Passive control of vortex induced vibration in internal flow using body shape

We present a concept for passive control of vortex induced vibration (VIV) that uses the body shape of a prismatic body as the control parameter in 2D internal flow. We consider that the Reynolds number based on the prism cross section height is 200 and that the blockage ratio of the channel is 2.5. The working fluid is water and the solid-to-fluid density ratio is 1, so that the prism presents neutral buoyancy and the body shape parameter γ acts as the only control parameter. Two very different fluid dynamics regimes are observed depending on γ with an abrupt transition between them for γ=γ_c, where γ_c represents a critical value obtained numerically. For γ<γ_c the cylinder oscillation is controlled by vortex shedding and represents a typical case of vortex induced vibration. For γ>γ_c the oscillation is a mixture of galloping and vortex induced vibration that causes the prism motion to shift from a stable periodic motion to a highly irregular pattern. The physical explanation for the change of regime is given based on the cylinder equation of motion.     

Linear and non-linear rheology of linear polydisperse polyethylene

Rheological techniques, size-exclusion chromatography, and molecular spectroscopy are the most widely used tools for describing polymer molecular structure in polyolefins. The detection of long-chain branching, and to some extent, its quantification, have been based on quantifying the deviation of polyethylene??s (PE) rheological behavior from that of a linear reference. Although metallocene-based PE has been extensively studied, linear polydisperse originating from Ziegler or Chromium-based catalysts are not often thoroughly considered, despite their high industrial importance. Within this work, we study the linear and non-linear rheology of a set of polydisperse PEs, for which the topological linearity is confirmed by GPC-MALLS measurements. Thus, we can safely quantify the effect of broad molecular weight distribution, high and ultra-high molecular weight fractions on rheological quantities and model parameters. Specifically, the zero-shear viscosity, ?? ₀ vs. M _w, relaxation spectra, phase lag vs. the complex modulus plot (van Gurp?CPalmen method) were applied and significant deviations from the ??rheologically linear?? behavior were observed, attributed only to M _w, M _z and polydispersity. Since the elongational viscosity was typical of linear PE, large-amplitude oscillatory shear and FT-Rheology were applied to quantify the non-linear rheological behavior. The latter was described by a single parameter, $Q=I_{3/1}/\gamma_0^2$ , which for linear polydisperse PE was correlated to the high molecular weight fraction and was constant over a broad range of applied Deborah numbers for the respective excitation frequencies. Since we need to correlate structural features such as broad MWD and HMW to polymer performance under processing conditions, we have to extend the analysis of linear rheological parameters, such as zero-shear viscosity, to non-linear parameters, e.g., the Q parameter quantified and used here.     

Experimental investigation of a confined flow downstream of a circular cylinder centred between two parallel walls

In this work, we present an experimental study of the wall confinement effect on the wake formation behind a circular cylinder of diameter d_c=10 mm and of length L_c=30d_c. The experiments were performed in a water tunnel with the dimensions (length=300d_c, height=3d_c, span L_c=30d_c). The confinement rate was r=1/3 and the Reynolds number was in the range of 30–277. The experiments were done using 2-D PIV measurements. The first instability was delayed by the confinement and the von Kármán vortices characteristics are different from the unconfined case. Proper orthogonal decomposition (POD) of the flow was used for a filtering purpose and to extract the energetic contribution of the different modes. A low-order representation of the flow, constructed from the first pair of modes in the well-defined region of the flow, shows that von Kármán vortices are equivalent to vanishing progressive waves. Measurements done above the cylinder show the presence of 3-D span instabilities showing great similarities with “Mode A” and “Mode B” found in the unconfined case.     

Macroscopic and microscopic examination of the relationship between crack velocity and path and Rayleigh surface wave speed in single crystal silicon

The speed of Rayleigh surface waves, denoted C_R, is the accepted upper limit for Mode I crack velocity in monolithic solids. In the current contribution, we discuss several critical issues associated with the velocity of Rayleigh surface waves and crack velocity in single crystal (SC) brittle solids, and the global and local influence of C_R on crack path selection in particular.Recent cleavage experiments in SC silicon showed that crack velocity at certain cleavage planes and crystallographic orientations cannot exceed a small fraction of C_R, and thereafter the crack deflects to other cleavage planes. Indeed, C_R defined by the continuum mechanics ignores atomistic phenomena occurring during rapid crack propagation, and therefore is limited in predicting the crack velocity. Examination of these anomalies shows that this limitation lies in microstructural lattice arrangement and in anisotropic phonon radiation during rapid crack propagation. Globally, C_R has no influence on the crack deflection phenomenon. However, the misfit in C_R between the original plane of propagation and the deflected plane generates local instabilities along the deflection zone.     

Transient shear rheology of carbon nanofiber/polystyrene melt composites

We characterize the transient shear rheology of polystyrene/carbon nanofiber composites. Our experimental measurements of the composites show increasing stress overshoot responses to transient shear as the carbon nanofiber concentration increases. We also find the steady state viscosity reached at long times during application of a constant shear rate increases with increasing carbon nanofiber concentration. Flow reversal experiments show the effects of nanofiber orientation and structural evolution on the composite's rheological response.We present a microstructurally based constitutive model where all but two parameters are determined by rheological characterization of the pure polymer and the shape and concentration of the nanoparticles. The Folgar-Tucker constant, C_I, is treated as a fitting parameter, while several definitions for the shape factors A, B, C and F are evaluated. We make note of the effects each parameter has on the model's predictions. We find that the constitutive model is in agreement with our experimentally measured transient shear rheology of the PS/CNF melt composites for the CNF concentrations and shear rates presented.     

The unsteady heat transfer due to a heat source in an MHD stretching sheet flow

The time evolution in the temperature field resulting from the sudden introduction of a heat source into the already fully established steady MHD flow of an electrically conducting fluid past a linearly stretching isothermal surface is considered. The problem is shown to be fully described by two dimensionless parameters, a modified magnetic field strength ?? and a heat source strength Q. Numerical solutions of the initial-value problem show that there is a critical value Q _c of the parameter Q, dependent on ??, such that, for Q<Q _c , the solution approaches a steady state at large times and, for Q>Q _c , the solutions grows exponentially large as time increases. This growth rate is determined through an eigenvalue problem which also determines the critical value Q _c . The limits of Q _c for both small and large values of ?? are discussed.     

Rheology of suspensions of spherical particles in a newtonian and a non-newtonian fluid

Properties of suspensions of spherical glass beads (25–38 μm dia.) in a Newtonian fluid and a non-Newtonian (NBS Fluid 40) fluid were measured at volume fractions, φ, of 0%, 10%, 20% and 30%. Measurements were made using a modified and computerized Weissenberg Rheogoniometer. Properties measured included steady shear viscosity, η($\text{γ}\text{.}$), first normal stress difference, N₁($\text{γ}\text{.}$), linear viscoelastic properties, η′(ω) and G′(ω), shear stress relaxation, σ^? ($\text{γ}\text{.}$, t), and growth, σ⁺($\text{γ}\text{.}$, t) and normal stress relaxation, N₁^?($\text{γ}\text{.}$, t).For a the Newtonian fluid, increasing φ causes both η and η′ to increase, with η′ showing a slight frequency dependence. Both N₁ and G′ are zero and stress relaxation and growth occur essentially instantaneously. For the NBS fluid, both η and η′ increse with φ at all $\text{γ}\text{.}$ and ω, respectively, the increase being greater as $\text{γ}\text{.}$ and ω approach zero. N₁ and G′ are less affected by the presence of the particles than η and η′ with the effect on G′ being more pronounced than on N₁. For fixed $\text{γ}\text{.}$, stress relaxation and growth exhibit greater non-linear effects as φ is increased. A model for predicting a priori the linear viscoelastic properties for suspensions was found to yeild reasonable estimates up to φ = 20%.     

Influence of NaClO3 on the rheological behaviour of a micellar solution of CPCl

It is now well know that a small addition of salt to a micellar solution often increases the zero-shear viscosity η₀ of the solution, the understanding of the behaviour at high salt content is more questionable. In this situation, addition of more salt induces a decrease of η₀. In this experimental work we investigate the linear and non-linear rheological behaviour of a new micellar system: CPCl (surfactant)/NaClO₃ (salt). Studies of the evolution of η₀ as well as G₀ (the elastic modulus) or τ_R (the relaxation time) are in agreement with the hypothesis of a diminution of the mean micellar length when, after the maximum η₀, the salt content increases. In the non-linear behaviour (non-Newtonian viscosity) the evolution of γ˙ _c, (which defines the occurrence of the shear thinning) with salt concentration C_S is also in agreement with such a hypothesis. Received: 29 March 1999/Accepted: 20 March 2000     

On stability of self-assembled nanoscale patterns

We conduct linear and nonlinear stability analyses on a paradigmatic model of nanostructure self-assembly. We focus on the spatio-temporal dynamics of the concentration field of deposition on a substrate. The physical parameter of interest is the mean concentration C₀ of the monolayer. Linear stability analysis of the system shows that a homogeneous monolayer is unstable when C₀ lies within a band symmetric about . On increasing C₀ from zero, the homogeneous solution destabilizes to a hexagonal array, which then transitions to stripes. Transitions to and from the hexagonal state are subcritical. Square patterns are unstable for all values of C₀ transitioning either to hexagons or stripes. Further, we present stability maps for striped arrays by considering possible instabilities. The analytical results are confirmed by numerical integrations of the Suo-Lu model. Our formalism provides a theoretical framework to understand guided self-assembly of nanostructures.     

Several effects of melt viscosity on the nature ofC p —T data aboveT g for acrylate,methacrylate, and hydrocarbon polymers

Using objective computerized statistical procedures, we have examined high precisionC _p data by DSC reported by Wunderlich and Gaur for a series of alkyl acrylate and methacrylate polymers. Although they claimed the data to be linear inT aboveT _g , our results do not support the linear model. One or two endothermic slope changes are revealed aboveT _g in lowT _f polymers (T _f < 20 °C) and at least one exothermic slope change in highT _f polymers (T _f > 20 °C).T _f is the flow temperature of Ueberreiter. Both the first endotherm and the first exotherm occur near (1.22 ± 0.07)T _g , suggesting aT _ll type phenomenon.T _ll varies as \(1/\bar M_n \) . The first exotherm is associated by us with wetting of the DSC pan by molten polymer on the first heating of particulate highT _f polymers. The rate of wetting, and presumably the magnitude of the exotherm, depends in part on the ratio,γ/η, whereγ is surface tension andη is melt viscosity of the molten polymer. Sinceγ is relatively constant, the molecular weight and temperature dependence for rate of wetting resides inη, which depends on \(\bar M_w \) . For \(\bar M_n > > \bar M_c \) , a second exothermic event caused by sintering, and also controlled by η, may be present. The interactive roles of \(\bar M_n ,\bar M_w ,\bar M_w /\bar M_n \) ;M _c (entanglement molecular weight); particle size, and heating rate onC _p —T behaviour are delineated for the first time. LowT _f hydrocarbon polymers, namely atactic polyalphaolefins,C ₃ ,C ₅ ,C ₆ ; PIB; and dienes, PBD and cis-PI, exhibit single or double endotherms. Other results on highT _f polymers showing exothermic effects, notably PS, PnBMA and polyglycidylmethacrylate are cited.     

Hydrodynamic behavior of an internally circulating fluidized bed with tubular gas distributors

To better understand the hydrodynamic behavior of an internally circulating fluidized bed, solids holdup in the down-comer （Eso）, solids circulation rate （Gs） and gas bypassing fraction （from down-comer to riser y~R, and from riser to down-comer yRD） were experimentally studied. The effects of gas velocities in the riser and in the down-comer （UR and UD）, orifice diameter in the draft tube （dor）, and draft tube height （HR） were investigated. Experimental results showed that increase of gas velocities led to increase in Gs and yDR, and slight decrease in yeD. Larger orifice diameter on the draft tube led to higher 8sD, Gs and yDR, but had insignificant influence on YRD. with increasing draft tube height, both Gs and YDR first increased and then decreased, while yRD first decreased and then increased. Proposed correlations for predicting the hydrodynamic parameters agreed reasonably well with experimental values.     

Flow in a spherical cavity due to a stokeslet

The earth is considered as a rigid spherical cavity of radius a filled with a highly viscous incompressible fluid of viscosity η. The non-axisymmetric problem of flow due to a stokeslet of strength F/8πη located at (0, 0, c), c < a with its axis along OX, O being the centre of the sphere, is discussed for small Reynolds numbers. The expressions for velocity and pressure are obtained in terms of A(r, θ, φ) and B(r, θ, φ), biharmonic and harmonic functions respectively, using a sphere theorem for non-axisymmetric flow inside a sphere. The drag on the sphere exerted by the fluid is found to be independent of the location of the stokeslet.     

Determination of flow activation energy at viscosity maximum for spherical and wormlike micelles of different lengths and flexibility

Steady shear rheological measurements were carried out on aqueous solutions containing 15 mM cetyltrimethylammonium bromide (CTABr) and a constant value of [MX] and temperature for MX = 2,3-; 2,4-; 2,5-; 2,6-; 3,4-; and 3,5-Cl₂BzNa with Bz^?representing C₆H₃CO_2?. Plots of zero shear viscosity (η ₀) vs. [MX] at 35 °C and 15 mM CTABr show the presence of single maximum and double maxima for MX = 2,3- and 3,5-Cl₂BzNa, respectively. Turbidity data (absorbance at 600 nm vs. [MX]) coupled with η ₀vs. [MX] data at 35 °C reveal indirectly the presence of vesicles along with wormlike micelles (WM) at MX / CTABr > 0. 7 for MX = 3,5-Cl₂BzNa. Temperature dependence of η ₀in the vicinity of the viscosity maximum shows nonlinear and linear Arrhenius behavior, within the temperature range of 20–55 °C, for MX = 2,3-; 2,4-; 2,5-; 3,4-; and 3,5-Cl₂BzNa, respectively. The values of η ₀, $\dot {\gamma }_{\text {cr}} $ (critical shear rate), and flow activation energy correlate with CTABr micellar binding constants of counterions.     

Effect of surfactant concentration on saturated flow boiling in vertical narrow annular channels

Saturated flow boiling of environmentally acceptable nonionic surfactant solutions of Alkyl (8–16) was compared to that of pure water. The concentration of surfactant solutions was in the range of 100–1000 ppm. The liquid flowed in an annular gap of 2.5 and 4.4 mm between two vertical tubes. The heat was transferred from the inner heated tube to two-phase flow in the range of mass flux from 5 to 18 kg/m² s and heat flux from 40 to 200 kW/m². Boiling curves of water were found to be heat flux and channel gap size dependent but essentially mass flux independent. An addition of surfactant to the water produced a large number of bubbles of small diameter, which, at high heat fluxes, tend to cover the entire heater surface with a vapor blanket. It was found that the heat transfer increased at low values of relative surfactant concentration C/C₀, reaches a maximum close to the value of C/C₀ = 1 (where C₀ = 300 ppm is the critical micelle concentration) and decreased with further increase in the amount of additive. The dependence of the maximal values of the relative heat transfer enhancement, obtained at the value of relative concentration of C/C₀ = 1, on the boiling number Bo may be presented as single curve for both gap sizes and the whole range of considered concentrations.     

Non-linear convection in a porous medium with internal heat sources

The paper studies non-linear thermal convection in a horizontal porous layer of fluid with nearly insulating boundaries and in the presence of internal heat sources. Square and hexagonal cells are found to be the only possible stable convection cells. Finite amplitude instability could exist for some particular forms of an internal heat source Q. For a uniform Q, the preferred flow pattern is that of hexagons for amplitude ε smaller than some critical value ε_c, while both squares and hexagonal cells are stable for ε ? ε_c. The convective motion is downward at the hexagonal cell's centers. For a non-uniform Q, the qualitative features of thermal convection depend on the actual form Q. In particular, a non-uniform Q can increase or decrease the cell's size and the critical Rayleigh number at the onset of convection, and stabilize or destabilize the convective motion in the form of hexagonal cells with either upward or downward motion at the cell's centers.     

Filling the gap between transient and steady shear rheology of aqueous graphene oxide dispersions

Even though the rheological behavior of aqueous graphene oxide (G-O) dispersions has been shown to be strongly time-dependent, only few transient measurements have been reported in the literature. In this work, we attempt to fill the gap between transient and steady shear rheological characterizations of aqueous G-O dispersions in the concentration range of 0.004 < ? <?3.5 wt%, by conducting comprehensive rheological measurements, including oscillatory shear flow, transient shear flow, and steady shear flow. Steady shear measurements have been performed after the evaluation of transient properties of the G-O dispersions, to assure steady-state conditions. We identify the critical concentration ? _c =?0.08 wt% (where G-O sheets start to interact) from oscillatory shear experiments. We find that the rheology of G-O dispersions strongly depends on the G-O concentration ?. Transient measurements of shear viscosity and first normal stress difference suggest that G-O dispersions behave like nematic polymeric liquid crystals at ?/? _c =?25, in agreement with other work reported in the literature. G-O dispersions also display a transition from negative to positive values of the first normal stress difference with increasing shear rates. Experimental findings of aqueous graphene oxide dispersions are compared and discussed with models and experiments reported for nematic polymeric liquid crystals, laponite, and organoclay dispersions.     

Rheological analysis of highly concentrated w/o emulsions

A series of highly concentrated lipophilic cosmetic emulsions were analysed, in order to determine their rheological and textural properties, as a function of their microstructure. The originality of this study lies in the methodology used, especially the shear-stress scanning analysis. The results of a very powerful and comprehensive dynamic rheological analysis suggest the existence of two critical volume fraction values: besides the “close-packed” value φ _c , a “slack-packed” value φ₀, close to 0.60 could be demonstrated. It has been shown that the close-packed structure is stable under shear; in constrast, the slack-packed configuration, defined as φ₀<φ<φ _c is unstable under shear. A comparison with theoretical models, especially that of Princen, showed good agreement and allowed the close-packed value φ _c to be defined more precisely as 0.67. The gap between 0.67 and 0.74 is probably indicative of a highly polydisperse distribution, as confirmed by microscopic analysis. Flow experiments confirmed the validity of Princen‘s model. Received: 20 February 1997 Accepted: 20 January 1998     

Lift force acting on single bubbles in linear shear flows

Lift coefficients, C_L, of single bubbles in linear shear flows are measured to investigate effects of the bubble shape, the liquid velocity gradient and the fluid property on C_L. The range of the Morton number, M, tested is from logM = − 6.6 to − 3.2. The shapes of bubbles are spherical and ellipsoidal. A correlation of bubble aspect ratio for single bubbles in infinite stagnant liquids proposed in our previous study can give good evaluations for bubbles in the linear shear flows. The C_L of spherical bubbles at low bubble Reynolds numbers, Re, depend on the dimensionless shear rate Sr and Re and decrease with increasing Re. These characteristics agree with the Legendre-Magnaudet correlation. The use of a single dimensionless group such as Re, the Eötvös number, the Weber number and the Capillary number cannot correlate C_L of non-spherical bubbles. The trend of the critical Re for the reversal of the sign of C_L is the same as that for the onset of oscillation of bubble motion, which supports the mechanism proposed by Adoua et al., at least within the range of −6.6 ≤ logM ≤ −3.2. An experimental database of C_L is provided for validation of available C_L models and CFD.     

Operator method for solving the plane elasticity problem for a strip with periodic cuts

In the present paper, we use the conformal mapping z/c = ζ?2a sin ζ (a, c?const, ζ = u + iv) of the strip {|v| ≤ v ₀, |u| < ∞} onto the domain D, which is a strip with symmetric periodic cuts. For the domain D, in the orthogonal system of isometric coordinates u, v, we solve the plane elasticity problem. We seek the biharmonic function in the form F = C ψ ₀ + S ψ*₀ + x(C ψ ₁ ? S ψ ₂) + y(C ψ ₂ + S ψ ₁), where C(v) and S(v) are the operator functions described in [1] and ψ ₀(u), …, ψ ₂(u) are the desired functions. The boundary conditions for the function F posed for v = ±v ₀ are equivalent to two operator equations for ψ ₁(u) and ψ ₂(u) and to two ordinary differential equations of first order for ψ ₀(u) and ψ*₀(u) [2]. By finding the functions ψ _j (u) in the form of trigonometric series with indeterminate coefficients and by solving the operator equations, we obtain infinite systems of linear equations for the unknown coefficients. We present an efficient method for solving these systems, which is based on studying stable recursive relations. In the present paper, we give an example of analysis of a specific strip (a = 1/4, v ₀ = 1) loaded on the boundary v = v ₀ by a normal load of intensity p. We find the particular solutions corresponding to the extension of the strip by the longitudinal force X ^∞ and to the transverse and pure bending of the strip due to the transverse force Y ^∞ and the constant moment M ^∞, respectively. We also present the graphs of normal and tangential stresses in the transverse cross-section x = 0 and study the stress concentration effect near the cut bottom.