Turbulent Entrainment Research Articles

Entrainment at multi-scales in shear-dominated and Rayleigh–Taylor turbulence

A partially turbulent flow continuously incorporates irrotational fluid into the turbulent region, a phenomenon known as entrainment. Although entrainment locally acts at viscous scales, the thin interface separating the turbulent from the irrotational region is extremely convoluted, and twisted in such a way that renders the global entrainment flux scale-independent. Despite turbulent entrainment being widely recognized as a multi-scale process, the theoretical basis for quantifying the entrainment flux at multi-scales is lacking. In this paper we derive an equation that allows us to quantify the local entrainment velocity at multi-scales. This is done by defining the local entrainment velocity as the propagation speed of an iso-surface of filtered enstrophy relative to the coarse-grained velocity field, and using the filtered enstrophy budget to split the total velocity into its individual components, i.e. viscous, inviscid, baroclinic and sub-filter. The equation is used to investigate the entrainment at multi-scales in simulated turbulent mixing layers, where turbulence is sustained by either a mean shear or an unstable buoyancy gradient (Rayleigh–Taylor turbulence).

Aerosol impacts on the entrainment efficiency of Arctic mixed-phase convection in a simulated air mass over open water

Abstract. Springtime Arctic mixed-phase convection over open water in the Fram Strait as observed during the recent ACLOUD (Arctic CLoud Observations Using airborne measurements during polar Day) field campaign is simulated at turbulence-resolving resolutions. The first objective is to assess the skill of large-eddy simulation (LES) in reproducing the observed mixed-phase convection. The second goal is to then use the model to investigate how aerosol modulates the way in which turbulent mixing and clouds transform the low-level air mass. The focus lies on the low-level thermal structure and lapse rate, the heating efficiency of turbulent entrainment, and the low-level energy budget. A composite case is constructed based on data collected by two research aircraft on 18 June 2017. Simulations are evaluated against independent datasets, showing that the observed thermodynamic, cloudy, and turbulent states are well reproduced. Sensitivity tests on cloud condensation nuclei (CCN) concentration are then performed, covering a broad range between pristine polar and polluted continental values. We find a significant response in the resolved mixed-phase convection, which is in line with previous LES studies. An increased CCN substantially enhances the depth of convection and liquid cloud amount, accompanied by reduced surface precipitation. Initializing with the in situ CCN data yields the best agreement with the cloud and turbulence observations, a result that prioritizes its measurement during field campaigns for supporting high-resolution modeling efforts. A deeper analysis reveals that CCN significantly increases the efficiency of radiatively driven entrainment in warming the boundary layer. The marked strengthening of the thermal inversion plays a key role in this effect. The low-level heat budget shifts from surface driven to radiatively driven. This response is accompanied by a substantial reduction in the surface energy budget, featuring a weakened flow of solar radiation into the ocean. Results are interpreted in the context of air–sea interactions, air mass transformations, and climate feedbacks at high latitudes.

A mathematical model for supercooling process and its application to frazil ice evolution

The calculation of the number of ice crystals for the model of frazil ice evolution is very important and affects the whole frazil events. In this paper, the general formula for the number of frazil ice crystals was established considering secondary nucleation, flocculation, gravity and turbulent entrainment, and ice crystals by melting. Meanwhile, two physical processes of secondary nucleation and flocculation were expressed by introducing critical impact velocity and the probability of flocculation from previous models. It has been found that the simulation results of frazil ice evolution are in good agreement with the experimental data and actual project. Then, Sobol method is carried out to judge parameters’ influence degree, which found the number of nuclei produced E is the most sensitive and has the greatest influence on the model results. In addition, sensitivity analysis of these parameters shows that they can affect the maximum supercooling and the period of supercooling. Therefore, the calculation method of the number of ice crystals is applied, which provides technical support for exploring the water temperature and internal relationship of frazil ice evolution.

Identifying key stages of radiation fog evolution using water vapor isotopes

Fog is tied to surface energy and water budgets. However, our knowledge about the processes leading to fog evolution is still fragmentary, and their adequate representation in numerical-weather-prediction and climate models remains challenging. Water vapor isotopes are widely used to investigate Earth's water cycle dynamics and can provide process-based insights into fog evolution. Although isotopes of water vapor and droplets during radiation fog have been reported, the intra-event isotope dynamics and the mechanisms controlling water vapor isotope variability during radiation fog evolution have hardly been investigated. We use water vapor isotopes (δ2Hv, dv) combined with meteorological and eddy-covariance measurements, plus vertical profiles from a high-resolution numerical-weather-prediction model (COSMO-1), to study the processes that influence radiation fog evolution. Variability in surface-humidity and water vapor isotopes is tied to the different stages (shallow, transitional, and deep fog) of radiation fog evolution and affected by condensation, turbulent entrainment, fog droplet deposition at the surface, and evaporation processes. Strong water vapor isotopic fluctuations during radiation fog are linked to fog lifting to stratus-clouds during nighttime that lead to fog dissipation at ground level. Our results reveal highly correlated atmospheric-specific-humidity (qa) and water vapor isotopes during dew formation which is typical before the onset of radiation fog and in combination with fog; whilst during fog periods, δ2Hv and dv show larger temporal variability than qa due to their sensitivity to fog dynamics. Particularly, during fog growth, entrainment of air from the fog-top caused increasing dv, which was otherwise constant during condensation. Furthermore, δ2Hv variability during the transition into deep fog likely indicated the alternation of condensation-induced-decrease and entrainment-induced-increase of δ2Hv. Compared to the temporal isotope variability (with a magnitude of 34.6‰ for δ2Hv) associated with large-scale cold-frontal-clouds, radiation fog evolution is found to be associated with isotope variability of a similar amplitude (24.6‰ for δ2Hv).

Influence of freestream turbulence on the near-field growth of a turbulent cylinder wake: Turbulent entrainment and wake meandering

The influence of freestream turbulence (FT) on near-field development of turbulent wakes is assessed with regards to both the entrainment rate of background fluid into the wake and the extent of wake meandering. It is shown that FT increases the entrainment rate into the near wake, and thereby the rate at which the wake spreads. The influence of FT on wake meandering is more complex, but it is shown that the integral length scale is the dominant property affecting meandering. In a novel control experiment, large-scale coherent motion in the wake is suppressed, and the far-wake results are recovered: that is, turbulent entrainment is reduced via the suppression of small-scale nibbling.

Entrainment Rates and Eddy Exchange Coefficients From Reanalysis Sea Surface Salinity Data

AbstractSimple analytic models developed in this study are applied to long‐term averages of reanalysis surface salinity data to quantify two fundamental properties of ocean currents. The first model is based on the new Freshening Length schema and its application to the Irminger Current yields a ratio of about 5 between the turbulent entrainment rates of surrounding fresher surface waters west and east of Greenland. The second model is based on the steady solution of the advection‐diffusion equation subject to suitable boundary conditions. The application of this model to the spreading of fresh, snow‐melt, water from the delta of the Po river in the northwest Adriatic Sea into the rest of the Sea yields a ratio of 8 × 104 m between the eddy exchange coefficient and the speed of advection in the Sea.

Turbulence structures and entrainment length scales in large offshore wind farms

Abstract. The flow inside and around large offshore wind farms can range from smaller structures associated with the mechanical turbulence generated by wind turbines to larger structures indicative of the mesoscale flow. In this study, we explore the variation in turbulence structures and dominant scales of vertical entrainment above large offshore wind farms located in the North Sea, using data obtained from a research aircraft. The aircraft was flown upstream, downstream, and above wind farm clusters. Under neutrally stratified conditions, there is high ambient turbulence in the atmosphere and an elevated energy dissipation rate compared to stable conditions. The intensity of small-scale turbulence structures is increased above and downstream of the wind farm, and it prevails over mesoscale fluctuations. But in stable stratification, mesoscale flow structures are not only dominant upstream of the wind farm but also downstream. We observed that the vertical flux of horizontal momentum is the main source of energy recovery in large offshore wind farms, and it strongly depends on the magnitude of the length scales of the vertical wind velocity component. The dominant length scales of entrainment range from 20 to ∼60 m above the wind farm in all stratification strengths, and in the wake flow these scales range from 10 to ∼100 m only under near-neutral stratification. For strongly stable conditions, negligible vertical entrainment of momentum was observed even just 2 km downstream of large wind farms. We also observed that there is a significant lateral momentum flux above the offshore wind farms, especially under strongly stable conditions, which suggests that these wind farms do not satisfy the conditions of an “infinite wind farm”.

R410A and R32 condensation heat transfer and flow patterns inside horizontal micro-fin and 3-D enhanced tubes

Micro-fin tube, 3-D enhanced tube and smooth tube with an inner diameter of 9.52 mm were used as test tubes to study the condensation heat transfer performance with R410A and R32 as the working fluids at different mass flow rates (150–400 kg/m2s) and vapor qualities (0.2–0.8). For R410A and R32, the heat transfer coefficient of the micro-fin tube is 2.0–2.2 times and 1.5–2.0 times that of the smooth tube, and the heat transfer coefficient of the 3-D enhanced tube is 1.4–1.5 times and 1.5–1.6 times that of the smooth tube, respectively. The micro-fin tube is effective in thinning the condensate thickness and reducing the thermal resistance. The 3-D enhanced tube promotes the generation of turbulence and droplet entrainment, which improves heat transfer of enhanced tubes. The heat transfer coefficient of R32 is greater than that of R410A due to its higher thermal conductivity, latent heat and specific heat capacity. The frictional pressure drop increases monotonically with the mass flow rate. Considering the increment in surface area and the additional pressure drop penalty, the performance evaluation factor of the enhanced tubes ranges from 0.9 to 1.4. The study presents flow pattern maps for smooth and enhanced tubes. Enhanced tubes promote the appearance of intermittent and annular flow.

Turbulent entrainment in finite-length wind farms

In this article, we present an entrainment-based model for predicting the flow and power output of finite-length wind farms. The model is an extension of the three-layer approach of Luzzatto-Fegiz & Caulfield (Phys. Rev. Fluids, vol. 3, 2018, 093802) for wind farms of infinite length, and assumes dependence of key flow quantities, such as the wind farm bulk velocity, on the streamwise distance from the farm entrance. To assist our analysis and validate the proposed model, we undertake a series of large-eddy simulations with different turbine spacing arrangements and layouts. Comparisons are also made with the top-down model with entrance effects of Meneveau (J. Turbul., vol. 13, 2012, N7) and data from the literature. The finite-length entrainment model is shown to be capable of capturing the power drop between contiguous rows of turbines as well as describing the advection and turbulent transport of kinetic energy in both the entrance and fully developed regions. The fully developed regime is approximated only deep in the wind farm, after approximately 15 rows of turbines. Our data suggest that for the cases considered in this study, the empirical coefficients that can be used to describe turbulent entrainment and transfers above the wind farm exhibit little dependence on the farm layout and may be considered constant for modelling purposes. However, the flow field within the wind farm layer can be strongly modulated by the turbine density (spacing) as well as the array layout, and to that extent it can be argued that they are both primary factors determining the wind farm power output.

Nutrient dynamics and coupling with biological processes and physical conditions in the Bohai Sea

The Bohai Sea is a habitat for economically important fish in China, but its ecological environment has changed significantly, and it is necessary to further clarify the dynamics and the internal resupply channels of nutrients in the Bohai Sea. Based on four field observations in the Bohai Sea from May to December 2019, the nutrient dynamics were addressed. The concentration of dissolved inorganic nutrients was depleted throughout the water column in spring and in the euphotic zone in summer and accumulated in the bottom water in summer and in the water column in autumn and winter. Relative phosphorus limitation was present in Laizhou Bay and its surrounding area in all seasons, while relative silicon limitation was evident in spring and relative nitrogen limitation was significant in summer in most other study aeras. The results of end-member mixing model illustrated significant seasonal differences in the nutrient uptake ratios, which may be related to various factors such as different phytoplankton composition and phosphorus turnover rates. Turbulent entrainment was an important nutrient pathway for primary production in the euphotic zone of Central Bohai Sea during the stratification season, with an estimated average nutrient flux of 6.04 ± 9.63, 0.22 ± 0.19 and 6.97 ± 6.61 mmol·m-2·d-1 for DIN, DIP and DSi, respectively.

Understanding Turbulent Flows with High-Speed Imaging

How the simultaneous application of flow measurement techniques and high-speed imaging sheds light on turbulent entrainment

How incoming turbulence affects wake recovery of an NREL-5MW wind turbine

The present work aims at investigating the effect of inflow turbulence on the wake recovery of the NREL-5MW reference wind turbine. The wake produced by a utility-scale wind turbine invested by both a laminar uniform inflow and a turbulent flow, is analyzed by means of proper-orthogonal decomposition (POD). The considered turbine is the NREL-5MW at tip-speed ratio λ = 7 and a diameter-based Reynolds number of the order 108. The flow is simulated through Large Eddy Simulation, where the forces exerted by the blades are modeled using the Actuator Line Method, whereas tower and nacelle are modeled employing the immersed boundary method. The main flow structures identified by modal decomposition in both of the considered cases are compared, and some differences emerge, which can be of great importance for the formulation of a reduced-order model. Among the most energetic modes, a high-frequency mode directly related to the tip vortices is found only in the flow case with laminar inflow. In the presence of inflow turbulence, the most energetic modes are all composed by large-scale low-frequency structures filling the whole domain. We evaluate the contribution of each POD mode to wake recovery reconstructing the total flux of mean kinetic energy due to turbulent fluctuations on a closed surface enclosing the wake of the wind turbine. In the laminar-inflow case, we have found that the POD modes related to the tip and root vortices do not contribute positively to the wake recovery, but they rather sustains the velocity gradient, as already established by Lignarolo et al. (2015) for a wind-turbine model. Whereas, in the turbulent-inflow case, all the most energetic modes contribute positively to wake recovery. These results clearly indicate that inflow turbulence should be taken into account for accurately estimate the entrainment process in the wake of wind turbines.NREL 5MW wind turbine, POD, laminar or turbulent inflow, wake recovery, turbulent kinetic energy entrainment.

Steam entrainment and heat transfer characteristic of steam submerged jet condensation within steam-water mixture layer

Steam-water interface and mixture layer are the key window for understanding the heat and mass transfer mechanism of steam submerged jet condensation. In this paper, the steam-water two-phase mixture layer is captured and the interfacial vortex is observed with a quasi-two-dimensional submerged steam jet visualization experimental platform. Then, the volume heat transfer capacity of steam-water mixture layer and heat transfer coefficient with steam-water inner interface are obtained. Furthermore, a new turbulent eddy entrainment model is developed to calculate the local entrainment mass rate and local condensation heat transfer coefficient. Both the local entrainment mass rate and local condensation heat transfer coefficient increases along steam jet direction, and reaches the maximum value at the tail of the mixture layer. The calculated condensation heat transfer coefficient ranges from 0.88 to 2.94 MW·m−2·K−1, which is about the half of the value of hypothetical heat transfer coefficient with inner interfacial area.

Hypolimnetic oxygen depletion in a deep oligomictic lake under climate change

Dissolved oxygen (DO) concentration is a fundamental metric to describe climate-related alterations in deep lakes. Increasing water temperatures enhance thermal stratification, leading in temperate basins to a growing isolation of deep waters. This leads to the depletion of hypolimnetic DO, which adds up to limited nutrient circulation and restricted replenishment of the trophogenic layers. With vanishing convective mixing, it is commonly believed that the only source of hypolimnetic DO replenishment will be represented by deep intrusions of cold oxygenated waters from the tributaries. In this study, we first analyse the 1993–2020 long-term observed trends of DO concentrations in the subalpine deep oligomictic Lake Maggiore (Italy/Switzerland). Then, through an algorithm calculating daily intrusion depths and mass discharges of DO for the major tributaries, we show that deep insertions are suppressed for increasing winter water temperatures and residual thermal stratification. Turbulent entrainment is proved fundamental for DO replenishment, leading to mass discharges of DO released into the deep hypolimnion up to more than two orders of magnitude larger than the original ones from the tributaries. Last, we discuss the results of simulations made through a one-dimensional coupled ecological–hydrodynamic model about the possible effects of a full turnover on DO concentrations in the deep hypolimnion. Two cases are displayed, with the turnover taking place either now or with an anoxic hypolimnion deriving from decades of isolation due to severe climate warming. Through this study, climate warming is shown to be a fundamental driver of DO in Lake Maggiore, its depletion harming both water quality and the ecosystem.

Entrainment, diffusion and effective compressibility in a self-similar turbulent jet

An experimental Lagrangian study based on particle tracking velocimetry has been completed in an incompressible turbulent round water jet freely spreading into water. The jet is seeded with tracers only through the nozzle: inhomogeneous seeding called nozzle seeding. The Lagrangian flow tagged by these tracers therefore does not contain any contribution from particles entrained into the jet from the quiescent surrounding fluid. The mean velocity field of the nozzle seeded flow, $\langle \boldsymbol {U}_{\boldsymbol {\varphi }} \rangle$ , is found to be essentially indistinguishable from the global mean velocity field of the jet, $\langle \boldsymbol {U} \rangle$ , for the axial velocity while significant deviations are found for the radial velocity. This results in an effective compressibility of the nozzle seeded flow for which $\boldsymbol {\nabla }\boldsymbol {\cdot } \langle \boldsymbol {U}_{\boldsymbol {\varphi }} \rangle \neq 0$ even though the global background flow is fully incompressible. By using mass conservation and self-similarity, we quantitatively explain the modified radial velocity profile and analytically express the missing contribution associated with entrained fluid particles. By considering a classical advection–diffusion description, we explicitly connect turbulent diffusion of mass (through the turbulent diffusivity $K_T$ ) and momentum (through the turbulent viscosity $\nu _T$ ) to entrainment. This results in new practical relations to experimentally determine the non-uniform spatial profiles of $K_T$ and $\nu _T$ (and hence of the turbulent Prandtl number $\sigma _T = \nu _T/K_T$ ) from simple measurements of the mean tracer concentration and axial velocity profiles. Overall, the proposed approach based on nozzle seeded flow gives new experimental and theoretical elements for a better comprehension of turbulent diffusion and entrainment in turbulent jets.

Realistic 3D hydrodynamics simulations find significant turbulent entrainment in massive stars

ABSTRACT Our understanding of stellar structure and evolution coming from one-dimensional (1D) stellar models is limited by uncertainties related to multidimensional processes taking place in stellar interiors. 1D models, however, can now be tested and improved with the help of detailed three-dimensional (3D) hydrodynamics models, which can reproduce complex multidimensional processes over short time-scales, thanks to the recent advances in computing resources. Among these processes, turbulent entrainment leading to mixing across convective boundaries is one of the least understood and most impactful. Here, we present the results from a set of hydrodynamics simulations of the neon-burning shell in a massive star, and interpret them in the framework of the turbulent entrainment law from geophysics. Our simulations differ from previous studies in their unprecedented degree of realism in reproducing the stellar environment. Importantly, the strong entrainment found in the simulations highlights the major flaws of the current implementation of convective boundary mixing in 1D stellar models. This study therefore calls for major revisions of how convective boundaries are modelled in 1D, and in particular the implementation of entrainment in these models. This will have important implications for supernova theory, nucleosynthesis, neutron stars, and black holes physics.

Effect of large scale roughness of block ramps on dissolved oxygen efficiency in water

Abstract Block ramps are generally characterized by super critical flow over the ramps, and the presence of roughness lying on the surface of the block ramps induces excessive turbulence, which causes some turbulent energy dissipation and air entrainment. Aeration in a block ramp is caused by the intensity of turbulence created in the water flow by surface roughness of the block ramp and hydraulic jump downstream of block ramp. Macro or large-scale roughness like boulders, as a protruding element on surface of block ramp, could increase intensify turbulence and flow aeration along block ramps. This paper presents an experimental investigation of the dissolved oxygen efficiency in block ramps with slopes of 1:3, 1:5 and 1:7, on which large-scale granular materials with different arrangement patterns were glued. Comparison of results indicated that, for both free and ramp hydraulic jumps, the block ramps with a slope of 1:3 and large-scale roughness increase the dissolved oxygen efficiency almost 20% above that of the similar smooth block ramps. By reducing of the slope of block ramps to 1:5, the dissolved oxygen efficiency of the block ramps with large surface roughness became 3 and 19% for free and ramp hydraulic jumps, respectively. However, the block ramps with 1:7 slope had corresponding dissolved oxygen efficiency of 19 and 32%, respectively. Furthermore, installation of large scale roughness with the structured arrangement have better performance to increase dissolved oxygen (DO) in comparison with the interlocked large-scale roughness.

Micro-droplet nucleation through solvent exchange in a turbulent buoyant jet

Solvent exchange is a process involving mixing between a good solvent with dissolved solute and a poor solvent. The process creates local oversaturation which causes the nucleation of minute solute droplets. Such ternary systems on a macro-scale have remained unexplored in the turbulent regime. We experimentally study the solvent exchange process by injecting mixtures of ethanol and trans-anethole into water, forming a turbulent buoyant jet in the upward direction. Locally, turbulent mixing causes oversaturation of the trans-anethole following turbulent entrainment. We optically measure the concentration of the nucleated droplets using a light attenuation technique and find that the radial concentration profile has a sub-Gaussian kurtosis. In contrast to the entrainment-based models, the spatial evolution of the oversaturation reveals continuous droplet nucleation downstream and radially across the jet, which we attribute to the limited mixing capacity of the jet. Although we are far from a full quantitative understanding, this work extends the knowledge on solvent exchange into the turbulent regime, and brings in a novel type of flow, broadening the scope of multicomponent, multiphase turbulent jets with phase transition.

Universal modulations of large-scale motions on entrainment of turbulent boundary layers

The modulations of high/low-speed large-scale motions (H/L-SMs) on the turbulent/non-turbulent interface (TNTI) and turbulent entrainment are investigated in turbulent boundary layers via both experimental and numerical studies. The spanwise locations of large-scale motions can be locked by the spanwise heterogeneity, so the boundary layers over such a configuration are investigated first as an instructive case. In the engulfment process, it is found that irrotational ‘bubbles’ near the TNTI are more likely to originate from engulfment, while bubbles far from the TNTI could be produced by the local turbulence itself. Additionally, H-SMs are found to enhance the engulfment by the sweep flow. In the nibbling process, a competition relationship is observed: L-SMs induce stronger instantaneous ‘nibbling’ events by transporting more fluids towards the TNTI, while the H-SMs induced a more distorted TNTI. Consequently, the integral nibbling flux is greater above H-SMs. Furthermore, the explored mechanisms are verified to be insensitive to the wall shapes such as smooth and homogeneous roughness walls, which demonstrates that these modulations are universal for turbulent boundary layers. Finally, a conceptual modulation model is proposed to illustrate the entrainment process above the large-scale motions.

Random Forest Predictions of Fine Ash Concentration and Charging Processes From Experimentally Generated Volcanic Discharges

AbstractExplosive volcanic plume rise is governed by the rate at which ambient air is ingested and heated by turbulent entrainment and mixing processes. A daunting observational challenge is to constrain the character of the underlying physical processes and their dependence on complex particle‐particle and particle‐gas interactions. Important clues may lie in the particle‐particle momentum exchange that gives rise to related electrical discharges near the vent during supersonic eruptions. Recent laboratory studies of positive and negative shock‐tube‐generated volcanic discharges show a correlation between fine ash concentration and the magnitude and number of positive discharges. Charge generation via collisions (triboelectrification) is hypothesized to be more efficient with high ash concentrations and at high decompression rates because collisions between particles become more frequent under these conditions. To understand the experimental data in greater detail, we train and implement a regression‐based random forest algorithm to quantitatively predict concentrations of fine ash using discharge count, magnitude and polarity as predictors. Using a metric for variable importance, we find in all, high pressure (HP, ≥10 MPa), and high ash mass experiments (HM, >22g) that positive discharge properties are most important when predicting fine ash concentration, consistent with triboelectrification as the predominant charging process under these conditions. This mechanism is not constrained for low‐pressure (LP, <10 MPa) conditions, suggesting a potential threshold decompression rate condition for this class of charging. This result provides insight into why near‐vent lightning is not a ubiquitous feature of explosive eruptions.