Forced Turbulence Research Articles

Modeling of Microbubble Flow and Coalescence Behavior in the Contact Zone of a Dissolved Air Flotation Tank Using a Computational Fluid Dynamics–Population Balance Model

Computational fluid dynamics coupled with a population balance model was implemented to resolve microbubble flow and coalescence behavior in the contact zone of a dissolved air flotation tank. Influences of two important interphase forces and coalescence models were examined. The results indicated that the lift force has negligible influence on gas holdup, while incorporating appropriate turbulent dispersion force model can substantially improve the predicted gas holdup and make it consistent with experimental data. The population balance model considering both the eddy-capture and velocity gradient mechanisms could accurately predict the bubble diameter and its size distribution. The relative difference between the simulated and the measured mean bubble diameter is lower than 10.2%. It was also found that bubble coalescence mainly happens below the nozzle inlet and around the nozzle inlet pipe, and the bubble coalescence was enhanced by the flow direction transition and nonuniform gas holdup distribution...

A scaling law for the recirculation zone length behind a bluff body in reacting flows

The recirculation zone length behind a bluff body is influenced by the turbulence intensity at the base of the body in isothermal flows and also the heat release and its interaction with turbulence in reacting flows. This relationship is observed to be nonlinear and is controlled by the balance of forces acting on the recirculation zone, which arise from the pressure and turbulence fields. The pressure force is directly influenced by the volumetric expansion resulting from the heat release, whereas the change in the turbulent shear force depends on the nonlinear interaction between turbulence and combustion. This behaviour is elucidated through a control volume analysis. A scaling relation for the recirculation zone length is deduced to relate the turbulence intensity and the amount of heat release. This relation is verified using the large eddy simulation data from 20 computations of isothermal flows and premixed flames that are stabilised behind the bluff body. The application of this scaling to flames in an open environment and behind a backward facing step is also explored. The observations and results are explained on a physical basis.

Turbulent windprint on a liquid surface

We investigate the effect of a light turbulent wind on a liquid surface, below the onset of wave generation. In that regime, the liquid surface is populated by small disorganised deformations elongated in the streamwise direction. Formally identified recently by Paquier et al. (Phys. Fluids, vol. 27, 2015, art. 122103), the deformations that occur below the wave onset were named wrinkles. We provide here a theoretical framework for this regime, using the viscous response of a free liquid surface submitted to arbitrary normal and tangential interfacial stresses at its upper boundary. We relate the spatio-temporal spectrum of the surface deformations to that of the applied interfacial pressure and shear stress fluctuations. For that, we evaluate the spatio-temporal statistics of the turbulent forcing using direct numerical simulation of a turbulent channel flow, assuming no coupling between the air and the liquid flows. Combining theory and numerical simulation, we obtain synthetic wrinkles fields that reproduce the experimental observations. We show that the wrinkles are a multi-scale superposition of random wakes generated by the turbulent fluctuations. They result mainly from the nearly isotropic pressure fluctuations generated in the boundary layer, rather than from the elongated shear stress fluctuations. The wrinkle regime described in this paper naturally arises as the viscous-saturated asymptotic of the inviscid growth theory of Phillips (J. Fluid Mech., vol. 2 (05), 1957, pp. 417–445). We finally discuss the possible relation between wrinkles and the onset of regular quasi-monochromatic waves at larger wind velocity. Experiments indicate that the onset of regular waves increases with liquid viscosity. Our theory suggests that regular waves are triggered when the wrinkle amplitude reaches a fraction of the viscous sublayer thickness. This implies that the turbulent fluctuations near the onset may play a key role in the triggering of exponential wave growth.

Error quantification of 3D homogeneous and isotropic turbulence measurements using 2D PIV

Particle image velocimetry (PIV) has become a popular non-intrusive tool for measuring various types of flows. However, when measuring three dimensional flows with 2D PIV, there is inherent measurement error due to out-of-plane motion. Errors in the measured velocity field propagate to turbulence statistics. Since this can distort the overall flow characteristics, it is important to understand the effect of this out-of-plane error. In this study, the effect of out-of-plane motion on turbulence statistics is quantified. Using forced isotropic turbulence direct numerical simulation (DNS) flow field data provided by the Johns Hopkins turbulence database (JHTDB), synthetic image tests are performed. Turbulence statistics such as turbulence kinetic energy, dissipation rate, Taylor microscale, Kolmogorov scale, and velocity correlations are calculated. Various test cases were simulated while controlling three main parameters which affect the out-of-plane motion: PIV interrogation window size, camera inter-frame time, and laser sheet thickness. The amount of out-of-plane motion was first quantified, and then the error variation according to these parameters was examined. This information can be useful when examining fully three dimensional flows such as homogeneous and isotropic turbulence via 2D PIV.

Dynamics of magnetic flux tubes in accretion discs of T Tauri stars

Abstract Dynamics of slender magnetic flux tubes (MFTs) in the accretion discs of T Tauri stars is investigated. We perform simulations taking into account buoyant, aerodynamic, and turbulent drag forces, radiative heat exchange between MFT and ambient gas, and magnetic field of the disc. The equations of MFT dynamics are solved using Runge–Kutta method of the fourth order. The simulations show that there are two regimes of MFT motion in absence of external magnetic field. In the region r < 0.2 au, the MFTs of radii $0.05 \le a_0 \le 0.16\, H$ (H is the scale height of the disc) with initial plasma beta of 1 experience thermal oscillations above the disc. The oscillations decay over some time, and MFTs continue upward motion afterwards. Thinner or thicker MFTs do not oscillate. MFT velocity increases with initial radius and magnetic field strength. MFTs rise periodically with velocities up to 5–15 km s−1 and periods of 0.5–10 yr determined by the toroidal magnetic field generation time. Approximately 20 per cent of disc mass and magnetic flux can escape to disc atmosphere via the magnetic buoyancy over characteristic time of disc evolution. MFTs dispersal forms expanding magnetized corona of the disc. External magnetic field causes MFT oscillations near the disc surface. These magnetic oscillations have periods from several days to 1–3 months at r < 0.6 au. The magnetic oscillations decay over few periods. We simulate MFT dynamics in accretion discs in the Chameleon I cluster. The simulations demonstrate that MFT oscillations can produce observed IR-variability of T Tauri stars.

Parametric study of the use and optimization of tuned mass dampers to control the wind‐ and seismic‐induced responses of a slender monument

SummaryPassive energy dissipation devices have been used around the world to mitigate the response of structures under dynamic excitations, such as wind or seismic loading. The use of tuned mass dampers (TMD) in tall and slender buildings to reduce unwanted responses has proved to be very effective. The main purpose of this work is to study the structural behavior of a 115‐m‐height slender monument fitted with TMDs subjected to simulated wind and seismic loading. Turbulent wind forces were calculated based on samples of turbulent wind speed simulated with an auto regressive and moving average (ARMA) model. Ground motions compatible with a seismic site spectrum were also simulated. An optimization approach is suggested to determine the parameters of the TMDs that reduce the structural response to the maximum. The effectiveness of the TMDs for reducing the structural response of the monument is discussed in detail, and the use of optimally tuned TMDs is emphasized.

Stochastic modeling of subgrid-scale effects on particle motion in forced isotropic turbulence

Abstract The subgrid-scale effects on particle motion were investigated in forced isotropic turbulence by DNS and prior-LES methods. In the DNS field, the importance of Kolmogorov scaling to preferential accumulation was validated by comparing the radial distribution functions under various particle Stokes numbers. The prior-LES fields were generated by filtering the DNS data. The subgrid-scale Stokes number (StSGS) is a useful tool for determining the effects of subgrid-scale eddies on particle motion. The subgrid-scale eddies tend to accumulate particles with StSGS 1 while has an adverse impact on the particles with StSGS

Turbulent electric current in the marine convective atmospheric boundary layer

The atmospheric boundary layer considered a part of the planetary global electric circuit is known to exhibit a most dramatically changing in space and time atmospheric electrical variables. Extremely low specific electrical conductivity in the lower atmosphere is accompanied by the work of the electric generator associated with turbulent dynamo realizing itself through the space charge transport by boundary layer flows. The electromotive force of this generator acting in fair weather atmospheric regions provides a contribution to the global potential drop between the lower ionosphere and the earth's surface. In this study, the vertical electric current density produced by the turbulent transfer of space charge is investigated in the cases of the buoyancy-dominated and shear-dominated convective boundary layer (CBL) over the oceans based on second-order dissipation-conditioned Lagrangian stochastic model (LSM) applied near air-sea interface and conjugated with first-order LSM in the rest of the CBL. The total electric charge flux is treated in terms of mechanical transfer of atmospheric ions and charged aerosol particles by Lagrangian turbulence together with the drift of small ions in the self-consistent electric field. This approach based on a transported probability density function method offers persuasive advantages for quantitative estimates of local perturbations in the fair-weather electric field created by the atmospheric space charge carried by turbulent flows. It is found that the space charge density vertical profile only slightly depends on turbulence everywhere except for the wavy boundary layer about 10 m thick, a new parameterization of space charge vertical profile is proposed. Based on the simulation results, it can be predicted that in the buoyancy-dominated CBLs the electric field must be greater than in the sheared CBLs with other things being equal. Turbulent electromotive force and changes in total downward atmospheric electric current density are quantified. Simulated vertical profiles of electrical conductivity, space charge, electric field, and turbulent current density reasonably well reproduce previously reported observation results.

Investigation on interphase force modeling for vertical and inclined upward adiabatic bubbly flow

Modeling of interphase forces plays an important role in two-phase bubbly flow simulation. Due to the complexity of two-phase interaction, a substantial number of models have been developed. The applicability and accuracy of these models have been investigated mainly for vertical cases. Study under inclined condition can rarely be found. In the present study the characteristics of different models for interphase forces, including drag force, lift force, wall lubrication force and turbulent dispersion force, are investigated. The effects of interphase forces on the phase distribution for vertical and inclined bubbly flow are evaluated by modeling of DEDALE (Grossetete, 1995) and Xing et al. (2013) experiments. It is found that interphase forces have some different influences on the phase distribution under vertical and inclined condition. Under vertical condition large lift force can result in the high peak of void fraction, whereas under inclined condition the lift force gives the opposite effect due to the change of liquid phase velocity field. Two sets of optimal model combination are obtained by stepwise screening. For the investigated vertical cases a set of model combination including the Ishii-Zuber drag force model, Saffman-Mei lift force model, Hosokawa wall lubrication force model and FAD turbulent dispersion force model is preferable. For investigated inclined cases a set of model combination including the Simonnet drag force model, Tomiyama lift force model, Hosokawa wall lubrication force model and FAD turbulent dispersion force model is the most suitable.

Numerical investigation on the influencing interphase forces on bubble size distribution around NACA0015 hydrofoil

Two-phase bubbly flows are prevalent in many industries and in nature. The aeration process that happens in the auto-venting turbine (AVT) is involved with two-phase bubbly flow downstream the turbine. The quality of the water in the turbine downstream is directly impacted by the bubble size distribution in the wake of turbine hydrofoils. In order to be able to accurately capture the physics associated with this process numerically, the interphase forces need to be considered carefully. Therefore, in this paper, the influence of interphase forces on the bubble size distribution around an NACA0015 hydrofoil is investigated. The numerical simulations require the consideration of the dynamic behaviors of two-phase flow and bubbles undergoing coalescence and breakup. For this purpose, the ensemble-averaged mass and momentum transport equations for continuous and dispersed phases are modeled within the two-fluid modelling framework. These equations are coupled with population balance equations (PBEs) to aptly account for the coalescence and breakup of the bubbles. The influence of the interphase forces: drag, lift, wall lubrication, virtual mass, turbulent dispersion forces, and turbulence transfer models, on the resulting bubble size distribution, is investigated and compared to existing experimental data.

Applying resolved-scale linearly forced isotropic turbulence in rational subgrid-scale modeling

In previous attempts of rational subgrid-scale (SGS) modeling by employing the Kolmogorov equation of filtered (KEF) quantities, it was necessary to assume that the resolved-scale second-order structure function is stationary. Forced isotropic turbulence is often used as a framework for establishing and validating such SGS models based on stationary restrictions, for it generates statistical stationary samples. However, traditional forcing method at low wavenumbers cannot provide an analytic form of forcing term for a complete KEF in physical space, which has been illustrated to be essential in the modeling of such SGS models. Thus, an alternative forcing method giving an analytic forcing term in physical space is needed for rational SGS modeling. Giving an analytic linear driving term in physical space, linearly forced isotropic turbulence should be considered an ideal theoretical framework for rational SGS modeling. In this paper, we demonstrate the feasibility of establishing a rational SGS model with stationary restriction based on linearly forced isotropic turbulence. The performance of this rational SGS model is validated. We, therefore, propose the use of linearly forced isotropic turbulence as a complement to free-decaying isotropic turbulence and low-wavenumber forced isotropic turbulence for SGS model validations.

Scale-dependent anisotropy in forced stratified turbulence

Scale-dependent anisotropy in forced stratified turbulence

Finite-time blow-up of classical solutions to the rotating shallow water system with degenerate viscosity

In this paper, we study the rotating shallow water system with initial data containing vacuum, the viscosity of the system is degenerate, and the Coriolis force, the capillary force and the turbulent drag force from fiction are involved. When a positive mass is surrounding by a bounded vacuum region (isolated mass group), initially, we prove that any classical solutions to the initial-boundary-value problem and periodic problem will blow up in finite time. This shows that the global weak solutions obtained in Bresch and Desjardins (Commun Math Phys 238(1–2):211–223, 2003) cannot be a classical one as long as the initial data admit an isolated mass group. It also shows that compared with the smoothing properties provided by capillarity and drag terms, the degeneracy of viscosity plays a prominent role in the global regularity problem and leads to finite-time singularity of smooth solutions.

Interphase forces analysis in the whole flow passage of a multiphase rotodynamic pump

To understand the internal flow and interphase forces characteristics in the multiphase rotodynamic pump, simulations were performed using ANSYS_CFX for the whole flow passage with medium combination of air-water. The reliability of simulation was verified by comparing with the experimental data of external characteristics. The results showed that the drag is dominant for the interphase forces in the impeller and guide vane passages, followed by the lift and added mass forces, then the turbulent dispersion force, and it can be neglected relative to drag. With the increased IGVF (inlet gas void fraction), all interphase forces in the impeller and guide vane passages will increase, also, the variation range of interphase forces in the impeller was greater than that in the guide vane.

Condensate in quasi-two-dimensional turbulence

Three-dimensional numerical simulations of forced turbulence in a thin layer show the transfer from the forcing to larger scales is by two-dimensional modes, and to smaller scales by three-dimensional modes, the latter providing a viscosity-independent dissipation.

Numerical study of trailing and leading vortex dynamics in a forced jet with coflow

The interaction of trailing and leading vortex structures in low Reynolds number (R = 1000) forced (varicose) jet with coflow is studied using Direct Numerical Simulation (DNS), where we report the dynamics of these vortices for a range of varying parameters. In a circular forced jet with Strouhal number 0.2, continuous formation of these vortices is observed which undergo pairing, tearing and disintegration. The forced jet is analyzed for varying frequency of forced perturbations, coflow temperature, turbulence intensity, momentum thickness, coflow intensity and Reynolds number at a constant forcing amplitude (15%). The observation reveals that any reduction in momentum thickness increases the circulation as well as energy capacity of the leading and the trailing vortices, thereby enhancing the vortex pairing time. However, the hot coflow increases the strength of the leading vortex to such an extent that the generated trailing vortex is weak and dissipates even before it undergoes vortex pairing, while an incomplete disintegration of the leading vortex occurs in this case. Moreover, the strength of leading and trailing vortices is found to decrease with an increase in coflow power, thereby leading to a weaker vortex pairing. The decrease in Reynolds number also reduces the intensity of trailing vortices; whereas, at a lower Reynolds number (Re) the trailing vortices dissipate soon after they form. The findings are achieved based on the analysis done by Proper Orthogonal Decomposition (POD), Dynamic Mode Decomposition (DMD), fast Fourier transform (FFT), Q-criterion and vortex tracking method to understand the dynamic interaction and behavior of the vortices.

Cosmic-ray propagation in the bi-stable interstellar medium

Context. Cosmic rays propagate through the galactic scales down to the smaller scales at which stars form. Cosmic rays are close to energy equipartition with the other components of the interstellar medium and can provide a support against gravity if pressure gradients develop. Aims. We study the propagation of cosmic rays within the turbulent and magnetised bi-stable interstellar gas. The conditions necessary for cosmic-ray trapping and cosmic-ray pressure gradient development are investigated. Methods. We derived an analytical value of the critical diffusion coefficient for cosmic-ray trapping within a turbulent medium, which follows the observed scaling relations. We then presented a numerical study using 3D simulations of the evolution of a mixture of interstellar gas and cosmic rays, in which turbulence is driven at varying scales by stochastic forcing within a box of 40 pc. We explored a large parameter space in which the cosmic-ray diffusion coefficient, the magnetisation, the driving scale, and the amplitude of the turbulence forcing, as well as the initial cosmic-ray energy density, vary. Results. We identify a clear transition in the interstellar dynamics for cosmic-ray diffusion coefficients below a critical value deduced from observed scaling relations. This critical diffusion depends on the characteristic length scale L of Dcrit ≃ 3.1 × 1023 cm2 s−1(L/1 pc)q+1, where the exponent q relates the turbulent velocity dispersion σ to the length scale as σ ~ Lq. Hence, in our simulations this transition occurs around Dcrit ≃ 1024–1025 cm2 s−1. The transition is recovered in all cases of our parameter study and is in very good agreement with our simple analytical estimate. In the trapped cosmic-ray regime, the induced cosmic-ray pressure gradients can modify the gas flow and provide a support against the thermal instability development. We discuss possible mechanisms that can significantly reduce the cosmic-ray diffusion coefficients within the interstellar medium. Conclusions. Cosmic-ray pressure gradients can develop and modify the evolution of thermally bi-stable gas for diffusion coefficients D0 ≤ 1025 cm2 s−1 or in regions where the cosmic-ray pressure exceeds the thermal one by more than a factor of ten. This study provides the basis for further works including more realistic cosmic-ray diffusion coefficients, as well as local cosmic-ray sources.

Examining and extending the concept of machine acceleration used in modelling the bubble-particle detachment in flotation

The bubble-particle (BP) detachment is a significant factor in controlling the recovery of coarse particles in mechanical flotation cells. It has been quantified by balancing the restoring force of surface tension and the centrifugal force exerted on the particle-bubble aggregate by the turbulent flow field using a “machine acceleration”. The concept of machine acceleration is useful because it links the mean energy dissipation rate of turbulence with the condition of the BP detachment. Here we further examine the concept of machine acceleration by applying the theory of isotropic turbulence. We confirm the known results of the first approximation for the inertial subrange. We also show that the turbulence acceleration has two principal components, i.e., the longitudinal and transverse components measured relatively to the BP centre-line. Significantly, the longitudinal component corresponds to the centrifugal force of turbulence against the restoring force of surface tension. The transverse component can be significant to quantifying the BP detachment if the turbulence shear is strong. We also extend the theory to cover the full range of isotropic turbulence, from the viscous to inertial subranges. Our estimation of the transition from the viscous to inertial subrange shows that the viscous effect can critically affect the BP detachment. Finally, our assessment of the contributions of the longitudinal and transverse components to the machine acceleration reveals the importance of the transverse component which can lead to a rather poor approximation for the machine acceleration as currently used. This paper shows that the effect of turbulence on the BP detachment should be better quantified using both the longitudinal and transverse components of turbulence acceleration rather than their modulus as the first approximation being termed the machine acceleration.

Direct numerical simulation of turbulence over systematically varied irregular rough surfaces

Lattice Boltzmann direct numerical simulation of turbulent open-channel flows over randomly distributed hemispheres at $Re_{\unicode[STIX]{x1D70F}}=600$ is carried out to reveal the influence of roughness parameters related to a probability density function of rough-surface elevation on turbulence by analysing the spatial and Reynolds- (double-) averaged Navier–Stokes equation. This study specifically concentrates on the influence of the root-mean-square roughness and the skewness, and profiles of turbulence statistics are compared by introducing an effective wall-normal distance defined as a wall-normal integrated plane porosity. The effective distance can completely collapse the total shear stress outside the roughness sublayer, and thus the similarity of the streamwise mean velocity is clearer by introducing the effective distance. In order to examine the influence of the root-mean-square roughness and the skewness on dynamical effects that contribute to an increase in the skin friction coefficient, the triple-integrated double-averaged Navier–Stokes equation is analysed. The main contributors to the skin friction coefficient are found to be turbulence and drag force. The turbulence contribution increases with the root-mean-square roughness and/or the skewness. The drag force contribution, on the other hand, increases in particular with the root-mean-square roughness whereas an increase in the skewness does not increase the drag force contribution because it does not necessarily increase the surface area of the roughness elements. The contribution of the mean velocity dispersion induced by spatial inhomogeneity of the rough surfaces substantially increases with the root-mean-square roughness. A linear correlation is confirmed between the root-mean-square roughness and the equivalent roughness while the equivalent roughness monotonically increases with the skewness. A new correlation function based on the root-mean-square roughness and the skewness is developed with the available experimental and direct numerical simulation data, and it is confirmed that the developed correlation reasonably predicts the equivalent roughness of various types of real rough surfaces.

CFD simulation of hydrodynamics in a high-pressure bubble column using three optimized drag models of bubble swarm

The gas–liquid flow characteristics in an air–water system were studied using electrical resistance tomography (ERT) in a pressurized gas–liquid bubble column with an inner diameter of 0.30 m and a height of 6.60 m. The effects of the superficial gas velocity and system pressure on the radial gas holdup were investigated under superficial gas velocities (0.120–0.312 m/s) and system pressures (0.5–2.0 MPa). Two-fluid computational fluid dynamics (CFD) was used to simulate the hydrodynamics of the bubble column in two- and three-dimensions, and the drag force, transverse lift force, turbulent dispersion force, and wall lubrication force were introduced for model correction. Based on the determination of the transverse lift force, turbulent diffusion force, and wall lubrication force in previous works of our group, three different of drag model schemes were proposed in this study. In the Model A, based on Roghair's drag model, a density correction and the gas holdup of large and small bubbles were introduced to correct the model; in the Model B, while the gas holdup of large bubbles was greater than 0.08, the influence of small bubbles was ignored. The small bubbles and liquid were integrated into a single phase (the dense phase), while the large bubbles were the dilute phase; in the Model C, an energy minimization multi-scale (EMMS) concept based on the double bubble size model was used, and relationship between the drag coefficient and the bubble diameter were introduced to modify the models. Moreover, through optimizing adjustment of the model parameter, the simulation results with the three models were found to be consistent with the experimental results obtained from ERT technique. These results may facilitate improvements in the design and scale-up of bubble columns with high-pressure and high superficial gas velocities, as well as the significance of further research.