Showing papers on "Turbulence published in 1997"

Blood flow in arteries

Abstract: Blood flow in arteries is dominated by unsteady flow phenomena. The cardiovascular system is an internal flow loop with multiple branches in which a complex liquid circulates. A nondimensional frequency parameter, the Womersley number, governs the relationship between the unsteady and viscous forces. Normal arterial flow is laminar with secondary flows generated at curves and branches. The arteries are living organs that can adapt to and change with the varying hemodynamic conditions. In certain circumstances, unusual hemodynamic conditions create an abnormal biological response. Velocity profile skewing can create pockets in which the direction of the wall shear stress oscillates. Atherosclerotic disease tends to be localized in these sites and results in a narrowing of the artery lumen—a stenosis. The stenosis can cause turbulence and reduce flow by means of viscous head losses and flow choking. Very high shear stresses near the throat of the stenosis can activate platelets and thereby induce thrombosis, which can totally block blood flow to the heart or brain. Detection and quantification of stenosis serve as the basis for surgical intervention. In the future, the study of arterial blood flow will lead to the prediction of individual hemodynamic flows in any patient, the development of diagnostic tools to quantify disease, and the design of devices that mimic or alter blood flow. This field is rich with challenging problems in fluid mechanics involving three-dimensional, pulsatile flows at the edge of turbulence.

Direct numerical simulation of turbulent flow over a backward-facing step

Abstract: Turbulent flow over a backward-facing step is studied by direct numerical solution of the Navier–Stokes equations. The simulation was conducted at a Reynolds number of 5100 based on the step height h and inlet free-stream velocity, and an expansion ratio of 1.20. Temporal behaviour of spanwise-averaged pressure fluctuation contours and reattachment length show evidence of an approximate periodic behaviour of the free shear layer with a Strouhal number of 0.06. The instantaneous velocity fields indicate that the reattachment location varies in the spanwise direction, and oscillates about a mean value of 6.28h. Statistical results show excellent agreement with experimental data by Jovic & Driver (1994). Of interest are two observations not previously reported for the backward-facing step flow: (a) at the relatively low Reynolds number considered, large negative skin friction is seen in the recirculation region; the peak |Cf| is about 2.5 times the value measured in experiments at high Reynolds numbers; (b) the velocity profiles in the recovery region fall below the universal log-law. The deviation of the velocity profile from the log-law indicates that the turbulent boundary layer is not fully recovered at 20 step heights behind the separation.The budgets of all Reynolds stress components have been computed. The turbulent kinetic energy budget in the recirculation region is similar to that of a turbulent mixing layer. The turbulent transport term makes a significant contribution to the budget and the peak dissipation is about 60% of the peak production. The velocity–pressure gradient correlation and viscous diffusion are negligible in the shear layer, but both are significant in the near-wall region. This trend is seen throughout the recirculation and reattachment region. In the recovery region, the budgets show that effects of the free shear layer are still present.

Collision statistics in an isotropic particle-laden turbulent suspension. Part 1. Direct numerical simulations

Abstract: Direct numerical simulations of heavy particles suspended in a turbulent fluid are performed to study the rate of inter-particle collisions as a function of the turbulence parameters and particle properties. The particle volume fractions are kept small (∼10−4) so that the system is well within the dilute limit. The fluid velocities are updated using a pseudo-spectral algorithm while the particle forces are approximated by Stokes drag. One unique aspect of the present simulations is that the particles have finite volumes (as opposed to point masses) and therefore particle collisions must be accounted for. The collision frequency is monitored over several eddy turnover times. It is found that particles with small Stokes numbers behave similarly to the prediction of Saffman & Turner (1956). On the other hand, particles with very large Stokes numbers have collision frequencies similar to kinetic theory (Abrahamson 1975). For intermediate Stokes numbers, the behaviour is complicated by two effects: (i) particles tend to collect in regions of low vorticity (high strain) due to a centrifugal effect (preferential concentration); (ii) particle pairs are less strongly correlated with each other, resulting in an increase in their relative velocity. Both effects tend to increase collision rates, however the scalings of the two effects are different, leading to the observed complex behaviour. An explanation for the entire range of Stokes numbers can be found by considering the relationship between the collision frequency and two statistical properties of the particle phase: the radial distribution function and the relative velocity probability density function. Statistical analysis of the data, in the context of this relationship, confirms the relationship and provides a quantitative description of how preferential concentration and particle decorrelation ultimately affect the collision frequency.

Langmuir turbulence in the ocean

Abstract: Solutions are analysed from large-eddy simulations of the phase-averaged equations for oceanic currents in the surface planetary boundary layer (PBL), where the averaging is over high-frequency surface gravity waves. These equations have additional terms proportional to the Lagrangian Stokes drift of the waves, including vortex and Coriolis forces and tracer advection. For the wind-driven PBL, the turbulent Langmuir number, Latur = (U∗/Us)1/2, measures the relative influences of directly wind-driven shear (with friction velocity U∗) and the Stokes drift Us. We focus on equilibrium solutions with steady, aligned wind and waves and a realistic Latur = 0.3. The mean current has an Eulerian volume transport to the right of the wind and against the Stokes drift. The turbulent vertical fluxes of momentum and tracers are enhanced by the presence of the Stokes drift, as are the turbulent kinetic energy and its dissipation and the skewness of vertical velocity. The dominant coherent structure in the turbulence is a Langmuir cell, which has its strongest vorticity aligned longitudinally (with the wind and waves) and intensified near the surface on the scale of the Stokes drift profile. Associated with this are down-wind surface convergence zones connected to interior circulations whose horizontal divergence axis is rotated about 45° to the right of the wind. The horizontal scale of the Langmuir cells expands with depth, and there are also intense motions on a scale finer than the dominant cells very near the surface. In a turbulent PBL, Langmuir cells have irregular patterns with finite correlation scales in space and time, and they undergo occasional mergers in the vicinity of Y-junctions between convergence zones.

Simplified Settling Velocity Formula for Sediment Particle

Abstract: A new and simplified formula for predicting the settling velocity of natural sediment particles is developed. The formula proposes an explicit relationship between the particle Reynolds number and a dimensionless particle parameter. It is applicable to a wide range of Reynolds numbers from the Stokes flow to the turbulent regime. The proposed formula has the highest degree of prediction accuracy when compared with other published formulas. It also agrees well with the widely used diagrams and tables proposed by the U.S. Inter-Agency Committee in 1957.

Magnetohydrodynamic Turbulence Revisited

Abstract: In 1965, Kraichnan proposed that MHD turbulence occurs as a result of collisions between oppositely directed Alfven wave packets. Recent work has generated some controversy over the nature of nonlinear couplings between colliding Alfven waves. We find that the resolution to much of the confusion lies in the existence of a new type of turbulence, intermediate turbulence, in which the cascade of energy in the inertial range exhibits properties intermediate between those of weak and strong turbulent cascades. Some properties of intermediate MHD turbulence are the following: (1) in common with weak turbulent cascades, wave packets belonging to the inertial range are long-lived; (2) however, components of the strain tensor are so large that, similar to the situation in strong turbulence, perturbation theory is not applicable; (3) the breakdown of perturbation theory results from the divergence of neighboring field lines due to wave packets whose perturbations in velocity and magnetic fields are localized, but whose perturbations in displacement are not; (4) three-wave interactions dominate individual collisions between wave packets, but interactions of all orders n ≥ 3 make comparable contributions to the intermediate turbulent energy cascade; (5) successive collisions are correlated since wave packets are distorted as they follow diverging field lines; (6) in common with the weak MHD cascade, there is no parallel cascade of energy, and the cascade to small perpendicular scales strengthens as it reaches higher wavenumbers; (7) for an appropriate weak excitation, there is a natural progression from a weak, through an intermediate, to a strong cascade.

Turbulence modeling validation

Abstract: The performances of four turbulence models are evaluated against eight selected experimental flow fields. The four models are the two-equation k-e model of Launder and Sharma, the two-equation k-a> model of Wilcox, the twoequation k-03 SST model of Menter, and the one-equation eddy-viscosity model of Spalart and Allmaras. The eight turbulent flows of the validation are four fully-developed freeshear flows, an incompressibl e boundary layer, and three complex flows with flow separation. The free-shear layer flows comprise a mixing layer, a round jet, a plane jet, and a plane wake flow. The three complex flows are comprised of an adverse-pressure-gradient boundary layer, an axisymmetric shock-wave/boundary-layer interaction, and a transonic RAE 2822 airfoil flow. The experimental data for these flows is well established and has been extensively used in model developments. The numerical predictions include mean velocity profiles, spreading rates, surface pressure coefficients, skin friction, and shear-stress profiles. Most significantly, this research includes a sensitivity study on the accuracy of the solutions with respect to the effects of freestream turbulence, grid resolution, grid spacing near the wall, initial conditions, numerical methods and codes, and free stream Mach number effects on incompressible flows.

The Protogalactic Origin for Cosmic Magnetic Fields

Abstract: It is demonstrated that strong magnetic fields are produced from a zero initial magnetic field during the pregalactic era, when the galaxy is first forming. Their development proceeds in three phases. In the first phase, weak magnetic fields are created by the Biermann battery mechanism. During the second phase, results from a numerical simulation make it appear likely that homogenous isotropic Kolmogorov turbulence develops that is associated with gravitational structure formation of galaxies. Assuming that this turbulence is real, then these weak magnetic fields will be amplified to strong magnetic fields by this Kolmogorov turbulence. During this second phase, the magnetic fields reach saturation with the turbulent power, but they are coherent only on the scale of the smallest eddy. During the third phase, which follows this saturation, it is expected that the magnetic field strength will increase to equipartition with the turbulent energy and that the coherence length of the magnetic fields will increase to the scale of the largest turbulent eddy, comparable to the scale of the entire galaxy. The resulting magnetic field represents a galactic magnetic field of primordial origin. No further dynamo action after the galaxy forms is necessary to explain the origin of magnetic fields. However, the magnetic field will certainly be altered by dynamo action once the galaxy and the galactic disk have formed. It is first shown by direct numerical simulations that thermoelectric currents associated with the Biermann battery build the field up from zero to 10-21 G in the regions about to collapse into galaxies, by z ~ 3. For weak fields, in the absence of dissipation, the cyclotron frequency -ωcyc = eB/mH c and ω/(1 + χ), where ∇ × v is the vorticity and χ is the degree of ionization, satisfy the same equations, and initial conditions ωcyc = ω = 0, so that, globally, -ωcyc(r, t) = ω(r, t)/(1 + χ). The vorticity grows rapidly after caustics (extreme nonlinearities) develop in the cosmic fluid. At this time, it is made plausible that turbulence has developed into Kolmogorov turbulence. Numerical simulations do not yet have the resolution to demonstrate that, during the second phase, the magnetic fields are amplified by the dynamo action of the turbulence. Instead, an analytic theory of the turbulent amplification of magnetic fields is employed to explore this phase of the magnetic field development. From this theory, it is shown that, assuming the turbulence is really Kolmogorov turbulence, the dynamo action of this protogalactic turbulence is able to amplify the magnetic fields by such a large factor during the collapse of the protogalaxy that the power into the magnetic field must reach saturation with the turbulent power. For the third phase, there is as yet no analytic theory capable of describing this phase. However, preliminary turbulence calculations currently in progress seem to confirm that the magnetic fields may proceed to equipartition with the turbulent energy, and that the coherence length may increase to the largest scales. Simple physical arguments are presented that show that this may be the case. Such an equipartition field is actually too strong to allow immediate collapse to a disk. Possible ways around this difficulty are discussed.

The instability of the shear layer separating from a bluff body

Abstract: Notwithstanding the fact that the instability of the separated shear layer in the cylinder wake has been extensively studied, there remains some uncertainty regarding not only the critical Reynolds number at which the instability manifests itself, but also the variation of its characteristic frequency with Reynolds number (Re). A large disparity exists in the literature in the precise value of the critical Reynolds number, with quoted values ranging from Re = 350 to Re = 3000. In the present paper, we demonstrate that the spanwise end conditions which control the primary mode of vortex shedding significantly affect the shear-layer instability. For parallel shedding conditions, shear-layer instability manifests itself at Re ≈ 1200, whereas for oblique shedding conditions it is inhibited until a significantly higher Re ≈ 2600, implying that even in the absence of a variation in free-stream turbulence level, the oblique angle of primary vortex shedding influences the onset of shear-layer instability, and contributes to the large disparity in quoted values of the critical Reynolds number. We confirm the existence of intermittency in shear-layer fluctuations and show that it is not related to the transverse motion of the shear layers past a fixed probe, as suggested previously. Such fluctuations are due to an intermittent streamwise movement of the transition point, or the location at which fluctuations develop rapidly in the shear layer.Following the original suggestion of Bloor (1964), it has generally been assumed in previous studies that the shear-layer frequency (normalized by the primary vortex shedding frequency) scales with Re1/2, although a careful examination of the actual data points from these studies does not support such a variation. We have reanalysed all of the actual data points from previous investigations and include our own measurements, to find that none of these studies yields a relationship which is close to Re1/2. A least-squares analysis which includes all of the previously available data produces a variation of the form Re0·67. Based on simple physical arguments that account for the variation of the characteristic velocity and length scales of the shear layer, we predict a variation for the normalized shear-layer frequency of the form Re0·7, which is in good agreement with the experimental measurements.

Suitability of upwind-biased finite difference schemes for large-eddy simulation of turbulent flows

Abstract: We have simulated flow past a circular cylinder at a Reynolds number of 3.9 X 10 3 using a solver that employs an energy-conservative second-order central difference scheme for spatial discretization. Detailed comparisons of turbulence statistics and energy spectra in the downstream wake region (7.0 < x/D < 10.0) have been made with the results of Beaudan and Moin and with experiments to assess the impact of numerical diffusion on the flowfield. Based on these comparisons, conclusions are drawn on the suitability of higher-order upwind schemes for LES in complex geometries.

Direct numerical simulation of the turbulent channel flow of a polymer solution

Abstract: In this work, we present from first principles a direct numerical simulation (DNS) of a fully turbulent channel flow of a dilute polymer solution. The polymer chains are modeled as finitely extensible and elastic dumbbells. The simulation algorithm is based on a semi-implicit, time-splitting technique which uses spectral approximations in the spatial coordinates. The computations are carried out on a CRAY T3D parallel computer. The simulations are carried out under fully turbulent conditions albeit, due to computational constraints, not at as high Reynolds number as that usually encountered in polymer-induced drag reduction experiments. In order to compensate for the lower Reynolds number, we simulate more elastic fluids than the ones encountered in drag reduction experiments resulting in Weissenberg numbers (a dimensionless number characterizing the flow elasticity) of similar magnitude. The simulations show that the polymer induces several changes in the turbulent flow characteristics, all of them consi...

Modeling the motion of a hot, turbulent gas

Abstract: This paper describes a new animation technique for modeling the turbulent rotational motion that occurs when a hot gas interacts with solid objects and the surrounding medium. The method is especially useful for scenes involving swirling steam, rolling or billowing smoke, and gusting wind. It can also model gas motion due to fans and heat convection. The method combines specialized forms of the equations of motion of a hot gas with an efficient method for solving volumetric differential equations at low resolutions. Particular emphasis is given to issues of computational efficiency and ease-of-use of the method by an animator. We present the details of our model, together with examples illustrating its use.

Using random walk models to simulate the vertical distribution of particles in a turbulent water column

Abstract: Random walk simulation has the potential to be an extremely powerful tool in the ~nvestigation of turbulence in environmental processes. However, care must be taken in applylng such simulat~ons to the mohon of particles in turbulent marine systems where turbulent diffusivity IS conlmonly spatially non-uniform. The problems associated with this nonuniformity are far from negligible and have been recognised for quite some time. However, incorrect implementat~ons continue to appear in the Literature. In this note computer simulations are presented to illustrate how and why these implementations are incorrect, and a slmple technique that can properly slmulate turbulent diffusion in the marine environment is discussed.

Nonlinear dynamics and pattern formation in turbulent wake transition

Abstract: Results are reported on direct numerical simulations of transition from two-dimensional to three-dimensional states due to secondary instability in the wake of a circular cylinder. These calculations quantify the nonlinear response of the system to three-dimensional perturbations near threshold for the two separate linear instabilities of the wake: mode A and mode B. The objectives are to classify the nonlinear form of the bifurcation to mode A and mode B and to identify the conditions under which the wake evolves to periodic, quasi-periodic, or chaotic states with respect to changes in spanwise dimension and Reynolds number. The onset of mode A is shown to occur through a subcritical bifurcation that causes a reduction in the primary oscillation frequency of the wake at saturation. In contrast, the onset of mode B occurs through a supercritical bifurcation with no frequency shift near threshold. Simulations of the three-dimensional wake for fixed Reynolds number and increasing spanwise dimension show that large systems evolve to a state of spatiotemporal chaos, and suggest that three-dimensionality in the wake leads to irregular states and fast transition to turbulence at Reynolds numbers just beyond the onset of the secondary instability. A key feature of these ‘turbulent’ states is the competition between self-excited, three-dimensional instability modes (global modes) in the mode A wavenumber band. These instability modes produce irregular spatiotemporal patterns and large-scale ‘spot-like’ disturbances in the wake during the breakdown of the regular mode A pattern. Simulations at higher Reynolds number show that long-wavelength interactions modulate fluctuating forces and cause variations in phase along the span of the cylinder that reduce the fluctuating amplitude of lift and drag. Results of both two-dimensional and three-dimensional simulations are presented for a range of Reynolds number from about 10 up to 1000.

Gradient and counter-gradient scalar transport in turbulent premixed flames

Abstract: In premixed turbulent combustion, the modelling of the turbulent flux of the mean reaction progress variable c, pul i c, remains somewhat controversial. Classical gradient transport assumptions based on the eddy viscosity concept are often used while both experimental data and theoretical analysis have pointed out the existence of counter-gradient turbulent diffusion. Direct numerical simulation (DNS) is used in this paper to provide basic information on the turbulent flux of c and study the occurrence of counter-gradient transport. The numerical configuration corresponds to two-or three-dimensional premixed flames in isotropic turbulent flow. The simulations correspond to various flame and flow conditions that are representative of flamelet combustion. They reveal that different flames will feature different turbulent transport properties and that these differences can be related to basic dynamical differences in the flame-flow interactions: counter-gradient diffusion occurs when the flow field near the flame is dominated by thermal dilatation due to chemical reaction, whereas gradient diffusion occurs when the flow field near the flame is dominated by the turbulent motions. The DNS-based analysis leads to a simple expression to describe the turbulent flux of c, which in turn leads to a simple criterion to delineate between the gradient and counter-gradient turbulent diffusion regimes. This criterion suggests that the occurrence of one regime or the other is determined primarily by the ratio of turbulence intensity divided by the laminar flame speed, u'/s L , and by the flame heat release factor, τ? (T b - T u )/T u , where T u and T b are respectively the temperature within unburnt and burnt gas. Consistent with the Bray-Moss-Libby theory, counter-gradient (gradient) diffusion is promoted by low (high) values of u'/s L and high (low) values of τ. DNS also shows that these results are not restricted to the turbulent transport of c. Similar results are found for the turbulent transport of flame surface density, Σ. The turbulent fluxes of c and Σ are strongly correlated in the simulated flames and counter-gradient (gradient) diffusion of c always coincides with counter-gradient (gradient) diffusion of Σ.

Description of a Turbulent Cascade by a Fokker-Planck Equation

Abstract: Fully developed turbulence is still regarded to be one of the main unsolved problems of classical physics. Great efforts have been made towards an understanding of small scale turbulent velocity fluctuations, which are assumed to be stationary, homogeneous, and isotropic in a statistical sense [1]. For large Reynolds numbers these fluctuations are supposed to exhibit universal behavior on scales smaller than the integral one. The elucidation of these properties apparently has to be based on applications of the tools of statistical mechanics. The quantity of main interest is the longitudinal velocity fluctuations yi on different length scales Li, yi › usx 1 Liy2, y, zd 2 usx 2 Liy2, y, zd , (1) where usx, y, zd is the x component of the velocity field at space point x, y, z. Based on the idea of an energy cascade, as a fundamental process governing the turbulence, we know from the pioneering works of the 1940s, cf. [1], that the velocity fluctuations are of the order yi ,s e L i d 1 y 3 . edenotes the energy dissipation (transfer) rate. However, it is commonly believed that intermittent fluctuations of the energy dissipation rate alters the scaling behavior. Intermittency effects show up in the changing shape of the probability density functions (pdf ) PLi syid as a function of Li and consequently lead for the scaling of the moments ksyid n l, L z n i to nonlinear n dependence of the scaling indices zn.

A theory of particle deposition in turbulent pipe flow

Abstract: The paper describes a theory of particle deposition based formally on the conservation equations of particle mass and momentum. These equations are formulated in an Eulerian coordinate system and are then Reynolds averaged, a procedure which generates a number of turbulence correlations, two of which are of prime importance. One represents ‘turbulent diffusion’ and the other ‘turbophoresis’, a convective drift of particles down gradients of mean-square fluctuating velocity. Turbophoresis is not a small correction; it dominates the particle dynamic behaviour in the diffusion-impaction and inertia-moderated regimes.Adopting a simple model for the turbophoretic force, the theory is used to calculate deposition from fully developed turbulent pipe flow. Agreement with experimental measurements is good. It is found that the Saffman lift force plays an important role in the inertia-moderated regime but that the effect of gravity on deposition from vertical flows is negligible. The model also predicts an increase in particle concentration close to the wall in the diffusion-impaction regime, a result which is partially corroborated by an independent ‘direct numerical simulation’ study.The new deposition theory represents a considerable advance in physical understanding over previous free-flight theories. It also offers many avenues for future development, particularly in the simultaneous calculation of laminar (pure inertial) and turbulent particle transport in more complex two- and three-dimensional geometries.

Eddy Viscosity Transport Equations and Their Relation to the k-ε Model

Abstract: A formalism will be presented which allows transforming two-equation eddy viscosity turbulence models into one-equation models. The transformation is based on Bradshaw’s assumption that the turbulent shear stress is proportional to the turbulent kinetic energy. This assumption is supported by experimental evidence for a large number of boundary layer flows and has led to improved predictions when incorporated into two-equation models of turbulence. Based on it, a new one-equation turbulence model will be derived from the k-e model. The model will be tested against the one-equation model of Baldwin and Barth, which is also derived from the k-e model (plus additional assumptions) and against its parent two-equation model. It will be shown that the assumptions involved in the derivation of the Baldwin-Barth model cause significant problems at the edge of a turbulent layer.

Application of neural networks to turbulence control for drag reduction

Abstract: A new adaptive controller based on a neural network was constructed and applied to turbulent channel flow for drag reduction. A simple control network, which employs blowing and suction at the wall based only on the wall-shear stresses in the spanwise direction, was shown to reduce the skin friction by as much as 20% in direct numerical simulations of a low-Reynolds number turbulent channel flow. Also, a stable pattern was observed in the distribution of weights associated with the neural network. This allowed us to derive a simple control scheme that produced the same amount of drag reduction. This simple control scheme generates optimum wall blowing and suction proportional to a local sum of the wall-shear stress in the spanwise direction. The distribution of corresponding weights is simple and localized, thus making real implementation relatively easy. Turbulence characteristics and relevant practical issues are also discussed.

Strongly turbulent Rayleigh–Bénard convection in mercury: comparison with results at moderate Prandtl number

Abstract: An experimental study of Rayleigh–Benard convection in the strongly turbulent regime is presented. We report results obtained at low Prandtl number (in mercury, Pr = 0.025), covering a range of Rayleigh numbers 5 × 106 < Ra < 5 × 109, and compare them with results at Pr∼1. The convective chamber consists of a cylindrical cell of aspect ratio 1.Heat flux measurements indicate a regime with Nusselt number increasing as Ra0.26, close to the 2/7 power observed at Pr∼1, but with a smaller prefactor, which contradicts recent theoretical predictions. A transition to a new turbulent regime is suggested for Ra ≃ 2 × 109, with significant increase of the Nusselt number. The formation of a large convective cell in the bulk is revealed by its thermal signature on the bottom and top plates. One frequency of the temperature oscillation is related to the velocity of this convective cell. We then obtain the typical temperature and velocity in the bulk versus the Rayleigh number, and compare them with similar results known for Pr∼1.We review two recent theoretical models, namely the mixing zone model of Castaing et al. (1989), and a model of the turbulent boundary layer by Shraiman & Siggia (1990). We discuss how these models fail at low Prandtl number, and propose modifications for this case. Specific scaling laws for fluids at low Prandtl number are then obtained, providing an interpretation of our experimental results in mercury, as well as extrapolations for other liquid metals.

Fluid mechanics of arterial stenosis: relationship to the development of mural thrombus.

Abstract: In this study, we analyzed blood flow through a model stenosis with Reynolds numbers ranging from 300 to 3,600 using both experimental and numerical methods. The jet produced at the throat was turbulent, leading to an axisymmetric region of slowly recirculating flow. For higher Reynolds numbers, this region became more disturbed and its length was reduced. The numerical predictions were confirmed by digital particle image velocimetry and used to describe the fluid dynamics mechanisms relevant to prior measurements of platelet deposition in canine blood flow (R.T. Schoephoersteret al., Atherosclerosis and Thrombosis 12:1806–1813, 1993). Actual deposition onto the wall was dependent on the wall shear stress distribution along the stenosis, increasing in areas of flow recirculation and reattachment. Platelet activation potential was analyzed under laminar and turbulent flow conditions in terms of the cumulative effect of the varying shear and elongational stresses, and the duration platelets are exposed to them along individual platelet paths. The cumulative product of shear rate and exposure time along a platelet path reached a value of 500, half the value needed for platelet activation under constant shear (J. M. Ramstacket al., Journal of Biomechanics 12: 113–125, 1979).

Drag reduction by polymer additives in a turbulent pipe flow : numerical and laboratory experiments

Abstract: In order to study the roles of stress anisotropy and of elasticity in the mechanism of drag reduction by polymer additives we investigate a turbulent pipe flow of a dilute polymer solution. The investigation is carried out by means of direct numerical simulation (DNS) and laser Doppler velocimetry (LDV). In our DNS two different models are used to describe the effects of polymers on the flow. The first is a constitutive equation based on Batchelor's theory of elongated particles suspended in a Newtonian solvent which models the viscous anisotropic effects caused by the polymer orientation. The second is an extension of the first model with an elastic component, and can be interpreted as an anisotropic Maxwell model. The LDV experiments have been carried out in a recirculating pipe flow facility in which we have used a solution of water and 20 w.p.p.m. Superfloc A110. Turbulence statistics up to the fourth moment, as well as power spectra of various velocity components, have been measured. The results of the drag-reduced flow are first compared with those of a standard turbulent pipe flow of water at the same friction velocity at a Reynolds number of Reτ≈1035. Next the results of the numerical simulation and of the measurements are compared in order to elucidate the role of polymers in the phenomenon of drag reduction. For the case of the viscous anisotropic polymer model, almost all turbulence statistics and power spectra calculated agree in a qualitative sense with the measurements. The addition of elastic effects, on the other hand, has an adverse effect on the drag reduction, i.e. the viscoelastic polymer model shows less drag reduction than the anisotropic model without elasticity. Moreover, for the case of the viscoelastic model not all turbulence statistics show the right behaviour. On the basis of these results, we propose that the viscous anisotropic stresses introduced by extended polymers play a key role in the mechanism of drag reduction by polymer additives.

A comparative study of subgrid scale models in homogeneous isotropic turbulence

Abstract: Recently, a number of studies have indicated that Large Eddy Simulation (LES) models are fairly insensitive to the adopted Subgrid Scale (SGS) models. In order to study this and to gain further insight into LES, simulations of forced and decaying homogeneous isotropic turbulence have been performed for Taylor Re numbers between 35 and 248 using various SGS models, representative of the contemporary state of the art. The predictive capability of the LES concept is analyzed by comparison with DNS data and with results obtained from a theoretical model of the energy spectrum. The resolved flow is examined by visualizing the morphology and by analyzing the distribution of resolved enstrophy, rate of strain, stretching, SGS kinetic energy, and viscosity. Furthermore, the correlation between eigenvalues of the resolved rate of strain tensor and the vorticity is investigated. Although the gross features of the flow appear independent of the SGS model, pronounced differences between the models become apparent whe...

Energy transfer in rotating turbulence

Abstract: The influence or rotation on the spectral energy transfer of homogeneous turbulence is investigated in this paper. Given the fact that linear dynamics, e.g. the inertial waves regime tackled in an RDT (Rapid Distortion Theory) fashion, cannot Affect st homogeneous isotropic turbulent flow, the study of nonlinear dynamics is of prime importance in the case of rotating flows. Previous theoretical (including both weakly nonlinear and EDQNM theories), experimental and DNS (Direct Numerical Simulation) results are gathered here and compared in order to give a self-consistent picture of the nonlinear effects of rotation on tile turbulence. The inhibition of the energy cascade, which is linked to a reduction of the dissipation rate, is shown to be related to a damping due to rotation of the energy transfer. A model for this effect is quantified by a model equation for the derivative-skewness factor, which only involves a micro-Rossby number Ro(sup omega) = omega'/(2(OMEGA))-ratio of rms vorticity and background vorticity as the relevant rotation parameter, in accordance with DNS and EDQNM results fit addition, anisotropy is shown also to develop through nonlinear interactions modified by rotation, in an intermediate range of Rossby numbers (Ro(omega) = (omega)' and Ro(omega)w greater than 1), which is characterized by a marco-Rossby number Ro(sup L) less than 1 and Ro(omega) greater than 1 which is characterized by a macro-Rossby number based on an integral lengthscale L and the micro-Rossby number previously defined. This anisotropy is mainly an angular drain of spectral energy which tends to concentrate energy in tile wave-plane normal to the rotation axis, which is exactly both the slow and the two-dimensional manifold. In Addition, a polarization of the energy distribution in this slow 2D manifold enhances horizontal (normal to the rotation axis) velocity components, and underlies the anisotropic structure of the integral lengthscales. Finally is demonstrated the ability of a generalized EDQNM (Eddy Damped Quasi-Normal Markovian) model to predict the underlying spectral transfer structure and all the subsequent developments of classic anisotropy indicators in physical space, when compared to recent LES results. Even if the applications mainly concern developed strong turbulence, a particular emphasis is given to the strong formal analogy of this EDQNM2 model with recent weakly nonlinear approaches to wave-turbulence.

The Earth's plasma sheet as a laboratory for flow turbulence in high-β MHD

Abstract: The bulk flows and magnetic-field fluctuations of the plasma sheet are investigated using single-point measurements from the ISEE-2 Fast Plasma Experiment and fluxgate magnetometer. Ten several-hour-long intervals of continuous data (with 3 s and 12 s time resolution) are analysed. The plasma-sheet flow appears to be strongly ‘turbulent’ (i.e. the flow is dominated by fluctuations that are unpredictable, with rms velocities[Gt ]mean velocities and with field fluctuations≈mean fields). The flow velocities are typically sub-Alfvenic. The flow-velocity probability distribution P(v) is constructed, and is found to be well fitted by exponential functions. Autocorrelation functions [Ascr ](τ) are constructed, and the autocorrelation times τcorr for the flow velocities are found to be about 2 min. From the flow measurements, an estimate of the mixing length in the plasma sheet is produced, yielding Lmix≈2 Earth radii; correspondingly, the plasma-sheet material appears to be well mixed in density and temperature. An eddy viscosity for the plasma sheet is also estimated. Power spectra, which are constructed from the v(t) and B(t) time series, have portions that are power laws with spectral indices that are near the range of those expected for turbulence theories. The plasma sheet may provide a laboratory for the study of turbulence in parameter regimes different from that of solar-wind turbulence: the plasma sheet is a β[Gt ]1, hot-ion plasma, and the turbulence may be strongly driven rather than well developed. The turbulent nature of the flow and the disordered nature of the magnetic field have implications for the transport of plasma-sheet material, for the penetration of the solar-wind electric field into the plasma sheet, and for the calculation of particle orbits in the magnetotail.

Turbulence Measurements in the Near Field of a Wingtip Vortex

Abstract: The roll-up of a wingtip vortex, at Reynolds number based on chord of 4.6 million was studied with an emphasis on suction side and near wake measurements. The research was conducted in a 32 in. x 48 in. low-speed wind tunnel. The half-wing model had a semi-span of 36 in. a chord of 48 in. and a rounded tip. Seven-hole pressure probe measurements of the velocity field surrounding the wingtip showed that a large axial velocity of up to 1.77 U(sub infinity) developed in the vortex core. This level of axial velocity has not been previously measured. Triple-wire probes have been used to measure all components of the Reynolds stress tensor. It was determined from correlation measurements that meandering of the vortex was small and did not appreciably contribute to the turbulence measurements. The flow was found to be turbulent in the near-field (as high as 24 percent RMS w - velocity on the edge of the core) and the turbulence decayed quickly with streamwise distance because of the nearly solid body rotation of the vortex core mean flow. A streamwise variation of the location of peak levels of turbulence, relative to the core centerline, was also found. Close to the trailing edge of the wing, the peak shear stress levels were found at the edge of the vortex core, whereas in the most downstream wake planes they occurred at a radius roughly equal to one-third of the vortex core radius. The Reynolds shear stresses were not aligned with the mean strain rate, indicating that an isotropic-eddy-viscosity based prediction method cannot accurately model the turbulence in the cortex. In cylindrical coordinates, with the origin at the vortex centerline, the radial normal stress was found to be larger than the circumferential.