Showing papers on "Shear flow published in 1993"

Hydrodynamic Stability Without Eigenvalues

Abstract: Fluid flows that are smooth at low speeds become unstable and then turbulent at higher speeds. This phenomenon has traditionally been investigated by linearizing the equations of flow and testing for unstable eigenvalues of the linearized problem, but the results of such investigations agree poorly in many cases with experiments. Nevertheless, linear effects play a central role in hydrodynamic instability. A reconciliation of these findings with the traditional analysis is presented based on the "pseudospectra" of the linearized problem, which imply that small perturbations to the smooth flow may be amplified by factors on the order of 105 by a linear mechanism even though all the eigenmodes decay monotonically. The methods suggested here apply also to other problems in the mathematical sciences that involve nonorthogonal eigenfunctions.

Stochastic forcing of the linearized Navier–Stokes equations

Abstract: Transient amplification of a particular set of favorably configured forcing functions in the stochastically driven Navier–Stokes equations linearized about a mean shear flow is shown to produce high levels of variance concentrated in a distinct set of response functions. The dominant forcing functions are found as solutions of a Lyapunov equation and the response functions are found as the distinct solutions of a related Lyapunov equation. Neither the forcing nor the response functions can be identified with the normal modes of the linearized dynamical operator. High variance levels are sustained in these systems under stochastic forcing, largely by transfer of energy from the mean flow to the perturbation field, despite the exponential stability of all normal modes of the system. From the perspective of modal analysis the explanation for this amplification of variance can be traced to the non‐normality of the linearized dynamical operator. The great amplification of perturbation variance found for Couette and Poiseuille flow implies a mechanism for producing and sustaining high levels of variance in shear flows from relatively small intrinsic or extrinsic forcing disturbances.

Boundary conditions for direct computation of aerodynamic sound generation

Abstract: A numerical scheme suitable for the computation of both the near field acoustic sources and the far field sound produced by turbulent free shear flows utilizing the Navier-Stokes equations is presented. To produce stable numerical schemes in the presence of shear, damping terms must be added to the boundary conditions. The numerical technique and boundary conditions are found to give stable results for computations of spatially evolving mixing layers.

Scaling laws for fully developed turbulent shear flows. Part 1. Basic hypotheses and analysis

Abstract: The present work consists of two parts. Here in Part 1, a scaling law (incomplete similarity with respect to local Reynolds number based on distance from the wall) is proposed for the mean velocity distribution in developed turbulent shear flow. The proposed scaling law involves a special dependence of the power exponent and multiplicative factor on the flow Reynolds number. It emerges that the universal logarithmic law is closely related to the envelope of a family of power-type curves, each corresponding to a fixed Reynolds number. A skin-friction law, corresponding to the proposed scaling law for the mean velocity distribution, is derived.In Part 2 (Barenblatt & Prostokishin 1993), both the scaling law for the velocity distribution and the corresponding friction law are compared with experimental data.

Design and construction of a linear shear stress flow chamber

Abstract: A new paralle plate flow chamber that has a linear variation of shear stress, starting from a predetermined maximum value at the entrance and falling to zero at the exit, has been designed and tested. This is in contrast to the usual rect-angular channel plan which produces a constant shear stress over the entire length. The new design is based on the theory of Hele-Shaw flow between parallel plates. To verify the efficacy of the flow channel, the effect of fluid shear stress on platelet adhesion to a fibrinogen-coated glass surface was tested. The percentage of attached platelets after 5 min of shear stress is shown to be a function of shear stress. With this new flow chamber, cell-cell interactions can be studied efficiently over a wide range of shear stress using a single run at constant discharge.

Chaotic transport by Rossby waves in shear flow

Abstract: Transport and mixing properties of Rossby waves in shear flow are studied using tools from Hamiltonian chaos theory. The destruction of barriers to transport is studied analytically, by using the resonance overlap criterion and the concept of separatrix reconnection, and numerically by using Poincare sections. Attention is restricted to the case of symmetric velocity profiles with a single maximum; the Bickley jet with velocity profile sech2 is considered in detail. Motivated by linear stability analysis and experimental results, a simple Hamiltonian model is proposed to study transport by waves in these shear flows. Chaotic transport, both for the general case and for the sech2 profile, is investigated. The resonance overlap criterion and the concept of separatrix reconnection are used to obtain an estimate for the destruction of barriers to transport and the notion of banded chaos is introduced to characterize the transport that typically occurs in symmetric shear flows. Comparison between the analytical estimates for barrier destruction and the numerical results is given. The role of potential vorticity conservation in chaotic transport is discussed. An area preserving map, termed standard nontwist map, is obtained from the Hamiltonian model. It is shown that the map reproduces the transport properties and the separatrix reconnection observed in the Hamiltonian model. The conclusions reached are used to explain experimental results on transport and mixing by Rossby waves in rotating fluids.

Three‐dimensional fluid simulations of the nonlinear drift‐resistive ballooning modes in tokamak edge plasmas

Abstract: A three‐dimensional study of the turbulence and sheared flow generated by the drift‐resistive ballooning modes in tokamak edge plasmas has been completed. The fluid simulations show that 10%–15% percent density fluctuations can develop in the nonlinear state when the self‐consistently generated shear flow is suppressed. These modes are also found to give rise to poloidally asymmetric particle transport. Characteristic scale lengths of these fluctuations are isotropic in the plane transverse to B and smaller than the connection length along the field line. Sheared poloidal flow is self‐consistently driven by both the Reynolds stress and the Stringer mechanisms. In the presence of self‐consistent shear flow, the transverse spectrum is no longer isotropic transverse to B. The vortices become elongated in the poloidal direction. Also, there is a substantial reduction in both the level of fluctuations of the density and potential and the associated particle transport. These features are in qualitative agreement with L–H transitions observed in tokamaks.

Turbulent shear flow over slowly moving waves

Abstract: We investigate the changes to a fully developed turbulent boundary layer caused by the presence of a two-dimensional moving wave of wavelength L = 2π/k and amplitude a. Attention is focused on small slopes, ak, and small wave speeds, c, so that the linear perturbations are calculated as asymptotic sequences in the limit (u* + c)/UB(L) → 0 (u* is the unperturbed friction velocity and UB(L) is the approach-flow mean velocity at height L). The perturbations can then be described by an extension of the four-layer asymptotic structure developed by Hunt, Leibovich & Richards (1988) to calculate the changes to a boundary layer passing over a low hill.When (u* + c)/UB(L) is small, the matched height, zm (the height where UB equals c), lies within an inner surface layer, where the perturbation Reynolds shear stress varies only slowly. Solutions across the matched height are then constructed by considering an equation for the shear stress. The importance of the shear-stress perturbation at the matched height implies that the inviscid theory of Miles (1957) is inappropriate in this parameter range. The perturbations above the inner surface layer are not directly influenced by the matched height and the region of reversed flow below zm: they are similar to the perturbations due to a static undulation, but the ‘effective roughness length’ that determines the shape of the unperturbed velocity profile is modified to zm = z0 exp (kc/u*).The solutions for the perturbations to the boundary layer are used to calculate the growth rate of waves, which is determined at leading order by the asymmetric pressure perturbation induced by the thickening of the perturbed boundary layer on the leeside of the wave crest. At first order in (u* + c)/UB(L), however, there are three new effects which, numerically, contribute significantly to the growth rate, namely: the asymmetries in both the normal and shear Reynolds stresses associated with the leeside thickening of the boundary layer, and asymmetric perturbations induced by the varying surface velocity associated with the fluid motion in the wave; further asymmetries induced by the variation in the surface roughness along the wave may also be important.

A mechanism for bypass transition from localized disturbances in wall-bounded shear flows

Abstract: The linear, nonlinear and breakdown stages in the transition of localized disturbances in plane Poiseuille flow is studied by direct numerical simulations and analysis of the linearized Navier–Stokes equations. Three-dimensionality plays a key role and allows for algebraic growth of the normal vorticity through the linear lift-up mechanism. This growth primarily generates elongated structures in the streamwise direction since it is largest at low streamwise wavenumbers. For finite-amplitude disturbances such structures will be generated essentially independent of the details of the initial disturbance, since the preferred nonlinear interactions transfer energy to low streamwise wavenumbers. The nonlinear interactions also give a decrease in the spanwise scales. For the stronger initial disturbances the streamwise vorticity associated with the slightly inclined streaks was found to roll up into distinct streamwise vortices in the vicinity of which breakdown occurred. The breakdown starts with a local rapid growth of the normal velocity bringing low-speed fluid out from the wall. This phenomenon is similar to the low-velocity spikes previously observed in transition experiments. Soon thereafter a small turbulent spot is formed. This scenario represents a bypass of the regular Tollmien–Schlichting, secondary instability process. The simulations have been carried out with a sufficient spatial resolution to ensure an accurate description of all stages of the breakdown and spot formation processes. The generality of the observed processes is substantiated by use of different types of initial disturbances and by Blasius boundary-layer simulations. The present results point in the direction of universality of the observed transition mechanisms for localized disturbances in wall-bounded shear flows.

Manipulation of free shear flows using piezoelectric actuators

Abstract: An air jet emanating from a square conduit having an equivalent diameter of 4.34 cm and a centreline velocity of 4 m/s is forced using four resonantly driven piezoelectric actuators placed along the sides of the square exit. Excitation is effected via amplitude modulation of the resonant carrier waveform. The flow is normally receptive to time–harmonic excitation at the modulating frequency but not at the resonant frequency of the actuators. When the excitation amplitude is high enough, the excitation waveform is demodulated by a nonlinear process that is connected with the formation and coalescence of nominally spanwise vortices in the forced segments of the jet shear layer. As a result, the modulating and carrier wave trains undergo spatial amplification and attenuation, respectively, downstream of the exit plane. Strong instabilities of the jet column are excited when the jet is forced at phase relationships between actuators that correspond (to lowest order) to the azimuthal modes m = 0, ±1, ±2, and −1 of an axisymmetric flow. The streamwise velocity component is measured phase locked to the modulating signal in planes normal to the mean flow. Resonantly driving the actuators with different carrier amplitudes results in a distorted mean flow having a featureless spectrum that can be tailored to provide favourable conditions for the introduction and propagation of desirable low-frequency disturbances.

Optimal perturbations and streak spacing in wall‐bounded turbulent shear flow

Abstract: The mean streak spacing of approximately 100 wall units that is observed in wall‐bounded turbulent shear flow is shown to be consistent with near‐wall streamwise vortices optimally configured to gain the most energy over an appropriate turbulent eddy turnover time. The streak spacing arising from the optimal perturbation increases with distance from the wall and is nearly independent of Reynolds number, in agreement with experiment.

Global linear stability analysis of weakly non-parallel shear flows

Abstract: The global linear stability of incompressible, two-dimensional shear flows is investigated under the assumptions that far-field pressure feedback between distant points in the flow field is negligible and that the basic flow is only weakly non-parallel, i.e. that its streamwise development is slow on the scale of a typical instability wavelength. This implies the general study of the temporal evolution of global modes, which are time-harmonic solutions of the linear disturbance equations, subject to homogeneous boundary conditions in all space directions. Flow domains of both doubly infinite and semi-infinite streamwise extent are considered and complete solutions are obtained within the framework of asymptotically matched WKBJ approximations. In both cases the global eigenfrequency is given, to leading order in the WKBJ parameter, by the absolute frequency ω0(Xt) at the dominant turning point Xt of the WKBJ approximation, while its quantization is provided by the connection of solutions across Xt. Within the context of the present analysis, global modes can therefore only become time-amplified or self-excited if the basic flow contains a region of absolute instability.

The lift on a small sphere in wall-bounded linear shear flows

Abstract: This paper presents a closed-form solution for the inertial lift force acting on a small rigid sphere that translates parallel to a flat wall in a linear shear flow. The results provide connections between results derived by other workers for various limiting cases. An analytical form for the lift force is derived in the limit of large separations. Some new results are presented for the disturbance flow created by a small rigid sphere translating through an unbounded linear shear flow.

Optimal excitation of three‐dimensional perturbations in viscous constant shear flow

Abstract: The three‐dimensional perturbations to viscous constant shear flow that increase maximally in energy over a chosen time interval are obtained by optimizing over the complete set of analytic solutions. These optimal perturbations are intrinsically three dimensional, of restricted morphology, and exhibit large energy growth on the advective time scale, despite the absence of exponential normal modal instability in constant shear flow. The optimal structures can be interpreted as combinations of two fundamental types of motion associated with two distinguishable growth mechanisms: streamwise vortices growing by advection of mean streamwise velocity to form streamwise streaks, and upstream tilting waves growing by the down gradient Reynolds stress mechanism of two‐dimensional shear instability. The optimal excitation over a chosen interval of time comprises a combination of these two mechanisms, characteristically giving rise to tilted roll vortices with greatly amplified perturbation energy. It is suggested that these disturbances provide the initial growth leading to transition to turbulence, in addition to providing an explanation for coherent structures in a wide variety of turbulent shear flows.

Scaling laws for fully developed turbulent shear flows. Part 2. Processing of experimental data

Abstract: In Part 1 of this work (Barenblatt 1993) a non-universal scaling law (depending on the Reynolds number) for the mean velocity distribution in fully developed turbulent shear flow was proposed, together with the corresponding skin friction law. The universal logarithmic law was also discussed and it was shown that it can be understood, in fact, as an asymptotic branch of the envelope of the curves corresponding to the scaling law.Here in Part 2 the comparisons with experimental data are presented in detail. The whole set of classic Nikuradze (1932) data, concerning both velocity distribution and skin friction, was chosen for comparison. The instructive coincidence of predictions with experimental data suggests the conclusion that the influence of molecular viscosity within the main body of fully developed turbulent shear flows remains essential, even at very large Reynolds numbers. Meanwhile, some incompleteness of the experimental data presented in the work of Nikuradze (1932) is noticed, namely the lack of data in the range of parameters where the difference between scaling law and universal logarithmic law predictions should be the largest.

Compressibility effects on the growth and structure of homogeneous turbulent shear flow

Abstract: Compressibility effects within decaying isotropic turbulence and homogeneous turbulent shear flow have been studied using direct numerical simulation. The objective of this work is to increase our understanding of compressible turbulence and to aid the development of turbulence models for compressible flows. The numerical simulations of compressible isotropic turbulence show that compressibility effects are highly dependent on the initial conditions. The shear flow simulations, on the other hand, show that measures of compressibility evolve to become independent of their initial values and are parameterized by the root mean square Mach number. The growth rate of the turbulence in compressible homogeneous shear flow is reduced compared to that in the incompressible case. The reduced growth rate is the result of an increase in the dissipation rate and energy transfer to internal energy by the pressure-dilatation correlation. Examination of the structure of compressible homogeneous shear flow reveals the presence of eddy shocklets, which are important for the increased dissipation rate of compressible turbulence.

Vortical and turbulent structure of a lobed mixer free shear layer

Abstract: An experimental investigation of the vortical and turbulent structure in a free shear lager downstream of a lobed mixer has been conducted. Pulsed-laser sheet flow visualization with smoke and three-dimensional velocity measurements with hot-film anemometry were obtained for a lobed-mixer configuration and a baseline, planar configuration. Laminar and turbulent initial boundary-lager conditions were documented for both cases. The main result of this investigation is that a new vortex structure was confirmed to exist for the lobed mixer in addition to the well-known streamwise vortex array, consistent with the work of Manning

Flocculation of fine-grained sediments due to differential settling

Abstract: The flocculation of fine-grained particles depends on collisions due to Brownian motion, fluid shear, and differential settling. Previous experimental work on the flocculation of fine-grained sediments has emphasized the effects of fluid shear. These effects are significant in high-turbulence regions. However, as the turbulence and fluid shear decrease, as, for example, in open waters away from shore, differential settling becomes the dominant mechanism for flocculation. In the present article, previous work on the effects of fluid shear is reviewed. However, the emphasis is on recent experimental work on the effects of differential settling on the flocculation of fine-grained, primarily inorganic particles. The transition in effects between situations where fluid shear is dominant and the other extreme, where differential settling is dominant, was also investigated and is discussed. The sediments used in these studies were natural bottom sediments from the Detroit River inlet to Lake Erie. The tests were initiated with disaggregated sediments and were continued as the particles aggregated and formed flocs. These flocs then grew until a steady state size distribution was reached. In order to reach a steady state the differential settling tests sometimes continued for as long as 30 days; they were done in both freshwater and seawater at sediment concentrations from 1 mg/L to 200 mg/L and with and without treatment to remove organic matter. Floe size distributions as a function of time were determined. From the experiments it is shown that the times to steady state and the steady state median diameters are much larger when differential settling is the dominant mechanism for flocculation than when fluid shear is the dominant mechanism for flocculation. It is also shown that the effects of sediment concentration and salinity are qualitatively similar; i.e., as these quantities increase, both the time to steady state and the steady state floe size decrease. Settling speeds of the flocculated particles were also measured; the settling speeds of flocs are much larger and increase more rapidly with floc diameter when produced by differential settling than when fluid shear is dominant.

Direct numerical simulation of three‐dimensional open‐channel flow with zero‐shear gas–liquid interface

Abstract: Turbulence structure in an open‐channel flow with a zero‐shear gas–liquid interface was numerically investigated by a three‐dimensional direct numerical simulation (DNS) based on a fifth‐order finite‐difference formulation, and the relationship between scalar transfer across a zero‐shear gas–liquid interface and organized motion near the interface was discussed. The numerical predictions of turbulence quantities were also compared with the measurements by means of a two‐color laser Doppler velocimeter. The results by the DNS show that the vertical motion is restrained in the interfacial region and there the turbulence energy is redistributed from the vertical direction to the streamwise and spanwise directions through the pressure fluctuation. The large‐scale eddies are generated by bursting phenomena in the wall region and they are lifted up toward the interfacial region. Then, the eddies renew the interface and promote the scalar transfer across the gas–liquid interface. Both the damping effect and the generation process of the surface‐renewal motions predicted by the DNS explain well the experimental results deduced in previously published studies. Furthermore, the predicted bursting frequency and mass transfer coefficient are in good agreement with the measurements.

The Rheology of Entangled Polymers at Very High Shear Rates

Abstract: One of the (few) unrealistic features of the Doi-Edwards model for entangled polymers is that it predicts a steady-state shear stress which decreases indefinitely as the shear rate is increased. As shown by Marrucci and Grizzuti (Gazz. Chim. Ital., 118 (1988) 179) this feature remains, even when one takes into account chain stretching due to elongation of the tube by the flow. Here we suggest a further mechanism for chain stretching which arises because the tube, even when fully aligned with the flow, has a finite lateral dimension which exposes different parts of the chain to different flow velocities. Using a simplified model, we predict the asymptotic behaviour of the shear stress and first-normal-stress difference, and show that stable flow is recovered at high enough shear rates.

Anomalous momentum transport from drift wave turbulence

Abstract: A sheared slab magnetic field model B=B0[ẑ+(x/Ls)ŷ], with inhomogeneous flows in the ŷ and ẑ directions, is used to perform a fully kinetic stability analysis of the ion temperature gradient (ITG) and dissipative trapped electron (DTE) modes. The concomitant quasilinear stress components that couple to the local perpendicular (y component) and parallel (z component) momentum transport are also calculated and the anomalous perpendicular and parallel viscous stresses obtained. A breakdown of the ITG‐induced viscous stresses are generally observed at moderate values of the sheared perpendicular flow. Even in the absence of external momentum sources, ion diamagnetic effects can generate an inhomogeneous radial electric field which gives rise to a sheared perpendicular flow which can sustain a sheared parallel flow. The effect of the perpendicular stress component in the momentum balance equations is generally small while the parallel stress component, which is primarily determined by the perpendicular flow shear, can dominate the usual neoclassical viscous stress terms. The large anomalous effect suggests that the neoclassical explanation of poloidal flows in tokamaks may be incorrect. The present results are in general agreement with existing experimental observations on momentum transport in tokamaks.

On the computer simulation of the deformation and breakup of colloidal aggregates in shear flow

Abstract: Computer simulations are used to investigate the deformation and breakup of colloidal aggregates in shear flow. It is argued that the aggregate radius depends on the shear rate via a power law S -m . The behavior of the aggregates strongly depends on the parameters of the particle interactions. In general the interaction potential of spherical particles is a superposition of central and noncentral components. The former depends only upon the distance between the centers of neighboring particles, while the latter can be described as a function of the angles between adjacent bonds. If the noncentral component is present, the aggregate is rigid ( m = m rigid ); i.e., its internal structure responds elastically to small deformations and can be characterized by the elastic moduli (e.g., Young modulus E ) and yield strength, σ a , depending upon the radius of gyration, R , and the internal volume fraction of particles, φ int , via power laws, E ∼ σ a ∝ R -γ ∝ φ γ1 int . The exponent m in this case can be identified with m rigid ≡ 1/γ. The exponent γ 1 is identical to the exponent characterizing the power-law dependence of the moduli of a colloid gel network consisting of interconnected fractal clusters upon volume fraction. The exponents m rigid , γ and γ 1 can be related to the exponents characterizing geometrical properties of the internal structure of the aggregate and its skeleton (such as fractal dimension d f , chemical dimension d 1 , etc.). For one special type of aggregate (fractal trees without loops with d f = 1.85-2.5, d 1 = 1.1-1.8) we found m rigid = 0.23-0.29, γ 1 = 3.4-7.0 in 3D. The values of γ 1 are in good agreement with the experimental data recently obtained for colloid gels. If the forces of the particles' interactions are purely central, the aggregate is soft ( m = m soft ); i.e., its internal structure does not respond elastically to small deformations. In this case the simulations of the disaggregation process in shear flow were carried out in the free draining approximation. The initial aggregate is broken into two or more secondary aggregates. It is established that the mean radius of these aggregates also depends on S via a power law with m soft = 0.4-0.5. Comparing the results of our analyses with the experimental data we found that in general m rigid and m soft can be considered the lower and upper bounds of m .

On the constitutive relations for dispersed particles in nonuniform flows. I: Dispersion in a simple shear flow

Abstract: The work presented follows on from a previous study in which a kinetic approach was used to generate the continuum equations for a dilute dispersed phase of noncolliding particles in a nonuniform turbulent flow. Here this approach is used to derive forms for the Reynolds stresses and the fluctuating interphase momentum transfer for particles at equilibrium in a bounded simple shear flow; the combination of the two also gives the total stress and long‐term particle diffusion coefficients. These forms are based on equilibrium solutions of a kinetic equation describing the transport of the particle phase space probability density

Stochastic Dynamics of Baroclinic Waves

Abstract: The maintenance of variance and attendant heat flux in linear, forced dissipative baroclinic shear flows subject to stochastic excitation is examined. The baroclinic problem, is intrinsically nonnormal and its stochastic dynamics is found to differ significantly from the more familiar stochastic dynamics of normal systems. When the shear is sufficiently great in comparison to dissipative effects, stochastic excitation supports highly enhanced variance levels in these nonnormal systems compared to variance levels supproted by the same forcing and dissipation in related normal systems. The eddy variance and associated heat flux are found to arise in response to transient amplification of a subset of forcing functions that obtain energy from the mean flow and project this energy on a distinct subset of response functions (EOFs) that are in turn distinct from the set of normal modes of the system. A method for obtaining the dominant forcing and response functions as well as the distribution of heat flux for a given flow is described.

Suspensions of prolate spheroids in Stokes flow. Part 1. Dynamics of a finite number of particles in an unbounded fluid

Abstract: A new simulation method is presented for low-Reynolds-number flow problems involving elongated particles in an unbounded fluid. The technique extends the principles of Stokesian dynamics, a multipole moment expansion method, to ellipsoidal particle shapes. The methodology is applied to prolate spheroids in particular, and shown to be efficient and accurate by comparison with other numerical methods for Stokes flow. The importance of hydrodynamic interactions is illustrated by examples on sedimenting spheroids and particles in a simple shear flow.

Effects of Surface Roughness on Point Contact EHL

Abstract: The effects of orientation of surface roughness, entrainment (rolling) velocity, and slide/roll ratio on micro-elastohydrodynamic lubrication (micro-EHL) are investigated under pointcontact conditions using the optical interferometry technique. Long bumps with constant height and wavelength produced artificially on the surface of a highly polished steel ball are used as a model roughness. It is shown that the asperities are elastically deformed and the magnitude depends on the film factor A, defined by the ratio of the central film thickness based on smooth surfaces to the composite surface roughness, as well as the surface kinematic conditions and the orientation of the asperities. It is also found that a thin or thick oil film formed at the inlet of the contact by a moving rough surface travels through the contact region at a speed very close to the average speed of the contacting surfaces. The possible mechanism is discussed.