Rms Velocity Fluctuations Research Articles

Response of the wake of an isolated particle to an isotropic turbulent flow

The interaction of an isolated spherical particle with an isotropic turbulent flow is considered using direct numerical simulations (DNS). The particle Reynolds number is varied from about 50 to 600 and the particle diameter is varied from about 1.5 to 10 times the Kolmogorov scale. The Reynolds number based on the Taylor microscale of the free-stream turbulent field considered here is 164. The DNS technique employed here is the first of its kind to address particle–turbulence interaction and it resolves the smallest scales in the free-stream turbulent flow and the complex vortical structures in the particle wake. The primary objective of this paper is to present new results on the effect of the free-stream turbulence on the particle wake and vortex shedding, and the modulation of free-stream turbulence in the particle wake. The parameters of the present simulations are comparable to those of the experimental study by Wu & Faeth (1994), and agreement between the present computational results and the experimental measurement is demonstrated.The effect of free-stream turbulence on the mean and instantaneous wake structure is studied. The time-averaged mean wake in a turbulent ambient flow shows a lower velocity deficit and a flatter profile. However, in agreement with the experimental results of Wu & Faeth the mean wake in a turbulent flow behaves like a self-preserving laminar wake. At Reynolds numbers below about 210 the effect of free-stream turbulence is to introduce wake oscillations. For Reynolds numbers in the range 210 to 280, free-stream turbulence is observed to promote early onset of vortex shedding. The nature of the shed vortices is somewhat different from that in a uniform flow. Increasing the free-stream turbulence intensity suppresses the process of vortex shedding, and only marginally increases the wake oscillation. The modulation of free-stream turbulence in the wake is studied in terms of the distribution of kinetic energy and RMS velocity fluctuation. The free-stream energy lost in the wake is recovered faster in a turbulent ambient flow than in a uniform ambient flow. The energy of the velocity fluctuation is enhanced in the wake at low free-stream intensities, and is damped or marginally increased at higher intensities. The fluctuation energy is not equi-partitioned among the streamwise and cross-stream components. The RMS streamwise fluctuation is always enhanced, whereas the RMS cross-stream fluctuation is enhanced only at low free-stream intensities, and damped at higher intensities.

Mapping random lithospheric heterogeneities in northern and central Europe

SUMMARY An energy-flux model (EFM) and a teleseismic fluctuation wavefield method (TFWM) have been applied to interpret the teleseismic P coda observed at three temporary and two permanent networks in northern and central Europe. The aim is to determine the small-scale random structure of the lithosphere below the receivers. Various subsets of these data have been exploited previously with one of the two methods. The main objectives here are: To compare the performance of both methods with synthetic data sets. To map the random structure of the lithosphere in terms of inverse scattering Q (Q−1s), correlation length a, RMS velocity fluctuation σ, thickness L of the scattering layer and autocorrelation function (ACF) using a combination of both methods. With TFWM, the product aσ2 can be reliably determined if L is known. L can be roughly estimated with EFM. Although EFM can, in principle, resolve a and σ separately, a is recovered with a rather large uncertainty. TFWM does not distinguish much between the ACF type, whereas with EFM determination of the ACF type is sometimes possible. By combining the results of both methods we determine improved random medium parameters of the lithosphere for eleven subregions in northern and central Europe. In the Baltic shield, Rhenohercynian belt, Ardenne and Brabant mountains, eastern Rhenish massif, Eifel, Hunsruck mountains, Lorraine, Frankonian Jura and massif Central scattering predominantly occurs in the crust. For the frequency range from 0.5 to 5 Hz correlation lengths of 1–7 km and rms velocity fluctuations of 3–7 per cent are obtained. For the Rhenohercynian belt (RH) and the N-German basin RMS velocity fluctuations and correlation lengths could not be resolved. The data from the N-German basin (NB) cannot be explained by scattering within the crust only. Smallest scattering Q was found in the N German basin (Qs≈ 100 at 1 Hz) and largest scattering Q in the Baltic shield (Qs≈ 450 at 2–3 Hz). For the Frankonian Jura only a Gaussian ACF can fit the Q−1s values. The data from the eastern Rhenish massif also indicate a random medium with Gaussian ACF. For all other subregions we cannot distinguish between exponential or Gaussian ACF for the random medium structure.

Transition from laminar to turbulent flow in liquid filled microtubes

The transition to turbulent flow is studied for liquids of different polarities in glass microtubes having diameters between 50 and 247 µm. The onset of transition occurs at Reynolds numbers of ~1,800–2,000, as indicated by greater-than-laminar pressure drop and micro-PIV measurements of mean velocity and rms velocity fluctuations at the centerline. Transition at anomalously low values of Reynolds number was never observed. Additionally, the results of more than 1,500 measurements of pressure drop versus flow rate confirm the macroscopic Poiseuille flow result for laminar flow resistance to within −1% systematic and ±2.5% rms random error for Reynolds numbers less than 1,800.

Large eddy simulation of a solid-fuel jet flame

Three-dimensional large eddy simulation (LES) is applied to a turbulent jet flame of a solid fuel, and the interactions among the dispersion, evaporation and combustion of the solid-fuel particles are investigated. The SGS turbulence and combustion models used are based upon the Smagorinsky model and the conserved scalar approach. The results show that the evaporation of the solid-fuel particles and the heat release produced by the reaction between the fuel vapor and oxidizer tend to increase the mean centerline gas velocity and the jet width and to decrease the rms velocity fluctuations from the values for a particle-laden jet without evaporation. In spite of the different particle-laden and heat release conditions, the radial profiles of the axial gas velocity, product mass fraction and gas temperature normalized by their centerline values and jet widths approach a Gaussian profile as the streamwise distance increases. The peak of the particle number density of the laden particles tends to shift outside as the streamwise distance increases, and the trend is observed further upstream for the higher heat release rate case. The evaporation of the fuel particles for the lower heat release rate takes place in the intermittent regions around the centerline, whereas the rate of evaporation for the higher heat release rate is proportional to the streamwise distance. These behaviors could be explained by considering the mass transfer from the particles to the fluid, the particle inertial force and the variation of the kinematic viscosity of fluid.

Statistical inversion of controlled-source seismic data using parabolic wave scattering theory

Summary Statistical parameters describing heterogeneity in the Proterozoic basement of the Baltic Shield were estimated from controlled-source seismic data, using a statistical inversion based on the theory of wave propagation through random media (WPRM), derived from the parabolic wave approximation. Synthetic plane-wave seismograms generated from models of random media show consistency with WPRM theory for forward propagation in the weak-scattering regime, whilst for two-way propagation a discrepancy exists that is due to contamination of the primary wave by backscattered energy. Inverse modelling of the real seismic data suggests that the upper crust to depths of ∼ 15 km can be characterized, subject to the range of spatial resolution of the method, by a medium with an exponential spatial autocorrelation function, an rms velocity fluctuation of 1.5 ± 0.5 per cent and a correlation length of 150 ± 50 m. Further inversions show that scattering is predominantly occurring in the uppermost ∼ 2 km of crust, where rms velocity fluctuation is 3 − 6 per cent. Although values of correlation distance are well constrained by these inversions, there is a trade-off between thickness of scattering layer and rms velocity perturbation estimates, with both being relatively poorly resolved. The higher near-surface heterogeneity is interpreted to arise from fractures in the basement rocks that close under lithostatic pressure for depths greater than 2 − 3 km.

Flow Field and Structure of Highly Turbulent Premixed Flames.

To examine the premixed flame structure in highly turbulent flow, by a cyclone-jet combustor, we have examined the flow field both in cold flow and in combustion field using LDV system. The turbulence scale has been obtained by Slot-Correlation method. The experiments have been conducted from the flamelet regime (Um=10 m/s) to the distributed reaction zone regime (Um=30 m/s) in combustion diagram. Results show that, in combustion filed, the mean axial velocity does not decrease as much and rms fluctuation velocity is lower along the center axis, compared with those in cold flow. It could be explained with the flow expansion in combustion. That is, the turbulence transport is reduced due to the existence of low-density gas in shear layer at the flame front, which leads to a longer potential core in combustion field than that in cold flow. Flame generated turbulence is observed in radial velocity distribution. The integral length scale becomes larger at the flame zone due to the flow expansion.

DNS and scaling law analysis of compressible turbulent channel flow

Fully developed compressible turbulent channel flow (Ma = 0.8, Re = 3300) is numerically simulated, and the data base of turbulence is established. The statistics such as density-weighted mean velocity and RMS velocity fluctuations in semi-local coordinates agree well with those from other DNS data. High order statistics (skewness and flatness factors) of velocity fluctuations of compressible turbulence are reported for the first time. Compressibility effects are also discussed. Pressure-dilatation absorbs part of the kinetic energy and makes the streaks of compressible channel flow more smooth. The scaling laws of compressible channel flow are also discussed. The conclusions are: (a) Scaling law is found in the center area of the channel, (b) In this area, ESS is also found, (c) When Mach number is not very high, compressibility has little effect on scaling exponents.

Modification of a vortex street by a polymer additive

A Kármán vortex street is created in a flowing soap film by a rod penetrating the film. The velocity field generated by this rod is modified by the addition of the polymer polyethylene oxide having a molecular weight of 5×106 and a concentration of 30 wppm. The rms velocity fluctuations behind the rod are strongly suppressed by the polymer additive and the power spectrum of the velocity fluctuations is modified as well. The experiments show that the polymer additive decreases the rate at which energy is injected into the flow. The measurements further indicate that the polymer introduces an elongational viscosity term into the Navier–Stokes equation.

Flow field analysis of a turbulent boundary layer over a riblet surface

The near-wall flow structures of a turbulent boundary layer over a riblet surface with semi-circular grooves were investigated experimentally for the cases of drag decreasing (s +=25.2) and drag increasing (s +=40.6). One thousand instantaneous velocity fields over riblets were measured using the velocity field measurement technique and compared with those above a smooth flat plate. The field of view was 6.75 × 6.75 mm2 in physical dimension, containing two grooves. Those instantaneous velocity fields were ensemble averaged to get turbulent statistics including turbulent intensities and turbulent kinetic energy. To see the global flow structure qualitatively, flow visualization was also carried out using the synchronized smoke-wire technique under the same experimental conditions. For the case of drag decreasing (s +=25.2), most of the streamwise vortices stay above the riblets, interacting with the riblet tips frequently. The riblet tips impede the spanwise movement of the streamwise vortices and induce secondary vortices. The normalized rms velocity fluctuations and turbulent kinetic energy are small near the riblet surface, compared with those over a smooth flat plate. Inside the riblet valleys, these are sufficiently small that the increased wetted surface area of the riblets can be compensated. In addition, in the outer region (y + > 30), these values are almost equal to or slightly smaller than those for the smooth plate. For the case of drag increasing (s +=40.6), however, most of the streamwise vortices stay inside the riblet valleys and contact directly with the riblet surface. The high-speed down-wash flow penetrating into the riblet valley interacts actively with the wetted riblet surface and increases the skin friction. The rms velocity fluctuations and turbulent kinetic energy have larger values compared with those over a smooth flat plate.

DNS of turbulent flow along passively permeable walls

Abstract Fully developed low-Reynolds-number turbulent flow through straight permeable pipes with circular cross-section is investigated by means of direct numerical simulation. Three different cases of wall permeability are treated and compared with the case of a solid wall. In two of these cases, the wall satisfies the no-slip condition, but allows for the wall normal velocity fluctuations in two different ways. In the third case, the pipe wall has rectangular openings of size (6 Δz + ×10( RΔϕ ) + ), regularly distributed over the whole surface, similar to a chessboard, where the white areas represent the openings and the black ones the solid wall. Velocity boundary conditions in the openings are such that the mean mass flux across the wall is zero and the flow in the openings is stress-free. All flows are driven by the same mean pressure gradient. Consequently, those flows which satisfy the no-slip condition have the same wall shear stress and hence the same turbulence Reynolds number Re τ =360. Pipe flow with wall openings exhibits a small, but finite Reynolds shear stress at the wall. If the friction velocity is defined via the total stress at this wall, the flow nominally has the same turbulence Reynolds number. The overall effect of a permeable wall with rectangular openings is a mean axial slip velocity at the wall and reduced viscous stress. In a thin near-wall layer of thickness ν / u τ , the turbulence activity is increased compared to the flow cases, where the velocity components satisfy the no-slip condition. All three rms-velocity fluctuations are non-zero. As a result the structure of the Reynolds stress tensor is modified in this region. This is also reflected in higher order central moments of the velocity fluctuations. A permeable wall with rectangular openings may be viewed as a model for a rough wall with a mean non-dimensional roughness height of 8.3 wall units. Close to such a wall the budgets of the Reynolds stress tensor differ strongly from those for flow along a smooth impermeable wall.

Particle dynamics in sheared granular matter

The particle dynamics and shear forces of granular matter in a Couette geometry are determined experimentally. The normalized tangential velocity V(y) declines strongly with distance y from the moving wall, independent of the shear rate and of the shear dynamics. Local rms velocity fluctuations deltaV(y) scale with the local velocity gradient to the power 0.4+/-0.05. These results agree with a locally Newtonian, continuum model, where the granular medium is assumed to behave as a liquid with a local temperature [deltaV(y)](2) and density dependent viscosity.

Finite difference modelling of P-wave scattering in the upper mantle

Summary Scattering within the upper mantle is prominently documented in the so-called high-frequency teleseismic Pn phase, generated by velocity fluctuations in the upper mantle. This phase is seen in many data sets from active and passive seismology. Whenever the source-generated frequencies are high enough (5–10 Hz) to allow their observation at large distances (>2000 km), this phase appears in the recordings of the Russian PNE programme, in other long-range refraction experiments, and in numerous recordings of earthquakes. Using a 2-D finite difference scheme we calculate complete synthetic seismograms in order to relate the scales of the fluctuation of the elastic parameters to wavefield properties. We discuss the influence of critical parameters on the scattering properties of the upper mantle and on the propagation mechanism of the teleseismic Pn: variations in vertical and horizontal correlation lengths, rms velocity fluctuations, thickness of the heterogeneous layer, and cross-correlation of P- and S-wave velocities. A teleseismic Pn phase arises only if the velocity fluctuations are strong enough to cause multiple scattering and if the horizontal correlation length exceeds the vertical by an order of magnitude. Our favourite model for the Russian PNE profiles includes a 100–150-km-thick zone of scatterers below the Moho, containing heterogeneities with a horizontal correlation length of 20 km, a vertical correlation length of 0.5 km and an rms velocity perturbation of 2 per cent, while keeping the P- and S-wave velocities correlated. As the teleseismic Pn is often observed, this scale of velocity fluctuations seems to be characteristic of the uppermost mantle. Anisotropy is likely to contribute to the inferred velocity fluctuations.

PIV measurements of the flow and turbulent characteristics of a round jet in crossflow

The instantaneous and ensemble averaged flow characteristics of a round jet issuing normally into a crossflow was studied using a flow visualization technique and Particle Image Velocimetry measurements. Experiments were performed at a jet-to-crossflow velocity ratio, 3.3 and two Reynolds numbers, 1,050 and 2,100, based on crossflow velocity and jet diameter. Instantaneous laser tomographic images of the vertical center plane of the crossflow jet show that there exists very different natures in the flow structures of the near field jet due to Reynolds number effect even though the velocity ratio is same. It is found that the shear layer becomes much thicker when the Reynolds number is 2,100 because of the strong entrainment of the inviscid fluid by turbulent interaction between the jet and crossflow. The mean and second order statistics are calculated by ensemble averaging over 1,000 realizations of instantaneous velocity fields. The detail characteristics of mean flow field, streamwise and vertical rms velocity fluctuations, and Reynolds shear stress distributions are presented. The new PIV results are compared with those from previous experimental and LES studies.

Flow Characteristics of Transitional Boundary Layers on an Airfoil in Wakes

Transition characteristics of a boundary layer on a NACA0012 airfoil are investigated by measuring unsteady velocity using hot wire anemometry. The airfoil is installed in the incoming wake generated by an airfoil aligned in tandem with zero angle of attack. Reynolds number based on the airfoil chord varies from 2.0×105 to 6.0×105; distance between two airfoils varies from 0.25 to 1.0 of the chord length. To measure skin friction coefficient identifying the transition onset and completion, an extended wall law is devised to accommodate transitional flows with pressure gradient and nonuniform inflows. Variations of the skin friction are quite similar to that of the flat plate boundary layer in the uniform turbulent inflow of high intensity. Measured velocity profiles are coincident with families generated by the modified wall law in the range up to y+=40. Turbulence intensity of the incoming wake shifts the onset location of transition upstream. The transitional region becomes longer as the airfoils approach one another and the Reynolds number increases. The mean velocity profile gradually varies from a laminar to logarithmic one during the transition. The maximum values of rms velocity fluctuations are located near y+=15-20. A strong positive skewness of velocity fluctuation is observed at the onset of transition and the overall rms level of velocity fluctuation reaches 3.0–3.5 in wall units. The database obtained will be useful in developing and evaluating turbulence models and computational schemes for transitional boundary layer. [S0098-2202(00)01603-5]

Manipulation of a jet in a cross flow

Abstract The effect of forcing on the mixing and velocity field of a jet in a cross flow is investigated for a jet-to-cross flow velocity ratio of R=1.0 using reactive-Mie-scattering flow-visualization and two-color Particle Image Velocimetry (PIV) techniques. Reactive-Mie-scattering images are used to assess the effect of forcing on molecular mixing, whereas double-exposed two-color PIV images are employed to obtain instantaneous velocity and corresponding vorticity distributions. The jet emanates from a square conduit and is manipulated by four piezoelectric actuators – one mounted along each side of the jet conduit near the jet-exit plane. Time-and phase-averaged distributions of velocity and rms velocity fluctuations in the x–y plane z=0 are also obtained. A novel approach is employed for processing jet and cross-flow fluids based on the size of the seeding particle. The present results show that when the jet is unforced, the “wake” of the jet contains a domain in which the magnitude of the velocity is very low compared to that of the cross-flow velocity, suggesting that the fluid within this domain is almost stagnant. When the jet is excited, the low-velocity domain in its wake is substantially reduced through vigorous mixing. Manipulation of the upstream and downstream segments of the jet shear layer also leads to an increase in the jet penetration into the cross flow (up to 30% as compared to the unforced case) and substantial mixing enhancement. Unlike in streamwise forcing where the jet fluid remains mainly in the central portion of the spanwise surface, spanwise forcing induces strong spanwise jet undulations.

Characterization of Turbulence in a Closed Flow

We investigate the closed flow between coaxial contra rotating disks, at moderate to high Reynolds numbers. We show that global (i.e. spatially averaged) quantities can be used to characterize the state of the flow and its degree of turbulence. We first report measurements on the driving torque and show how it depends on the manner momentum is imparted to the fluid. We then show that pressure measurements at the flow boundary provide a good estimate of the rms velocity fluctuations in the flow and that it reveals the transition to turbulence in the flow volume. Finally, we show that once the transition has occurred, the knowledge of the same global quantities allows the calculation of fundamental turbulence characteristics such as the rms velocity fluctuations, the effective integral length scale L * , Taylor's microscale λ and Kolmogorov's dissipation length η. That these quantities may be obtained from measuring devices removed from the bulk of the flow is of importance for the study of fluid motion in complex geometries and/or using corrosive fluids

Wave propagation in a multiple-scattering upper mantle-observations and modelling

SUMMARY A striking feature of Russian long-range seismic refraction data from Peaceful Nuclear Explosions is the observation of a high-frequency teleseismic P, phase, which travels with a group velocity of 8.0 km s-l out to distances of several thousands of kilometres. Modelling using the reflectivity method shows that this phase can be understood as the response of an upper mantle that contains random RMS velocity fluctuations of about 44 per cent superimposed on a positive velocity gradient. This class of model explains the existence of the teleseismic P,, its high-frequency content and its coda length. A teleseismic P, can only be generated if velocity fluctuations are strong enough to cause multiple scattering and occur on a subwavelength scale. Cross-correlation properties of P- and S-wave velocity fluctuations exert a substantial influence on the wavefield. A completely unexpected phase can be observed if the fluctuations are imposed on a negative gradient

Dynamics of Grains in Driven Granular Media

ABSTRACTWe use diffusing-wave spectroscopy (DWS) to study microscopic dynamics in the interior of 3-dimensional granular systems. We study two granular systems where particle motions are excited by different driving mechanisms – gravity-driven channel flow and a gas-fluidized bed. In both instances we obtain detailed information about short-time collisional dynamics such as rms velocity fluctuations, mean free paths, and collision frequencies. We also observe a slow crossover from short-time ballistic motions to long-time, grain-scale diffusive motions.

Numerical analysis of turbulent cross stresses and pressure in the developing region of an axisymmetric jet

A numerical study was conducted of the transition region of an axisymmetric isothermal jet, from 10 to 44 diameters downstream of the nozzle exit. The transition region is of particular interest because if offers an opportunity to examine the relationship among physical quantities in a developing flow. A model for the Reynolds cross-stress terms was developed from empirical correlations of mean velocity. It was then used, along with correlations for RMS velocities, to numerically predict pressure in the developing region. This turbulence model is more accurate than experimental measurements in high Reynolds number, transitional flows because the scales of turbulence in these conditions are too small to resolve experimentally. Numerical results show that close coupling exists between the mean axial velocity and the Reynolds cross-stresses. Similarly, a close relationship exists between the axial and radial RMS velocity fluctuations and the developing pressure gradients in the axial and radial direction. Therefore, when the mean velocities reach fully similar form, similarity of Reynolds cross stresses is also required. The axial and radial fluctuations continue to develop, and asymptotically approach similar forms at rates closely matching the decay of the mean pressure gradients. The information presented here can be used to test turbulence models applied to developing flows.

Concentric annular flow with centerbody rotation of a Newtonian and a shear-thinning liquid

Measurements of the radial distributions of the axial and tangential components of velocity and rms velocity fluctuations are presented together with friction factor versus Reynolds number data for two liquids, one Newtonian, the other a shear-thinning polymer, in laminar, transitional, and turbulent flow in an annular geometry with a rotating centerbody of radius ratio 0.506. In all flow regimes, the friction factor is increased by centerbody rotation. However, the influence is slight and most apparent for laminar flow of the Newtonian fluid. Laser Doppier anenometry (LDA) measurements of the tangential velocity reveal three distinct regions across the radial gap with a central region of almost constant angular momentum, which diminishes in magnitude as the Reynolds number increases. Axial velocity measurements show only slight deviations from what would be expected for the case without centerbody rotation. In turbulent flow, the axial velocity fluctuations decrease progressively with increasing Reynolds number for all fluids. For the polymeric liquid, the tangential velocity fluctuations are somewhat suppressed, especially at high Reynolds numbers where the influence of centerbody rotation is reduced. Over a limited range of (low) Reynolds numbers and rotation speeds, the generation and advection of Taylor vortices produces complex flow patterns. Limited measurements are reported for the vortex advection speed.