# 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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### Stability analysis of a rotor system with fluid applying wave resonance theory

Physics of Fluids, Volume 32, Issue 5, May 2020.

There is a great influence of the stability of a rotor system filled with fluid on the performance of the rotor. Wave resonance theory and the model established by Wolf are applied to study the stability boundaries. First, the resonant frequencies of the radial–circular waves on the nonviscous, incompressible fluid are obtained in a rotor with radial baffles. Based on the Navier–Stokes equations of the fluid, a simple form of the Bessel equation is derived by the perturbation method. Then, the relationship of the radial–circular wave frequencies and the rotation frequencies is obtained. Furthermore, the unstable regions under varying modes are predicted, and the effects of the fluid-fill ratio on the unstable regions are analyzed. In order to verify the accuracy of this model, a comparison is made with the model by Wolf. The results show that two lower boundaries of the unstable regions are in good agreement, while the upper boundaries do not coincide with the internal resonance when the baffle is equal to 2. The mechanism of the stability of a rotor filled with fluid is revealed in the case of the chamber without baffles.

There is a great influence of the stability of a rotor system filled with fluid on the performance of the rotor. Wave resonance theory and the model established by Wolf are applied to study the stability boundaries. First, the resonant frequencies of the radial–circular waves on the nonviscous, incompressible fluid are obtained in a rotor with radial baffles. Based on the Navier–Stokes equations of the fluid, a simple form of the Bessel equation is derived by the perturbation method. Then, the relationship of the radial–circular wave frequencies and the rotation frequencies is obtained. Furthermore, the unstable regions under varying modes are predicted, and the effects of the fluid-fill ratio on the unstable regions are analyzed. In order to verify the accuracy of this model, a comparison is made with the model by Wolf. The results show that two lower boundaries of the unstable regions are in good agreement, while the upper boundaries do not coincide with the internal resonance when the baffle is equal to 2. The mechanism of the stability of a rotor filled with fluid is revealed in the case of the chamber without baffles.

Categories: Latest papers in fluid mechanics

### Numerical study of Taylor–Couette flow with longitudinal corrugated surface

Physics of Fluids, Volume 32, Issue 5, May 2020.

This study investigates the Taylor–Couette flow (TCF) with a longitudinal corrugated surface on a stationary outer cylinder and a rotating smooth inner cylinder using large eddy simulation for three values of amplitude to wavelength ratios (A*) (0.1875, 0.2149, and 0.25) to explore the influence of the corrugated surface on the flow structures and the variation of torque for a wider range of Reynolds numbers (Re) (60–650). From the results, four flow regimes are observed. At Re = 60, initially, a pair of secondary vortices appears at the inner wall of the minimum gap region and it evolves to a pair of axisymmetric stationary wall induced vortices (ASSWIVs) in the maximum gap region. As Re increases to 80, 85, and 103 for the three values of A* (0.1875, 0.2149, and 0.25), respectively, another pair of axisymmetric stationary secondary vortices is seen at the minimum gap region of the inner wall. A further increase in Re (Re > 125, 130, and 138 for the three values of A*, respectively) results in the appearance of axisymmetric periodic secondary axial flow. Increasing Re further (Re > 225, 240, and 260 for A* = 0.25, 0.2149, and 0.1875, respectively) leads to the emergence of non-axisymmetric and non-periodic secondary axial flow (NANPSAF) with an azimuthal wave. Generally, the torque in TCF with the corrugated surface is found to be lower than TCF with a smooth surface except for the occurrence of the ASSWIV flow regime and weak axial secondary flow in the NANPSAF regime.

This study investigates the Taylor–Couette flow (TCF) with a longitudinal corrugated surface on a stationary outer cylinder and a rotating smooth inner cylinder using large eddy simulation for three values of amplitude to wavelength ratios (A*) (0.1875, 0.2149, and 0.25) to explore the influence of the corrugated surface on the flow structures and the variation of torque for a wider range of Reynolds numbers (Re) (60–650). From the results, four flow regimes are observed. At Re = 60, initially, a pair of secondary vortices appears at the inner wall of the minimum gap region and it evolves to a pair of axisymmetric stationary wall induced vortices (ASSWIVs) in the maximum gap region. As Re increases to 80, 85, and 103 for the three values of A* (0.1875, 0.2149, and 0.25), respectively, another pair of axisymmetric stationary secondary vortices is seen at the minimum gap region of the inner wall. A further increase in Re (Re > 125, 130, and 138 for the three values of A*, respectively) results in the appearance of axisymmetric periodic secondary axial flow. Increasing Re further (Re > 225, 240, and 260 for A* = 0.25, 0.2149, and 0.1875, respectively) leads to the emergence of non-axisymmetric and non-periodic secondary axial flow (NANPSAF) with an azimuthal wave. Generally, the torque in TCF with the corrugated surface is found to be lower than TCF with a smooth surface except for the occurrence of the ASSWIV flow regime and weak axial secondary flow in the NANPSAF regime.

Categories: Latest papers in fluid mechanics

### An atomic-level study of the N2–N2 collision process at temperatures up to 2000 K

Physics of Fluids, Volume 32, Issue 5, May 2020.

This article studies the mechanics of the N2–N2 collision process at temperatures up to 2000 K through an extensive set of classical trajectory calculations of binary collisions. It is found that key postcollision characteristics, namely, the deflection angle and the rotational–translational energy exchange rate, are significantly affected by precollision values of the rotational energies of the molecules, which is not addressed in commonly used collision models. On the macroscopic scale, such a behavior will lead to viscosity collision cross section and relaxation rate becoming dependent on both translational and rotational temperatures, as well as on the form of the nonequilibrium rotational energy distribution.

This article studies the mechanics of the N2–N2 collision process at temperatures up to 2000 K through an extensive set of classical trajectory calculations of binary collisions. It is found that key postcollision characteristics, namely, the deflection angle and the rotational–translational energy exchange rate, are significantly affected by precollision values of the rotational energies of the molecules, which is not addressed in commonly used collision models. On the macroscopic scale, such a behavior will lead to viscosity collision cross section and relaxation rate becoming dependent on both translational and rotational temperatures, as well as on the form of the nonequilibrium rotational energy distribution.

Categories: Latest papers in fluid mechanics

### Characteristics of wall-attached motions in open channel flows

Physics of Fluids, Volume 32, Issue 5, May 2020.

Time-resolved particle image velocimetry measurements with sufficient spatial resolutions combined with coherence spectrum analysis were adopted to investigate the geometric and kinematic features of wall-attached motions in open channel flows. Results indicate that the diagnosed streamwise wavelength of wall-attached motions λxWA based on a given near zero coherence spectrum threshold exhibits a constant streamwise wavelength/wall-normal distance ratio accompanied with a roughly constant inclination angle within y+ > ∼100 and y/h ≤ 0.7 [y+ is the inner-scale normalized distance to the wall y with y+ = y/(ν/uτ) (ν is the kinematic viscosity and uτ is the friction velocity) and h is the water depth], meaning that they are geometrically self-similar. However, in the free-surface region, where y/h > 0.7, the diagnosed wall-attached motions are non-self-similar with λxWA increasing more dramatically and reaching up to ∼20h at the free surface, which is comparable to the typical scales of very-large-scale motions therein. The wall-attached motions are demonstrated to be both energetic and stress active. Within y/h < 0.7, the wall-attached motions with the streamwise wavelength greater than λxWA (including both the self-similar and non-self-similar wavelength range portions) carry more than 40% of the streamwise turbulent kinetic energy (TKE) and 30% of Reynolds shear stress. Beyond y/h = 0.7, where the self-similar portions vanish, all the wall-attached motions are non-self-similar wall-attached motions, which themselves still maintain considerable strength even at the free surface and contribute to 25% of the streamwise TKE and 10% of the Reynolds shear stress therein.

Time-resolved particle image velocimetry measurements with sufficient spatial resolutions combined with coherence spectrum analysis were adopted to investigate the geometric and kinematic features of wall-attached motions in open channel flows. Results indicate that the diagnosed streamwise wavelength of wall-attached motions λxWA based on a given near zero coherence spectrum threshold exhibits a constant streamwise wavelength/wall-normal distance ratio accompanied with a roughly constant inclination angle within y+ > ∼100 and y/h ≤ 0.7 [y+ is the inner-scale normalized distance to the wall y with y+ = y/(ν/uτ) (ν is the kinematic viscosity and uτ is the friction velocity) and h is the water depth], meaning that they are geometrically self-similar. However, in the free-surface region, where y/h > 0.7, the diagnosed wall-attached motions are non-self-similar with λxWA increasing more dramatically and reaching up to ∼20h at the free surface, which is comparable to the typical scales of very-large-scale motions therein. The wall-attached motions are demonstrated to be both energetic and stress active. Within y/h < 0.7, the wall-attached motions with the streamwise wavelength greater than λxWA (including both the self-similar and non-self-similar wavelength range portions) carry more than 40% of the streamwise turbulent kinetic energy (TKE) and 30% of Reynolds shear stress. Beyond y/h = 0.7, where the self-similar portions vanish, all the wall-attached motions are non-self-similar wall-attached motions, which themselves still maintain considerable strength even at the free surface and contribute to 25% of the streamwise TKE and 10% of the Reynolds shear stress therein.

Categories: Latest papers in fluid mechanics

### Control of unsteady partial cavitation and cloud cavitation in marine engineering and hydraulic systems

Physics of Fluids, Volume 32, Issue 5, May 2020.

Cavitation is a process of liquid evaporation, bubble or vapor sheet formation, and further collapse of vapor structures, which plays a destructive role in many industrial applications. In marine transport and hydraulic machinery, cavitation usually occurs nearby the surface of a ship propeller and rudder, impeller blades in a pump, and distributor vanes and runner blades in a hydroturbine and causes various undesirable effects such as vibrations of frameworks and/or moving parts, material erosion, and noise enhancement. Based on an extensive literature review, this research is aimed at an experimental investigation of a passive approach to control cavitation on a benchmark hydrofoil using a wedge-type vortex generator in different flow regimes with a high Reynolds number. In this study, we employed a high-speed imaging method to explore the spatial patterns and time evolutions of cavitation structures and utilized a hydroacoustic pressure transducer to record and analyze local pressure pulsations due to the collapse of the cavities in the hydrofoil wake region. The results show that the examined control technique is quite effective and capable of hindering the formation of cloud cavities and reducing the amplitude of pressure pulsations associated with unsteady cavitation dynamics. This study provides important experimental information, which can be useful for improving industrial technologies and for promoting new developments in this particular research field.

Cavitation is a process of liquid evaporation, bubble or vapor sheet formation, and further collapse of vapor structures, which plays a destructive role in many industrial applications. In marine transport and hydraulic machinery, cavitation usually occurs nearby the surface of a ship propeller and rudder, impeller blades in a pump, and distributor vanes and runner blades in a hydroturbine and causes various undesirable effects such as vibrations of frameworks and/or moving parts, material erosion, and noise enhancement. Based on an extensive literature review, this research is aimed at an experimental investigation of a passive approach to control cavitation on a benchmark hydrofoil using a wedge-type vortex generator in different flow regimes with a high Reynolds number. In this study, we employed a high-speed imaging method to explore the spatial patterns and time evolutions of cavitation structures and utilized a hydroacoustic pressure transducer to record and analyze local pressure pulsations due to the collapse of the cavities in the hydrofoil wake region. The results show that the examined control technique is quite effective and capable of hindering the formation of cloud cavities and reducing the amplitude of pressure pulsations associated with unsteady cavitation dynamics. This study provides important experimental information, which can be useful for improving industrial technologies and for promoting new developments in this particular research field.

Categories: Latest papers in fluid mechanics

### Study on the transient characteristics of pulsation bubble near a free surface based on finite volume method and front tracking method

Physics of Fluids, Volume 32, Issue 5, May 2020.

The pulsation bubble dynamics near a free surface have significant engineering applications. Based on the finite volume method, a front tracking method coupled with an extrapolation technique is applied to study the transient characteristics of the pulsation bubble near the free surface with the different stand-off distance parameter γ and buoyancy parameter δ (the parameters are defined in Sec. II D). By comparison, the numerical results agree well with the results from the spark-generated bubble experiment. For the cases with small δ, (i) the phenomenon that the bubble top is elongated is no longer obvious while γ > 2.0, (ii) with the decrease in γ, the bubble centroid at the minimum volume is gradually away from the free surface except for migrating upward while 0.85 < γ < 1.0, and (iii) while γ > 1.2, the free surface begins to fall with the bubble collapse after rising during the expansion stage and almost falls back to its original position while γ > 2.4. For the cases with γ = 1.0–1.13, (i) while δ > 0.2293, the jet penetrates the bubble before the bubble reaches its minimum volume, and both are contrary while δ < 0.2293, (ii) while δ > 0.4636, the free surface begins to fall with the bubble collapse after rising during the expansion stage, and (iii) the bubble is always migrating toward the free surface while δ > 0.4109. Meanwhile, the phenomena such as the inward jet formed inside the toroidal bubble, the toroidal bubble split, and the water skirt are also analyzed.

The pulsation bubble dynamics near a free surface have significant engineering applications. Based on the finite volume method, a front tracking method coupled with an extrapolation technique is applied to study the transient characteristics of the pulsation bubble near the free surface with the different stand-off distance parameter γ and buoyancy parameter δ (the parameters are defined in Sec. II D). By comparison, the numerical results agree well with the results from the spark-generated bubble experiment. For the cases with small δ, (i) the phenomenon that the bubble top is elongated is no longer obvious while γ > 2.0, (ii) with the decrease in γ, the bubble centroid at the minimum volume is gradually away from the free surface except for migrating upward while 0.85 < γ < 1.0, and (iii) while γ > 1.2, the free surface begins to fall with the bubble collapse after rising during the expansion stage and almost falls back to its original position while γ > 2.4. For the cases with γ = 1.0–1.13, (i) while δ > 0.2293, the jet penetrates the bubble before the bubble reaches its minimum volume, and both are contrary while δ < 0.2293, (ii) while δ > 0.4636, the free surface begins to fall with the bubble collapse after rising during the expansion stage, and (iii) the bubble is always migrating toward the free surface while δ > 0.4109. Meanwhile, the phenomena such as the inward jet formed inside the toroidal bubble, the toroidal bubble split, and the water skirt are also analyzed.

Categories: Latest papers in fluid mechanics

### A microfluidic rectifier for Newtonian fluids using asymmetric converging–diverging microchannels

Physics of Fluids, Volume 32, Issue 5, May 2020.

Flow rectification for Newtonian fluids remains challenging compared with that for non-Newtonian fluids because the physical properties of Newtonian fluids are independent of the structure of flow channels, and flow rectification can only be achieved through direction-dependent flow scenarios. In this work, we fabricate a microfluidic rectifier for Newtonian fluids using asymmetric converging–diverging microchannels. The highest diodicity measured for the rectifier is 1.77, which is 15%–54% higher than previous microfluidic rectifiers for Newtonian fluids. An expression for the diodicity is developed based on two scaling laws for the flow resistances in the forward and backward directions. Numerical simulations are also performed to confirm the experiments.

Flow rectification for Newtonian fluids remains challenging compared with that for non-Newtonian fluids because the physical properties of Newtonian fluids are independent of the structure of flow channels, and flow rectification can only be achieved through direction-dependent flow scenarios. In this work, we fabricate a microfluidic rectifier for Newtonian fluids using asymmetric converging–diverging microchannels. The highest diodicity measured for the rectifier is 1.77, which is 15%–54% higher than previous microfluidic rectifiers for Newtonian fluids. An expression for the diodicity is developed based on two scaling laws for the flow resistances in the forward and backward directions. Numerical simulations are also performed to confirm the experiments.

Categories: Latest papers in fluid mechanics

### Coarse-graining, compressibility, and thermal fluctuation scaling in dissipative particle dynamics employed with pre-determined input parameters

Physics of Fluids, Volume 32, Issue 5, May 2020.

In this study, a Dissipative Particle Dynamics (DPD) method is employed with its input parameters directly determined from the fluid properties, such as the fluid mass density, water compressibility, and viscosity. The investigation of thermal fluctuation scaling requires constant fluid properties, and this proposed DPD version meets this requirement. Its numerical verifications in simple or complex fluids under viscometric or non-viscometric flows indicate that (i) the level of thermal fluctuations in the DPD model for both types of fluids is consistently reduced with an increase in the coarse-graining level and (ii) viscometric or non-viscometric flows of a model fluid at different coarse-graining levels have a similar behavior. Furthermore, to reduce the compressibility effect of the DPD fluid in simulating incompressible flows, a new simple treatment is presented and shown to be very effective.

In this study, a Dissipative Particle Dynamics (DPD) method is employed with its input parameters directly determined from the fluid properties, such as the fluid mass density, water compressibility, and viscosity. The investigation of thermal fluctuation scaling requires constant fluid properties, and this proposed DPD version meets this requirement. Its numerical verifications in simple or complex fluids under viscometric or non-viscometric flows indicate that (i) the level of thermal fluctuations in the DPD model for both types of fluids is consistently reduced with an increase in the coarse-graining level and (ii) viscometric or non-viscometric flows of a model fluid at different coarse-graining levels have a similar behavior. Furthermore, to reduce the compressibility effect of the DPD fluid in simulating incompressible flows, a new simple treatment is presented and shown to be very effective.

Categories: Latest papers in fluid mechanics

### Application of the Lambert W function to steady shearing Newtonian flows with logarithmic wall slip

Physics of Fluids, Volume 32, Issue 5, May 2020.

We consider various viscometric flows of a Newtonian fluid, i.e., plane, annular, and circular Couette flows and planar and axisymmetric Poiseuille flows, in the presence of wall slip that follows a logarithmic slip law. We derive analytical solutions in terms of the Lambert W function. The effects of logarithmic slip on these flows are discussed, and comparisons of the results with their Navier-slip counterparts are made.

We consider various viscometric flows of a Newtonian fluid, i.e., plane, annular, and circular Couette flows and planar and axisymmetric Poiseuille flows, in the presence of wall slip that follows a logarithmic slip law. We derive analytical solutions in terms of the Lambert W function. The effects of logarithmic slip on these flows are discussed, and comparisons of the results with their Navier-slip counterparts are made.

Categories: Latest papers in fluid mechanics

### Solid-flow interactions of a large aspect ratio cylinder in a shallow open channel

Physics of Fluids, Volume 32, Issue 5, May 2020.

The complex wake created by an emergent slender circular cylinder in a shallow open channel flow is studied at a cylinder Reynolds number (ReD) of 3300 and at a subcritical Froude number of 0.58 in water. Methodical laser Doppler velocimetry measurements were taken in a very fine grid in three horizontal planes at near bed, mid-depth, and near free surface both upstream and downstream of the cylinder. Demarcation of the entire wake region starting from the first point of the onset of disturbed flow upstream to undisturbed flow downstream entirely based on experiments successfully added a novel contribution to the research on wake flow over a single cylinder. The proximity of the bed and free surface has a significant effect on the structure of the wake compared to the mid-depth. The size, shape, and development of the recirculation region behind the cylinder vary in the vertical direction from the bed to free surface. The longest wake closure point was found in the near bed region and the shortest was found near the free surface. The new model developed pertinent to longitudinal velocity deficit can be used as a velocity deficit scale for the entire far wake region for shallow wakes at mid-depth and near free surface. Urms/Us profiles along the transverse direction initially show a double peak behavior for all three levels, and well away from the cylinder downstream, the double peak becomes broader and less distinct, which is attributed to the effect of the separating shear layers. It is also noted that the wake characteristics of slender cylinders are significantly different from those of wakes generated by cylinders with small aspect ratios.

The complex wake created by an emergent slender circular cylinder in a shallow open channel flow is studied at a cylinder Reynolds number (ReD) of 3300 and at a subcritical Froude number of 0.58 in water. Methodical laser Doppler velocimetry measurements were taken in a very fine grid in three horizontal planes at near bed, mid-depth, and near free surface both upstream and downstream of the cylinder. Demarcation of the entire wake region starting from the first point of the onset of disturbed flow upstream to undisturbed flow downstream entirely based on experiments successfully added a novel contribution to the research on wake flow over a single cylinder. The proximity of the bed and free surface has a significant effect on the structure of the wake compared to the mid-depth. The size, shape, and development of the recirculation region behind the cylinder vary in the vertical direction from the bed to free surface. The longest wake closure point was found in the near bed region and the shortest was found near the free surface. The new model developed pertinent to longitudinal velocity deficit can be used as a velocity deficit scale for the entire far wake region for shallow wakes at mid-depth and near free surface. Urms/Us profiles along the transverse direction initially show a double peak behavior for all three levels, and well away from the cylinder downstream, the double peak becomes broader and less distinct, which is attributed to the effect of the separating shear layers. It is also noted that the wake characteristics of slender cylinders are significantly different from those of wakes generated by cylinders with small aspect ratios.

Categories: Latest papers in fluid mechanics

### Coalescence of vertically aligned drops over a superhydrophobic surface

Physics of Fluids, Volume 32, Issue 5, May 2020.

The coalescence process of two liquid droplets where one is placed initially over the other is investigated. The lower drop is placed over a horizontal surface in a sessile configuration. The liquids of interest selected are water, glycerin, and Cs-alloy. The two liquid drops merge under atmospheric conditions. The substrate is superhydrophobic with respect to the three liquids, the equilibrium contact angle being 150°. For the combined drop, the Bond number is ∼0.2. Numerical simulations have been performed in an axisymmetric coordinate system along with supporting experiments. A variety of contact line models reported in the literature have been adopted and compared. Experiments are carried out for validation against simulation with water as the liquid medium. The coalescence phenomenon is recorded by a high-speed camera. The two drops coalesce spontaneously and generate interfacial shapes, velocity fields, footprint, and wall shear stress in time. In water, the combined drop recoils from the surface before spreading over the surface and approaching equilibrium. This trend, including the instant and height of recoil, is correctly realized in the contact line models. Additionally, two distinct timescales originate during the coalescence process. These are associated with inertia and surface tension at small times and inertia–viscosity for longer durations. The instantaneous footprint radius and the average wall shear stress fall to zero during recoil, increase then to a maximum, and diminish to zero with damped oscillations over the longer timescale. Recoil is seen in water as well as Cs-alloy, but not in glycerin. Despite differences in the instantaneous data, these predictions are broadly reproduced by each of the contact line models.

The coalescence process of two liquid droplets where one is placed initially over the other is investigated. The lower drop is placed over a horizontal surface in a sessile configuration. The liquids of interest selected are water, glycerin, and Cs-alloy. The two liquid drops merge under atmospheric conditions. The substrate is superhydrophobic with respect to the three liquids, the equilibrium contact angle being 150°. For the combined drop, the Bond number is ∼0.2. Numerical simulations have been performed in an axisymmetric coordinate system along with supporting experiments. A variety of contact line models reported in the literature have been adopted and compared. Experiments are carried out for validation against simulation with water as the liquid medium. The coalescence phenomenon is recorded by a high-speed camera. The two drops coalesce spontaneously and generate interfacial shapes, velocity fields, footprint, and wall shear stress in time. In water, the combined drop recoils from the surface before spreading over the surface and approaching equilibrium. This trend, including the instant and height of recoil, is correctly realized in the contact line models. Additionally, two distinct timescales originate during the coalescence process. These are associated with inertia and surface tension at small times and inertia–viscosity for longer durations. The instantaneous footprint radius and the average wall shear stress fall to zero during recoil, increase then to a maximum, and diminish to zero with damped oscillations over the longer timescale. Recoil is seen in water as well as Cs-alloy, but not in glycerin. Despite differences in the instantaneous data, these predictions are broadly reproduced by each of the contact line models.

Categories: Latest papers in fluid mechanics

### Flow topology and its transformation inside droplets traveling in rectangular microchannels

Physics of Fluids, Volume 32, Issue 5, May 2020.

The flow topology inside a droplet acts directly on the cells or substances enclosed therein and is, therefore, of great significance in controlling the living environment of cells and the biochemical reaction process. In this paper, the flow characteristics inside droplets moving in rectangular microchannels are studied experimentally by particle image velocimetry for capillary numbers ranging from 10−5 to 10−2. In order to decouple the effects of total flow, droplet spacing, viscosity ratio, droplet size, and the depth-to-width ratio of the channel on the flow field, the droplet trains with a designed initial state are first produced by controlling the two-phase flow rate and setting up an auxiliary inlet, which is used to adjust the droplet size and spacing, and then run at a set flow rate. As the total flow increases, the flow topologies inside the plunger droplet gradually change from four eddies to two at relatively high viscosity ratios, whereas the opposite transition direction is observed in the low-viscosity-ratio system. The flow topology inside spherical droplets is unaffected by the total flow or capillary number, invariably producing double vortices. The effect of the channel wall on the droplet boundary decreases as the droplet spacing increases or the droplet size decreases. Assuming the continuity of the fluid mass, the competition between the gutter-flow driving stress and the oil-film resistance determines the boundary velocity of the droplet. The oil-film resistance dominates the motion of the droplet boundary in high-aspect-ratio channels, resulting in the negative rotation of the boundary velocity vectors and six vortices in the interior of the droplet. The results are conducive to the further development of microfluidic flow cytometry, particle concentration control, and droplet micromixers.

The flow topology inside a droplet acts directly on the cells or substances enclosed therein and is, therefore, of great significance in controlling the living environment of cells and the biochemical reaction process. In this paper, the flow characteristics inside droplets moving in rectangular microchannels are studied experimentally by particle image velocimetry for capillary numbers ranging from 10−5 to 10−2. In order to decouple the effects of total flow, droplet spacing, viscosity ratio, droplet size, and the depth-to-width ratio of the channel on the flow field, the droplet trains with a designed initial state are first produced by controlling the two-phase flow rate and setting up an auxiliary inlet, which is used to adjust the droplet size and spacing, and then run at a set flow rate. As the total flow increases, the flow topologies inside the plunger droplet gradually change from four eddies to two at relatively high viscosity ratios, whereas the opposite transition direction is observed in the low-viscosity-ratio system. The flow topology inside spherical droplets is unaffected by the total flow or capillary number, invariably producing double vortices. The effect of the channel wall on the droplet boundary decreases as the droplet spacing increases or the droplet size decreases. Assuming the continuity of the fluid mass, the competition between the gutter-flow driving stress and the oil-film resistance determines the boundary velocity of the droplet. The oil-film resistance dominates the motion of the droplet boundary in high-aspect-ratio channels, resulting in the negative rotation of the boundary velocity vectors and six vortices in the interior of the droplet. The results are conducive to the further development of microfluidic flow cytometry, particle concentration control, and droplet micromixers.

Categories: Latest papers in fluid mechanics

### Estimation of mean turbulent kinetic energy and temperature variance dissipation rates using a spectral chart method

Physics of Fluids, Volume 32, Issue 5, May 2020.

A method aimed at estimating [math]k and [math]θ, respectively, the mean dissipation rates of turbulent kinetic energy k and half the temperature variance [math], is developed for slightly heated turbulent flows of air. It is limited to a Prandtl number near unity and applicable to flows where temperature can be treated as a passive scalar. A significant advantage of the method is that [math]k and [math]θ can both be estimated from the measurement of a temperature frequency spectrum, Gθθ(f). The method relies on the collapse in the dissipative range of one-dimensional temperature spectra, ϕθ(k1η), when normalized with [math]θ, [math]k, and ν. This collapse ensues from a similarity analysis of scale-by-scale budgets of the second-order structure function for the temperature. A generic spectrum [math], defined in the wavenumber range 0.07 ≤ k1η ≤ 0.7, is used to construct a spectral chart. The method has been tested in several flows and found to be reliable. In particular, it is tested on the axis of a slightly heated round jet, where [math]k and [math]θ can be estimated accurately via the budgets of k and [math], and the agreement between these estimates and the spectral chart results is almost perfect.

A method aimed at estimating [math]k and [math]θ, respectively, the mean dissipation rates of turbulent kinetic energy k and half the temperature variance [math], is developed for slightly heated turbulent flows of air. It is limited to a Prandtl number near unity and applicable to flows where temperature can be treated as a passive scalar. A significant advantage of the method is that [math]k and [math]θ can both be estimated from the measurement of a temperature frequency spectrum, Gθθ(f). The method relies on the collapse in the dissipative range of one-dimensional temperature spectra, ϕθ(k1η), when normalized with [math]θ, [math]k, and ν. This collapse ensues from a similarity analysis of scale-by-scale budgets of the second-order structure function for the temperature. A generic spectrum [math], defined in the wavenumber range 0.07 ≤ k1η ≤ 0.7, is used to construct a spectral chart. The method has been tested in several flows and found to be reliable. In particular, it is tested on the axis of a slightly heated round jet, where [math]k and [math]θ can be estimated accurately via the budgets of k and [math], and the agreement between these estimates and the spectral chart results is almost perfect.

Categories: Latest papers in fluid mechanics

### Numerical study on transition structures of oblique detonations with expansion wave from finite-length cowl

Physics of Fluids, Volume 32, Issue 5, May 2020.

The oblique detonation wave (ODW) triggered by a semi-infinite cowl or wedge has been widely studied, but the effects of finite-length cowls require further clarification to enhance their applicability. Based on two-dimensional inviscid Euler equations and a two-step induction–reaction model, two structures with smooth and abrupt transitions are simulated, and their interactions with the cowl-induced expansion wave are investigated. The expansion waves located downstream and far away from the initiation zone do not affect the macroscopic structures of the ODW. However, when the expansion waves move upstream, the structures evolve into a decoupled shock and a reactive front. Alongside findings from previous studies, these results indicate that the initiation mechanism, rather than the transition type, determines the near-quenching evolution of the structure. Moreover, given the same parameter settings for the chemical and inflow gas dynamics, these numerical results show that the abrupt transition evolves into a smooth transition under an expansion wave disturbance. This demonstrates that the local wave interaction plays a key role in the ODW structures.

The oblique detonation wave (ODW) triggered by a semi-infinite cowl or wedge has been widely studied, but the effects of finite-length cowls require further clarification to enhance their applicability. Based on two-dimensional inviscid Euler equations and a two-step induction–reaction model, two structures with smooth and abrupt transitions are simulated, and their interactions with the cowl-induced expansion wave are investigated. The expansion waves located downstream and far away from the initiation zone do not affect the macroscopic structures of the ODW. However, when the expansion waves move upstream, the structures evolve into a decoupled shock and a reactive front. Alongside findings from previous studies, these results indicate that the initiation mechanism, rather than the transition type, determines the near-quenching evolution of the structure. Moreover, given the same parameter settings for the chemical and inflow gas dynamics, these numerical results show that the abrupt transition evolves into a smooth transition under an expansion wave disturbance. This demonstrates that the local wave interaction plays a key role in the ODW structures.

Categories: Latest papers in fluid mechanics

### A smoothed particle hydrodynamics study of a non-isothermal and thermally anisotropic fused deposition modeling process for a fiber-filled composite

Physics of Fluids, Volume 32, Issue 5, May 2020.

A smoothed particle hydrodynamics method is employed to study the mechanical and thermal behaviors of a fiber-filled composite with an anisotropic thermal conductivity (which is coupled to the orientation of the fibers) in a three-dimensional printing process for one- and two-layer deposition. Using a microstructure-based fiber suspension model with a fiber orientation-dependent thermal conductivity model, a temperature-shear-thinning viscosity model, and a microstructure constitutive model, the effect of the nozzle temperature on the fiber alignment when printing one layer and the mechanical and thermal interactions between two printed layers are investigated. It is found that the anisotropic thermal conductivity (fiber-orientation-dependent) enhances the fiber alignment in the printing direction in the upper half layer and reduces it in the lower half at a relatively high fiber concentration (Φ = 0.2). For the one-layer deposition, the fiber alignment in the printing direction is enhanced in the lower half of the layer with an increase in the nozzle temperature. This tendency is more pronounced with the increase in both the fiber concentration and the aspect ratio. On the two-layer deposition, the fiber alignment of the first layer experiences a “reciprocating” evolution due to the squeezing from the second layer, thus creating an enhancement in the upper half and a reduction in the lower half in the fiber alignment in the first layer (with respect to the printing direction). Increasing the fiber concentration or the aspect ratio amplifies this variation for the first layer. Increasing the substrate velocity also leads to some variations in the fiber alignment.

A smoothed particle hydrodynamics method is employed to study the mechanical and thermal behaviors of a fiber-filled composite with an anisotropic thermal conductivity (which is coupled to the orientation of the fibers) in a three-dimensional printing process for one- and two-layer deposition. Using a microstructure-based fiber suspension model with a fiber orientation-dependent thermal conductivity model, a temperature-shear-thinning viscosity model, and a microstructure constitutive model, the effect of the nozzle temperature on the fiber alignment when printing one layer and the mechanical and thermal interactions between two printed layers are investigated. It is found that the anisotropic thermal conductivity (fiber-orientation-dependent) enhances the fiber alignment in the printing direction in the upper half layer and reduces it in the lower half at a relatively high fiber concentration (Φ = 0.2). For the one-layer deposition, the fiber alignment in the printing direction is enhanced in the lower half of the layer with an increase in the nozzle temperature. This tendency is more pronounced with the increase in both the fiber concentration and the aspect ratio. On the two-layer deposition, the fiber alignment of the first layer experiences a “reciprocating” evolution due to the squeezing from the second layer, thus creating an enhancement in the upper half and a reduction in the lower half in the fiber alignment in the first layer (with respect to the printing direction). Increasing the fiber concentration or the aspect ratio amplifies this variation for the first layer. Increasing the substrate velocity also leads to some variations in the fiber alignment.

Categories: Latest papers in fluid mechanics

### Nonlinear dynamics of thin liquid films subjected to mixed-frequency electrical field

Physics of Fluids, Volume 32, Issue 5, May 2020.

The nonlinear dynamics of the interface between both perfect and leaky dielectric liquid films, interposed between two parallel electrodes, are investigated under the effect of mixed-frequency electric fields. A coupled system of evolution equations is derived in dimensionless form, by employing the long-wave approximation. The linear stability analysis is implemented in accordance with the characteristics of each specific case, namely, the constant (DC) and the altering (AC) fields. In particular, the response of the system to the multi-mode AC electrical field is analyzed. Assisted by the conclusions of the theoretical investigation, the initial-boundary-value problem associated with the coupled system of evolution equations is solved numerically for several parameter sets. The system behavior is studied by monitoring the evolution process and by examining the steady/quasi-steady pillar formations in the nonlinear regime. The possibility to generate interface profiles of diverse topological forms, to manipulate their features, and to control the time dependent progress and the film rupture by imposing different combinations of frequencies and/or amplitudes of the corresponding mode is confirmed.

The nonlinear dynamics of the interface between both perfect and leaky dielectric liquid films, interposed between two parallel electrodes, are investigated under the effect of mixed-frequency electric fields. A coupled system of evolution equations is derived in dimensionless form, by employing the long-wave approximation. The linear stability analysis is implemented in accordance with the characteristics of each specific case, namely, the constant (DC) and the altering (AC) fields. In particular, the response of the system to the multi-mode AC electrical field is analyzed. Assisted by the conclusions of the theoretical investigation, the initial-boundary-value problem associated with the coupled system of evolution equations is solved numerically for several parameter sets. The system behavior is studied by monitoring the evolution process and by examining the steady/quasi-steady pillar formations in the nonlinear regime. The possibility to generate interface profiles of diverse topological forms, to manipulate their features, and to control the time dependent progress and the film rupture by imposing different combinations of frequencies and/or amplitudes of the corresponding mode is confirmed.

Categories: Latest papers in fluid mechanics

### Combination of counterflow jet and cavity for heat flux and drag reduction

Physics of Fluids, Volume 32, Issue 5, May 2020.

In the present work, a computational study is carried out to explore the potential of a combination of a forward-facing cavity and a counterflow jet for drag and heat flux mitigation for an axisymmetric body in a supersonic free stream of Mach 2. A comparison between the axisymmetric body with a forward-facing cavity and counterflow jet and the baseline geometry without the cavity and jet is made. The first part of this study focuses on capturing the transition point of the two counterflow jet modes, Long Penetration Mode (LPM) and Short Penetration Mode (SPM), by changing the pressure ratio of the nozzle. It gave an appropriate nozzle operating pressure selection based on the design requirement. The LPM is found to be suitable when only drag reduction is required, while the SPM provides both drag and heat flux reduction, but at a higher operating jet pressure. Next, a study is conducted to characterize the effect of the angle of attack on system performance. The LPM shows improvement over the baseline geometry for only a narrow range of angles of attack, while the SPM provides improved performance for a wider range of angles of attack. The effect of cavity and cavity dimensions on performance is then studied.

In the present work, a computational study is carried out to explore the potential of a combination of a forward-facing cavity and a counterflow jet for drag and heat flux mitigation for an axisymmetric body in a supersonic free stream of Mach 2. A comparison between the axisymmetric body with a forward-facing cavity and counterflow jet and the baseline geometry without the cavity and jet is made. The first part of this study focuses on capturing the transition point of the two counterflow jet modes, Long Penetration Mode (LPM) and Short Penetration Mode (SPM), by changing the pressure ratio of the nozzle. It gave an appropriate nozzle operating pressure selection based on the design requirement. The LPM is found to be suitable when only drag reduction is required, while the SPM provides both drag and heat flux reduction, but at a higher operating jet pressure. Next, a study is conducted to characterize the effect of the angle of attack on system performance. The LPM shows improvement over the baseline geometry for only a narrow range of angles of attack, while the SPM provides improved performance for a wider range of angles of attack. The effect of cavity and cavity dimensions on performance is then studied.

Categories: Latest papers in fluid mechanics

### Underwater bubble collapse on a ridge-patterned structure

Physics of Fluids, Volume 32, Issue 5, May 2020.

This experimental study reports the collapse of an underwater bubble near a patterned structure with ridges and grooves. When a bubble is generated by a spark above a ridge, the entire bubble collapses toward the structure after its full expansion, or it is split into two smaller bubbles because of a radial jet induced by bubble contraction. These distinct collapse modes are dependent on the surface geometry of the structure and determined by the contracting speed of a bubble part inside the cross section of an adjacent groove. For a bubble that collapses in a groove, water flows induced from the tops of adjacent ridges collide with each other in the middle of the groove cross section, and this collision occurs if the effective width of the groove is small enough. For the bubble-splitting radial jet mode on the ridge and the collision mode in the groove, some energy of the bubble is lost during its contraction and, accordingly, the strength of the re-entrant jet toward the surface is weakened. Thus, these modes may be effective for reducing erosion on the structure surface, which is supported by our simple experiment for damage assessment.

This experimental study reports the collapse of an underwater bubble near a patterned structure with ridges and grooves. When a bubble is generated by a spark above a ridge, the entire bubble collapses toward the structure after its full expansion, or it is split into two smaller bubbles because of a radial jet induced by bubble contraction. These distinct collapse modes are dependent on the surface geometry of the structure and determined by the contracting speed of a bubble part inside the cross section of an adjacent groove. For a bubble that collapses in a groove, water flows induced from the tops of adjacent ridges collide with each other in the middle of the groove cross section, and this collision occurs if the effective width of the groove is small enough. For the bubble-splitting radial jet mode on the ridge and the collision mode in the groove, some energy of the bubble is lost during its contraction and, accordingly, the strength of the re-entrant jet toward the surface is weakened. Thus, these modes may be effective for reducing erosion on the structure surface, which is supported by our simple experiment for damage assessment.

Categories: Latest papers in fluid mechanics

### Linear surface gravity waves on current for a general inertial viewer

Physics of Fluids, Volume 32, Issue 5, May 2020.

Marine measurement instrumentation, such as free-floating wave buoys, drones, and autonomous unmanned vehicles, often propagates in different directions and velocities relative to the fluid and waves. Convention assumes that these different instrumentations provide Galilean invariant descriptions of the wave field. Herein, it is shown that Galilean invariance exists for the water wave problem only in a restricted sense. The impact of this loss of invariance is investigated using a new formulation of the water wave problem, which is generalized for both current and an arbitrary inertial viewer. In the still water limit, the boundary value problem is shown to be non-invariant under Galilean transformations. This impacts the dispersion relation and interpretation of measurements. It also explains the appearance of wave modes on current, which have no analogy on still water. These modes do not appear in a still water formulation because it is a degenerate representation exhibiting a loss of Galilean symmetries. The approach provides a more complete solution of the wave–current boundary value problem by making a clear distinction between current and viewer velocity effects. Numerical examples that demonstrate the importance of the results on calculating wave characteristics are given.

Marine measurement instrumentation, such as free-floating wave buoys, drones, and autonomous unmanned vehicles, often propagates in different directions and velocities relative to the fluid and waves. Convention assumes that these different instrumentations provide Galilean invariant descriptions of the wave field. Herein, it is shown that Galilean invariance exists for the water wave problem only in a restricted sense. The impact of this loss of invariance is investigated using a new formulation of the water wave problem, which is generalized for both current and an arbitrary inertial viewer. In the still water limit, the boundary value problem is shown to be non-invariant under Galilean transformations. This impacts the dispersion relation and interpretation of measurements. It also explains the appearance of wave modes on current, which have no analogy on still water. These modes do not appear in a still water formulation because it is a degenerate representation exhibiting a loss of Galilean symmetries. The approach provides a more complete solution of the wave–current boundary value problem by making a clear distinction between current and viewer velocity effects. Numerical examples that demonstrate the importance of the results on calculating wave characteristics are given.

Categories: Latest papers in fluid mechanics

### Influence of the wettability on the residual fluid saturation for homogeneous and heterogeneous porous systems

Physics of Fluids, Volume 32, Issue 5, May 2020.

The influence of wettability on the residual fluid saturation is analyzed for homogeneous and heterogeneous porous systems. Several simulations under different wettability, flow rate, and heterogeneity conditions were carried out using a two-component lattice-Boltzmann method. The fluid flow driving force and initial conditions were imposed using a specific methodology that allows a clear distinction between the results obtained for immiscible displacement when the porous medium is initially saturated with one fluid (called primary) and when two fluids are filling the porous spaces (called secondary). The results show that the primary sweeping process is more effective when the displaced fluid is non-wetting. We observe that the heterogeneity has an important role for the whole process since it disturbs the fluid interfaces inducing the flow in the longitudinal and transversal directions, improving considerably the effectiveness of the primary displacement when compared with ideally homogeneous cases. We noted that for oil contact angles, θo, higher than a critical value, no residual oil is found. In all homogeneous cases, the critical value is 120°. The residual fluid increases proportionally to the capillary number for primary displacements, but it also depends on the system heterogeneity and wetting conditions. For secondary displacements in heterogeneous systems, the highest residual oil saturation is found for completely oil-wet conditions, with values ranging from 29% to 41% and tending to zero for all cases when θo > 120°. The initial water–oil distribution is found to be a determining factor in the amount of trapped oil after the waterflooding process.

The influence of wettability on the residual fluid saturation is analyzed for homogeneous and heterogeneous porous systems. Several simulations under different wettability, flow rate, and heterogeneity conditions were carried out using a two-component lattice-Boltzmann method. The fluid flow driving force and initial conditions were imposed using a specific methodology that allows a clear distinction between the results obtained for immiscible displacement when the porous medium is initially saturated with one fluid (called primary) and when two fluids are filling the porous spaces (called secondary). The results show that the primary sweeping process is more effective when the displaced fluid is non-wetting. We observe that the heterogeneity has an important role for the whole process since it disturbs the fluid interfaces inducing the flow in the longitudinal and transversal directions, improving considerably the effectiveness of the primary displacement when compared with ideally homogeneous cases. We noted that for oil contact angles, θo, higher than a critical value, no residual oil is found. In all homogeneous cases, the critical value is 120°. The residual fluid increases proportionally to the capillary number for primary displacements, but it also depends on the system heterogeneity and wetting conditions. For secondary displacements in heterogeneous systems, the highest residual oil saturation is found for completely oil-wet conditions, with values ranging from 29% to 41% and tending to zero for all cases when θo > 120°. The initial water–oil distribution is found to be a determining factor in the amount of trapped oil after the waterflooding process.

Categories: Latest papers in fluid mechanics