beträgt maximal 5%. Er nimmt mit steigenderRe-Zahl bis auf etwa 0,7% beiRe=10⁷ ab. 4. Vergleicht man die vorliegenden Meßergebnisse mit denen anderer Autoren, so erkennt man, daß sich mit zunehmender relativer Rauhigkeit die kritischeRe-Zahl verringert. Gleichzeitig ergibt sich im überkritischen Strömungsbereich eine Vergrößerung des Druckverlustbeiwertes. Unterhalb der kritischenRe-Zahl ist der Rauhigkeitseinfluß vernachlässigbar.

     

The development of acoustic generators and their application as a boundary layer transition control device

An experimental investigation of a controllable artificial boundary layer transition by means of electro-acoustic generators was carried out in flat-plate boundary layers. The acoustic generators were flush mounted with the model surface in order to minimize local surface roughnesses which may cause flow instabilities in the laminar boundary layer. The dependence of the input power, pulse ratio, and input frequency of the acoustic generators on the transition threshold values of the input power were determined with surface hot films. In addition, the functional application of the acoustic generators for a controllable artificial boundary layer transition was examined qualitatively by flow visualizations applying the liquid crystal technique.List of symbols A fluctuating component of the hot film anemometer output voltage - time mean hot film anemometer output voltage - ₀ time mean hot film anemometer output voltage at zero velocity - B spectral component of any measured quantity (the used dB-scale is referred to 1 Volt) - time mean hot wire anemometer output voltage - ₀ time mean hot wire anemometer output voltage at zero velocity - f frequency - I _av average input current of the acoustic generator - P mean input power of the acoustic generator - p pressure - Re Reynolds number, Re=U x t/ - t time - t _i period of pulse signal - t _p pulse width of input power - t _s time after switching off heating lamp - U freestream velocity - blowing or sucking velocity produced by the acoustic generator - x longitudinal coordinate from the leading edge (Fig. 2) - x _t distance from the flat plate to the transition location - y coordinate normal to the wall (Fig. 2) - z spanwise coordinate (Fig. 2) - angle of incidence - pulse ratio t _p /t _I - kinematic viscosity - density - ₀ wall shear stress     

Rheological behaviour of two-phase flow of solid particles in a gas

The present investigation was concerned with the rheological behaviour of dilute suspensions of solid particles in a gas in a vertical cocurrent flow moving upwards. Starting from the experimentally determined dependence of the pressure drop on the concentration of solid particles and the Reynolds number of the carrier medium in the steady flow region, the rheological parameters were estimated using pseudo-shear diagrams. Air was the carrier medium and the dispersed phase was one of six fractions of polypropylene powder and five fractions of glass ballotini. The results show that the investigated two-phase systems have pseudoplastic character which becomes more pronounced with increases in concentration, equivalent diameter and density of solid particles in the flowing suspension. C _d coefficient of particle resistance - d _e equivalent diameter of particles - D column diameter - Fr Froude number - g gravitational acceleration - K rheological parameter - L length - n rheological parameter - p _t pressure drop due to friction - p _m total pressure drop - p _ag pressure drop due to acceleration of the gas phase - p _as pressure drop due to acceleration of the solid phase - p _g hydrostatic pressure of the gas phase - p _s specific effective weight of the dispersed phase - r radius - Re Reynolds number - Re _p Reynolds number of a particle - Re _G generalized Reynolds number - Re _G1 generalized Reynolds number relating to the end of the laminar flow region - Re _G2 generalized Reynolds number relating to the beginning of the turbulent flow region - w _z axial component of velocity - u _t steady free-fall velocity of a single particle - w average velocity - w _g average velocity of the gas phase - w _s average velocity of the dispersed phase of solid particles - relative mass fraction of solid particles - x _s volume fraction of solid particles - _g coefficient of pressure drop due to friction - µ dynamic viscosity - _g density of the gas phase - _m density of the suspension - _s density of solid particles - _ds density of the dispersed phase - _w shear stress at the wall