ALBERT

Description: Experiments were conducted to measure the collisional particle pressure in both cocurrent and countercurrent flows of liquid-solid mixtures. The collisional particle pressure, or granular pressure, is the additional pressure exerted on the containing walls of a particulate system due to the particle collisions. The present experiments involve both a liquid-fluidized bed using glass, plastic or steel spheres and a vertical gravity-driven flow using glass spheres. The particle pressure was measured using a high-frequency-response flush-mounted pressure transducer. Detailed recordings were made of many different particle collisions with the active face of this transducer. The solids fraction of the flowing mixtures was measured using an impedance volume fraction meter. Results show that the magnitude of the measured particle pressure increases from low concentrations (〈10% solid volume fraction), reaches a maximum for intermediate values of solid fraction (30-40%), and decreases again for more concentrated mixtures (〉40%). The measured collisional particle pressure appears to scale with the particle dynamic pressure based on the particle density and terminal velocity. Results were obtained and compared for a range of particle sizes, as well as for two different test section diameters. In addition, a detailed analysis of the collisions was performed that included the probability density functions for the collision duration and collision impulse. Two distinct contributions to the collisional particle pressure were identified: one contribution from direct contact of particles with the pressure transducer, and the second one resulting from particle collisions in the bulk that are transmitted through the liquid to the pressure transducer.

Description: We examine the inviscid flow generated around a body moving impulsively from rest with a constant velocity U in a constant density gradient, ∇ρ0, which is assumed to be weak in the sense ε = a|∇ρ0|/ρ0 ≪ 1, where a is the length scale of the body. In the absence of a density gradient (ε = 0), the flow is irrotational and no force acts on the body. When 0 〈 ε ≪ 1, vorticity is generated by a baroclinic torque and vortex stretching, which introduce a rotational component into the flow. The aim is to calculate both the flow around the body and the force acting on it. When a two-dimensional body moves perpendicularly to the density gradient U·∇ρ0 = 0, the density and velocity field are both steady in the body's frame of reference and the vorticity field decays with distance from the body. When a three-dimensional body moves perpendicularly to the density gradient, the vorticity field is regular in the main flow region, script D signM, but is singular in a thin inner region script D signI located adjacent to the body and to the downstream-attached streamline, and the flow is characterized by trailing horseshoe vortices. When the body moves parallel to the density gradient U × ∇ρ0 = 0, the density field is unsteady in the body's frame of reference; however to leading order the flow is steady in the region script D signM moving with the body for Ut/a ≫ 1. In the thin region script D signI of thickness O(aε), the density gradient and vorticity are singular. When U × ∇ρ0 = 0 this singularity leads to a downstream 'jet' with velocities of O(-(U·∇ρ0)U a/(ρ0U)) on the downstream attached streamline(s). In the far field the flow is characterized by a sink of strength CMscript V sign(U·∇ρ0)/2ρ0, located at the origin, where CM is the added-mass coefficient of the body and script V sign is the body's volume. The forces acting on a body moving steadily in a weak density gradient are calculated by considering the steady relative velocity field in region script D signM and evaluating the momentum flux far from the body. When U·∇ρ0 = 0, a lift force, CLscript V sign(U × ∇ρ0) × U, pushes the body towards the denser fluid, where the lift coefficient is CL = CM/2 for a three-dimensional body, that is axisymmetric about U, and is CL = (CM + 1)/2 for a two-dimensional body. The direction of the lift force is unchanged when U is reversed. A general expression for the forces on bodies moving in a weak shear and perpendicularly to a density gradient is calculated. When U × ∇ρ0 = 0, a drag force -CDscript D sign(U·∇ρ0)U retards the body as it moves into denser fluid, where the drag coefficient is CD = CM/2, for both two- and three-dimensional axisymmetric bodies. The direction of the drag force changes sign when U is reversed. There are two contributions to the drag calculation from the far field; the first is from the wake 'jet' on the attached streamline(s) caused by the rotational component of the flow and this leads to an accelerating force. The second and larger contribution arises from a downstream density variation, caused by the distortion of the isopycnal surfaces by the primary irrotational flow, and this leads to a drag force. When cylinders or spheres move with a velocity U at arbitrary orientation to the density gradient, it is shown that they are acted on by a linear combination of lift and drag forces. Calculations of their trajectories show that they initially slow down or accelerate on a length scale of order ρ0/|∇ρ0| (independent of script V sign and U) as they move into regions of increasing or decreasing density, but in general they turn and ultimately move parallel to the density gradient in the direction of increasing density gradient.

Description: In Hammerton & Kerschen (1996), the effect of the nose radius of a body on boundary-layer receptivity was analysed for the case of a symmetric mean flow past a two-dimensional body with a parabolic leading edge. A low-Mach-number two-dimensional flow was considered. The radius of curvature of the leading edge, rn, enters the theory through a Strouhal number, S ωrn/U, where ω is the frequency of the unsteady free-stream disturbance and U is the mean flow speed. Numerical results revealed that the variation of receptivity for small S was very different for free-stream acoustic waves propagating parallel to the mean flow and those free-stream waves propagating at an angle to the mean flow. In this paper the small-S asymptotic theory is presented. For free-stream acoustic waves propagating parallel to the symmetric mean flow, the receptivity is found to vary linearly with S, giving a small increase in the amplitude of the receptivity coefficient for small S compared to the flat-plate value. In contrast, for oblique free-stream acoustic waves, the receptivity varies with S1/2, leading to a sharp decrease in the amplitude of the receptivity coefficient relative to the flat-plate value. Comparison of the asymptotic theory with numerical results obtained in the earlier paper confirms the asymptotic results but reveals that the numerical results diverge from the asymptotic result for unexpectedly small values of S.

Description: The so-called Crocco integral establishes a relation between the velocity and temperature distributions in steady boundary layer flow. It corresponds to an exact solution of the flow equations in the case of unity Prandtl number and an adiabatic wall, where it reduces to the condition that the total enthalpy remains constant throughout the boundary layer, irrespective of pressure gradient and compressibility. The effect of Prandtl number is usually incorporated by assuming a constant recovery factor across the entire boundary layer. Strictly, however, this modification is in conflict with the conservation-of-energy principle. In search of a more complete expression for the Crocco integral the present study applies an asymptotic solution approach to the energy equation in constant-property flow. The analysis of self-similar boundary layer solutions results in a formulation of the Crocco integral which correctly incorporates the effect of Prandtl number to first order, and that is complete in the sense that it satisfies the energy conservation requirement. Furthermore, the result is found to be applicable not only to self-similar boundary layers, but also to provide a solution to the laminar flow equations in general as well. The effect of varying properties is considered with regard to the extension of the expression to more general flow conditions. In addition to the asymptotic expression for the Crocco integral, asymptotic solutions are also obtained for the recovery factor for various classes of flows.

Description: The equation relating second- and third-order velocity structure functions was presented by Kolmogorov; Monin attempted to derive that equation on the basis of local isotropy. Recently, concerns have been raised to the effect that Kolmogorov's equation and an ancillary incompressibility condition governing the third-order structure function were proven only on the restrictive basis of isotropy and that the statistic involving pressure that appears in the derivation of Kolmogorov's equation might not vanish on the basis of local isotropy. These concerns are resolved. In so doing, results are obtained for the second- and third-order statistics on the basis of local homogeneity without use of local isotropy. These results are applicable to future studies of the approach toward local isotropy. Accuracy of Kolmogorov's equation is shown to be more sensitive to anisotropy of the third-order structure function than to anisotropy of the second-order structure function. Kolmogorov's 4/5 law for the inertial range of the third-order structure function is obtained without use of the incompressibility conditions on the second- and third-order structure functions. A generalization of Kolmogorov's 4/5 law, which applies to the inertial range of locally homogeneous turbulence at very large Reynolds numbers, is shown to also apply to the energy-containing range for the more restrictive case of stationary, homogeneous turbulence. The variety of derivations of Kolmogorov's and Monin's equations leads to a wide range of applicability to experimental conditions, including, in some cases, turbulence of moderate Reynolds number.

Description: Stokesian Dynamics has been used to investigate the origins of shear thickening in concentrated colloidal suspensions. For this study, we considered a monolayer suspension composed of charge-stabilized non-Brownian monosized rigid spheres dispersed at an areal fraction of φ a = 0.74 in a Newtonian liquid. The suspension was subjected to a linear shear field. In agreement with established experimental data, our results indicate that shear thickening in this system is associated with an order-disorder transition of the suspension microstructure. Below the critical shear rate at which this transition occurs, the suspension microstructure consists of two-dimensional analogues of experimentally observed sliding layer configurations. Above this critical shear rate, suspensions are disordered, contain particle clusters, and exhibit viscosities and microstructures characteristic of suspensions of non-Brownian hard spheres. In addition, suspensions possessing the sliding layer microstructure at the beginning of supercritical shearing tend to retain this microstructure for a period of time before disordering. The onset of this disorder is due to the formation of particle doublets within the suspension. Once formed, these doublets rotate, due to the bulk motion, and disrupt the long-range order of the suspension. The cross-stream component of the centre-to-centre separation vector associated with the two particles forming a doublet, which is zero when the doublet is perfectly aligned with the bulk velocity vector, grows exponentially with time. This strongly suggests that the evolution of these doublets is due to a change in the stability of the sliding layer configurations, with this type of ordered microstructure being linearly unstable above a critical shear rate. This contention is supported by results of a stability analysis. The analysis shows that a single string of particles is subject to a linear instability leading to the formation of particle doublets. Simulations were repeated with different numbers of particles in the computational domain, with the results found to be qualitatively independent of system size.

Description: This paper is concerned with the problem of viscous flow in an elastic tube. Elastic tubes collapse (buckle non-axisymmetrically) when the transmural pressure (internal minus external pressure) falls below a critical value. The tube's large deformation during the buckling leads to a strong interaction between the fluid and solid mechanics. In this study, the steady three-dimensional Stokes equations are used to analyse the slow viscous flow in such a tube whose deformation is described by geometrically nonlinear shell theory. Finite element methods are used to solve the large-displacement fluid-structure interaction problem. Typical wall deformations and flow fields in the strongly collapsed tube are shown. Extensive parameter studies illustrate the tube's flow characteristics (e.g. volume flux as a function of the applied pressure drop through the tube) for boundary conditions corresponding to the four fundamental experimental setups. It is shown that lubrication theory provides an excellent approximation of the fluid traction while being computationally much less expensive than the solution of the full Stokes equations. Finally, the computational predictions for the flow characteristics and the wall deformation are compared to the results obtained from an experiment.

Description: When a small amount of marked solute is released into a stratified fluid, there is lateral dispersion of the marked solute and a larger lateral dispersion of any density anomaly. The method of moments is used to calculate the two dispersion coefficients. The excess dispersion for the density is shown to be proportional to the fractional density decrease from the bed to the free surface and to the cube of the water depth, and inversely proportional to the vertical mixing for lateral momentum. For weak turbulent mixing the stratification-induced lateral dispersion for the density anomaly can be several orders of magnitude greater than the lateral turbulent mixing for marked solute.

Description: In most practical situations, turbulent premixed flames are ducted and, accordingly, subjected to externally imposed pressure gradients. These pressure gradients may induce strong modifications of the turbulent flame structure because of buoyancy effects between heavy cold fresh and light hot burnt gases. In the present work, the influence of a constant acceleration, inducing large pressure gradients, on a premixed turbulent flame is studied using direct numerical simulations. A favourable pressure gradient, i.e. a pressure decrease from unburnt to burnt gases, is found to decrease the flame wrinkling, the flame brush thickness, and the turbulent flame speed. It also promotes counter-gradient turbulent transport. On the other hand, adverse pressure gradients tend to increase the flame brush thickness and turbulent flame speed, and promote classical gradient turbulent transport. As proposed by Libby (1989), the turbulent flame speed is modified by a buoyancy term linearly dependent on both the imposed pressure gradient and the integral length scale lt. A simple model for the turbulent flux u″ c″ is also proposed, validated from simulation data and compared to existing models. It is shown that turbulent premixed flames can exhibit both gradient and counter-gradient transport and a criterion integrating the effects of pressure gradients is derived to differentiate between these regimes. In fact, counter-gradient diffusion may occur in most practical ducted flames.

Description: An analysis of the three-dimensional instability of two-dimensional viscoelastic elliptical flows is presented, extending the inviscid analysis of Bayly (1986) to include both viscous and elastic effects. The problem is governed by three parameters: E, a geometric parameter related to the ellipticity; Re, a wavenumber-based Reynolds number; and De, the Deborah number based on the period of the base flow. New modes and mechanisms of instability are discovered. The flow is generally susceptible to instabilities in the form of propagating plane waves with a rotating wavevector, the tip of which traces an ellipse of the same eccentricity as the flow, but with the major and minor axes interchanged. Whereas a necessary condition for purely inertial instability is that the wavevector has a non-vanishing component along the vortex axis, the viscoelastic modes of instability are most prominent when their wavevectors do vanish along this axis. Our analytical and numerical results delineate the region of parameter space of (E, Re, De) for which the new instability exists. A simple model oscillator equation of the Mathieu type is developed and shown to embody the essential qualitative and quantitative features of the secular viscoelastic instability. The cause of the instability is a buckling of the 'compressed' polymers as they are perturbed transversely during a particular phase of the passage of the rotating plane wave.