Entrainment Velocity Research Articles

Lagrangian coherent structures and entrainment near the turbulent/non-turbulent interface of a gravity current

In this paper, we employ the theory of Lagrangian coherent structures for three-dimensional vortex eduction and investigate the effect of large-scale vortical structures on the turbulent/non-turbulent interface (TNTI) and entrainment of a gravity current. The gravity current is realized experimentally and different levels of stratification are examined. For flow measurements, we use a multivolume three-dimensional particle tracking velocimetry technique. To identify vortical Lagrangian coherent structures (VLCSs), a fully automated three-dimensional extraction algorithm for multiple flow structures based on the so-called Lagrangian-averaged vorticity deviation method is implemented. The size, the orientation and the shape of the VLCSs are analysed and the results show that these characteristics depend only weakly on the strength of the stratification. Through conditional analysis, we provide evidence that VLCSs modulate the average TNTI height, consequently affecting the entrainment process. Furthermore, VLCSs influence the local entrainment velocity and organize the flow field on both the turbulent and non-turbulent sides of the gravity current boundary.

Thermal elastohydrodynamic lubrication analysis of helical gear pair under starved lubrication condition

AbstractIn the present study, thermal starved elastohydrodynamic lubrication (EHL) model is developed for a helical gear pair. The influences of inlet oil‐supply layer, input speed, lubricant viscosity, and surface roughness on the lubrication behaviour are investigated. The minimum film thickness, temperature rise of teeth surfaces and oil film, and the friction coefficient are predicted along the line of action (LOA). Results show that the effects of inlet oil‐supply layer, input speed, and lubrication viscosity on the tribological performance are remarkable. Under the starved lubrication, the influence of inlet oil supply on the temperature rise is insignificant. Meanwhile, the effect of surface roughness has been discussed. It reveals that the roughness texture along the entrainment velocity direction has significant influence on the lubrication characteristics. The results provide the tribological guidance for design of a helical gear pair in engineering.

Film thickness build-up in zero entrainment velocity wide point contacts

Abstract In this work, elastohydrodynamic wide point contacts are studied under Zero Entrainment Velocity (ZEV) conditions. Contrary to classical rolling-sliding contacts, no hydrodynamic lift (oil wedge effect) is expected in stationary isothermal ZEV contacts. However, both experiments and numerical simulations taking into account temperature gradients in the thickness of the lubricant show the occurrence of a full-film lubrication regime over a large range of surface velocities, contact loads and external temperatures. Numerical simulations, including thermal effects but neither transient nor wall slip effects, are in good agreement with experimental film thickness measurements. They allow for both a qualitative description of the mechanisms at stake and to a first tentative minimum film thickness prediction under those specific conditions.

Effect of arbitrary entrainment angle in elastohydrodynamic lubrication elliptical and circular contacts

Conventional elastohydrodynamic lubrication models assume parallel surface velocities such as in cam-follower and ball bearing systems. However, many important machine elements like hypoid gear and spiral bevel, the sliding and entrainment velocities are along different directions that could possibly influence the elastohydrodynamic lubrication performance characteristics significantly. For such complex conditions, the existing film thickness formulae and shear-thinning correction factors available in the literature are not suitable. Therefore, this paper investigates the effect of arbitrarily oriented surface velocity vectors on elastohydrodynamic lubrication characteristics considering realistic rheological models and experimentally established viscosity–pressure and compressibility laws. The Reynolds equation employed herein includes the surface velocity components along both the reference axes in the plane of contact. The elastohydrodynamic lubrication film thickness is found to deviate up to a maximum of 61% with respect to its conventional value. This deviation in film thickness behavior is shown to be a function of ellipticity and shear-thinning parameters.

Numerical simulation of transient mixed elastohydrodynamic lubrication for spiral bevel gears

Abstract In spiral bevel gears, the entraining velocity, contact load and radii of curvature along tooth surface are always changed dramatically, which results in remarkable transient squeezing effect on lubricating performance, especially it operates in high-speed and heavy-load conditions. Available elastohydrodynamic lubrication (EHL) and mixed EHL studies for spiral bevel gears are mainly performed under quasi-static (steady-state) assumptions which ignores these transient influences. Therefore, in this paper, a transient mixed EHL model for spiral bevel gears is presented, in which takes into account most variable parameters along meshing surface including contact load, contact radii of curvature, entraining and sliding velocity vectors. Note that all these transient parameters of spiral bevel gears are employed from the results of loaded tooth contact analysis (LTCA). In order to improve the computational efficiency and convergent accuracy with a relatively dense grids, the progressive mesh densification (PMD) method for this transient mixed EHL model is also introduced. A comparison between the present transient mixed EHL model and those data from literature is executed to verify the correctness of the newly developed model. After that, systematically investigations of transient squeezing impact are carried out for spiral bevel gears and compared with the corresponding steady-state EHL results with and without real machined surface roughness. The obtained results reveal that the transient squeezing action can significantly affect the film thickness distribution in each contact zone and along the meshing track line in spiral bevel gears, and lead to dramatic growth in asperity contact area as well. Besides, the steady-state EHL appears to be greatly overestimated the lubricating characteristics for spiral bevel gears.

Competing Effects of Droplet Sedimentation and Wind Shear on Entrainment in Stratocumulus

AbstractThe joint effect of droplet sedimentation and wind shear on cloud top entrainment in stratocumulus is investigated with direct numerical simulations. Although it is well understood that droplet sedimentation weakens entrainment while wind shear enhances entrainment, there is no consensus on the magnitude of each process. We find that the entrainment reduction by droplet sedimentation is sufficiently strong to completely compensate the entrainment enhancement by wind shear, and thus, droplet sedimentation and wind shear effects can be equally important for cloud top entrainment. For instance, for the subtropical conditions considered here, droplet sedimentation weakens entrainment by up to 40% while wind shear enhances entrainment by up to 40%. This result implies that the droplet size distribution can substantially affect cloud lifetimes not only because of its effect on rain formation but also because of its effect on cloud top entrainment, which emphasizes the need for a better characterization of droplet size distributions in stratocumulus. A second implication is that entrainment velocity parametrizations should pay equal attention to droplet sedimentation and to wind shear effects.

Kinematics of local entrainment and detrainment in a turbulent jet

In this paper we investigate the continuous, local exchange of fluid elements as they are entrained and detrained across the turbulent/non-turbulent interface (TNTI) in a high Reynolds number axisymmetric jet. To elucidate characteristic kinematic features of local entrainment and detrainment processes, simultaneous high-speed particle image velocimetry and planar laser-induced fluorescence measurements were undertaken. Using an interface-tracking technique, we evaluate and analyse the conditional dependence of local entrainment velocity in a frame of reference moving with the TNTI in terms of the interface geometry and the local flow field. We find that the local entrainment velocity is intermittent with a characteristic length scale of the order of the Taylor micro-scale and that the contribution to the net entrainment rate arises from the imbalance between local entrainment and detrainment rates that occurs with a ratio of two parts of entrainment to one part detrainment. On average, an increase in local entrainment is correlated with excursions of the TNTI towards jet centreline into regions of higher streamwise momentum, convex surface curvature facing the turbulent side of the jet and along the leading edges of the interface. In contrast, detrainment is correlated with excursions of the TNTI away from the jet centreline into regions of lower streamwise momentum, concave surface curvature and along the trailing edge. We find that strong entrainment is characterised by a local counterflow velocity field in the frame of reference moving with the TNTI which enhances the transport of rotational and irrotational fluid elements. On the other hand, detrainment is characterised by locally uniform flow fields with the local fluid velocity on either side of the TNTI advecting in the same direction. These local flow patterns and the strength of entrainment or detrainment rates are also observed to be strongly influenced by the presence and relative strength of vortical structures which are of the order of the Taylor micro-scale that populate the turbulent region along the jet boundary.

Variation of zero entraining velocity dimple in grease-lubricated reciprocating motion

In this study, experiments were conducted on a ball-on-disk test rig using optical interferometry to explore the variation in grease film thickness under zero entraining velocity reciprocating motion. The steel ball and the sapphire disk move at equal speeds but in opposite directions within a triangle wave. Three types of commercially available bearing greases with different consistencies, Centoplex 2EP, Centoplex 3, and MP-3, were used in these experiments. The variations in the surface dimple phenomenon with decreasing maximum surface velocity, differing grease consistency, and grease starvation conditions were studied. Results showed that the grease consistency exerts a significant influence on the surface dimple and the starvation severity.

A Simplified Model for the Baroclinic and Barotropic Ocean Response to Moving Tropical Cyclones: 2. Model and Simulations

AbstractA simplified analytical model is developed to describe the baroclinic and barotropic ocean response to moving tropical cyclones (TCs) and their associated pycnocline erosions. The model builds on classical mixed‐layer (ML) models and linear models of ocean response to transient events. As suggested, disturbances of the upper ocean stratification caused by the ML development shall not strongly impact the dynamics of baroclinic modes. Accordingly, the baroclinic response can be estimated using the prestorm ocean stratification condition. To the contrary, the ML is strongly coupled with these interior motions, through the TC‐induced upwelling response that affects the entrainment velocity. The ML temperature is then strongly dependent on the local temperature gradient in the upper layer. The model is represented by a set of analytical relationships providing rapid calculations for the ocean response to TC, given a prescribed wind velocity field traveling over an ocean with arbitrary stratification. Compared to satellite observations, simulations demonstrate the model ability to quantitatively reproduce the observed shape and magnitudes of the sea surface height and the sea surface temperature (SST) anomalies. Remarkably, the model is robust and efficient for a wide range of variability of TC characteristics (max wind speed, radius, shape of wind profile, and translation velocity), parameters of the ocean stratification, and Coriolis parameter. Simulations provide solid evidences about the key role of TC‐induced upwelling in the ML cooling and formation of SST wake. Cross‐track advection by wind‐driven currents, though small compared with TC translation velocity, can significantly contribute to broaden the shape and offset of the SST wake. Given its effectiveness and low computational burden, the proposed model can be introduced as a computational module into atmospheric numerical models of TC‐coupled evolution with the ocean, through the resulting local changes of surface enthalpy fluxes.

Estimates of entrainment in closed cellular marine stratocumulus clouds from the MAGIC field campaign

Entrainment of warm, dry air from above the boundary layer into the cloud layer has a significant impact on stratocumulus clouds in the marine boundary layer. During the MAGIC field campaign, the Atmospheric Radiation Measurement (ARM) mobile facility was deployed aboard a container ship that made regular transects between Los Angeles, California and Honolulu, Hawaii. Observations made during MAGIC transects were collocated with observations from the Geostationary Operational Environmental Satellite (GOES‐15) and European Centre for Medium‐range Weather Forecasting (ECMWF) reanalysis model. From these data, hourly estimates of entrainment velocities in closed cellular stratocumulus cloud conditions were calculated from the mixed‐layer mass budget equation, modified to accommodate observations sampled from a moving platform. The technique is demonstrated using observations collected during Leg 15A (46 h) and then extended to 178 h of data. The average entrainment velocity was 7.83 ± 5.23 mm/s, and the average large‐scale vertical air motion at cloud top (obtained from reanalysis) was −2.56 ± 3.31 mm/s. The vertical air motion at cloud top was positive (upward) during 36 h (∼20%) with a mean of 2.68 mm/s. Entrainment velocity is highly variable and on average the MAGIC observations show no dependence of entrainment velocity on longitude or any pronounced diurnal cycle. When binned by inversion strength, the mean entrainment velocity and mean large‐scale vertical air motion mirrored each other, with both exhibiting substantial variability. Collectively, our results suggest a mean entrainment‐velocity behaviour associated with the background state, with large changes in entrainment velocity forced by strong variability in internal boundary‐layer properties like turbulence, radiation, and inversion strength. This cautions against using climatological mean estimates of entrainment velocities or neglecting instances with upward large‐scale vertical air motion.

Turbidity currents propagating down a slope into a stratified saline ambient fluid

Results are presented from highly resolved three-dimensional simulations of turbidity currents down a shallow slope into a stratified saline ambient, for various stratifications and particle settling velocity configurations. The front velocity is computed and the results are compared directly to experimental data by Snow and Sutherland (J Fluid Mech 755:251–273, 2014) and to an existing scaling law for gravity currents in stratified environments but on flat bottoms, with close agreement. The entrainment velocity of the ambient fluid into the current is computed from the DNS data and shows strong space time variability. The intrusion of the current into the ambient fluid is computed and compared to the experimental results of Snow and Sutherland (2014), an existing scaling law proposed by those authors, and a new model with increasing levels of complexity. The numerical results highlight the sensitivity of scaling tools to the choice of entrainment coefficient and their limitations in low entrainment but high settling rate scenarios. The new, simpler scaling relation for the intrusion depth is shown to be more robust and predictive in such cases. The energy budget of the flow is analysed in order to explain the governing processes in terms of energy transfers, with a focus on energy losses and potential to kinetic energy transfers. Particular attention is given to the Stokes losses with varying settling velocities, which validates the prediction of the concentration in the intrusion depth model introduced.

Turbulent Transport in the Gray Zone: A Large Eddy Model Intercomparison Study of the CONSTRAIN Cold Air Outbreak Case

AbstractTo quantify the turbulent transport at gray zone length scales between 1 and 10 km, the Lagrangian evolution of the CONSTRAIN cold air outbreak case was simulated with seven large eddy models. The case is characterized by rather large latent and sensible heat fluxes and a rapid deepening rate of the boundary layer. In some models the entrainment velocity exceeds 4 cm/s. A significant fraction of this growth is attributed to a strong longwave radiative cooling of the inversion layer. The evolution and the timing of the breakup of the stratocumulus cloud deck differ significantly among the models. Sensitivity experiments demonstrate that a decrease in the prescribed cloud droplet number concentration and the inclusion of ice microphysics both act to speed up the thinning of the stratocumulus by enhancing the production of precipitation. In all models the formation of mesoscale fluctuations is clearly evident in the cloud fields and also in the horizontal wind velocity. Resolved vertical fluxes remain important for scales up to 10 km. The simulation results show that the resolved vertical velocity variance gradually diminishes with a coarsening of the horizontal mesh, but the total vertical fluxes of heat, moisture, and momentum are only weakly affected. This is a promising result as it demonstrates the potential use of a mesh size‐dependent turbulent length scale for convective boundary layers at gray zone model resolutions.

Effect of laser surface texturing on friction behaviour in elastohydrodynamically lubricated point contacts under different sliding-rolling conditions

The Laser Surface Texturing (LST) technique has been largely investigated to improve the tribological performance of lubricated contacts. The present contribution is aimed at scrutinizing the influence of three texture configurations fabricated by LST on the tribological performance of elastohydrodynamic (EHD) point contacts under different slide-to-roll ratios (SRR), entrainment velocities and inlet temperatures. Friction experiments were conducted through a series of ball-on-disk tests in the MTM-2 (Mini-Traction Machine) tribometer. Main results showed that the texture configurations promoted significant effects under boundary and mixed lubrication conditions, and also affected the full-film EHD regime at higher temperatures. Furthermore, the tribological performance of textured samples was strongly related to the texture depth. Shallower texture designs (∼0.5 μm) reduced friction compared to untextured material, whereas deeper features (>1 μm) generally led to detrimental results. In general, dimples configuration decreased the lift-off speed and promoted full-film EHD conditions for a larger range of speeds, whereas radial curved grooves yielded to friction reduction under mixed lubrication conditions, moving the transition from boundary to mixed regimes to lower speeds, especially for intermediate lubricant viscosity.

Compressible mixing layer in shock-induced separation

Unsteadiness in separated shock–boundary layer interactions have been previously analysed in order to propose a scenario of entrainment–discharge as the origin of unsteadiness. It was assumed that the fluid in the separated zone is entrained by the free shear layer formed at its edge, and that this layer follows the properties of the canonical mixing layer. This last point is addressed by reanalysing the velocity measurements in an oblique shock reflection at a nominal Mach number of 2.3 and for two cases of flow deviation ($8^{\circ }$ and $9.5^{\circ }$). The rate of spatial growth of this layer is evaluated from the spatial growth of the turbulent stress profiles. Moreover, the entrainment velocity at the edge of the layer is determined from the mean velocity profiles. It is shown that the values of turbulent shear stress, spreading rate and entrainment velocity are consistent, and that they follow the classical laws for turbulent transport in compressible shear layers. Moreover, the measurements suggest that the vertical normal stress is sensitive to compressibility, so that the anisotropy of turbulence is affected by high Mach numbers. Dimensional considerations proposed by Brown & Roshko (J. Fluid Mech., vol. 64, 1974, 775–781) are reformulated to explain this observed trend.

Frontolysis by surface heat flux in the eastern Japan Sea: importance of mixed layer depth

Frontolysis mechanisms by which surface heat flux relaxes the sea surface temperature (SST) front in the eastern Japan Sea (JS) are investigated in detail using observational datasets. On the warm southern side of the front, larger air–sea specific humidity and temperature differences induce stronger turbulent heat release compared to the cool northern side. As a result, stronger wintertime cooling and weaker summertime warming occur south of the front, and the meridional gradient in the surface net heat flux (NHF) tends to relax the SST front throughout the year. In the mixed-layer deepening phase (September–January), a higher entrainment velocity occurs on the warm southern side because of weaker stratification. Since the resulting thicker mixed layer on the southern side is less sensitive to surface cooling, the mixed layer depth (MLD) gradient damps the frontolysis by the NHF gradient. In the shoaling phase (April–June), a deeper mixed layer south of the front is caused by the weaker warming and reduced sensitivity of the thicker mixed layer to a shoaling effect by shortwave radiation. Owing to weaker sensitivity of the thicker mixed layer on the southern side to surface warming, the MLD gradient enhances the frontolysis by the NHF gradient. Therefore, it is shown that the mixed layer processes cause seasonality of weaker (stronger) frontolysis by surface heat fluxes, damping (enhancing) the frontolysis by the NHF gradient in winter (summer). This study reveals unique features of the frontolysis in the eastern JS compared with the Agulhas Return Current and Kuroshio Extension regions.

Understanding the dissipation of continental fog by analysing the LWP budget using idealized LES and in situ observations

Physical processes relevant for the dissipation of thick, continental fog after sunrise are studied through observations from the SIRTA observatory and idealized sensitivity studies with the large‐eddy simulation model DALES. Observations of 250 fog events over 7 years show that more than half of the fog dissipations after sunrise are transitions to stratus lasting 2 hr or more. From the simulations, we quantify the contribution of each process to the liquid water path (LWP) budget of the fog. Radiative cooling is the main source of LWP, while surface turbulent heat fluxes are the most important process contributing to loss of LWP, followed by the absorption of solar radiation, the mixing with unsaturated air at the fog top and the deposition of cloud droplets. The loss of LWP by surface heat fluxes is very sensitive to the Bowen ratio, which is importantly affected by the availability of liquid water on the surface; in a run without liquid on the surface, fog dissipation occurred 85 min earlier than in the Baseline simulation. The variability of stratification and humidity above fog top is documented by 47 radiosondes and cloud radar. Using DALES, we find that the variability in stratification has an important impact on the entrainment velocity; a three times more rapid fog‐top entrainment enables the cloud base to lift from the ground 90 min earlier in weak stratification than in strong stratification in the model. With relatively dry overlying air, the fog evaporates faster than if the air is near saturation, leading to 70 min earlier dissipation in our simulations. Continuous observations of the temperature and humidity profiles of the layer overlying the fog could therefore be useful for understanding and anticipating fog dissipation.

Numerical simulation of lubricated DLC-coated point contacts under infinite sliding conditions

Abstract This article examines the influence of low thermal inertia coatings, such as diamond-like carbon coatings, on the lubrication of point contacts operating under zero entrainment velocity conditions. Stationary thermal elasto-hydrodynamic simulations are performed to analyze modifications to the thermal viscosity wedge mechanism induced by the presence of such coatings. Three configurations, namely a steel-steel contact, a DLC coated steel-DLC coated steel contact and a steel-DLC coated steel contact, are investigated. For each configuration, temperature, pressure and film thickness profiles are presented in order to discuss the tribological performances (film thickness and traction) of low inertia coatings under these very specific lubrication conditions. In particular, the detrimental effect of having only one coated surface is highlighted and explained.

Crucial role of solid body temperature on elastohydrodynamic film thickness and traction

Abstract The effect of the solid body temperature effect on film thickness and traction in elastohydrodynamic lubrication (EHL) has been studied numerically. At a moderate entrainment velocity, the EHL film behavior is controlled by the solid body temperature as the oil heats up to the body temperature before entering the contact zone and thus the film thickness decreases. For high velocity conditions, inlet shear and compressive heating also contribute to the reduction of film thickness. The results indicate that the measured film thickness and traction on disc machines might be lower than the expected values when the disc temperature exceeds the supplied oil temperature.

Characterization of wind-shear effects on entrainment in a convective boundary layer

Direct numerical simulations are used to characterize wind-shear effects on entrainment in a barotropic convective boundary layer (CBL) that grows into a linearly stratified atmosphere. We consider weakly to strongly unstable conditions $-z_{enc}/L_{Ob}\gtrsim 4$, where $z_{enc}$ is the encroachment CBL depth and $L_{Ob}$ is the Obukhov length. Dimensional analysis allows us to characterize such a sheared CBL by a normalized CBL depth, a Froude number and a Reynolds number. The first two non-dimensional quantities embed the dependence of the system on time, on the surface buoyancy flux, and on the buoyancy stratification and wind velocity in the free atmosphere. We show that the dependence of entrainment-zone properties on these two non-dimensional quantities can be expressed in terms of just one independent variable, the ratio between a shear scale $(\unicode[STIX]{x0394}z_{i})_{s}\equiv \sqrt{1/3}\unicode[STIX]{x0394}u/N_{0}$ and a convective scale $(\unicode[STIX]{x0394}z_{i})_{c}\equiv 0.25z_{enc}$, where $\unicode[STIX]{x0394}u$ is the velocity increment across the entrainment zone, and $N_{0}$ is the buoyancy frequency of the free atmosphere. Here $(\unicode[STIX]{x0394}z_{i})_{s}$ and $(\unicode[STIX]{x0394}z_{i})_{c}$ represent the entrainment-zone thickness in the limits of weak convective instability (strong wind) and strong convective instability (weak wind), respectively. We derive scaling laws for the CBL depth, the entrainment-zone thickness, the mean entrainment velocity and the entrainment-flux ratio as functions of $(\unicode[STIX]{x0394}z_{i})_{s}/(\unicode[STIX]{x0394}z_{i})_{c}$. These scaling laws can also be expressed as functions of only a Richardson number $(N_{0}z_{enc}/\unicode[STIX]{x0394}u)^{2}$, but not in terms of only the stability parameter $-z_{enc}/L_{Ob}$.

Effect of Nozzle Geometry on Flowfield for High Subsonic Jets

The present Paper aims to present a comparative study of the external and internal flow characteristics through an axisymmetric circular convergent nozzle, a nonserpentine convergent nozzle with an elliptic exit, and a shallow single serpentine convergent nozzle with an elliptic exit under the fully expanded condition at a nozzle pressure ratio of 1.6. The static wall pressure measurements reveal that, due to the axisymmetric shape, the conventional circular nozzle shows symmetric jet development. However, the flow through the serpentine nozzle follows its curvature, making the flow through it asymmetric. The upper and the lower walls have different flow expansion due to the secondary flow created by the wall curvature and transition. This asymmetric nature of the flow through the serpentine nozzle also vectors the external jet toward the lower wall. The saddle-shaped velocity profile is observed along the major axis plane of serpentine nozzle. The nozzles with elliptic exits show higher mass entrainment and faster velocity decay as compared to the conventional circular nozzle. The nonserpentine elliptic nozzle shows the maximum velocity decay with the fastest decay rate among the three nozzles considered. This nozzle also shows the maximum mass entrainment across its major as well as minor axes and thus reduces the length of the external jet more effectively.