# 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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### Risk assessment of COVID infection by respiratory droplets from cough for various ventilation scenarios inside an elevator: An OpenFOAM-based computational fluid dynamics analysis

Physics of Fluids, Volume 34, Issue 1, January 2022.

Respiratory droplets—which may contain disease spreading virus—exhaled during speaking, coughing, or sneezing are one of the significant causes for the spread of the ongoing COVID-19 pandemic. The droplet dispersion depends on the surrounding air velocity, ambient temperature, and relative humidity. In a confined space like an elevator, the risk of transmission becomes higher when there is an infected person inside the elevator with other individuals. In this work, a numerical investigation is carried out in a three-dimensional domain resembling an elevator using OpenFoam. Three different modes of air ventilation, viz., quiescent, axial exhaust draft, and exhaust fan, have been considered to investigate the effect of ventilation on droplet transmission for two different climatic conditions (30 [math], 50% relative humidity and 10 [math], 90% relative humidity). The risk assessment is quantified using a risk factor based on the time-averaged droplet count present near the passenger's hand to head region (risky height zone). The risk factor drops from 40% in a quiescent scenario to 0% in an exhaust fan ventilation condition in a hot dry environment. In general, cold humid conditions are safer than hot dry conditions as the droplets settle down quickly below the risky height zone owing to their larger masses maintained by negligible evaporation. However, an exhaust fan renders the domain in a hot dry ambience completely safe (risk factor, 0%) in 5.5 s whereas it takes 7.48 s for a cold humid ambience.

Respiratory droplets—which may contain disease spreading virus—exhaled during speaking, coughing, or sneezing are one of the significant causes for the spread of the ongoing COVID-19 pandemic. The droplet dispersion depends on the surrounding air velocity, ambient temperature, and relative humidity. In a confined space like an elevator, the risk of transmission becomes higher when there is an infected person inside the elevator with other individuals. In this work, a numerical investigation is carried out in a three-dimensional domain resembling an elevator using OpenFoam. Three different modes of air ventilation, viz., quiescent, axial exhaust draft, and exhaust fan, have been considered to investigate the effect of ventilation on droplet transmission for two different climatic conditions (30 [math], 50% relative humidity and 10 [math], 90% relative humidity). The risk assessment is quantified using a risk factor based on the time-averaged droplet count present near the passenger's hand to head region (risky height zone). The risk factor drops from 40% in a quiescent scenario to 0% in an exhaust fan ventilation condition in a hot dry environment. In general, cold humid conditions are safer than hot dry conditions as the droplets settle down quickly below the risky height zone owing to their larger masses maintained by negligible evaporation. However, an exhaust fan renders the domain in a hot dry ambience completely safe (risk factor, 0%) in 5.5 s whereas it takes 7.48 s for a cold humid ambience.

Categories: Latest papers in fluid mechanics

### Numerical study of droplet thermocapillary migration behavior on wettability-confined tracks using a three-dimensional color-gradient lattice Boltzmann model

Physics of Fluids, Volume 34, Issue 1, January 2022.

Thermocapillary migration describes the phenomenon whereby liquid droplets move from warm to cold regions on a nonuniformly heated hydrophilic surface. Surface modifications can be applied to manipulate this migration process. In the present study, a three-dimensional color-gradient lattice Boltzmann model is used to investigate the droplet migration behavior on a series of wettability-confined tracks subject to a uniform temperature gradient. The model is validated by simulating the thermocapillary-driven flow with two superimposed planar fluids in a heated microchannel and the capillary penetration of a wetting fluid in a capillary tube. An in-depth study of the wettability-confined tracks confirms the capacity to manipulate the droplet migration process, that is, the wettability-confined tracks can accelerate thermocapillary migration compared with a smooth surface. The effects of changes in the viscosity ratio and interfacial tension are investigated, and it is found that a lower viscosity ratio and larger interfacial tension cause the droplet to migrate faster. Moreover, a systematic study of the track vertex angle is conducted, and the mechanism through which this parameter influences the droplet migration is analyzed. Then the effect of the track wettability on droplet migration is explored and analyzed. Finally, a serial wettability-confined track is designed to realize long-distance droplet migration, and the narrow side width of the connection region is found to play a key role in determining whether the droplets can migrate over long distances. The results provide some guidance for designing tracks that enable precise droplet migration control.

Thermocapillary migration describes the phenomenon whereby liquid droplets move from warm to cold regions on a nonuniformly heated hydrophilic surface. Surface modifications can be applied to manipulate this migration process. In the present study, a three-dimensional color-gradient lattice Boltzmann model is used to investigate the droplet migration behavior on a series of wettability-confined tracks subject to a uniform temperature gradient. The model is validated by simulating the thermocapillary-driven flow with two superimposed planar fluids in a heated microchannel and the capillary penetration of a wetting fluid in a capillary tube. An in-depth study of the wettability-confined tracks confirms the capacity to manipulate the droplet migration process, that is, the wettability-confined tracks can accelerate thermocapillary migration compared with a smooth surface. The effects of changes in the viscosity ratio and interfacial tension are investigated, and it is found that a lower viscosity ratio and larger interfacial tension cause the droplet to migrate faster. Moreover, a systematic study of the track vertex angle is conducted, and the mechanism through which this parameter influences the droplet migration is analyzed. Then the effect of the track wettability on droplet migration is explored and analyzed. Finally, a serial wettability-confined track is designed to realize long-distance droplet migration, and the narrow side width of the connection region is found to play a key role in determining whether the droplets can migrate over long distances. The results provide some guidance for designing tracks that enable precise droplet migration control.

Categories: Latest papers in fluid mechanics

### Study on characteristics of fragment size distribution generated via droplet breakup by high-speed gas flow

Physics of Fluids, Volume 34, Issue 1, January 2022.

In a design of scramjet engine using liquid hydrocarbon fuels, predictions of the fragment size distribution generated by liquid droplet breakup in high-speed gas flow are useful. However, the characteristics of fragment size distribution may be unclear, especially in high-velocity flows. In this study, the diameter of fragments formed by the disintegration of water droplets in a high-speed gas flow behind the shock wave was measured. The fragment diameters of several μm to several tens of μm moving at high speeds were clearly captured via high resolution visualization using a microscope and pulse laser with a flash time of 20 ns as a backlight. The parameters used to measure the fragment diameter from the captured images were determined from calibration experiments using a device that can change the working distance; thus, highly reliable particle size measurements were conducted. From the experimental results, the time variation in the volume probability density distribution of fragments size, Sauter mean diameter (SMD), and mass median diameter (MMD) were calculated. As a result, it was clarified that the volume probability density was successfully described by a root-normal distribution for high Weber number, for which catastrophic breakup should occur according to conventional classification. It was also observed that SMD and MMD increase with time, and the ratio of MMD to SMD was found to be 1.2, except at the initial stage. In this study, the characteristics of size distribution of the fragments generated by liquid droplet breakup in high-velocity flows, which was unclear, has been clarified.

In a design of scramjet engine using liquid hydrocarbon fuels, predictions of the fragment size distribution generated by liquid droplet breakup in high-speed gas flow are useful. However, the characteristics of fragment size distribution may be unclear, especially in high-velocity flows. In this study, the diameter of fragments formed by the disintegration of water droplets in a high-speed gas flow behind the shock wave was measured. The fragment diameters of several μm to several tens of μm moving at high speeds were clearly captured via high resolution visualization using a microscope and pulse laser with a flash time of 20 ns as a backlight. The parameters used to measure the fragment diameter from the captured images were determined from calibration experiments using a device that can change the working distance; thus, highly reliable particle size measurements were conducted. From the experimental results, the time variation in the volume probability density distribution of fragments size, Sauter mean diameter (SMD), and mass median diameter (MMD) were calculated. As a result, it was clarified that the volume probability density was successfully described by a root-normal distribution for high Weber number, for which catastrophic breakup should occur according to conventional classification. It was also observed that SMD and MMD increase with time, and the ratio of MMD to SMD was found to be 1.2, except at the initial stage. In this study, the characteristics of size distribution of the fragments generated by liquid droplet breakup in high-velocity flows, which was unclear, has been clarified.

Categories: Latest papers in fluid mechanics

### Nonlinear interaction among second mode resonance waves in high-speed boundary layers using the method of multiple scales

Physics of Fluids, Volume 34, Issue 1, January 2022.

Nonlinear interaction among resonance waves prior to transition has been observed in earlier numerical and experimental studies. However, these earlier studies were performed for incompressible or compressible flow with a wave triad composed of either Tollmien–Schlichting mode or oblique and planner first modes or crossflow mode. In the case of high-speed flow, the significance of first mode waves becomes lesser, or in most cases, it is not responsible for instability, and second mode waves mostly dominate the flow. The nonlinear interaction among resonance waves in a high-speed boundary layer where a wave triad is composed of second mode waves is presented. The nonlinear interaction formulation is performed using the method of multiple scales. The nonparallel effect has been taken into account by considering the mean flow to be slightly nonparallel. A detuning parameter is used for the wavenumbers, whereas frequencies are assumed to be perfectly tuned, satisfying the resonance condition. Based on the eigenfunctions' distribution normal to the wall, it is observed that the temperature disturbance is more dominant than the other disturbances. With an increase in Mach number, the disturbances shift toward the boundary layer edge. A significant increase in amplification factor due to wave interaction has been observed. The maximum amplification factor for the second mode wave due to wave interaction has increased by around 20% of its non-interaction value. Although the non-interaction amplification factor for the difference mode is much smaller than the other modes, its interaction amplification factor has increased more significantly. The amplification factor for the difference mode has increased almost by 60% due to wave interaction.

Nonlinear interaction among resonance waves prior to transition has been observed in earlier numerical and experimental studies. However, these earlier studies were performed for incompressible or compressible flow with a wave triad composed of either Tollmien–Schlichting mode or oblique and planner first modes or crossflow mode. In the case of high-speed flow, the significance of first mode waves becomes lesser, or in most cases, it is not responsible for instability, and second mode waves mostly dominate the flow. The nonlinear interaction among resonance waves in a high-speed boundary layer where a wave triad is composed of second mode waves is presented. The nonlinear interaction formulation is performed using the method of multiple scales. The nonparallel effect has been taken into account by considering the mean flow to be slightly nonparallel. A detuning parameter is used for the wavenumbers, whereas frequencies are assumed to be perfectly tuned, satisfying the resonance condition. Based on the eigenfunctions' distribution normal to the wall, it is observed that the temperature disturbance is more dominant than the other disturbances. With an increase in Mach number, the disturbances shift toward the boundary layer edge. A significant increase in amplification factor due to wave interaction has been observed. The maximum amplification factor for the second mode wave due to wave interaction has increased by around 20% of its non-interaction value. Although the non-interaction amplification factor for the difference mode is much smaller than the other modes, its interaction amplification factor has increased more significantly. The amplification factor for the difference mode has increased almost by 60% due to wave interaction.

Categories: Latest papers in fluid mechanics

### Numerical simulation of flow over flapping wings in tandem: Wingspan effects

Physics of Fluids, Volume 34, Issue 1, January 2022.

We report direct numerical simulations of a pair of wings in horizontal tandem configuration to analyze the effect of their aspect ratio on the flow and the aerodynamic performance of the system. The wings are immersed in a uniform free stream at the Reynolds number Re = 1000, and they undergo heaving and pitching oscillation with the Strouhal number St = 0.7. The aspect ratios of forewing and hindwing vary between 2 and 4. The aerodynamic performance of the system is dictated by the interaction between the trailing edge vortex (TEV) shed by the forewing and the induced leading-edge vortex formed on the hindwing. The aerodynamic performance of the forewing is similar to that of an isolated wing irrespective of the aspect ratio of the hindwing, with a small modulating effect produced by the forewing–hindwing interactions. On the other hand, the aerodynamic performance of the hindwing is clearly affected by the interaction with the forewing's TEV. Tandem configurations with a larger aspect ratio on the forewing than on the hindwing result in a quasi-two-dimensional flow structure on the latter. This yields an 8% increase in the time-averaged thrust coefficient of the hindwing, with no change in its propulsive efficiency.

We report direct numerical simulations of a pair of wings in horizontal tandem configuration to analyze the effect of their aspect ratio on the flow and the aerodynamic performance of the system. The wings are immersed in a uniform free stream at the Reynolds number Re = 1000, and they undergo heaving and pitching oscillation with the Strouhal number St = 0.7. The aspect ratios of forewing and hindwing vary between 2 and 4. The aerodynamic performance of the system is dictated by the interaction between the trailing edge vortex (TEV) shed by the forewing and the induced leading-edge vortex formed on the hindwing. The aerodynamic performance of the forewing is similar to that of an isolated wing irrespective of the aspect ratio of the hindwing, with a small modulating effect produced by the forewing–hindwing interactions. On the other hand, the aerodynamic performance of the hindwing is clearly affected by the interaction with the forewing's TEV. Tandem configurations with a larger aspect ratio on the forewing than on the hindwing result in a quasi-two-dimensional flow structure on the latter. This yields an 8% increase in the time-averaged thrust coefficient of the hindwing, with no change in its propulsive efficiency.

Categories: Latest papers in fluid mechanics

### Spatial and temporal evolution of three-dimensional thermovibrational convection in a cubic cavity with various thermal boundary conditions

Physics of Fluids, Volume 34, Issue 1, January 2022.

Thermovibrational flow in a differentially heated cubic cavity with vibrations applied in a direction parallel to the imposed temperature gradient is investigated by solving numerically the governing equations for mass, momentum, and energy in their original nonlinear form. A parametric analysis is conducted through the stepwise examination of the following degrees of freedom: magnitude of the Rayleigh number and the thermal behavior of the sidewalls. A complete characterization of the emerging time-varying convective structures is attempted in terms of spatial symmetries broken or retained, related temporal evolution, and global parameters, such as the Nusselt number. It is shown that the intrinsically three-dimensional nature of the problem and its sensitivity to the thermal boundary conditions can have a remarkable influence on the multiplicity of emerging solutions and the system temporal response.

Thermovibrational flow in a differentially heated cubic cavity with vibrations applied in a direction parallel to the imposed temperature gradient is investigated by solving numerically the governing equations for mass, momentum, and energy in their original nonlinear form. A parametric analysis is conducted through the stepwise examination of the following degrees of freedom: magnitude of the Rayleigh number and the thermal behavior of the sidewalls. A complete characterization of the emerging time-varying convective structures is attempted in terms of spatial symmetries broken or retained, related temporal evolution, and global parameters, such as the Nusselt number. It is shown that the intrinsically three-dimensional nature of the problem and its sensitivity to the thermal boundary conditions can have a remarkable influence on the multiplicity of emerging solutions and the system temporal response.

Categories: Latest papers in fluid mechanics

### Carriers of Sargassum and mechanism for coastal inundation in the Caribbean Sea

Physics of Fluids, Volume 34, Issue 1, January 2022.

We identify effective carriers of Sargassum in the Caribbean Sea and describe a mechanism for coastal choking. Revealed from satellite altimetry, the carriers of Sargassum are mesoscale eddies (vortices of 50-km radius or larger) with coherent material (i.e., fluid) boundaries. These are observer-independent—unlike eddy boundaries identified with instantaneously closed streamlines of the altimetric sea-surface height field—and furthermore harbor finite-time attractors for networks of elastically connected finite-size buoyant or “inertial” particles dragged by ocean currents and winds, a mathematical abstraction of Sargassum rafts. The mechanism of coastal inundation, identified using a minimal model of surface-intensified Caribbean Sea eddies, is thermal instability in the presence of bottom topography.

We identify effective carriers of Sargassum in the Caribbean Sea and describe a mechanism for coastal choking. Revealed from satellite altimetry, the carriers of Sargassum are mesoscale eddies (vortices of 50-km radius or larger) with coherent material (i.e., fluid) boundaries. These are observer-independent—unlike eddy boundaries identified with instantaneously closed streamlines of the altimetric sea-surface height field—and furthermore harbor finite-time attractors for networks of elastically connected finite-size buoyant or “inertial” particles dragged by ocean currents and winds, a mathematical abstraction of Sargassum rafts. The mechanism of coastal inundation, identified using a minimal model of surface-intensified Caribbean Sea eddies, is thermal instability in the presence of bottom topography.

Categories: Latest papers in fluid mechanics

### Acoustic streaming in water induced by an asymmetric dielectric-barrier-discharge plasma actuator at the initiation stage

Physics of Fluids, Volume 34, Issue 1, January 2022.

When acoustic waves with broadband frequency and high amplitude pass through a medium, it absorbs their momentum to induce a quasi-steady flow, which is commonly referred to as acoustic streaming (AS). The acoustic energy in AS is clean energy, and actuators that release acoustic energy by AS can control flow without contacting the controlled object and have considerable potential in microfluidic systems for enhancing transport and mixing. Recently, AS was observed to be induced in quiescent air by a dielectric-barrier-discharge plasma actuator. However, a normal AS flow and a tangential wall jet can be created by the plasma actuator in quiescent air. The AS flow suffers unavoidably from the induced wall jet. For example, the location of the production of the AS flow moves downstream of the upper electrode under the influence of the induced wall jet. In addition, whether the plasma actuator can generate AS in a liquid is the key to applying AS in biomedicine and remains unknown. Here, an asymmetric dielectric-barrier-discharge plasma actuator during the first sinusoidal high-voltage cycle when the induced flow field and the effect of the heating are not significant is suspended over the surface of distilled water but not in contact with the water. Importantly, AS in distilled water produced by a plasma actuator and causing depressions in the liquid surface is first observed by using the highly accurate phase-locked image-freezing schlieren technique. Based on the results, the formation process for AS in distilled water is proposed.

When acoustic waves with broadband frequency and high amplitude pass through a medium, it absorbs their momentum to induce a quasi-steady flow, which is commonly referred to as acoustic streaming (AS). The acoustic energy in AS is clean energy, and actuators that release acoustic energy by AS can control flow without contacting the controlled object and have considerable potential in microfluidic systems for enhancing transport and mixing. Recently, AS was observed to be induced in quiescent air by a dielectric-barrier-discharge plasma actuator. However, a normal AS flow and a tangential wall jet can be created by the plasma actuator in quiescent air. The AS flow suffers unavoidably from the induced wall jet. For example, the location of the production of the AS flow moves downstream of the upper electrode under the influence of the induced wall jet. In addition, whether the plasma actuator can generate AS in a liquid is the key to applying AS in biomedicine and remains unknown. Here, an asymmetric dielectric-barrier-discharge plasma actuator during the first sinusoidal high-voltage cycle when the induced flow field and the effect of the heating are not significant is suspended over the surface of distilled water but not in contact with the water. Importantly, AS in distilled water produced by a plasma actuator and causing depressions in the liquid surface is first observed by using the highly accurate phase-locked image-freezing schlieren technique. Based on the results, the formation process for AS in distilled water is proposed.

Categories: Latest papers in fluid mechanics

### A maximum entropy formalism model for the breakup of a droplet

Physics of Fluids, Volume 34, Issue 1, January 2022.

A model for the prediction of the size and velocity distribution of daughter droplets created by the breakup of an unstable parent droplet is proposed. The basis of the model is the maximum entropy formalism, which states that the most probable joint probability density function (JPDF) for the daughter droplet population is the one that maximizes the Bayesian entropy conditional on the enforcement of a set of constraints, which are the conservation laws for the problem. The result is a closed-form expression for the JPDF. Validation against experimental and Direct Numerical Simulations data over the bag, multimode, and sheet-thinning breakup regimes is included. Predictions from the model show that the daughter droplet velocity distribution widens as the droplet size decreases. This result is due to a heightened sensitivity to drag force with lower droplet inertia and coincides with spray behavior. The velocity distribution is found to be near Gaussian. The model does not treat size and velocity as independently distributed, as generally assumed in the literature. In fact, marginal conditional densities derived from JPDF show that the distribution of size and velocity are interrelated.

A model for the prediction of the size and velocity distribution of daughter droplets created by the breakup of an unstable parent droplet is proposed. The basis of the model is the maximum entropy formalism, which states that the most probable joint probability density function (JPDF) for the daughter droplet population is the one that maximizes the Bayesian entropy conditional on the enforcement of a set of constraints, which are the conservation laws for the problem. The result is a closed-form expression for the JPDF. Validation against experimental and Direct Numerical Simulations data over the bag, multimode, and sheet-thinning breakup regimes is included. Predictions from the model show that the daughter droplet velocity distribution widens as the droplet size decreases. This result is due to a heightened sensitivity to drag force with lower droplet inertia and coincides with spray behavior. The velocity distribution is found to be near Gaussian. The model does not treat size and velocity as independently distributed, as generally assumed in the literature. In fact, marginal conditional densities derived from JPDF show that the distribution of size and velocity are interrelated.

Categories: Latest papers in fluid mechanics

### Vortex dynamics of supercritical carbon dioxide flow past a heated circular cylinder at low Reynolds numbers

Physics of Fluids, Volume 34, Issue 1, January 2022.

The vortex dynamics in the steady regime and laminar vortex shedding regime with Reynolds number (Re) ranging from 15 to 150 are systematically investigated for supercritical carbon dioxide (SCO2) through a high-resolution numerical method in this paper. Numerical results of constant-property air are validated with the available experimental and numerical data from various angles. Excellent agreements are found between the present work and the previous studies. By comparing one vortex shedding process between SCO2 and conventional air, it is found that for SCO2 the period from the initial growth state of one vortex to its dominant state of inducing a new counter-rotating vortex on the other side of the body wake is accelerated, which contributes to the higher Strouhal frequency of SCO2 to a certain extent. By analyzing the development of lift coefficient history and the instantaneous vorticity near the onset of vortex shedding, transition from the steady separated flow to the primary wake instability for SCO2 is found between Re of 28 and 29, exactly 28.2 predicted by the intersection of the fitting curves of the base suction, much lower than the classical value (∼ 47). The wake bubble in the steady regime enlarges in size as Re increases, while in the laminar shedding regime the mean recirculation region decreases with Re. The distributions of local quantities, such as pressure coefficient, friction coefficient, and Nusselt number along the circumference, are presented to understand the development of the flow. The two dimensionality of the wake is confirmed at Re of 150 by comparing with the three-dimensional calculation. A new three-term correlation is proposed to represent the Strouhal–Reynolds number relation for SCO2 in parallel shedding mode.

The vortex dynamics in the steady regime and laminar vortex shedding regime with Reynolds number (Re) ranging from 15 to 150 are systematically investigated for supercritical carbon dioxide (SCO2) through a high-resolution numerical method in this paper. Numerical results of constant-property air are validated with the available experimental and numerical data from various angles. Excellent agreements are found between the present work and the previous studies. By comparing one vortex shedding process between SCO2 and conventional air, it is found that for SCO2 the period from the initial growth state of one vortex to its dominant state of inducing a new counter-rotating vortex on the other side of the body wake is accelerated, which contributes to the higher Strouhal frequency of SCO2 to a certain extent. By analyzing the development of lift coefficient history and the instantaneous vorticity near the onset of vortex shedding, transition from the steady separated flow to the primary wake instability for SCO2 is found between Re of 28 and 29, exactly 28.2 predicted by the intersection of the fitting curves of the base suction, much lower than the classical value (∼ 47). The wake bubble in the steady regime enlarges in size as Re increases, while in the laminar shedding regime the mean recirculation region decreases with Re. The distributions of local quantities, such as pressure coefficient, friction coefficient, and Nusselt number along the circumference, are presented to understand the development of the flow. The two dimensionality of the wake is confirmed at Re of 150 by comparing with the three-dimensional calculation. A new three-term correlation is proposed to represent the Strouhal–Reynolds number relation for SCO2 in parallel shedding mode.

Categories: Latest papers in fluid mechanics

### Experimental study on the evolution of mode waves in laminar boundary layer on a large-scale flat plate

Physics of Fluids, Volume 34, Issue 1, January 2022.

In this research, to study the hypersonic boundary-layer transition, experiments were conducted on a large-scale flat plate with a length of 3.2 m at a zero angle of attack in the hypersonic shock tunnel duplicating flight conditions. Surface-mounted piezoelectric pressure sensors and coaxial thermocouples were, respectively, used to measure the pressure fluctuations and wall heat transfer. The spatial distribution of heat transfer was used to distinguish the transition. Under the test conditions of Ma = 7.0, T0 = 2120 K, and Re∞ = 6.08 × 105 m−1, no transition occurred, and under the test conditions of Ma = 7.0, T0 = 2220 K, and Re∞ = 1.23 × 106 m−1, the transition position was s = 2.06 m. The repeatability of the experiment was found to be good. Furthermore, focus was placed on the spectral and spatial/temporal evolution characteristics of pressure fluctuations in the laminar boundary layer. The experiment captured the three frequency distributions of mode waves in the laminar flow zone. Among the mode waves distributed in the three frequency bands, the low-/high-frequency bands were dominant, and the mid-frequency band exhibited a staged contribution. The amplitude energy percentages of the high- and low-frequency mode waves exhibited opposite trends in both time and space, which means that the disturbance energy will be distributed among the various harmonics in the laminar stage.

In this research, to study the hypersonic boundary-layer transition, experiments were conducted on a large-scale flat plate with a length of 3.2 m at a zero angle of attack in the hypersonic shock tunnel duplicating flight conditions. Surface-mounted piezoelectric pressure sensors and coaxial thermocouples were, respectively, used to measure the pressure fluctuations and wall heat transfer. The spatial distribution of heat transfer was used to distinguish the transition. Under the test conditions of Ma = 7.0, T0 = 2120 K, and Re∞ = 6.08 × 105 m−1, no transition occurred, and under the test conditions of Ma = 7.0, T0 = 2220 K, and Re∞ = 1.23 × 106 m−1, the transition position was s = 2.06 m. The repeatability of the experiment was found to be good. Furthermore, focus was placed on the spectral and spatial/temporal evolution characteristics of pressure fluctuations in the laminar boundary layer. The experiment captured the three frequency distributions of mode waves in the laminar flow zone. Among the mode waves distributed in the three frequency bands, the low-/high-frequency bands were dominant, and the mid-frequency band exhibited a staged contribution. The amplitude energy percentages of the high- and low-frequency mode waves exhibited opposite trends in both time and space, which means that the disturbance energy will be distributed among the various harmonics in the laminar stage.

Categories: Latest papers in fluid mechanics

### Image features of a splashing drop on a solid surface extracted using a feedforward neural network

Physics of Fluids, Volume 34, Issue 1, January 2022.

This article reports nonintuitive characteristic of a splashing drop on a solid surface discovered through extracting image features using a feedforward neural network (FNN). Ethanol of area-equivalent radius about 1.29 mm was dropped from impact heights ranging from 4 cm to 60 cm (splashing threshold 20 cm) and impacted on a hydrophilic surface. The images captured when half of the drop impacted the surface were labeled according to their outcome, splashing or nonsplashing, and were used to train an FNN. A classification accuracy [math] was achieved. To extract the image features identified by the FNN for classification, the weight matrix of the trained FNN for identifying splashing drops was visualized. Remarkably, the visualization showed that the trained FNN identified the contour height of the main body of the impacting drop as an important characteristic differentiating between splashing and nonsplashing drops, which has not been reported in previous studies. This feature was found throughout the impact, even when one and three-quarters of the drop impacted the surface. To confirm the importance of this image feature, the FNN was retrained to classify using only the main body without checking for the presence of ejected secondary droplets. The accuracy was still [math], confirming that the contour height is an important feature distinguishing splashing from nonsplashing drops. Several aspects of drop impact are analyzed and discussed with the aim of identifying the possible mechanism underlying the difference in contour height between splashing and nonsplashing drops.

This article reports nonintuitive characteristic of a splashing drop on a solid surface discovered through extracting image features using a feedforward neural network (FNN). Ethanol of area-equivalent radius about 1.29 mm was dropped from impact heights ranging from 4 cm to 60 cm (splashing threshold 20 cm) and impacted on a hydrophilic surface. The images captured when half of the drop impacted the surface were labeled according to their outcome, splashing or nonsplashing, and were used to train an FNN. A classification accuracy [math] was achieved. To extract the image features identified by the FNN for classification, the weight matrix of the trained FNN for identifying splashing drops was visualized. Remarkably, the visualization showed that the trained FNN identified the contour height of the main body of the impacting drop as an important characteristic differentiating between splashing and nonsplashing drops, which has not been reported in previous studies. This feature was found throughout the impact, even when one and three-quarters of the drop impacted the surface. To confirm the importance of this image feature, the FNN was retrained to classify using only the main body without checking for the presence of ejected secondary droplets. The accuracy was still [math], confirming that the contour height is an important feature distinguishing splashing from nonsplashing drops. Several aspects of drop impact are analyzed and discussed with the aim of identifying the possible mechanism underlying the difference in contour height between splashing and nonsplashing drops.

Categories: Latest papers in fluid mechanics

### Numerical investigation of a high-speed train underbody flows: Studying flow structures through large-eddy simulation and assessment of steady and unsteady Reynolds-averaged Navier–Stokes and improved delayed detached eddy simulation performance

Physics of Fluids, Volume 34, Issue 1, January 2022.

The underbody flow of a truncated, 1:10 scaled, CRH380A model is investigated at Re = 2.78 × 105 in this paper. The large-eddy simulation (LES) is used to study the main features of the development of the underbody flow under the snowplow, in the bogie/cavity region and after the cavity (equip-cabin region). A grid independence study and a validation against experimental data have been done prior to the investigation. The snowplow region is dominated by a pair of separated counter-rotating vortices, which further affects the downstream flow. A strong shear layer is observed in the cavity region, and the turbulent flow is intensively triggered by the shear instability and the complex bogie components within the cavity region. The equip-cabin region allows the turbulent flow to develop without any disturbance, decreasing the turbulence intensity. Moreover, the steady and unsteady Reynolds-averaged Navier–Stokes (RANS, URANS) model and the improved delayed detached eddy simulation (IDDES) are used to compute the same flow, and to compare the results to LES. The solution differences, in terms of aerodynamic forces and the underbody flow state, are analyzed. Specifically, the minimum velocity discrepancy, at line2, between RANS (URANS) and LES is 14.4%, while IDDES is 3.6%. The solution accuracy vs the computational cost is also reported.

The underbody flow of a truncated, 1:10 scaled, CRH380A model is investigated at Re = 2.78 × 105 in this paper. The large-eddy simulation (LES) is used to study the main features of the development of the underbody flow under the snowplow, in the bogie/cavity region and after the cavity (equip-cabin region). A grid independence study and a validation against experimental data have been done prior to the investigation. The snowplow region is dominated by a pair of separated counter-rotating vortices, which further affects the downstream flow. A strong shear layer is observed in the cavity region, and the turbulent flow is intensively triggered by the shear instability and the complex bogie components within the cavity region. The equip-cabin region allows the turbulent flow to develop without any disturbance, decreasing the turbulence intensity. Moreover, the steady and unsteady Reynolds-averaged Navier–Stokes (RANS, URANS) model and the improved delayed detached eddy simulation (IDDES) are used to compute the same flow, and to compare the results to LES. The solution differences, in terms of aerodynamic forces and the underbody flow state, are analyzed. Specifically, the minimum velocity discrepancy, at line2, between RANS (URANS) and LES is 14.4%, while IDDES is 3.6%. The solution accuracy vs the computational cost is also reported.

Categories: Latest papers in fluid mechanics

### New equations of state describing both the dynamic viscosity and self-diffusion coefficient for potassium and thallium in their fluid phases

Physics of Fluids, Volume 34, Issue 1, January 2022.

Experimental data on the viscosity and self-diffusion coefficient of two metallic compounds in their fluid phases, that is, potassium and thallium, are modeled using the translational elastic mode theory, which has been successfully applied to the case of water. It is shown that this theory allows the experimental data to be accounted for in accordance with their uncertainties and, above all, it allows the different variations observed between the different authors to be explained. Particularly in the case of thallium, this theory makes it possible to represent viscosity data with much better precision than the so-called reference equation of state. The dilute-gas limit laws connecting various parameters of the theory obtained in the case of water are confirmed here and thus give them a universal character. The elastic mode theory is accompanied by the development of new equations of state, mainly to describe properties along the saturated vapor pressure curve, which greatly extend the temperature range of application of these equations compared to those found in the literature. The whole analysis thus makes it possible to propose precise values of various thermodynamic parameters at the melting and boiling temperature corresponding to atmospheric pressure.

Experimental data on the viscosity and self-diffusion coefficient of two metallic compounds in their fluid phases, that is, potassium and thallium, are modeled using the translational elastic mode theory, which has been successfully applied to the case of water. It is shown that this theory allows the experimental data to be accounted for in accordance with their uncertainties and, above all, it allows the different variations observed between the different authors to be explained. Particularly in the case of thallium, this theory makes it possible to represent viscosity data with much better precision than the so-called reference equation of state. The dilute-gas limit laws connecting various parameters of the theory obtained in the case of water are confirmed here and thus give them a universal character. The elastic mode theory is accompanied by the development of new equations of state, mainly to describe properties along the saturated vapor pressure curve, which greatly extend the temperature range of application of these equations compared to those found in the literature. The whole analysis thus makes it possible to propose precise values of various thermodynamic parameters at the melting and boiling temperature corresponding to atmospheric pressure.

Categories: Latest papers in fluid mechanics

### Transient performance analysis of a novel design of portable magnetic refrigeration system

Physics of Fluids, Volume 34, Issue 1, January 2022.

The widely used ice chamber-based cold storage for the transportation and storage of vaccines has several disadvantages, including uncontrolled overall temperature, water accumulation, and frequent ice pack renewal. Therefore, in this work, we numerically studied a novel vaccine storage system by coupling magnetic refrigeration and ice packs developed by conserving the advantages of an ice-based system. A two-dimensional numerical model is developed to analyze the magnetohydrodynamic natural convection in the storage chamber. Gadolinium of 0.08 kg is used to produce a cooling power of 31.514 W and a coefficient of performance of 1.3. With the constant heat leaked of 0.828 W into the system with dimensions of (0.1 × 0.1) m, the average life of the ice pack of 0.75 kg is 1.03 h. By introducing the magnetocaloric effect, the life of the same ice pack can be infinite with no load. The dynamic mode decomposition analysis reveals that the most dominant fluid interaction occurs between the cooled gadolinium plate and the adjacent fluid, resulting in efficient cooling of the air chamber. The developed vaccine chamber design will significantly improve the existing ice pack system with a nominal increase in cost and system weight.

The widely used ice chamber-based cold storage for the transportation and storage of vaccines has several disadvantages, including uncontrolled overall temperature, water accumulation, and frequent ice pack renewal. Therefore, in this work, we numerically studied a novel vaccine storage system by coupling magnetic refrigeration and ice packs developed by conserving the advantages of an ice-based system. A two-dimensional numerical model is developed to analyze the magnetohydrodynamic natural convection in the storage chamber. Gadolinium of 0.08 kg is used to produce a cooling power of 31.514 W and a coefficient of performance of 1.3. With the constant heat leaked of 0.828 W into the system with dimensions of (0.1 × 0.1) m, the average life of the ice pack of 0.75 kg is 1.03 h. By introducing the magnetocaloric effect, the life of the same ice pack can be infinite with no load. The dynamic mode decomposition analysis reveals that the most dominant fluid interaction occurs between the cooled gadolinium plate and the adjacent fluid, resulting in efficient cooling of the air chamber. The developed vaccine chamber design will significantly improve the existing ice pack system with a nominal increase in cost and system weight.

Categories: Latest papers in fluid mechanics

### Effects of viscoelasticity on the onset of vortex shedding and forces applied on a cylinder in unsteady flow regime

Physics of Fluids, Volume 34, Issue 1, January 2022.

The present paper aims to investigate the effect of viscoelasticity on the onset of vortex shedding of a high concentration polymer solution over a cylinder using the finite volume method for the first time. To describe the behavior of the viscoelastic fluid, mathematically, the Phan–Thien–Tanner (PTT) model is employed. The convergence problems are resolved using the rheoFoam solver developed by previous researchers based on the log-conformation method. The exact critical Reynolds number ([math]), which corresponds to the onset of vortex shedding, is estimated by implementing numerous unsteady simulations at each elasticity number (El). The [math] is also calculated at every retardation ratio ([math]) and elongational viscosity. The results revealed a significant impact of viscoelasticity on [math] so that the flow of a high viscosity ratio PTT becomes unstable at higher Re (at very low El) or lower Re (at higher El), compared to a Newtonian fluid. In addition, [math] decreases linearly with [math] according to [math] and increases with extensional viscosity. It is also found that [math] plays a vital role in the effect of viscoelasticity on the flow parameters. The averaged drag coefficient ([math]) and the amplitude of lift coefficient ([math]) do not have similar behaviors for low and high [math]. Moreover, viscoelasticity enlarges the vortices and increases the shedding frequency. A comprehensive physical analysis of flow structures is carried out using the distribution of time-averaged stress components and pressure over the cylinder. The numerical results demonstrated the three regimes of drag reduction at El < 0.015, drag enhancement at 0.015 < E1 < 1, and a Newtonian behavior at El > 1 that is an opposite trend compared to a steady regime. The variations of [math] with El are also similar to [math], but at different critical elasticity numbers (El = 0.005 and 2). It is found that the normal stress changes the drag force by the variation of pressure distribution over the cylinder, while the shear stress directly affects the drag and lift forces. In addition, the viscoelasticity decreases the size of the vortices behind the cylinder and increases their vorticity, and changes the position of maximum normal stress, which leads to drag variations. It was also concluded that the higher the elongational viscosities, the lower the shedding frequency.

The present paper aims to investigate the effect of viscoelasticity on the onset of vortex shedding of a high concentration polymer solution over a cylinder using the finite volume method for the first time. To describe the behavior of the viscoelastic fluid, mathematically, the Phan–Thien–Tanner (PTT) model is employed. The convergence problems are resolved using the rheoFoam solver developed by previous researchers based on the log-conformation method. The exact critical Reynolds number ([math]), which corresponds to the onset of vortex shedding, is estimated by implementing numerous unsteady simulations at each elasticity number (El). The [math] is also calculated at every retardation ratio ([math]) and elongational viscosity. The results revealed a significant impact of viscoelasticity on [math] so that the flow of a high viscosity ratio PTT becomes unstable at higher Re (at very low El) or lower Re (at higher El), compared to a Newtonian fluid. In addition, [math] decreases linearly with [math] according to [math] and increases with extensional viscosity. It is also found that [math] plays a vital role in the effect of viscoelasticity on the flow parameters. The averaged drag coefficient ([math]) and the amplitude of lift coefficient ([math]) do not have similar behaviors for low and high [math]. Moreover, viscoelasticity enlarges the vortices and increases the shedding frequency. A comprehensive physical analysis of flow structures is carried out using the distribution of time-averaged stress components and pressure over the cylinder. The numerical results demonstrated the three regimes of drag reduction at El < 0.015, drag enhancement at 0.015 < E1 < 1, and a Newtonian behavior at El > 1 that is an opposite trend compared to a steady regime. The variations of [math] with El are also similar to [math], but at different critical elasticity numbers (El = 0.005 and 2). It is found that the normal stress changes the drag force by the variation of pressure distribution over the cylinder, while the shear stress directly affects the drag and lift forces. In addition, the viscoelasticity decreases the size of the vortices behind the cylinder and increases their vorticity, and changes the position of maximum normal stress, which leads to drag variations. It was also concluded that the higher the elongational viscosities, the lower the shedding frequency.

Categories: Latest papers in fluid mechanics

### Experimental investigation on flow characteristics of compressible oscillating jet

Physics of Fluids, Volume 34, Issue 1, January 2022.

An experimental study was performed to investigate the characteristics of a self-sustained oscillating jet emitted from a double feedback channel fluidic oscillator under high pressure inlet conditions. The working fluid was N2 gas from a portable liquid nitrogen tank. The pressure, temperature, and flow rate were measured, and z-type schlieren visualization was performed to study the high-frequency oscillating jet at nozzle pressure ratios (NPRs) of 4–16. A proper orthogonal decomposition (POD) technique was performed on schlieren images, and a Fast Fourier transform was performed on time coefficients of POD modes to calculate the frequency of oscillations. The results show that for the examined NPRs, the frequency of the oscillating jet is independent of the pressure and flow rate, which contrasts with previous studies. However, the flow behavior varies when changing the NPR. The frequency did not increase with increasing supply pressure. In order to find the main reason for the fixed frequency, a second-order mass spring system was assumed. An equation is also proposed for obtaining the resonance frequency of the double feedback fluidic oscillator.

An experimental study was performed to investigate the characteristics of a self-sustained oscillating jet emitted from a double feedback channel fluidic oscillator under high pressure inlet conditions. The working fluid was N2 gas from a portable liquid nitrogen tank. The pressure, temperature, and flow rate were measured, and z-type schlieren visualization was performed to study the high-frequency oscillating jet at nozzle pressure ratios (NPRs) of 4–16. A proper orthogonal decomposition (POD) technique was performed on schlieren images, and a Fast Fourier transform was performed on time coefficients of POD modes to calculate the frequency of oscillations. The results show that for the examined NPRs, the frequency of the oscillating jet is independent of the pressure and flow rate, which contrasts with previous studies. However, the flow behavior varies when changing the NPR. The frequency did not increase with increasing supply pressure. In order to find the main reason for the fixed frequency, a second-order mass spring system was assumed. An equation is also proposed for obtaining the resonance frequency of the double feedback fluidic oscillator.

Categories: Latest papers in fluid mechanics

### On analysis and stochastic modeling of the particle kinetic energy equation in particle-laden isotropic turbulent flows

Physics of Fluids, Volume 34, Issue 1, January 2022.

We analyze three-dimensional particle-laden, isotropic turbulence to develop an understanding of inertial particle dynamics from a kinetic energy perspective. Data trends implying inhomogeneous sampling of the flow by particles are identified and used to support a proposed particle behavior: particles appear to accumulate in regions of low flow kinetic energy over time because they lose kinetic energy and slow down in such regions, ultimately causing them to spend more time there. To elucidate this behavior, we derive a particle kinetic energy equation from the particle momentum equation, which incorporates inertial effects through the Schiller–Naumann drag correlation. Upon extracting fundamental physics from this equation, hypotheses regarding the role of the Stokes number in the temporal change of particle kinetic energy and the previously proposed particle behavior are evaluated using simulation data considering three Stokes numbers. Finally, a Fokker–Planck equation is used to derive the steady-state probability density function of the particle kinetic energy. The model fits the simulation data well and provides a tool for further investigation into understanding preferential concentration, as well as a reduced order model for predicting particle kinetic energy in turbulent flows.

We analyze three-dimensional particle-laden, isotropic turbulence to develop an understanding of inertial particle dynamics from a kinetic energy perspective. Data trends implying inhomogeneous sampling of the flow by particles are identified and used to support a proposed particle behavior: particles appear to accumulate in regions of low flow kinetic energy over time because they lose kinetic energy and slow down in such regions, ultimately causing them to spend more time there. To elucidate this behavior, we derive a particle kinetic energy equation from the particle momentum equation, which incorporates inertial effects through the Schiller–Naumann drag correlation. Upon extracting fundamental physics from this equation, hypotheses regarding the role of the Stokes number in the temporal change of particle kinetic energy and the previously proposed particle behavior are evaluated using simulation data considering three Stokes numbers. Finally, a Fokker–Planck equation is used to derive the steady-state probability density function of the particle kinetic energy. The model fits the simulation data well and provides a tool for further investigation into understanding preferential concentration, as well as a reduced order model for predicting particle kinetic energy in turbulent flows.

Categories: Latest papers in fluid mechanics

### The transition to turbulence in rarefaction-driven Rayleigh–Taylor mixing: Effects of diffuse interface

Physics of Fluids, Volume 34, Issue 1, January 2022.

Effects of interface diffusion on the transition to turbulence in rarefaction-driven flows are numerically investigated via Implicit Large-Eddy simulation. Three-dimensional, multimode perturbations are imposed on the diffuse interface between Air and SF6, with various diffusion layer thicknesses. A non-constant acceleration ranging from [math] to [math], where g0 is the acceleration due to gravity, is generated by the interaction between the interface and a rarefaction wave. Evolution of first- and second-order statistics, instantaneous flow structures, and the power spectrum of turbulent kinetic energy as well as spatial distributions of energy budget are evaluated, in order to confirm the accuracy and robustness of the mixed mass transition criterion proposed here. Meanwhile, it turns out that transitional behaviors are mainly governed by Reynolds normal stresses in the plane perpendicular to the streamwise direction. Furthermore, as interface diffuses, the decrease in peak values of pressure and advection components dominated in the laminar regimes, particularly at the bubble tips, eventually leads to transition delay.

Effects of interface diffusion on the transition to turbulence in rarefaction-driven flows are numerically investigated via Implicit Large-Eddy simulation. Three-dimensional, multimode perturbations are imposed on the diffuse interface between Air and SF6, with various diffusion layer thicknesses. A non-constant acceleration ranging from [math] to [math], where g0 is the acceleration due to gravity, is generated by the interaction between the interface and a rarefaction wave. Evolution of first- and second-order statistics, instantaneous flow structures, and the power spectrum of turbulent kinetic energy as well as spatial distributions of energy budget are evaluated, in order to confirm the accuracy and robustness of the mixed mass transition criterion proposed here. Meanwhile, it turns out that transitional behaviors are mainly governed by Reynolds normal stresses in the plane perpendicular to the streamwise direction. Furthermore, as interface diffuses, the decrease in peak values of pressure and advection components dominated in the laminar regimes, particularly at the bubble tips, eventually leads to transition delay.

Categories: Latest papers in fluid mechanics

### Nonlinear liquid sloshing in an upright circular container: Modal responses and higher-order harmonics

Physics of Fluids, Volume 34, Issue 1, January 2022.

Nonlinear sloshing in an upright circular container near the lowest natural frequency is analyzed by using a fully nonlinear overset-mesh-based harmonic polynomial cell method, two weakly nonlinear Narimanov–Moiseev-type multimodal models and a linear multimodal method. Modal responses are extracted from the fully nonlinear results based on a simple but accurate least-square procedure using the time series of free-surface wave elevations, which provides new ways to delve into the underlying modal responses and energy transfer between modes, as well as to verify the validity of ordering assumptions in the weakly nonlinear models. Wavelet analyses are also performed for the wave elevations and generalized coordinates of the modes to better understand the time-frequency information of the higher harmonics of the sloshing responses and energy transfer in a nonlinear process. Planar harmonic sloshing state, swirling harmonic sloshing state, and periodically modulated sloshing state are analyzed. It is found that the energy is more dispersed among different modes in the periodically modulated sloshing state, which means higher natural modes are consequential. In general, energies are found to transfer from lower to higher natural modes and between symmetric and antisymmetric natural modes. The results also show that the [math] and [math] responses are dominated by only first and second harmonics, respectively, while the [math] response contains non-negligible first and third harmonic contribution. At last, the influence of initial disturbance is examined, demonstrating that different initial disturbances may lead to the different rotation direction of the swirling waves and the sloshing-wave responses in the transient stage, while the main characteristics of the sloshing waves are robust and independent of initial conditions.

Nonlinear sloshing in an upright circular container near the lowest natural frequency is analyzed by using a fully nonlinear overset-mesh-based harmonic polynomial cell method, two weakly nonlinear Narimanov–Moiseev-type multimodal models and a linear multimodal method. Modal responses are extracted from the fully nonlinear results based on a simple but accurate least-square procedure using the time series of free-surface wave elevations, which provides new ways to delve into the underlying modal responses and energy transfer between modes, as well as to verify the validity of ordering assumptions in the weakly nonlinear models. Wavelet analyses are also performed for the wave elevations and generalized coordinates of the modes to better understand the time-frequency information of the higher harmonics of the sloshing responses and energy transfer in a nonlinear process. Planar harmonic sloshing state, swirling harmonic sloshing state, and periodically modulated sloshing state are analyzed. It is found that the energy is more dispersed among different modes in the periodically modulated sloshing state, which means higher natural modes are consequential. In general, energies are found to transfer from lower to higher natural modes and between symmetric and antisymmetric natural modes. The results also show that the [math] and [math] responses are dominated by only first and second harmonics, respectively, while the [math] response contains non-negligible first and third harmonic contribution. At last, the influence of initial disturbance is examined, demonstrating that different initial disturbances may lead to the different rotation direction of the swirling waves and the sloshing-wave responses in the transient stage, while the main characteristics of the sloshing waves are robust and independent of initial conditions.

Categories: Latest papers in fluid mechanics