Initial Reynolds Number Research Articles

On the dynamics of bubbles passing through a sand bed layer

Abstract The present research paper reports the outcomes of an extensive laboratory investigation examining the effects of grain size and air discharge on bubble dynamics of bubble plumes passing through a sand bed layer. The effects of sand layer thickness and grain size on bubble characteristics such as bubble size, bubble concentration and velocity, and interfacial area within bubble plumes are studied for a wide range of air discharges. The experiments revealed 58% reduction on the mode bubble size when the sand bed thickness increased from 33 to 66 times of the nozzle diameter. The distribution of bubble size along the main axis of the plume indicated a linear correlation while bubble size distribution became more uniform with relatively smaller bubbles when air passes through a sand bed layer. A sand bed layer significantly improved the formation of uniform bubbly flow with relatively smaller bubbles sizes. Moreover, an increase in the thickness of sand bed layer reduced the mean bubble velocity and consequently extended the residence time of bubbles. Non-linear correlations were observed between particle size and bubble velocity and empirical correlations were formulated to estimate mean bubble diameter and bubble velocity for different bed particle sizes and initial air discharges. The frequency of bubbles increased with increasing air discharge and the sand bed layer almost doubled the frequency of bubbles. The interfacial area of bubbles, which is an indicator of the contact surface between air and water, increased by approximately 32% when the initial Reynolds number doubled.

Modeling of vibrational nonequilibrium effects on pressure Hessian tensor using physics-assisted deep neural networks

This study focuses on modeling the effect of vibrational nonequilibrium on the pressure Hessian tensor. The pressure Hessian tensor is one of the unclosed processes involved in the velocity gradient evolution equation. Accessing the velocity gradient tensor following a fluid particle is needed to understand the physics of various nonlinear turbulent processes. Our modeling strategy employs a combination of two different deep neural networks (DNNs) to model the magnitude and the directional aspects of the vibrational nonequilibrium tensor separately. Both the DNNs are optimized using two appropriate physics-assisted custom loss functions, comparing the desired features of the DNN predictions against the exact behavior observed in the direct numerical simulation (DNS) database. A detailed investigation of four different DNS databases of vibrationally excited decaying compressible turbulence with different initial Reynolds numbers, Mach numbers, and vibrational Damköhler numbers is performed to identify the appropriate normalized forms of input and output quantities for the two neural networks. The training of both the DNNs is done using the DNS data of merely one simulation. The trained models are then subjected to extensive evaluation against different DNS databases. Indeed, the new model captures many DNS features quite well. Such an extensive evaluation of the new model proves the generalizability of the model, at least in the range of parameters involved in our study.

Kinetic investigation of Kelvin–Helmholtz instability with nonequilibrium effects in a force field

The Kelvin–Helmholtz (KH) instability in a force field is simulated and investigated using a two-component discrete Boltzmann method. Both hydrodynamic and thermodynamic nonequilibrium effects in the evolution of KH instability are analyzed in two distinct states: interface roll-up and non-roll-up. It is interesting to note that there are critical thresholds for initial amplitude and Reynolds number, both of which are determined based on the vertical density gradient. Specifically, when the initial amplitude and Reynolds number exceed their respective critical thresholds, the interface undergoes roll-up. Conversely, if these parameters fall below their critical values, the interface fails to roll up. Moreover, the initial amplitude promotes the development of density gradients, mixing degree, mixing width, viscous stress tensor strength, and heat flux strength. In contrast, the Reynolds number enhances the evolution of density gradients but dampens the mixing degree, viscous stress tensor strength, and heat flux intensity. The effect of the Reynolds number on mixing width is analyzed as well.

Understanding the Influence of the Buoyancy Sign on Buoyancy-Driven Particle Clouds

A numerical model was developed to investigate the behavior of round buoyancy-driven particle clouds in a quiescent ambient. The model was validated by comparing model simulations with prior experimental and numerical results and then applied the model to examine the difference between releases of positively and negatively buoyant particles. The particle cloud model used the entrainment assumption while approximating the flow field induced by the cloud as a Hill’s spherical vortex. The motion of individual particles was resolved using a particle tracking equation that considered the forces acting on them and the induced velocity field. The simulation results showed that clouds with the same initial buoyancy magnitude and particle Reynolds number behaved differently depending on whether the particles were more dense or less dense than the ambient fluid. This was found even for very low initial buoyancy releases, suggesting that the sign of the buoyancy is always important and that, therefore, the Boussinesq assumption is never fully appropriate for such flows.

Self-ordering and organization of a staggered oblate particle pair in three-dimensional square ducts

We numerically investigate the formation and ordering of staggered oblate particle pairs in three-dimensional straight ducts with a square cross section. The lattice Boltzmann method is employed to simulate rigid particle pairs in a Newtonian liquid. The effects of initial axial spacing, Reynolds number, blockage ratio, and particle aspect ratio on the formation process, migration behavior, and interparticle spacing are explored in detail. Current results indicate that the process from initial to final steady state can be divided into two stages. The first stage is rapid migration from initial positions toward equilibrium positions under shear-induced lift force and wall-induced repulsive force. The second stage is the slow self-assembly of stable particle pairs in the axial direction due to the interparticle interaction. Interestingly, initial axial spacing significantly affects the formation process of particle pairs but does not affect the final steady state. It is found that the equilibrium positions of staggered particle pairs move slightly toward the duct walls, and the axial spacing increases with increasing Reynolds number or particle aspect ratio, or decreasing blockage ratio. For a staggered particle pair, the second particle will occupy the eddy center induced by the first focusing particle. Based on the existing data, a correlation is put forward to predict the axial interparticle spacing of staggered oblate particle pairs in duct flows. The present results may give insights into manipulating and comprehending non-spherical particle dynamics in microfluidic applications.

Calculation of Mixed Oil Volume for Sequential Transportation of Crude Oil Pipelines with Variable Temperature and Low Reynolds Number

In order to meet the differentiated demand of oil refiners for crude oil, improve the operating load ratio of long-distance pipelines, and reduce one-time investment, sequential transportation process has been widely used in long-distance crude oil pipelines in China. There are many studies on the calculation method of the mixed oil quantity of sequential transportation of refined oil, but due to its complex influencing factors, there is no general calculation model accepted by everyone. For the sequential transportation of crude oil pipelines, most of them have the characteristics of variable temperature and low Reynolds number, and it is more difficult to accurately calculate the mixed oil quantity than the refined oil pipeline. Through the analysis of the characteristics of oil mixing and hydraulic characteristics of sequential oil transportation, combined with the operation example of an oil pipeline in China, the calculation results of the diffusion theory formula, the Austin-Palfrey empirical formula and the equivalent pipeline length formula were compared and analyzed. The results show that the “equivalent pipeline length method” considers the influence of flow, pipe diameter and conveying distance on oil mixing, and takes into account the oil mixture caused by the change of initial oil mix and Reynolds number, which is more suitable for calculating the mixed oil quantity of sequential transportation of crude oil pipelines. However, for the sequential transportation of crude oil pipelines with low Reynolds number and variable temperature, the amount of oil mixed will be increased. According to the comparative analysis of actual cases, the correction coefficient is increased by 1.5 times on the basis of theoretical calculation, and the calculated value is in good agreement with the actual value, and the deviation is within 5%. It can be used as a reference for the design and operation management of variable temperature and low Reynolds number crude oil sequential transportation pipeline.

Numerical investigation into the blending characteristics of opposed wall jets in a finite field with different stagger distances

Strong turbulence is generated by the blending of opposed staggered jets (OSJs). This turbulence results in fluid mixing and energy dissipation, which are crucial for pollutant dilution and the filling of navigation lock chambers. A renormalization group k-ε turbulence model is adopted to conduct three-dimensional simulations of OSJs at various stagger distances. The blending characteristics of two square water jets at eight stagger distances L* within a finite field are examined; here, L* is defined as the distance between the center lines of the staggered jets divided by the jet diameter. The initial Reynolds number and inlet diameter of the jets for the numerical simulations are set to 2.99 × 106 and 0.6 m, respectively. The numerical results show that there is a linear correlation between the decay exponent and the jet half-width, both of which increase and then gradually stabilize with increasing L*. Intriguingly, the vortex strength and blending length both increase at first before decreasing as L* increases, and the blending effectiveness distribution mirrors these fluctuations. Moreover, a decay model for the axial velocity is formulated in terms of the decay exponent and L*. These investigations yield substantial theoretical results underpinning fluid mixing and orifice arrangement in navigation lock chambers.

Numerical simulation of particles beneath a towed circular cylinder

This study investigates particle dynamics around a towed circular cylinder near a wall. The flow field obtained from a numerical model based on the Reynolds-Average Navier–Stokes equations is utilized to estimate the particle trajectories computed using a Lagrangian approach. The simulated flow resembles a towed fishing gear and the particles which represent sea stars, muscles, and sediments are seeded at the seabed. The ejection of particles from the seabed is related to the upward flow induced by lee-wake vortex shedding. The effect of the gap between the cylinder and the seabed is investigated, where an increased distance leads to fewer ejected particles and distinct trajectories. Furthermore, for the same relative distance to the seabed, a larger diameter cylinder, and hence a different relative initial position and Reynolds number, leads to fewer ejected particles. The optimal position of the fishing net of a towed fishing gear relative to the cylinder is investigated based on the trajectories.

Transient aerodynamics of a square cylinder under downburst-like accelerating flows reproduced in a multiple-fan wind tunnel

Aerodynamic and pressure coefficients of a sectional model of a sharp-edged square cylinder, at zero incidence angle, are experimentally evaluated in accelerating flow conditions through the use of a multiple-fan wind tunnel. Different unsteady flows are reproduced, characterized by flow parameters which dictate the initial and target velocities, as well as the flow acceleration and deceleration, and the temporal spacing between the ramp-up and the ramp-down. The accelerating turbulent flows reproduced during the campaign are consistent with those typical of full-scale downbursts.The ensemble mean of the mean drag coefficient in unsteady conditions reveals to be either comparable or definitely lower than the one relevant to the steady case. The drop seems to increase for higher levels of the acceleration and to be enhanced for the ramp-up conditions, while the ramp-down case suggests a lower level of reduction. This non-symmetric pattern appears to be mitigated when the starting wind velocity increases, reflecting a higher initial Reynolds number. Same comments, but with greater discrepancies compared to the steady conditions, might be addressed for the standard deviation of the lift coefficient connected with vortex shedding. Both these findings point out the presence of fluid-memory effects associated with the acceleration, which might affect the development of vortex shedding and the consequent bluff-body aerodynamics in transient conditions. This is also confirmed by the analyses of the mean pressure distributions. In particular, the detailed scrutiny of specific pressure coefficients reflects their different level of interference with the wake and the model edge.

Lattice Boltzmann simulation of neutrally buoyant circular slip particle motion in a clockwise double-lid-driven square cavity

This paper is on the motion of a neutrally buoyant but circular slip particle in a clockwise double-lid-driven square cavity. The slip flow at the particle surface is implemented by the lattice Boltzmann method with corrected slip boundary schemes. The effects of slip length (Ls), initial particle position, Reynolds number (Re), and particle size (D) are studied on the migration of the slip particle. The motion of the circular slip particle is dominated by the centrifugal and boundary-repulsion forces. The results show that the cavity center is the unique fixed point, and once the slip particle initially deviates from the cavity center, it is always stabilized at the same limit cycle. With the increase in slip length, the limit cycle of the circular slip particle is closer to the cavity boundaries, which brings a stronger centrifugal force to balance the increased boundary-confinement effect. As the slip length, Ls, exceeds 0.02D, the limit cycle forms more quickly than the circular no-slip particle. When Re increases to within 1000, the limit cycle is squashed along the leading diagonal of the cavity and pushed toward the boundaries; however, when Re increases beyond 1000, two developing secondary vortices confine the limit cycle to shrink toward the cavity center. With the increase in particle size, the enhanced boundary confinements lead to the shrinkage of the limit cycle toward the cavity center.

Effect of initial velocity distribution and Reynolds number on two-dimensional wall jet of transition region impinging

Effect of initial velocity distribution and Reynolds number on two-dimensional wall jet of transition region impinging

Study of the reverse transition in pipe flow

In the reverse transition in pipe flow, turbulent flow changes to less disturbed laminar flow. The entropy of the flow appears to decrease. This study examined the reverse transition experimentally and theoretically using entropy change and momentum balance models, not in terms of disturbance in the flow. The reverse transition was accomplished by decreasing the Reynolds number. The transitions approximately correlated with local Reynolds numbers. The initial Reynolds number of the transition became larger, and the pressure at low Reynolds numbers was greater than in ordinary pipe flow. These behaviours were caused by turbulent flow in the pipe undergoing a reverse transition. We showed that the entropy did not decrease in the reverse transition by including the entropy due to friction in the development region.

Lattice Boltzmann solidification modeling of forced convection internal flows applied to Gen-IV nuclear reactor coolants

Generation-IV nuclear reactors involve novel coolants such as molten salts and lead. One of the issues that must be assessed with these coolants is the risk of solidification during reactor operation owing to their high melting temperature. However, the numerical simulation of solidification problems is computationally demanding. In this work, we assess the applicability of Lattice Boltzmann Method (LBM) to nuclear coolants solidification problems under laminar internal forced flow conditions. The double distribution Total Enthalpy-Partially Saturated Method is implemented in the open-source code OpenLB and compared against more standard Finite-Volume Computational Fluid Dynamics (FV-CFD) results, which uses the enthalpy-porosity Eulerian Multiphase method, in commercial code Star-CCM+. The test cases comprise the solidification of two fluids with significantly different Prandtl numbers, molten salt and lead, in a 3D pipe geometry in laminar flow conditions with an initial Reynolds number of 100. The solid interface advances from the cooled wall towards the bulk of the pipe reducing the area of flow passage as the transient evolves. Results of LBM velocity fields, solid fraction profiles, temperature fields, and pressure fields are in good agreement with FV-CFD results for both coolants. Furthermore, LBM stability and accuracy limits are independently explored for molten salts and lead using Two-Relaxation Time (TRT) and Bhatnagar-Gross-Krook (BGK) collision operators. Simulation time between FV-CFD and LBM is also contrasted for both coolants. In this work, LBM solvers use explicit time schemes with a regular grid, whereas FV-CFD solutions are able to include implicit time schemes and near-wall mesh refinement. For molten salt flows (high Prandtl number) FV-CFD allows for considerably larger timesteps than LBM, which is limited by the maximum lattice Mach number limitation and stability considerations. For lead flows (low Prandtl number), the implicit scheme in FV-CFD is limited in terms of accuracy for large timesteps due to the limiting Fourier-number. On the other hand, LBM does not present notable stability issues for lead and the lattice Mach number limit is not as relevant as for the molten salt case for this Reynolds number, allowing for faster simulation times than FV-CFD.

Scalar transport and nucleation in quasi-two-dimensional starting jets and puffs

We experimentally investigate the early-stage scalar mixing and transport with solvent exchange in a quasi-two-dimensional (quasi-2D) jet. We inject an ethanol/oil mixture upward into quiescent water, forming quasi-2D turbulent buoyant jets and triggering the ouzo effect with initial Reynolds numbers, Re0=420,840, and 1680. We study two different modes of fluid supply: continuous injection to study a starting jet and finite volume injection to study a puff. While both modes start with the jet stage, the puff exhibits different characteristics in transport, entrainment, mixing, and nucleation, due to the lack of continuous fluid supply. We also inject a dyed ethanol solution as a passive scalar reference case, such that the effect of nucleation for the ethanol/oil mixture can be disentangled.For the starting jets, the total nucleated mass from the ouzo mixture seems very similar to that of the passive scalar total mass, indicating a primary nucleation site slightly above the virtual origin above the injection needle, supplying the mass flux like the passive scalar injection. With continuous mixing above the primary nucleation site, the mildly increasing nucleation rate suggests the occurrence of secondary nucleation throughout the entire ouzo jet.For the puffs, we show that the puff with the smallest Re0 propagates the fastest and its entrainment lasts the longest. We attribute the superior performance to the buoyancy effect, which transforms a turbulent puff into a turbulent thermal, and has been proven to have stronger entrainment. Although the entrainment and nucleation reduce drastically when the injection stops, the mild mixing still leads to non-zero nucleation rates and the reduced decay of the mean puff concentrations for the ouzo mixture.Adapting the theoretical framework established in Landel et al. (2012b) for quasi-2D turbulent jets and puffs, we successfully model the transport of the horizontally-integrated concentrations for the passive scalar. The fitted advection and dispersion coefficients are then used to model the transport of the ouzo mixture, from which the spatial–temporal evolution of the nucleation rate can be extracted. The spatial distribution of the nucleation rate sheds new light on the solvent exchange process in transient turbulent jet flows.

Direct numerical simulations of the Taylor–Green vortex interacting with a hydrogen diffusion flame: Reynolds number and non-unity-Lewis number effects

Understanding the interactions between hydrogen flame and turbulent vortices is important for developing the next-generation carbon neutral combustion systems. In the present work, we perform several direct numerical simulation cases to study the dynamics of a hydrogen diffusion flame embedded in the Taylor–Green Vortex (TGV). The evolution of flame and vortex is investigated for a range of initial Reynolds numbers up to 3200 with different mass diffusion models. We show that the vortices dissipate rapidly in cases at low Reynolds numbers, while the consistent stretching, splitting, and twisting of vortex tubes are observed in cases with evident turbulence transition at high Reynolds numbers. Regarding the interactions between the flame and vortex, it is demonstrated that the heat release generated by the flame has suppression effects on the turbulence intensity and its development of the TGV. Meanwhile, the intense turbulence provides abundant kinetic energy, accelerating the mixing of the diffusion flame with a contribution to a higher strain rate and larger curvatures of the flame. Considering the effects of the non-unity-Lewis number, it is revealed that the flame strength is more intense in the cases with the mixture-averaged model. However, this effect is relatively suppressed under the impacts of the intense turbulence.

The effect of Prandtl number on decaying stratified turbulence

The effects of the variation in the Prandtl number on turbulence in a stably-stratified fluid is investigated by direct numerical simulation. The results of simulations are presented of the homogeneous decay of turbulence for a given initial Froude number and three different initial Reynolds numbers of increasing values. For each of these cases results for two different Prandtl numbers, 1 and 7, are shown. Various statistics are put forward, including kinetic and potential energy decay rates, kinetic and potential energy dissipation rates, buoyancy fluxes, energy spectra, and statistics conditioned on the local value of the vertical density gradient. It is found that the effect of increasing the Prandtl number is to increase the kinetic energy dissipation rate, while decreasing the potential energy dissipation rate. There is a notable transfer of potential to kinetic energy for the higher Prandtl number case. Finally there is evidence, based upon the analysis of vertical planes and statistics conditional on the local density gradient, that most irreversible mixing of both density and momentum occurs in regions of stronger static stability.

Experimental investigation on high-pressure methane jet characteristic single-hole injector

High-pressure gas direct injection (DI) technology benefits engines with high efficiency and clean emissions, and the gas jet process causes crucial effects especially inside an mm-size space. This study presents an investigation on the high-pressure methane jet characteristics from a single-hole injector by analysing jet performance parameters including jet impact force, gas jet impulse, and jet mass flow rate. The results show that the methane jet exhibited a two-zone behaviour along the jet direction in the spatial dimension induced by high-speed jet flow from the nozzle: zone 1 near the nozzle—the jet impact force and jet impulse increased consistently except for a fluctuation due to shock wave effects induced by the sonic jet and no entrainment occurs, and zone II farther away from the nozzle—the jet impact force and jet impulse became stable when the shock wave effects became weak and the jet impulse was conserved with a linear conservation boundary. The Mach disk height was exactly the turning point of two zones. Moreover, the methane jet parameters, such as the methane jet mass flow rate, jet initial jet impact force, jet impulse, and Reynolds number had a monotonous and linearly increasing correlation with injection pressure.

Frame invariant neural network closures for Kraichnan turbulence

Numerical simulations of geophysical and atmospheric flows have to rely on parameterizations of subgrid scale processes due to their limited spatial resolution. Despite substantial progress in developing parameterization (or closure) models for subgrid scale (SGS) processes using physical insights and mathematical approximations, they remain imperfect and can lead to inaccurate predictions. In recent years, machine learning has been successful in extracting complex patterns from high-resolution spatio-temporal data, leading to improved parameterization models, and ultimately better coarse grid prediction. However, the inability to satisfy known physics and poor generalization hinders the application of these models for real-world problems. In this work, we put forth a frame invariant closure approach to improve the accuracy and generalizability of deep learning-based subgrid scale closure models by embedding physical symmetries directly into the structure of the neural network. Specifically, we utilized specialized layers within the convolutional neural network in such a way that desired constraints are theoretically guaranteed without the need for any regularization terms. We demonstrate our framework for a two-dimensional decaying turbulence test case mostly characterized by the forward enstrophy cascade. We show that our frame invariant SGS model (i) accurately predicts the subgrid scale source term, (ii) respects the physical symmetries such as translation, Galilean, and rotation invariance, and (iii) is numerically stable when implemented in coarse-grid simulation with generalization to different initial conditions and Reynolds number. This work opens up a possibility of connecting physics-based theories and data-driven modeling paradigms, and thus represents a promising step towards the development of physically consistent data-driven turbulence closure models.

Grid-point and time-step requirements for large-eddy simulation and Reynolds-averaged Navier–Stokes of stratified wakes

Estimates of grid-point and time-step requirements exist for many canonical flows but not for stratified wakes. The purpose of this work is to fill in this gap. We apply the basic meshing principles and estimate the grid-point and time-step requirements for Reynolds-averaged Navier–Stokes (RANS) and large-eddy simulation (LES) of stratified wake flows at high Reynolds numbers, as arise in many geophysical, aircraft, and undersea vehicle systems. Scales representative of a submarine operating in a stably stratified ocean environment are considered, and the quantitative conclusions reached here can be adapted accordingly for particular applications. For a submarine, typical wake conditions are Re0=108 and Fr0=102, and wakes extend to Nt = 1000, where Re0 and Fr0 are the initial Reynolds number and the internal Froude number of the wake, respectively, and N is the buoyancy frequency. We consider both spatially developing and temporally evolving wakes. We show that the grid points required for LES and RANS do not depend on the Reynolds number. The ratio of the grid points needed for LES and RANS is proportional to (Nt2,LW)2/3, where t2,LW marks the end of the late wake and the end of a computational fluid dynamics calculation. According to the present conservative estimates, 0.36×1012 and 0.7×109 grid points are needed for LES and RANS of a spatially developing wake. The numbers are 8×109 and 3×106 for LES and RANS of a temporally evolving wake.

Pair of particle chain self-organization in a square channel flow of Giesekus viscoelastic fluid

Pair of particle chain self-organization in a square channel flow of Giesekus viscoelastic fluid is studied by the direct forcing/fictitious domain method. The effects of particle diameter, initial particle distance, shear-thinning (n), Weissenberg number (Wi), and Reynolds number (Re) are explored to analyze the mechanism of particle chain self-organization in Giesekus viscoelastic fluid. The results show that the small particle at the equilibrium position moves faster than the larger one and then catches up with it to form a particle chain, in which the large and small particles are located at the front and the end of the chain, respectively. The particle pair with the same diameter cannot form the chain in Giesekus viscoelastic fluid. In addition, the larger the diameter ratio and the initial particle distance, the larger the absolute value of the particle velocity difference, the earlier the particle chain is formed. The particle chain will be formed early with increasing n, Re, and Wi.