# 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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### Pulsed-jet propulsion via shape deformation of an axisymmetric swimmer

Physics of Fluids, Volume 32, Issue 8, August 2020.

By using an axisymmetric immersed-boundary model, we numerically investigate the thrust generation of a deformable body via pulsed jetting. We focus on a single discharging process resulting from the deflation of the body as inspired by the jetting mechanism of cephalopods, such as squids. We examine three jet velocity profiles, namely, impulsive, half-cosine, and cosine, in the relatively low Reynolds number regime. For the impulsive profile, we demonstrate via wake visualization that the leading vortex ring does not pinch off from the trailing jet although its circulation stops growing after a critical formation number (hereby, the formation number is defined as the ratio between the length and diameter of the jet plug) of 6–7. The exact value of the critical formation number depends on the jet velocity profile, suggesting that jet acceleration and viscous dissipation play significant roles in vortex ring evolution. In terms of thrust generation, our results indicate that besides the jet momentum flux, an important source of thrust generation is jet acceleration. The implication is that the jet velocity profile is a key factor in determining the propulsive performance.

By using an axisymmetric immersed-boundary model, we numerically investigate the thrust generation of a deformable body via pulsed jetting. We focus on a single discharging process resulting from the deflation of the body as inspired by the jetting mechanism of cephalopods, such as squids. We examine three jet velocity profiles, namely, impulsive, half-cosine, and cosine, in the relatively low Reynolds number regime. For the impulsive profile, we demonstrate via wake visualization that the leading vortex ring does not pinch off from the trailing jet although its circulation stops growing after a critical formation number (hereby, the formation number is defined as the ratio between the length and diameter of the jet plug) of 6–7. The exact value of the critical formation number depends on the jet velocity profile, suggesting that jet acceleration and viscous dissipation play significant roles in vortex ring evolution. In terms of thrust generation, our results indicate that besides the jet momentum flux, an important source of thrust generation is jet acceleration. The implication is that the jet velocity profile is a key factor in determining the propulsive performance.

Categories: Latest papers in fluid mechanics

### Novel similarities in the free-surface profiles and velocities of solitary waves traveling over a very steep beach

Physics of Fluids, Volume 32, Issue 8, August 2020.

This study investigates experimentally similarity and Froude number similitude (FNS) in the dimensionless flow features of three solitary waves traveling on a 1:3 sloping beach. These three waves, designated as cases A, B, and C, respectively, have different heights H0 (=5.8 cm, 2.9 cm, and 1.815 cm) and still water depths h0 (=16.0 cm, 8.0 cm, and 5.0 cm), but identical ratios H0/h0 (=0.363). A high-speed particle image velocimetry system is employed to obtain the free surface profiles (FSPs) and velocity fields/profiles. These features include the free surface elevation (FSE)/FSP time series; velocity fields and profiles, positions, and propagation speeds of flow demarcation curves; times and maximum onshore distances of the maximum run-up heights (MRHs); and times and onshore distances of hydraulic jumps for cases A and B. When the swash tip of a solitary wave reaches the MRH, the contact point becomes almost immobile for a short time interval, with the contact angle changing from obtuse, via right, to acute angle. For cases A and B, the similarities in the dimensionless MRHs and times, at which the run-down motions of the wave tips start, are affirmed. These facts highlight that the swash tips and contact points are subject to complex interactions among gravity force, viscous friction, and surface tension of fluid. Case C, having the smallest length scale, is only focused on the arrival or starting time of the MRH or run-down motion and the MRH and used as a counterexample to demonstrate the absence of similarity or FNS due to the relatively prominent effects of viscous friction and surface tension.

This study investigates experimentally similarity and Froude number similitude (FNS) in the dimensionless flow features of three solitary waves traveling on a 1:3 sloping beach. These three waves, designated as cases A, B, and C, respectively, have different heights H0 (=5.8 cm, 2.9 cm, and 1.815 cm) and still water depths h0 (=16.0 cm, 8.0 cm, and 5.0 cm), but identical ratios H0/h0 (=0.363). A high-speed particle image velocimetry system is employed to obtain the free surface profiles (FSPs) and velocity fields/profiles. These features include the free surface elevation (FSE)/FSP time series; velocity fields and profiles, positions, and propagation speeds of flow demarcation curves; times and maximum onshore distances of the maximum run-up heights (MRHs); and times and onshore distances of hydraulic jumps for cases A and B. When the swash tip of a solitary wave reaches the MRH, the contact point becomes almost immobile for a short time interval, with the contact angle changing from obtuse, via right, to acute angle. For cases A and B, the similarities in the dimensionless MRHs and times, at which the run-down motions of the wave tips start, are affirmed. These facts highlight that the swash tips and contact points are subject to complex interactions among gravity force, viscous friction, and surface tension of fluid. Case C, having the smallest length scale, is only focused on the arrival or starting time of the MRH or run-down motion and the MRH and used as a counterexample to demonstrate the absence of similarity or FNS due to the relatively prominent effects of viscous friction and surface tension.

Categories: Latest papers in fluid mechanics

### Energy loss and developing length during reciprocating flow in a pipe with a free-end

Physics of Fluids, Volume 32, Issue 8, August 2020.

Direct numerical simulations of reciprocating pipe flow in a straight pipe with a free-end are presented. The range of amplitudes and frequencies studied span the laminar regime and the beginning of transition toward a conditionally turbulent flow. Two primary results are reported: the measurement of the flow development length and the loss of energy, both due to the presence of the free-end. Two regimes of flow are identified with distinct length scales. For low frequencies, the development length scales with the pipe diameter D. However, for higher frequencies, the development length scales with the Stokes layer thickness [math]. The energy loss is studied by calculating the viscous dissipation function, indicating where energy is lost, and allowing the energy lost due to the presence of the free-end to be isolated. While strong vortices are formed and convected from the exit, most of the energy they dissipate is lost within a few pipe diameters of the exit. It is shown that these trends continue even as the amplitude and frequency are increased so that the flow begins to transition from a laminar toward a turbulent state. Two modes of instability are observed in the Stokes layers near the free-end, one short wavelength mode with a wavelength set by the Stokes layer thickness and the other long wavelength mode with a wavelength set by the amplitude of the oscillatory flow. These modes are related to those observed in the fully developed oscillatory flow.

Direct numerical simulations of reciprocating pipe flow in a straight pipe with a free-end are presented. The range of amplitudes and frequencies studied span the laminar regime and the beginning of transition toward a conditionally turbulent flow. Two primary results are reported: the measurement of the flow development length and the loss of energy, both due to the presence of the free-end. Two regimes of flow are identified with distinct length scales. For low frequencies, the development length scales with the pipe diameter D. However, for higher frequencies, the development length scales with the Stokes layer thickness [math]. The energy loss is studied by calculating the viscous dissipation function, indicating where energy is lost, and allowing the energy lost due to the presence of the free-end to be isolated. While strong vortices are formed and convected from the exit, most of the energy they dissipate is lost within a few pipe diameters of the exit. It is shown that these trends continue even as the amplitude and frequency are increased so that the flow begins to transition from a laminar toward a turbulent state. Two modes of instability are observed in the Stokes layers near the free-end, one short wavelength mode with a wavelength set by the Stokes layer thickness and the other long wavelength mode with a wavelength set by the amplitude of the oscillatory flow. These modes are related to those observed in the fully developed oscillatory flow.

Categories: Latest papers in fluid mechanics

### Global characteristics of transverse jets of aviation kerosene–long-chain alcohol blends

Physics of Fluids, Volume 32, Issue 8, August 2020.

Long-chain alcohol is a promising alternative for commercial fuels. This study aims at experimentally determining the characteristics of transverse jets using long-chain alcohol in aviation applications. The surface wavelength, breakup regime, upper trajectory of a transverse jet, and liquid column breakup point location are investigated. The column breakup and surface breakup are both observed in experiments, and in the surface breakup regime, there exist bag breakup, multimode breakup, and shear breakup. Shear breakup appears in the conditions with Weg lower than 80. An equation for predicting the upper trajectory of aviation kerosene–long chain alcohol (AKL) blends is proposed. Addition of n-butanol makes the upper trajectory lower, whereas addition of n-pentanol makes the upper trajectory higher. Two equations are proposed for predicting the horizontal and vertical positions of the liquid column breakup point, taking Weg, Oh, and q into account. Blending of n-butanol increases xb and zb, whereas the addition of n-pentanol decreases them. By introducing Kelvin–Helmholtz instability and Rayleigh–Taylor instability into the theoretical analysis, λs is showed to be related with Weg and Oh. Using the results of theoretical analysis, as well as the experimental data, a prediction equation for λs is proposed. The variation of λs caused by fuel modification is studied, the λs is shortened with the addition of long-chain alcohol, and aviation kerosene–n-pentanol blends show shorter surface wavelengths than those of aviation kerosene–n-butanol blends with the same blending ratios. This work provides a better understanding of the characteristics of AKL blends, which will be useful in expanding aviation applications of this fuel.

Long-chain alcohol is a promising alternative for commercial fuels. This study aims at experimentally determining the characteristics of transverse jets using long-chain alcohol in aviation applications. The surface wavelength, breakup regime, upper trajectory of a transverse jet, and liquid column breakup point location are investigated. The column breakup and surface breakup are both observed in experiments, and in the surface breakup regime, there exist bag breakup, multimode breakup, and shear breakup. Shear breakup appears in the conditions with Weg lower than 80. An equation for predicting the upper trajectory of aviation kerosene–long chain alcohol (AKL) blends is proposed. Addition of n-butanol makes the upper trajectory lower, whereas addition of n-pentanol makes the upper trajectory higher. Two equations are proposed for predicting the horizontal and vertical positions of the liquid column breakup point, taking Weg, Oh, and q into account. Blending of n-butanol increases xb and zb, whereas the addition of n-pentanol decreases them. By introducing Kelvin–Helmholtz instability and Rayleigh–Taylor instability into the theoretical analysis, λs is showed to be related with Weg and Oh. Using the results of theoretical analysis, as well as the experimental data, a prediction equation for λs is proposed. The variation of λs caused by fuel modification is studied, the λs is shortened with the addition of long-chain alcohol, and aviation kerosene–n-pentanol blends show shorter surface wavelengths than those of aviation kerosene–n-butanol blends with the same blending ratios. This work provides a better understanding of the characteristics of AKL blends, which will be useful in expanding aviation applications of this fuel.

Categories: Latest papers in fluid mechanics

### Invisibility concentrator for water waves

Physics of Fluids, Volume 32, Issue 8, August 2020.

We theoretically design and experimentally demonstrate an invisibility concentrator, consisting of several truncated cylinders, for water waves based on a scattering cancellation method. The invisibility concentrator works by controlling the scattered waves from the target device. Our simulated and experimental results verify the concentration of waves and show the effective invisibility of the designed concentrator. This approach provides the possibility of simultaneously realizing wave concentration and an invisibility cloak, which has potential applications in energy harvesting.

We theoretically design and experimentally demonstrate an invisibility concentrator, consisting of several truncated cylinders, for water waves based on a scattering cancellation method. The invisibility concentrator works by controlling the scattered waves from the target device. Our simulated and experimental results verify the concentration of waves and show the effective invisibility of the designed concentrator. This approach provides the possibility of simultaneously realizing wave concentration and an invisibility cloak, which has potential applications in energy harvesting.

Categories: Latest papers in fluid mechanics

### Passive and active control of turbulent flows

Physics of Fluids, Volume 32, Issue 8, August 2020.

Categories: Latest papers in fluid mechanics

### Flow of yield stress materials through annular abrupt expansion–contractions

Physics of Fluids, Volume 32, Issue 8, August 2020.

We present an experimental study of the flow of yield stress materials through annular abrupt expansions–contractions, to evaluate the flow invasion into the cavity formed in the larger cross section region. Steady inertialess flows of Carbopol® aqueous dispersions were investigated. The flow pattern reveals yielded and unyielded regions, which were visualized using tracer particles, laser sheets, and a digital camera. The yield surfaces were identified in the experiments by choosing large enough exposure times that allow sufficient particle displacement in the yielded region. To estimate the amount of fluid that remains stagnant in the cavity, we defined the invasion ratio, a quantity that was determined through image processing for different combinations of the governing parameters. The influence of the cavity diameter and axial length, eccentricity, and inlet velocity on the invasion ratio was investigated. Fore-aft asymmetric yield surfaces were observed for all tests, probably due to elastic effects.

We present an experimental study of the flow of yield stress materials through annular abrupt expansions–contractions, to evaluate the flow invasion into the cavity formed in the larger cross section region. Steady inertialess flows of Carbopol® aqueous dispersions were investigated. The flow pattern reveals yielded and unyielded regions, which were visualized using tracer particles, laser sheets, and a digital camera. The yield surfaces were identified in the experiments by choosing large enough exposure times that allow sufficient particle displacement in the yielded region. To estimate the amount of fluid that remains stagnant in the cavity, we defined the invasion ratio, a quantity that was determined through image processing for different combinations of the governing parameters. The influence of the cavity diameter and axial length, eccentricity, and inlet velocity on the invasion ratio was investigated. Fore-aft asymmetric yield surfaces were observed for all tests, probably due to elastic effects.

Categories: Latest papers in fluid mechanics

### Vibrational relaxation time measurements in shock-heated oxygen and air from 2000 K to 9000 K using ultraviolet laser absorption

Physics of Fluids, Volume 32, Issue 8, August 2020.

Vibrational relaxation times of oxygen (O2) were measured behind reflected shocks in shock-tube experiments with O2 and nitrogen (N2) collision partners. To determine relaxation times, a tunable ultraviolet laser absorption diagnostic probed time-histories involving the fourth (v″ = 4), fifth (v″ = 5), and sixth (v″ = 6) vibrational levels of the ground electronic state of O2. Taking the ratio of two absorbance time-histories involving different vibrational levels yielded vibrational temperature time-histories that were fit to isolate the relevant vibrational relaxation times. Pure O2 experiments were used to isolate the vibration–translation (VT) relaxation time of O2 with O2. Results for [math] agree with the Millikan and White correlation at temperatures below 4000 K. However, high-temperature data deviate from the Millikan and White correlation, exhibiting a reduced temperature dependence—an observation that remains consistent with previous experimental studies. Additional experiments in 10% and 21% O2 in N2 mixtures were used to isolate both the VT and vibration–vibration (VV) relaxation times of O2 with N2. The data for [math] exceed the Millikan and White correlation by 70% but show reasonable agreement with previous data below 5000 K. High-temperature results again show a reduced temperature dependence, but this study shows longer relaxation times than the previous work. The data for [math] exceed the semi-empirical relation developed by Berend et al. [“Vibration-vibration energy exchange in N2 with O2 and HCl collision partners,” J. Chem. Phys. 57, 3601–3604 (1972)] by 70% but overlap with previous measurements. Due to insensitivity of the chemical system to VV transfer at high temperatures, results for [math] were only measured below 6000 K.

Vibrational relaxation times of oxygen (O2) were measured behind reflected shocks in shock-tube experiments with O2 and nitrogen (N2) collision partners. To determine relaxation times, a tunable ultraviolet laser absorption diagnostic probed time-histories involving the fourth (v″ = 4), fifth (v″ = 5), and sixth (v″ = 6) vibrational levels of the ground electronic state of O2. Taking the ratio of two absorbance time-histories involving different vibrational levels yielded vibrational temperature time-histories that were fit to isolate the relevant vibrational relaxation times. Pure O2 experiments were used to isolate the vibration–translation (VT) relaxation time of O2 with O2. Results for [math] agree with the Millikan and White correlation at temperatures below 4000 K. However, high-temperature data deviate from the Millikan and White correlation, exhibiting a reduced temperature dependence—an observation that remains consistent with previous experimental studies. Additional experiments in 10% and 21% O2 in N2 mixtures were used to isolate both the VT and vibration–vibration (VV) relaxation times of O2 with N2. The data for [math] exceed the Millikan and White correlation by 70% but show reasonable agreement with previous data below 5000 K. High-temperature results again show a reduced temperature dependence, but this study shows longer relaxation times than the previous work. The data for [math] exceed the semi-empirical relation developed by Berend et al. [“Vibration-vibration energy exchange in N2 with O2 and HCl collision partners,” J. Chem. Phys. 57, 3601–3604 (1972)] by 70% but overlap with previous measurements. Due to insensitivity of the chemical system to VV transfer at high temperatures, results for [math] were only measured below 6000 K.

Categories: Latest papers in fluid mechanics

### Linear stability of the flow of a second order fluid past a wedge

Physics of Fluids, Volume 32, Issue 8, August 2020.

The linear stability analysis of Rivlin–Ericksen fluids of second order is investigated for boundary layer flows, where a semi-infinite wedge is placed symmetrically with respect to the flow direction. Second order fluids belong to a larger family of fluids called order fluids, which is one of the first classes proposed to model departures from Newtonian behavior. Second order fluids can model non-zero normal stress differences, which is an essential feature of viscoelastic fluids. The linear stability properties are studied for both signs of the elasticity number K, which characterizes the non-Newtonian response of the fluid. Stabilization is observed for the temporal and spatial evolution of two-dimensional disturbances when K > 0 in terms of increase of critical Reynolds numbers and reduction of growth rates, whereas the flow is less stable when K < 0. By extending the analysis to three-dimensional disturbances, we show that a positive elasticity number K destabilizes streamwise independent waves, while the opposite happens for K < 0. We show that, as for Newtonian fluids, the non-modal amplification of streamwise independent disturbances is the most dangerous mechanism for transient energy growth, which is enhanced when K > 0 and diminished when K < 0.

The linear stability analysis of Rivlin–Ericksen fluids of second order is investigated for boundary layer flows, where a semi-infinite wedge is placed symmetrically with respect to the flow direction. Second order fluids belong to a larger family of fluids called order fluids, which is one of the first classes proposed to model departures from Newtonian behavior. Second order fluids can model non-zero normal stress differences, which is an essential feature of viscoelastic fluids. The linear stability properties are studied for both signs of the elasticity number K, which characterizes the non-Newtonian response of the fluid. Stabilization is observed for the temporal and spatial evolution of two-dimensional disturbances when K > 0 in terms of increase of critical Reynolds numbers and reduction of growth rates, whereas the flow is less stable when K < 0. By extending the analysis to three-dimensional disturbances, we show that a positive elasticity number K destabilizes streamwise independent waves, while the opposite happens for K < 0. We show that, as for Newtonian fluids, the non-modal amplification of streamwise independent disturbances is the most dangerous mechanism for transient energy growth, which is enhanced when K > 0 and diminished when K < 0.

Categories: Latest papers in fluid mechanics

### Analysis of combustion acoustic phenomena in compression–ignition engines using large eddy simulation

Physics of Fluids, Volume 32, Issue 8, August 2020.

As computational capabilities continue to grow, exploring the limits of computational fluid dynamics to capture complex and elusive phenomena, which are otherwise difficult to study by experimental techniques, is one of the main targets for the research community. This paper presents a detailed analysis of the physical processes that lead to combustion noise emissions in internal combustion engines. In particular, diesel combustion in a compression–ignition (CI) engine is studied in order to understand the singular behavior of the in-cylinder flow field responsible for the acoustic emissions. The main objective is, therefore, to improve the understanding of the phenomena involved in CI engine noise using large eddy simulations. Several visualization methods are employed to investigate the connection between combustion behavior and its effects on the pressure field. In addition, proper orthogonal decomposition is used to analyze the modal energy distribution among all the acoustic modes. The results show that the acoustic signature is fundamentally conditioned by the intensity of the premixed combustion rather than by the pressure oscillations generated by turbulent fluctuations in the flame surface established during the diffusion stage.

As computational capabilities continue to grow, exploring the limits of computational fluid dynamics to capture complex and elusive phenomena, which are otherwise difficult to study by experimental techniques, is one of the main targets for the research community. This paper presents a detailed analysis of the physical processes that lead to combustion noise emissions in internal combustion engines. In particular, diesel combustion in a compression–ignition (CI) engine is studied in order to understand the singular behavior of the in-cylinder flow field responsible for the acoustic emissions. The main objective is, therefore, to improve the understanding of the phenomena involved in CI engine noise using large eddy simulations. Several visualization methods are employed to investigate the connection between combustion behavior and its effects on the pressure field. In addition, proper orthogonal decomposition is used to analyze the modal energy distribution among all the acoustic modes. The results show that the acoustic signature is fundamentally conditioned by the intensity of the premixed combustion rather than by the pressure oscillations generated by turbulent fluctuations in the flame surface established during the diffusion stage.

Categories: Latest papers in fluid mechanics

### Transport and deposition of dilute microparticles in turbulent thermal convection

Physics of Fluids, Volume 32, Issue 8, August 2020.

We analyze the transport and deposition behavior of dilute microparticles in turbulent Rayleigh–Bénard convection. Two-dimensional direct numerical simulations were carried out for the Rayleigh number (Ra) of 108 and the Prandtl number (Pr) of 0.71 (corresponding to the working fluids of air). The Lagrangian point particle model was used to describe the motion of microparticles in the turbulence. Our results show that the suspended particles are homogeneously distributed in the turbulence for the Stokes number (St) less than 10−3, and they tend to cluster into bands for 10−3 ≲ St ≲ 10−2. At even larger St, the microparticles will quickly sediment in the convection. We also calculate the mean-square displacement (MSD) of the particle’s trajectories. At short time intervals, the MSD exhibits a ballistic regime, and it is isotropic in vertical and lateral directions; at longer time intervals, the MSD reflects a confined motion for the particles, and it is anisotropic in different directions. We further obtained a phase diagram of the particle deposition positions on the wall, and we identified three deposition states depending on the particle’s density and diameter. An interesting finding is that the dispersed particles preferred to deposit on the vertical wall where the hot plumes arise, which is verified by tilting the cell and altering the rotation direction of the large-scale circulation.

We analyze the transport and deposition behavior of dilute microparticles in turbulent Rayleigh–Bénard convection. Two-dimensional direct numerical simulations were carried out for the Rayleigh number (Ra) of 108 and the Prandtl number (Pr) of 0.71 (corresponding to the working fluids of air). The Lagrangian point particle model was used to describe the motion of microparticles in the turbulence. Our results show that the suspended particles are homogeneously distributed in the turbulence for the Stokes number (St) less than 10−3, and they tend to cluster into bands for 10−3 ≲ St ≲ 10−2. At even larger St, the microparticles will quickly sediment in the convection. We also calculate the mean-square displacement (MSD) of the particle’s trajectories. At short time intervals, the MSD exhibits a ballistic regime, and it is isotropic in vertical and lateral directions; at longer time intervals, the MSD reflects a confined motion for the particles, and it is anisotropic in different directions. We further obtained a phase diagram of the particle deposition positions on the wall, and we identified three deposition states depending on the particle’s density and diameter. An interesting finding is that the dispersed particles preferred to deposit on the vertical wall where the hot plumes arise, which is verified by tilting the cell and altering the rotation direction of the large-scale circulation.

Categories: Latest papers in fluid mechanics

### Stability and control of an annular rotor/stator cavity limit cycle

Physics of Fluids, Volume 32, Issue 8, August 2020.

Rotating cavity flows have been widely studied for years because of many implications that these have on industrial applications. These flows can indeed generate, under specific conditions, self-sustained oscillations that can be noisy or even dangerous for the integrity of a system. The coherent structures or flow modes composing this unsteady phenomenon usually called “pressure band phenomenon” are misunderstood and therefore difficult to control. In the present study, the dynamics of an annular rotor/stator cavity is investigated to shed some light on the flow organization and identify control strategies based on reliable theory and analysis to stabilize the observed undesired flow modes. No specific tool is known today to control a multi-frequency phenomenon. To address this first issue, the mode dominance and interactions appearing in this multi-frequency problem are investigated, thanks to dynamic mode tracking and control [M. Queguineur et al., “Dynamic mode tracking and control with a relaxation method,” Phys. Fluids 31, 034101 (2019)]. The benefit of this method is to be able to follow in time several modes while controlling them one by one and observe mode dominance and interactions. This purely numerical controller shows that, here, the dominant mode of the annular cavity is at the source of another low frequency mode. Based on this information and to develop a physically relevant control strategy, the global linear stability framework previously used by Queguineur et al. [“Large eddy simulations and global stability analyses of an annular and cylindrical rotor/stator cavity limit cycles,” Phys. Fluids 31, 104109 (2019)] is further developed to make use of the sensitivity to a base flow modification theory. This specific analysis indeed enables us to point out the exact location where the base flow should be modified to shift the dominant mode frequency and/or growth rate. In this context, passive controller positioning is identified for the studied annular cavity flow. Such strategies are then validated through new large eddy simulations of a controlled cavity using low amplitude injection/suction demonstrating the adequacy of the analysis and control strategy.

Rotating cavity flows have been widely studied for years because of many implications that these have on industrial applications. These flows can indeed generate, under specific conditions, self-sustained oscillations that can be noisy or even dangerous for the integrity of a system. The coherent structures or flow modes composing this unsteady phenomenon usually called “pressure band phenomenon” are misunderstood and therefore difficult to control. In the present study, the dynamics of an annular rotor/stator cavity is investigated to shed some light on the flow organization and identify control strategies based on reliable theory and analysis to stabilize the observed undesired flow modes. No specific tool is known today to control a multi-frequency phenomenon. To address this first issue, the mode dominance and interactions appearing in this multi-frequency problem are investigated, thanks to dynamic mode tracking and control [M. Queguineur et al., “Dynamic mode tracking and control with a relaxation method,” Phys. Fluids 31, 034101 (2019)]. The benefit of this method is to be able to follow in time several modes while controlling them one by one and observe mode dominance and interactions. This purely numerical controller shows that, here, the dominant mode of the annular cavity is at the source of another low frequency mode. Based on this information and to develop a physically relevant control strategy, the global linear stability framework previously used by Queguineur et al. [“Large eddy simulations and global stability analyses of an annular and cylindrical rotor/stator cavity limit cycles,” Phys. Fluids 31, 104109 (2019)] is further developed to make use of the sensitivity to a base flow modification theory. This specific analysis indeed enables us to point out the exact location where the base flow should be modified to shift the dominant mode frequency and/or growth rate. In this context, passive controller positioning is identified for the studied annular cavity flow. Such strategies are then validated through new large eddy simulations of a controlled cavity using low amplitude injection/suction demonstrating the adequacy of the analysis and control strategy.

Categories: Latest papers in fluid mechanics

### Impact of a small disk on a sessile water drop

Physics of Fluids, Volume 32, Issue 8, August 2020.

We address the details of events that follow the impact of a small solid disk on a water drop sitting on another disk of the same diameter. We experimentally demonstrate that fast squeezing of a low-viscosity liquid drop between two approaching disks leads to the formation of complex, radially expanding liquid structures (splashes) outside of the disks. The spatial and temporal dynamics of these splashes are tracked via high-speed video recording and flash photography. We analyze the mechanisms that control the shapes and breakup processes of these structures and derive a mathematical model for their behavior using simple physical arguments. Our investigation indicates that liquid structure formation is the result of a rapid increase in the velocity of liquid ejection from the gap between disks with time.

We address the details of events that follow the impact of a small solid disk on a water drop sitting on another disk of the same diameter. We experimentally demonstrate that fast squeezing of a low-viscosity liquid drop between two approaching disks leads to the formation of complex, radially expanding liquid structures (splashes) outside of the disks. The spatial and temporal dynamics of these splashes are tracked via high-speed video recording and flash photography. We analyze the mechanisms that control the shapes and breakup processes of these structures and derive a mathematical model for their behavior using simple physical arguments. Our investigation indicates that liquid structure formation is the result of a rapid increase in the velocity of liquid ejection from the gap between disks with time.

Categories: Latest papers in fluid mechanics

### Intermittent fluctuations due to Lorentzian pulses in turbulent thermal convection

Physics of Fluids, Volume 32, Issue 8, August 2020.

Turbulent motions due to flux-driven thermal convection are investigated by numerical simulations and stochastic modeling. Tilting of convection cells leads to the formation of sheared flows and quasi-periodic relaxation oscillations for the energy integrals far from the threshold for linear instability. The probability density function for the temperature and radial velocity fluctuations in the fluid layer changes from a normal distribution at the onset of turbulence to a distribution with an exponential tail for large fluctuation amplitudes for strongly driven systems. The frequency power spectral density has an exponential shape, which is a signature of deterministic chaos. By use of a novel deconvolution method, this is shown to result from the presence of Lorentzian pulses in the underlying time series, demonstrating that exponential frequency spectra can also persist in turbulent flow regimes.

Turbulent motions due to flux-driven thermal convection are investigated by numerical simulations and stochastic modeling. Tilting of convection cells leads to the formation of sheared flows and quasi-periodic relaxation oscillations for the energy integrals far from the threshold for linear instability. The probability density function for the temperature and radial velocity fluctuations in the fluid layer changes from a normal distribution at the onset of turbulence to a distribution with an exponential tail for large fluctuation amplitudes for strongly driven systems. The frequency power spectral density has an exponential shape, which is a signature of deterministic chaos. By use of a novel deconvolution method, this is shown to result from the presence of Lorentzian pulses in the underlying time series, demonstrating that exponential frequency spectra can also persist in turbulent flow regimes.

Categories: Latest papers in fluid mechanics

### Distinct coalescence behaviors of hot and cold drops in the presence of a surrounding viscous liquid

Physics of Fluids, Volume 32, Issue 8, August 2020.

Coalescence of a millimeter-sized drop initially touching a pool of the same liquid in the presence of another surrounding viscous liquid is studied in this work, wherein the drop may be hotter or colder than its surroundings. Moreover, the effect of the outer fluid viscosity on the coalescence dynamics and thermal convection is examined. An axisymmetric numerical model is employed to investigate the drop merger dynamics, wherein the drop and pool are modeled as water fluid, and the surroundings are modeled as silicone oils of different viscosities. The coalescence behaviors of hot and cold drops are found to be significantly different, especially at higher temperature differences. An otherwise partial coalescence for an isothermal system turns into a case of total coalescence when the drop is made colder than its surroundings, whereas the behavior in the case of a hot drop does not depart qualitatively from that of a corresponding isothermal system. Thermal convection has been examined in terms of the penetration depth of hot or cold fluid into the pool. Hot drops are found to have a greater penetration depth as compared to cold drops for higher viscosities of the surrounding fluid. The penetration depth is also related to the size of the leading vortex ring and the maximum vorticity magnitude.

Coalescence of a millimeter-sized drop initially touching a pool of the same liquid in the presence of another surrounding viscous liquid is studied in this work, wherein the drop may be hotter or colder than its surroundings. Moreover, the effect of the outer fluid viscosity on the coalescence dynamics and thermal convection is examined. An axisymmetric numerical model is employed to investigate the drop merger dynamics, wherein the drop and pool are modeled as water fluid, and the surroundings are modeled as silicone oils of different viscosities. The coalescence behaviors of hot and cold drops are found to be significantly different, especially at higher temperature differences. An otherwise partial coalescence for an isothermal system turns into a case of total coalescence when the drop is made colder than its surroundings, whereas the behavior in the case of a hot drop does not depart qualitatively from that of a corresponding isothermal system. Thermal convection has been examined in terms of the penetration depth of hot or cold fluid into the pool. Hot drops are found to have a greater penetration depth as compared to cold drops for higher viscosities of the surrounding fluid. The penetration depth is also related to the size of the leading vortex ring and the maximum vorticity magnitude.

Categories: Latest papers in fluid mechanics

### Smoothed particle hydrodynamics simulation of converging Richtmyer–Meshkov instability

Physics of Fluids, Volume 32, Issue 8, August 2020.

The Smoothed Particle Hydrodynamics (SPH) method based on the Harten–Lax–van Leer Riemann solver is improved to study converging Richtmyer–Meshkov instability (RMI). A new density summation algorithm is proposed, which greatly suppresses the pressure oscillation at the material interface. The one-dimensional Sod problem is first simulated for code verification. Then, the SPH program is extended to two dimensions to simulate the converging RMI at a square air/SF6 interface, and the numerical results compare well with the experimental ones [Si et al., “Experimental investigation of cylindrical converging shock waves interacting with a polygonal heavy gas cylinder,” J. Fluid Mech. 784, 225–251 (2015)]. Nonlinear mode coupling and pressure disturbance are found to act evidently, causing a very fast growth spike. Performing a Fourier analysis of the interface profiles, amplitude growths of the first three harmonics are obtained. The first harmonic presents an increasing growth rate at early stages due to geometric convergence. The second harmonic experiences a long period of linear growth due to the counteraction between geometric convergence and nonlinearity, whereas the third harmonic saturates very early for stronger nonlinearity. For all three harmonics, the perturbation growth rate reduces evidently at the late stage due to the Rayleigh–Taylor stabilization caused by interface deceleration. It is found that the instability growth at early stages depends heavily on the incident shock strength, while the late-stage asymptotic growth rate is nearly constant, regardless of shock strength. It is also found that intensifying the incident shock is an effective way to produce extreme thermodynamic state at the geometric center even though it causes a faster instability growth.

The Smoothed Particle Hydrodynamics (SPH) method based on the Harten–Lax–van Leer Riemann solver is improved to study converging Richtmyer–Meshkov instability (RMI). A new density summation algorithm is proposed, which greatly suppresses the pressure oscillation at the material interface. The one-dimensional Sod problem is first simulated for code verification. Then, the SPH program is extended to two dimensions to simulate the converging RMI at a square air/SF6 interface, and the numerical results compare well with the experimental ones [Si et al., “Experimental investigation of cylindrical converging shock waves interacting with a polygonal heavy gas cylinder,” J. Fluid Mech. 784, 225–251 (2015)]. Nonlinear mode coupling and pressure disturbance are found to act evidently, causing a very fast growth spike. Performing a Fourier analysis of the interface profiles, amplitude growths of the first three harmonics are obtained. The first harmonic presents an increasing growth rate at early stages due to geometric convergence. The second harmonic experiences a long period of linear growth due to the counteraction between geometric convergence and nonlinearity, whereas the third harmonic saturates very early for stronger nonlinearity. For all three harmonics, the perturbation growth rate reduces evidently at the late stage due to the Rayleigh–Taylor stabilization caused by interface deceleration. It is found that the instability growth at early stages depends heavily on the incident shock strength, while the late-stage asymptotic growth rate is nearly constant, regardless of shock strength. It is also found that intensifying the incident shock is an effective way to produce extreme thermodynamic state at the geometric center even though it causes a faster instability growth.

Categories: Latest papers in fluid mechanics

### Experimental investigation on the propagation characteristics of internal solitary waves based on a developed piecewise dynamic mode decomposition method

Physics of Fluids, Volume 32, Issue 8, August 2020.

The propagation of internal solitary waves (ISWs) flowing over the submerged topography is a strongly nonlinear process. To extract the dynamic characteristics of this process, an improved dynamic mode decomposition method is proposed in this paper, which is named piecewise dynamic mode decomposition (PDMD). The innovation of this method is to split the entire evolution process into several quasi-linear segments before modal analyzing to reduce the requirements on the spatial and temporal resolutions of input measured data. A feasible criterion for linearity is introduced by combining the proper orthogonal decomposition method, which is an important basis of PDMD. The data used in the analysis are provided by the experiments conducted in a stratified wave tank. The experimental conditions are set as ISWs flowing over two typical bottom topographies. The interfacial displacement and flow field information are analyzed as the measured data. Through reconstruction and modal analysis of experimental data, the effectiveness and flexibility of PDMD are verified for the ISW problem. The physical meaning of segmentation points can be explained. Based on the results of model decomposition, the main propagation characteristics of ISWs under different conditions are discussed. The evolution of the waveform or local flow phenomena can be simplified to the superposition of linear modes with frequency information.

The propagation of internal solitary waves (ISWs) flowing over the submerged topography is a strongly nonlinear process. To extract the dynamic characteristics of this process, an improved dynamic mode decomposition method is proposed in this paper, which is named piecewise dynamic mode decomposition (PDMD). The innovation of this method is to split the entire evolution process into several quasi-linear segments before modal analyzing to reduce the requirements on the spatial and temporal resolutions of input measured data. A feasible criterion for linearity is introduced by combining the proper orthogonal decomposition method, which is an important basis of PDMD. The data used in the analysis are provided by the experiments conducted in a stratified wave tank. The experimental conditions are set as ISWs flowing over two typical bottom topographies. The interfacial displacement and flow field information are analyzed as the measured data. Through reconstruction and modal analysis of experimental data, the effectiveness and flexibility of PDMD are verified for the ISW problem. The physical meaning of segmentation points can be explained. Based on the results of model decomposition, the main propagation characteristics of ISWs under different conditions are discussed. The evolution of the waveform or local flow phenomena can be simplified to the superposition of linear modes with frequency information.

Categories: Latest papers in fluid mechanics

### Jet formation and deep seal phenomena associated with inclined oil entry of rotating steel spheres

Physics of Fluids, Volume 32, Issue 8, August 2020.

The jet formation and deep seal phenomena following the inclined oil entry of rotating steel spheres were experimentally investigated. The results were compared with those obtained from vertical and non-rotating oil entry of the same spheres. It had been observed that the jet formation could be classified into two processes. First, a thin primary jet was formed immediately after deep seal. Second, the same jet became significantly thicker following the complete collapse of the air cavity at the oil surface. The inclined oil jet would gradually turn toward the vertical plane, while the angle between the primary jet and the quiescent oil surface was found to decrease when the Reynolds number of the spheres increased. The deep seal time was also independent of both linear and angular sphere velocities, while the vertical deep seal displacement increased with the Froude number.

The jet formation and deep seal phenomena following the inclined oil entry of rotating steel spheres were experimentally investigated. The results were compared with those obtained from vertical and non-rotating oil entry of the same spheres. It had been observed that the jet formation could be classified into two processes. First, a thin primary jet was formed immediately after deep seal. Second, the same jet became significantly thicker following the complete collapse of the air cavity at the oil surface. The inclined oil jet would gradually turn toward the vertical plane, while the angle between the primary jet and the quiescent oil surface was found to decrease when the Reynolds number of the spheres increased. The deep seal time was also independent of both linear and angular sphere velocities, while the vertical deep seal displacement increased with the Froude number.

Categories: Latest papers in fluid mechanics

### Airflow driven fluid–structure interaction subjected to aqueous-based liquid spraying

Physics of Fluids, Volume 32, Issue 8, August 2020.

Artificial saliva sprays are commonly used to remedy vocal folds surface hydration. Vocal folds surface hydration and its effect on their auto-oscillation are studied experimentally using artificial vocal folds. The airflow is used to excite the vocal folds into auto-oscillation after which the vocal folds surface is sprayed with a liquid. The validity of the findings described in a previous study [A. Bouvet, X. Pelorson, and A. Van Hirtum, “Influence of water spraying on an oscillating channel,” J. Fluids Struct. 93, 102840 (2020)] concerning the effect of water spraying is further investigated. First, artificial saliva sprays (up to 5 ml) are sprayed instead of water. It is shown that this allows us to address the effect of increased dynamic viscosity (up to 8 times compared to water) as other artificial saliva properties affecting air–liquid mixing and surface wettability remain similar to water. Second, the Reynolds number in the dry stage is systematically increased (with 60%) for constant spraying volume ≥3 ml. Regardless of the sprayed liquid and Reynolds number, oscillation cycles are characterized by an increase in mean upstream pressure, cycle-to-cycle variability, and a decrease in oscillation frequency due period doubling. Increasing the dynamic viscosity tends to reduce the magnitude of these tendencies for spraying volumes smaller than 3 ml, indicating that viscous liquid–gas mixing affects the flow regime. Systematic Reynolds number variation shows that liquid spraying increases the oscillation onset threshold pressure and that the magnitude of general tendencies is reduced. The assessed conditions and features are pertinent to human voice production after hydration with an artificial saliva spray burst.

Artificial saliva sprays are commonly used to remedy vocal folds surface hydration. Vocal folds surface hydration and its effect on their auto-oscillation are studied experimentally using artificial vocal folds. The airflow is used to excite the vocal folds into auto-oscillation after which the vocal folds surface is sprayed with a liquid. The validity of the findings described in a previous study [A. Bouvet, X. Pelorson, and A. Van Hirtum, “Influence of water spraying on an oscillating channel,” J. Fluids Struct. 93, 102840 (2020)] concerning the effect of water spraying is further investigated. First, artificial saliva sprays (up to 5 ml) are sprayed instead of water. It is shown that this allows us to address the effect of increased dynamic viscosity (up to 8 times compared to water) as other artificial saliva properties affecting air–liquid mixing and surface wettability remain similar to water. Second, the Reynolds number in the dry stage is systematically increased (with 60%) for constant spraying volume ≥3 ml. Regardless of the sprayed liquid and Reynolds number, oscillation cycles are characterized by an increase in mean upstream pressure, cycle-to-cycle variability, and a decrease in oscillation frequency due period doubling. Increasing the dynamic viscosity tends to reduce the magnitude of these tendencies for spraying volumes smaller than 3 ml, indicating that viscous liquid–gas mixing affects the flow regime. Systematic Reynolds number variation shows that liquid spraying increases the oscillation onset threshold pressure and that the magnitude of general tendencies is reduced. The assessed conditions and features are pertinent to human voice production after hydration with an artificial saliva spray burst.

Categories: Latest papers in fluid mechanics

### Multifactorial analysis of ion concentration polarization for microfluidic preconcentrating applications using response surface method

Physics of Fluids, Volume 32, Issue 7, July 2020.

Ion concentration polarization (ICP) in a microfluidic device requires a precise balance of forces on charged molecules to achieve high concentrating efficiency. It is, thus, of considerable interest to study the impact of all governing parameters on ICP performance. Experimental study of the ICP multifactorial phenomenon seems impractical and costly. We report a systematic approach to understand the impacts of governing parameters on the ICP phenomenon using a robust numerical model established in COMSOL Multiphysics®. We varied the buffer concentration, applied voltage, and microchannel length to study their impacts on the ICP phenomenon. Then, we developed a statistical model via the response surface method (RSM) for the numerical results to study the direct and interactive effects of the mentioned parameters on ICP optimization. It was found that the buffer concentration (Cbuffer) plays a key role in the enrichment factor (EF); however, simultaneous impacts of the applied voltage and channel length must be considered as well to enhance EF. For low buffer concentrations, Cbuffer < 0.1 mM, the ionic conductivity was found to be independent of Cbuffer, while for high buffer concentrations, Cbuffer > 1 mM, the ionic conductivity was directly linked to Cbuffer. In addition, the RSM-based model prediction for a certain buffer concentration (∼1 mM) highlighted that an electric field of 20 V/cm–30 V/cm is suitable for the initial design of experiments in ICP microdevices.

Ion concentration polarization (ICP) in a microfluidic device requires a precise balance of forces on charged molecules to achieve high concentrating efficiency. It is, thus, of considerable interest to study the impact of all governing parameters on ICP performance. Experimental study of the ICP multifactorial phenomenon seems impractical and costly. We report a systematic approach to understand the impacts of governing parameters on the ICP phenomenon using a robust numerical model established in COMSOL Multiphysics®. We varied the buffer concentration, applied voltage, and microchannel length to study their impacts on the ICP phenomenon. Then, we developed a statistical model via the response surface method (RSM) for the numerical results to study the direct and interactive effects of the mentioned parameters on ICP optimization. It was found that the buffer concentration (Cbuffer) plays a key role in the enrichment factor (EF); however, simultaneous impacts of the applied voltage and channel length must be considered as well to enhance EF. For low buffer concentrations, Cbuffer < 0.1 mM, the ionic conductivity was found to be independent of Cbuffer, while for high buffer concentrations, Cbuffer > 1 mM, the ionic conductivity was directly linked to Cbuffer. In addition, the RSM-based model prediction for a certain buffer concentration (∼1 mM) highlighted that an electric field of 20 V/cm–30 V/cm is suitable for the initial design of experiments in ICP microdevices.

Categories: Latest papers in fluid mechanics