# 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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### Vibration-induced floatation of a heavy liquid drop on a lighter liquid film

Physics of Fluids, Volume 31, Issue 8, August 2019.

We carry out a theoretical study of vibration-induced saturation of the Rayleigh-Taylor instability for an isolated liquid drop on the surface of a less dense finite-thickness carrier film. Without vibration, a heavy drop falls through the carrier film by forming a stretching liquid column until the bottom tip of the column reaches the solid substrate and the carrier film ruptures. We show that an externally applied vertical vibration prevents the rupture of the film and enables stable flotation of the drop. A hydrodynamic model is used to study the effect of inertia on the long-time dynamics of the drop. It is shown that rupture can only be prevented when the Reynolds number is nonzero.

We carry out a theoretical study of vibration-induced saturation of the Rayleigh-Taylor instability for an isolated liquid drop on the surface of a less dense finite-thickness carrier film. Without vibration, a heavy drop falls through the carrier film by forming a stretching liquid column until the bottom tip of the column reaches the solid substrate and the carrier film ruptures. We show that an externally applied vertical vibration prevents the rupture of the film and enables stable flotation of the drop. A hydrodynamic model is used to study the effect of inertia on the long-time dynamics of the drop. It is shown that rupture can only be prevented when the Reynolds number is nonzero.

Categories: Latest papers in fluid mechanics

### Direct simulation Monte Carlo on petaflop supercomputers and beyond

Physics of Fluids, Volume DSMC2019, Issue 1, November 2019.

The gold-standard definition of the Direct Simulation Monte Carlo (DSMC) method is given in the 1994 book by Bird [Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Clarendon Press, Oxford, UK, 1994)], which refined his pioneering earlier papers in which he first formulated the method. In the intervening 25 years, DSMC has become the method of choice for modeling rarefied gas dynamics in a variety of scenarios. The chief barrier to applying DSMC to more dense or even continuum flows is its computational expense compared to continuum computational fluid dynamics methods. The dramatic (nearly billion-fold) increase in speed of the largest supercomputers over the last 30 years has thus been a key enabling factor in using DSMC to model a richer variety of flows, due to the method’s inherent parallelism. We have developed the open-source SPARTA DSMC code with the goal of running DSMC efficiently on the largest machines, both current and future. It is largely an implementation of Bird’s 1994 formulation. Here, we describe algorithms used in SPARTA to enable DSMC to operate in parallel at the scale of many billions of particles or grid cells, or with billions of surface elements. We give a few examples of the kinds of fundamental physics questions and engineering applications that DSMC can address at these scales.

The gold-standard definition of the Direct Simulation Monte Carlo (DSMC) method is given in the 1994 book by Bird [Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Clarendon Press, Oxford, UK, 1994)], which refined his pioneering earlier papers in which he first formulated the method. In the intervening 25 years, DSMC has become the method of choice for modeling rarefied gas dynamics in a variety of scenarios. The chief barrier to applying DSMC to more dense or even continuum flows is its computational expense compared to continuum computational fluid dynamics methods. The dramatic (nearly billion-fold) increase in speed of the largest supercomputers over the last 30 years has thus been a key enabling factor in using DSMC to model a richer variety of flows, due to the method’s inherent parallelism. We have developed the open-source SPARTA DSMC code with the goal of running DSMC efficiently on the largest machines, both current and future. It is largely an implementation of Bird’s 1994 formulation. Here, we describe algorithms used in SPARTA to enable DSMC to operate in parallel at the scale of many billions of particles or grid cells, or with billions of surface elements. We give a few examples of the kinds of fundamental physics questions and engineering applications that DSMC can address at these scales.

Categories: Latest papers in fluid mechanics

### Direct simulation Monte Carlo on petaflop supercomputers and beyond

Physics of Fluids, Volume 31, Issue 8, August 2019.

The gold-standard definition of the Direct Simulation Monte Carlo (DSMC) method is given in the 1994 book by Bird [Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Clarendon Press, Oxford, UK, 1994)], which refined his pioneering earlier papers in which he first formulated the method. In the intervening 25 years, DSMC has become the method of choice for modeling rarefied gas dynamics in a variety of scenarios. The chief barrier to applying DSMC to more dense or even continuum flows is its computational expense compared to continuum computational fluid dynamics methods. The dramatic (nearly billion-fold) increase in speed of the largest supercomputers over the last 30 years has thus been a key enabling factor in using DSMC to model a richer variety of flows, due to the method’s inherent parallelism. We have developed the open-source SPARTA DSMC code with the goal of running DSMC efficiently on the largest machines, both current and future. It is largely an implementation of Bird’s 1994 formulation. Here, we describe algorithms used in SPARTA to enable DSMC to operate in parallel at the scale of many billions of particles or grid cells, or with billions of surface elements. We give a few examples of the kinds of fundamental physics questions and engineering applications that DSMC can address at these scales.

The gold-standard definition of the Direct Simulation Monte Carlo (DSMC) method is given in the 1994 book by Bird [Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Clarendon Press, Oxford, UK, 1994)], which refined his pioneering earlier papers in which he first formulated the method. In the intervening 25 years, DSMC has become the method of choice for modeling rarefied gas dynamics in a variety of scenarios. The chief barrier to applying DSMC to more dense or even continuum flows is its computational expense compared to continuum computational fluid dynamics methods. The dramatic (nearly billion-fold) increase in speed of the largest supercomputers over the last 30 years has thus been a key enabling factor in using DSMC to model a richer variety of flows, due to the method’s inherent parallelism. We have developed the open-source SPARTA DSMC code with the goal of running DSMC efficiently on the largest machines, both current and future. It is largely an implementation of Bird’s 1994 formulation. Here, we describe algorithms used in SPARTA to enable DSMC to operate in parallel at the scale of many billions of particles or grid cells, or with billions of surface elements. We give a few examples of the kinds of fundamental physics questions and engineering applications that DSMC can address at these scales.

Categories: Latest papers in fluid mechanics

### Improved upper bounds on the energy dissipation rate for shear flow with injection and suction

Physics of Fluids, Volume 31, Issue 8, August 2019.

Improved upper bounds on viscous energy dissipation rates of wall-driven shear flow subject to uniform injection and suction rates are computationally determined. The so-called “background” variational formulation is implemented via a time-stepping numerical scheme to determine optimal estimates. Shear flow Reynolds numbers range from 50 to 40 000 with injection angles up to 2°. The computed upper bounds for preselected angles of injection at high Reynolds numbers significantly improve the rigorously estimated ones. Our results suggest that the steady laminar flow is nonlinearly stable for angles of injection greater than 2°.

Improved upper bounds on viscous energy dissipation rates of wall-driven shear flow subject to uniform injection and suction rates are computationally determined. The so-called “background” variational formulation is implemented via a time-stepping numerical scheme to determine optimal estimates. Shear flow Reynolds numbers range from 50 to 40 000 with injection angles up to 2°. The computed upper bounds for preselected angles of injection at high Reynolds numbers significantly improve the rigorously estimated ones. Our results suggest that the steady laminar flow is nonlinearly stable for angles of injection greater than 2°.

Categories: Latest papers in fluid mechanics

### Ultra-local model-based control of the square-back Ahmed body wake flow

Physics of Fluids, Volume 31, Issue 8, August 2019.

This paper presents a new model-free control approach applied to a dynamical fluidic system. The main objective is to evaluate the ability of this closed-loop control technique to control the bistability of a turbulent wake flow past to a square-back Ahmed body. This bistable behavior occurs for some configurations depending mainly on the ground clearance. Due to the unsteady position of the wake vortex cores, the bistable phenomenon is responsible of a strong variation of the lateral force (drift force) and of a slight drag increase. Consequently, mitigating the wake symmetry-breaking modes can induce a substantial drag reduction. The feedback controller controls the drift using its ultralocal approximation and the estimation of its dynamics. The control signal is then applied to lateral blower actuators to suppress the spanwise bistability. The drift force is used as feedback to sense the wake flow, and concomitant velocity, forces, and pressure measurements are performed at a nominal Reynolds number of Reh = 2.86 × 105 to quantify and demonstrate the effectiveness of the present closed-loop control. Results show that for various actuation velocity ratios, the bistability suppression can lead to a drag reduction up to 2.5% with an energy consumption evaluated to be less than 0.6% of the aerodynamic power saving for the worst investigated case.

This paper presents a new model-free control approach applied to a dynamical fluidic system. The main objective is to evaluate the ability of this closed-loop control technique to control the bistability of a turbulent wake flow past to a square-back Ahmed body. This bistable behavior occurs for some configurations depending mainly on the ground clearance. Due to the unsteady position of the wake vortex cores, the bistable phenomenon is responsible of a strong variation of the lateral force (drift force) and of a slight drag increase. Consequently, mitigating the wake symmetry-breaking modes can induce a substantial drag reduction. The feedback controller controls the drift using its ultralocal approximation and the estimation of its dynamics. The control signal is then applied to lateral blower actuators to suppress the spanwise bistability. The drift force is used as feedback to sense the wake flow, and concomitant velocity, forces, and pressure measurements are performed at a nominal Reynolds number of Reh = 2.86 × 105 to quantify and demonstrate the effectiveness of the present closed-loop control. Results show that for various actuation velocity ratios, the bistability suppression can lead to a drag reduction up to 2.5% with an energy consumption evaluated to be less than 0.6% of the aerodynamic power saving for the worst investigated case.

Categories: Latest papers in fluid mechanics

### A deep learning enabler for nonintrusive reduced order modeling of fluid flows

Physics of Fluids, Volume 31, Issue 8, August 2019.

In this paper, we introduce a modular deep neural network (DNN) framework for data-driven reduced order modeling of dynamical systems relevant to fluid flows. We propose various DNN architectures which numerically predict evolution of dynamical systems by learning from either using discrete state or slope information of the system. Our approach has been demonstrated using both residual formula and backward difference scheme formulas. However, it can be easily generalized into many different numerical schemes as well. We give a demonstration of our framework for three examples: (i) Kraichnan-Orszag system, an illustrative coupled nonlinear ordinary differential equation, (ii) Lorenz system exhibiting chaotic behavior, and (iii) a nonintrusive model order reduction framework for the two-dimensional Boussinesq equations with a differentially heated cavity flow setup at various Rayleigh numbers. Using only snapshots of state variables at discrete time instances, our data-driven approach can be considered truly nonintrusive since any prior information about the underlying governing equations is not required for generating the reduced order model. Our a posteriori analysis shows that the proposed data-driven approach is remarkably accurate and can be used as a robust predictive tool for nonintrusive model order reduction of complex fluid flows.

In this paper, we introduce a modular deep neural network (DNN) framework for data-driven reduced order modeling of dynamical systems relevant to fluid flows. We propose various DNN architectures which numerically predict evolution of dynamical systems by learning from either using discrete state or slope information of the system. Our approach has been demonstrated using both residual formula and backward difference scheme formulas. However, it can be easily generalized into many different numerical schemes as well. We give a demonstration of our framework for three examples: (i) Kraichnan-Orszag system, an illustrative coupled nonlinear ordinary differential equation, (ii) Lorenz system exhibiting chaotic behavior, and (iii) a nonintrusive model order reduction framework for the two-dimensional Boussinesq equations with a differentially heated cavity flow setup at various Rayleigh numbers. Using only snapshots of state variables at discrete time instances, our data-driven approach can be considered truly nonintrusive since any prior information about the underlying governing equations is not required for generating the reduced order model. Our a posteriori analysis shows that the proposed data-driven approach is remarkably accurate and can be used as a robust predictive tool for nonintrusive model order reduction of complex fluid flows.

Categories: Latest papers in fluid mechanics

### Diffusivity ratio effect on the onset of the buoyancy-driven instability of an A + B → C chemical reaction system in a Hele-Shaw cell: Numerical simulations and comparison with experiments

Physics of Fluids, Volume 31, Issue 8, August 2019.

The effect of different diffusivities on the evolution of buoyancy-driven instability in a reactive-diffusion system is analyzed. For an instantaneous A + B → C chemical reaction in a Hele-Shaw cell, where a less dense phase of A is layered on top of a denser solution of B, the temporal evolution of the instability motion is traced numerically by using the Fourier spectral method. As expected, the evolution of instabilities can be controlled by chemical factors, such as the ratios of diffusivities, reactant concentrations, and densification coefficients. Double diffusive effects accelerate and hinder the evolution of instabilities and induce the onset of instabilities without an adverse density gradient. The present numerical simulation explains the previous experiments for the NH3 + CH3COOH → CH3COONH4 reaction in a Hele-Shaw cell, which was devised to explain the impact of the chemical reaction in geological CO2 sequestration.

The effect of different diffusivities on the evolution of buoyancy-driven instability in a reactive-diffusion system is analyzed. For an instantaneous A + B → C chemical reaction in a Hele-Shaw cell, where a less dense phase of A is layered on top of a denser solution of B, the temporal evolution of the instability motion is traced numerically by using the Fourier spectral method. As expected, the evolution of instabilities can be controlled by chemical factors, such as the ratios of diffusivities, reactant concentrations, and densification coefficients. Double diffusive effects accelerate and hinder the evolution of instabilities and induce the onset of instabilities without an adverse density gradient. The present numerical simulation explains the previous experiments for the NH3 + CH3COOH → CH3COONH4 reaction in a Hele-Shaw cell, which was devised to explain the impact of the chemical reaction in geological CO2 sequestration.

Categories: Latest papers in fluid mechanics

### Numerical study of droplet formation in the ordinary and modified T-junctions

Physics of Fluids, Volume 31, Issue 8, August 2019.

This work presents a flexible manipulation solution on droplet formation based on the modified T-junction with a rectangular rib to reduce the droplet size and improve monodispersity. The droplet formation in the ordinary and modified T-junctions is numerically investigated using the verified three-dimensional volume of fluid method. The results reveal that the modified T-junction can significantly enlarge the dripping regime and droplet-generable regimes while decreasing the jetting regime. In the modified T-junction, the droplet detachment is much easier as the detachment driving forces are strengthened, while the resistance forces are weakened. By investigating the droplet formation in the ordinary and different modified T-junctions with change in viscosity, surface tension, and wall wettability, it is found that the dominant geometric factor affecting the droplet formation is the rib height, not the rib width. Based on the rib height, two modified scaling laws are proposed to predict droplet size in squeezing and dripping regimes. The wall wettability can deteriorate the droplet formation in the ordinary T-junction, while the rib in the modified T-junction can weaken this adverse effect.

This work presents a flexible manipulation solution on droplet formation based on the modified T-junction with a rectangular rib to reduce the droplet size and improve monodispersity. The droplet formation in the ordinary and modified T-junctions is numerically investigated using the verified three-dimensional volume of fluid method. The results reveal that the modified T-junction can significantly enlarge the dripping regime and droplet-generable regimes while decreasing the jetting regime. In the modified T-junction, the droplet detachment is much easier as the detachment driving forces are strengthened, while the resistance forces are weakened. By investigating the droplet formation in the ordinary and different modified T-junctions with change in viscosity, surface tension, and wall wettability, it is found that the dominant geometric factor affecting the droplet formation is the rib height, not the rib width. Based on the rib height, two modified scaling laws are proposed to predict droplet size in squeezing and dripping regimes. The wall wettability can deteriorate the droplet formation in the ordinary T-junction, while the rib in the modified T-junction can weaken this adverse effect.

Categories: Latest papers in fluid mechanics

### Single diffusive magnetohydrodynamic pressure driven miscible displacement flows in a channel

Physics of Fluids, Volume 31, Issue 8, August 2019.

We investigate the influence of a magnetic field on the single diffusive pressure driven miscible displacement of a low viscous fluid by a high viscous one in a channel using the streamline upwind Petrov-Galerkin based finite element method. We perform transient numerical simulations of the governing continuity and Navier–Stokes equations with magnetohydrodynamic effects coupled with the convection–diffusion solute concentration equation. We have assumed concentration-dependent viscosity and neglected the density contrast. Our computational results are found to match quite well with the other results from the literature. We report that the presence of a magnetic field can suppress the interface instabilities characterized by intense convective mixing and roll-up phenomena for the classical situation of a less viscous fluid displacing a more viscous one. We have found various new types of instability patterns with the combined influences of the Hartmann number, Reynolds number, and Schmidt number. We show that the mushroomlike structure at the tip of the leading finger grows in volume with enhancing magnetic field strength, whereas follows the reverse trend as the Reynolds number is increased. Finally, to examine the effect of magnetic field on the global stability characteristics, we have performed a dynamic mode decomposition analysis. Our analysis demonstrates that by effectively maneuvering the dimensionless parameters, the displacement rate can be enhanced, and this is attributed to the acceleration in fluid mixing. Apart from the fundamental importance, we trust that the results obtained from this study may help in improving the operating efficiency of the modern generation process industries.

We investigate the influence of a magnetic field on the single diffusive pressure driven miscible displacement of a low viscous fluid by a high viscous one in a channel using the streamline upwind Petrov-Galerkin based finite element method. We perform transient numerical simulations of the governing continuity and Navier–Stokes equations with magnetohydrodynamic effects coupled with the convection–diffusion solute concentration equation. We have assumed concentration-dependent viscosity and neglected the density contrast. Our computational results are found to match quite well with the other results from the literature. We report that the presence of a magnetic field can suppress the interface instabilities characterized by intense convective mixing and roll-up phenomena for the classical situation of a less viscous fluid displacing a more viscous one. We have found various new types of instability patterns with the combined influences of the Hartmann number, Reynolds number, and Schmidt number. We show that the mushroomlike structure at the tip of the leading finger grows in volume with enhancing magnetic field strength, whereas follows the reverse trend as the Reynolds number is increased. Finally, to examine the effect of magnetic field on the global stability characteristics, we have performed a dynamic mode decomposition analysis. Our analysis demonstrates that by effectively maneuvering the dimensionless parameters, the displacement rate can be enhanced, and this is attributed to the acceleration in fluid mixing. Apart from the fundamental importance, we trust that the results obtained from this study may help in improving the operating efficiency of the modern generation process industries.

Categories: Latest papers in fluid mechanics

### Direct molecular simulation of internal energy relaxation and dissociation in oxygen

Physics of Fluids, Volume DSMC2019, Issue 1, November 2019.

A variant of the direct simulation Monte Carlo (DSMC) method, referred to as direct molecular simulation (DMS), is used to study oxygen dissociation from first principles. The sole model input to the DMS calculations consists of 12 potential energy surfaces that govern O2 + O2 and O + O2 collisions, including all spin-spatial degenerate configurations, in the ground electronic state. DMS calculations are representative of the gas evolution behind a strong shock wave, where molecular oxygen excites rotationally and vibrationally before ultimately dissociating and reaching a quasi-steady-state (QSS). Vibrational relaxation time constants are presented for both O2 + O2 and O + O2 collisions and are found to agree closely with experimental data. Compared to O2 + O2 collisions, vibrational relaxation due to O + O2 collisions is found to be ten times faster and to have a weak dependence on temperature. Dissociation rate constants in the QSS dissociation phase are presented for both O2 + O2 and O + O2 collisions and agree (within experimental uncertainty) with rates inferred from shock-tube experiments. Both experiments and simulations indicate that the QSS dissociation rate coefficients for O + O2 interactions are about two times greater than the ones for O2 + O2. DMS calculations predict this to be a result of nonequilibrium (non-Boltzmann) internal energy distributions. Specifically, the increased dissociation rate is caused by faster vibrational relaxation, due to O + O2 collisions, which alters the vibrational energy distribution function in the QSS by populating higher energy states that readily dissociate. Although existing experimental data appear to support this prediction, experiments with lower uncertainty are needed for quantitative validation. The DMS data presented for rovibrational relaxation and dissociation in oxygen could be used to formulate models for DSMC and computational fluid dynamics methods.

A variant of the direct simulation Monte Carlo (DSMC) method, referred to as direct molecular simulation (DMS), is used to study oxygen dissociation from first principles. The sole model input to the DMS calculations consists of 12 potential energy surfaces that govern O2 + O2 and O + O2 collisions, including all spin-spatial degenerate configurations, in the ground electronic state. DMS calculations are representative of the gas evolution behind a strong shock wave, where molecular oxygen excites rotationally and vibrationally before ultimately dissociating and reaching a quasi-steady-state (QSS). Vibrational relaxation time constants are presented for both O2 + O2 and O + O2 collisions and are found to agree closely with experimental data. Compared to O2 + O2 collisions, vibrational relaxation due to O + O2 collisions is found to be ten times faster and to have a weak dependence on temperature. Dissociation rate constants in the QSS dissociation phase are presented for both O2 + O2 and O + O2 collisions and agree (within experimental uncertainty) with rates inferred from shock-tube experiments. Both experiments and simulations indicate that the QSS dissociation rate coefficients for O + O2 interactions are about two times greater than the ones for O2 + O2. DMS calculations predict this to be a result of nonequilibrium (non-Boltzmann) internal energy distributions. Specifically, the increased dissociation rate is caused by faster vibrational relaxation, due to O + O2 collisions, which alters the vibrational energy distribution function in the QSS by populating higher energy states that readily dissociate. Although existing experimental data appear to support this prediction, experiments with lower uncertainty are needed for quantitative validation. The DMS data presented for rovibrational relaxation and dissociation in oxygen could be used to formulate models for DSMC and computational fluid dynamics methods.

Categories: Latest papers in fluid mechanics