# Physics of Fluids

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

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### Effect of thermal convection on thermocapillary migration of a surfactant-laden droplet in a microchannel

Physics of Fluids, Volume 32, Issue 9, September 2020.

Despite its significance in droplet-based microfluidic technologies with the use of thermal stimuli and surfactants, coupling effects of thermal- and surfactant-induced Marangoni stresses on the transport of droplets in microchannels are not fully uncovered yet. To facilitate studies in this area, we present a three-dimensional numerical study on the thermocapillary migration of an insoluble-surfactant-laden droplet under Poiseuille flow in a microchannel. This work is realized via our own front-tracking finite-difference method with further integration of the energy conservation equation and the surface surfactant transport equation. Our numerical results agree well with the previously reported analytical results for ambient conditions with negligible thermal convection. In this study, we mainly focus on the effects of the thermal convection at high thermal Peclet numbers and find that it induces a significant change in the thermal Marangoni stress. As a consequence, the migration of surfactant-laden droplets in the microchannel is significantly retarded by the thermal convection, which is observed for two different ambient conditions, i.e., the imposed temperature increasing or decreasing along the main flow direction. To understand the mechanism underlying the effects of the thermal convection, we analyze the distributions of the temperature, surfactant concentration, and the thermal- and surfactant-induced surface tension variations over the droplet surface. Notably, the surfactant-induced Marangoni stress always opposes the thermal-induced Marangoni stress for the entire range of thermal Peclet numbers considered in this study, but the competition between them is significantly alternated by the thermal convection in a quantitative manner.

Despite its significance in droplet-based microfluidic technologies with the use of thermal stimuli and surfactants, coupling effects of thermal- and surfactant-induced Marangoni stresses on the transport of droplets in microchannels are not fully uncovered yet. To facilitate studies in this area, we present a three-dimensional numerical study on the thermocapillary migration of an insoluble-surfactant-laden droplet under Poiseuille flow in a microchannel. This work is realized via our own front-tracking finite-difference method with further integration of the energy conservation equation and the surface surfactant transport equation. Our numerical results agree well with the previously reported analytical results for ambient conditions with negligible thermal convection. In this study, we mainly focus on the effects of the thermal convection at high thermal Peclet numbers and find that it induces a significant change in the thermal Marangoni stress. As a consequence, the migration of surfactant-laden droplets in the microchannel is significantly retarded by the thermal convection, which is observed for two different ambient conditions, i.e., the imposed temperature increasing or decreasing along the main flow direction. To understand the mechanism underlying the effects of the thermal convection, we analyze the distributions of the temperature, surfactant concentration, and the thermal- and surfactant-induced surface tension variations over the droplet surface. Notably, the surfactant-induced Marangoni stress always opposes the thermal-induced Marangoni stress for the entire range of thermal Peclet numbers considered in this study, but the competition between them is significantly alternated by the thermal convection in a quantitative manner.

Categories: Latest papers in fluid mechanics

### Electric field induced dynamics of viscoplastic droplets in shear flow

Physics of Fluids, Volume 32, Issue 9, September 2020.

We investigate the dynamics of viscoplastic droplets under the combined action of electric field and shear flow by performing direct numerical simulations. The electro-hydrodynamic equations are solved in a two-dimensional finite volume framework, and the interface is captured using a volume-of-fluid approach. The rheology of the viscoplastic droplet is modeled as a Bingham plastic fluid. Both the drop and the surrounding medium are considered to be perfect dielectric fluids. The simulations reveal that in the sole presence of the shear flow, the plasticity of the fluid plays a pivotal role in deciding the magnitude of droplet deformation and orientation. The local viscosity inside the drop is significantly augmented for higher plasticity of the fluid. Under the action of the electric field, the droplet deformation and orientation can be suitably tuned by varying the magnitude of the permittivity contrast between the fluids. The droplets experience enhanced deformation and preferred orientation against the flow direction when the permittivity ratio is greater than unity. Increasing the droplet plasticity leads to reduction in the droplet deformation. Conversely, by increasing the electric field strength, the deformation of the droplets can be notably enhanced, with a stronger response observed for a permittivity ratio beyond unity. Finally, it is observed that by suitably manipulating the strength of the shear flow and the electric field, droplet breakup can be engendered. The mode of droplet disintegration differs due to variation of the parameters, which can be attributed to the competing influence of shear and electric forces on the droplet.

We investigate the dynamics of viscoplastic droplets under the combined action of electric field and shear flow by performing direct numerical simulations. The electro-hydrodynamic equations are solved in a two-dimensional finite volume framework, and the interface is captured using a volume-of-fluid approach. The rheology of the viscoplastic droplet is modeled as a Bingham plastic fluid. Both the drop and the surrounding medium are considered to be perfect dielectric fluids. The simulations reveal that in the sole presence of the shear flow, the plasticity of the fluid plays a pivotal role in deciding the magnitude of droplet deformation and orientation. The local viscosity inside the drop is significantly augmented for higher plasticity of the fluid. Under the action of the electric field, the droplet deformation and orientation can be suitably tuned by varying the magnitude of the permittivity contrast between the fluids. The droplets experience enhanced deformation and preferred orientation against the flow direction when the permittivity ratio is greater than unity. Increasing the droplet plasticity leads to reduction in the droplet deformation. Conversely, by increasing the electric field strength, the deformation of the droplets can be notably enhanced, with a stronger response observed for a permittivity ratio beyond unity. Finally, it is observed that by suitably manipulating the strength of the shear flow and the electric field, droplet breakup can be engendered. The mode of droplet disintegration differs due to variation of the parameters, which can be attributed to the competing influence of shear and electric forces on the droplet.

Categories: Latest papers in fluid mechanics

### Pore-scale modeling of wettability effects on infiltration behavior in liquid composite molding

Physics of Fluids, Volume 32, Issue 9, September 2020.

The effect of wettability on the infiltration behavior in the liquid composite molding process has not been fully studied, and the available evidence appears to be conflicting. Based on the three-dimensional microcomputed tomography images of porous media, a series of immiscible displacement simulations under a wide range of wettability conditions was established by the phase field method. Interestingly, we found that increasing the affinity of the porous matrix for the invading fluid can increase the displacement efficiency and reduce the void content until the critical wetting transition is reached, beyond which the displacement efficiency decreases sharply. The nonmonotonic behavior of the wettability effect can be explained by the competition among complex and intriguing pore-scale displacement events, mainly involving the Haines jump, cooperative pore filling, and corner flow. These novel findings provide a theoretical basis for extracting the optimal wettability range, thus minimizing the void content formed during the liquid infiltration process.

The effect of wettability on the infiltration behavior in the liquid composite molding process has not been fully studied, and the available evidence appears to be conflicting. Based on the three-dimensional microcomputed tomography images of porous media, a series of immiscible displacement simulations under a wide range of wettability conditions was established by the phase field method. Interestingly, we found that increasing the affinity of the porous matrix for the invading fluid can increase the displacement efficiency and reduce the void content until the critical wetting transition is reached, beyond which the displacement efficiency decreases sharply. The nonmonotonic behavior of the wettability effect can be explained by the competition among complex and intriguing pore-scale displacement events, mainly involving the Haines jump, cooperative pore filling, and corner flow. These novel findings provide a theoretical basis for extracting the optimal wettability range, thus minimizing the void content formed during the liquid infiltration process.

Categories: Latest papers in fluid mechanics

### Bifractal nature of turbulent reaction waves at high Damköhler and Karlovitz numbers

Physics of Fluids, Volume 32, Issue 9, September 2020.

Governing physical mechanisms of the influence of Kolmogorov turbulence on a reaction wave (e.g., a premixed flame) are often discussed by adopting (combustion) regime diagrams. While two limiting regimes associated with (i) a high Damköhler number Da, but a low Karlovitz number Ka, or (ii) a low Da, but a high Ka drew significant amount of attention, the third limiting regime associated with (iii) Da ≫ 1 and Ka ≫ 1 has yet been beyond the mainstream discussions in the literature. The present work aims at filling this knowledge gap by adapting the contemporary understanding of the fundamentals of the regimes (i) and (ii) in order to describe the basic features of the influence of intense turbulence on a reaction wave in the regime (iii). More specifically, in that regime, the entire turbulence spectrum is divided in two subranges: small-scale and large-scale eddies whose influence on the reaction wave is modeled similarly to the regimes (ii) and (i), respectively. Accordingly, the surface of the reaction wave is hypothesized to be a bifractal with two different fractal dimensions of Df = 8/3 and 7/3 at small and large scales, respectively. The boundary between the two ranges is found by equating the local eddy turn-over time to the laminar-wave time scale. Finally, a simple scaling of UT ∝ u′ is obtained for the turbulent consumption velocity at Da ≫ 1 and Ka ≫ 1. Here, u′ is the rms turbulent velocity.

Governing physical mechanisms of the influence of Kolmogorov turbulence on a reaction wave (e.g., a premixed flame) are often discussed by adopting (combustion) regime diagrams. While two limiting regimes associated with (i) a high Damköhler number Da, but a low Karlovitz number Ka, or (ii) a low Da, but a high Ka drew significant amount of attention, the third limiting regime associated with (iii) Da ≫ 1 and Ka ≫ 1 has yet been beyond the mainstream discussions in the literature. The present work aims at filling this knowledge gap by adapting the contemporary understanding of the fundamentals of the regimes (i) and (ii) in order to describe the basic features of the influence of intense turbulence on a reaction wave in the regime (iii). More specifically, in that regime, the entire turbulence spectrum is divided in two subranges: small-scale and large-scale eddies whose influence on the reaction wave is modeled similarly to the regimes (ii) and (i), respectively. Accordingly, the surface of the reaction wave is hypothesized to be a bifractal with two different fractal dimensions of Df = 8/3 and 7/3 at small and large scales, respectively. The boundary between the two ranges is found by equating the local eddy turn-over time to the laminar-wave time scale. Finally, a simple scaling of UT ∝ u′ is obtained for the turbulent consumption velocity at Da ≫ 1 and Ka ≫ 1. Here, u′ is the rms turbulent velocity.

Categories: Latest papers in fluid mechanics

### Correction of second-order slip condition for higher Knudsen numbers by approximation of free-molecular diffusion

Physics of Fluids, Volume 32, Issue 9, September 2020.

The computational predictions of channel and pipe flows with classical models and no-slip condition at the wall reach excellent results for lower Knudsen numbers (Kn) only. Linear slip models reach a very good approximation of measurement results over the region of 10−3 < Kn < 10−1. The numerical results of higher-order slip models match experimental data up to Kn ≈ 1. The present work derives an analytical model for the transition from the slip regime to the free-molecular flows by the superposition of diffuse molecular boundary reflection and the molecular diffusion inside the bulk flow. The methodology of the present publication models the mass flow resulting from the molecular diffusion for the approximation of the mass flow in microchannels and micropipes for the regime of molecular mass flows (1 < Kn < 100) in an excellent way. The present model shows good agreement with the former models, measurement data, and direct simulation Monte Carlo results for the complete region from the transitional regime up to free-molecular flow (10−2 < Kn < 102).

The computational predictions of channel and pipe flows with classical models and no-slip condition at the wall reach excellent results for lower Knudsen numbers (Kn) only. Linear slip models reach a very good approximation of measurement results over the region of 10−3 < Kn < 10−1. The numerical results of higher-order slip models match experimental data up to Kn ≈ 1. The present work derives an analytical model for the transition from the slip regime to the free-molecular flows by the superposition of diffuse molecular boundary reflection and the molecular diffusion inside the bulk flow. The methodology of the present publication models the mass flow resulting from the molecular diffusion for the approximation of the mass flow in microchannels and micropipes for the regime of molecular mass flows (1 < Kn < 100) in an excellent way. The present model shows good agreement with the former models, measurement data, and direct simulation Monte Carlo results for the complete region from the transitional regime up to free-molecular flow (10−2 < Kn < 102).

Categories: Latest papers in fluid mechanics

### The effects of double-diffusion and viscous dissipation on the oscillatory convection in a viscoelastic fluid saturated porous layer

Physics of Fluids, Volume 32, Issue 9, September 2020.

The effects of the double-diffusion and viscous dissipation on the convective instability in a horizontal porous layer are investigated. The porous medium is saturated with a binary viscoelastic fluid. The Oldroyd-B model of viscoelastic fluid is considered. Constant temperature and concentration differences are maintained between the boundaries. A basic flow is present in the horizontal direction. The governing parameters are the thermal Rayleigh number (RaT), solutal Rayleigh number (RaS), Gebhart number (Ge), Lewis number (Le), Péclet number (Pe), dimensionless relaxation time (λ1), and dimensionless retardation time (λ2). A small perturbation to the basic flow is assumed, and a linear stability analysis is performed. A detailed discussion is carried out considering RaT as the eigenvalue. The critical wave number and frequency are also derived for a wide range of Lewis numbers and solutal Rayleigh numbers. The oscillatory modes are analyzed. It is found that transverse rolls are the preferred mode for the onset of oscillatory convection, except for some special cases. Moreover, a negative solutal Rayleigh number stabilizes the flow. An opposite effect is seen in the presence of a positive solutal Rayleigh number.

The effects of the double-diffusion and viscous dissipation on the convective instability in a horizontal porous layer are investigated. The porous medium is saturated with a binary viscoelastic fluid. The Oldroyd-B model of viscoelastic fluid is considered. Constant temperature and concentration differences are maintained between the boundaries. A basic flow is present in the horizontal direction. The governing parameters are the thermal Rayleigh number (RaT), solutal Rayleigh number (RaS), Gebhart number (Ge), Lewis number (Le), Péclet number (Pe), dimensionless relaxation time (λ1), and dimensionless retardation time (λ2). A small perturbation to the basic flow is assumed, and a linear stability analysis is performed. A detailed discussion is carried out considering RaT as the eigenvalue. The critical wave number and frequency are also derived for a wide range of Lewis numbers and solutal Rayleigh numbers. The oscillatory modes are analyzed. It is found that transverse rolls are the preferred mode for the onset of oscillatory convection, except for some special cases. Moreover, a negative solutal Rayleigh number stabilizes the flow. An opposite effect is seen in the presence of a positive solutal Rayleigh number.

Categories: Latest papers in fluid mechanics

### Data-driven order reduction and velocity field reconstruction using neural networks: The case of a turbulent boundary layer

Physics of Fluids, Volume 32, Issue 9, September 2020.

We present a data-driven methodology to achieve the identification of coherent structure dynamics and system order reduction of an experimental turbulent boundary layer flow. The flow is characterized using time-resolved optical flow particle image velocimetry, leading to dense velocity fields that can be used both to monitor the overall dynamics of the flow and to define as many local visual sensors as needed. A Proper Orthogonal Decomposition (POD) is first applied to define a reduced-order system. A non-linear mapping between the local upstream sensors (inputs sensors) and the full-field dynamics (POD coefficients) as outputs is sought using an optimal focused time-delay Artificial Neural Network (ANN). The choices of sensors, ANN architecture, and training parameters are shown to play a critical role. It is verified that a shallow ANN, with the proper sensor memory size, can lead to a satisfying full-field dynamics identification, coherent structure reconstruction, and system order reduction of this turbulent flow.

We present a data-driven methodology to achieve the identification of coherent structure dynamics and system order reduction of an experimental turbulent boundary layer flow. The flow is characterized using time-resolved optical flow particle image velocimetry, leading to dense velocity fields that can be used both to monitor the overall dynamics of the flow and to define as many local visual sensors as needed. A Proper Orthogonal Decomposition (POD) is first applied to define a reduced-order system. A non-linear mapping between the local upstream sensors (inputs sensors) and the full-field dynamics (POD coefficients) as outputs is sought using an optimal focused time-delay Artificial Neural Network (ANN). The choices of sensors, ANN architecture, and training parameters are shown to play a critical role. It is verified that a shallow ANN, with the proper sensor memory size, can lead to a satisfying full-field dynamics identification, coherent structure reconstruction, and system order reduction of this turbulent flow.

Categories: Latest papers in fluid mechanics

### Near-wall effect on flow around an elliptic cylinder translating above a plane wall

Physics of Fluids, Volume 32, Issue 9, September 2020.

In this work, the flow over an elliptic cylinder near a moving wall is investigated for Reynolds numbers less than 150. Here, the ratio between the gap (i.e., the distance between the cylinder and the wall) and the length of the semi-major axis of the elliptic cylinder varies from 0.1 to 5. This ratio is hereafter denoted as the gap ratio. The resulting Kármán vortex street, the two-layered wake, and the secondary vortex street have been investigated and visualized. Numerical simulations show that for the steady flow, the wake is composed of two asymmetric recirculation vortices, while a decrease in the gap ratio suppresses the vortex shed from the lower part of the cylinder. For the unsteady flow, the wake can be classified into four different patterns based on the wake structures (the Kármán vortex street, the two-layered wake, and the secondary vortex street). The regions of these wake patterns are given in the gap ratio and Reynolds number space, showing that the critical Reynolds number for the transition between different patterns increases as the gap ratio decreases. An overall increase in the mean drag coefficient with increasing gap ratios is observed, except for a sudden drop that occurs within a small gap ratio range. Moreover, as the gap ratio increases, the onset location of the two-layered wake first decreases due to a decrease in flow velocity in the gap and then increases due to the weakening of the wall suppression effect.

In this work, the flow over an elliptic cylinder near a moving wall is investigated for Reynolds numbers less than 150. Here, the ratio between the gap (i.e., the distance between the cylinder and the wall) and the length of the semi-major axis of the elliptic cylinder varies from 0.1 to 5. This ratio is hereafter denoted as the gap ratio. The resulting Kármán vortex street, the two-layered wake, and the secondary vortex street have been investigated and visualized. Numerical simulations show that for the steady flow, the wake is composed of two asymmetric recirculation vortices, while a decrease in the gap ratio suppresses the vortex shed from the lower part of the cylinder. For the unsteady flow, the wake can be classified into four different patterns based on the wake structures (the Kármán vortex street, the two-layered wake, and the secondary vortex street). The regions of these wake patterns are given in the gap ratio and Reynolds number space, showing that the critical Reynolds number for the transition between different patterns increases as the gap ratio decreases. An overall increase in the mean drag coefficient with increasing gap ratios is observed, except for a sudden drop that occurs within a small gap ratio range. Moreover, as the gap ratio increases, the onset location of the two-layered wake first decreases due to a decrease in flow velocity in the gap and then increases due to the weakening of the wall suppression effect.

Categories: Latest papers in fluid mechanics

### A dual mesh control domain method for the solution of nonlinear Poisson’s equation and the Navier–Stokes equations for incompressible fluids

Physics of Fluids, Volume 32, Issue 9, September 2020.

In this study, the dual mesh control domain method, which employs the finite element approximation of the primary variables and the finite volume idea of satisfying the governing equations over a control domain, is used for the numerical solution of the Navier–Stokes equations governing the flows of viscous incompressible fluids using the penalty function formulation for two-dimensional analysis. The primal mesh is the mesh of finite elements used to interpolate the velocity field, while the dual mesh of control domains is used to satisfy the integral form of the Navier–Stokes equations, and thus, the method shares certain desirable features of the two popular methods. Numerical examples involving nonlinear Poisson’s equation and the Navier–Stokes equations are presented to illustrate the methodology and accuracy compared to the finite element and finite volume solutions, the latter depending on the scheme used to solve the discretized equations.

In this study, the dual mesh control domain method, which employs the finite element approximation of the primary variables and the finite volume idea of satisfying the governing equations over a control domain, is used for the numerical solution of the Navier–Stokes equations governing the flows of viscous incompressible fluids using the penalty function formulation for two-dimensional analysis. The primal mesh is the mesh of finite elements used to interpolate the velocity field, while the dual mesh of control domains is used to satisfy the integral form of the Navier–Stokes equations, and thus, the method shares certain desirable features of the two popular methods. Numerical examples involving nonlinear Poisson’s equation and the Navier–Stokes equations are presented to illustrate the methodology and accuracy compared to the finite element and finite volume solutions, the latter depending on the scheme used to solve the discretized equations.

Categories: Latest papers in fluid mechanics

### Settling characteristics of bidisperse dilute suspension in the vortex shedding regime

Physics of Fluids, Volume 32, Issue 9, September 2020.

In a fully periodic domain, monodisperse particles form clusters while settling in stagnant fluids at high Reynolds numbers (Re > 250) and dilute suspensions (solid volume fraction less than 1%). This is due to the entrapment of particles in the wakes developed by upstream particles. In this paper, this phenomenon is investigated for suspensions containing particles of different sizes that shed vortices during settling. To model the particle–fluid and particle–particle interactions, the immersed boundary method and discrete element method are used, respectively. Initially, the particles are randomly distributed in the computational domain and allowed to settle under the action of gravity. The gravitational force acting on the particles is adjusted to obtain the desired Reynolds number. The total solid volume fraction used in the simulations is about 0.1%, and the settling Reynolds number, which is based on the Sauter mean diameter, ranges from 250 to 450. Two particle diameter ratios (i.e., diameter of larger particles to smaller particles) of 2:1 and 3:1 are studied. For each particle diameter ratio, the mass fraction for each particle size varies from 0.2 to 0.8. For comparison, simulations of monodisperse particles settling under similar conditions are also conducted, and the average settling velocity, particle velocity fluctuations, and particle microstructures are studied. The simulation results show that, in the case of bidisperse particles, the settling characteristics are dominated by the larger-sized particles. Finally, the physics behind the studied anomalies is discussed in detail.

In a fully periodic domain, monodisperse particles form clusters while settling in stagnant fluids at high Reynolds numbers (Re > 250) and dilute suspensions (solid volume fraction less than 1%). This is due to the entrapment of particles in the wakes developed by upstream particles. In this paper, this phenomenon is investigated for suspensions containing particles of different sizes that shed vortices during settling. To model the particle–fluid and particle–particle interactions, the immersed boundary method and discrete element method are used, respectively. Initially, the particles are randomly distributed in the computational domain and allowed to settle under the action of gravity. The gravitational force acting on the particles is adjusted to obtain the desired Reynolds number. The total solid volume fraction used in the simulations is about 0.1%, and the settling Reynolds number, which is based on the Sauter mean diameter, ranges from 250 to 450. Two particle diameter ratios (i.e., diameter of larger particles to smaller particles) of 2:1 and 3:1 are studied. For each particle diameter ratio, the mass fraction for each particle size varies from 0.2 to 0.8. For comparison, simulations of monodisperse particles settling under similar conditions are also conducted, and the average settling velocity, particle velocity fluctuations, and particle microstructures are studied. The simulation results show that, in the case of bidisperse particles, the settling characteristics are dominated by the larger-sized particles. Finally, the physics behind the studied anomalies is discussed in detail.

Categories: Latest papers in fluid mechanics

### A three-dimensional unified gas-kinetic wave-particle solver for flow computation in all regimes

Physics of Fluids, Volume 32, Issue 9, September 2020.

In this paper, the unified gas-kinetic wave-particle (UGKWP) method has been constructed on a three-dimensional unstructured mesh with parallel computing for multiscale flow simulation. Based on the direct modeling methodology, the unified gas-kinetic scheme (UGKS) models the flow dynamics directly on the numerical mesh size and time step scales, and it is able to capture the flow dynamics from the kinetic scale particle transport to the hydrodynamic wave propagation seamlessly according to the local cell Knudsen number. Instead of discretizing the particle velocity space in UGKS, the UGKWP method is composed of evolution of deterministic wave and stochastic particles. With dynamic wave-particle decomposition according to the cell Knudsen number, the UGKWP method is able to capture the continuum wave interaction and rarefied particle transport under a unified framework and achieves high efficiency in different flow regimes. The UGKWP flow solver is constructed in three-dimensional space and is validated by many test cases at different Mach and Knudsen numbers. The examples include a 3D shock tube problem, lid-driven cubic cavity flow, high-speed flow passing through a cubic object, and hypersonic flow around a space vehicle. The parallel performance has been tested on the Tianhe-2 supercomputer, and reasonable parallel performance has been observed up to 1000 cores. With the wave-particle formulation, the UGKWP method has great potential in solving three-dimensional multiscale transport problems with the co-existence of continuum and rarefied flow regimes, especially for the high-speed rarefied and continuum flow simulation around a space vehicle in near-space flight, where the local Knudsen number can vary significantly with five or six orders of magnitude differences.

In this paper, the unified gas-kinetic wave-particle (UGKWP) method has been constructed on a three-dimensional unstructured mesh with parallel computing for multiscale flow simulation. Based on the direct modeling methodology, the unified gas-kinetic scheme (UGKS) models the flow dynamics directly on the numerical mesh size and time step scales, and it is able to capture the flow dynamics from the kinetic scale particle transport to the hydrodynamic wave propagation seamlessly according to the local cell Knudsen number. Instead of discretizing the particle velocity space in UGKS, the UGKWP method is composed of evolution of deterministic wave and stochastic particles. With dynamic wave-particle decomposition according to the cell Knudsen number, the UGKWP method is able to capture the continuum wave interaction and rarefied particle transport under a unified framework and achieves high efficiency in different flow regimes. The UGKWP flow solver is constructed in three-dimensional space and is validated by many test cases at different Mach and Knudsen numbers. The examples include a 3D shock tube problem, lid-driven cubic cavity flow, high-speed flow passing through a cubic object, and hypersonic flow around a space vehicle. The parallel performance has been tested on the Tianhe-2 supercomputer, and reasonable parallel performance has been observed up to 1000 cores. With the wave-particle formulation, the UGKWP method has great potential in solving three-dimensional multiscale transport problems with the co-existence of continuum and rarefied flow regimes, especially for the high-speed rarefied and continuum flow simulation around a space vehicle in near-space flight, where the local Knudsen number can vary significantly with five or six orders of magnitude differences.

Categories: Latest papers in fluid mechanics

### Sonneting critical heat flux: New insights in boiling multiphase flow

Physics of Fluids, Volume 32, Issue 9, September 2020.

Boiling—a process widely used for its good heat transferability—is limited by a phenomenon known as critical heat flux (CHF). Our experiments revealed a new CHF mechanism that is different from previously believed theories; we refer to it as “sonneting CHF.” At CHF, the flow pattern changes from bubbly flow to slug/churn flow and then to an unusual reverse annular flow, leading to a significant rise in the heater surface temperature. The reverse annular flow, however, does not sustain but breaks down into a chaotic flow pattern, resulting in unprecedented quenching of the heater surface. The flow pattern shortly reverts back to bubbly flow; this entire process repeats for a few cycles, where the heater surface temperature rises and falls with amplitudes increasing in each cycle until the heater trips. The maximum removal-surface heat flux is significantly higher than the CHF. This new understanding will enable flexible and innovative boiling systems for several energy applications.

Boiling—a process widely used for its good heat transferability—is limited by a phenomenon known as critical heat flux (CHF). Our experiments revealed a new CHF mechanism that is different from previously believed theories; we refer to it as “sonneting CHF.” At CHF, the flow pattern changes from bubbly flow to slug/churn flow and then to an unusual reverse annular flow, leading to a significant rise in the heater surface temperature. The reverse annular flow, however, does not sustain but breaks down into a chaotic flow pattern, resulting in unprecedented quenching of the heater surface. The flow pattern shortly reverts back to bubbly flow; this entire process repeats for a few cycles, where the heater surface temperature rises and falls with amplitudes increasing in each cycle until the heater trips. The maximum removal-surface heat flux is significantly higher than the CHF. This new understanding will enable flexible and innovative boiling systems for several energy applications.

Categories: Latest papers in fluid mechanics

### Analysis of free surface oscillations of a droplet due to ultrasonic wave impingement

Physics of Fluids, Volume 32, Issue 9, September 2020.

An analytical approach based on the linear potential theory is employed to enlighten the fundamental physics of atomization of droplets with an impinging sound wave, with a particular application in surface acoustic wave (SAW) atomization. When a plane sound wave, originated from the gas or the liquid side (resembling SAW), impinges on a liquid droplet, capillary waves are generated. It is shown that, for both cases, spatial phase-locking between the sound spherical modes and the free surface oscillations occurs. Hence, capillary waves will have the same spatial modes of the sound wave. The frequency spectrum analysis shows that the phase-locking causes two types of waves: the natural capillary waves with a wide range of frequencies, two to five orders of magnitude smaller than the impinging sound wave, and the forced wave, with a frequency equal to that of the sound wave. Since the instability of these surface waves leads to separation of droplets from the surface and the size of these droplets is correlated with the wavelength of the surface waves, this well explains the previous observations that droplets with a wide range of sizes are generated in the SAW experiments. Finally, a correlation is also proposed for predicting the atomized droplet size, which gives the size order for the generated droplets in SAW with good accuracy. The correlation could also suggest the possible size for remote atomization of the droplets by sound wave propagated in gas.

An analytical approach based on the linear potential theory is employed to enlighten the fundamental physics of atomization of droplets with an impinging sound wave, with a particular application in surface acoustic wave (SAW) atomization. When a plane sound wave, originated from the gas or the liquid side (resembling SAW), impinges on a liquid droplet, capillary waves are generated. It is shown that, for both cases, spatial phase-locking between the sound spherical modes and the free surface oscillations occurs. Hence, capillary waves will have the same spatial modes of the sound wave. The frequency spectrum analysis shows that the phase-locking causes two types of waves: the natural capillary waves with a wide range of frequencies, two to five orders of magnitude smaller than the impinging sound wave, and the forced wave, with a frequency equal to that of the sound wave. Since the instability of these surface waves leads to separation of droplets from the surface and the size of these droplets is correlated with the wavelength of the surface waves, this well explains the previous observations that droplets with a wide range of sizes are generated in the SAW experiments. Finally, a correlation is also proposed for predicting the atomized droplet size, which gives the size order for the generated droplets in SAW with good accuracy. The correlation could also suggest the possible size for remote atomization of the droplets by sound wave propagated in gas.

Categories: Latest papers in fluid mechanics

### Cross-stream migration of droplets in a confined shear-thinning viscoelastic flow: Role of shear-thinning induced lift

Physics of Fluids, Volume 32, Issue 9, September 2020.

Shear-thinning viscoelastic (STVE) flows exhibit intriguing phenomena owing to their complex rheology and the coupling of various forces involved. Here, we present an understanding of the cross-stream migration of droplets in a confined STVE flow and unravel the role of a shear-thinning induced lift force (FSM) in their dynamical behavior. We perform experiments with popular STVE liquids of different molecular weights and concentrations (c) for Reynolds numbers Re < 1 and Weissenberg numbers Wi = 0.01–7.4. Our results reveal larger droplets (of drop-to-channel ratio β ≥ 0.28) that follow their original streamlines, whereas smaller droplets (β ≤ 0.2) exhibit center ward migration and the migration rates depend upon the drop-to-medium viscosity (k) and elasticity (ξ) ratios. The lateral displacement of droplets is tracked using high-speed imaging that is used to estimate the relevant forces using suitable correlations. We find that the migration dynamics of droplets is underpinned by the non-inertial lift (FNIL), viscoelastic lift (FVM, FVD), and shear-thinning induced lift (FSM) forces. We provide experimental evidence of the proposed FSM and, from analytical scaling and empirical modeling, develop an expression for FSM ∼ [math] (with R2 = 0.95) for an object at a distance h from the wall and with a drop in viscosity Δμ and strain rate [math] across its diameter D. Our study sheds light on the underlying dynamics on droplets in an STVE medium and opens up avenues for sorting and focusing of drops in an STVE medium at low Re.

Shear-thinning viscoelastic (STVE) flows exhibit intriguing phenomena owing to their complex rheology and the coupling of various forces involved. Here, we present an understanding of the cross-stream migration of droplets in a confined STVE flow and unravel the role of a shear-thinning induced lift force (FSM) in their dynamical behavior. We perform experiments with popular STVE liquids of different molecular weights and concentrations (c) for Reynolds numbers Re < 1 and Weissenberg numbers Wi = 0.01–7.4. Our results reveal larger droplets (of drop-to-channel ratio β ≥ 0.28) that follow their original streamlines, whereas smaller droplets (β ≤ 0.2) exhibit center ward migration and the migration rates depend upon the drop-to-medium viscosity (k) and elasticity (ξ) ratios. The lateral displacement of droplets is tracked using high-speed imaging that is used to estimate the relevant forces using suitable correlations. We find that the migration dynamics of droplets is underpinned by the non-inertial lift (FNIL), viscoelastic lift (FVM, FVD), and shear-thinning induced lift (FSM) forces. We provide experimental evidence of the proposed FSM and, from analytical scaling and empirical modeling, develop an expression for FSM ∼ [math] (with R2 = 0.95) for an object at a distance h from the wall and with a drop in viscosity Δμ and strain rate [math] across its diameter D. Our study sheds light on the underlying dynamics on droplets in an STVE medium and opens up avenues for sorting and focusing of drops in an STVE medium at low Re.

Categories: Latest papers in fluid mechanics

### Two-phase flow boiling in a microfluidic channel at high mass flux

Physics of Fluids, Volume 32, Issue 9, September 2020.

We report the experimental investigations of two-phase flow boiling heat transfer characteristics of a refrigerant in a microfluidic channel at a high mass flux (more than 1000 kg/m2 s). We investigate the heat transfer coefficients at a heat flux range of 7.63 kW/m2–49.46 kW/m2, mass flux range of 600 kg/m2 s–1400 kg/m2 s (high mass flux), and saturation temperature range of 23 °C–31 °C. We propose the new two-phase flow boiling heat transfer correlation of a refrigerant, which is used as the working fluid for the present experiments, at the microfluidic scale. We experimentally establish the functional relationship of two-phase flow boiling heat transfer correlation of the refrigerant during flow boiling in a rectangular microchannel with the Reynolds number, the boiling number, and the Weber number. We believe that the inferences of this study may provide a design basis for the micro-heat exchanger, typically used for thermal management in electronic devices, micro-electro-mechanical systems, and electric vehicle battery cooling system.

We report the experimental investigations of two-phase flow boiling heat transfer characteristics of a refrigerant in a microfluidic channel at a high mass flux (more than 1000 kg/m2 s). We investigate the heat transfer coefficients at a heat flux range of 7.63 kW/m2–49.46 kW/m2, mass flux range of 600 kg/m2 s–1400 kg/m2 s (high mass flux), and saturation temperature range of 23 °C–31 °C. We propose the new two-phase flow boiling heat transfer correlation of a refrigerant, which is used as the working fluid for the present experiments, at the microfluidic scale. We experimentally establish the functional relationship of two-phase flow boiling heat transfer correlation of the refrigerant during flow boiling in a rectangular microchannel with the Reynolds number, the boiling number, and the Weber number. We believe that the inferences of this study may provide a design basis for the micro-heat exchanger, typically used for thermal management in electronic devices, micro-electro-mechanical systems, and electric vehicle battery cooling system.

Categories: Latest papers in fluid mechanics

### Anomalous features in internal cylinder flow instabilities subject to uncertain rotational effects

Physics of Fluids, Volume 32, Issue 9, September 2020.

We study the flow dynamics inside a high-speed rotating cylinder after introducing strong symmetry-breaking disturbance factors at cylinder wall motion. We propose and formulate a mathematically robust stochastic model for the rotational motion of the cylinder wall alongside the stochastic representation of incompressible Navier–Stokes equations. We employ a comprehensive stochastic computational fluid dynamics framework combining the spectral/hp element method and the probabilistic collocation method to obtain high-fidelity realizations of our mathematical model in order to quantify the propagation of parametric uncertainty for dynamics-representative quantities of interests. We observe that the modeled symmetry-breaking disturbances cause a flow instability arising from the wall. Utilizing global sensitivity analysis approaches, we identify the dominant source of uncertainty in our proposed model. We next perform a qualitative and quantitative statistical analysis on the fluctuating fields characterizing the fingerprints and measures of intense and rapidly evolving non-Gaussian behavior through space and time. We claim that such non-Gaussian statistics essentially emerge and evolve due to an intensified presence of coherent vortical motions initially triggered by the flow instability due to the symmetry-breaking rotation of the cylinder. We show that this mechanism causes memory effects in the flow dynamics in a way that noticeable anomaly in the time-scaling of enstrophy record is observed in the long run apart from the onset of instability. Our findings suggest an effective strategy to exploit controlled flow instabilities in order to enhance the turbulent mixing in engineering applications.

We study the flow dynamics inside a high-speed rotating cylinder after introducing strong symmetry-breaking disturbance factors at cylinder wall motion. We propose and formulate a mathematically robust stochastic model for the rotational motion of the cylinder wall alongside the stochastic representation of incompressible Navier–Stokes equations. We employ a comprehensive stochastic computational fluid dynamics framework combining the spectral/hp element method and the probabilistic collocation method to obtain high-fidelity realizations of our mathematical model in order to quantify the propagation of parametric uncertainty for dynamics-representative quantities of interests. We observe that the modeled symmetry-breaking disturbances cause a flow instability arising from the wall. Utilizing global sensitivity analysis approaches, we identify the dominant source of uncertainty in our proposed model. We next perform a qualitative and quantitative statistical analysis on the fluctuating fields characterizing the fingerprints and measures of intense and rapidly evolving non-Gaussian behavior through space and time. We claim that such non-Gaussian statistics essentially emerge and evolve due to an intensified presence of coherent vortical motions initially triggered by the flow instability due to the symmetry-breaking rotation of the cylinder. We show that this mechanism causes memory effects in the flow dynamics in a way that noticeable anomaly in the time-scaling of enstrophy record is observed in the long run apart from the onset of instability. Our findings suggest an effective strategy to exploit controlled flow instabilities in order to enhance the turbulent mixing in engineering applications.

Categories: Latest papers in fluid mechanics

### Correlation between linear and nonlinear material functions under large amplitude oscillatory shear

Physics of Fluids, Volume 32, Issue 9, September 2020.

Fourier transform rheology is the most frequently used method to interpret the nonlinear rheological behavior of complex fluids under large amplitude oscillatory shear (LAOS). However, the unclear relationship between the higher harmonics and the fundamental harmonic obscures the physical meaning of the nonlinear functions. Here, we hypothesize that all the nonlinear oscillatory shear functions and normal stress functions can be expressed as linear combinations of linear viscoelastic functions or their derivatives at different frequencies under both strain-controlled LAOS (LAOStrain) and stress-controlled LAOS (LAOStress). We check this hypothesis using the time-strain separable Wagner model, Giesekus model, and modified Leonov model. We find such correlations between the nonlinear material functions and the linear material functions are intrinsic for viscoelastic liquids under LAOStrain, and for viscoelastic solids under LAOStress. Finally, these correlations are justified by a viscoelastic standard polydimethylsiloxane, an ethylene–octene multiblock copolymer melt, and a typical simple yield stress material (0.25 wt. % Carbopol).

Fourier transform rheology is the most frequently used method to interpret the nonlinear rheological behavior of complex fluids under large amplitude oscillatory shear (LAOS). However, the unclear relationship between the higher harmonics and the fundamental harmonic obscures the physical meaning of the nonlinear functions. Here, we hypothesize that all the nonlinear oscillatory shear functions and normal stress functions can be expressed as linear combinations of linear viscoelastic functions or their derivatives at different frequencies under both strain-controlled LAOS (LAOStrain) and stress-controlled LAOS (LAOStress). We check this hypothesis using the time-strain separable Wagner model, Giesekus model, and modified Leonov model. We find such correlations between the nonlinear material functions and the linear material functions are intrinsic for viscoelastic liquids under LAOStrain, and for viscoelastic solids under LAOStress. Finally, these correlations are justified by a viscoelastic standard polydimethylsiloxane, an ethylene–octene multiblock copolymer melt, and a typical simple yield stress material (0.25 wt. % Carbopol).

Categories: Latest papers in fluid mechanics

### On determining the power-law fluid friction factor in a partially porous channel using the lattice Boltzmann method

Physics of Fluids, Volume 32, Issue 9, September 2020.

In the present work, the power-law fluid flow in a channel partially filled with a porous medium is numerically investigated using the lattice Boltzmann method (LBM). The porous domain, placed in the lower half of the channel, is represented according to a heterogeneous approach by a matrix of solid square disconnected blocks. The apparent viscosity of the power-law fluid is computed by locally varying the LBM relaxation factor. The results show the influence of geometry (porosity, number of obstacles, and hydraulic diameter), inertia (Reynolds number), and fluid properties (power-law index) over the partially porous-to-impermeable channel friction factor ratio. In general, the higher the porosity and the lower the number of obstacles, Reynolds number, and power-law index, the lower the friction factor. Finally, a correlation for the friction factor ratio as a function of the free region hydraulic diameter, permeability, and power-law index is presented for a specific channel configuration.

In the present work, the power-law fluid flow in a channel partially filled with a porous medium is numerically investigated using the lattice Boltzmann method (LBM). The porous domain, placed in the lower half of the channel, is represented according to a heterogeneous approach by a matrix of solid square disconnected blocks. The apparent viscosity of the power-law fluid is computed by locally varying the LBM relaxation factor. The results show the influence of geometry (porosity, number of obstacles, and hydraulic diameter), inertia (Reynolds number), and fluid properties (power-law index) over the partially porous-to-impermeable channel friction factor ratio. In general, the higher the porosity and the lower the number of obstacles, Reynolds number, and power-law index, the lower the friction factor. Finally, a correlation for the friction factor ratio as a function of the free region hydraulic diameter, permeability, and power-law index is presented for a specific channel configuration.

Categories: Latest papers in fluid mechanics

### Validation of finite element analysis strategy to investigate acoustic levitation in a two-axis acoustic levitator

Physics of Fluids, Volume 32, Issue 9, September 2020.

A two-axis acoustic levitator can be used to generate a standing pressure wave capable of levitating solid and liquid particles at appropriate input conditions. This work proposes a simulation framework to investigate the two-axis levitation particle stability using a commercial, computational fluid dynamics software based on the harmonic solution to the acoustic wave equation. The simulation produced predictions of the standing wave that include a strong “+” shaped pattern of nodes and anti-nodes that are aligned with the levitator axes. To verify the simulation, a levitator was built and used to generate the standing wave. The field was probed with a microphone and a motorized-scanning system. After scaling the simulated pressure to the measured pressure, the magnitudes of the sound pressure level at corresponding high-pressure locations were different by no more than 5%. This is the first time a measurement of a two-axis levitator standing pressure wave has been presented and shown to verify simulations. As an additional verification, the authors consulted high speed camera measurements of a reference-levitator transducer, which was found to have a maximum peak-to-peak displacement of 50 ± 5 μm. The reference-levitator is known to levitate water at 160 dB. The system for this work was simulated to match the operation of the reference-levitator so that it produced sound pressure levels of 160 dB. This pressure was achieved when the transducer maximum peak-to-peak displacement was 50.8 µm. The agreement between the two levitators’ displacements provides good justification that the modeling approach presented here produces reliable results.

A two-axis acoustic levitator can be used to generate a standing pressure wave capable of levitating solid and liquid particles at appropriate input conditions. This work proposes a simulation framework to investigate the two-axis levitation particle stability using a commercial, computational fluid dynamics software based on the harmonic solution to the acoustic wave equation. The simulation produced predictions of the standing wave that include a strong “+” shaped pattern of nodes and anti-nodes that are aligned with the levitator axes. To verify the simulation, a levitator was built and used to generate the standing wave. The field was probed with a microphone and a motorized-scanning system. After scaling the simulated pressure to the measured pressure, the magnitudes of the sound pressure level at corresponding high-pressure locations were different by no more than 5%. This is the first time a measurement of a two-axis levitator standing pressure wave has been presented and shown to verify simulations. As an additional verification, the authors consulted high speed camera measurements of a reference-levitator transducer, which was found to have a maximum peak-to-peak displacement of 50 ± 5 μm. The reference-levitator is known to levitate water at 160 dB. The system for this work was simulated to match the operation of the reference-levitator so that it produced sound pressure levels of 160 dB. This pressure was achieved when the transducer maximum peak-to-peak displacement was 50.8 µm. The agreement between the two levitators’ displacements provides good justification that the modeling approach presented here produces reliable results.

Categories: Latest papers in fluid mechanics

### Comprehensive study of monatomic fluid flow through elliptical carbon nanotubes

Physics of Fluids, Volume 32, Issue 9, September 2020.

To achieve a realistic model of a carbon nanotube (CNT) membrane, a good understanding of the effects associated with CNT deformations is a key issue. In this study, using molecular dynamics simulation, argon flow through elliptical CNTs is studied. Two armchair CNTs (6, 6) and (10, 10) were considered. The results demonstrated non-uniform dependency of the flow rate to eccentricity of the tube, leading to an unexpectedly increased flow rate in some cases. The effects of tube size, temperature, and pressure gradient are investigated, and longitudinal variations of the interatomic potential and average axial velocity in different segments of the cross section are presented to justify the abnormal behavior of the flow rate with eccentricity. The results showed a significant deviation from the macroscale expectations and approved elliptical deformation as a non-negligible change in the overall flow rate, which should be considered in predictive models of CNT membranes.

To achieve a realistic model of a carbon nanotube (CNT) membrane, a good understanding of the effects associated with CNT deformations is a key issue. In this study, using molecular dynamics simulation, argon flow through elliptical CNTs is studied. Two armchair CNTs (6, 6) and (10, 10) were considered. The results demonstrated non-uniform dependency of the flow rate to eccentricity of the tube, leading to an unexpectedly increased flow rate in some cases. The effects of tube size, temperature, and pressure gradient are investigated, and longitudinal variations of the interatomic potential and average axial velocity in different segments of the cross section are presented to justify the abnormal behavior of the flow rate with eccentricity. The results showed a significant deviation from the macroscale expectations and approved elliptical deformation as a non-negligible change in the overall flow rate, which should be considered in predictive models of CNT membranes.

Categories: Latest papers in fluid mechanics