Local Mean Velocity Research Articles

Fluctuation–response inequality out of equilibrium

We present an approach to response around arbitrary out-of-equilibrium states in the form of a fluctuation-response inequality (FRI). We study the response of an observable to a perturbation of the underlying stochastic dynamics. We find that the magnitude of the response is bounded from above by the fluctuations of the observable in the unperturbed system and the Kullback-Leibler divergence between the probability densities describing the perturbed and the unperturbed system. This establishes a connection between linear response and concepts of information theory. We show that in many physical situations, the relative entropy may be expressed in terms of physical observables. As a direct consequence of this FRI, we show that for steady-state particle transport, the differential mobility is bounded by the diffusivity. For a "virtual" perturbation proportional to the local mean velocity, we recover the thermodynamic uncertainty relation (TUR) for steady-state transport processes. Finally, we use the FRI to derive a generalization of the uncertainty relation to arbitrary dynamics, which involves higher-order cumulants of the observable. We provide an explicit example, in which the TUR is violated but its generalization is satisfied with equality.

Flow characterization of a pulsating heat pipe through the wavelet analysis of pressure signals

Pulsating Heat Pipes are two phase passive heat transfer devices characterized by a thermally induced two phase oscillating flow. The correct detection of the dominant frequencies of such oscillations is fundamental to fully characterize the device thermofluidic operation but the studies available in the literature are very heterogenous and results are often discordant. In this work, the concept of dominant frequency in Pulsating Heat Pipes is thoroughly discussed and defined analytically. The wavelet transform is used to characterize the fluid pressure signal in the frequency domain varying the heat power input at the evaporator and in the condenser zone of a full-scale Pulsating Heat Pipe tested in microgravity conditions. During the slug-plug flow regime, the dominant frequencies falls in the range 0.6–0.9 Hz, showing an increasing trend with the heat load input. The Cross-Correlation reveals that the two signals at the evaporator and at the condenser are very similar. Finally, the instantaneous angle of phase is calculated and lies between 310 and 360 deg. This value can be physically interpreted as a repeatable time shift between the two signals that can be used to evaluate the flow local mean velocity (0.09–0.13 m/s) constituting a valuable alternative to the visualization techniques.

Open channel flow within and above a layered vegetation: Experiments and first-order closure modeling

Flow within vegetation characterized by non-uniform roughness density is drawing significant research attention given its relevance to a plethora of applications in eco-hydraulics including river restoration, and flow in wetland and marshes. The focus here is on flume experiments and modeling of the mean longitudinal velocity profile in a two layered cylindrical vegetation system. Layer 1 represents the region close to the channel bottom where the flow experiences maximum drag due to the densely placed vegetation, while layer 2 represents the flow region above the short vegetation characterized by a smaller vegetation density. Considering the aforementioned arrangements, a new analytical model based on Reynolds-averaged closure principles is proposed to describe the vertical distribution of mean streamwise velocity in an open channel with two different vegetation densities. In the proposed model, the one-dimensional steady and planar-homogeneous momentum equation is used where the turbulent eddy viscosity is assumed to be linearly related to the local mean velocity. The proposed analytical model has been calibrated using experiments reported here in which vegetation is represented by using circular plastic cylinders of two different heights. The proposed model is further tested against published experiments with similar arrangements. In total, 22 different experimental conditions with distinct densities, rigidity, and flow depths have been analyzed. The Root Mean Square Error (RMSE) of the velocity comparisons is found to be less than 0.0342 m/s, which is acceptable.

Mean Velocity and Shear Stress Distribution in Floating Treatment Wetlands: An Analytical Study

AbstractFloating treatment wetlands (FTWs) are efficient at wastewater treatment; however, data and physical models describing water flow through them remain limited. A two‐domain model is proposed dividing the flow region into an upper part characterizing the flow through suspended vegetation and an inner part describing the vegetation‐free zone. The suspended vegetation domain is represented as a porous medium characterized by constant permeability thereby allowing Biot's Law to be used to describe the mean velocity and stress profiles. The flow in the inner part is bounded by asymmetric stresses arising from interactions with the suspended vegetated (porous) base and solid channel bed. An asymmetric eddy viscosity model is employed to derive an integral expression for the shear stress and the mean velocity profiles in this inner layer. The solution features an asymmetric shear stress index that reflects two different roughness conditions over the vegetation‐induced auxiliary bed and the physical channel bed. A phenomenological model is then presented to explain this index. An expression for the penetration depth into the porous medium defined by 10% of the maximum shear stress is also derived. The predicted shear stress profile, local mean velocity profile, and bulk velocity agree with the limited experiments published in the literature.

Maximum Entropy Method for Solving the Turbulent Channel Flow Problem.

There are two components in this work that allow for solutions of the turbulent channel flow problem: One is the Galilean-transformed Navier-Stokes equation which gives a theoretical expression for the Reynolds stress (u′v′); and the second the maximum entropy principle which provides the spatial distribution of turbulent kinetic energy. The first concept transforms the momentum balance for a control volume moving at the local mean velocity, breaking the momentum exchange down to its basic components, u′v′, u′2, pressure and viscous forces. The Reynolds stress gradient budget confirms this alternative interpretation of the turbulence momentum balance, as validated with DNS data. The second concept of maximum entropy principle states that turbulent kinetic energy in fully-developed flows will distribute itself until the maximum entropy is attained while conforming to the physical constraints. By equating the maximum entropy state with maximum allowable (viscous) dissipation at a given Reynolds number, along with other constraints, we arrive at function forms (inner and outer) for the turbulent kinetic energy. This allows us to compute the Reynolds stress, then integrate it to obtain the velocity profiles in channel flows. The results agree well with direct numerical simulation (DNS) data at Reτ = 400 and 1000.

Fluid particle dynamics and the non-local origin of the Reynolds shear stress

The causative factors leading to the Reynolds shear stress distribution in turbulent channel flow are analysed via a backward particle path analysis. It is found that the classical displacement transport mechanism, by which changes in the mean velocity field over a mixing time correlate with the wall-normal velocity, is the dominant source of Reynolds shear stress. Approximately 20 % of channel flow at any given time contains fluid motions that contribute to displacement transport. Much rarer events provide a small but non-negligible contribution to the Reynolds shear stress due to fluid particle accelerations and long-lived correlations deriving from structural features of the near-wall flow. The Reynolds shear stress in channel flow is shown to be a non-local phenomenon that is not conducive to description via a local model and particularly one depending directly on the local mean velocity gradient.

Slug flow models: Feasible domain and sensitivity to input distributions

The present work discusses the feasible and validity domains of unit-cell slug models. The models of Dukler and Hubbard (Ind. Eng. Chem. Fund. 14 (4): 337–347, 1975) and Orell (Chem. Eng. Sci. 60 (5):1371–1381, 2005) are particularly considered as reference models, for they are based on distinct formulation hypotheses. A parameter sensitivity analysis is also carried out to assess the uncertainty in predicted slug length distributions. The work further discusses a kinematic methodology for the estimation of slug length distributions, a problem of great interest in the design and determination of the operational conditions of gas-liquid separators. The results are validated through new experiments and the data of Ujang et al. (Int. J. Multiphase Flow 32 (5): 527–552, 2006). The new experiments introduce data (including the pdf distributions) on pressure gradients, bubble lengths, passage frequency and translational velocity of bubbles. Particle image velocimetry measurements furnish the local mean velocity profiles in the continuous phase of the liquid slug and film.

The Reynolds stress in turbulence from a Lagrangian perspective

We present a unique method for solving for the Reynolds stress in turbulent canonical flows, based on the momentum balance for a control volume moving at the local mean velocity. A differential transform converts this momentum balance to a solvable form. Validations with experimental and computational data in simple geometries show quite good results. An alternate Lagrangian analytical method is offered, leading to a potential closure method for the Reynolds stress in terms of computable turbulence parameters.

Comparative PIV and LDA studies of Newtonian and non-Newtonian flows in an agitated tank

The paper presents results of an experimental study of the fluid velocity field in a stirred tank equipped with a Prochem Maxflo T (PMT) type impeller which was rotating at a constant frequency of N = 4.1 or 8.2 s−1 inducing transitional (Re = 499 or 1307) or turbulent (Re = 2.43 × 104) flow of the fluid. The experiments were performed for a Newtonian fluid (water) and a non-Newtonian fluid (0.2 wt% aqueous solution of carboxymethyl cellulose, CMC) exhibiting mild viscoelastic properties. Measurements were carried out using laser light scattering on tracer particles which follow the flow (2-D PIV). For both the water and the CMC solution one primary and two secondary circulation loops were observed within the fluid volume; however, the secondary loops were characterized by much lower intensity. The applied PMT-type impeller produced in the Newtonian fluid an axial primary flow, whilst in the non-Newtonian fluid the flow was more radial. The results obtained in the form of the local mean velocity components were in satisfactory agreement with the literature data from LDA. Distribution of the shear rate in the studied system was also analyzed. For the non-Newtonian fluid an area was computed where the elastic force dominates over the viscous one. The area was nearly matching the region occupied by the primary circulation loop.

Complementarity of PALM and SOFI for super-resolution live-cell imaging of focal adhesions.

Live-cell imaging of focal adhesions requires a sufficiently high temporal resolution, which remains a challenge for super-resolution microscopy. Here we address this important issue by combining photoactivated localization microscopy (PALM) with super-resolution optical fluctuation imaging (SOFI). Using simulations and fixed-cell focal adhesion images, we investigate the complementarity between PALM and SOFI in terms of spatial and temporal resolution. This PALM-SOFI framework is used to image focal adhesions in living cells, while obtaining a temporal resolution below 10 s. We visualize the dynamics of focal adhesions, and reveal local mean velocities around 190 nm min−1. The complementarity of PALM and SOFI is assessed in detail with a methodology that integrates a resolution and signal-to-noise metric. This PALM and SOFI concept provides an enlarged quantitative imaging framework, allowing unprecedented functional exploration of focal adhesions through the estimation of molecular parameters such as fluorophore densities and photoactivation or photoswitching kinetics.

Pressure Fluctuations induced by a Hypersonic Turbulent Boundary Layer.

Direct numerical simulations (DNS) are used to examine the pressure fluctuations generated by a spatially-developed Mach 5.86 turbulent boundary layer. The unsteady pressure field is analyzed at multiple wall-normal locations, including those at the wall, within the boundary layer (including inner layer, the log layer, and the outer layer), and in the free stream. The statistical and structural variations of pressure fluctuations as a function of wall-normal distance are highlighted. Computational predictions for mean velocity profiles and surface pressure spectrum are in good agreement with experimental measurements, providing a first ever comparison of this type at hypersonic Mach numbers. The simulation shows that the dominant frequency of boundary-layer-induced pressure fluctuations shifts to lower frequencies as the location of interest moves away from the wall. The pressure wave propagates with a speed nearly equal to the local mean velocity within the boundary layer (except in the immediate vicinity of the wall) while the propagation speed deviates from the Taylor's hypothesis in the free stream. Compared with the surface pressure fluctuations, which are primarily vortical, the acoustic pressure fluctuations in the free stream exhibit a significantly lower dominant frequency, a greater spatial extent, and a smaller bulk propagation speed. The freestream pressure structures are found to have similar Lagrangian time and spatial scales as the acoustic sources near the wall. As the Mach number increases, the freestream acoustic fluctuations exhibit increased radiation intensity, enhanced energy content at high frequencies, shallower orientation of wave fronts with respect to the flow direction, and larger propagation velocity.

Velocity field characteristics of the turbulent jet induced by direct contact condensation of steam jet in crossflow of water in a vertical pipe

Direct contact condensation of jets in fluid has been widely applied in many industrial applications owing to the low requirement of driving potential and high efficiency of heat and mass transfer. Here, experiments are carried out to investigate the velocity field characteristics of the turbulent jet induced by direct contact condensation of steam jet in crossflow of water in a vertical pipe. Visual equipment is specially invented to investigate the velocity field characteristics by using Particle Image Velocimetry (PIV) measurement technique. The high intensity laser light reflected by the pure steam region just outside the nozzle-exit brings out severe damage to the CCD camera. To solve this technical problem, a black plate is adopted to shield the pure steam region. According to the contours of the velocity fields and streamlines, the influences of jet momentum ratio, jet Reynolds number and water temperature on the jet flow field are explored. The jet centerline trajectory equations in exponential form are established based on the local maximum mean velocity. By introducing the jet Reynolds number and jet momentum ratio, the correlation for prediction of jet centerline trajectory equations is proposed, and the predicted results are within 30% of the experimental data. The reciprocal of the local maximum mean velocity and the half-width of the jet are proportional to the downstream coordinate along the jet velocity centerline trajectory. The scaled velocity field complies with the self-similarity principle.

The Fluxes and Behaviour of Plumes Inferred from Measurements of Coherent Structures within Images of the Bulk Flow

ABSTRACTThis paper describes how measurements of the movement of identifiable features at the edge of a turbulent plume can be interpreted to determine the properties of the mean flow and consequently, using plume theory, can be used to make estimates of the fluxes of volume (mass), momentum, and buoyancy in a plume. This means that video recordings of smoke rising from a chimney or buoyant material from a source on the sea bed can be used to make accurate estimates of the source conditions for the plume. At best we can estimate the volume flux and buoyancy flux to within about 5% and 15% of the actual values, respectively. Although this is restricted to the case of a plume rising in a stationary and unstratified environment, we show that the results may be of practical use in other more complex situations. In addition, we demonstrate that large-scale (turbulent) coherent structures at the plume edge form on a scale approximately 40% of the local (mean) plume half-width and travel at almost 60% of the average local (mean) velocity in the plume.

Vertical variations of coral reef drag forces

AbstractModeling flow in a coral reef requires a closure model that links the local drag force to the local mean velocity. However, the spatial flow variations make it difficult to predict the distribution of the local drag. Here we report on vertical profiles of measured drag and velocity in a laboratory reef that was made of 81 Pocillopora Meandrina colony skeletons, densely arranged along a tilted flume. Two corals were CT‐scanned, sliced horizontally, and printed using a 3‐D printer. Drag was measured as a function of height above the bottom by connecting the slices to drag sensors. Profiles of velocity were measured in‐between the coral branches and above the reef. Measured drag of whole colonies shows an excellent agreement with previous field and laboratory studies; however, these studies never showed how drag varies vertically. The vertical distribution of drag is reported as a function of flow rate and water level. When the water level is the same as the reef height, Reynolds stresses are negligible and the drag force per unit fluid mass is nearly constant. However, when the water depth is larger, Reynolds stress gradients become significant and drag increases with height. An excellent agreement was found between the drag calculated by a momentum budget and the measured drag of the individual printed slices. Finally, we propose a modified formulation of the drag coefficient that includes the normal dispersive stress term and results in reduced variations of the drag coefficient at the cost of introducing an additional coefficient.

CLASH-VLT: Substructure in the galaxy cluster MACS J1206.2-0847 from kinematics of galaxy populations

In the effort to understand the link between the structure of galaxy clusters and their galaxy populations, we focus on MACSJ1206.2-0847 at z~0.44 and probe its substructure in the projected phase space through the spectrophotometric properties of a large number of galaxies from the CLASH-VLT survey. Our analysis is mainly based on an extensive spectroscopic dataset of 445 member galaxies, mostly acquired with VIMOS@VLT as part of our ESO Large Programme, sampling the cluster out to a radius ~2R200 (4 Mpc). We classify 412 galaxies as passive, with strong Hdelta absorption (red and blue galaxies, and with emission lines from weak to very strong. A number of tests for substructure detection are applied to analyze the galaxy distribution in the velocity space, in 2D space, and in 3D projected phase-space. Studied in its entirety, the cluster appears as a large-scale relaxed system with a few secondary, minor overdensities in 2D distribution. We detect no velocity gradients or evidence of deviations in local mean velocities. The main feature is the WNW-ESE elongation. The analysis of galaxy populations per spectral class highlights a more complex scenario. The passive galaxies and red strong Hdelta galaxies trace the cluster center and the WNW-ESE elongated structure. The red strong Hdelta galaxies also mark a secondary, dense peak ~2 Mpc at ESE. The emission line galaxies cluster in several loose structures, mostly outside R200. The observational scenario agrees with MACS J1206.2-0847 having WNW-ESE as the direction of the main cluster accretion, traced by passive galaxies and red strong Hdelta galaxies. The red strong Hdelta galaxies, interpreted as poststarburst galaxies, date a likely important event 1-2 Gyr before the epoch of observation. The emission line galaxies trace a secondary, ongoing infall where groups are accreted along several directions.

Evaluation of the inertial dissipation method within boundary layers using numerical simulations

AbstractWe evaluated the accuracy of the inertial dissipation method to estimate the rate of dissipation of turbulent kinetic energy within boundary layers by performing well‐resolved numerical simulations of turbulent channel flows and comparing the dissipation calculated directly from the data, with that deduced from the frequency spectra. The convection velocity, commonly used to convert frequency spectra into wave number spectra is found to be larger than the local mean velocity by approximately a factor of 2 near the bed and about 10% in the logarithmic layer and beyond. Usage of the standard Kolmogorov constants (particularly in the vertical and spanwise directions) also leads to significant errors (50% or more) in computation of dissipation. Usage of the optimal Kolmogorov constants and the convection velocity, obtained from the simulation results could result in improved accuracy in dissipation calculation with the inertial method.

Experimental characterization of vertical gas–liquid pipe flow for annular and liquid loading conditions using dual Wire-Mesh Sensor

In gas well production, liquid is produced in two forms, droplets entrained in the gas core and liquid film flowing on the tubing wall. For most of the gas well life cycle, the predominant flow pattern is annular flow. As gas wells mature, the produced gas flow rate reduces decreasing the liquid carrying capability initiating the condition where the liquid film is unstable and flow pattern changes from fully cocurrent annular flow to partially cocurrent annular flow. The measurement and visualization of annular flow and liquid loading characteristics is of great importance from a technical point of view for process control or from a theoretical point of view for the improvement and validation of current modeling approaches. In this experimental investigation, a Wire-Mesh technique based on conductance measurements was applied to enhance the understanding of the air-water flow in vertical pipes. The flow test section consisting of a 76mm ID pipe, 18m long was employed to generate annular flow and liquid loading at low pressure conditions. A 16×16 wire configuration sensor is used to determine the void fraction within the cross-section of the pipe. Data sets were collected with a sampling frequency of 10,000Hz. Physical flow parameters were extracted based on processed raw measured data obtained by the sensors using signal processing. In this work, the principle of Wire-Mesh Sensors and the methodology of flow parameter extraction are described. From the obtained raw data, time series of void fraction, mean local void fraction distribution, characteristic frequencies and structure velocities are determined for different superficial liquid and gas velocities that ranged from 0.005 to 0.1m/s and from 10 to 40m/s, respectively. In order to investigate dependence of liquid loading phenomenon on viscosity, three different liquid viscosities were used. Results from the Wire-Mesh Sensors are compared with results obtained from previous experimental work using Quick Closing Valves and existing modeling approaches available in the literature.

Theory and Simulation for Traffic Characteristics on the Highway with a Slowdown Section.

We study the traffic characteristics on a single-lane highway with a slowdown section using the deterministic cellular automaton (CA) model. Based on the theoretical analysis, the relationships among local mean densities, velocities, traffic fluxes, and global densities are derived. The results show that two critical densities exist in the evolutionary process of traffic state, and they are significant demarcation points for traffic phase transition. Furthermore, the changing laws of the two critical densities with different length of limit section are also investigated. It is shown that only one critical density appears if a highway is not slowdown section; nevertheless, with the growing length of slowdown section, one critical density separates into two critical densities; if the entire highway is slowdown section, they finally merge into one. The contrastive analysis proves that the analytical results are consistent with the numerical ones.

An Experimental Investigation of Turbulent Convection Velocities in a Turbulent Boundary Layer

Turbulent convection velocities in a turbulent boundary layer at a Reynolds number of R e 𝜃 = 2250 are examined via the use of a high repetition rate particle image velocimetry measurement undertaken in a water tunnel. Multiple cameras are used to improve the spatial dynamic range of the measurement and reduce the bias towards large-scale structures while simultaneously capturing a wall-normal domain of 0.06δ to 1.7δ. The impact of measurement noise is minimized via careful temporal and spatial filtering of the velocity fields as guided by the comparison of temporal and spatial velocity power spectra with spatially filtered direct numerical simulation data, enabling an estimation of the effective noise-limited spatial and temporal dynamic range of the present experimental measurement. Space-time correlations and phase-spectra are used to estimate the mean and streamwise wave-number dependent convection velocities at various heights above the wall. Results reveal convection velocities greater than the local mean velocity in the lower log layer, decreasing to a level 3.5 % lower than the mean velocity in the upper log and wake regions. The convection velocity is shown to depend on the streamwise length scale and is found to decrease at higher wave-numbers for all wall-normal locations. Comparison between the measured and reconstructed spatial fields show that Taylor’s hypothesis can only be applied over short streamwise distances of less than 1δ in the buffer and inner log-layer, while larger projection distances (≥3δ) are possible in the outer-log and wake region of the turbulent boundary layer.

Stacking analysis of 12CO and 13CO spectra of NGC 3627: Existence of non-optically thick 12CO emission?

Abstract We stacked 12CO and 13CO spectra of NGC 3627 after redefining the velocity axis of each spectrum of the mapping data so that the zero corresponds to the local mean velocity of the 12CO spectra. The signal-to-noise ratios of the resulting spectra are improved by a factor of up to 3.2 compared to those obtained with normal stacking analysis. We successfully detect a weak 13CO emission from the interarm region where the emission was not detected in the individual pointings. We compare the integrated intensity ratios $I_{^{12}\rm {CO}}/I_{^{13}{\rm CO}}$ among six characteristic regions (center, bar, bar-end, offset, arm, and interarm). We find that $I_{^{12}\rm {CO}}/I_{^{13}{\rm CO}}$ in the bar and interarm are higher than those in the other regions by a factor of ∼ 2 and $I_{^{12}\rm {CO}}/I_{^{13}{\rm CO}}$ in the center is moderately high. These high $I_{^{12}\rm {CO}}/I_{^{13}{\rm CO}}$ ratios in the bar and center are attributed to a high intensity ratio ($T_{^{12}\rm {CO}}/T_{^{13}{\rm CO}}$), and that in the interarm is attributed to a high ratio of the full width at half maximum of spectra (FWHM$_{^{12}\rm {CO}}/$FWHM$_{^{13}{\rm CO}}$). The difference between FWHM$_{^{12}{\rm CO}}$ and FWHM$_{^{13}{\rm CO}}$ of the interarm indicates the existence of two components, one with a narrow line width (∼ FWHM$_{\rm ^{13}CO}$) and the other with a broad line width (∼ FWHM$_{\rm ^{12}CO}$). Additionally, the $T_{^{12}\rm {CO}}/T_{^{13}{\rm CO}}$ ratio in the broad-line-width component of the interarm is higher than the other regions. The high $T_{^{12}\rm {CO}}/T_{^{13}{\rm CO}}$ in the center and bar and of the broad-line-width component in the interarm suggest the existence of non-optically thick 12CO components. We find that more than half of the 12CO emissions of the interarm are likely to be radiated from the diffuse component. Our result suggests that the use of a universal CO-to-H2 conversion factor might lead to an overestimation of molecular gas mass and underestimation of star-formation efficiency in the interarm by a factor of a few.