Showing papers on "Shear flow published in 1983"

A theory for the rapid flow of identical, smooth, nearly elastic, spherical particles

Abstract: We focus attention on an idealized granular material comprised of identical, smooth, imperfectly elastic, spherical particles which is flowing at such a density and is being deformed at such a rate that particles interact only through binary collisions with their neighbours. Using general forms of the probability distribution functions for the velocity of a single particle and for the likelihood of binary collisions, we derive local expressions for the balance of mass, linear momentum and fluctuation kinetic energy, and integral expressions for the stress, energy flux and energy dissipation that appear in them. We next introduce simple, physically plausible, forms for the probability densities which contain as parameters the mean density, the mean velocity and the mean specific kinetic energy of the velocity fluctuations. This allows us to carry out the integrations for the stress, energy flux and energy dissipation and to express these in terms of the mean fields. Finally, we determine the behaviour of these fields as solutions to the balance laws. As an illustration of this we consider the shear flow maintained between two parallel horizontal plates in relative motion.

Coherent structures—reality and myth

Abstract: The nature and significance of large‐scale coherent structures in turblent shear flows are addressed. A definition for the coherent structure is proposed and its implications discussed. The characteristic coherent structure properties are identified and the analytical and experimental constraints in the eduction of coherent structures are examined. Following a few comments on coherent motions in wall layers, the accumulated knowledge from a number of recent and ongoing coherent structure investigations in excited and unexcited free shear flows in the author’s laboratory is reviewed. Also briefly addressed are effects of initial conditions, the role of coherent structures in jet noise production and broadband noise amplification, the feedback effect of coherent structures, the use of the Taylor hypothesis in coherent structure description, negative production, turbulence suppression via excitation, validity of the Reynolds number similarity hypothesis, etc. From the detailed quantitative results, a picture of the state of the art in coherent structure studies emerges. While coherent structures are highly interesting characteristic features of (perhaps all) turbulent shear flows, it is argued that their dynamical significance has been overemphasized. These are predominant only in their early stages of formation following instability, or in resonant situations and excited flows, or in regions adjacent to a wall of a turbulent boundary layer. The coherent Reynolds stress, vorticity, and production are comparable to (and not an order of magnitude larger than) the time‐average Reynolds stress, vorticity, and production, respectively, in fully developed states of turbulent shear flows, where incoherent turbulence is also important and cannot be ignored. The concept and importance of coherent structures are here to stay; understanding and modeling of turbulent shear flows will be incomplete without them; but they are not all that matter in turbulent shear flows.

Secondary instability of wall-bounded shear flows

Abstract: The present analysis of a secondary instability in a wide class of wall-bounded parallel shear flows indicates that two-dimensional, finite amplitude waves are exponentially unstable to infinitessimal three-dimensional disturbances. The instability appears to be the prototype of transitional instability in such flows as Poiseuille flow, Couette flow, and flat plate boundary layers, in that it has the convective time scales observed in the typical transitions. The energetics and vorticity dynamics of the instability are discussed, and it is shown that the two-dimensional perturbation without directly providing energy to the disturbance. The three-dimensional instability requires that a threshold two-dimensional amplitude be achieved. It is found possible to identify experimental features of transitional spot structure with aspects of the nonlinear two-dimensional/linear three-dimensional instability.

Improved turbulence models based on large eddy simulation of homogeneous, incompressible turbulent flows

Abstract: The physical bases of large eddy simulation and subgrid modeling are studied. A subgrid scale similarity model is developed that can account for system rotation. Large eddy simulations of homogeneous shear flows with system rotation were carried out. Apparently contradictory experimental results were explained. The main effect of rotation is to increase the transverse length scales in the rotation direction, and thereby decrease the rates of dissipation. Experimental results are shown to be affected by conditions at the turbulence producing grid, which make the initial states a function of the rotation rate. A two equation model is proposed that accounts for effects of rotation and shows good agreement with experimental results. In addition, a Reynolds stress model is developed that represents the turbulence structure of homogeneous shear flows very well and can account also for the effects of system rotation.

Shear-flow instability at the interface between two viscous fluids

Abstract: We consider the linear stability of the cocurrent flow of two fluids of different viscosity in an infinite region (the viscous analogue of the classical Kelvin-Helmholtz problem). Attention is confined to the simplest case, Couette flow, and we solve the problem using both numerical and asymptotic techniques. We find that the flow is always unstable (in the absence of surface tension). The instability arises at the interface between the two fluids and occurs for short wavelengths, when viscosity rather than inertia is the dominant physical effect.

Computer ‘‘experiment’’ for nonlinear thermodynamics of Couette flow

Abstract: Nonequilibrium computer simulations reveal that the equation of state of fluids undergoing shear flow, varies with strain rate. This observation prompted the development of a nonlinear generalization of irreversible thermodynamics to describe steady planar Couette flow, very far from equilibrium. In this paper we use computer simulation to perform a quantitative test of a prediction of this thermodynamics. The prediction tested is: fluids which exhibit positive shear dilatancy for isothermal shear flow should also cool as the strain rate is increased while keeping the internal energy constant. To perform calculations of this effect a new nonequilibrium molecular dynamics algorithm was developed to simulate Couette flow at constant internal energy.

An Integral Constitutive Equation for Mixed Flows: Viscoelastic Characterization

Abstract: A viscoelasticconstitutive equation of the single‐integral form has been designed. Its memory function is factored into a time‐dependent part and a strain‐dependent part. The time function is the usual series of exponential relaxations. Its relaxation times and weighting coefficients are determined by nonlinear regression on linear viscoelastic data: stress relaxation after small‐strain and small‐amplitude sinusoidal oscillations. The relative accuracy of linear and nonlinear regression fitting is compared. The strain‐dependent function is new. It is of a simple sigmoidal form with only two parameters: one determined from shear and the other from extensional data. Its sigmoidal form provides a finite linear viscoelastic region, a steady viscosity in uniaxial extension, and a well‐behaved power‐law shear viscosity at high shear rate. An efficient strategy for collecting sufficient data to determine the parameters of the equation is described. Predictions of the equation are tested against shear and extension data collected on the Rheometrics System Four for two polydimethylsiloxanes and against data for other polymer melts from the literature. Both uniaxial and biaxial extension as well as shear data are described. Transient shear normal stresses are somewhat underpredicted. The constitutive equation has the potential for modeling mixed shear and extensional flows as encountered in processing operations and is simple enough to be attractive for efficient computer‐aided analysis by modern finite element methods.

Finite Element Computational Fluid Mechanics

Abstract: Finite element analysis as applied to the broad spectrum of computational fluid mechanics is analyzed. The finite element solution methodology is derived, developed, and applied directly to the differential equation systems governing classes of problems in fluid mechanics. The heat conduction equation is used to reveal the essence and elegance of finite element theory, including higher order accuracy and convergence. The algorithm is extended to the pervasive nonlinearity of the Navier-Stokes equations. A specific fluid mechanics problem class is analyzed with an even mix of theory and applications, including turbulence closure and the solution of turbulent flows.

Instabilities of dynamic thermocapillary liquid layers. Part 2. Surface- wave instabilities

Abstract: A planar liquid layer is bounded below by a rigid plate and above by an interface with a passive gas. A steady shear flow is set up by imposing a temperature gradient along the layer and driving the motion by thermocapillarity. This dynamic state is susceptible to surface-wave instabilities that couple the interfacial deflection to the underlying shear flow. These instabilities are found to be directly related to the two-dimensional waves on an isothermal layer subject to wind shear as described by Miles and by Smith & Davis. Hence the surface-tension gradients are important only in that they drive the basic shear flow. The surface-wave stability characteristics for liquid layers with and without return-flow profiles are presented, and special attention is paid to long-wave instabilities. Comparisons are made with available experimental observations.

Secondary Instability of Plane Channel Flow to Subharmonic Three-Dimensional Disturbances

Abstract: A linear secondary instability mechanism is presented that leads to the occurrence of subharmonic three‐dimensional disturbances in wall‐bounded shear flows. The instability originates from the periodic redistribution of vorticity in the shear flow by small but finite‐amplitude Tollmien–Schlichting waves. Low threshold amplitudes and other characteristics of this instability are consistent with experiments and may elucidate various obscure observations.

Solitary drift waves in the presence of magnetic shear

Abstract: The two‐component fluid equations describing electron‐drift and ion‐acoustic waves in a nonuniform magnetized plasma are shown to possess nonlinear two‐dimensional solitary wave solutions. In the presence of magnetic shear, radiative shear damping is exponentially small in Ls/Ln for solitary drift waves, in contrast to linear waves.

Effects of imperfect spatial resolution on measurements of wall-bounded turbulentbx shear flows

Abstract: The effects of imperfect spatial resolution on hot-film and hot-wire measurements of wall-bounded turbulent shear flows were studied. Two hot-film probes of different length were used for measurements of fully developed turbulent channel flow in a water tunnel. In the near-wall region significant effects of spanwise spatial averaging due to finite probe size were found for a probe 32 viscous units long. The maximum turbulence intensity attained a 10% lower value than that for a probe about half as long, and the zero-crossing of the skewness factor was shifted away from the wall. This could be attributed to spatial averaging of narrow low-speed regions. Results for different Reynolds numbers, but with the same sensor length in viscous units, showed that Reynolds-number effects are small, and that much of the reported discrepancies for turbulence measurements in the near-wall region can be ascribed to effects of imperfect spatial resolution. Also the number of events detected with the variable-interval time-averaging (VITA) technique was found to depend strongly on the sensor length, especially for events with short duration.

Fully Developed Periodic Turbulent Pipe Flow. Part 1. Main Experimental Results and Comparison with Predictions

Abstract: The present paper is the first part of a two-part report on a detailed investigation of periodic turbulent pipe flow. In this investigation, experimental data on instantaneous velocity and wall shear stress were obtained at a mean Reynolds number of 50000 in a fully developed turbulent pipe flow in which the volumetric flow rate was varied sinusoidally with time around the mean. Two oscillation frequencies at significant levels of flow modulation were studied in detail. The higher of these frequencies was of the order of the turbulent bursting frequency in the flow, and the other can be regarded as an intermediate frequency at which the flow still departed significantly from quasi-steady behaviour. While a few similar experiments have been reported in the recent literature, the present study stands out from the others in respect of the flow regimes investigated, the magnitude of flow modulation, the detailed nature of the measurements and most importantly the identification of a relevant parameter to characterize unsteady shear flows. The present paper contains the main experimental results and comparisons of these results with the results of a numerical calculation procedure which employs a well-known quasi-steady turbulence closure model. The experimental data are used to study the manner in which the time-mean, the ensemble-averaged and the random flow properties are influenced by flow oscillation at moderate to high frequencies. In addition, the data are also used to bring out the capability and limitations of quasi-steady turbulence modelling in the prediction of unsteady shear flows. A further and more detailed analysis of the experimental data, results of some additional experiments and a discussion on the characterization of turbulent shear flows are provided in Part 2 (Ramaprian & Tu 1983).

Orientation development in thermotropic liquid crystal polymers

Abstract: Thermotropic liquid crystal polymers are a new class of polymeric materials that consist of rigid backbone molecules and thus, even in the quiescent condition, take extended chain conformation to form optically anisotropic melts A systematic investigation was carried out on how this type of material responds to two basic flow fields: shear and elongation Rheological properties of the polymer in these flow fields have also been measured It was found that a high level of molecular orientation was readily obtained by elongational flow but not with shear flow Specifically, extraordinarily high orientation was obtained when the melt was subjected to small elongational strains, whiel shear strain or shear rate had little effect A possible mechanism to explain these behaviors is illustrated based on the existing observations or theories of rodlike molecules This finding was used to interpret the orientation distribution in the extruded and injection-molded articles

Fully developed periodic turbulent pipe flow. Part 2. The detailed structure of the flow

Abstract: The main experimental results of the study of periodic turbulent pipe flow have been described in Part 1 of this report. In this second part, these experimental data are examined in greater detail to understand the effect of imposed oscillation on the flow structure, at moderate to large oscillation frequencies. Data on phase and amplitude and energy spectrum are used to study the effect of the imposed oscillation on the turbulence structure at these interactive frequencies of oscillation. Additional experiments which were performed to study the effect of oscillation frequency on the flow structure are also reported. Based on the present observations as well as on the data from other sources, it is inferred that turbulent shear flows respond very differently from laminar shear flows to imposed unsteadiness. A turbulent Stokes number relevant for characterizing the unsteady turbulent shear flows is identified and used to classify such flows.

Nonlinear saturation of Rayleigh–Taylor instability in thin films

Abstract: A general mechanism of nonlinear saturation of instabiities in flowing films is described using the Rayleigh–Taylor instability as an example The combined action of flow shear and surface tension is the essence of the saturation mechanism As a result, the streamwise perturbations of the interface that would rupture a stagnant film do not rupture a film flowing in a certain range of shear rates

The breakup of small drops and bubbles in shear flows

Abstract: The problem of determining the deformation and burst of a single drop freely suspended in another fluid undergoing shear is of fundamental importance in a variety of physical processes of practical significance; for example, the rheology of emulsions and the dispersion of one fluid phase into another. It was studied both theoretically and experimentally by G. I . Taylor,’.’ who, as he has with many of the other topics in fluid mechanics, obtained quantitative results that were not only the first on the subject but which remain among the most important and fundamental in this field. The systems considered experimentally by Taylor’ are depicted in FIGURES l a and I b. An initially spherical liquid drop of radius a and viscosity Ap was placed in a fluid, with which it was immiscible, of equal density and of viscosity p. A steady shear of strength G was then applied and the drop was found to deform into a steady shape if G was maintained below a critical value G,, but the drop broke when G exceeded G,. The two shear flows set up by Taylor’ were: ( I ) the “hyperbolic” flow, u, = Gx, ug = Gy3 with u , and u , being the corresponding velocity components along the x and y directions, respectively, which is a pure straining motion without vorticity, and (2) the simple shear flow, u, = Gy3 ug = 0, which, as is well known, consists of a pure straining motion, with its principal axis of extension along the diagonal in the xy plane, plus a solid body rotation about the origin. In the absence of inertial erects, which were indeed negligible in Taylor’s experiments,’ the independent parameters, in addition to the type of shear being impressed, are: C , the strength of the shear flow; a, the radius of the initially spherical drop, p, the viscosity of the ambient fluid; A, the viscosity ratio; and y. the interfacial tension. Hence, the deformation, D = ( L B ) / ( L + B ) , where L and B are the half-length and the half-breadth of the drop, respectively, becomes a function of only two dimensionless groups, i.e., the capillary number ( k ’ = Gwa/y) and the viscosity ratio, A. Taylor’ found that, for fixed A, D was linear in Gpa/y for small values of the capillary number k ’ , but that, beyond a certain range, the slope of the D versus k ’ curve increased rapidly in many cases until a point was reached where a steady drop shape could no longer be maintained and the drop burst. There were conditions, however-most notably with high viscosity drops (A >> 1) in a simple shear flow-for which a limiting deformation was attained and drop breakup did not occur. Examples of these two types of deformation curves are sketched in FIGURE 2. From a practical point of view, the quantity of primary interest is the critical shear

Shear Fracture in Cone‐Plate Rheometry

Abstract: When subject to moderate shear rates in a cone‐plate and parallel plate rheometer, viscoelastic samples tend to fracture at the edge of the sample thus preventing the measurement of viscosity and normal stresses at high shear rates. An explanation of this behavior has been given in terms of a critical elastic strain energy by Hutton and we offer an alternative explanation based on fracture mechanics. It is shown here that fracture occurs if |N2|>2Γ/3a, where N2 is the second normal stress difference, Γ is the surface tension coefficient, and a is the size of the fracture. The experimental data presented here show that this equation correctly predicts the occurrence of shear fracture and also the shear rate at which it occurs. At high shear rates, Newtonian liquids and some viscoelastic liquids are ejected from the cone‐plate and parallel plate rheometer due to the effect of centrifugal forces. For a Newtonian liquid a simple consideration of the centrifugal and surface tension forces at the sample edge pr...

Flow Properties of Time‐Dependent Foodstuffs

Abstract: In this work, a new model for viscosity decay at constant shear rate is tested and the thixotropic behavior of representative food products is experimentally analyzed. The equilibrium viscosity (or steady‐state viscosity) of some food products, obtained after a sufficiently long time of shear at a constant shear rate, is found to be well represented by the Herschel‐Bulkley model and by an exponential model in which a maximum of two terms of an infinite series are required. The model for viscosity decay, that is, the decrease in viscosity with time at constant shear rate, assumes nth order kinetics for the decay of a structural parameter λ. The rate constant k, for the decay of λ, is found to be a power law function of the shear rate. The equation for structure decay is combined with a scalar constitutive equation for the shear stress and the resulting model represents adequately the data for viscosity decay of foodstuffs in the range of shear rates 50<γ<5420 s−1. Data for suspensions such as tomato juice...

Hydromagnetic waves in a differentially rotating sphere

Abstract: The linear stability of a uniformly internally heated, self-gravitating, rapidly rotating fluid sphere is investigated in the presence of an azimuthal magnetic field B 0 ( r , θ)ϕ and azimuthal shear flow U 0 ( r , θ)ϕ (where ( r , θ, ϕ) are spherical polar coordinates). Solutions are calculated numerically for magnetic field strengths that produce a Lorentz force comparable in magnitude to that of the Coriolis force. The critical Rayleigh number R c is found to reach a minimum here and the qualitative behaviour of the thermally driven instabilities in the absence of a shear flow ( U 0 = 0) is similar to that found by earlier workers (e.g. Fearn 1979 b ) for the simpler basic state B 0 = r sin θ. The effect of a shear flow is followed as its strength (measured by the magnetic Reynolds number R m ) is increased from zero. In the case where the ratio q of thermal to magnetic diffusivities is small ( q [Lt ] 1) the effect of the flow becomes significant when R m = O(q) . For R m > q three features are evident as R m is increased: the perturbation in the temperature field (but not the other variables when R m O (1)) becomes increasingly localized at some point ( r L , θ L ); the phase speed of the instability tends towards the fluid velocity at that point; and R c increases with R m with the suggestion that R c ∝ R m / q for R m [Gt ] q although the numerical resolution is insufficient to verify this. Greater resolution is achieved for a simpler problem which retains the essential physics and is described in the accompanying paper (Fearn & Proctor 1983). The possible significance of these results to the geomagnetic secular variation is discussed.

The effect of Brownian diffusion on shear-induced coagulation of colloidal dispersions

Abstract: The effect of a small amount of Brownian diffusion on shear-induced coagulation of spherical particles has been calculated. This has been accomplished by considering the binary collision process between a test sphere and identical spheres interacting with the test sphere through induced-dipole attraction, electrostatic repulsion and hydrodynamically induced forces. The effect of diffusion is found by means of an expansion in inverse Peclet number. Specific calculations were performed for uniaxial extension and for laminar shear flow. It is found that Brownian diffusion, the effect of which is nonlinearly coupled with flow type and strength, can act to increase or decrease the coagulation rate.

A shear-flow instability in a circular geometry

Abstract: A circular shear zone is created in a thin layer of fluid The Kelvin-Helmholtz instability induces regular, steady patterns of m vortices The experimental conditions are such that neither the centrifugal nor the Coriolis forces play a role in the motion The state of the flow is defined by a Reynolds number, the value of which is controlled by the imposed velocities The pattern of vortices can be characterized by its wavevector k or by m, the order of its symmetry As k is quantized, its evolution, due to an increase or a decrease of the controlled stress, leads to transitions between patterns of different m The transitory states between different symmetries are investigated The experiments are performed with a soap film which provides a new type of visualization of an air flow

Effect of boundary absorption upon longitudinal dispersion in shear flows

Abstract: Boundary absorption causes a depletion of contaminant. Since the boundary tends to be the region of lowest velocity and of strongest shear, the remaining contaminant experiences on average an increased advection velocity, a reduced rate of shear dispersion, and a tendency to develop skewness towards the rear. Here it is shown how all these effects can be incorporated into a delay-diffusion description of the longitudinal dispersion process (Smith 1981). It is the accurate reproduction of the skewness that permits a delay-diffusion equation to become applicable at an earlier stage than the more conventional diffusion-equation models for longitudinal dispersion, and before there has been an undue loss of contaminant through the boundary.

Effects of weak bed load on the Universal Law of the Wall

Abstract: Two-dimensional equilibrium boundary-layer flows were investigated in an open water channel with a width/depth ratio of 6 for a smooth bed of 0.16 mm quartz grains (d50) and compared with those of an immobile smooth cemented bed with the same sand roughness. For flows at Reynolds numbers between 20,000, representing onset of erosion, and 28,000, before appearance of rhomboid ripples, quartz grains rolled over an otherwise smooth sand bed with a density of ≤40 grains cm−1 s−1. Then the universal law of the wall, as obtained for the fixed, smooth sand bed, could not be confirmed by the data. Instead, (1) a logarithmic layer was found that extended further into the wake region and had a reduced value of von Karman's constant κ = 0.32 ± 0.04, (2) the friction diagram indicated Reynolds number dependent drag reduction, and (3) the logarithmic layer extended down to the top of the rolling grains at ReU >25,000. These results are interpreted as a new class of wall-bounded shear flow with different momentum transfer processes and a velocity-defect law throughout the flow down to the top of the rolling grains. Some conclusions are discussed for sedimentological and engineering problems in which this type of flow is the rule rather than the exception.

Three-dimensional tertiary motions in a plane shear layer

Abstract: The nonlinear evolution of instabilities of a plane-parallel shear flow with an inflection-point profile is studied. The particular example of the cubic-profile flow generated in an inclined layer heated from above and cooled from below is chosen because it exhibits supercritical bifurcations for secondary and tertiary flows. Since the limit of small Prandtl number is assumed, buoyancy effects caused by temperature perturbations are negligible. The analysis describes first the transition to transverse roll-like vortices which become unstable at slightly supercritical Grashof numbers to a vortex-pairing instability with alternating pairing in the spanwise direction. Three-dimensional finite-amplitude solutions for this tertiary mode of motion are computed and discussed. Finally the question of the stability of the tertiary flow is addressed.

Influence of equilibrium shear flow along the magnetic field on the resistive tearing instability

Abstract: The influence of shear plasma flow along the magnetic field on the resistive tearing instability has been investigated in plane geometry. It is shown that such flows, even at significantly sub‐Alfvenic speeds, have a destabilizing effect. Moreover, in nonsymmetric cases, the well‐known threshold for tearing mode instability Δ′ext =0 is removed. Thus, in magnetic configurations which would otherwise be stable in the absence of flow, a shear plasma flow can induce instability. Approximate growth rates have been obtained for tokamaks with significant equilibrium plasma rotation and an application to the ISX‐B experiments is briefly discussed.

Particle-Dynamics Calculations of Shear Flow

Abstract: Two-dimensional discrete particle computer models similar to those of P. Cundall (ref. 1, 2) are described. The “soft-particle” approach used in these models allows them to be applied over a wide range of conditions from static situations through rapid shear conditions. Surface friction between particles and with boundary walls is explicitly modeled. Particular attention is paid to the modeling of dynamic situations wherein the energy losses and momentum transfer during inter-particulate collisions play important roles. Comparisons with analytic solutions have verified the numerical techniques and direct comparison with physical tests involving several particles have verified the models' ability to calculate the motion of real materials. Direct shear tests on oil shale rubble and corresponding calculations indicate qualitatively similar circulation phenomena and both showed large fluctuations in the magnitude of the shearing force. Incline chute flow calculations are providing detailed descriptions of individual particle paths in which shearing and size segregation phenomena can be observed. Initial comparisons with experiments indicate somewhat slower segregation in two-dimensional calculations than in experiments with spherical particles.