# Latest papers in fluid mechanics

### Settling dynamics of two spheres in a suspension of Brownian rods

Physics of Fluids - Wed, 07/03/2019 - 06:04
Physics of Fluids, Volume 31, Issue 7, July 2019.
We investigate via numerical simulations the settling dynamics of two non-Brownian rigid spheres in a dilute suspension of Brownian rods at low Reynolds numbers. Specifically, this work focuses on how the overall settling dynamics is affected by the coupling between the flow field around the spheres and the orientation of the rods. The Brownian motion introduces a finite relaxation time in the suspending medium which is modeled as a continuum. When the spheres fall along their centerline, the spheres experience two contributions: one Newtonian and a non-Newtonian contribution due to the presence of the Brownian rods. The interactions between the two settling spheres are evaluated as a function of Péclet number (Pe) and the distance between the centers of the spheres. Repulsive interactions are found, and these interactions are affected by Pe and the distance between the centers of the spheres. An analysis of the flow fields highlights the origin of these repulsive interactions in non-Newtonian elongational effects.

### Settling dynamics of two spheres in a suspension of Brownian rods

Physics of Fluids - Wed, 07/03/2019 - 06:04
Physics of Fluids, Volume 31, Issue 7, July 2019.
We investigate via numerical simulations the settling dynamics of two non-Brownian rigid spheres in a dilute suspension of Brownian rods at low Reynolds numbers. Specifically, this work focuses on how the overall settling dynamics is affected by the coupling between the flow field around the spheres and the orientation of the rods. The Brownian motion introduces a finite relaxation time in the suspending medium which is modeled as a continuum. When the spheres fall along their centerline, the spheres experience two contributions: one Newtonian and a non-Newtonian contribution due to the presence of the Brownian rods. The interactions between the two settling spheres are evaluated as a function of Péclet number (Pe) and the distance between the centers of the spheres. Repulsive interactions are found, and these interactions are affected by Pe and the distance between the centers of the spheres. An analysis of the flow fields highlights the origin of these repulsive interactions in non-Newtonian elongational effects.

### Investigation of chemical reaction during sodium alginate drop impact on calcium chloride film

Physics of Fluids - Wed, 07/03/2019 - 06:04
Physics of Fluids, Volume 31, Issue 7, July 2019.
The objective of this work is to study the chemical reaction between sodium alginate drop and calcium chloride film and instantaneous formation of calcium alginate gel. The complexity of this work is the simultaneous effect of both liquid and solid surface on drop impact gelation process. The sodium alginate concentration in the drop fluid, liquid film thickness, and drop impingement height are varied and the observations are captured using a high speed camera. Several interesting phenomena like splashing and jet break up occur depending on the drop impingement velocity, drop concentration, and film thickness. Crosslinking reaction and mixing mechanisms are schematically explained accounting the role of capillary wave propagation within the liquid film. A mathematical model on drop spreading on the solid surface after penetrating the liquid film is developed to predict the theoretical gel length for ultrathin and thin film regimes. Maximum spreading diameter of the drop postimpact on the liquid film is predicted from the model. However, the experimentally measured solidified gel length deviates from the theoretical values and these deviations are utilized to measure the rate of crosslinking gelation and instantaneous solidification. Different hydrodynamic parameters such as the crater depth, crater contact time, and crater dissipation energy are evaluated for the dynamics of gelation. Finally, the kinetics of gelation with the variation of liquid film thickness are determined for alginate drop concentrations and drop impingement heights.

### Investigation of chemical reaction during sodium alginate drop impact on calcium chloride film

Physics of Fluids - Wed, 07/03/2019 - 06:04
Physics of Fluids, Volume 31, Issue 7, July 2019.
The objective of this work is to study the chemical reaction between sodium alginate drop and calcium chloride film and instantaneous formation of calcium alginate gel. The complexity of this work is the simultaneous effect of both liquid and solid surface on drop impact gelation process. The sodium alginate concentration in the drop fluid, liquid film thickness, and drop impingement height are varied and the observations are captured using a high speed camera. Several interesting phenomena like splashing and jet break up occur depending on the drop impingement velocity, drop concentration, and film thickness. Crosslinking reaction and mixing mechanisms are schematically explained accounting the role of capillary wave propagation within the liquid film. A mathematical model on drop spreading on the solid surface after penetrating the liquid film is developed to predict the theoretical gel length for ultrathin and thin film regimes. Maximum spreading diameter of the drop postimpact on the liquid film is predicted from the model. However, the experimentally measured solidified gel length deviates from the theoretical values and these deviations are utilized to measure the rate of crosslinking gelation and instantaneous solidification. Different hydrodynamic parameters such as the crater depth, crater contact time, and crater dissipation energy are evaluated for the dynamics of gelation. Finally, the kinetics of gelation with the variation of liquid film thickness are determined for alginate drop concentrations and drop impingement heights.

### On the formation and morphology of coherent particulate structures in non-isothermal enclosures subjected to rotating g-jitters

Physics of Fluids - Wed, 07/03/2019 - 06:04
Physics of Fluids, Volume 31, Issue 7, July 2019.
The strategy undertaken in the author’s earlier work [M. Lappa, “The patterning behaviour and accumulation of spherical particles in a vibrated non-isothermal liquid,” Phys. Fluids 26(9), 093301 (2014) and M. Lappa, “On the multiplicity and symmetry of particle attractors in confined non-isothermal fluids subjected to inclined vibrations,” Int. J. Multiphase Flow 93, 71–83 (2017)] based on the use of polarized (purely translational) vibrations for achieving the segregation or accumulation of solid particles in specific regions of an initially dilute dispersion is further pursued by allowing the direction of vibrations to change in time with respect to the applied temperature difference. In particular, the potential of the considered approach in separating the particles from the liquid is explored under the assumption that the angular velocity by which the vibrations axis rotates about a fixed axis is of the same order of magnitude or smaller (one or two orders of magnitude) than the frequency of shaking. A new family of particle coherent structures is identified in the physical space, which can be distinguished from the companion category of particle attractors for fixed vibration direction due to its increased symmetry properties. It is shown how the average nonlinear effects produced by the rotation of the vibration axis, together with those induced by the finite size of the enclosure, accumulate over time leading to the observed fascinating variety of symmetrical patterns.

### On the formation and morphology of coherent particulate structures in non-isothermal enclosures subjected to rotating g-jitters

Physics of Fluids - Wed, 07/03/2019 - 06:04
Physics of Fluids, Volume 31, Issue 7, July 2019.
The strategy undertaken in the author’s earlier work [M. Lappa, “The patterning behaviour and accumulation of spherical particles in a vibrated non-isothermal liquid,” Phys. Fluids 26(9), 093301 (2014) and M. Lappa, “On the multiplicity and symmetry of particle attractors in confined non-isothermal fluids subjected to inclined vibrations,” Int. J. Multiphase Flow 93, 71–83 (2017)] based on the use of polarized (purely translational) vibrations for achieving the segregation or accumulation of solid particles in specific regions of an initially dilute dispersion is further pursued by allowing the direction of vibrations to change in time with respect to the applied temperature difference. In particular, the potential of the considered approach in separating the particles from the liquid is explored under the assumption that the angular velocity by which the vibrations axis rotates about a fixed axis is of the same order of magnitude or smaller (one or two orders of magnitude) than the frequency of shaking. A new family of particle coherent structures is identified in the physical space, which can be distinguished from the companion category of particle attractors for fixed vibration direction due to its increased symmetry properties. It is shown how the average nonlinear effects produced by the rotation of the vibration axis, together with those induced by the finite size of the enclosure, accumulate over time leading to the observed fascinating variety of symmetrical patterns.

### Effect of wall proximity on the flow over a cube and the implications for the noise emitted

Physics of Fluids - Wed, 07/03/2019 - 06:04
Physics of Fluids, Volume 31, Issue 7, July 2019.
The flow over an object such as a cube and the resulting aerodynamic noise are affected by its proximity to a wall. To evaluate the effect of wall proximity on the aerodynamics induced by a cube, numerical investigations have been performed for the flow past the cube elevated to different heights above a solid surface, using the delayed detached eddy simulation method. A benchmark case of a wall-mounted cube in uniform flow is first studied, which gives commendable agreement with the available measurement results, validating the numerical methodology adopted. Subsequently, the cube is elevated to different heights above the ground. Detailed flow topologies around the cube affected by the elevated height are investigated. In addition, the effect of wall proximity on near-wall flow patterns and distributions of the surface pressure are also analyzed. After examining the flow features, the far-field noise emitted from the cube at different elevated heights is predicted by using the Ffowcs Williams-Hawkings acoustic analogy and some implications of the effect of wall proximity on the emitted noise are summarized. For the wall-mounted cube, the noise is greatest along the lateral direction. As the cube is lifted, the radiated sound in the vertical direction increases rapidly and peaks at one quarter of its side length above the ground. The noise induced by the cube tends to be broadband although broad peaks at a Strouhal number of around 0.1 are observed in the vertical and the lateral directions.

### Effect of wall proximity on the flow over a cube and the implications for the noise emitted

Physics of Fluids - Wed, 07/03/2019 - 06:04
Physics of Fluids, Volume 31, Issue 7, July 2019.
The flow over an object such as a cube and the resulting aerodynamic noise are affected by its proximity to a wall. To evaluate the effect of wall proximity on the aerodynamics induced by a cube, numerical investigations have been performed for the flow past the cube elevated to different heights above a solid surface, using the delayed detached eddy simulation method. A benchmark case of a wall-mounted cube in uniform flow is first studied, which gives commendable agreement with the available measurement results, validating the numerical methodology adopted. Subsequently, the cube is elevated to different heights above the ground. Detailed flow topologies around the cube affected by the elevated height are investigated. In addition, the effect of wall proximity on near-wall flow patterns and distributions of the surface pressure are also analyzed. After examining the flow features, the far-field noise emitted from the cube at different elevated heights is predicted by using the Ffowcs Williams-Hawkings acoustic analogy and some implications of the effect of wall proximity on the emitted noise are summarized. For the wall-mounted cube, the noise is greatest along the lateral direction. As the cube is lifted, the radiated sound in the vertical direction increases rapidly and peaks at one quarter of its side length above the ground. The noise induced by the cube tends to be broadband although broad peaks at a Strouhal number of around 0.1 are observed in the vertical and the lateral directions.

### Theoretical analysis of tensor perturbations for uncertainty quantification of Reynolds averaged and subgrid scale closures

Physics of Fluids - Wed, 07/03/2019 - 06:03
Physics of Fluids, Volume 31, Issue 7, July 2019.
With the advent of improved computational resources, alternate design approaches that explicitly account for uncertainty in predictions, such as robust- and reliability-based design, are superseding deterministic design approaches in aerospace applications. In this context, accounting for the structural uncertainties in turbulence models has been identified as the greatest challenge toward simulation based design. At present, the primary methodology to estimate the structural uncertainty in turbulence models is based on tensor perturbations applied to the modeled Reynolds stress tensor. This methodology has been applied with success to a variety of problems in engineering analysis and design under uncertainty. However, the modeling rationale of this perturbation approach is still not unearthed. While we know that the procedure works in generating uncertainty estimates that account for the discrepancy in turbulence simulations, we do not know why it works or even how exactly it works. This may lead to its application to cases of turbulent flows or under conditions where it should not perform well. This could potentially lead to analyses that are misleading, or even designs that are hazardous. In this article, we outline the underlying modeling structure represented by this tensor perturbation procedure. The exact limitations addressed by each step of the perturbation methodology are isolated and explicated. This analysis enables us to identify the limitations of this procedure and outline the specific phenomena and types of turbulence model uncertainty where its application would be equivocal. Additionally, we outline how this enables us to derive quasirealizability conditions on the perturbations.

### Theoretical analysis of tensor perturbations for uncertainty quantification of Reynolds averaged and subgrid scale closures

Physics of Fluids - Wed, 07/03/2019 - 06:03
Physics of Fluids, Volume 31, Issue 7, July 2019.
With the advent of improved computational resources, alternate design approaches that explicitly account for uncertainty in predictions, such as robust- and reliability-based design, are superseding deterministic design approaches in aerospace applications. In this context, accounting for the structural uncertainties in turbulence models has been identified as the greatest challenge toward simulation based design. At present, the primary methodology to estimate the structural uncertainty in turbulence models is based on tensor perturbations applied to the modeled Reynolds stress tensor. This methodology has been applied with success to a variety of problems in engineering analysis and design under uncertainty. However, the modeling rationale of this perturbation approach is still not unearthed. While we know that the procedure works in generating uncertainty estimates that account for the discrepancy in turbulence simulations, we do not know why it works or even how exactly it works. This may lead to its application to cases of turbulent flows or under conditions where it should not perform well. This could potentially lead to analyses that are misleading, or even designs that are hazardous. In this article, we outline the underlying modeling structure represented by this tensor perturbation procedure. The exact limitations addressed by each step of the perturbation methodology are isolated and explicated. This analysis enables us to identify the limitations of this procedure and outline the specific phenomena and types of turbulence model uncertainty where its application would be equivocal. Additionally, we outline how this enables us to derive quasirealizability conditions on the perturbations.

### Flow dynamics of a dandelion pappus: A linear stability approach

Physical Review Fluids - Tue, 07/02/2019 - 11:00

Author(s): P. G. Ledda, L. Siconolfi, F. Viola, S. Camarri, and F. Gallaire

A dandelion pappus is modelled as a porous disk. A stability analysis finds that if the disk is sufficiently porous the steady wake is stable and consists in a separated recirculating vortex ring, which allows a long-distance dispersal of the dandelion seeds.

[Phys. Rev. Fluids 4, 071901(R)] Published Tue Jul 02, 2019

### Effect of the irreversible $\text{A}+\text{B}→\text{C}$ reaction on the onset and the growth of the buoyancy-driven instability in a porous medium: Asymptotic, linear, and nonlinear stability analyses

Physical Review Fluids - Tue, 07/02/2019 - 11:00

Author(s): Min Chan Kim

A theoretical analysis of the effect of an irreversible A+B→C reaction on the growth of a buoyancy-driven instability in a Hele-Shaw cell, taking different diffusivities into account, is presented.

[Phys. Rev. Fluids 4, 073901] Published Tue Jul 02, 2019

### A lattice Boltzmann method for simulating viscoelastic drops

Physics of Fluids - Tue, 07/02/2019 - 04:38
Physics of Fluids, Volume 31, Issue 7, July 2019.
We report some numerical simulations of multiphase viscoelastic fluids based on an algorithm that employs a diffusive-interface lattice Boltzmann method together with a lattice advection-diffusion scheme, the former used to model the macroscopic hydrodynamic equations for multiphase fluids and the latter to describe the polymer dynamics modeled by the Oldroyd-B constitutive model. The multiphase model is validated by a simulation of Newtonian drop deformation under steady shear. The viscoelastic model is validated by simulating a simple shear flow of an Oldroyd-B fluid. The coupled algorithm is used to simulate the viscoelastic drop deformation in shear flow. The numerical results are compared with the results from conventional methods, showing a good agreement. We study the viscosity (density) ratio effect on the bubble rising in viscoelastic liquids and demonstrate a nonmonotonic relation between the length of the bubble tail and the polymer relaxation time.

### A lattice Boltzmann method for simulating viscoelastic drops

Physics of Fluids - Tue, 07/02/2019 - 04:38
Physics of Fluids, Volume 31, Issue 7, July 2019.
We report some numerical simulations of multiphase viscoelastic fluids based on an algorithm that employs a diffusive-interface lattice Boltzmann method together with a lattice advection-diffusion scheme, the former used to model the macroscopic hydrodynamic equations for multiphase fluids and the latter to describe the polymer dynamics modeled by the Oldroyd-B constitutive model. The multiphase model is validated by a simulation of Newtonian drop deformation under steady shear. The viscoelastic model is validated by simulating a simple shear flow of an Oldroyd-B fluid. The coupled algorithm is used to simulate the viscoelastic drop deformation in shear flow. The numerical results are compared with the results from conventional methods, showing a good agreement. We study the viscosity (density) ratio effect on the bubble rising in viscoelastic liquids and demonstrate a nonmonotonic relation between the length of the bubble tail and the polymer relaxation time.

### Fluidity enhancement of hard-to-fluidize nanoparticles by mixing with hydrophilic nanosilica and fluid catalytic cracking particles: Experimental and theoretical study

Physics of Fluids - Tue, 07/02/2019 - 04:38
Physics of Fluids, Volume 31, Issue 7, July 2019.
As a low-cost method, hydrophilic SiO2 nanoparticles (NPs) and fluid catalytic cracking (FCC) coarse particles were used as assistant materials to improve the fluidity of Al2O3 and TiO2 hard-to-fluidize nanopowders. To decrease the strong electrostatic forces between the hydrophilic nanopowders, prepared samples were fluidized in the presence of methanol vapor. Results revealed that the amount of SiO2 NPs, increased from 5 to 50 wt. %, has a beneficial effect on the fluidization quality of the binary (hard-to-fluidize NPs + SiO2) and ternary (hard-to-fluidize NPs + SiO2 + FCC) mixtures. However, the amount of FCC particles when it varied from 15 to 30 wt. % in the ternary mixtures should meet the optimal point, beyond which the fluidization quality was declined due to the segregation phenomenon. The laboratory results showed that the cost-effective ternary samples fluidized more homogeneously with higher bed expansions compared to the binary samples. In this regard, (Al2O3 + 20 wt. % SiO2) + 15 wt. % FCC and (TiO2 + 20 wt. % SiO2) + 15 wt. % FCC ternary samples were proposed as the alternatives of Al2O3 + 50 wt. % SiO2 and TiO2 + 50 wt. % SiO2 binary mixtures, respectively.

### Fluidity enhancement of hard-to-fluidize nanoparticles by mixing with hydrophilic nanosilica and fluid catalytic cracking particles: Experimental and theoretical study

Physics of Fluids - Tue, 07/02/2019 - 04:38
Physics of Fluids, Volume 31, Issue 7, July 2019.
As a low-cost method, hydrophilic SiO2 nanoparticles (NPs) and fluid catalytic cracking (FCC) coarse particles were used as assistant materials to improve the fluidity of Al2O3 and TiO2 hard-to-fluidize nanopowders. To decrease the strong electrostatic forces between the hydrophilic nanopowders, prepared samples were fluidized in the presence of methanol vapor. Results revealed that the amount of SiO2 NPs, increased from 5 to 50 wt. %, has a beneficial effect on the fluidization quality of the binary (hard-to-fluidize NPs + SiO2) and ternary (hard-to-fluidize NPs + SiO2 + FCC) mixtures. However, the amount of FCC particles when it varied from 15 to 30 wt. % in the ternary mixtures should meet the optimal point, beyond which the fluidization quality was declined due to the segregation phenomenon. The laboratory results showed that the cost-effective ternary samples fluidized more homogeneously with higher bed expansions compared to the binary samples. In this regard, (Al2O3 + 20 wt. % SiO2) + 15 wt. % FCC and (TiO2 + 20 wt. % SiO2) + 15 wt. % FCC ternary samples were proposed as the alternatives of Al2O3 + 50 wt. % SiO2 and TiO2 + 50 wt. % SiO2 binary mixtures, respectively.

### Characteristics of liquefied soil motion in wavy environment

Physics of Fluids - Tue, 07/02/2019 - 04:38
Physics of Fluids, Volume 31, Issue 7, July 2019.
The soil on a seabed will fluctuate with the waves after liquefaction. In this paper, the Massachusetts Institute of Technology General Circulation Model (MITgcm) is applied to investigate the particle movement of the liquefied soil. In the model, viscosity and other parameters were appropriately adjusted to simulate the motion of liquefied soil. The simulated results are consistent with the experimental results. When compared with the theory of Stokes wave, the model is more accurate as the viscosity is taken into consideration. The aforementioned results demonstrate that the MITgcm can be applied successfully to simulate the liquefied soil.

### Characteristics of liquefied soil motion in wavy environment

Physics of Fluids - Tue, 07/02/2019 - 04:38
Physics of Fluids, Volume 31, Issue 7, July 2019.
The soil on a seabed will fluctuate with the waves after liquefaction. In this paper, the Massachusetts Institute of Technology General Circulation Model (MITgcm) is applied to investigate the particle movement of the liquefied soil. In the model, viscosity and other parameters were appropriately adjusted to simulate the motion of liquefied soil. The simulated results are consistent with the experimental results. When compared with the theory of Stokes wave, the model is more accurate as the viscosity is taken into consideration. The aforementioned results demonstrate that the MITgcm can be applied successfully to simulate the liquefied soil.

### Numerical studies of the flow structure and aerodynamic forces on two tandem square cylinders with different chamfered-corner ratios

Physics of Fluids - Tue, 07/02/2019 - 04:38
Physics of Fluids, Volume 31, Issue 7, July 2019.
Three-dimensional large eddy simulations were carried out to investigate the flow over two tandem square cylinders for a fixed spacing ratio of L/D = 4 and a Reynolds number of 5.3 × 103, where L is the cylinder center-to-center distance between the cylinders and D is the cylinder width. The corners of each cylinder were chamfered with a ratio of ξ = B/D = 0%, 5%, 10%, and 15%, where B is the chamfered corner dimension. The focus is given on how ξ influences the flow structure, wake recirculation bubble, flow separation bubble, Strouhal number (St), aerodynamic force, and phase lag (ϕ) between vortex sheddings from the cylinders. With increasing ξ, the recirculation bubble length and minimum velocity in the wake of the upstream cylinder remain more or less constant and are close to those of a single cylinder, while the minimum velocity in the wake of the downstream cylinder dramatically drops between ξ = 0% and 5%. While the flow over the downstream remains attached on the side surfaces, that over the upstream cylinder forms primary and secondary side-surface bubbles on the side surface, and both shrink with increasing ξ. In addition, the leading chamfered corners are accompanied by corner bubbles that play an important role in the flow structure modification. Therefore, the time-mean drag and fluctuating lift of the upstream cylinder remarkably decrease for 0% ≤ ξ ≤ 5% and remain almost unchanged for 5% < ξ ≤ 15%, whereas those on the downstream cylinder diminish in the whole range of 0% ≤ ξ ≤ 15%. The Strouhal number (St) being identical for the two cylinders grows from 0.104 to 0.132 when ξ is increased from 0% to 15%. Overall, the influence of ξ on the wake structure and aerodynamics is remarkable for 0% ≤ ξ ≤ 5% because of the corner bubbles and is less for 5% < ξ ≤ 15%.

### Numerical studies of the flow structure and aerodynamic forces on two tandem square cylinders with different chamfered-corner ratios

Physics of Fluids - Tue, 07/02/2019 - 04:38
Physics of Fluids, Volume 31, Issue 7, July 2019.
Three-dimensional large eddy simulations were carried out to investigate the flow over two tandem square cylinders for a fixed spacing ratio of L/D = 4 and a Reynolds number of 5.3 × 103, where L is the cylinder center-to-center distance between the cylinders and D is the cylinder width. The corners of each cylinder were chamfered with a ratio of ξ = B/D = 0%, 5%, 10%, and 15%, where B is the chamfered corner dimension. The focus is given on how ξ influences the flow structure, wake recirculation bubble, flow separation bubble, Strouhal number (St), aerodynamic force, and phase lag (ϕ) between vortex sheddings from the cylinders. With increasing ξ, the recirculation bubble length and minimum velocity in the wake of the upstream cylinder remain more or less constant and are close to those of a single cylinder, while the minimum velocity in the wake of the downstream cylinder dramatically drops between ξ = 0% and 5%. While the flow over the downstream remains attached on the side surfaces, that over the upstream cylinder forms primary and secondary side-surface bubbles on the side surface, and both shrink with increasing ξ. In addition, the leading chamfered corners are accompanied by corner bubbles that play an important role in the flow structure modification. Therefore, the time-mean drag and fluctuating lift of the upstream cylinder remarkably decrease for 0% ≤ ξ ≤ 5% and remain almost unchanged for 5% < ξ ≤ 15%, whereas those on the downstream cylinder diminish in the whole range of 0% ≤ ξ ≤ 15%. The Strouhal number (St) being identical for the two cylinders grows from 0.104 to 0.132 when ξ is increased from 0% to 15%. Overall, the influence of ξ on the wake structure and aerodynamics is remarkable for 0% ≤ ξ ≤ 5% because of the corner bubbles and is less for 5% < ξ ≤ 15%.