Turbulent Core Research Articles

Numerical investigation on thermal–hydraulic performance of supercritical LNG in a Zigzag mini-channel of printed circuit heat exchanger

• Flow mechanism of supercritical hydrocarbon fluids was investigated. • Comparison on thermal performances for two hydrocarbon fluids was compared. • Correlations for supercritical hydrocarbon fluids in a mini-channel were proposed. Printed circuit heat exchanger (PCHE) is receiving wide attention as a new kind of compact heat exchanger. It is considered as a promising vaporizer in floating liquefied natural gas (FLNG) vessels due to its compactness and high efficiency. In this paper, the numerical model with two Zigzag mini-channels was built. The cross section was a semicircle with the diameter of 1.5 mm and the overall length was 200 mm. In the simulation, SST k - ω turbulent model was employed and validated against experimental data of supercritical CO 2 flow. The mechanism of flow and heat transfer was investigated, and the influence of operating parameters including mass flux, outlet pressure and inlet temperature was analyzed from the perspective of high-speed components of turbulent core area, degree of flow separation, energy transport and dissipation rate. The results indicated that the worse flow performance and better heat transfer performance exhibited at higher mass flux and inlet temperature conditions, whereas the higher outlet pressure conditions exhibited the better flow and heat transfer performances. Correlations for the Fanning friction factor and Nusselt number were developed within a deviation of ±5%, aiming to apply to the prediction of thermal–hydraulic performance of supercritical LNG.

Completing the protostellar luminosity function in Cygnus-X with SOFIA/FORCAST imaging

ABSTRACT We present a new SOFIA/FORCAST mid-infrared survey of luminous protostars and crowded star-forming environments in Cygnus X, the nearest million-solar mass molecular cloud complex. We derive bolometric luminosities for over 1000 sources in the region with these new data in combination with extant Spitzer and UKIDSS photometry, with 63 new luminous protostar candidates identified by way of the high-quality SOFIA/FORCAST data. By including FORCAST data, we construct protostellar luminosity functions (PLFs) with improved completeness at the high luminosity end. The PLFs are well described by a power-law function with an index of ∼−0.5. Based on the Herschel temperature and column density measurements, we find no obvious dependence of the PLFs on the local gas temperature, but PLFs in regions of high stellar density or gas column density exhibit some excess at higher luminosities. Through the comparison between our observed PLFs and existing accretion models, both the turbulent core and the competitive accretion models are consistent with our results, while the isothermal sphere model is disfavoured. The implications of these results on the star formation process are discussed.

CFD modeling of turbulent flow for Non-Newtonian fluids in rough pipes

Non-Newtonian fluids are pumped under laminar and turbulent regimes through pipes in numerous industries. Proper calculation of pressure losses is essential to optimize available horsepower. In actual practice, no pipe surface is smooth. Pipe roughness has significant influence on the pressure loss for turbulent flow. In this study, a mechanistic model is developed to predict pressure losses of Herschel-Bulkley and Power-Law fluids in rough pipes for the turbulent flow regime. A numerical scheme is applied to the proposed model to obtain an approximate solution. The proposed model is separated into two sub-problems in order to obtain a numerical solution. One is solved analytically for the viscous sublayer, which is determined by pipe roughness and the other is solved numerically by the virtue of the central difference approximation along with the frozen non-linear term for the turbulent core region. Moreover, an experimental study is conducted using two different high viscous polymer base fluids with two different concentrations and three different rough pipe diameters. The mechanistic model results are compared with experimental data in this study and presented by Subramanian (1995). Absolute Average Percent Error (AAPE) of 13.3% is calculated for the proposed model compared to experimental measurements.

Turbulent entrainment in viscoelastic fluids

Direct numerical simulations (DNS) of turbulent fronts spreading into an irrotational flow region are used to analyse the turbulent entrainment mechanism for viscoelastic fluids. The simulations use the FENE-P fluid model and are initiated from DNS of isotropic turbulence with Weissenberg and turbulence Reynolds numbers varying in the ranges $1.30 \le Wi \le 3.46$ and $206 \le Re_{\lambda }^{0} \le 404$, respectively. The enstrophy dynamics near the turbulent/non-turbulent interface (TNTI) layer, that separates regions of turbulent and irrotational flow, includes a new mechanism – the viscoelastic production – caused by the interaction between the vorticity field and the polymer stresses. This term can be a sink or a source of enstrophy in the turbulent core region of the flow, depending on the Weissenberg number, and contributes to the initial growth of the enstrophy in the viscous superlayer, together with the viscous diffusion, which is the only mechanism present for Newtonian fluids. For low and moderate Weissenberg numbers the scaling of the TNTI layer is similar to the scaling of TNTI layers for Newtonian fluids, but this is no longer the case at high Weissenberg numbers where the enstrophy tends to be concentrated into thin vortex sheets instead of vortex tubes. Finally, it is shown that the substantial decrease of the entrainment rates observed in turbulent flows of viscoelastic fluids, compared with Newtonian fluids, is caused by a reduction of the surface area and fractal dimension of the irrotational boundary, originated by the depletion of ‘active’ scales of motion in the fluid solvent caused by the viscoelasticity.

A Three-Dimensional Model of Turbulent Core Annular Flow Regime

In this study, three-dimensional (3D) turbulent core annular flow (CAF) regime is investigated numerically. The proposed model is based on the 3D Reynolds average Navier–Stokes (RANS) equations combined with a pure convective transport equation of the volume of fluid (VOF) to predict the interface between the oil and water phases. The k-ω turbulence model is adopted to better reproduce the oil and water flow characteristics. The two-phase (CAF) regime can be predicted by two inlet configurations: the T-junction (3D-T) and the straight pipe (3D-S). These two configurations are simulated and compared for pipe diameter D = 0.026 m and pipe length L = 4 m . For these two inlet configurations, the computed mixture velocity profile and the water volume fraction at a test section z = 100 D were compared to experimental measurements. The 3D-T configuration gives more appropriate results. The 3D-S slightly overestimates the maximum velocity at the test section and the lower and upper water layer of the (CAF) flow is shifted in the upward direction. For the 3D-T, the relative error in the pressure drop is 3.3%. However, for the 3D-S, this error is 13.0%.

A new formation scenario of a counter-rotating circumstellar disk: Spiral-arm accretion from a circumbinary disk in a triple protostar system

Abstract We present the evolution of rotational directions of circumstellar disks in a triple protostar system simulated from a turbulent molecular cloud core with no magnetic field. We find a new formation pathway of a counter-rotating circumstellar disk in such triple systems. The tertiary protostar forms via the circumbinary disk fragmentation and the initial rotational directions of all three circumstellar disks are almost parallel to that of the orbital motion of the binary system. Their mutual gravito-hydrodynamical interaction for the subsequent ∼104 yr greatly disturbs the orbit of the tertiary, and the rotational directions of the tertiary disk and star are reversed due to the spiral-arm accretion of the circumbinary disk. The counter-rotation of the tertiary circumstellar disk continues to the end of the simulation (∼6.4 × 104 yr after its formation), implying that the counter-rotating disk is long-lived. This new formation pathway during the disk evolution in Class 0/I young stellar objects possibly explains the counter-rotating disks recently discovered by ALMA.

Transition of the initial mass function in the metal-poor environments

Abstract We study star cluster formation in a low-metallicity environment using three dimensional hydrodynamic simulations. Starting from a turbulent cloud core, we follow the formation and growth of protostellar systems with different metallicities ranging from 10−6 to 0.1 Z⊙. The cooling induced by dust grains promotes fragmentation at small scales and the formation of low-mass stars with M* ∼ 0.01–0.1 M⊙ While the number of low-mass stars increases with metallicity, when Z/Z⊙ ≳ 10−5. the stellar mass distribution is still top-heavy for Z/Z⊙ ≲ 10−2 compared to the Chabrier initial mass function (IMF). In these cases, star formation begins after the turbulent motion decays and a single massive cloud core monolithically collapses to form a central massive stellar system. The circumstellar disk preferentially feeds the mass to the central massive stars, making the mass distribution top-heavy. When Z/Z⊙ = 0.1, collisions of the turbulent flows promote the onset of the star formation and a highly filamentary structure develops owing to efficient fine-structure line cooling. In this case, the mass supply to the massive stars is limited by the local gas reservoir and the mass is shared among the stars, leading to a Chabrier-like IMF. We conclude that cooling at the scales of the turbulent motion promotes the development of the filamentary structure and works as an important factor leading to the present-day IMF.

Collapse of turbulent massive cores with ambipolar diffusion and hybrid radiative transfer

Context.Massive stars form in magnetized and turbulent environments and are often located in stellar clusters. The accretion and outflows mechanisms associated with forming massive stars and the origin of the stellar multiplicity of their system are poorly understood.Aims.We study the effect of magnetic fields and turbulence on the accretion mechanism of massive protostars and their multiplicity. We also focus on disk formation as a prerequisite for outflow launching.Methods.We present a series of four radiation-magnetohydrodynamical simulations of the collapse of a massive magnetized, turbulent core of 100M⊙with the adaptive-mesh-refinement code RAMSES, including a hybrid radiative transfer method for stellar irradiation and ambipolar diffusion. We varied the Mach and Alfvénic Mach numbers to probe sub- and super-Alfvénic turbulence and sub- and supersonic turbulence regimes.Results.Sub-Alfvénic turbulence leads to single stellar systems, and super-Alfvénic turbulence leads to binary formation from disk fragmentation following the collision of spiral arms, with mass ratios of 1.1–1.6 and a separation of several hundred AU that increases with initial turbulent support and with time. In these runs, infalling gas reaches the individual disks through a transient circumbinary structure. Magnetically regulated, thermally dominated (plasma betaβ> 1) Keplerian disks form in all runs, with sizes 100–200 AU and masses 1–8M⊙. The disks around primary and secondary sink particles have similar properties. We obtain mass accretion rates of ~10−4M⊙yr−1onto the protostars and observe higher accretion rates onto the secondary stars than onto their primary star companion. The primary disk orientation is found to be set by the initial angular momentum carried by turbulence rather than by magnetic fields. Even without turbulence, axisymmetry and north–south symmetry with respect to the disk plane are broken by the interchange instability and thermally dominated streamers, respectively.Conclusions.Small (≲300 AU) massive protostellar disks such as those that are frequently observed today can so far only be reproduced in the presence of (moderate) magnetic fields with ambipolar diffusion, even in a turbulent medium. The interplay between magnetic fields and turbulence sets the multiplicity of stellar clusters. A plasma betaβ> 1 is a good indicator for distinguishing streamers and individual disks from their surroundings.

Deposition Process and Equivalent Markov Motion of High-Inertia Particles in a Long Straight Pipeline

Abstract Two methods are used to study the process of particle deposition in a turbulent pipe flow. The Monte Carlo method tracks 10,000 particles in the turbulent pipe flow to reproduce the deposition process of the particles. The deposition velocity of the particles is determined by calculating the proportion of particles passing through the test section. The simplified deposition model uses an equivalent Markov motion instead of the radial movement of the particle in the turbulent core. The probability that a particle leaves the turbulent core depends on the radial particle position and the probability density distribution of the random vortex. The probability that a particle penetrates the boundary layer can be solved by integrating the probability density distribution of radial particle velocity. The deposition velocity of particles can be obtained by calculating the probability of an individual particle leaving the turbulent core and penetrating the boundary layer. Five experimental data series from the literature are applied to examine the predictive abilities of the two methods. The results demonstrate that the Monte Carlo method can be properly used to track the particle deposition process in the diffusion–impaction and inertia-moderated regimes. The simplified model is suitable for high-inertia particles.

The relation between shearing motions and the turbulent/non-turbulent interface in a turbulent planar jet

The relation between shearing motions and the turbulent/non-turbulent interfacial (TNTI) layer is studied with direct numerical simulation of a temporally evolving planar jet. Small-scale shear layers are detected with the triple decomposition of the velocity gradient tensor, which is decomposed into shear, rotation, and elongation tensors. The shear layers are found in the turbulent sublayer more frequently than in the turbulent core region although they hardly appear in the viscous superlayer. The shear layers undergo a biaxial strain with stretching in the shear vorticity direction and compression in the interface normal direction. This compressive strain is related to the non-turbulent fluid, which is relatively advected toward the shear layer. The shear layer thickness in the TNTI layer is well predicted by Burgers vortex layer. The velocity jump of the shear layer is about seven times the Kolmogorov velocity both in the turbulent core region and the TNTI layer. However, the layer thickness normalized by the Kolmogorov scale is about 6 in the turbulent core region and decreases in the TNTI layer, where consequently, the shear Reynolds number becomes small. The shear layers have significant contributions to the enstrophy production in the turbulent sublayer and the viscous enstrophy-diffusion toward the viscous superlayer. The shear layer and the outer edge of the TNTI layer have a curvature radius of about 50 times the Kolmogorov scale. The alignment between the shear layer orientation and the interface normal direction confirms that the shear layers near the interface are mostly parallel to the TNTI layer.

Role of vortical structures for enstrophy and scalar transport in flows with and without stable stratification

We investigate the enstrophy dynamics in relation to objective Eulerian coherent structures (OECSs) and their impact on the enstrophy and scalar transport near the turbulent/non-turbulent interface (TNTI) in flows with and without stable stratification. We confirm that vortex-stretching produces enstrophy inside the boundaries of the OECSs, while viscous diffusion transfers the enstrophy across the boundaries of the structures. Although often overlooked in the literature, viscous dissipation of enstrophy within the boundaries of vortical structures is significant. Conversely, for the weakly stratified flows also investigated here, the effect of the baroclinic torque is negligible. We provide evidence that the OECSs advect the passive/active scalar and redistribute it via molecular diffusion. Finally, we use conditional analysis to show that the typical profiles of the enstrophy and scalar transport equation terms across the TNTI are compatible with the presence of OECSs positioned at the edge between the turbulent sublayer and the turbulent core region. We show that when these profiles are further conditioned to the presence of OECSs, their magnitude is considerably higher.

Mechanisms of entrainment in a turbulent boundary layer

Data from direct numerical simulation of a zero-pressure-gradient incompressible turbulent boundary layer (TBL) [You and Zaki, “Conditional statistics and flow structures in turbulent boundary layers buffeted by free-stream disturbances,” J. Fluid Mech. 866, 526 (2019)] are analyzed to examine the entrainment process. The two mechanisms by which the outer irrotational flow can be entrained into the turbulent region and their relative contribution to the growth of the spatially developing boundary layer are evaluated: (i) nibbling is the enstrophy transport across the turbulent/non-turbulent interface (TNTI), and (ii) engulfment is the entrapment of pockets of irrotational flow inside the TBL prior to finally breaking apart. The relative importance of the two mechanisms depends on the normalized vorticity threshold adopted to identify the TNTI. Our choice of this threshold highlights the structure of the TNTI and entrainment within this layer by engulfment of irrotational pockets. The sizes of the engulfed pockets are of the same order as the heads of the hairpin vortices underneath the TNTI. The vortices straddle larger streaky structures of internal layers and cause handle shaped deformations on the TNTI, which leads to engulfment as they fold onto themselves and entrap the external potential flow. Three dynamical regions are distinguished: a TNTI region (interface layer), an adjustment region, and the turbulent core. The first of these is further sub-divided into a viscous superlayer and a turbulent sublayer. It is shown as the irrotational fluid elements cross the interface layer toward the turbulent core, a smooth transition from the non-focal topology to the well-known primarily focal topology of fully developed turbulence occur. The viscous superlayer is similar to previously studied flow configurations, such as jets and mixing layers. In contrast, vorticity stretching in the turbulent sublayer is significantly weaker in the boundary layer relative to free-shear flows, which results in a smaller rate of entrainment by nibbling.

Non-equilibrium behavior of large-scale axial vortex cores

A logical basis for incorporating pressure non-equilibrium and turbulent eddy viscosity in an incompressible vortex model is presented. The infrasonic acoustic source implied in our earlier work has been examined. Finally, this non-equilibrium turbulent vortex core is shown to dissipate mechanical energy more slowly than a Burgers vortex, helping us to explain the persistence of axial vortices in nature. Recent molecular dynamics simulations replicate aspects of this non-equilibrium pressure behavior.

Computational study on effect of Mahua natural surfactant on the flow properties of heavy crude oil in a 90° bend

In this paper, A computational study is performed in this paper to investigate the influence of natural surfactant in a 90° bend on the flow properties of heavy Crude Oil. In ANSYS Fluent, computational fluid dynamics (CFD) code is used to investigate the flow phenomena in horizontal pipe bends. A suitable approach for transporting heavy oil through pipes is blending of surfactant with heavy crude oil for 'core annular flow' (CAF). This analysis analyzes the core annular flow numerically using the Large Eddy Simulation (LES). The prime objective of present work is to achieve understanding of the actions of high-sulphur crude oil flow across turbulent core annular flow in transporting pipes line. High-sulphur crude oil blended and additives are the two-phases in horizontal pipe.

On the combined effect of internal and external intermittency in turbulent non-premixed jet flames

This paper analyzes the combined effect of internal intermittency and external intermittency on the dynamics of small-scale turbulent mixing in a turbulent non-premixed jet flame. The phenomenon of external intermittency in turbulent jet flames originates from a very thin layer, known as turbulent/non-turbulent interface, that separates the inner turbulent core from the outer irrotational surrounding fluid. The impact of external intermittency on turbulence is evaluated across the jet flame by the self-similarity scaling of higher-order structure functions of the mixture fraction. It is shown that the scaling of structure functions exhibits a growing departure from the prediction of classical scaling laws toward the edge of the flame. Empirical evidence is provided that this departure is primarily due to external intermittency and the associated break down of self-similarity. External intermittency creates local gradients that are significantly more intense compared to those created by internal intermittency alone. As chemical reactions usually take place in thin layers in the vicinity of the turbulent/non-turbulent interface, an accurate statistical description of these intense events is necessary to predict the turbulence-chemistry interaction. The study is based on data from a highly-resolved direct numerical simulation of a temporally evolving planar jet flame.

Relationship between Axial Width and Flow Characteristics of Pump Chamber in Double Volute Centrifugal Pump

The axial width of pump chamber has a great influence on the flow characteristics of the pump chamber in the centrifugal pump. A single-stage single-suction double volute centrifugal pump with a semi-open impeller was selected as the object. For the 6 different pump chamber axial width, it was concluded that the pump chamber pressure at the different angles (0°, 90°, 180°, 270°) along the radial variation characteristics according to the contrast analysis of the pump cavity pressure field, velocity field distribution. The correlation between the pump chamber pressure and the impeller radius was revealed. The tangential velocity and radial velocity along the axial distribution curves were draw. The results show that when the axial width of pump chamber increases from 23.9 mm to 43.9 mm, the pressure value of the same radial position increases gradually. The radial pressure difference is decreasing. At the same axial width of pump chamber, the pressure mean increases along the radial approximately parabola. The tangential velocity of different angular directions has little difference in axial distribution. The mean of dimensionless tangential velocity in the turbulent core area decreases from 0.32 to 0.19 with the increasing of pump chamber axial width. The radial velocity varies is greatly along the axial direction. There are eddies at the directions of 0ånd 180°, but the mean of radial velocity in the turbulent core area is about 0. This research provides the reference for centrifugal pump hydraulic design, structural design and the accurate calculation of axial force.

Nonadiabatic Turbulence Driving during Gravitational Collapse

Abstract We investigate the generation of turbulence during the prestellar gravitational contraction of a turbulent spherical core. We define the ratio g of the one-dimensional turbulent velocity dispersion to the gravitational velocity to then analytically estimate g under the assumptions of (a) equipartition or virial equilibrium between the gravitational ( ) and turbulent kinetic ( ) energies and (b) stationarity of transfer from gravitational to turbulent energy (implying cst). In the equipartition and virial cases, we find and , respectively; in the stationary case we find , where η is an efficiency factor, is the energy injection scale of the turbulence, and R is the core’s radius. Next, we perform AMR simulations of the prestellar collapse of an isothermal, transonic turbulent core at two different resolutions, and a nonturbulent control simulation. We find that the turbulent simulations collapse at the same rate as the nonturbulent one, so that the turbulence generation does not significantly slow down the collapse. We also find that (a) the simulations approach near balance between the rates of energy injection from the collapse and of turbulence dissipation; (b) , close to the “virial” value (turbulence is 30% ∼ 40% of nonthermal linewidth); (c) the injection scale is , and (d) the “turbulent pressure” scales as , an apparently nearly adiabatic scaling. We propose that this scaling and the nearly virial values of the turbulent velocity dispersion may be reconciled with the nondelayed collapse rate if the turbulence is dissipated as soon as it is generated.

The SOFIA Massive (SOMA) Star Formation Survey. III. From Intermediate- to High-mass Protostars

Abstract We present SOFIA–FORCAST images of 14 intermediate-mass protostar candidates as part of the SOFIA Massive (SOMA) Star Formation Survey. We build spectral energy distributions, also using archival Spitzer, Herschel, and IRAS data. We then fit the spectral energy distributions with radiative transfer models of Zhang & Tan, based on turbulent core accretion theory, to estimate key protostellar properties. With the addition of these intermediate-mass sources, based on average properties derived from SED fitting, SOMA protostars span luminosities from , current protostellar masses from , and ambient clump mass surface densities, , from . A wide range of evolutionary states of the individual protostars and of the protocluster environments is also probed. We have also considered about 50 protostars identified in infrared dark clouds that are expected to be at the earliest stages of their evolution. With this global sample, most of the evolutionary stages of high- and intermediate-mass protostars are probed. The best-fitting models show no evidence that a threshold value of the protocluster clump mass surface density is required to form protostars up to . However, to form more massive protostars, there is tentative evidence that needs to be . We discuss how this is consistent with expectations from core accretion models that include internal feedback from the forming massive star.

A new modeling approach for mixture fraction statistics based on dissipation elements

The probabilty density function (PDF) of the mixture fraction is of integral importance to a large number of combustion models. Here, a novel modelling approach for the PDF of the mixture fraction is proposed which employs dissipation elements. While being restricted to the commonly used mean and variance of the mixture fraction, this model approach individually considers contributions of the laminar regions as well as the turbulent core and the turbulent/non-turbulent interface region. The later region poses a highly intermittent part of the flow which is of high relevance to the non-premixed combustion of pure hydrocarbon fuels. The model assumptions are justified by means of the gradient trajectory based analysis of high fidelity direct numerical simulation (DNS) datasets of two turbulent inert configurations and a turbulent non-premixed jet flame. The new dissipation element based model is validated against the DNS datasets and a comparison with the beta PDF is presented.

The dependence of episodic accretion on eccentricity during the formation of binary stars

Context. Episodic accretion has been observed in short-period binaries, where bursts of accretion occur at periastron. The binary trigger hypothesis has also been suggested as a driver for accretion during protostellar stages. Aims. Our goal is to investigate how the strength of episodic accretion bursts depends on eccentricity. Methods. We investigate the binary trigger hypothesis in longer-period (> 20 yr) binaries by carrying out three-dimensional magnetohydrodynamical simulations of the formation of low-mass binary stars down to final separations of ∼10 AU, including the effects of gas turbulence and magnetic fields. We ran two simulations with an initial turbulent gas core of one solar mass each and two different initial turbulent Mach numbers, ℳ = σv/cs = 0.1 and ℳ = 0.2, for 6500 yr after protostar formation. Results. We observe bursts of accretion at periastron during the early stages when the eccentricity of the binary system is still high. We find that this correlation between bursts of accretion and passing periastron breaks down at later stages because of the gradual circularisation of the orbits. For eccentricities greater than e = 0.2, we observe episodic accretion triggered near periastron. However, we do not find any strong correlation between the strength of episodic accretion and eccentricity. The strength of accretion is defined as the ratio of the burst accretion rate to the quiescent accretion rate. We determine that accretion events are likely triggered by torques between the rotation of the circumstellar disc and the approaching binary stars. We compare our results with observational data of episodic accretion in short-period binaries and find good agreement between our simulations and the observations. Conclusions. We conclude that episodic accretion is a universal mechanism operating in eccentric young binary-star systems, independent of separation, and it should be observable in long-period binaries as well as in short-period binaries. Nevertheless, the strength depends on the torques and hence the separation at periastron.