# Physics of Fluids

Table of Contents for Physics of Fluids. List of articles from both the latest and ahead of print issues.

*Updated:*10 hours 49 min ago

### Evaluation of particle-based continuum methods for a coupling with the direct simulation Monte Carlo method based on a nozzle expansion

Physics of Fluids, Volume 31, Issue 7, July 2019.

This paper investigates three different particle-based continuum methods, the ellipsoidal statistical Bhatnagar-Gross-Krook (ESBGK) and Fokker-Planck (ESFP) methods and the Low Diffusion (LD) method, for a coupling with the direct simulation Monte Carlo (DSMC) method. After a short description of the methods and their implementation, including the coupling concept for the LD-DSMC, simulation results of a nozzle expansion are compared with available experimental measurements and a DSMC simulation. Excellent agreement between ESBGK, ESFP, and DSMC can be observed in the throat of the nozzle, while the LD method fails to predict the correct velocity, temperature, and density profile. Further downstream, only the DSMC and the coupled ESBGK/ESFP-DSMC simulations are able to reproduce the measured rotational temperature profiles. A performance comparison shows the possible computational savings of a coupled ESBGK/ESFP-DSMC simulation, where a speedup of four orders of magnitude can be observed compared to a regular DSMC simulation.

This paper investigates three different particle-based continuum methods, the ellipsoidal statistical Bhatnagar-Gross-Krook (ESBGK) and Fokker-Planck (ESFP) methods and the Low Diffusion (LD) method, for a coupling with the direct simulation Monte Carlo (DSMC) method. After a short description of the methods and their implementation, including the coupling concept for the LD-DSMC, simulation results of a nozzle expansion are compared with available experimental measurements and a DSMC simulation. Excellent agreement between ESBGK, ESFP, and DSMC can be observed in the throat of the nozzle, while the LD method fails to predict the correct velocity, temperature, and density profile. Further downstream, only the DSMC and the coupled ESBGK/ESFP-DSMC simulations are able to reproduce the measured rotational temperature profiles. A performance comparison shows the possible computational savings of a coupled ESBGK/ESFP-DSMC simulation, where a speedup of four orders of magnitude can be observed compared to a regular DSMC simulation.

Categories: Latest papers in fluid mechanics

### On the particle discretization in hypersonic nonequilibrium flows with the direct simulation Monte Carlo method

Physics of Fluids, Volume 31, Issue 7, July 2019.

To help understand the discrete molecular behaviors in a nonequilibrium state, this work investigated the statistical and physical features of particle discretization for the direct simulation Monte Carlo method with no time counter collision scheme in hypersonic flows. Different functionals, particle discretization errors of four macroscopic quantities, were studied by averaging their values throughout four flow regions. Specifically, a linear convergence behavior [math], an independence of Nc, and an inverted V-type variation of discretization errors were observed for different functionals and in different regions, where Nc is the particle number per cell. The magnitude of discretization error was found to be positively related to the degree of local nonequilibrium effect. Further microscopic analyses indicated that the mean collision separation is independent of Nc even if ⟨Nc⟩ < 10. Instead, the variation of collision frequency with a turning point of ⟨Nc⟩ ≈ 10 was found to be responsible for the observed convergence behaviors. An overestimation of collision frequency with decreased Nc appeared when ⟨Nc⟩ > 10 because of a reduced maximal relative velocity. Meanwhile, an underestimation of collision frequency with decreased Nc appeared when ⟨Nc⟩ < 10 because of repeated collisions. In addition, the effect of repeated collisions was enhanced by a strong kinetic and thermodynamic nonequilibrium in such a way that the mixed and inverted V-type trend of particle discretization errors inside the shock wave was observed.

To help understand the discrete molecular behaviors in a nonequilibrium state, this work investigated the statistical and physical features of particle discretization for the direct simulation Monte Carlo method with no time counter collision scheme in hypersonic flows. Different functionals, particle discretization errors of four macroscopic quantities, were studied by averaging their values throughout four flow regions. Specifically, a linear convergence behavior [math], an independence of Nc, and an inverted V-type variation of discretization errors were observed for different functionals and in different regions, where Nc is the particle number per cell. The magnitude of discretization error was found to be positively related to the degree of local nonequilibrium effect. Further microscopic analyses indicated that the mean collision separation is independent of Nc even if ⟨Nc⟩ < 10. Instead, the variation of collision frequency with a turning point of ⟨Nc⟩ ≈ 10 was found to be responsible for the observed convergence behaviors. An overestimation of collision frequency with decreased Nc appeared when ⟨Nc⟩ > 10 because of a reduced maximal relative velocity. Meanwhile, an underestimation of collision frequency with decreased Nc appeared when ⟨Nc⟩ < 10 because of repeated collisions. In addition, the effect of repeated collisions was enhanced by a strong kinetic and thermodynamic nonequilibrium in such a way that the mixed and inverted V-type trend of particle discretization errors inside the shock wave was observed.

Categories: Latest papers in fluid mechanics

### On the particle discretization in hypersonic nonequilibrium flows with the direct simulation Monte Carlo method

Physics of Fluids, Volume 31, Issue 7, July 2019.

To help understand the discrete molecular behaviors in a nonequilibrium state, this work investigated the statistical and physical features of particle discretization for the direct simulation Monte Carlo method with no time counter collision scheme in hypersonic flows. Different functionals, particle discretization errors of four macroscopic quantities, were studied by averaging their values throughout four flow regions. Specifically, a linear convergence behavior [math], an independence of Nc, and an inverted V-type variation of discretization errors were observed for different functionals and in different regions, where Nc is the particle number per cell. The magnitude of discretization error was found to be positively related to the degree of local nonequilibrium effect. Further microscopic analyses indicated that the mean collision separation is independent of Nc even if ⟨Nc⟩ < 10. Instead, the variation of collision frequency with a turning point of ⟨Nc⟩ ≈ 10 was found to be responsible for the observed convergence behaviors. An overestimation of collision frequency with decreased Nc appeared when ⟨Nc⟩ > 10 because of a reduced maximal relative velocity. Meanwhile, an underestimation of collision frequency with decreased Nc appeared when ⟨Nc⟩ < 10 because of repeated collisions. In addition, the effect of repeated collisions was enhanced by a strong kinetic and thermodynamic nonequilibrium in such a way that the mixed and inverted V-type trend of particle discretization errors inside the shock wave was observed.

To help understand the discrete molecular behaviors in a nonequilibrium state, this work investigated the statistical and physical features of particle discretization for the direct simulation Monte Carlo method with no time counter collision scheme in hypersonic flows. Different functionals, particle discretization errors of four macroscopic quantities, were studied by averaging their values throughout four flow regions. Specifically, a linear convergence behavior [math], an independence of Nc, and an inverted V-type variation of discretization errors were observed for different functionals and in different regions, where Nc is the particle number per cell. The magnitude of discretization error was found to be positively related to the degree of local nonequilibrium effect. Further microscopic analyses indicated that the mean collision separation is independent of Nc even if ⟨Nc⟩ < 10. Instead, the variation of collision frequency with a turning point of ⟨Nc⟩ ≈ 10 was found to be responsible for the observed convergence behaviors. An overestimation of collision frequency with decreased Nc appeared when ⟨Nc⟩ > 10 because of a reduced maximal relative velocity. Meanwhile, an underestimation of collision frequency with decreased Nc appeared when ⟨Nc⟩ < 10 because of repeated collisions. In addition, the effect of repeated collisions was enhanced by a strong kinetic and thermodynamic nonequilibrium in such a way that the mixed and inverted V-type trend of particle discretization errors inside the shock wave was observed.

Categories: Latest papers in fluid mechanics

### Simple multi-sections unit-cell model for sound absorption characteristics of lotus-type porous metals

Physics of Fluids, Volume 31, Issue 7, July 2019.

This paper presents a simple multisection unit-cell model (UCM) with which to investigate the sound absorption characteristics of lotus-type porous metals (LTPMs). This model is inspired by analyzing micrographs of the LTPMs and by considering the relationship between the average pore diameter and the porosity. The multisection UCM is used to establish the analytical relationships between the basic nonacoustic parameters (namely, flow resistivity, tortuosity, and porosity) and the sound absorption characteristics of the LTPMs. The analytical predictions are compared with existing experimental data and with analytical results from a uniform UCM. Good agreement is found between the multisections UCM and the existing experimental results. The comparative relationships of the sound absorption coefficients of the LTPMs and uniform and graded open-cell foam aluminum are plotted as well.

This paper presents a simple multisection unit-cell model (UCM) with which to investigate the sound absorption characteristics of lotus-type porous metals (LTPMs). This model is inspired by analyzing micrographs of the LTPMs and by considering the relationship between the average pore diameter and the porosity. The multisection UCM is used to establish the analytical relationships between the basic nonacoustic parameters (namely, flow resistivity, tortuosity, and porosity) and the sound absorption characteristics of the LTPMs. The analytical predictions are compared with existing experimental data and with analytical results from a uniform UCM. Good agreement is found between the multisections UCM and the existing experimental results. The comparative relationships of the sound absorption coefficients of the LTPMs and uniform and graded open-cell foam aluminum are plotted as well.

Categories: Latest papers in fluid mechanics

### Simple multi-sections unit-cell model for sound absorption characteristics of lotus-type porous metals

Physics of Fluids, Volume 31, Issue 7, July 2019.

This paper presents a simple multisection unit-cell model (UCM) with which to investigate the sound absorption characteristics of lotus-type porous metals (LTPMs). This model is inspired by analyzing micrographs of the LTPMs and by considering the relationship between the average pore diameter and the porosity. The multisection UCM is used to establish the analytical relationships between the basic nonacoustic parameters (namely, flow resistivity, tortuosity, and porosity) and the sound absorption characteristics of the LTPMs. The analytical predictions are compared with existing experimental data and with analytical results from a uniform UCM. Good agreement is found between the multisections UCM and the existing experimental results. The comparative relationships of the sound absorption coefficients of the LTPMs and uniform and graded open-cell foam aluminum are plotted as well.

This paper presents a simple multisection unit-cell model (UCM) with which to investigate the sound absorption characteristics of lotus-type porous metals (LTPMs). This model is inspired by analyzing micrographs of the LTPMs and by considering the relationship between the average pore diameter and the porosity. The multisection UCM is used to establish the analytical relationships between the basic nonacoustic parameters (namely, flow resistivity, tortuosity, and porosity) and the sound absorption characteristics of the LTPMs. The analytical predictions are compared with existing experimental data and with analytical results from a uniform UCM. Good agreement is found between the multisections UCM and the existing experimental results. The comparative relationships of the sound absorption coefficients of the LTPMs and uniform and graded open-cell foam aluminum are plotted as well.

Categories: Latest papers in fluid mechanics

### Inertial instabilities in a microfluidic mixing-separating device

Physics of Fluids, Volume 31, Issue 7, July 2019.

Combining and separating fluid streams at the microscale has many scientific, industrial, and medical applications. This numerical and experimental study explores inertial instabilities in so-called mixing-separating micro-geometries. The geometry consists of two straight square parallel channels with flow from opposite directions and a central gap that allows the streams to interact, mix, or remain separate (often also referred to as the H-geometry). Under creeping-flow conditions (the Reynolds number tending to zero), the flow is steady, two-dimensional, and produces a sharp interface between fluid streams entering the geometry from opposite directions. When Re exceeds a critical value, one of two different supercritical, inertial instabilities appears which leads to significant changes in the flow pattern and an increased level of interaction between the two streams, although the flow remains steady. The exact form of the instability is dependent on the gap size and the Reynolds number, and we identify two distinct instabilities, one of which appears in devices with large gaps and another which appears in devices with small gaps. At intermediate gap sizes, both instabilities can occur in the same device (at different onset Re). The experimental results for one gap size are used to validate our numerical method, which is then applied to a wider range of gap sizes. The results suggest that the gap size is of primary importance in determining the type of instability that occurs. With a judicious choice of gap size, the instabilities can be exploited (or avoided) in scientific, medical, or other microfluidic applications.

Combining and separating fluid streams at the microscale has many scientific, industrial, and medical applications. This numerical and experimental study explores inertial instabilities in so-called mixing-separating micro-geometries. The geometry consists of two straight square parallel channels with flow from opposite directions and a central gap that allows the streams to interact, mix, or remain separate (often also referred to as the H-geometry). Under creeping-flow conditions (the Reynolds number tending to zero), the flow is steady, two-dimensional, and produces a sharp interface between fluid streams entering the geometry from opposite directions. When Re exceeds a critical value, one of two different supercritical, inertial instabilities appears which leads to significant changes in the flow pattern and an increased level of interaction between the two streams, although the flow remains steady. The exact form of the instability is dependent on the gap size and the Reynolds number, and we identify two distinct instabilities, one of which appears in devices with large gaps and another which appears in devices with small gaps. At intermediate gap sizes, both instabilities can occur in the same device (at different onset Re). The experimental results for one gap size are used to validate our numerical method, which is then applied to a wider range of gap sizes. The results suggest that the gap size is of primary importance in determining the type of instability that occurs. With a judicious choice of gap size, the instabilities can be exploited (or avoided) in scientific, medical, or other microfluidic applications.

Categories: Latest papers in fluid mechanics

### Inertial instabilities in a microfluidic mixing-separating device

Physics of Fluids, Volume 31, Issue 7, July 2019.

Combining and separating fluid streams at the microscale has many scientific, industrial, and medical applications. This numerical and experimental study explores inertial instabilities in so-called mixing-separating micro-geometries. The geometry consists of two straight square parallel channels with flow from opposite directions and a central gap that allows the streams to interact, mix, or remain separate (often also referred to as the H-geometry). Under creeping-flow conditions (the Reynolds number tending to zero), the flow is steady, two-dimensional, and produces a sharp interface between fluid streams entering the geometry from opposite directions. When Re exceeds a critical value, one of two different supercritical, inertial instabilities appears which leads to significant changes in the flow pattern and an increased level of interaction between the two streams, although the flow remains steady. The exact form of the instability is dependent on the gap size and the Reynolds number, and we identify two distinct instabilities, one of which appears in devices with large gaps and another which appears in devices with small gaps. At intermediate gap sizes, both instabilities can occur in the same device (at different onset Re). The experimental results for one gap size are used to validate our numerical method, which is then applied to a wider range of gap sizes. The results suggest that the gap size is of primary importance in determining the type of instability that occurs. With a judicious choice of gap size, the instabilities can be exploited (or avoided) in scientific, medical, or other microfluidic applications.

Combining and separating fluid streams at the microscale has many scientific, industrial, and medical applications. This numerical and experimental study explores inertial instabilities in so-called mixing-separating micro-geometries. The geometry consists of two straight square parallel channels with flow from opposite directions and a central gap that allows the streams to interact, mix, or remain separate (often also referred to as the H-geometry). Under creeping-flow conditions (the Reynolds number tending to zero), the flow is steady, two-dimensional, and produces a sharp interface between fluid streams entering the geometry from opposite directions. When Re exceeds a critical value, one of two different supercritical, inertial instabilities appears which leads to significant changes in the flow pattern and an increased level of interaction between the two streams, although the flow remains steady. The exact form of the instability is dependent on the gap size and the Reynolds number, and we identify two distinct instabilities, one of which appears in devices with large gaps and another which appears in devices with small gaps. At intermediate gap sizes, both instabilities can occur in the same device (at different onset Re). The experimental results for one gap size are used to validate our numerical method, which is then applied to a wider range of gap sizes. The results suggest that the gap size is of primary importance in determining the type of instability that occurs. With a judicious choice of gap size, the instabilities can be exploited (or avoided) in scientific, medical, or other microfluidic applications.

Categories: Latest papers in fluid mechanics

### Experimental and numerical studies on the flow characteristics and separation properties of dispersed liquid-liquid flows

Physics of Fluids, Volume 31, Issue 7, July 2019.

The local dynamics of spatially developing liquid-liquid dispersed flows at low superficial velocities, ranging from 0.2 to 0.8 m s−1, are investigated. The dispersions are generated with an in-line static mixer. Detailed measurements with laser-based diagnostic tools are conducted at two axial pipe locations downstream of the mixer, namely, at 15 and 135 equivalent pipe diameters. Different flow patterns are recorded, and their development along the streamwise direction is shown to depend on the initial size and concentration of the drops as well as the mixture velocity. The drop size is accurately predicted by an empirical formula. The variations in drop concentration over the pipe cross-section along the pipe result in local changes of the physical properties of the mixture and consequently in asymmetrical velocity profiles, with the maxima of the velocity located in the drop-free region. Computational fluid dynamics simulations based on a mixture approach predict the experimental results close to the experimental uncertainties for the majority of the cases. The simulation results reveal that gravity and lift forces, as well as shear-induced diffusion are the most important mechanisms affecting the drop migration. It is found that the drops behave as suspensions of rigid spheres for the conditions investigated, despite the deformation effects, which are found experimentally to be stronger at the densely packed region.

The local dynamics of spatially developing liquid-liquid dispersed flows at low superficial velocities, ranging from 0.2 to 0.8 m s−1, are investigated. The dispersions are generated with an in-line static mixer. Detailed measurements with laser-based diagnostic tools are conducted at two axial pipe locations downstream of the mixer, namely, at 15 and 135 equivalent pipe diameters. Different flow patterns are recorded, and their development along the streamwise direction is shown to depend on the initial size and concentration of the drops as well as the mixture velocity. The drop size is accurately predicted by an empirical formula. The variations in drop concentration over the pipe cross-section along the pipe result in local changes of the physical properties of the mixture and consequently in asymmetrical velocity profiles, with the maxima of the velocity located in the drop-free region. Computational fluid dynamics simulations based on a mixture approach predict the experimental results close to the experimental uncertainties for the majority of the cases. The simulation results reveal that gravity and lift forces, as well as shear-induced diffusion are the most important mechanisms affecting the drop migration. It is found that the drops behave as suspensions of rigid spheres for the conditions investigated, despite the deformation effects, which are found experimentally to be stronger at the densely packed region.

Categories: Latest papers in fluid mechanics

### Experimental and numerical studies on the flow characteristics and separation properties of dispersed liquid-liquid flows

Physics of Fluids, Volume 31, Issue 7, July 2019.

The local dynamics of spatially developing liquid-liquid dispersed flows at low superficial velocities, ranging from 0.2 to 0.8 m s−1, are investigated. The dispersions are generated with an in-line static mixer. Detailed measurements with laser-based diagnostic tools are conducted at two axial pipe locations downstream of the mixer, namely, at 15 and 135 equivalent pipe diameters. Different flow patterns are recorded, and their development along the streamwise direction is shown to depend on the initial size and concentration of the drops as well as the mixture velocity. The drop size is accurately predicted by an empirical formula. The variations in drop concentration over the pipe cross-section along the pipe result in local changes of the physical properties of the mixture and consequently in asymmetrical velocity profiles, with the maxima of the velocity located in the drop-free region. Computational fluid dynamics simulations based on a mixture approach predict the experimental results close to the experimental uncertainties for the majority of the cases. The simulation results reveal that gravity and lift forces, as well as shear-induced diffusion are the most important mechanisms affecting the drop migration. It is found that the drops behave as suspensions of rigid spheres for the conditions investigated, despite the deformation effects, which are found experimentally to be stronger at the densely packed region.

The local dynamics of spatially developing liquid-liquid dispersed flows at low superficial velocities, ranging from 0.2 to 0.8 m s−1, are investigated. The dispersions are generated with an in-line static mixer. Detailed measurements with laser-based diagnostic tools are conducted at two axial pipe locations downstream of the mixer, namely, at 15 and 135 equivalent pipe diameters. Different flow patterns are recorded, and their development along the streamwise direction is shown to depend on the initial size and concentration of the drops as well as the mixture velocity. The drop size is accurately predicted by an empirical formula. The variations in drop concentration over the pipe cross-section along the pipe result in local changes of the physical properties of the mixture and consequently in asymmetrical velocity profiles, with the maxima of the velocity located in the drop-free region. Computational fluid dynamics simulations based on a mixture approach predict the experimental results close to the experimental uncertainties for the majority of the cases. The simulation results reveal that gravity and lift forces, as well as shear-induced diffusion are the most important mechanisms affecting the drop migration. It is found that the drops behave as suspensions of rigid spheres for the conditions investigated, despite the deformation effects, which are found experimentally to be stronger at the densely packed region.

Categories: Latest papers in fluid mechanics

### Phase field lattice Boltzmann model for air-water two phase flows

Physics of Fluids, Volume 31, Issue 7, July 2019.

Two phase flows occur in different forms with liquid and gas in general, among which, the interaction of the flow of air and water is a common scenario. However, modeling the two phase flow still remains a challenge due to the large density ratio between them and different space-time scales involved in the flow regimes. In the present work, the lattice Boltzmann (LB) model capable of handling large density ratio (1000) and high Reynolds number (104) simultaneously is proposed. The present model consists of two sets of LB equations, one for the flow field in terms of normalized pressure-velocity formulation and the other for the solution of the conservative Allen-Cahn equation to capture the interface. The numerical tests such as stationary drop, bubble coalescence, and capillary wave decay have been performed, and the results exhibit excellent mass conservation property. The capability of the present model to handle complex scenarios has been tested through test cases, for example, rise of an air bubble, splash of a water droplet on a wet bed, and Rayleigh-Taylor instability. In all test cases, the simulation results agree well with the available reference data. Finally, as an application of the present model, the breaking of a deep water wave with high Reynolds number (104) is simulated. The plunging breaker with wave overturning and the generation of secondary jet and splashes are well described by the present LB model. The evolution of wave energy dissipation during and after breaking is in agreement with the reference data.

Two phase flows occur in different forms with liquid and gas in general, among which, the interaction of the flow of air and water is a common scenario. However, modeling the two phase flow still remains a challenge due to the large density ratio between them and different space-time scales involved in the flow regimes. In the present work, the lattice Boltzmann (LB) model capable of handling large density ratio (1000) and high Reynolds number (104) simultaneously is proposed. The present model consists of two sets of LB equations, one for the flow field in terms of normalized pressure-velocity formulation and the other for the solution of the conservative Allen-Cahn equation to capture the interface. The numerical tests such as stationary drop, bubble coalescence, and capillary wave decay have been performed, and the results exhibit excellent mass conservation property. The capability of the present model to handle complex scenarios has been tested through test cases, for example, rise of an air bubble, splash of a water droplet on a wet bed, and Rayleigh-Taylor instability. In all test cases, the simulation results agree well with the available reference data. Finally, as an application of the present model, the breaking of a deep water wave with high Reynolds number (104) is simulated. The plunging breaker with wave overturning and the generation of secondary jet and splashes are well described by the present LB model. The evolution of wave energy dissipation during and after breaking is in agreement with the reference data.

Categories: Latest papers in fluid mechanics

### Phase field lattice Boltzmann model for air-water two phase flows

Physics of Fluids, Volume 31, Issue 7, July 2019.

Two phase flows occur in different forms with liquid and gas in general, among which, the interaction of the flow of air and water is a common scenario. However, modeling the two phase flow still remains a challenge due to the large density ratio between them and different space-time scales involved in the flow regimes. In the present work, the lattice Boltzmann (LB) model capable of handling large density ratio (1000) and high Reynolds number (104) simultaneously is proposed. The present model consists of two sets of LB equations, one for the flow field in terms of normalized pressure-velocity formulation and the other for the solution of the conservative Allen-Cahn equation to capture the interface. The numerical tests such as stationary drop, bubble coalescence, and capillary wave decay have been performed, and the results exhibit excellent mass conservation property. The capability of the present model to handle complex scenarios has been tested through test cases, for example, rise of an air bubble, splash of a water droplet on a wet bed, and Rayleigh-Taylor instability. In all test cases, the simulation results agree well with the available reference data. Finally, as an application of the present model, the breaking of a deep water wave with high Reynolds number (104) is simulated. The plunging breaker with wave overturning and the generation of secondary jet and splashes are well described by the present LB model. The evolution of wave energy dissipation during and after breaking is in agreement with the reference data.

Two phase flows occur in different forms with liquid and gas in general, among which, the interaction of the flow of air and water is a common scenario. However, modeling the two phase flow still remains a challenge due to the large density ratio between them and different space-time scales involved in the flow regimes. In the present work, the lattice Boltzmann (LB) model capable of handling large density ratio (1000) and high Reynolds number (104) simultaneously is proposed. The present model consists of two sets of LB equations, one for the flow field in terms of normalized pressure-velocity formulation and the other for the solution of the conservative Allen-Cahn equation to capture the interface. The numerical tests such as stationary drop, bubble coalescence, and capillary wave decay have been performed, and the results exhibit excellent mass conservation property. The capability of the present model to handle complex scenarios has been tested through test cases, for example, rise of an air bubble, splash of a water droplet on a wet bed, and Rayleigh-Taylor instability. In all test cases, the simulation results agree well with the available reference data. Finally, as an application of the present model, the breaking of a deep water wave with high Reynolds number (104) is simulated. The plunging breaker with wave overturning and the generation of secondary jet and splashes are well described by the present LB model. The evolution of wave energy dissipation during and after breaking is in agreement with the reference data.

Categories: Latest papers in fluid mechanics

### Modeling and verification of the Richtmyer–Meshkov instability linear growth rate of the dense gas-particle flow

Physics of Fluids, Volume 31, Issue 7, July 2019.

The multiphase Richtmyer–Meshkov instability (RMI) often occurs in supernova events and inertial confinement fusion processes, where it plays a critical role. In the evolution of the RMI process, the particle phase may have either a dilute or a dense pattern. Previous studies have mainly focused on the dilute pattern. Currently, there is no published research on the theoretical growth model of the dense gas-particle flow. In this work, a new Atwood number model was developed with the assumption of a small Stokes number and shown to be effective for the RMI of the dense gas-particle flow. The Atwood number model was characterized by the moment coupling parameters and the ratio of the volume fractions of the two phases. Further derivation showed that it was consistent with the original Richtmyer’s model and the dilute gas-particle flow model. In addition, the theoretical growth rate was modeled to predict the evolution law of the mix zone width for the dense gas-particle flow. The presence of the particle phase inhibited the growth rate of the RMI, which emphasized the effect of the solid phase. The corresponding numerical simulations were also performed based on the compressible multiphase particle-in-cell method for different cases of the particle volume fraction. The numerical results demonstrated the accuracy of the theoretical growth rate model. Additionally, a brief analysis of the flow structures and cloud motion during the RMI process was performed.

The multiphase Richtmyer–Meshkov instability (RMI) often occurs in supernova events and inertial confinement fusion processes, where it plays a critical role. In the evolution of the RMI process, the particle phase may have either a dilute or a dense pattern. Previous studies have mainly focused on the dilute pattern. Currently, there is no published research on the theoretical growth model of the dense gas-particle flow. In this work, a new Atwood number model was developed with the assumption of a small Stokes number and shown to be effective for the RMI of the dense gas-particle flow. The Atwood number model was characterized by the moment coupling parameters and the ratio of the volume fractions of the two phases. Further derivation showed that it was consistent with the original Richtmyer’s model and the dilute gas-particle flow model. In addition, the theoretical growth rate was modeled to predict the evolution law of the mix zone width for the dense gas-particle flow. The presence of the particle phase inhibited the growth rate of the RMI, which emphasized the effect of the solid phase. The corresponding numerical simulations were also performed based on the compressible multiphase particle-in-cell method for different cases of the particle volume fraction. The numerical results demonstrated the accuracy of the theoretical growth rate model. Additionally, a brief analysis of the flow structures and cloud motion during the RMI process was performed.

Categories: Latest papers in fluid mechanics

### Modeling and verification of the Richtmyer–Meshkov instability linear growth rate of the dense gas-particle flow

Physics of Fluids, Volume 31, Issue 7, July 2019.

The multiphase Richtmyer–Meshkov instability (RMI) often occurs in supernova events and inertial confinement fusion processes, where it plays a critical role. In the evolution of the RMI process, the particle phase may have either a dilute or a dense pattern. Previous studies have mainly focused on the dilute pattern. Currently, there is no published research on the theoretical growth model of the dense gas-particle flow. In this work, a new Atwood number model was developed with the assumption of a small Stokes number and shown to be effective for the RMI of the dense gas-particle flow. The Atwood number model was characterized by the moment coupling parameters and the ratio of the volume fractions of the two phases. Further derivation showed that it was consistent with the original Richtmyer’s model and the dilute gas-particle flow model. In addition, the theoretical growth rate was modeled to predict the evolution law of the mix zone width for the dense gas-particle flow. The presence of the particle phase inhibited the growth rate of the RMI, which emphasized the effect of the solid phase. The corresponding numerical simulations were also performed based on the compressible multiphase particle-in-cell method for different cases of the particle volume fraction. The numerical results demonstrated the accuracy of the theoretical growth rate model. Additionally, a brief analysis of the flow structures and cloud motion during the RMI process was performed.

The multiphase Richtmyer–Meshkov instability (RMI) often occurs in supernova events and inertial confinement fusion processes, where it plays a critical role. In the evolution of the RMI process, the particle phase may have either a dilute or a dense pattern. Previous studies have mainly focused on the dilute pattern. Currently, there is no published research on the theoretical growth model of the dense gas-particle flow. In this work, a new Atwood number model was developed with the assumption of a small Stokes number and shown to be effective for the RMI of the dense gas-particle flow. The Atwood number model was characterized by the moment coupling parameters and the ratio of the volume fractions of the two phases. Further derivation showed that it was consistent with the original Richtmyer’s model and the dilute gas-particle flow model. In addition, the theoretical growth rate was modeled to predict the evolution law of the mix zone width for the dense gas-particle flow. The presence of the particle phase inhibited the growth rate of the RMI, which emphasized the effect of the solid phase. The corresponding numerical simulations were also performed based on the compressible multiphase particle-in-cell method for different cases of the particle volume fraction. The numerical results demonstrated the accuracy of the theoretical growth rate model. Additionally, a brief analysis of the flow structures and cloud motion during the RMI process was performed.

Categories: Latest papers in fluid mechanics

### On vortex intensification due to stretching out of weak satellites

Physics of Fluids, Volume 31, Issue 7, July 2019.

The interaction of two essentially unequal vortices is studied for the two-dimensional inviscid model. The curved stretching out of a weak satellite, localized at the periphery of the main vortex, is described analytically in the passive scalar approximation. The rate of energy transfer from the satellite to the main vortex is shown to increase with the curvature of the satellite orbit characterized by the ratio of the satellite size to its distance from the main vortex center. Such a mechanism of the energy cascade is distinct from previously considered symmetric deformations by external flows with a uniform strain rate when the energy is preserved for localized vortices with zero circulation in an unbounded domain. Therefore, asymmetric stretching out of satellites along curved orbits with the finite circumference is crucial for the vortex intensification and can serve as an important ingredient of inverse energy cascade in the two-dimensional turbulence.

The interaction of two essentially unequal vortices is studied for the two-dimensional inviscid model. The curved stretching out of a weak satellite, localized at the periphery of the main vortex, is described analytically in the passive scalar approximation. The rate of energy transfer from the satellite to the main vortex is shown to increase with the curvature of the satellite orbit characterized by the ratio of the satellite size to its distance from the main vortex center. Such a mechanism of the energy cascade is distinct from previously considered symmetric deformations by external flows with a uniform strain rate when the energy is preserved for localized vortices with zero circulation in an unbounded domain. Therefore, asymmetric stretching out of satellites along curved orbits with the finite circumference is crucial for the vortex intensification and can serve as an important ingredient of inverse energy cascade in the two-dimensional turbulence.

Categories: Latest papers in fluid mechanics

### On vortex intensification due to stretching out of weak satellites

Physics of Fluids, Volume 31, Issue 7, July 2019.

The interaction of two essentially unequal vortices is studied for the two-dimensional inviscid model. The curved stretching out of a weak satellite, localized at the periphery of the main vortex, is described analytically in the passive scalar approximation. The rate of energy transfer from the satellite to the main vortex is shown to increase with the curvature of the satellite orbit characterized by the ratio of the satellite size to its distance from the main vortex center. Such a mechanism of the energy cascade is distinct from previously considered symmetric deformations by external flows with a uniform strain rate when the energy is preserved for localized vortices with zero circulation in an unbounded domain. Therefore, asymmetric stretching out of satellites along curved orbits with the finite circumference is crucial for the vortex intensification and can serve as an important ingredient of inverse energy cascade in the two-dimensional turbulence.

The interaction of two essentially unequal vortices is studied for the two-dimensional inviscid model. The curved stretching out of a weak satellite, localized at the periphery of the main vortex, is described analytically in the passive scalar approximation. The rate of energy transfer from the satellite to the main vortex is shown to increase with the curvature of the satellite orbit characterized by the ratio of the satellite size to its distance from the main vortex center. Such a mechanism of the energy cascade is distinct from previously considered symmetric deformations by external flows with a uniform strain rate when the energy is preserved for localized vortices with zero circulation in an unbounded domain. Therefore, asymmetric stretching out of satellites along curved orbits with the finite circumference is crucial for the vortex intensification and can serve as an important ingredient of inverse energy cascade in the two-dimensional turbulence.

Categories: Latest papers in fluid mechanics

### A micropolar-Newtonian blood flow model through a porous layered artery in the presence of a magnetic field

Physics of Fluids, Volume 31, Issue 7, July 2019.

In this work, we present a two-phase model of blood flow through a porous layered artery in the presence of a uniform magnetic field. The characteristic of suspensions in blood allows us to assume blood as a micropolar fluid in the core region and plasma as a Newtonian fluid in the peripheral region of a blood vessel. The wall of a blood vessel is porous and composed of a thin Brinkman transition layer followed by a Darcy porous layer of different permeabilities. A magnetic field of uniform strength is transversally applied to the direction of blood flow. The authors obtained an analytical solution of the problem of blood flow through the composite porous walled artery. Analytical expressions for the flow velocity, microrotational velocity, flow rate, and stresses at the wall have been obtained in the closed form using the modified Bessel function. The effects of various flow parameters on the two-fluid model of blood flow are analyzed graphically. An important conclusion which is drawn from the solution of the present problem is that the different permeabilities of Darcy and Brinkman regions of the porous layered artery have a significant effect on the flow. The present work is validated from the previously published literature studies.

In this work, we present a two-phase model of blood flow through a porous layered artery in the presence of a uniform magnetic field. The characteristic of suspensions in blood allows us to assume blood as a micropolar fluid in the core region and plasma as a Newtonian fluid in the peripheral region of a blood vessel. The wall of a blood vessel is porous and composed of a thin Brinkman transition layer followed by a Darcy porous layer of different permeabilities. A magnetic field of uniform strength is transversally applied to the direction of blood flow. The authors obtained an analytical solution of the problem of blood flow through the composite porous walled artery. Analytical expressions for the flow velocity, microrotational velocity, flow rate, and stresses at the wall have been obtained in the closed form using the modified Bessel function. The effects of various flow parameters on the two-fluid model of blood flow are analyzed graphically. An important conclusion which is drawn from the solution of the present problem is that the different permeabilities of Darcy and Brinkman regions of the porous layered artery have a significant effect on the flow. The present work is validated from the previously published literature studies.

Categories: Latest papers in fluid mechanics

### A micropolar-Newtonian blood flow model through a porous layered artery in the presence of a magnetic field

Physics of Fluids, Volume 31, Issue 7, July 2019.

In this work, we present a two-phase model of blood flow through a porous layered artery in the presence of a uniform magnetic field. The characteristic of suspensions in blood allows us to assume blood as a micropolar fluid in the core region and plasma as a Newtonian fluid in the peripheral region of a blood vessel. The wall of a blood vessel is porous and composed of a thin Brinkman transition layer followed by a Darcy porous layer of different permeabilities. A magnetic field of uniform strength is transversally applied to the direction of blood flow. The authors obtained an analytical solution of the problem of blood flow through the composite porous walled artery. Analytical expressions for the flow velocity, microrotational velocity, flow rate, and stresses at the wall have been obtained in the closed form using the modified Bessel function. The effects of various flow parameters on the two-fluid model of blood flow are analyzed graphically. An important conclusion which is drawn from the solution of the present problem is that the different permeabilities of Darcy and Brinkman regions of the porous layered artery have a significant effect on the flow. The present work is validated from the previously published literature studies.

In this work, we present a two-phase model of blood flow through a porous layered artery in the presence of a uniform magnetic field. The characteristic of suspensions in blood allows us to assume blood as a micropolar fluid in the core region and plasma as a Newtonian fluid in the peripheral region of a blood vessel. The wall of a blood vessel is porous and composed of a thin Brinkman transition layer followed by a Darcy porous layer of different permeabilities. A magnetic field of uniform strength is transversally applied to the direction of blood flow. The authors obtained an analytical solution of the problem of blood flow through the composite porous walled artery. Analytical expressions for the flow velocity, microrotational velocity, flow rate, and stresses at the wall have been obtained in the closed form using the modified Bessel function. The effects of various flow parameters on the two-fluid model of blood flow are analyzed graphically. An important conclusion which is drawn from the solution of the present problem is that the different permeabilities of Darcy and Brinkman regions of the porous layered artery have a significant effect on the flow. The present work is validated from the previously published literature studies.

Categories: Latest papers in fluid mechanics

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

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.

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.

Categories: Latest papers in fluid mechanics

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

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.

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.

Categories: Latest papers in fluid mechanics

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

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.

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.

Categories: Latest papers in fluid mechanics